%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG061+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 : n021.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 16:36:06 EDT 2023 % Result : Theorem 13.97s 2.64s % Output : Proof 75.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG061+1 : TPTP v8.1.2. Released v2.7.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.34 % Computer : n021.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Mon Aug 28 03:56:43 EDT 2023 % 0.17/0.34 % CPUTime : % 0.20/0.59 ________ _____ % 0.20/0.59 ___ __ \_________(_)________________________________ % 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.59 (2023-06-19) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2023 % 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.59 Amanda Stjerna. % 0.20/0.59 Free software under BSD-3-Clause. % 0.20/0.59 % 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.60 Running up to 7 provers in parallel. % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.49/1.62 Prover 1: Preprocessing ... % 6.79/1.66 Prover 4: Preprocessing ... % 6.79/1.66 Prover 5: Preprocessing ... % 6.79/1.67 Prover 0: Preprocessing ... % 6.79/1.67 Prover 2: Preprocessing ... % 6.79/1.67 Prover 6: Preprocessing ... % 6.79/1.67 Prover 3: Preprocessing ... % 10.21/2.17 Prover 4: Constructing countermodel ... % 10.21/2.20 Prover 2: Constructing countermodel ... % 10.21/2.21 Prover 1: Constructing countermodel ... % 10.21/2.24 Prover 3: Constructing countermodel ... % 10.21/2.25 Prover 0: Constructing countermodel ... % 10.21/2.29 Prover 6: Constructing countermodel ... % 13.97/2.63 Prover 6: proved (2014ms) % 13.97/2.63 % 13.97/2.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.97/2.64 % 13.97/2.64 Prover 3: stopped % 13.97/2.64 Prover 2: stopped % 13.97/2.65 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.97/2.65 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.97/2.65 Prover 0: stopped % 14.32/2.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.32/2.67 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.24/2.85 Prover 5: Constructing countermodel ... % 15.24/2.87 Prover 5: stopped % 15.24/2.88 Prover 10: Preprocessing ... % 15.24/2.88 Prover 7: Preprocessing ... % 15.24/2.88 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.24/2.91 Prover 8: Preprocessing ... % 15.24/2.94 Prover 11: Preprocessing ... % 16.86/3.01 Prover 13: Preprocessing ... % 16.86/3.07 Prover 8: Constructing countermodel ... % 17.36/3.12 Prover 10: Constructing countermodel ... % 17.36/3.14 Prover 7: Constructing countermodel ... % 18.24/3.19 Prover 11: Constructing countermodel ... % 18.52/3.23 Prover 13: Constructing countermodel ... % 62.80/9.12 Prover 13: stopped % 62.80/9.12 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 64.22/9.25 Prover 16: Preprocessing ... % 66.24/9.51 Prover 16: Constructing countermodel ... % 69.89/9.97 Prover 1: Found proof (size 16653) % 69.89/9.97 Prover 1: proved (9358ms) % 69.89/9.97 Prover 16: stopped % 69.89/9.97 Prover 8: stopped % 69.89/9.97 Prover 4: stopped % 69.89/9.97 Prover 11: stopped % 69.89/9.97 Prover 10: stopped % 69.89/9.97 Prover 7: stopped % 69.89/9.97 % 69.89/9.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 69.89/9.97 % 71.06/10.27 % SZS output start Proof for theBenchmark % 71.06/10.30 Assumptions after simplification: % 71.06/10.30 --------------------------------- % 71.06/10.30 % 71.06/10.30 (ax1) % 71.37/10.36 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 71.37/10.36 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 71.37/10.36 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 71.37/10.36 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 71.37/10.36 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 71.37/10.36 [v23: $i] : ? [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = % 71.37/10.36 v22 & op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, e4) = v19 & op(e3, e3) = % 71.37/10.36 v18 & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2, e4) = % 71.37/10.36 v14 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) = v11 & op(e2, e0) = % 71.37/10.36 v10 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = v7 & op(e1, e1) = v6 % 71.37/10.36 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 71.37/10.36 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & % 71.37/10.36 $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & % 71.37/10.36 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 71.37/10.36 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v24 = e3 | % 71.37/10.36 v24 = e2 | v24 = e1 | v24 = e0) & (v23 = e4 | v23 = e3 | v23 = e2 | v23 = % 71.37/10.36 e1 | v23 = e0) & (v22 = e4 | v22 = e3 | v22 = e2 | v22 = e1 | v22 = e0) & % 71.37/10.36 (v21 = e4 | v21 = e3 | v21 = e2 | v21 = e1 | v21 = e0) & (v20 = e4 | v20 = % 71.37/10.36 e3 | v20 = e2 | v20 = e1 | v20 = e0) & (v19 = e4 | v19 = e3 | v19 = e2 | % 71.37/10.36 v19 = e1 | v19 = e0) & (v18 = e4 | v18 = e3 | v18 = e2 | v18 = e1 | v18 = % 71.37/10.36 e0) & (v17 = e4 | v17 = e3 | v17 = e2 | v17 = e1 | v17 = e0) & (v16 = e4 | % 71.37/10.36 v16 = e3 | v16 = e2 | v16 = e1 | v16 = e0) & (v15 = e4 | v15 = e3 | v15 = % 71.37/10.36 e2 | v15 = e1 | v15 = e0) & (v14 = e4 | v14 = e3 | v14 = e2 | v14 = e1 | % 71.37/10.36 v14 = e0) & (v13 = e4 | v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 % 71.37/10.36 = e4 | v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e4 | v11 = e3 | % 71.37/10.36 v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e4 | v10 = e3 | v10 = e2 | v10 = % 71.37/10.36 e1 | v10 = e0) & (v9 = e4 | v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = % 71.37/10.36 e4 | v8 = e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e4 | v7 = e3 | v7 = e2 % 71.37/10.36 | v7 = e1 | v7 = e0) & (v6 = e4 | v6 = e3 | v6 = e2 | v6 = e1 | v6 = e0) & % 71.37/10.36 (v5 = e4 | v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e4 | v4 = e3 | v4 % 71.37/10.36 = e2 | v4 = e1 | v4 = e0) & (v3 = e4 | v3 = e3 | v3 = e2 | v3 = e1 | v3 = % 71.37/10.36 e0) & (v2 = e4 | v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e4 | v1 = % 71.37/10.36 e3 | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1 % 71.37/10.36 | v0 = e0)) % 71.37/10.36 % 71.37/10.36 (ax3) % 71.37/10.38 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 71.37/10.38 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 71.37/10.38 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 71.37/10.38 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 71.37/10.38 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 71.37/10.38 [v23: $i] : ? [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = % 71.37/10.38 v20 & op(e4, e1) = v15 & op(e4, e0) = v8 & op(e3, e4) = v22 & op(e3, e3) = % 71.37/10.38 v21 & op(e3, e2) = v19 & op(e3, e1) = v14 & op(e3, e0) = v7 & op(e2, e4) = % 71.37/10.38 v18 & op(e2, e3) = v17 & op(e2, e2) = v16 & op(e2, e1) = v13 & op(e2, e0) = % 71.37/10.38 v6 & op(e1, e4) = v12 & op(e1, e3) = v11 & op(e1, e2) = v10 & op(e1, e1) = % 71.37/10.38 v9 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 71.37/10.38 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & % 71.37/10.38 $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & % 71.37/10.38 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 71.37/10.38 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v23 = e4 | % 71.37/10.38 v20 = e4 | v15 = e4 | v8 = e4) & (v24 = e4 | v22 = e4 | v18 = e4 | v12 = % 71.37/10.38 e4 | v4 = e4) & (v24 = e3 | v23 = e3 | v20 = e3 | v15 = e3 | v8 = e3) & % 71.37/10.38 (v24 = e3 | v22 = e3 | v18 = e3 | v12 = e3 | v4 = e3) & (v24 = e2 | v23 = e2 % 71.37/10.38 | v20 = e2 | v15 = e2 | v8 = e2) & (v24 = e2 | v22 = e2 | v18 = e2 | v12 = % 71.37/10.38 e2 | v4 = e2) & (v24 = e1 | v23 = e1 | v20 = e1 | v15 = e1 | v8 = e1) & % 71.37/10.38 (v24 = e1 | v22 = e1 | v18 = e1 | v12 = e1 | v4 = e1) & (v24 = e0 | v23 = e0 % 71.37/10.38 | v20 = e0 | v15 = e0 | v8 = e0) & (v24 = e0 | v22 = e0 | v18 = e0 | v12 = % 71.37/10.38 e0 | v4 = e0) & (v23 = e4 | v21 = e4 | v17 = e4 | v11 = e4 | v3 = e4) & % 71.37/10.38 (v23 = e3 | v21 = e3 | v17 = e3 | v11 = e3 | v3 = e3) & (v23 = e2 | v21 = e2 % 71.37/10.38 | v17 = e2 | v11 = e2 | v3 = e2) & (v23 = e1 | v21 = e1 | v17 = e1 | v11 = % 71.37/10.38 e1 | v3 = e1) & (v23 = e0 | v21 = e0 | v17 = e0 | v11 = e0 | v3 = e0) & % 71.37/10.38 (v22 = e4 | v21 = e4 | v19 = e4 | v14 = e4 | v7 = e4) & (v22 = e3 | v21 = e3 % 71.37/10.38 | v19 = e3 | v14 = e3 | v7 = e3) & (v22 = e2 | v21 = e2 | v19 = e2 | v14 = % 71.37/10.38 e2 | v7 = e2) & (v22 = e1 | v21 = e1 | v19 = e1 | v14 = e1 | v7 = e1) & % 71.37/10.38 (v22 = e0 | v21 = e0 | v19 = e0 | v14 = e0 | v7 = e0) & (v20 = e4 | v19 = e4 % 71.37/10.38 | v16 = e4 | v10 = e4 | v2 = e4) & (v20 = e3 | v19 = e3 | v16 = e3 | v10 = % 71.37/10.38 e3 | v2 = e3) & (v20 = e2 | v19 = e2 | v16 = e2 | v10 = e2 | v2 = e2) & % 71.37/10.38 (v20 = e1 | v19 = e1 | v16 = e1 | v10 = e1 | v2 = e1) & (v20 = e0 | v19 = e0 % 71.37/10.38 | v16 = e0 | v10 = e0 | v2 = e0) & (v18 = e4 | v17 = e4 | v16 = e4 | v13 = % 71.37/10.38 e4 | v6 = e4) & (v18 = e3 | v17 = e3 | v16 = e3 | v13 = e3 | v6 = e3) & % 71.37/10.38 (v18 = e2 | v17 = e2 | v16 = e2 | v13 = e2 | v6 = e2) & (v18 = e1 | v17 = e1 % 71.37/10.38 | v16 = e1 | v13 = e1 | v6 = e1) & (v18 = e0 | v17 = e0 | v16 = e0 | v13 = % 71.37/10.38 e0 | v6 = e0) & (v15 = e4 | v14 = e4 | v13 = e4 | v9 = e4 | v1 = e4) & % 71.37/10.38 (v15 = e3 | v14 = e3 | v13 = e3 | v9 = e3 | v1 = e3) & (v15 = e2 | v14 = e2 % 71.37/10.38 | v13 = e2 | v9 = e2 | v1 = e2) & (v15 = e1 | v14 = e1 | v13 = e1 | v9 = % 71.37/10.38 e1 | v1 = e1) & (v15 = e0 | v14 = e0 | v13 = e0 | v9 = e0 | v1 = e0) & % 71.37/10.38 (v12 = e4 | v11 = e4 | v10 = e4 | v9 = e4 | v5 = e4) & (v12 = e3 | v11 = e3 % 71.37/10.38 | v10 = e3 | v9 = e3 | v5 = e3) & (v12 = e2 | v11 = e2 | v10 = e2 | v9 = % 71.37/10.38 e2 | v5 = e2) & (v12 = e1 | v11 = e1 | v10 = e1 | v9 = e1 | v5 = e1) & % 71.37/10.38 (v12 = e0 | v11 = e0 | v10 = e0 | v9 = e0 | v5 = e0) & (v8 = e4 | v7 = e4 | % 71.37/10.38 v6 = e4 | v5 = e4 | v0 = e4) & (v8 = e3 | v7 = e3 | v6 = e3 | v5 = e3 | v0 % 71.37/10.38 = e3) & (v8 = e2 | v7 = e2 | v6 = e2 | v5 = e2 | v0 = e2) & (v8 = e1 | v7 % 71.37/10.38 = e1 | v6 = e1 | v5 = e1 | v0 = e1) & (v4 = e4 | v3 = e4 | v2 = e4 | v1 = % 71.37/10.38 e4 | v0 = e4) & (v4 = e3 | v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (v4 = % 71.37/10.38 e2 | v3 = e2 | v2 = e2 | v1 = e2 | v0 = e2) & (v4 = e1 | v3 = e1 | v2 = e1 % 71.37/10.38 | v1 = e1 | v0 = e1) & (v0 = e0 | ((v8 = e0 | v7 = e0 | v6 = e0 | v5 = e0) % 71.37/10.38 & (v4 = e0 | v3 = e0 | v2 = e0 | v1 = e0)))) % 71.37/10.38 % 71.37/10.38 (ax4) % 71.37/10.39 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 71.37/10.39 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 71.37/10.39 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 71.37/10.39 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 71.37/10.39 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 71.37/10.39 [v23: $i] : ? [v24: $i] : ( ~ (v24 = v23) & ~ (v24 = v22) & ~ (v24 = v21) & % 71.37/10.39 ~ (v24 = v20) & ~ (v24 = v19) & ~ (v24 = v14) & ~ (v24 = v9) & ~ (v24 = % 71.37/10.39 v4) & ~ (v23 = v22) & ~ (v23 = v21) & ~ (v23 = v20) & ~ (v23 = v18) & % 71.37/10.39 ~ (v23 = v13) & ~ (v23 = v8) & ~ (v23 = v3) & ~ (v22 = v21) & ~ (v22 = % 71.37/10.39 v20) & ~ (v22 = v17) & ~ (v22 = v12) & ~ (v22 = v7) & ~ (v22 = v2) & % 71.37/10.39 ~ (v21 = v20) & ~ (v21 = v16) & ~ (v21 = v11) & ~ (v21 = v6) & ~ (v21 = % 71.37/10.39 v1) & ~ (v20 = v15) & ~ (v20 = v10) & ~ (v20 = v5) & ~ (v20 = v0) & ~ % 71.37/10.39 (v19 = v18) & ~ (v19 = v17) & ~ (v19 = v16) & ~ (v19 = v15) & ~ (v19 = % 71.37/10.39 v14) & ~ (v19 = v9) & ~ (v19 = v4) & ~ (v18 = v17) & ~ (v18 = v16) & % 71.37/10.39 ~ (v18 = v15) & ~ (v18 = v13) & ~ (v18 = v8) & ~ (v18 = v3) & ~ (v17 = % 71.37/10.39 v16) & ~ (v17 = v15) & ~ (v17 = v12) & ~ (v17 = v7) & ~ (v17 = v2) & % 71.37/10.39 ~ (v16 = v15) & ~ (v16 = v11) & ~ (v16 = v6) & ~ (v16 = v1) & ~ (v15 = % 71.37/10.39 v10) & ~ (v15 = v5) & ~ (v15 = v0) & ~ (v14 = v13) & ~ (v14 = v12) & % 71.37/10.39 ~ (v14 = v11) & ~ (v14 = v10) & ~ (v14 = v9) & ~ (v14 = v4) & ~ (v13 = % 71.37/10.39 v12) & ~ (v13 = v11) & ~ (v13 = v10) & ~ (v13 = v8) & ~ (v13 = v3) & % 71.37/10.39 ~ (v12 = v11) & ~ (v12 = v10) & ~ (v12 = v7) & ~ (v12 = v2) & ~ (v11 = % 71.37/10.39 v10) & ~ (v11 = v6) & ~ (v11 = v1) & ~ (v10 = v5) & ~ (v10 = v0) & ~ % 71.37/10.39 (v9 = v8) & ~ (v9 = v7) & ~ (v9 = v6) & ~ (v9 = v5) & ~ (v9 = v4) & ~ % 71.37/10.39 (v8 = v7) & ~ (v8 = v6) & ~ (v8 = v5) & ~ (v8 = v3) & ~ (v7 = v6) & ~ % 71.37/10.39 (v7 = v5) & ~ (v7 = v2) & ~ (v6 = v5) & ~ (v6 = v1) & ~ (v5 = v0) & ~ % 71.37/10.39 (v4 = v3) & ~ (v4 = v2) & ~ (v4 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ % 71.37/10.39 (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & % 71.37/10.39 op(e4, e4) = v24 & op(e4, e3) = v19 & op(e4, e2) = v14 & op(e4, e1) = v9 & % 71.37/10.39 op(e4, e0) = v4 & op(e3, e4) = v23 & op(e3, e3) = v18 & op(e3, e2) = v13 & % 71.37/10.39 op(e3, e1) = v8 & op(e3, e0) = v3 & op(e2, e4) = v22 & op(e2, e3) = v17 & % 71.37/10.39 op(e2, e2) = v12 & op(e2, e1) = v7 & op(e2, e0) = v2 & op(e1, e4) = v21 & % 71.37/10.39 op(e1, e3) = v16 & op(e1, e2) = v11 & op(e1, e1) = v6 & op(e1, e0) = v1 & % 71.37/10.39 op(e0, e4) = v20 & op(e0, e3) = v15 & op(e0, e2) = v10 & op(e0, e1) = v5 & % 71.37/10.39 op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) % 71.37/10.39 & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 71.37/10.39 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 71.37/10.39 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 71.37/10.39 % 71.37/10.39 (ax5) % 71.37/10.39 ~ (e4 = e3) & ~ (e4 = e2) & ~ (e4 = e1) & ~ (e4 = e0) & ~ (e3 = e2) & ~ % 71.37/10.39 (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ (e1 = e0) & $i(e4) % 71.37/10.39 & $i(e3) & $i(e2) & $i(e1) & $i(e0) % 71.37/10.39 % 71.37/10.39 (ax6) % 71.37/10.39 op(e4, e4) = e2 & op(e2, e2) = e3 & op(e1, e2) = e0 & op(e1, e1) = e4 & $i(e4) % 71.37/10.39 & $i(e3) & $i(e2) & $i(e1) & $i(e0) % 71.37/10.39 % 71.37/10.39 (co1) % 71.37/10.41 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 71.37/10.41 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 71.37/10.41 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 71.37/10.41 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 71.37/10.41 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 71.37/10.41 [v23: $i] : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? % 71.37/10.41 [v28: $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? % 71.37/10.41 [v33: $i] : ? [v34: $i] : ? [v35: $i] : ? [v36: $i] : ? [v37: $i] : ? % 71.37/10.41 [v38: $i] : ? [v39: $i] : ? [v40: $i] : ? [v41: $i] : ? [v42: $i] : ? % 71.37/10.41 [v43: $i] : ? [v44: $i] : ? [v45: $i] : ? [v46: $i] : ? [v47: $i] : ? % 71.37/10.41 [v48: $i] : ? [v49: $i] : ? [v50: $i] : ? [v51: $i] : ? [v52: $i] : ? % 71.37/10.41 [v53: $i] : ? [v54: $i] : ? [v55: $i] : ? [v56: $i] : ? [v57: $i] : ? % 71.37/10.41 [v58: $i] : ? [v59: $i] : ? [v60: $i] : ? [v61: $i] : ? [v62: $i] : ? % 71.37/10.41 [v63: $i] : ? [v64: $i] : ? [v65: $i] : ? [v66: $i] : ? [v67: $i] : ? % 71.37/10.41 [v68: $i] : ? [v69: $i] : (op(e4, v66) = v68 & op(e4, v63) = v65 & op(e4, % 71.37/10.41 v60) = v62 & op(e4, v57) = v59 & op(e4, v54) = v55 & op(e4, v41) = v42 & % 71.37/10.41 op(e4, v28) = v29 & op(e4, v15) = v16 & op(e4, v4) = v69 & op(e4, e4) = v4 & % 71.37/10.41 op(e4, e3) = v54 & op(e4, e2) = v41 & op(e4, e1) = v28 & op(e4, e0) = v15 & % 71.37/10.41 op(e3, v66) = v67 & op(e3, v54) = v56 & op(e3, v50) = v52 & op(e3, v47) = % 71.37/10.41 v49 & op(e3, v44) = v46 & op(e3, v38) = v39 & op(e3, v25) = v26 & op(e3, % 71.37/10.41 v12) = v13 & op(e3, v3) = v53 & op(e3, e4) = v66 & op(e3, e3) = v3 & % 71.37/10.41 op(e3, e2) = v38 & op(e3, e1) = v25 & op(e3, e0) = v12 & op(e2, v63) = v64 & % 71.37/10.41 op(e2, v50) = v51 & op(e2, v41) = v43 & op(e2, v38) = v40 & op(e2, v34) = % 71.37/10.41 v36 & op(e2, v31) = v33 & op(e2, v22) = v23 & op(e2, v9) = v10 & op(e2, v2) % 71.37/10.41 = v37 & op(e2, e4) = v63 & op(e2, e3) = v50 & op(e2, e2) = v2 & op(e2, e1) = % 71.37/10.41 v22 & op(e2, e0) = v9 & op(e1, v60) = v61 & op(e1, v47) = v48 & op(e1, v34) % 71.37/10.41 = v35 & op(e1, v28) = v30 & op(e1, v25) = v27 & op(e1, v22) = v24 & op(e1, % 71.37/10.41 v18) = v20 & op(e1, v6) = v7 & op(e1, v1) = v21 & op(e1, e4) = v60 & % 71.37/10.41 op(e1, e3) = v47 & op(e1, e2) = v34 & op(e1, e1) = v1 & op(e1, e0) = v6 & % 71.37/10.41 op(e0, v57) = v58 & op(e0, v44) = v45 & op(e0, v31) = v32 & op(e0, v18) = % 71.37/10.41 v19 & op(e0, v15) = v17 & op(e0, v12) = v14 & op(e0, v9) = v11 & op(e0, v6) % 71.37/10.41 = v8 & op(e0, v0) = v5 & op(e0, e4) = v57 & op(e0, e3) = v44 & op(e0, e2) = % 71.37/10.41 v31 & op(e0, e1) = v18 & op(e0, e0) = v0 & $i(v69) & $i(v68) & $i(v67) & % 71.37/10.41 $i(v66) & $i(v65) & $i(v64) & $i(v63) & $i(v62) & $i(v61) & $i(v60) & % 71.37/10.41 $i(v59) & $i(v58) & $i(v57) & $i(v56) & $i(v55) & $i(v54) & $i(v53) & % 71.37/10.41 $i(v52) & $i(v51) & $i(v50) & $i(v49) & $i(v48) & $i(v47) & $i(v46) & % 71.37/10.41 $i(v45) & $i(v44) & $i(v43) & $i(v42) & $i(v41) & $i(v40) & $i(v39) & % 71.37/10.41 $i(v38) & $i(v37) & $i(v36) & $i(v35) & $i(v34) & $i(v33) & $i(v32) & % 71.37/10.41 $i(v31) & $i(v30) & $i(v29) & $i(v28) & $i(v27) & $i(v26) & $i(v25) & % 71.37/10.41 $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & % 71.37/10.41 $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & % 71.37/10.41 $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 71.37/10.41 $i(v2) & $i(v1) & $i(v0) & (v4 = e4 | v3 = e4 | v2 = e4 | v1 = e4 | v0 = e4) % 71.37/10.41 & (v4 = e3 | v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (v4 = e2 | v3 = e2 | % 71.37/10.41 v2 = e2 | v1 = e2 | v0 = e2) & (v4 = e1 | v3 = e1 | v2 = e1 | v1 = e1 | v0 % 71.37/10.41 = e1) & (v4 = e0 | v3 = e0 | v2 = e0 | v1 = e0 | v0 = e0) & ((v68 = e3 & % 71.37/10.41 ~ (v67 = e4)) | (v65 = e2 & ~ (v64 = e4)) | (v62 = e1 & ~ (v61 = e4)) % 71.37/10.41 | (v59 = e0 & ~ (v58 = e4))) & ((v56 = e4 & ~ (v55 = e3)) | (v52 = e2 & % 71.37/10.41 ~ (v51 = e3)) | (v49 = e1 & ~ (v48 = e3)) | (v46 = e0 & ~ (v45 = e3))) % 71.37/10.41 & ((v43 = e4 & ~ (v42 = e2)) | (v40 = e3 & ~ (v39 = e2)) | (v36 = e1 & ~ % 71.37/10.41 (v35 = e2)) | (v33 = e0 & ~ (v32 = e2))) & ((v30 = e4 & ~ (v29 = e1)) % 71.37/10.41 | (v27 = e3 & ~ (v26 = e1)) | (v24 = e2 & ~ (v23 = e1)) | (v20 = e0 & ~ % 71.37/10.41 (v19 = e1))) & ((v17 = e4 & ~ (v16 = e0)) | (v14 = e3 & ~ (v13 = e0)) % 71.37/10.41 | (v11 = e2 & ~ (v10 = e0)) | (v8 = e1 & ~ (v7 = e0)))) % 71.37/10.41 % 71.37/10.41 (function-axioms) % 71.37/10.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3, % 71.37/10.41 v2) = v1) | ~ (op(v3, v2) = v0)) % 71.37/10.41 % 71.37/10.41 Further assumptions not needed in the proof: % 71.37/10.41 -------------------------------------------- % 71.37/10.41 ax2 % 71.37/10.41 % 71.37/10.41 Those formulas are unsatisfiable: % 71.37/10.41 --------------------------------- % 71.37/10.41 % 71.37/10.41 Begin of proof % 71.37/10.42 | % 71.37/10.42 | ALPHA: (ax1) implies: % 71.81/10.43 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 71.81/10.43 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 71.81/10.43 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 71.81/10.43 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 71.81/10.43 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 71.81/10.43 | [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = v22 & % 71.81/10.43 | op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, e4) = v19 & op(e3, e3) = % 71.81/10.43 | v18 & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2, % 71.81/10.43 | e4) = v14 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) = v11 % 71.81/10.43 | & op(e2, e0) = v10 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = % 71.81/10.43 | v7 & op(e1, e1) = v6 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) % 71.81/10.43 | = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) % 71.81/10.43 | & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) % 71.81/10.43 | & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) % 71.81/10.43 | & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 71.81/10.43 | $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v24 = e3 | v24 = e2 | v24 = e1 % 71.81/10.43 | | v24 = e0) & (v23 = e4 | v23 = e3 | v23 = e2 | v23 = e1 | v23 = % 71.81/10.43 | e0) & (v22 = e4 | v22 = e3 | v22 = e2 | v22 = e1 | v22 = e0) & (v21 % 71.81/10.43 | = e4 | v21 = e3 | v21 = e2 | v21 = e1 | v21 = e0) & (v20 = e4 | v20 % 71.81/10.43 | = e3 | v20 = e2 | v20 = e1 | v20 = e0) & (v19 = e4 | v19 = e3 | v19 % 71.81/10.43 | = e2 | v19 = e1 | v19 = e0) & (v18 = e4 | v18 = e3 | v18 = e2 | v18 % 71.81/10.43 | = e1 | v18 = e0) & (v17 = e4 | v17 = e3 | v17 = e2 | v17 = e1 | v17 % 71.81/10.43 | = e0) & (v16 = e4 | v16 = e3 | v16 = e2 | v16 = e1 | v16 = e0) & % 71.81/10.43 | (v15 = e4 | v15 = e3 | v15 = e2 | v15 = e1 | v15 = e0) & (v14 = e4 | % 71.81/10.43 | v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e4 | v13 = e3 | % 71.81/10.43 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e4 | v12 = e3 | v12 = e2 | % 71.81/10.43 | v12 = e1 | v12 = e0) & (v11 = e4 | v11 = e3 | v11 = e2 | v11 = e1 | % 71.81/10.43 | v11 = e0) & (v10 = e4 | v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) % 71.81/10.43 | & (v9 = e4 | v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e4 | v8 = % 71.81/10.43 | e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e4 | v7 = e3 | v7 = e2 | % 71.81/10.43 | v7 = e1 | v7 = e0) & (v6 = e4 | v6 = e3 | v6 = e2 | v6 = e1 | v6 = % 71.81/10.43 | e0) & (v5 = e4 | v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e4 % 71.81/10.43 | | v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e4 | v3 = e3 | v3 % 71.81/10.43 | = e2 | v3 = e1 | v3 = e0) & (v2 = e4 | v2 = e3 | v2 = e2 | v2 = e1 % 71.81/10.43 | | v2 = e0) & (v1 = e4 | v1 = e3 | v1 = e2 | v1 = e1 | v1 = e0) & % 71.81/10.43 | (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0)) % 71.81/10.43 | % 71.81/10.43 | ALPHA: (ax3) implies: % 71.81/10.44 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 71.81/10.44 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 71.81/10.44 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 71.81/10.44 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 71.81/10.44 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 71.81/10.44 | [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = v20 & % 71.81/10.44 | op(e4, e1) = v15 & op(e4, e0) = v8 & op(e3, e4) = v22 & op(e3, e3) = % 71.81/10.44 | v21 & op(e3, e2) = v19 & op(e3, e1) = v14 & op(e3, e0) = v7 & op(e2, % 71.81/10.44 | e4) = v18 & op(e2, e3) = v17 & op(e2, e2) = v16 & op(e2, e1) = v13 % 71.81/10.44 | & op(e2, e0) = v6 & op(e1, e4) = v12 & op(e1, e3) = v11 & op(e1, e2) % 71.81/10.44 | = v10 & op(e1, e1) = v9 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, % 71.81/10.44 | e3) = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & % 71.81/10.44 | $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & % 71.81/10.44 | $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & % 71.81/10.44 | $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 71.81/10.44 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v23 = e4 | v20 = e4 | % 71.81/10.44 | v15 = e4 | v8 = e4) & (v24 = e4 | v22 = e4 | v18 = e4 | v12 = e4 | % 71.81/10.44 | v4 = e4) & (v24 = e3 | v23 = e3 | v20 = e3 | v15 = e3 | v8 = e3) & % 71.81/10.44 | (v24 = e3 | v22 = e3 | v18 = e3 | v12 = e3 | v4 = e3) & (v24 = e2 | % 71.81/10.44 | v23 = e2 | v20 = e2 | v15 = e2 | v8 = e2) & (v24 = e2 | v22 = e2 | % 71.81/10.44 | v18 = e2 | v12 = e2 | v4 = e2) & (v24 = e1 | v23 = e1 | v20 = e1 | % 71.81/10.44 | v15 = e1 | v8 = e1) & (v24 = e1 | v22 = e1 | v18 = e1 | v12 = e1 | % 71.81/10.44 | v4 = e1) & (v24 = e0 | v23 = e0 | v20 = e0 | v15 = e0 | v8 = e0) & % 71.81/10.44 | (v24 = e0 | v22 = e0 | v18 = e0 | v12 = e0 | v4 = e0) & (v23 = e4 | % 71.81/10.44 | v21 = e4 | v17 = e4 | v11 = e4 | v3 = e4) & (v23 = e3 | v21 = e3 | % 71.81/10.44 | v17 = e3 | v11 = e3 | v3 = e3) & (v23 = e2 | v21 = e2 | v17 = e2 | % 71.81/10.44 | v11 = e2 | v3 = e2) & (v23 = e1 | v21 = e1 | v17 = e1 | v11 = e1 | % 71.81/10.44 | v3 = e1) & (v23 = e0 | v21 = e0 | v17 = e0 | v11 = e0 | v3 = e0) & % 71.81/10.44 | (v22 = e4 | v21 = e4 | v19 = e4 | v14 = e4 | v7 = e4) & (v22 = e3 | % 71.81/10.44 | v21 = e3 | v19 = e3 | v14 = e3 | v7 = e3) & (v22 = e2 | v21 = e2 | % 71.81/10.44 | v19 = e2 | v14 = e2 | v7 = e2) & (v22 = e1 | v21 = e1 | v19 = e1 | % 71.81/10.44 | v14 = e1 | v7 = e1) & (v22 = e0 | v21 = e0 | v19 = e0 | v14 = e0 | % 71.81/10.44 | v7 = e0) & (v20 = e4 | v19 = e4 | v16 = e4 | v10 = e4 | v2 = e4) & % 71.81/10.44 | (v20 = e3 | v19 = e3 | v16 = e3 | v10 = e3 | v2 = e3) & (v20 = e2 | % 71.81/10.44 | v19 = e2 | v16 = e2 | v10 = e2 | v2 = e2) & (v20 = e1 | v19 = e1 | % 71.81/10.44 | v16 = e1 | v10 = e1 | v2 = e1) & (v20 = e0 | v19 = e0 | v16 = e0 | % 71.81/10.44 | v10 = e0 | v2 = e0) & (v18 = e4 | v17 = e4 | v16 = e4 | v13 = e4 | % 71.81/10.44 | v6 = e4) & (v18 = e3 | v17 = e3 | v16 = e3 | v13 = e3 | v6 = e3) & % 71.81/10.44 | (v18 = e2 | v17 = e2 | v16 = e2 | v13 = e2 | v6 = e2) & (v18 = e1 | % 71.81/10.44 | v17 = e1 | v16 = e1 | v13 = e1 | v6 = e1) & (v18 = e0 | v17 = e0 | % 71.81/10.44 | v16 = e0 | v13 = e0 | v6 = e0) & (v15 = e4 | v14 = e4 | v13 = e4 | % 71.81/10.44 | v9 = e4 | v1 = e4) & (v15 = e3 | v14 = e3 | v13 = e3 | v9 = e3 | v1 % 71.81/10.45 | = e3) & (v15 = e2 | v14 = e2 | v13 = e2 | v9 = e2 | v1 = e2) & (v15 % 71.81/10.45 | = e1 | v14 = e1 | v13 = e1 | v9 = e1 | v1 = e1) & (v15 = e0 | v14 = % 71.81/10.45 | e0 | v13 = e0 | v9 = e0 | v1 = e0) & (v12 = e4 | v11 = e4 | v10 = % 71.81/10.45 | e4 | v9 = e4 | v5 = e4) & (v12 = e3 | v11 = e3 | v10 = e3 | v9 = e3 % 71.81/10.45 | | v5 = e3) & (v12 = e2 | v11 = e2 | v10 = e2 | v9 = e2 | v5 = e2) & % 71.81/10.45 | (v12 = e1 | v11 = e1 | v10 = e1 | v9 = e1 | v5 = e1) & (v12 = e0 | % 71.81/10.45 | v11 = e0 | v10 = e0 | v9 = e0 | v5 = e0) & (v8 = e4 | v7 = e4 | v6 % 71.81/10.45 | = e4 | v5 = e4 | v0 = e4) & (v8 = e3 | v7 = e3 | v6 = e3 | v5 = e3 % 71.81/10.45 | | v0 = e3) & (v8 = e2 | v7 = e2 | v6 = e2 | v5 = e2 | v0 = e2) & % 71.81/10.45 | (v8 = e1 | v7 = e1 | v6 = e1 | v5 = e1 | v0 = e1) & (v4 = e4 | v3 = % 71.81/10.45 | e4 | v2 = e4 | v1 = e4 | v0 = e4) & (v4 = e3 | v3 = e3 | v2 = e3 | % 71.81/10.45 | v1 = e3 | v0 = e3) & (v4 = e2 | v3 = e2 | v2 = e2 | v1 = e2 | v0 = % 71.81/10.45 | e2) & (v4 = e1 | v3 = e1 | v2 = e1 | v1 = e1 | v0 = e1) & (v0 = e0 % 71.81/10.45 | | ((v8 = e0 | v7 = e0 | v6 = e0 | v5 = e0) & (v4 = e0 | v3 = e0 | % 71.81/10.45 | v2 = e0 | v1 = e0)))) % 71.81/10.45 | % 71.81/10.45 | ALPHA: (ax4) implies: % 71.81/10.45 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 71.81/10.45 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 71.81/10.45 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 71.81/10.45 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 71.81/10.45 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 71.81/10.45 | [v24: $i] : ( ~ (v24 = v23) & ~ (v24 = v22) & ~ (v24 = v21) & ~ (v24 % 71.81/10.45 | = v20) & ~ (v24 = v19) & ~ (v24 = v14) & ~ (v24 = v9) & ~ (v24 % 71.81/10.45 | = v4) & ~ (v23 = v22) & ~ (v23 = v21) & ~ (v23 = v20) & ~ (v23 % 71.81/10.45 | = v18) & ~ (v23 = v13) & ~ (v23 = v8) & ~ (v23 = v3) & ~ (v22 = % 71.81/10.45 | v21) & ~ (v22 = v20) & ~ (v22 = v17) & ~ (v22 = v12) & ~ (v22 = % 71.81/10.45 | v7) & ~ (v22 = v2) & ~ (v21 = v20) & ~ (v21 = v16) & ~ (v21 = % 71.81/10.45 | v11) & ~ (v21 = v6) & ~ (v21 = v1) & ~ (v20 = v15) & ~ (v20 = % 71.81/10.45 | v10) & ~ (v20 = v5) & ~ (v20 = v0) & ~ (v19 = v18) & ~ (v19 = % 71.81/10.45 | v17) & ~ (v19 = v16) & ~ (v19 = v15) & ~ (v19 = v14) & ~ (v19 = % 71.81/10.45 | v9) & ~ (v19 = v4) & ~ (v18 = v17) & ~ (v18 = v16) & ~ (v18 = % 71.81/10.45 | v15) & ~ (v18 = v13) & ~ (v18 = v8) & ~ (v18 = v3) & ~ (v17 = % 71.81/10.45 | v16) & ~ (v17 = v15) & ~ (v17 = v12) & ~ (v17 = v7) & ~ (v17 = % 71.81/10.45 | v2) & ~ (v16 = v15) & ~ (v16 = v11) & ~ (v16 = v6) & ~ (v16 = % 71.81/10.45 | v1) & ~ (v15 = v10) & ~ (v15 = v5) & ~ (v15 = v0) & ~ (v14 = % 71.81/10.45 | v13) & ~ (v14 = v12) & ~ (v14 = v11) & ~ (v14 = v10) & ~ (v14 = % 71.81/10.45 | v9) & ~ (v14 = v4) & ~ (v13 = v12) & ~ (v13 = v11) & ~ (v13 = % 71.81/10.45 | v10) & ~ (v13 = v8) & ~ (v13 = v3) & ~ (v12 = v11) & ~ (v12 = % 71.81/10.45 | v10) & ~ (v12 = v7) & ~ (v12 = v2) & ~ (v11 = v10) & ~ (v11 = % 71.81/10.45 | v6) & ~ (v11 = v1) & ~ (v10 = v5) & ~ (v10 = v0) & ~ (v9 = v8) % 71.81/10.45 | & ~ (v9 = v7) & ~ (v9 = v6) & ~ (v9 = v5) & ~ (v9 = v4) & ~ (v8 % 71.81/10.45 | = v7) & ~ (v8 = v6) & ~ (v8 = v5) & ~ (v8 = v3) & ~ (v7 = v6) & % 71.81/10.45 | ~ (v7 = v5) & ~ (v7 = v2) & ~ (v6 = v5) & ~ (v6 = v1) & ~ (v5 = % 71.81/10.45 | v0) & ~ (v4 = v3) & ~ (v4 = v2) & ~ (v4 = v1) & ~ (v4 = v0) & % 71.81/10.45 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = % 71.81/10.45 | v0) & ~ (v1 = v0) & op(e4, e4) = v24 & op(e4, e3) = v19 & op(e4, % 71.81/10.45 | e2) = v14 & op(e4, e1) = v9 & op(e4, e0) = v4 & op(e3, e4) = v23 & % 71.81/10.45 | op(e3, e3) = v18 & op(e3, e2) = v13 & op(e3, e1) = v8 & op(e3, e0) = % 71.81/10.45 | v3 & op(e2, e4) = v22 & op(e2, e3) = v17 & op(e2, e2) = v12 & op(e2, % 71.81/10.45 | e1) = v7 & op(e2, e0) = v2 & op(e1, e4) = v21 & op(e1, e3) = v16 & % 71.81/10.45 | op(e1, e2) = v11 & op(e1, e1) = v6 & op(e1, e0) = v1 & op(e0, e4) = % 71.81/10.45 | v20 & op(e0, e3) = v15 & op(e0, e2) = v10 & op(e0, e1) = v5 & op(e0, % 71.81/10.45 | e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & % 71.81/10.45 | $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & % 71.81/10.45 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 71.81/10.45 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 71.81/10.45 | % 71.81/10.45 | ALPHA: (ax5) implies: % 71.81/10.45 | (4) ~ (e1 = e0) % 71.81/10.45 | (5) ~ (e2 = e0) % 71.81/10.45 | (6) ~ (e2 = e1) % 71.81/10.45 | (7) ~ (e3 = e1) % 71.81/10.45 | (8) ~ (e3 = e2) % 71.81/10.45 | (9) ~ (e4 = e1) % 71.81/10.45 | (10) ~ (e4 = e2) % 71.81/10.45 | (11) ~ (e4 = e3) % 71.81/10.45 | % 71.81/10.45 | ALPHA: (ax6) implies: % 71.81/10.46 | (12) op(e1, e1) = e4 % 71.81/10.46 | (13) op(e1, e2) = e0 % 71.81/10.46 | (14) op(e2, e2) = e3 % 71.81/10.46 | (15) op(e4, e4) = e2 % 71.81/10.46 | % 71.81/10.46 | ALPHA: (co1) implies: % 71.81/10.47 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 71.81/10.47 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 71.81/10.47 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 71.81/10.47 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 71.81/10.47 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] % 71.81/10.47 | : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: % 71.81/10.47 | $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? % 71.81/10.47 | [v33: $i] : ? [v34: $i] : ? [v35: $i] : ? [v36: $i] : ? [v37: $i] % 71.81/10.47 | : ? [v38: $i] : ? [v39: $i] : ? [v40: $i] : ? [v41: $i] : ? [v42: % 71.81/10.47 | $i] : ? [v43: $i] : ? [v44: $i] : ? [v45: $i] : ? [v46: $i] : ? % 71.81/10.47 | [v47: $i] : ? [v48: $i] : ? [v49: $i] : ? [v50: $i] : ? [v51: $i] % 71.81/10.47 | : ? [v52: $i] : ? [v53: $i] : ? [v54: $i] : ? [v55: $i] : ? [v56: % 71.81/10.47 | $i] : ? [v57: $i] : ? [v58: $i] : ? [v59: $i] : ? [v60: $i] : ? % 71.81/10.47 | [v61: $i] : ? [v62: $i] : ? [v63: $i] : ? [v64: $i] : ? [v65: $i] % 71.81/10.47 | : ? [v66: $i] : ? [v67: $i] : ? [v68: $i] : ? [v69: $i] : (op(e4, % 71.81/10.47 | v66) = v68 & op(e4, v63) = v65 & op(e4, v60) = v62 & op(e4, v57) = % 71.81/10.47 | v59 & op(e4, v54) = v55 & op(e4, v41) = v42 & op(e4, v28) = v29 & % 71.81/10.47 | op(e4, v15) = v16 & op(e4, v4) = v69 & op(e4, e4) = v4 & op(e4, e3) % 71.81/10.47 | = v54 & op(e4, e2) = v41 & op(e4, e1) = v28 & op(e4, e0) = v15 & % 71.81/10.47 | op(e3, v66) = v67 & op(e3, v54) = v56 & op(e3, v50) = v52 & op(e3, % 71.81/10.47 | v47) = v49 & op(e3, v44) = v46 & op(e3, v38) = v39 & op(e3, v25) = % 71.81/10.47 | v26 & op(e3, v12) = v13 & op(e3, v3) = v53 & op(e3, e4) = v66 & % 71.81/10.47 | op(e3, e3) = v3 & op(e3, e2) = v38 & op(e3, e1) = v25 & op(e3, e0) = % 71.81/10.47 | v12 & op(e2, v63) = v64 & op(e2, v50) = v51 & op(e2, v41) = v43 & % 71.81/10.47 | op(e2, v38) = v40 & op(e2, v34) = v36 & op(e2, v31) = v33 & op(e2, % 71.81/10.47 | v22) = v23 & op(e2, v9) = v10 & op(e2, v2) = v37 & op(e2, e4) = % 71.81/10.47 | v63 & op(e2, e3) = v50 & op(e2, e2) = v2 & op(e2, e1) = v22 & op(e2, % 71.81/10.47 | e0) = v9 & op(e1, v60) = v61 & op(e1, v47) = v48 & op(e1, v34) = % 71.81/10.47 | v35 & op(e1, v28) = v30 & op(e1, v25) = v27 & op(e1, v22) = v24 & % 71.81/10.47 | op(e1, v18) = v20 & op(e1, v6) = v7 & op(e1, v1) = v21 & op(e1, e4) % 71.81/10.47 | = v60 & op(e1, e3) = v47 & op(e1, e2) = v34 & op(e1, e1) = v1 & % 71.81/10.47 | op(e1, e0) = v6 & op(e0, v57) = v58 & op(e0, v44) = v45 & op(e0, % 71.81/10.47 | v31) = v32 & op(e0, v18) = v19 & op(e0, v15) = v17 & op(e0, v12) = % 71.81/10.47 | v14 & op(e0, v9) = v11 & op(e0, v6) = v8 & op(e0, v0) = v5 & op(e0, % 71.81/10.47 | e4) = v57 & op(e0, e3) = v44 & op(e0, e2) = v31 & op(e0, e1) = v18 % 71.81/10.47 | & op(e0, e0) = v0 & $i(v69) & $i(v68) & $i(v67) & $i(v66) & $i(v65) % 71.81/10.47 | & $i(v64) & $i(v63) & $i(v62) & $i(v61) & $i(v60) & $i(v59) & % 71.81/10.47 | $i(v58) & $i(v57) & $i(v56) & $i(v55) & $i(v54) & $i(v53) & $i(v52) % 71.81/10.47 | & $i(v51) & $i(v50) & $i(v49) & $i(v48) & $i(v47) & $i(v46) & % 71.81/10.47 | $i(v45) & $i(v44) & $i(v43) & $i(v42) & $i(v41) & $i(v40) & $i(v39) % 71.81/10.47 | & $i(v38) & $i(v37) & $i(v36) & $i(v35) & $i(v34) & $i(v33) & % 71.81/10.47 | $i(v32) & $i(v31) & $i(v30) & $i(v29) & $i(v28) & $i(v27) & $i(v26) % 71.81/10.47 | & $i(v25) & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & % 71.81/10.47 | $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) % 71.81/10.47 | & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 71.81/10.47 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v4 = e4 | v3 % 71.81/10.47 | = e4 | v2 = e4 | v1 = e4 | v0 = e4) & (v4 = e3 | v3 = e3 | v2 = e3 % 71.81/10.47 | | v1 = e3 | v0 = e3) & (v4 = e2 | v3 = e2 | v2 = e2 | v1 = e2 | v0 % 71.81/10.47 | = e2) & (v4 = e1 | v3 = e1 | v2 = e1 | v1 = e1 | v0 = e1) & (v4 = % 71.81/10.47 | e0 | v3 = e0 | v2 = e0 | v1 = e0 | v0 = e0) & ((v68 = e3 & ~ (v67 % 71.81/10.47 | = e4)) | (v65 = e2 & ~ (v64 = e4)) | (v62 = e1 & ~ (v61 = % 71.81/10.47 | e4)) | (v59 = e0 & ~ (v58 = e4))) & ((v56 = e4 & ~ (v55 = % 71.81/10.47 | e3)) | (v52 = e2 & ~ (v51 = e3)) | (v49 = e1 & ~ (v48 = e3)) % 71.81/10.47 | | (v46 = e0 & ~ (v45 = e3))) & ((v43 = e4 & ~ (v42 = e2)) | (v40 % 71.81/10.47 | = e3 & ~ (v39 = e2)) | (v36 = e1 & ~ (v35 = e2)) | (v33 = e0 & % 71.81/10.47 | ~ (v32 = e2))) & ((v30 = e4 & ~ (v29 = e1)) | (v27 = e3 & ~ % 71.81/10.47 | (v26 = e1)) | (v24 = e2 & ~ (v23 = e1)) | (v20 = e0 & ~ (v19 = % 71.81/10.47 | e1))) & ((v17 = e4 & ~ (v16 = e0)) | (v14 = e3 & ~ (v13 = % 71.81/10.47 | e0)) | (v11 = e2 & ~ (v10 = e0)) | (v8 = e1 & ~ (v7 = e0)))) % 71.81/10.47 | % 71.81/10.47 | DELTA: instantiating (3) with fresh symbols all_4_0, all_4_1, all_4_2, % 71.81/10.47 | all_4_3, all_4_4, all_4_5, all_4_6, all_4_7, all_4_8, all_4_9, % 71.81/10.47 | all_4_10, all_4_11, all_4_12, all_4_13, all_4_14, all_4_15, all_4_16, % 71.81/10.47 | all_4_17, all_4_18, all_4_19, all_4_20, all_4_21, all_4_22, all_4_23, % 71.81/10.47 | all_4_24 gives: % 71.81/10.47 | (17) ~ (all_4_0 = all_4_1) & ~ (all_4_0 = all_4_2) & ~ (all_4_0 = % 71.81/10.47 | all_4_3) & ~ (all_4_0 = all_4_4) & ~ (all_4_0 = all_4_5) & ~ % 71.81/10.47 | (all_4_0 = all_4_10) & ~ (all_4_0 = all_4_15) & ~ (all_4_0 = % 71.81/10.47 | all_4_20) & ~ (all_4_1 = all_4_2) & ~ (all_4_1 = all_4_3) & ~ % 71.81/10.47 | (all_4_1 = all_4_4) & ~ (all_4_1 = all_4_6) & ~ (all_4_1 = all_4_11) % 71.81/10.47 | & ~ (all_4_1 = all_4_16) & ~ (all_4_1 = all_4_21) & ~ (all_4_2 = % 71.81/10.47 | all_4_3) & ~ (all_4_2 = all_4_4) & ~ (all_4_2 = all_4_7) & ~ % 71.81/10.47 | (all_4_2 = all_4_12) & ~ (all_4_2 = all_4_17) & ~ (all_4_2 = % 71.81/10.47 | all_4_22) & ~ (all_4_3 = all_4_4) & ~ (all_4_3 = all_4_8) & ~ % 71.81/10.47 | (all_4_3 = all_4_13) & ~ (all_4_3 = all_4_18) & ~ (all_4_3 = % 71.81/10.47 | all_4_23) & ~ (all_4_4 = all_4_9) & ~ (all_4_4 = all_4_14) & ~ % 71.81/10.47 | (all_4_4 = all_4_19) & ~ (all_4_4 = all_4_24) & ~ (all_4_5 = % 71.81/10.47 | all_4_6) & ~ (all_4_5 = all_4_7) & ~ (all_4_5 = all_4_8) & ~ % 71.81/10.47 | (all_4_5 = all_4_9) & ~ (all_4_5 = all_4_10) & ~ (all_4_5 = % 71.81/10.47 | all_4_15) & ~ (all_4_5 = all_4_20) & ~ (all_4_6 = all_4_7) & ~ % 71.81/10.47 | (all_4_6 = all_4_8) & ~ (all_4_6 = all_4_9) & ~ (all_4_6 = all_4_11) % 71.81/10.47 | & ~ (all_4_6 = all_4_16) & ~ (all_4_6 = all_4_21) & ~ (all_4_7 = % 71.81/10.47 | all_4_8) & ~ (all_4_7 = all_4_9) & ~ (all_4_7 = all_4_12) & ~ % 71.81/10.47 | (all_4_7 = all_4_17) & ~ (all_4_7 = all_4_22) & ~ (all_4_8 = % 71.81/10.47 | all_4_9) & ~ (all_4_8 = all_4_13) & ~ (all_4_8 = all_4_18) & ~ % 71.81/10.47 | (all_4_8 = all_4_23) & ~ (all_4_9 = all_4_14) & ~ (all_4_9 = % 71.81/10.47 | all_4_19) & ~ (all_4_9 = all_4_24) & ~ (all_4_10 = all_4_11) & ~ % 71.81/10.47 | (all_4_10 = all_4_12) & ~ (all_4_10 = all_4_13) & ~ (all_4_10 = % 71.81/10.47 | all_4_14) & ~ (all_4_10 = all_4_15) & ~ (all_4_10 = all_4_20) & ~ % 71.81/10.47 | (all_4_11 = all_4_12) & ~ (all_4_11 = all_4_13) & ~ (all_4_11 = % 71.81/10.47 | all_4_14) & ~ (all_4_11 = all_4_16) & ~ (all_4_11 = all_4_21) & ~ % 71.81/10.47 | (all_4_12 = all_4_13) & ~ (all_4_12 = all_4_14) & ~ (all_4_12 = % 71.81/10.47 | all_4_17) & ~ (all_4_12 = all_4_22) & ~ (all_4_13 = all_4_14) & ~ % 71.81/10.47 | (all_4_13 = all_4_18) & ~ (all_4_13 = all_4_23) & ~ (all_4_14 = % 71.81/10.47 | all_4_19) & ~ (all_4_14 = all_4_24) & ~ (all_4_15 = all_4_16) & ~ % 71.81/10.47 | (all_4_15 = all_4_17) & ~ (all_4_15 = all_4_18) & ~ (all_4_15 = % 71.81/10.47 | all_4_19) & ~ (all_4_15 = all_4_20) & ~ (all_4_16 = all_4_17) & ~ % 71.81/10.47 | (all_4_16 = all_4_18) & ~ (all_4_16 = all_4_19) & ~ (all_4_16 = % 71.81/10.47 | all_4_21) & ~ (all_4_17 = all_4_18) & ~ (all_4_17 = all_4_19) & ~ % 71.81/10.47 | (all_4_17 = all_4_22) & ~ (all_4_18 = all_4_19) & ~ (all_4_18 = % 71.81/10.47 | all_4_23) & ~ (all_4_19 = all_4_24) & ~ (all_4_20 = all_4_21) & ~ % 71.81/10.47 | (all_4_20 = all_4_22) & ~ (all_4_20 = all_4_23) & ~ (all_4_20 = % 71.81/10.47 | all_4_24) & ~ (all_4_21 = all_4_22) & ~ (all_4_21 = all_4_23) & ~ % 71.81/10.47 | (all_4_21 = all_4_24) & ~ (all_4_22 = all_4_23) & ~ (all_4_22 = % 71.81/10.47 | all_4_24) & ~ (all_4_23 = all_4_24) & op(e4, e4) = all_4_0 & op(e4, % 71.81/10.47 | e3) = all_4_5 & op(e4, e2) = all_4_10 & op(e4, e1) = all_4_15 & % 71.81/10.47 | op(e4, e0) = all_4_20 & op(e3, e4) = all_4_1 & op(e3, e3) = all_4_6 & % 71.81/10.47 | op(e3, e2) = all_4_11 & op(e3, e1) = all_4_16 & op(e3, e0) = all_4_21 % 71.81/10.47 | & op(e2, e4) = all_4_2 & op(e2, e3) = all_4_7 & op(e2, e2) = all_4_12 % 71.81/10.47 | & op(e2, e1) = all_4_17 & op(e2, e0) = all_4_22 & op(e1, e4) = all_4_3 % 71.81/10.47 | & op(e1, e3) = all_4_8 & op(e1, e2) = all_4_13 & op(e1, e1) = all_4_18 % 71.81/10.47 | & op(e1, e0) = all_4_23 & op(e0, e4) = all_4_4 & op(e0, e3) = all_4_9 % 71.81/10.47 | & op(e0, e2) = all_4_14 & op(e0, e1) = all_4_19 & op(e0, e0) = % 71.81/10.47 | all_4_24 & $i(all_4_0) & $i(all_4_1) & $i(all_4_2) & $i(all_4_3) & % 71.81/10.47 | $i(all_4_4) & $i(all_4_5) & $i(all_4_6) & $i(all_4_7) & $i(all_4_8) & % 71.81/10.47 | $i(all_4_9) & $i(all_4_10) & $i(all_4_11) & $i(all_4_12) & % 71.81/10.47 | $i(all_4_13) & $i(all_4_14) & $i(all_4_15) & $i(all_4_16) & % 71.81/10.47 | $i(all_4_17) & $i(all_4_18) & $i(all_4_19) & $i(all_4_20) & % 71.81/10.47 | $i(all_4_21) & $i(all_4_22) & $i(all_4_23) & $i(all_4_24) % 71.81/10.47 | % 71.81/10.47 | ALPHA: (17) implies: % 71.81/10.48 | (18) ~ (all_4_23 = all_4_24) % 71.81/10.48 | (19) ~ (all_4_22 = all_4_24) % 71.81/10.48 | (20) ~ (all_4_22 = all_4_23) % 71.81/10.48 | (21) ~ (all_4_21 = all_4_24) % 71.81/10.48 | (22) ~ (all_4_21 = all_4_23) % 71.81/10.48 | (23) ~ (all_4_21 = all_4_22) % 71.81/10.48 | (24) ~ (all_4_20 = all_4_24) % 71.81/10.48 | (25) ~ (all_4_20 = all_4_23) % 71.81/10.48 | (26) ~ (all_4_20 = all_4_22) % 71.81/10.48 | (27) ~ (all_4_20 = all_4_21) % 71.81/10.48 | (28) ~ (all_4_19 = all_4_24) % 71.81/10.48 | (29) ~ (all_4_18 = all_4_23) % 71.81/10.48 | (30) ~ (all_4_18 = all_4_19) % 71.81/10.48 | (31) ~ (all_4_17 = all_4_22) % 71.81/10.48 | (32) ~ (all_4_17 = all_4_19) % 71.81/10.48 | (33) ~ (all_4_17 = all_4_18) % 71.81/10.48 | (34) ~ (all_4_16 = all_4_21) % 71.81/10.48 | (35) ~ (all_4_16 = all_4_19) % 71.81/10.48 | (36) ~ (all_4_16 = all_4_18) % 71.81/10.48 | (37) ~ (all_4_16 = all_4_17) % 71.81/10.48 | (38) ~ (all_4_15 = all_4_20) % 71.81/10.48 | (39) ~ (all_4_15 = all_4_19) % 71.81/10.48 | (40) ~ (all_4_15 = all_4_18) % 71.81/10.48 | (41) ~ (all_4_15 = all_4_17) % 71.81/10.48 | (42) ~ (all_4_14 = all_4_24) % 71.81/10.48 | (43) ~ (all_4_14 = all_4_19) % 71.81/10.48 | (44) ~ (all_4_13 = all_4_23) % 71.81/10.48 | (45) ~ (all_4_13 = all_4_18) % 71.81/10.48 | (46) ~ (all_4_13 = all_4_14) % 71.81/10.48 | (47) ~ (all_4_12 = all_4_22) % 71.81/10.48 | (48) ~ (all_4_12 = all_4_17) % 71.81/10.48 | (49) ~ (all_4_12 = all_4_14) % 71.81/10.48 | (50) ~ (all_4_12 = all_4_13) % 71.81/10.48 | (51) ~ (all_4_11 = all_4_21) % 71.81/10.48 | (52) ~ (all_4_11 = all_4_16) % 71.81/10.48 | (53) ~ (all_4_11 = all_4_14) % 71.81/10.48 | (54) ~ (all_4_11 = all_4_13) % 71.81/10.48 | (55) ~ (all_4_11 = all_4_12) % 71.81/10.48 | (56) ~ (all_4_10 = all_4_20) % 71.81/10.48 | (57) ~ (all_4_10 = all_4_15) % 71.81/10.48 | (58) ~ (all_4_10 = all_4_14) % 71.81/10.48 | (59) ~ (all_4_10 = all_4_13) % 71.81/10.48 | (60) ~ (all_4_10 = all_4_12) % 71.81/10.48 | (61) ~ (all_4_10 = all_4_11) % 71.81/10.48 | (62) ~ (all_4_9 = all_4_24) % 71.81/10.48 | (63) ~ (all_4_9 = all_4_19) % 71.81/10.48 | (64) ~ (all_4_9 = all_4_14) % 71.81/10.48 | (65) ~ (all_4_8 = all_4_23) % 71.81/10.48 | (66) ~ (all_4_8 = all_4_18) % 71.81/10.48 | (67) ~ (all_4_8 = all_4_13) % 71.81/10.48 | (68) ~ (all_4_8 = all_4_9) % 71.81/10.48 | (69) ~ (all_4_7 = all_4_22) % 71.81/10.48 | (70) ~ (all_4_7 = all_4_17) % 71.81/10.48 | (71) ~ (all_4_7 = all_4_12) % 71.81/10.48 | (72) ~ (all_4_7 = all_4_9) % 71.81/10.48 | (73) ~ (all_4_7 = all_4_8) % 71.81/10.48 | (74) ~ (all_4_6 = all_4_21) % 71.81/10.48 | (75) ~ (all_4_6 = all_4_16) % 71.81/10.48 | (76) ~ (all_4_6 = all_4_11) % 71.81/10.48 | (77) ~ (all_4_6 = all_4_9) % 71.81/10.48 | (78) ~ (all_4_6 = all_4_8) % 71.81/10.48 | (79) ~ (all_4_6 = all_4_7) % 71.81/10.48 | (80) ~ (all_4_5 = all_4_20) % 71.81/10.48 | (81) ~ (all_4_5 = all_4_15) % 71.81/10.48 | (82) ~ (all_4_5 = all_4_10) % 71.81/10.48 | (83) ~ (all_4_5 = all_4_9) % 71.81/10.48 | (84) ~ (all_4_5 = all_4_8) % 71.81/10.48 | (85) ~ (all_4_5 = all_4_7) % 71.81/10.48 | (86) ~ (all_4_5 = all_4_6) % 71.81/10.48 | (87) ~ (all_4_4 = all_4_24) % 71.81/10.48 | (88) ~ (all_4_4 = all_4_19) % 71.81/10.48 | (89) ~ (all_4_4 = all_4_14) % 71.81/10.48 | (90) ~ (all_4_4 = all_4_9) % 71.81/10.48 | (91) ~ (all_4_3 = all_4_23) % 71.81/10.48 | (92) ~ (all_4_3 = all_4_18) % 71.81/10.48 | (93) ~ (all_4_3 = all_4_13) % 71.81/10.48 | (94) ~ (all_4_3 = all_4_8) % 71.81/10.48 | (95) ~ (all_4_3 = all_4_4) % 71.81/10.48 | (96) ~ (all_4_2 = all_4_22) % 71.81/10.48 | (97) ~ (all_4_2 = all_4_17) % 71.81/10.48 | (98) ~ (all_4_2 = all_4_12) % 71.81/10.48 | (99) ~ (all_4_2 = all_4_7) % 71.81/10.48 | (100) ~ (all_4_2 = all_4_4) % 71.81/10.48 | (101) ~ (all_4_2 = all_4_3) % 71.81/10.48 | (102) ~ (all_4_1 = all_4_21) % 71.81/10.48 | (103) ~ (all_4_1 = all_4_16) % 71.81/10.48 | (104) ~ (all_4_1 = all_4_11) % 71.81/10.48 | (105) ~ (all_4_1 = all_4_6) % 71.81/10.48 | (106) ~ (all_4_1 = all_4_4) % 71.81/10.48 | (107) ~ (all_4_1 = all_4_3) % 71.81/10.48 | (108) ~ (all_4_1 = all_4_2) % 71.81/10.48 | (109) ~ (all_4_0 = all_4_20) % 71.81/10.48 | (110) ~ (all_4_0 = all_4_15) % 71.81/10.48 | (111) ~ (all_4_0 = all_4_10) % 71.81/10.48 | (112) ~ (all_4_0 = all_4_5) % 71.81/10.48 | (113) ~ (all_4_0 = all_4_4) % 71.81/10.48 | (114) ~ (all_4_0 = all_4_3) % 71.81/10.48 | (115) ~ (all_4_0 = all_4_2) % 71.81/10.48 | (116) ~ (all_4_0 = all_4_1) % 71.81/10.48 | (117) op(e0, e0) = all_4_24 % 71.81/10.48 | (118) op(e0, e1) = all_4_19 % 71.81/10.48 | (119) op(e0, e2) = all_4_14 % 71.81/10.48 | (120) op(e0, e3) = all_4_9 % 71.81/10.48 | (121) op(e0, e4) = all_4_4 % 71.81/10.49 | (122) op(e1, e0) = all_4_23 % 71.81/10.49 | (123) op(e1, e1) = all_4_18 % 71.81/10.49 | (124) op(e1, e2) = all_4_13 % 71.81/10.49 | (125) op(e1, e3) = all_4_8 % 71.81/10.49 | (126) op(e1, e4) = all_4_3 % 71.81/10.49 | (127) op(e2, e0) = all_4_22 % 71.81/10.49 | (128) op(e2, e1) = all_4_17 % 71.81/10.49 | (129) op(e2, e2) = all_4_12 % 71.81/10.49 | (130) op(e2, e3) = all_4_7 % 71.81/10.49 | (131) op(e2, e4) = all_4_2 % 71.81/10.49 | (132) op(e3, e0) = all_4_21 % 71.81/10.49 | (133) op(e3, e1) = all_4_16 % 71.81/10.49 | (134) op(e3, e2) = all_4_11 % 71.81/10.49 | (135) op(e3, e3) = all_4_6 % 71.81/10.49 | (136) op(e3, e4) = all_4_1 % 71.81/10.49 | (137) op(e4, e0) = all_4_20 % 71.81/10.49 | (138) op(e4, e1) = all_4_15 % 71.81/10.49 | (139) op(e4, e2) = all_4_10 % 71.81/10.49 | (140) op(e4, e3) = all_4_5 % 71.81/10.49 | (141) op(e4, e4) = all_4_0 % 71.81/10.49 | % 71.81/10.49 | DELTA: instantiating (1) with fresh symbols all_6_0, all_6_1, all_6_2, % 71.81/10.49 | all_6_3, all_6_4, all_6_5, all_6_6, all_6_7, all_6_8, all_6_9, % 71.81/10.49 | all_6_10, all_6_11, all_6_12, all_6_13, all_6_14, all_6_15, all_6_16, % 71.81/10.49 | all_6_17, all_6_18, all_6_19, all_6_20, all_6_21, all_6_22, all_6_23, % 71.81/10.49 | all_6_24 gives: % 71.81/10.49 | (142) op(e4, e4) = all_6_0 & op(e4, e3) = all_6_1 & op(e4, e2) = all_6_2 & % 71.81/10.49 | op(e4, e1) = all_6_3 & op(e4, e0) = all_6_4 & op(e3, e4) = all_6_5 & % 71.81/10.49 | op(e3, e3) = all_6_6 & op(e3, e2) = all_6_7 & op(e3, e1) = all_6_8 & % 71.81/10.49 | op(e3, e0) = all_6_9 & op(e2, e4) = all_6_10 & op(e2, e3) = all_6_11 % 71.81/10.49 | & op(e2, e2) = all_6_12 & op(e2, e1) = all_6_13 & op(e2, e0) = % 71.81/10.49 | all_6_14 & op(e1, e4) = all_6_15 & op(e1, e3) = all_6_16 & op(e1, e2) % 71.81/10.49 | = all_6_17 & op(e1, e1) = all_6_18 & op(e1, e0) = all_6_19 & op(e0, % 71.81/10.49 | e4) = all_6_20 & op(e0, e3) = all_6_21 & op(e0, e2) = all_6_22 & % 71.81/10.49 | op(e0, e1) = all_6_23 & op(e0, e0) = all_6_24 & $i(all_6_0) & % 71.81/10.49 | $i(all_6_1) & $i(all_6_2) & $i(all_6_3) & $i(all_6_4) & $i(all_6_5) & % 71.81/10.49 | $i(all_6_6) & $i(all_6_7) & $i(all_6_8) & $i(all_6_9) & $i(all_6_10) % 71.81/10.49 | & $i(all_6_11) & $i(all_6_12) & $i(all_6_13) & $i(all_6_14) & % 71.81/10.49 | $i(all_6_15) & $i(all_6_16) & $i(all_6_17) & $i(all_6_18) & % 71.81/10.49 | $i(all_6_19) & $i(all_6_20) & $i(all_6_21) & $i(all_6_22) & % 71.81/10.49 | $i(all_6_23) & $i(all_6_24) & (all_6_0 = e4 | all_6_0 = e3 | all_6_0 % 71.81/10.49 | = e2 | all_6_0 = e1 | all_6_0 = e0) & (all_6_1 = e4 | all_6_1 = e3 % 71.81/10.49 | | all_6_1 = e2 | all_6_1 = e1 | all_6_1 = e0) & (all_6_2 = e4 | % 71.81/10.49 | all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | all_6_2 = e0) & % 71.81/10.49 | (all_6_3 = e4 | all_6_3 = e3 | all_6_3 = e2 | all_6_3 = e1 | all_6_3 % 71.81/10.49 | = e0) & (all_6_4 = e4 | all_6_4 = e3 | all_6_4 = e2 | all_6_4 = e1 % 71.81/10.49 | | all_6_4 = e0) & (all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e2 | % 71.81/10.49 | all_6_5 = e1 | all_6_5 = e0) & (all_6_6 = e4 | all_6_6 = e3 | % 71.81/10.49 | all_6_6 = e2 | all_6_6 = e1 | all_6_6 = e0) & (all_6_7 = e4 | % 71.81/10.49 | all_6_7 = e3 | all_6_7 = e2 | all_6_7 = e1 | all_6_7 = e0) & % 71.81/10.49 | (all_6_8 = e4 | all_6_8 = e3 | all_6_8 = e2 | all_6_8 = e1 | all_6_8 % 71.81/10.49 | = e0) & (all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e2 | all_6_9 = e1 % 71.81/10.49 | | all_6_9 = e0) & (all_6_10 = e4 | all_6_10 = e3 | all_6_10 = e2 | % 71.81/10.49 | all_6_10 = e1 | all_6_10 = e0) & (all_6_11 = e4 | all_6_11 = e3 | % 71.81/10.49 | all_6_11 = e2 | all_6_11 = e1 | all_6_11 = e0) & (all_6_12 = e4 | % 71.81/10.49 | all_6_12 = e3 | all_6_12 = e2 | all_6_12 = e1 | all_6_12 = e0) & % 71.81/10.49 | (all_6_13 = e4 | all_6_13 = e3 | all_6_13 = e2 | all_6_13 = e1 | % 71.81/10.49 | all_6_13 = e0) & (all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e2 | % 71.81/10.49 | all_6_14 = e1 | all_6_14 = e0) & (all_6_15 = e4 | all_6_15 = e3 | % 71.81/10.49 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 = e0) & (all_6_16 = e4 | % 71.81/10.49 | all_6_16 = e3 | all_6_16 = e2 | all_6_16 = e1 | all_6_16 = e0) & % 71.81/10.49 | (all_6_17 = e4 | all_6_17 = e3 | all_6_17 = e2 | all_6_17 = e1 | % 71.81/10.49 | all_6_17 = e0) & (all_6_18 = e4 | all_6_18 = e3 | all_6_18 = e2 | % 71.81/10.49 | all_6_18 = e1 | all_6_18 = e0) & (all_6_19 = e4 | all_6_19 = e3 | % 71.81/10.49 | all_6_19 = e2 | all_6_19 = e1 | all_6_19 = e0) & (all_6_20 = e4 | % 71.81/10.49 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 = e0) & % 71.81/10.49 | (all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e2 | all_6_21 = e1 | % 71.81/10.49 | all_6_21 = e0) & (all_6_22 = e4 | all_6_22 = e3 | all_6_22 = e2 | % 71.81/10.49 | all_6_22 = e1 | all_6_22 = e0) & (all_6_23 = e4 | all_6_23 = e3 | % 71.81/10.49 | all_6_23 = e2 | all_6_23 = e1 | all_6_23 = e0) & (all_6_24 = e4 | % 71.81/10.49 | all_6_24 = e3 | all_6_24 = e2 | all_6_24 = e1 | all_6_24 = e0) % 71.81/10.49 | % 71.81/10.49 | ALPHA: (142) implies: % 71.81/10.49 | (143) op(e0, e0) = all_6_24 % 71.81/10.49 | (144) op(e0, e1) = all_6_23 % 71.81/10.49 | (145) op(e0, e2) = all_6_22 % 71.81/10.49 | (146) op(e0, e3) = all_6_21 % 71.81/10.49 | (147) op(e0, e4) = all_6_20 % 71.81/10.49 | (148) op(e1, e0) = all_6_19 % 71.81/10.49 | (149) op(e1, e1) = all_6_18 % 71.81/10.49 | (150) op(e1, e2) = all_6_17 % 71.81/10.49 | (151) op(e1, e3) = all_6_16 % 71.81/10.49 | (152) op(e1, e4) = all_6_15 % 71.81/10.49 | (153) op(e2, e0) = all_6_14 % 71.81/10.49 | (154) op(e2, e1) = all_6_13 % 71.81/10.49 | (155) op(e2, e2) = all_6_12 % 71.81/10.49 | (156) op(e2, e3) = all_6_11 % 71.81/10.49 | (157) op(e2, e4) = all_6_10 % 71.81/10.50 | (158) op(e3, e0) = all_6_9 % 71.81/10.50 | (159) op(e3, e1) = all_6_8 % 71.81/10.50 | (160) op(e3, e2) = all_6_7 % 71.81/10.50 | (161) op(e3, e3) = all_6_6 % 71.81/10.50 | (162) op(e3, e4) = all_6_5 % 71.81/10.50 | (163) op(e4, e0) = all_6_4 % 71.81/10.50 | (164) op(e4, e1) = all_6_3 % 71.81/10.50 | (165) op(e4, e2) = all_6_2 % 71.81/10.50 | (166) op(e4, e3) = all_6_1 % 71.81/10.50 | (167) op(e4, e4) = all_6_0 % 71.81/10.50 | (168) all_6_22 = e4 | all_6_22 = e3 | all_6_22 = e2 | all_6_22 = e1 | % 71.81/10.50 | all_6_22 = e0 % 71.81/10.50 | (169) all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e2 | all_6_21 = e1 | % 71.81/10.50 | all_6_21 = e0 % 71.81/10.50 | (170) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | % 71.81/10.50 | all_6_20 = e0 % 71.81/10.50 | (171) all_6_19 = e4 | all_6_19 = e3 | all_6_19 = e2 | all_6_19 = e1 | % 71.81/10.50 | all_6_19 = e0 % 71.81/10.50 | (172) all_6_16 = e4 | all_6_16 = e3 | all_6_16 = e2 | all_6_16 = e1 | % 71.81/10.50 | all_6_16 = e0 % 71.81/10.50 | (173) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | % 71.81/10.50 | all_6_15 = e0 % 71.81/10.50 | (174) all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e2 | all_6_14 = e1 | % 71.81/10.50 | all_6_14 = e0 % 71.81/10.50 | (175) all_6_13 = e4 | all_6_13 = e3 | all_6_13 = e2 | all_6_13 = e1 | % 71.81/10.50 | all_6_13 = e0 % 71.81/10.50 | (176) all_6_11 = e4 | all_6_11 = e3 | all_6_11 = e2 | all_6_11 = e1 | % 71.81/10.50 | all_6_11 = e0 % 71.81/10.50 | (177) all_6_10 = e4 | all_6_10 = e3 | all_6_10 = e2 | all_6_10 = e1 | % 71.81/10.50 | all_6_10 = e0 % 71.81/10.50 | (178) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e2 | all_6_9 = e1 | all_6_9 = % 71.81/10.50 | e0 % 71.81/10.50 | (179) all_6_7 = e4 | all_6_7 = e3 | all_6_7 = e2 | all_6_7 = e1 | all_6_7 = % 71.81/10.50 | e0 % 71.81/10.50 | (180) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e2 | all_6_5 = e1 | all_6_5 = % 71.81/10.50 | e0 % 71.81/10.50 | (181) all_6_4 = e4 | all_6_4 = e3 | all_6_4 = e2 | all_6_4 = e1 | all_6_4 = % 71.81/10.50 | e0 % 71.81/10.50 | (182) all_6_3 = e4 | all_6_3 = e3 | all_6_3 = e2 | all_6_3 = e1 | all_6_3 = % 71.81/10.50 | e0 % 71.81/10.50 | (183) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | all_6_2 = % 71.81/10.50 | e0 % 71.81/10.50 | (184) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e2 | all_6_1 = e1 | all_6_1 = % 71.81/10.50 | e0 % 71.81/10.50 | % 71.81/10.50 | DELTA: instantiating (16) with fresh symbols all_8_0, all_8_1, all_8_2, % 71.81/10.50 | all_8_3, all_8_4, all_8_5, all_8_6, all_8_7, all_8_8, all_8_9, % 71.81/10.50 | all_8_10, all_8_11, all_8_12, all_8_13, all_8_14, all_8_15, all_8_16, % 71.81/10.50 | all_8_17, all_8_18, all_8_19, all_8_20, all_8_21, all_8_22, all_8_23, % 71.81/10.50 | all_8_24, all_8_25, all_8_26, all_8_27, all_8_28, all_8_29, all_8_30, % 71.81/10.50 | all_8_31, all_8_32, all_8_33, all_8_34, all_8_35, all_8_36, all_8_37, % 71.81/10.50 | all_8_38, all_8_39, all_8_40, all_8_41, all_8_42, all_8_43, all_8_44, % 71.81/10.50 | all_8_45, all_8_46, all_8_47, all_8_48, all_8_49, all_8_50, all_8_51, % 71.81/10.50 | all_8_52, all_8_53, all_8_54, all_8_55, all_8_56, all_8_57, all_8_58, % 71.81/10.50 | all_8_59, all_8_60, all_8_61, all_8_62, all_8_63, all_8_64, all_8_65, % 71.81/10.50 | all_8_66, all_8_67, all_8_68, all_8_69 gives: % 71.81/10.51 | (185) op(e4, all_8_3) = all_8_1 & op(e4, all_8_6) = all_8_4 & op(e4, % 71.81/10.51 | all_8_9) = all_8_7 & op(e4, all_8_12) = all_8_10 & op(e4, all_8_15) % 71.81/10.51 | = all_8_14 & op(e4, all_8_28) = all_8_27 & op(e4, all_8_41) = % 71.81/10.51 | all_8_40 & op(e4, all_8_54) = all_8_53 & op(e4, all_8_65) = all_8_0 & % 71.81/10.51 | op(e4, e4) = all_8_65 & op(e4, e3) = all_8_15 & op(e4, e2) = all_8_28 % 71.81/10.51 | & op(e4, e1) = all_8_41 & op(e4, e0) = all_8_54 & op(e3, all_8_3) = % 71.81/10.51 | all_8_2 & op(e3, all_8_15) = all_8_13 & op(e3, all_8_19) = all_8_17 & % 71.81/10.51 | op(e3, all_8_22) = all_8_20 & op(e3, all_8_25) = all_8_23 & op(e3, % 71.81/10.51 | all_8_31) = all_8_30 & op(e3, all_8_44) = all_8_43 & op(e3, % 71.81/10.51 | all_8_57) = all_8_56 & op(e3, all_8_66) = all_8_16 & op(e3, e4) = % 71.81/10.51 | all_8_3 & op(e3, e3) = all_8_66 & op(e3, e2) = all_8_31 & op(e3, e1) % 71.81/10.51 | = all_8_44 & op(e3, e0) = all_8_57 & op(e2, all_8_6) = all_8_5 & % 71.81/10.51 | op(e2, all_8_19) = all_8_18 & op(e2, all_8_28) = all_8_26 & op(e2, % 71.81/10.51 | all_8_31) = all_8_29 & op(e2, all_8_35) = all_8_33 & op(e2, % 71.81/10.51 | all_8_38) = all_8_36 & op(e2, all_8_47) = all_8_46 & op(e2, % 71.81/10.51 | all_8_60) = all_8_59 & op(e2, all_8_67) = all_8_32 & op(e2, e4) = % 71.81/10.51 | all_8_6 & op(e2, e3) = all_8_19 & op(e2, e2) = all_8_67 & op(e2, e1) % 71.81/10.51 | = all_8_47 & op(e2, e0) = all_8_60 & op(e1, all_8_9) = all_8_8 & % 71.81/10.51 | op(e1, all_8_22) = all_8_21 & op(e1, all_8_35) = all_8_34 & op(e1, % 71.81/10.51 | all_8_41) = all_8_39 & op(e1, all_8_44) = all_8_42 & op(e1, % 71.81/10.51 | all_8_47) = all_8_45 & op(e1, all_8_51) = all_8_49 & op(e1, % 71.81/10.51 | all_8_63) = all_8_62 & op(e1, all_8_68) = all_8_48 & op(e1, e4) = % 71.81/10.51 | all_8_9 & op(e1, e3) = all_8_22 & op(e1, e2) = all_8_35 & op(e1, e1) % 71.81/10.51 | = all_8_68 & op(e1, e0) = all_8_63 & op(e0, all_8_12) = all_8_11 & % 71.81/10.51 | op(e0, all_8_25) = all_8_24 & op(e0, all_8_38) = all_8_37 & op(e0, % 71.81/10.51 | all_8_51) = all_8_50 & op(e0, all_8_54) = all_8_52 & op(e0, % 71.81/10.51 | all_8_57) = all_8_55 & op(e0, all_8_60) = all_8_58 & op(e0, % 71.81/10.51 | all_8_63) = all_8_61 & op(e0, all_8_69) = all_8_64 & op(e0, e4) = % 71.81/10.51 | all_8_12 & op(e0, e3) = all_8_25 & op(e0, e2) = all_8_38 & op(e0, e1) % 71.81/10.51 | = all_8_51 & op(e0, e0) = all_8_69 & $i(all_8_0) & $i(all_8_1) & % 71.81/10.51 | $i(all_8_2) & $i(all_8_3) & $i(all_8_4) & $i(all_8_5) & $i(all_8_6) & % 71.81/10.51 | $i(all_8_7) & $i(all_8_8) & $i(all_8_9) & $i(all_8_10) & $i(all_8_11) % 71.81/10.51 | & $i(all_8_12) & $i(all_8_13) & $i(all_8_14) & $i(all_8_15) & % 71.81/10.51 | $i(all_8_16) & $i(all_8_17) & $i(all_8_18) & $i(all_8_19) & % 71.81/10.51 | $i(all_8_20) & $i(all_8_21) & $i(all_8_22) & $i(all_8_23) & % 71.81/10.51 | $i(all_8_24) & $i(all_8_25) & $i(all_8_26) & $i(all_8_27) & % 71.81/10.51 | $i(all_8_28) & $i(all_8_29) & $i(all_8_30) & $i(all_8_31) & % 71.81/10.51 | $i(all_8_32) & $i(all_8_33) & $i(all_8_34) & $i(all_8_35) & % 71.81/10.51 | $i(all_8_36) & $i(all_8_37) & $i(all_8_38) & $i(all_8_39) & % 71.81/10.51 | $i(all_8_40) & $i(all_8_41) & $i(all_8_42) & $i(all_8_43) & % 71.81/10.51 | $i(all_8_44) & $i(all_8_45) & $i(all_8_46) & $i(all_8_47) & % 71.81/10.51 | $i(all_8_48) & $i(all_8_49) & $i(all_8_50) & $i(all_8_51) & % 71.81/10.51 | $i(all_8_52) & $i(all_8_53) & $i(all_8_54) & $i(all_8_55) & % 71.81/10.51 | $i(all_8_56) & $i(all_8_57) & $i(all_8_58) & $i(all_8_59) & % 71.81/10.51 | $i(all_8_60) & $i(all_8_61) & $i(all_8_62) & $i(all_8_63) & % 71.81/10.51 | $i(all_8_64) & $i(all_8_65) & $i(all_8_66) & $i(all_8_67) & % 71.81/10.51 | $i(all_8_68) & $i(all_8_69) & (all_8_65 = e4 | all_8_66 = e4 | % 71.81/10.51 | all_8_67 = e4 | all_8_68 = e4 | all_8_69 = e4) & (all_8_65 = e3 | % 71.81/10.51 | all_8_66 = e3 | all_8_67 = e3 | all_8_68 = e3 | all_8_69 = e3) & % 71.81/10.51 | (all_8_65 = e2 | all_8_66 = e2 | all_8_67 = e2 | all_8_68 = e2 | % 71.81/10.51 | all_8_69 = e2) & (all_8_65 = e1 | all_8_66 = e1 | all_8_67 = e1 | % 71.81/10.51 | all_8_68 = e1 | all_8_69 = e1) & (all_8_65 = e0 | all_8_66 = e0 | % 71.81/10.51 | all_8_67 = e0 | all_8_68 = e0 | all_8_69 = e0) & ((all_8_1 = e3 & % 71.81/10.51 | ~ (all_8_2 = e4)) | (all_8_4 = e2 & ~ (all_8_5 = e4)) | (all_8_7 % 71.81/10.51 | = e1 & ~ (all_8_8 = e4)) | (all_8_10 = e0 & ~ (all_8_11 = e4))) % 71.81/10.51 | & ((all_8_13 = e4 & ~ (all_8_14 = e3)) | (all_8_17 = e2 & ~ % 71.81/10.51 | (all_8_18 = e3)) | (all_8_20 = e1 & ~ (all_8_21 = e3)) | % 71.81/10.51 | (all_8_23 = e0 & ~ (all_8_24 = e3))) & ((all_8_26 = e4 & ~ % 71.81/10.51 | (all_8_27 = e2)) | (all_8_29 = e3 & ~ (all_8_30 = e2)) | % 71.81/10.51 | (all_8_33 = e1 & ~ (all_8_34 = e2)) | (all_8_36 = e0 & ~ % 71.81/10.51 | (all_8_37 = e2))) & ((all_8_39 = e4 & ~ (all_8_40 = e1)) | % 71.81/10.51 | (all_8_42 = e3 & ~ (all_8_43 = e1)) | (all_8_45 = e2 & ~ % 71.81/10.51 | (all_8_46 = e1)) | (all_8_49 = e0 & ~ (all_8_50 = e1))) & % 71.81/10.51 | ((all_8_52 = e4 & ~ (all_8_53 = e0)) | (all_8_55 = e3 & ~ (all_8_56 % 71.81/10.51 | = e0)) | (all_8_58 = e2 & ~ (all_8_59 = e0)) | (all_8_61 = e1 % 71.81/10.51 | & ~ (all_8_62 = e0))) % 71.81/10.51 | % 71.81/10.51 | ALPHA: (185) implies: % 71.81/10.51 | (186) op(e0, e0) = all_8_69 % 71.81/10.51 | (187) op(e0, e1) = all_8_51 % 71.81/10.51 | (188) op(e0, e2) = all_8_38 % 71.81/10.51 | (189) op(e0, e3) = all_8_25 % 71.81/10.51 | (190) op(e0, e4) = all_8_12 % 71.81/10.51 | (191) op(e0, all_8_63) = all_8_61 % 71.81/10.51 | (192) op(e0, all_8_60) = all_8_58 % 71.81/10.51 | (193) op(e0, all_8_57) = all_8_55 % 71.81/10.51 | (194) op(e0, all_8_54) = all_8_52 % 71.81/10.51 | (195) op(e0, all_8_51) = all_8_50 % 71.81/10.51 | (196) op(e0, all_8_38) = all_8_37 % 71.81/10.51 | (197) op(e0, all_8_12) = all_8_11 % 71.81/10.51 | (198) op(e1, e0) = all_8_63 % 71.81/10.51 | (199) op(e1, e1) = all_8_68 % 71.81/10.51 | (200) op(e1, e2) = all_8_35 % 71.81/10.51 | (201) op(e1, e3) = all_8_22 % 71.81/10.51 | (202) op(e1, e4) = all_8_9 % 71.81/10.51 | (203) op(e1, all_8_63) = all_8_62 % 71.81/10.51 | (204) op(e1, all_8_51) = all_8_49 % 71.81/10.51 | (205) op(e1, all_8_47) = all_8_45 % 71.81/10.51 | (206) op(e1, all_8_44) = all_8_42 % 71.81/10.51 | (207) op(e1, all_8_41) = all_8_39 % 71.81/10.51 | (208) op(e1, all_8_35) = all_8_34 % 71.81/10.51 | (209) op(e1, all_8_22) = all_8_21 % 71.81/10.51 | (210) op(e1, all_8_9) = all_8_8 % 71.81/10.51 | (211) op(e2, e0) = all_8_60 % 71.81/10.51 | (212) op(e2, e1) = all_8_47 % 71.81/10.51 | (213) op(e2, e2) = all_8_67 % 71.81/10.51 | (214) op(e2, e3) = all_8_19 % 71.81/10.51 | (215) op(e2, e4) = all_8_6 % 71.81/10.51 | (216) op(e2, all_8_60) = all_8_59 % 71.81/10.51 | (217) op(e2, all_8_47) = all_8_46 % 71.81/10.51 | (218) op(e2, all_8_38) = all_8_36 % 71.81/10.51 | (219) op(e2, all_8_35) = all_8_33 % 71.81/10.51 | (220) op(e2, all_8_31) = all_8_29 % 71.81/10.51 | (221) op(e2, all_8_28) = all_8_26 % 71.81/10.51 | (222) op(e2, all_8_19) = all_8_18 % 71.81/10.51 | (223) op(e2, all_8_6) = all_8_5 % 71.81/10.51 | (224) op(e3, e0) = all_8_57 % 71.81/10.51 | (225) op(e3, e1) = all_8_44 % 71.81/10.51 | (226) op(e3, e2) = all_8_31 % 71.81/10.51 | (227) op(e3, e3) = all_8_66 % 71.81/10.51 | (228) op(e3, e4) = all_8_3 % 71.81/10.51 | (229) op(e3, all_8_44) = all_8_43 % 71.81/10.51 | (230) op(e3, all_8_31) = all_8_30 % 71.81/10.51 | (231) op(e3, all_8_25) = all_8_23 % 71.81/10.51 | (232) op(e3, all_8_22) = all_8_20 % 71.81/10.51 | (233) op(e3, all_8_19) = all_8_17 % 71.81/10.51 | (234) op(e3, all_8_15) = all_8_13 % 71.81/10.51 | (235) op(e3, all_8_3) = all_8_2 % 71.81/10.51 | (236) op(e4, e0) = all_8_54 % 71.81/10.51 | (237) op(e4, e1) = all_8_41 % 71.81/10.51 | (238) op(e4, e2) = all_8_28 % 71.81/10.51 | (239) op(e4, e3) = all_8_15 % 71.81/10.51 | (240) op(e4, e4) = all_8_65 % 71.81/10.51 | (241) op(e4, all_8_54) = all_8_53 % 71.81/10.51 | (242) op(e4, all_8_41) = all_8_40 % 71.81/10.51 | (243) op(e4, all_8_28) = all_8_27 % 71.81/10.51 | (244) op(e4, all_8_15) = all_8_14 % 71.81/10.51 | (245) op(e4, all_8_12) = all_8_10 % 71.81/10.51 | (246) op(e4, all_8_9) = all_8_7 % 71.81/10.51 | (247) op(e4, all_8_6) = all_8_4 % 71.81/10.51 | (248) op(e4, all_8_3) = all_8_1 % 71.81/10.51 | (249) (all_8_52 = e4 & ~ (all_8_53 = e0)) | (all_8_55 = e3 & ~ (all_8_56 % 71.81/10.51 | = e0)) | (all_8_58 = e2 & ~ (all_8_59 = e0)) | (all_8_61 = e1 & % 71.81/10.51 | ~ (all_8_62 = e0)) % 71.81/10.51 | (250) (all_8_39 = e4 & ~ (all_8_40 = e1)) | (all_8_42 = e3 & ~ (all_8_43 % 71.81/10.51 | = e1)) | (all_8_45 = e2 & ~ (all_8_46 = e1)) | (all_8_49 = e0 & % 71.81/10.51 | ~ (all_8_50 = e1)) % 71.81/10.52 | (251) (all_8_26 = e4 & ~ (all_8_27 = e2)) | (all_8_29 = e3 & ~ (all_8_30 % 71.81/10.52 | = e2)) | (all_8_33 = e1 & ~ (all_8_34 = e2)) | (all_8_36 = e0 & % 71.81/10.52 | ~ (all_8_37 = e2)) % 71.81/10.52 | (252) (all_8_13 = e4 & ~ (all_8_14 = e3)) | (all_8_17 = e2 & ~ (all_8_18 % 71.81/10.52 | = e3)) | (all_8_20 = e1 & ~ (all_8_21 = e3)) | (all_8_23 = e0 & % 71.81/10.52 | ~ (all_8_24 = e3)) % 71.81/10.52 | (253) (all_8_1 = e3 & ~ (all_8_2 = e4)) | (all_8_4 = e2 & ~ (all_8_5 = % 71.81/10.52 | e4)) | (all_8_7 = e1 & ~ (all_8_8 = e4)) | (all_8_10 = e0 & ~ % 71.81/10.52 | (all_8_11 = e4)) % 71.81/10.52 | (254) all_8_65 = e0 | all_8_66 = e0 | all_8_67 = e0 | all_8_68 = e0 | % 71.81/10.52 | all_8_69 = e0 % 71.81/10.52 | (255) all_8_65 = e1 | all_8_66 = e1 | all_8_67 = e1 | all_8_68 = e1 | % 71.81/10.52 | all_8_69 = e1 % 71.81/10.52 | % 71.81/10.52 | DELTA: instantiating (2) with fresh symbols all_10_0, all_10_1, all_10_2, % 71.81/10.52 | all_10_3, all_10_4, all_10_5, all_10_6, all_10_7, all_10_8, all_10_9, % 71.81/10.52 | all_10_10, all_10_11, all_10_12, all_10_13, all_10_14, all_10_15, % 71.81/10.52 | all_10_16, all_10_17, all_10_18, all_10_19, all_10_20, all_10_21, % 71.81/10.52 | all_10_22, all_10_23, all_10_24 gives: % 71.81/10.52 | (256) op(e4, e4) = all_10_0 & op(e4, e3) = all_10_1 & op(e4, e2) = all_10_4 % 71.81/10.52 | & op(e4, e1) = all_10_9 & op(e4, e0) = all_10_16 & op(e3, e4) = % 71.81/10.52 | all_10_2 & op(e3, e3) = all_10_3 & op(e3, e2) = all_10_5 & op(e3, e1) % 71.81/10.52 | = all_10_10 & op(e3, e0) = all_10_17 & op(e2, e4) = all_10_6 & op(e2, % 71.81/10.52 | e3) = all_10_7 & op(e2, e2) = all_10_8 & op(e2, e1) = all_10_11 & % 71.81/10.52 | op(e2, e0) = all_10_18 & op(e1, e4) = all_10_12 & op(e1, e3) = % 71.81/10.52 | all_10_13 & op(e1, e2) = all_10_14 & op(e1, e1) = all_10_15 & op(e1, % 71.81/10.52 | e0) = all_10_19 & op(e0, e4) = all_10_20 & op(e0, e3) = all_10_21 & % 71.81/10.52 | op(e0, e2) = all_10_22 & op(e0, e1) = all_10_23 & op(e0, e0) = % 71.81/10.52 | all_10_24 & $i(all_10_0) & $i(all_10_1) & $i(all_10_2) & $i(all_10_3) % 71.81/10.52 | & $i(all_10_4) & $i(all_10_5) & $i(all_10_6) & $i(all_10_7) & % 71.81/10.52 | $i(all_10_8) & $i(all_10_9) & $i(all_10_10) & $i(all_10_11) & % 71.81/10.52 | $i(all_10_12) & $i(all_10_13) & $i(all_10_14) & $i(all_10_15) & % 71.81/10.52 | $i(all_10_16) & $i(all_10_17) & $i(all_10_18) & $i(all_10_19) & % 71.81/10.52 | $i(all_10_20) & $i(all_10_21) & $i(all_10_22) & $i(all_10_23) & % 71.81/10.52 | $i(all_10_24) & (all_10_0 = e4 | all_10_1 = e4 | all_10_4 = e4 | % 71.81/10.52 | all_10_9 = e4 | all_10_16 = e4) & (all_10_0 = e4 | all_10_2 = e4 | % 71.81/10.52 | all_10_6 = e4 | all_10_12 = e4 | all_10_20 = e4) & (all_10_0 = e3 | % 71.81/10.52 | all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | all_10_16 = e3) & % 71.81/10.52 | (all_10_0 = e3 | all_10_2 = e3 | all_10_6 = e3 | all_10_12 = e3 | % 71.81/10.52 | all_10_20 = e3) & (all_10_0 = e2 | all_10_1 = e2 | all_10_4 = e2 | % 71.81/10.52 | all_10_9 = e2 | all_10_16 = e2) & (all_10_0 = e2 | all_10_2 = e2 | % 71.81/10.52 | all_10_6 = e2 | all_10_12 = e2 | all_10_20 = e2) & (all_10_0 = e1 | % 71.81/10.52 | all_10_1 = e1 | all_10_4 = e1 | all_10_9 = e1 | all_10_16 = e1) & % 71.81/10.52 | (all_10_0 = e1 | all_10_2 = e1 | all_10_6 = e1 | all_10_12 = e1 | % 71.81/10.52 | all_10_20 = e1) & (all_10_0 = e0 | all_10_1 = e0 | all_10_4 = e0 | % 71.81/10.52 | all_10_9 = e0 | all_10_16 = e0) & (all_10_0 = e0 | all_10_2 = e0 | % 71.81/10.52 | all_10_6 = e0 | all_10_12 = e0 | all_10_20 = e0) & (all_10_1 = e4 | % 71.81/10.52 | all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | all_10_21 = e4) & % 71.81/10.52 | (all_10_1 = e3 | all_10_3 = e3 | all_10_7 = e3 | all_10_13 = e3 | % 71.81/10.52 | all_10_21 = e3) & (all_10_1 = e2 | all_10_3 = e2 | all_10_7 = e2 | % 71.81/10.52 | all_10_13 = e2 | all_10_21 = e2) & (all_10_1 = e1 | all_10_3 = e1 | % 71.81/10.52 | all_10_7 = e1 | all_10_13 = e1 | all_10_21 = e1) & (all_10_1 = e0 | % 71.81/10.52 | all_10_3 = e0 | all_10_7 = e0 | all_10_13 = e0 | all_10_21 = e0) & % 71.81/10.52 | (all_10_2 = e4 | all_10_3 = e4 | all_10_5 = e4 | all_10_10 = e4 | % 71.81/10.52 | all_10_17 = e4) & (all_10_2 = e3 | all_10_3 = e3 | all_10_5 = e3 | % 71.81/10.52 | all_10_10 = e3 | all_10_17 = e3) & (all_10_2 = e2 | all_10_3 = e2 | % 71.81/10.52 | all_10_5 = e2 | all_10_10 = e2 | all_10_17 = e2) & (all_10_2 = e1 | % 71.81/10.52 | all_10_3 = e1 | all_10_5 = e1 | all_10_10 = e1 | all_10_17 = e1) & % 71.81/10.52 | (all_10_2 = e0 | all_10_3 = e0 | all_10_5 = e0 | all_10_10 = e0 | % 71.81/10.52 | all_10_17 = e0) & (all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 | % 71.81/10.52 | all_10_14 = e4 | all_10_22 = e4) & (all_10_4 = e3 | all_10_5 = e3 | % 71.81/10.52 | all_10_8 = e3 | all_10_14 = e3 | all_10_22 = e3) & (all_10_4 = e2 | % 71.81/10.52 | all_10_5 = e2 | all_10_8 = e2 | all_10_14 = e2 | all_10_22 = e2) & % 71.81/10.52 | (all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 71.81/10.52 | all_10_22 = e1) & (all_10_4 = e0 | all_10_5 = e0 | all_10_8 = e0 | % 71.81/10.52 | all_10_14 = e0 | all_10_22 = e0) & (all_10_6 = e4 | all_10_7 = e4 | % 71.81/10.52 | all_10_8 = e4 | all_10_11 = e4 | all_10_18 = e4) & (all_10_6 = e3 | % 71.81/10.52 | all_10_7 = e3 | all_10_8 = e3 | all_10_11 = e3 | all_10_18 = e3) & % 71.81/10.52 | (all_10_6 = e2 | all_10_7 = e2 | all_10_8 = e2 | all_10_11 = e2 | % 71.81/10.52 | all_10_18 = e2) & (all_10_6 = e1 | all_10_7 = e1 | all_10_8 = e1 | % 71.81/10.52 | all_10_11 = e1 | all_10_18 = e1) & (all_10_6 = e0 | all_10_7 = e0 | % 71.81/10.52 | all_10_8 = e0 | all_10_11 = e0 | all_10_18 = e0) & (all_10_9 = e4 | % 71.81/10.52 | all_10_10 = e4 | all_10_11 = e4 | all_10_15 = e4 | all_10_23 = e4) % 71.81/10.52 | & (all_10_9 = e3 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 71.81/10.52 | all_10_23 = e3) & (all_10_9 = e2 | all_10_10 = e2 | all_10_11 = e2 % 71.81/10.52 | | all_10_15 = e2 | all_10_23 = e2) & (all_10_9 = e1 | all_10_10 = % 71.81/10.52 | e1 | all_10_11 = e1 | all_10_15 = e1 | all_10_23 = e1) & (all_10_9 % 71.81/10.52 | = e0 | all_10_10 = e0 | all_10_11 = e0 | all_10_15 = e0 | all_10_23 % 71.81/10.52 | = e0) & (all_10_12 = e4 | all_10_13 = e4 | all_10_14 = e4 | % 71.81/10.52 | all_10_15 = e4 | all_10_19 = e4) & (all_10_12 = e3 | all_10_13 = e3 % 71.81/10.52 | | all_10_14 = e3 | all_10_15 = e3 | all_10_19 = e3) & (all_10_12 = % 71.81/10.52 | e2 | all_10_13 = e2 | all_10_14 = e2 | all_10_15 = e2 | all_10_19 = % 71.81/10.52 | e2) & (all_10_12 = e1 | all_10_13 = e1 | all_10_14 = e1 | all_10_15 % 71.81/10.52 | = e1 | all_10_19 = e1) & (all_10_12 = e0 | all_10_13 = e0 | % 71.81/10.52 | all_10_14 = e0 | all_10_15 = e0 | all_10_19 = e0) & (all_10_16 = e4 % 71.81/10.52 | | all_10_17 = e4 | all_10_18 = e4 | all_10_19 = e4 | all_10_24 = % 71.81/10.52 | e4) & (all_10_16 = e3 | all_10_17 = e3 | all_10_18 = e3 | all_10_19 % 71.81/10.52 | = e3 | all_10_24 = e3) & (all_10_16 = e2 | all_10_17 = e2 | % 71.81/10.52 | all_10_18 = e2 | all_10_19 = e2 | all_10_24 = e2) & (all_10_16 = e1 % 71.81/10.52 | | all_10_17 = e1 | all_10_18 = e1 | all_10_19 = e1 | all_10_24 = % 71.81/10.52 | e1) & (all_10_20 = e4 | all_10_21 = e4 | all_10_22 = e4 | all_10_23 % 71.81/10.52 | = e4 | all_10_24 = e4) & (all_10_20 = e3 | all_10_21 = e3 | % 71.81/10.52 | all_10_22 = e3 | all_10_23 = e3 | all_10_24 = e3) & (all_10_20 = e2 % 71.81/10.52 | | all_10_21 = e2 | all_10_22 = e2 | all_10_23 = e2 | all_10_24 = % 71.81/10.52 | e2) & (all_10_20 = e1 | all_10_21 = e1 | all_10_22 = e1 | all_10_23 % 71.81/10.52 | = e1 | all_10_24 = e1) & (all_10_24 = e0 | ((all_10_16 = e0 | % 71.81/10.52 | all_10_17 = e0 | all_10_18 = e0 | all_10_19 = e0) & (all_10_20 % 71.81/10.52 | = e0 | all_10_21 = e0 | all_10_22 = e0 | all_10_23 = e0))) % 71.81/10.52 | % 71.81/10.52 | ALPHA: (256) implies: % 71.81/10.53 | (257) op(e0, e0) = all_10_24 % 71.81/10.53 | (258) op(e0, e1) = all_10_23 % 71.81/10.53 | (259) op(e0, e2) = all_10_22 % 71.81/10.53 | (260) op(e0, e3) = all_10_21 % 71.81/10.53 | (261) op(e0, e4) = all_10_20 % 71.81/10.53 | (262) op(e1, e0) = all_10_19 % 71.81/10.53 | (263) op(e1, e1) = all_10_15 % 71.81/10.53 | (264) op(e1, e2) = all_10_14 % 71.81/10.53 | (265) op(e1, e3) = all_10_13 % 71.81/10.53 | (266) op(e1, e4) = all_10_12 % 71.81/10.53 | (267) op(e2, e0) = all_10_18 % 71.81/10.53 | (268) op(e2, e1) = all_10_11 % 71.81/10.53 | (269) op(e2, e2) = all_10_8 % 71.81/10.53 | (270) op(e2, e3) = all_10_7 % 71.81/10.53 | (271) op(e2, e4) = all_10_6 % 71.81/10.53 | (272) op(e3, e0) = all_10_17 % 71.81/10.53 | (273) op(e3, e1) = all_10_10 % 71.81/10.53 | (274) op(e3, e2) = all_10_5 % 71.81/10.53 | (275) op(e3, e3) = all_10_3 % 71.81/10.53 | (276) op(e3, e4) = all_10_2 % 71.81/10.53 | (277) op(e4, e0) = all_10_16 % 71.81/10.53 | (278) op(e4, e1) = all_10_9 % 71.81/10.53 | (279) op(e4, e2) = all_10_4 % 71.81/10.53 | (280) op(e4, e3) = all_10_1 % 71.81/10.53 | (281) op(e4, e4) = all_10_0 % 71.81/10.53 | (282) all_10_24 = e0 | ((all_10_16 = e0 | all_10_17 = e0 | all_10_18 = e0 | % 71.81/10.53 | all_10_19 = e0) & (all_10_20 = e0 | all_10_21 = e0 | all_10_22 = % 71.81/10.53 | e0 | all_10_23 = e0)) % 71.81/10.53 | (283) all_10_20 = e1 | all_10_21 = e1 | all_10_22 = e1 | all_10_23 = e1 | % 71.81/10.53 | all_10_24 = e1 % 71.81/10.53 | (284) all_10_20 = e2 | all_10_21 = e2 | all_10_22 = e2 | all_10_23 = e2 | % 71.81/10.53 | all_10_24 = e2 % 71.81/10.53 | (285) all_10_20 = e3 | all_10_21 = e3 | all_10_22 = e3 | all_10_23 = e3 | % 71.81/10.53 | all_10_24 = e3 % 71.81/10.53 | (286) all_10_20 = e4 | all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 71.81/10.53 | all_10_24 = e4 % 71.81/10.53 | (287) all_10_16 = e2 | all_10_17 = e2 | all_10_18 = e2 | all_10_19 = e2 | % 71.81/10.53 | all_10_24 = e2 % 71.81/10.53 | (288) all_10_16 = e3 | all_10_17 = e3 | all_10_18 = e3 | all_10_19 = e3 | % 71.81/10.53 | all_10_24 = e3 % 71.81/10.53 | (289) all_10_16 = e4 | all_10_17 = e4 | all_10_18 = e4 | all_10_19 = e4 | % 71.81/10.53 | all_10_24 = e4 % 71.81/10.53 | (290) all_10_12 = e1 | all_10_13 = e1 | all_10_14 = e1 | all_10_15 = e1 | % 71.81/10.53 | all_10_19 = e1 % 71.81/10.53 | (291) all_10_12 = e2 | all_10_13 = e2 | all_10_14 = e2 | all_10_15 = e2 | % 71.81/10.53 | all_10_19 = e2 % 71.81/10.53 | (292) all_10_12 = e3 | all_10_13 = e3 | all_10_14 = e3 | all_10_15 = e3 | % 71.81/10.53 | all_10_19 = e3 % 71.81/10.53 | (293) all_10_9 = e0 | all_10_10 = e0 | all_10_11 = e0 | all_10_15 = e0 | % 71.81/10.53 | all_10_23 = e0 % 71.81/10.53 | (294) all_10_9 = e1 | all_10_10 = e1 | all_10_11 = e1 | all_10_15 = e1 | % 71.81/10.53 | all_10_23 = e1 % 71.81/10.53 | (295) all_10_9 = e2 | all_10_10 = e2 | all_10_11 = e2 | all_10_15 = e2 | % 71.81/10.53 | all_10_23 = e2 % 71.81/10.53 | (296) all_10_9 = e3 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 71.81/10.53 | all_10_23 = e3 % 71.81/10.53 | (297) all_10_6 = e0 | all_10_7 = e0 | all_10_8 = e0 | all_10_11 = e0 | % 71.81/10.53 | all_10_18 = e0 % 71.81/10.53 | (298) all_10_6 = e1 | all_10_7 = e1 | all_10_8 = e1 | all_10_11 = e1 | % 71.81/10.53 | all_10_18 = e1 % 71.81/10.53 | (299) all_10_6 = e2 | all_10_7 = e2 | all_10_8 = e2 | all_10_11 = e2 | % 71.81/10.53 | all_10_18 = e2 % 71.81/10.53 | (300) all_10_6 = e4 | all_10_7 = e4 | all_10_8 = e4 | all_10_11 = e4 | % 71.81/10.53 | all_10_18 = e4 % 71.81/10.53 | (301) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 71.81/10.53 | all_10_22 = e1 % 71.81/10.53 | (302) all_10_4 = e2 | all_10_5 = e2 | all_10_8 = e2 | all_10_14 = e2 | % 71.81/10.53 | all_10_22 = e2 % 71.81/10.53 | (303) all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | % 71.81/10.53 | all_10_22 = e4 % 71.81/10.53 | (304) all_10_2 = e0 | all_10_3 = e0 | all_10_5 = e0 | all_10_10 = e0 | % 71.81/10.53 | all_10_17 = e0 % 71.81/10.53 | (305) all_10_2 = e1 | all_10_3 = e1 | all_10_5 = e1 | all_10_10 = e1 | % 71.81/10.53 | all_10_17 = e1 % 71.81/10.53 | (306) all_10_2 = e2 | all_10_3 = e2 | all_10_5 = e2 | all_10_10 = e2 | % 71.81/10.53 | all_10_17 = e2 % 71.81/10.53 | (307) all_10_2 = e3 | all_10_3 = e3 | all_10_5 = e3 | all_10_10 = e3 | % 71.81/10.53 | all_10_17 = e3 % 71.81/10.53 | (308) all_10_2 = e4 | all_10_3 = e4 | all_10_5 = e4 | all_10_10 = e4 | % 71.81/10.53 | all_10_17 = e4 % 71.81/10.53 | (309) all_10_1 = e0 | all_10_3 = e0 | all_10_7 = e0 | all_10_13 = e0 | % 71.81/10.53 | all_10_21 = e0 % 71.81/10.53 | (310) all_10_1 = e2 | all_10_3 = e2 | all_10_7 = e2 | all_10_13 = e2 | % 71.81/10.53 | all_10_21 = e2 % 71.81/10.53 | (311) all_10_1 = e3 | all_10_3 = e3 | all_10_7 = e3 | all_10_13 = e3 | % 71.81/10.53 | all_10_21 = e3 % 71.81/10.53 | (312) all_10_1 = e4 | all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | % 71.81/10.53 | all_10_21 = e4 % 71.81/10.54 | (313) all_10_0 = e0 | all_10_2 = e0 | all_10_6 = e0 | all_10_12 = e0 | % 71.81/10.54 | all_10_20 = e0 % 71.81/10.54 | (314) all_10_0 = e0 | all_10_1 = e0 | all_10_4 = e0 | all_10_9 = e0 | % 71.81/10.54 | all_10_16 = e0 % 71.81/10.54 | (315) all_10_0 = e1 | all_10_2 = e1 | all_10_6 = e1 | all_10_12 = e1 | % 71.81/10.54 | all_10_20 = e1 % 71.81/10.54 | (316) all_10_0 = e1 | all_10_1 = e1 | all_10_4 = e1 | all_10_9 = e1 | % 71.81/10.54 | all_10_16 = e1 % 71.81/10.54 | (317) all_10_0 = e3 | all_10_2 = e3 | all_10_6 = e3 | all_10_12 = e3 | % 71.81/10.54 | all_10_20 = e3 % 71.81/10.54 | (318) all_10_0 = e3 | all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | % 71.81/10.54 | all_10_16 = e3 % 71.81/10.54 | (319) all_10_0 = e4 | all_10_2 = e4 | all_10_6 = e4 | all_10_12 = e4 | % 71.81/10.54 | all_10_20 = e4 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_6_24, all_8_69, e0, e0, % 71.81/10.54 | simplifying with (143), (186) gives: % 71.81/10.54 | (320) all_8_69 = all_6_24 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_8_69, all_10_24, e0, e0, % 71.81/10.54 | simplifying with (186), (257) gives: % 71.81/10.54 | (321) all_10_24 = all_8_69 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_4_24, all_10_24, e0, e0, % 71.81/10.54 | simplifying with (117), (257) gives: % 71.81/10.54 | (322) all_10_24 = all_4_24 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_8_51, all_10_23, e1, e0, % 71.81/10.54 | simplifying with (187), (258) gives: % 71.81/10.54 | (323) all_10_23 = all_8_51 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_6_23, all_10_23, e1, e0, % 71.81/10.54 | simplifying with (144), (258) gives: % 71.81/10.54 | (324) all_10_23 = all_6_23 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_4_19, all_10_23, e1, e0, % 71.81/10.54 | simplifying with (118), (258) gives: % 71.81/10.54 | (325) all_10_23 = all_4_19 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_8_38, all_10_22, e2, e0, % 71.81/10.54 | simplifying with (188), (259) gives: % 71.81/10.54 | (326) all_10_22 = all_8_38 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_6_22, all_10_22, e2, e0, % 71.81/10.54 | simplifying with (145), (259) gives: % 71.81/10.54 | (327) all_10_22 = all_6_22 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_4_14, all_10_22, e2, e0, % 71.81/10.54 | simplifying with (119), (259) gives: % 71.81/10.54 | (328) all_10_22 = all_4_14 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_6_21, all_8_25, e3, e0, % 71.81/10.54 | simplifying with (146), (189) gives: % 71.81/10.54 | (329) all_8_25 = all_6_21 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_8_25, all_10_21, e3, e0, % 71.81/10.54 | simplifying with (189), (260) gives: % 71.81/10.54 | (330) all_10_21 = all_8_25 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_4_9, all_10_21, e3, e0, % 71.81/10.54 | simplifying with (120), (260) gives: % 71.81/10.54 | (331) all_10_21 = all_4_9 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_8_12, all_10_20, e4, e0, % 71.81/10.54 | simplifying with (190), (261) gives: % 71.81/10.54 | (332) all_10_20 = all_8_12 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_6_20, all_10_20, e4, e0, % 71.81/10.54 | simplifying with (147), (261) gives: % 71.81/10.54 | (333) all_10_20 = all_6_20 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_4_4, all_10_20, e4, e0, % 71.81/10.54 | simplifying with (121), (261) gives: % 71.81/10.54 | (334) all_10_20 = all_4_4 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_6_19, all_8_63, e0, e1, % 71.81/10.54 | simplifying with (148), (198) gives: % 71.81/10.54 | (335) all_8_63 = all_6_19 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_8_63, all_10_19, e0, e1, % 71.81/10.54 | simplifying with (198), (262) gives: % 71.81/10.54 | (336) all_10_19 = all_8_63 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_4_23, all_10_19, e0, e1, % 71.81/10.54 | simplifying with (122), (262) gives: % 71.81/10.54 | (337) all_10_19 = all_4_23 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_4_18, all_8_68, e1, e1, % 71.81/10.54 | simplifying with (123), (199) gives: % 71.81/10.54 | (338) all_8_68 = all_4_18 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with e4, all_8_68, e1, e1, % 71.81/10.54 | simplifying with (12), (199) gives: % 71.81/10.54 | (339) all_8_68 = e4 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_8_68, all_10_15, e1, e1, % 71.81/10.54 | simplifying with (199), (263) gives: % 71.81/10.54 | (340) all_10_15 = all_8_68 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_6_18, all_10_15, e1, e1, % 71.81/10.54 | simplifying with (149), (263) gives: % 71.81/10.54 | (341) all_10_15 = all_6_18 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_6_17, all_8_35, e2, e1, % 71.81/10.54 | simplifying with (150), (200) gives: % 71.81/10.54 | (342) all_8_35 = all_6_17 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_4_13, all_8_35, e2, e1, % 71.81/10.54 | simplifying with (124), (200) gives: % 71.81/10.54 | (343) all_8_35 = all_4_13 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_6_17, all_10_14, e2, e1, % 71.81/10.54 | simplifying with (150), (264) gives: % 71.81/10.54 | (344) all_10_14 = all_6_17 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with e0, all_10_14, e2, e1, % 71.81/10.54 | simplifying with (13), (264) gives: % 71.81/10.54 | (345) all_10_14 = e0 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_6_16, all_8_22, e3, e1, % 71.81/10.54 | simplifying with (151), (201) gives: % 71.81/10.54 | (346) all_8_22 = all_6_16 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_8_22, all_10_13, e3, e1, % 71.81/10.54 | simplifying with (201), (265) gives: % 71.81/10.54 | (347) all_10_13 = all_8_22 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_4_8, all_10_13, e3, e1, % 71.81/10.54 | simplifying with (125), (265) gives: % 71.81/10.54 | (348) all_10_13 = all_4_8 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_6_15, all_8_9, e4, e1, % 71.81/10.54 | simplifying with (152), (202) gives: % 71.81/10.54 | (349) all_8_9 = all_6_15 % 71.81/10.54 | % 71.81/10.54 | GROUND_INST: instantiating (function-axioms) with all_8_9, all_10_12, e4, e1, % 71.81/10.54 | simplifying with (202), (266) gives: % 71.81/10.54 | (350) all_10_12 = all_8_9 % 71.81/10.54 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_4_3, all_10_12, e4, e1, % 71.81/10.55 | simplifying with (126), (266) gives: % 71.81/10.55 | (351) all_10_12 = all_4_3 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_4_22, all_8_60, e0, e2, % 71.81/10.55 | simplifying with (127), (211) gives: % 71.81/10.55 | (352) all_8_60 = all_4_22 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_8_60, all_10_18, e0, e2, % 71.81/10.55 | simplifying with (211), (267) gives: % 71.81/10.55 | (353) all_10_18 = all_8_60 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_6_14, all_10_18, e0, e2, % 71.81/10.55 | simplifying with (153), (267) gives: % 71.81/10.55 | (354) all_10_18 = all_6_14 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_6_13, all_8_47, e1, e2, % 71.81/10.55 | simplifying with (154), (212) gives: % 71.81/10.55 | (355) all_8_47 = all_6_13 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_8_47, all_10_11, e1, e2, % 71.81/10.55 | simplifying with (212), (268) gives: % 71.81/10.55 | (356) all_10_11 = all_8_47 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_4_17, all_10_11, e1, e2, % 71.81/10.55 | simplifying with (128), (268) gives: % 71.81/10.55 | (357) all_10_11 = all_4_17 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_4_12, all_6_12, e2, e2, % 71.81/10.55 | simplifying with (129), (155) gives: % 71.81/10.55 | (358) all_6_12 = all_4_12 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_6_12, all_8_67, e2, e2, % 71.81/10.55 | simplifying with (155), (213) gives: % 71.81/10.55 | (359) all_8_67 = all_6_12 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_8_67, all_10_8, e2, e2, % 71.81/10.55 | simplifying with (213), (269) gives: % 71.81/10.55 | (360) all_10_8 = all_8_67 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with e3, all_10_8, e2, e2, % 71.81/10.55 | simplifying with (14), (269) gives: % 71.81/10.55 | (361) all_10_8 = e3 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_4_7, all_8_19, e3, e2, % 71.81/10.55 | simplifying with (130), (214) gives: % 71.81/10.55 | (362) all_8_19 = all_4_7 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_8_19, all_10_7, e3, e2, % 71.81/10.55 | simplifying with (214), (270) gives: % 71.81/10.55 | (363) all_10_7 = all_8_19 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_6_11, all_10_7, e3, e2, % 71.81/10.55 | simplifying with (156), (270) gives: % 71.81/10.55 | (364) all_10_7 = all_6_11 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_8_6, all_10_6, e4, e2, % 71.81/10.55 | simplifying with (215), (271) gives: % 71.81/10.55 | (365) all_10_6 = all_8_6 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_6_10, all_10_6, e4, e2, % 71.81/10.55 | simplifying with (157), (271) gives: % 71.81/10.55 | (366) all_10_6 = all_6_10 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_4_2, all_10_6, e4, e2, % 71.81/10.55 | simplifying with (131), (271) gives: % 71.81/10.55 | (367) all_10_6 = all_4_2 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_6_9, all_8_57, e0, e3, % 71.81/10.55 | simplifying with (158), (224) gives: % 71.81/10.55 | (368) all_8_57 = all_6_9 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_8_57, all_10_17, e0, e3, % 71.81/10.55 | simplifying with (224), (272) gives: % 71.81/10.55 | (369) all_10_17 = all_8_57 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_4_21, all_10_17, e0, e3, % 71.81/10.55 | simplifying with (132), (272) gives: % 71.81/10.55 | (370) all_10_17 = all_4_21 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_8_44, all_10_10, e1, e3, % 71.81/10.55 | simplifying with (225), (273) gives: % 71.81/10.55 | (371) all_10_10 = all_8_44 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_6_8, all_10_10, e1, e3, % 71.81/10.55 | simplifying with (159), (273) gives: % 71.81/10.55 | (372) all_10_10 = all_6_8 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_4_16, all_10_10, e1, e3, % 71.81/10.55 | simplifying with (133), (273) gives: % 71.81/10.55 | (373) all_10_10 = all_4_16 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_4_11, all_8_31, e2, e3, % 71.81/10.55 | simplifying with (134), (226) gives: % 71.81/10.55 | (374) all_8_31 = all_4_11 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_8_31, all_10_5, e2, e3, % 71.81/10.55 | simplifying with (226), (274) gives: % 71.81/10.55 | (375) all_10_5 = all_8_31 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_6_7, all_10_5, e2, e3, % 71.81/10.55 | simplifying with (160), (274) gives: % 71.81/10.55 | (376) all_10_5 = all_6_7 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_6_6, all_8_66, e3, e3, % 71.81/10.55 | simplifying with (161), (227) gives: % 71.81/10.55 | (377) all_8_66 = all_6_6 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_8_66, all_10_3, e3, e3, % 71.81/10.55 | simplifying with (227), (275) gives: % 71.81/10.55 | (378) all_10_3 = all_8_66 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_4_6, all_10_3, e3, e3, % 71.81/10.55 | simplifying with (135), (275) gives: % 71.81/10.55 | (379) all_10_3 = all_4_6 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_6_5, all_8_3, e4, e3, % 71.81/10.55 | simplifying with (162), (228) gives: % 71.81/10.55 | (380) all_8_3 = all_6_5 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_8_3, all_10_2, e4, e3, % 71.81/10.55 | simplifying with (228), (276) gives: % 71.81/10.55 | (381) all_10_2 = all_8_3 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_4_1, all_10_2, e4, e3, % 71.81/10.55 | simplifying with (136), (276) gives: % 71.81/10.55 | (382) all_10_2 = all_4_1 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_6_4, all_8_54, e0, e4, % 71.81/10.55 | simplifying with (163), (236) gives: % 71.81/10.55 | (383) all_8_54 = all_6_4 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_8_54, all_10_16, e0, e4, % 71.81/10.55 | simplifying with (236), (277) gives: % 71.81/10.55 | (384) all_10_16 = all_8_54 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_4_20, all_10_16, e0, e4, % 71.81/10.55 | simplifying with (137), (277) gives: % 71.81/10.55 | (385) all_10_16 = all_4_20 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_6_3, all_8_41, e1, e4, % 71.81/10.55 | simplifying with (164), (237) gives: % 71.81/10.55 | (386) all_8_41 = all_6_3 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_8_41, all_10_9, e1, e4, % 71.81/10.55 | simplifying with (237), (278) gives: % 71.81/10.55 | (387) all_10_9 = all_8_41 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_4_15, all_10_9, e1, e4, % 71.81/10.55 | simplifying with (138), (278) gives: % 71.81/10.55 | (388) all_10_9 = all_4_15 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_8_28, all_10_4, e2, e4, % 71.81/10.55 | simplifying with (238), (279) gives: % 71.81/10.55 | (389) all_10_4 = all_8_28 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_6_2, all_10_4, e2, e4, % 71.81/10.55 | simplifying with (165), (279) gives: % 71.81/10.55 | (390) all_10_4 = all_6_2 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_4_10, all_10_4, e2, e4, % 71.81/10.55 | simplifying with (139), (279) gives: % 71.81/10.55 | (391) all_10_4 = all_4_10 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_6_1, all_8_15, e3, e4, % 71.81/10.55 | simplifying with (166), (239) gives: % 71.81/10.55 | (392) all_8_15 = all_6_1 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_8_15, all_10_1, e3, e4, % 71.81/10.55 | simplifying with (239), (280) gives: % 71.81/10.55 | (393) all_10_1 = all_8_15 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_4_5, all_10_1, e3, e4, % 71.81/10.55 | simplifying with (140), (280) gives: % 71.81/10.55 | (394) all_10_1 = all_4_5 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_4_0, all_6_0, e4, e4, % 71.81/10.55 | simplifying with (141), (167) gives: % 71.81/10.55 | (395) all_6_0 = all_4_0 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_6_0, all_8_65, e4, e4, % 71.81/10.55 | simplifying with (167), (240) gives: % 71.81/10.55 | (396) all_8_65 = all_6_0 % 71.81/10.55 | % 71.81/10.55 | GROUND_INST: instantiating (function-axioms) with all_8_65, all_10_0, e4, e4, % 71.81/10.55 | simplifying with (240), (281) gives: % 71.81/10.56 | (397) all_10_0 = all_8_65 % 71.81/10.56 | % 71.81/10.56 | GROUND_INST: instantiating (function-axioms) with e2, all_10_0, e4, e4, % 71.81/10.56 | simplifying with (15), (281) gives: % 71.81/10.56 | (398) all_10_0 = e2 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (397), (398) imply: % 71.81/10.56 | (399) all_8_65 = e2 % 71.81/10.56 | % 71.81/10.56 | SIMP: (399) implies: % 71.81/10.56 | (400) all_8_65 = e2 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (393), (394) imply: % 71.81/10.56 | (401) all_8_15 = all_4_5 % 71.81/10.56 | % 71.81/10.56 | SIMP: (401) implies: % 71.81/10.56 | (402) all_8_15 = all_4_5 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (381), (382) imply: % 71.81/10.56 | (403) all_8_3 = all_4_1 % 71.81/10.56 | % 71.81/10.56 | SIMP: (403) implies: % 71.81/10.56 | (404) all_8_3 = all_4_1 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (378), (379) imply: % 71.81/10.56 | (405) all_8_66 = all_4_6 % 71.81/10.56 | % 71.81/10.56 | SIMP: (405) implies: % 71.81/10.56 | (406) all_8_66 = all_4_6 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (389), (391) imply: % 71.81/10.56 | (407) all_8_28 = all_4_10 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (389), (390) imply: % 71.81/10.56 | (408) all_8_28 = all_6_2 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (375), (376) imply: % 71.81/10.56 | (409) all_8_31 = all_6_7 % 71.81/10.56 | % 71.81/10.56 | SIMP: (409) implies: % 71.81/10.56 | (410) all_8_31 = all_6_7 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (365), (367) imply: % 71.81/10.56 | (411) all_8_6 = all_4_2 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (365), (366) imply: % 71.81/10.56 | (412) all_8_6 = all_6_10 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (363), (364) imply: % 71.81/10.56 | (413) all_8_19 = all_6_11 % 71.81/10.56 | % 71.81/10.56 | SIMP: (413) implies: % 71.81/10.56 | (414) all_8_19 = all_6_11 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (360), (361) imply: % 71.81/10.56 | (415) all_8_67 = e3 % 71.81/10.56 | % 71.81/10.56 | SIMP: (415) implies: % 71.81/10.56 | (416) all_8_67 = e3 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (387), (388) imply: % 71.81/10.56 | (417) all_8_41 = all_4_15 % 71.81/10.56 | % 71.81/10.56 | SIMP: (417) implies: % 71.81/10.56 | (418) all_8_41 = all_4_15 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (371), (373) imply: % 71.81/10.56 | (419) all_8_44 = all_4_16 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (371), (372) imply: % 71.81/10.56 | (420) all_8_44 = all_6_8 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (356), (357) imply: % 71.81/10.56 | (421) all_8_47 = all_4_17 % 71.81/10.56 | % 71.81/10.56 | SIMP: (421) implies: % 71.81/10.56 | (422) all_8_47 = all_4_17 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (350), (351) imply: % 71.81/10.56 | (423) all_8_9 = all_4_3 % 71.81/10.56 | % 71.81/10.56 | SIMP: (423) implies: % 71.81/10.56 | (424) all_8_9 = all_4_3 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (347), (348) imply: % 71.81/10.56 | (425) all_8_22 = all_4_8 % 71.81/10.56 | % 71.81/10.56 | SIMP: (425) implies: % 71.81/10.56 | (426) all_8_22 = all_4_8 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (344), (345) imply: % 71.81/10.56 | (427) all_6_17 = e0 % 71.81/10.56 | % 71.81/10.56 | SIMP: (427) implies: % 71.81/10.56 | (428) all_6_17 = e0 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (340), (341) imply: % 71.81/10.56 | (429) all_8_68 = all_6_18 % 71.81/10.56 | % 71.81/10.56 | SIMP: (429) implies: % 71.81/10.56 | (430) all_8_68 = all_6_18 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (384), (385) imply: % 71.81/10.56 | (431) all_8_54 = all_4_20 % 71.81/10.56 | % 71.81/10.56 | SIMP: (431) implies: % 71.81/10.56 | (432) all_8_54 = all_4_20 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (369), (370) imply: % 71.81/10.56 | (433) all_8_57 = all_4_21 % 71.81/10.56 | % 71.81/10.56 | SIMP: (433) implies: % 71.81/10.56 | (434) all_8_57 = all_4_21 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (353), (354) imply: % 71.81/10.56 | (435) all_8_60 = all_6_14 % 71.81/10.56 | % 71.81/10.56 | SIMP: (435) implies: % 71.81/10.56 | (436) all_8_60 = all_6_14 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (336), (337) imply: % 71.81/10.56 | (437) all_8_63 = all_4_23 % 71.81/10.56 | % 71.81/10.56 | SIMP: (437) implies: % 71.81/10.56 | (438) all_8_63 = all_4_23 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (332), (334) imply: % 71.81/10.56 | (439) all_8_12 = all_4_4 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (332), (333) imply: % 71.81/10.56 | (440) all_8_12 = all_6_20 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (330), (331) imply: % 71.81/10.56 | (441) all_8_25 = all_4_9 % 71.81/10.56 | % 71.81/10.56 | SIMP: (441) implies: % 71.81/10.56 | (442) all_8_25 = all_4_9 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (326), (328) imply: % 71.81/10.56 | (443) all_8_38 = all_4_14 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (326), (327) imply: % 71.81/10.56 | (444) all_8_38 = all_6_22 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (323), (325) imply: % 71.81/10.56 | (445) all_8_51 = all_4_19 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (323), (324) imply: % 71.81/10.56 | (446) all_8_51 = all_6_23 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (321), (322) imply: % 71.81/10.56 | (447) all_8_69 = all_4_24 % 71.81/10.56 | % 71.81/10.56 | SIMP: (447) implies: % 71.81/10.56 | (448) all_8_69 = all_4_24 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (380), (404) imply: % 71.81/10.56 | (449) all_6_5 = all_4_1 % 71.81/10.56 | % 71.81/10.56 | SIMP: (449) implies: % 71.81/10.56 | (450) all_6_5 = all_4_1 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (411), (412) imply: % 71.81/10.56 | (451) all_6_10 = all_4_2 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (349), (424) imply: % 71.81/10.56 | (452) all_6_15 = all_4_3 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (439), (440) imply: % 71.81/10.56 | (453) all_6_20 = all_4_4 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (392), (402) imply: % 71.81/10.56 | (454) all_6_1 = all_4_5 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (362), (414) imply: % 71.81/10.56 | (455) all_6_11 = all_4_7 % 71.81/10.56 | % 71.81/10.56 | SIMP: (455) implies: % 71.81/10.56 | (456) all_6_11 = all_4_7 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (346), (426) imply: % 71.81/10.56 | (457) all_6_16 = all_4_8 % 71.81/10.56 | % 71.81/10.56 | SIMP: (457) implies: % 71.81/10.56 | (458) all_6_16 = all_4_8 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (329), (442) imply: % 71.81/10.56 | (459) all_6_21 = all_4_9 % 71.81/10.56 | % 71.81/10.56 | SIMP: (459) implies: % 71.81/10.56 | (460) all_6_21 = all_4_9 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (407), (408) imply: % 71.81/10.56 | (461) all_6_2 = all_4_10 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (374), (410) imply: % 71.81/10.56 | (462) all_6_7 = all_4_11 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (342), (343) imply: % 71.81/10.56 | (463) all_6_17 = all_4_13 % 71.81/10.56 | % 71.81/10.56 | SIMP: (463) implies: % 71.81/10.56 | (464) all_6_17 = all_4_13 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (443), (444) imply: % 71.81/10.56 | (465) all_6_22 = all_4_14 % 71.81/10.56 | % 71.81/10.56 | SIMP: (465) implies: % 71.81/10.56 | (466) all_6_22 = all_4_14 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (386), (418) imply: % 71.81/10.56 | (467) all_6_3 = all_4_15 % 71.81/10.56 | % 71.81/10.56 | SIMP: (467) implies: % 71.81/10.56 | (468) all_6_3 = all_4_15 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (419), (420) imply: % 71.81/10.56 | (469) all_6_8 = all_4_16 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (355), (422) imply: % 71.81/10.56 | (470) all_6_13 = all_4_17 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (445), (446) imply: % 71.81/10.56 | (471) all_6_23 = all_4_19 % 71.81/10.56 | % 71.81/10.56 | SIMP: (471) implies: % 71.81/10.56 | (472) all_6_23 = all_4_19 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (383), (432) imply: % 71.81/10.56 | (473) all_6_4 = all_4_20 % 71.81/10.56 | % 71.81/10.56 | SIMP: (473) implies: % 71.81/10.56 | (474) all_6_4 = all_4_20 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (368), (434) imply: % 71.81/10.56 | (475) all_6_9 = all_4_21 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (352), (436) imply: % 71.81/10.56 | (476) all_6_14 = all_4_22 % 71.81/10.56 | % 71.81/10.56 | SIMP: (476) implies: % 71.81/10.56 | (477) all_6_14 = all_4_22 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (335), (438) imply: % 71.81/10.56 | (478) all_6_19 = all_4_23 % 71.81/10.56 | % 71.81/10.56 | SIMP: (478) implies: % 71.81/10.56 | (479) all_6_19 = all_4_23 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (396), (400) imply: % 71.81/10.56 | (480) all_6_0 = e2 % 71.81/10.56 | % 71.81/10.56 | SIMP: (480) implies: % 71.81/10.56 | (481) all_6_0 = e2 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (377), (406) imply: % 71.81/10.56 | (482) all_6_6 = all_4_6 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (359), (416) imply: % 71.81/10.56 | (483) all_6_12 = e3 % 71.81/10.56 | % 71.81/10.56 | SIMP: (483) implies: % 71.81/10.56 | (484) all_6_12 = e3 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (339), (430) imply: % 71.81/10.56 | (485) all_6_18 = e4 % 71.81/10.56 | % 71.81/10.56 | COMBINE_EQS: (338), (430) imply: % 71.81/10.57 | (486) all_6_18 = all_4_18 % 71.81/10.57 | % 71.81/10.57 | COMBINE_EQS: (320), (448) imply: % 71.81/10.57 | (487) all_6_24 = all_4_24 % 71.81/10.57 | % 71.81/10.57 | COMBINE_EQS: (395), (481) imply: % 71.81/10.57 | (488) all_4_0 = e2 % 71.81/10.57 | % 71.81/10.57 | SIMP: (488) implies: % 71.81/10.57 | (489) all_4_0 = e2 % 71.81/10.57 | % 71.81/10.57 | COMBINE_EQS: (358), (484) imply: % 71.81/10.57 | (490) all_4_12 = e3 % 71.81/10.57 | % 71.81/10.57 | SIMP: (490) implies: % 71.81/10.57 | (491) all_4_12 = e3 % 71.81/10.57 | % 71.81/10.57 | COMBINE_EQS: (428), (464) imply: % 71.81/10.57 | (492) all_4_13 = e0 % 71.81/10.57 | % 71.81/10.57 | COMBINE_EQS: (485), (486) imply: % 71.81/10.57 | (493) all_4_18 = e4 % 71.81/10.57 | % 71.81/10.57 | COMBINE_EQS: (343), (492) imply: % 71.81/10.57 | (494) all_8_35 = e0 % 71.81/10.57 | % 71.81/10.57 | COMBINE_EQS: (354), (477) imply: % 71.81/10.57 | (495) all_10_18 = all_4_22 % 71.81/10.57 | % 71.81/10.57 | COMBINE_EQS: (341), (485) imply: % 71.81/10.57 | (496) all_10_15 = e4 % 71.81/10.57 | % 71.81/10.57 | COMBINE_EQS: (364), (456) imply: % 71.81/10.57 | (497) all_10_7 = all_4_7 % 71.81/10.57 | % 71.81/10.57 | COMBINE_EQS: (376), (462) imply: % 71.81/10.57 | (498) all_10_5 = all_4_11 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (116), (489) imply: % 71.81/10.57 | (499) ~ (all_4_1 = e2) % 71.81/10.57 | % 71.81/10.57 | SIMP: (499) implies: % 71.81/10.57 | (500) ~ (all_4_1 = e2) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (115), (489) imply: % 71.81/10.57 | (501) ~ (all_4_2 = e2) % 71.81/10.57 | % 71.81/10.57 | SIMP: (501) implies: % 71.81/10.57 | (502) ~ (all_4_2 = e2) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (114), (489) imply: % 71.81/10.57 | (503) ~ (all_4_3 = e2) % 71.81/10.57 | % 71.81/10.57 | SIMP: (503) implies: % 71.81/10.57 | (504) ~ (all_4_3 = e2) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (113), (489) imply: % 71.81/10.57 | (505) ~ (all_4_4 = e2) % 71.81/10.57 | % 71.81/10.57 | SIMP: (505) implies: % 71.81/10.57 | (506) ~ (all_4_4 = e2) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (112), (489) imply: % 71.81/10.57 | (507) ~ (all_4_5 = e2) % 71.81/10.57 | % 71.81/10.57 | SIMP: (507) implies: % 71.81/10.57 | (508) ~ (all_4_5 = e2) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (111), (489) imply: % 71.81/10.57 | (509) ~ (all_4_10 = e2) % 71.81/10.57 | % 71.81/10.57 | SIMP: (509) implies: % 71.81/10.57 | (510) ~ (all_4_10 = e2) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (110), (489) imply: % 71.81/10.57 | (511) ~ (all_4_15 = e2) % 71.81/10.57 | % 71.81/10.57 | SIMP: (511) implies: % 71.81/10.57 | (512) ~ (all_4_15 = e2) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (109), (489) imply: % 71.81/10.57 | (513) ~ (all_4_20 = e2) % 71.81/10.57 | % 71.81/10.57 | SIMP: (513) implies: % 71.81/10.57 | (514) ~ (all_4_20 = e2) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (98), (491) imply: % 71.81/10.57 | (515) ~ (all_4_2 = e3) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (93), (492) imply: % 71.81/10.57 | (516) ~ (all_4_3 = e0) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (92), (493) imply: % 71.81/10.57 | (517) ~ (all_4_3 = e4) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (71), (491) imply: % 71.81/10.57 | (518) ~ (all_4_7 = e3) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (67), (492) imply: % 71.81/10.57 | (519) ~ (all_4_8 = e0) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (66), (493) imply: % 71.81/10.57 | (520) ~ (all_4_8 = e4) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (60), (491) imply: % 71.81/10.57 | (521) ~ (all_4_10 = e3) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (59), (492) imply: % 71.81/10.57 | (522) ~ (all_4_10 = e0) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (55), (491) imply: % 71.81/10.57 | (523) ~ (all_4_11 = e3) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (54), (492) imply: % 71.81/10.57 | (524) ~ (all_4_11 = e0) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (50), (491), (492) imply: % 71.81/10.57 | (525) ~ (e3 = e0) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (49), (491) imply: % 71.81/10.57 | (526) ~ (all_4_14 = e3) % 71.81/10.57 | % 71.81/10.57 | SIMP: (526) implies: % 71.81/10.57 | (527) ~ (all_4_14 = e3) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (48), (491) imply: % 71.81/10.57 | (528) ~ (all_4_17 = e3) % 71.81/10.57 | % 71.81/10.57 | SIMP: (528) implies: % 71.81/10.57 | (529) ~ (all_4_17 = e3) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (47), (491) imply: % 71.81/10.57 | (530) ~ (all_4_22 = e3) % 71.81/10.57 | % 71.81/10.57 | SIMP: (530) implies: % 71.81/10.57 | (531) ~ (all_4_22 = e3) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (46), (492) imply: % 71.81/10.57 | (532) ~ (all_4_14 = e0) % 71.81/10.57 | % 71.81/10.57 | SIMP: (532) implies: % 71.81/10.57 | (533) ~ (all_4_14 = e0) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (45), (492), (493) imply: % 71.81/10.57 | (534) ~ (e4 = e0) % 71.81/10.57 | % 71.81/10.57 | SIMP: (534) implies: % 71.81/10.57 | (535) ~ (e4 = e0) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (44), (492) imply: % 71.81/10.57 | (536) ~ (all_4_23 = e0) % 71.81/10.57 | % 71.81/10.57 | SIMP: (536) implies: % 71.81/10.57 | (537) ~ (all_4_23 = e0) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (40), (493) imply: % 71.81/10.57 | (538) ~ (all_4_15 = e4) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (36), (493) imply: % 71.81/10.57 | (539) ~ (all_4_16 = e4) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (33), (493) imply: % 71.81/10.57 | (540) ~ (all_4_17 = e4) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (30), (493) imply: % 71.81/10.57 | (541) ~ (all_4_19 = e4) % 71.81/10.57 | % 71.81/10.57 | SIMP: (541) implies: % 71.81/10.57 | (542) ~ (all_4_19 = e4) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (29), (493) imply: % 71.81/10.57 | (543) ~ (all_4_23 = e4) % 71.81/10.57 | % 71.81/10.57 | SIMP: (543) implies: % 71.81/10.57 | (544) ~ (all_4_23 = e4) % 71.81/10.57 | % 71.81/10.57 | REDUCE: (248), (404) imply: % 71.81/10.57 | (545) op(e4, all_4_1) = all_8_1 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (247), (411) imply: % 71.81/10.57 | (546) op(e4, all_4_2) = all_8_4 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (246), (424) imply: % 71.81/10.57 | (547) op(e4, all_4_3) = all_8_7 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (245), (439) imply: % 71.81/10.57 | (548) op(e4, all_4_4) = all_8_10 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (244), (402) imply: % 71.81/10.57 | (549) op(e4, all_4_5) = all_8_14 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (243), (407) imply: % 71.81/10.57 | (550) op(e4, all_4_10) = all_8_27 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (242), (418) imply: % 71.81/10.57 | (551) op(e4, all_4_15) = all_8_40 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (241), (432) imply: % 71.81/10.57 | (552) op(e4, all_4_20) = all_8_53 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (235), (404) imply: % 71.81/10.57 | (553) op(e3, all_4_1) = all_8_2 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (234), (402) imply: % 71.81/10.57 | (554) op(e3, all_4_5) = all_8_13 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (233), (362) imply: % 71.81/10.57 | (555) op(e3, all_4_7) = all_8_17 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (232), (426) imply: % 71.81/10.57 | (556) op(e3, all_4_8) = all_8_20 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (231), (442) imply: % 71.81/10.57 | (557) op(e3, all_4_9) = all_8_23 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (230), (374) imply: % 71.81/10.57 | (558) op(e3, all_4_11) = all_8_30 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (229), (419) imply: % 71.81/10.57 | (559) op(e3, all_4_16) = all_8_43 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (223), (411) imply: % 71.81/10.57 | (560) op(e2, all_4_2) = all_8_5 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (222), (362) imply: % 71.81/10.57 | (561) op(e2, all_4_7) = all_8_18 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (221), (407) imply: % 71.81/10.57 | (562) op(e2, all_4_10) = all_8_26 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (220), (374) imply: % 71.81/10.57 | (563) op(e2, all_4_11) = all_8_29 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (219), (494) imply: % 71.81/10.57 | (564) op(e2, e0) = all_8_33 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (218), (443) imply: % 71.81/10.57 | (565) op(e2, all_4_14) = all_8_36 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (217), (422) imply: % 71.81/10.57 | (566) op(e2, all_4_17) = all_8_46 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (216), (352) imply: % 71.81/10.57 | (567) op(e2, all_4_22) = all_8_59 % 71.81/10.57 | % 71.81/10.57 | REDUCE: (210), (424) imply: % 71.81/10.57 | (568) op(e1, all_4_3) = all_8_8 % 71.81/10.57 | % 71.81/10.58 | REDUCE: (209), (426) imply: % 71.81/10.58 | (569) op(e1, all_4_8) = all_8_21 % 71.81/10.58 | % 71.81/10.58 | REDUCE: (208), (494) imply: % 71.81/10.58 | (570) op(e1, e0) = all_8_34 % 71.81/10.58 | % 71.81/10.58 | REDUCE: (207), (418) imply: % 71.81/10.58 | (571) op(e1, all_4_15) = all_8_39 % 71.81/10.58 | % 71.81/10.58 | REDUCE: (206), (419) imply: % 71.81/10.58 | (572) op(e1, all_4_16) = all_8_42 % 71.81/10.58 | % 71.81/10.58 | REDUCE: (205), (422) imply: % 71.81/10.58 | (573) op(e1, all_4_17) = all_8_45 % 71.81/10.58 | % 71.81/10.58 | REDUCE: (204), (445) imply: % 71.81/10.58 | (574) op(e1, all_4_19) = all_8_49 % 71.81/10.58 | % 71.81/10.58 | REDUCE: (203), (438) imply: % 71.81/10.58 | (575) op(e1, all_4_23) = all_8_62 % 71.81/10.58 | % 71.81/10.58 | REDUCE: (197), (439) imply: % 71.81/10.58 | (576) op(e0, all_4_4) = all_8_11 % 71.81/10.58 | % 71.81/10.58 | REDUCE: (196), (443) imply: % 71.81/10.58 | (577) op(e0, all_4_14) = all_8_37 % 71.81/10.58 | % 71.81/10.58 | REDUCE: (195), (445) imply: % 71.81/10.58 | (578) op(e0, all_4_19) = all_8_50 % 71.81/10.58 | % 71.81/10.58 | REDUCE: (194), (432) imply: % 71.81/10.58 | (579) op(e0, all_4_20) = all_8_52 % 71.81/10.58 | % 71.81/10.58 | REDUCE: (193), (434) imply: % 71.81/10.58 | (580) op(e0, all_4_21) = all_8_55 % 71.81/10.58 | % 71.81/10.58 | REDUCE: (192), (352) imply: % 71.81/10.58 | (581) op(e0, all_4_22) = all_8_58 % 71.81/10.58 | % 71.81/10.58 | REDUCE: (191), (438) imply: % 71.81/10.58 | (582) op(e0, all_4_23) = all_8_61 % 71.81/10.58 | % 71.81/10.58 | GROUND_INST: instantiating (function-axioms) with all_4_23, all_8_34, e0, e1, % 71.81/10.58 | simplifying with (122), (570) gives: % 71.81/10.58 | (583) all_8_34 = all_4_23 % 71.81/10.58 | % 71.81/10.58 | GROUND_INST: instantiating (function-axioms) with all_4_22, all_8_33, e0, e2, % 71.81/10.58 | simplifying with (127), (564) gives: % 71.81/10.58 | (584) all_8_33 = all_4_22 % 71.81/10.58 | % 71.81/10.58 | BETA: splitting (282) gives: % 71.81/10.58 | % 71.81/10.58 | Case 1: % 71.81/10.58 | | % 71.81/10.58 | | (585) all_10_24 = e0 % 71.81/10.58 | | % 71.81/10.58 | | COMBINE_EQS: (322), (585) imply: % 71.81/10.58 | | (586) all_4_24 = e0 % 71.81/10.58 | | % 71.81/10.58 | | COMBINE_EQS: (448), (586) imply: % 71.81/10.58 | | (587) all_8_69 = e0 % 71.81/10.58 | | % 71.81/10.58 | | REDUCE: (87), (586) imply: % 71.81/10.58 | | (588) ~ (all_4_4 = e0) % 71.81/10.58 | | % 71.81/10.58 | | REDUCE: (62), (586) imply: % 71.81/10.58 | | (589) ~ (all_4_9 = e0) % 71.81/10.58 | | % 71.81/10.58 | | REDUCE: (28), (586) imply: % 71.81/10.58 | | (590) ~ (all_4_19 = e0) % 71.81/10.58 | | % 71.81/10.58 | | REDUCE: (24), (586) imply: % 71.81/10.58 | | (591) ~ (all_4_20 = e0) % 71.81/10.58 | | % 71.81/10.58 | | REDUCE: (21), (586) imply: % 71.81/10.58 | | (592) ~ (all_4_21 = e0) % 71.81/10.58 | | % 71.81/10.58 | | REDUCE: (19), (586) imply: % 71.81/10.58 | | (593) ~ (all_4_22 = e0) % 71.81/10.58 | | % 71.81/10.58 | | BETA: splitting (255) gives: % 71.81/10.58 | | % 71.81/10.58 | | Case 1: % 71.81/10.58 | | | % 71.81/10.58 | | | (594) all_8_65 = e1 % 71.81/10.58 | | | % 71.81/10.58 | | | REF_CLOSE: (6), (400), (594) are inconsistent by sub-proof #170. % 71.81/10.58 | | | % 71.81/10.58 | | Case 2: % 71.81/10.58 | | | % 71.81/10.58 | | | (595) ~ (all_8_65 = e1) % 71.81/10.58 | | | (596) all_8_66 = e1 | all_8_67 = e1 | all_8_68 = e1 | all_8_69 = e1 % 71.81/10.58 | | | % 71.81/10.58 | | | BETA: splitting (596) gives: % 71.81/10.58 | | | % 71.81/10.58 | | | Case 1: % 71.81/10.58 | | | | % 71.81/10.58 | | | | (597) all_8_66 = e1 % 71.81/10.58 | | | | % 71.81/10.58 | | | | COMBINE_EQS: (406), (597) imply: % 71.81/10.58 | | | | (598) all_4_6 = e1 % 71.81/10.58 | | | | % 71.81/10.58 | | | | SIMP: (598) implies: % 71.81/10.58 | | | | (599) all_4_6 = e1 % 71.81/10.58 | | | | % 71.81/10.58 | | | | COMBINE_EQS: (379), (599) imply: % 71.81/10.58 | | | | (600) all_10_3 = e1 % 71.81/10.58 | | | | % 71.81/10.58 | | | | REDUCE: (86), (599) imply: % 71.81/10.58 | | | | (601) ~ (all_4_5 = e1) % 71.81/10.58 | | | | % 71.81/10.58 | | | | REDUCE: (79), (599) imply: % 71.81/10.58 | | | | (602) ~ (all_4_7 = e1) % 71.81/10.58 | | | | % 71.81/10.58 | | | | SIMP: (602) implies: % 71.81/10.58 | | | | (603) ~ (all_4_7 = e1) % 71.81/10.58 | | | | % 71.81/10.58 | | | | REDUCE: (78), (599) imply: % 71.81/10.58 | | | | (604) ~ (all_4_8 = e1) % 71.81/10.58 | | | | % 71.81/10.58 | | | | SIMP: (604) implies: % 71.81/10.58 | | | | (605) ~ (all_4_8 = e1) % 71.81/10.58 | | | | % 71.81/10.58 | | | | REDUCE: (77), (599) imply: % 71.81/10.58 | | | | (606) ~ (all_4_9 = e1) % 71.81/10.58 | | | | % 71.81/10.58 | | | | SIMP: (606) implies: % 71.81/10.58 | | | | (607) ~ (all_4_9 = e1) % 71.81/10.58 | | | | % 71.81/10.58 | | | | REDUCE: (76), (599) imply: % 71.81/10.58 | | | | (608) ~ (all_4_11 = e1) % 71.81/10.58 | | | | % 71.81/10.58 | | | | SIMP: (608) implies: % 71.81/10.58 | | | | (609) ~ (all_4_11 = e1) % 71.81/10.58 | | | | % 71.81/10.58 | | | | REDUCE: (75), (599) imply: % 71.81/10.58 | | | | (610) ~ (all_4_16 = e1) % 71.81/10.58 | | | | % 71.81/10.58 | | | | SIMP: (610) implies: % 71.81/10.58 | | | | (611) ~ (all_4_16 = e1) % 71.81/10.58 | | | | % 71.81/10.58 | | | | REDUCE: (74), (599) imply: % 71.81/10.58 | | | | (612) ~ (all_4_21 = e1) % 71.81/10.58 | | | | % 71.81/10.58 | | | | SIMP: (612) implies: % 71.81/10.58 | | | | (613) ~ (all_4_21 = e1) % 71.81/10.58 | | | | % 71.81/10.58 | | | | BETA: splitting (173) gives: % 71.81/10.58 | | | | % 71.81/10.58 | | | | Case 1: % 71.81/10.58 | | | | | % 71.81/10.58 | | | | | (614) all_6_15 = e2 % 71.81/10.58 | | | | | % 71.81/10.58 | | | | | REF_CLOSE: (452), (504), (614) are inconsistent by sub-proof #169. % 71.81/10.58 | | | | | % 71.81/10.58 | | | | Case 2: % 71.81/10.58 | | | | | % 71.81/10.58 | | | | | (615) ~ (all_6_15 = e2) % 71.81/10.58 | | | | | (616) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e1 | all_6_15 = e0 % 71.81/10.58 | | | | | % 71.81/10.58 | | | | | BETA: splitting (172) gives: % 71.81/10.58 | | | | | % 71.81/10.58 | | | | | Case 1: % 71.81/10.58 | | | | | | % 71.81/10.58 | | | | | | (617) all_6_16 = e2 % 71.81/10.58 | | | | | | % 71.81/10.58 | | | | | | COMBINE_EQS: (458), (617) imply: % 71.81/10.58 | | | | | | (618) all_4_8 = e2 % 71.81/10.58 | | | | | | % 71.81/10.58 | | | | | | SIMP: (618) implies: % 71.81/10.58 | | | | | | (619) all_4_8 = e2 % 71.81/10.58 | | | | | | % 71.81/10.58 | | | | | | REDUCE: (73), (619) imply: % 71.81/10.58 | | | | | | (620) ~ (all_4_7 = e2) % 71.81/10.58 | | | | | | % 71.81/10.58 | | | | | | REDUCE: (68), (619) imply: % 71.81/10.58 | | | | | | (621) ~ (all_4_9 = e2) % 71.81/10.58 | | | | | | % 71.81/10.58 | | | | | | SIMP: (621) implies: % 71.81/10.58 | | | | | | (622) ~ (all_4_9 = e2) % 71.81/10.58 | | | | | | % 71.81/10.58 | | | | | | REDUCE: (65), (619) imply: % 71.81/10.58 | | | | | | (623) ~ (all_4_23 = e2) % 71.81/10.58 | | | | | | % 71.81/10.58 | | | | | | SIMP: (623) implies: % 71.81/10.58 | | | | | | (624) ~ (all_4_23 = e2) % 71.81/10.58 | | | | | | % 71.81/10.58 | | | | | | REDUCE: (556), (619) imply: % 71.81/10.58 | | | | | | (625) op(e3, e2) = all_8_20 % 71.81/10.58 | | | | | | % 71.81/10.58 | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_11, % 71.81/10.58 | | | | | | all_8_20, e2, e3, simplifying with (134), (625) gives: % 71.81/10.58 | | | | | | (626) all_8_20 = all_4_11 % 71.81/10.58 | | | | | | % 71.81/10.58 | | | | | | BETA: splitting (179) gives: % 71.81/10.58 | | | | | | % 71.81/10.58 | | | | | | Case 1: % 71.81/10.58 | | | | | | | % 71.81/10.58 | | | | | | | (627) all_6_7 = e2 % 71.81/10.58 | | | | | | | % 71.81/10.58 | | | | | | | COMBINE_EQS: (462), (627) imply: % 71.81/10.58 | | | | | | | (628) all_4_11 = e2 % 71.81/10.58 | | | | | | | % 71.81/10.58 | | | | | | | SIMP: (628) implies: % 71.81/10.58 | | | | | | | (629) all_4_11 = e2 % 71.81/10.58 | | | | | | | % 71.81/10.58 | | | | | | | COMBINE_EQS: (498), (629) imply: % 71.81/10.58 | | | | | | | (630) all_10_5 = e2 % 71.81/10.58 | | | | | | | % 71.81/10.58 | | | | | | | REDUCE: (53), (629) imply: % 71.81/10.58 | | | | | | | (631) ~ (all_4_14 = e2) % 71.81/10.58 | | | | | | | % 71.81/10.58 | | | | | | | SIMP: (631) implies: % 71.81/10.58 | | | | | | | (632) ~ (all_4_14 = e2) % 71.81/10.58 | | | | | | | % 71.81/10.58 | | | | | | | REDUCE: (51), (629) imply: % 71.81/10.58 | | | | | | | (633) ~ (all_4_21 = e2) % 71.81/10.58 | | | | | | | % 71.81/10.58 | | | | | | | SIMP: (633) implies: % 71.81/10.58 | | | | | | | (634) ~ (all_4_21 = e2) % 71.81/10.58 | | | | | | | % 71.81/10.58 | | | | | | | REDUCE: (558), (629) imply: % 71.81/10.58 | | | | | | | (635) op(e3, e2) = all_8_30 % 71.81/10.58 | | | | | | | % 71.81/10.58 | | | | | | | REDUCE: (134), (629) imply: % 71.81/10.58 | | | | | | | (636) op(e3, e2) = e2 % 71.81/10.58 | | | | | | | % 71.81/10.58 | | | | | | | BETA: splitting (284) gives: % 71.81/10.58 | | | | | | | % 71.81/10.58 | | | | | | | Case 1: % 71.81/10.58 | | | | | | | | % 71.81/10.58 | | | | | | | | (637) all_10_20 = e2 % 71.81/10.58 | | | | | | | | % 71.81/10.58 | | | | | | | | COMBINE_EQS: (334), (637) imply: % 71.81/10.58 | | | | | | | | (638) all_4_4 = e2 % 71.81/10.58 | | | | | | | | % 71.81/10.58 | | | | | | | | REDUCE: (506), (638) imply: % 71.81/10.59 | | | | | | | | (639) $false % 71.81/10.59 | | | | | | | | % 71.81/10.59 | | | | | | | | CLOSE: (639) is inconsistent. % 71.81/10.59 | | | | | | | | % 71.81/10.59 | | | | | | | Case 2: % 71.81/10.59 | | | | | | | | % 71.81/10.59 | | | | | | | | (640) all_10_21 = e2 | all_10_22 = e2 | all_10_23 = e2 | % 71.81/10.59 | | | | | | | | all_10_24 = e2 % 71.81/10.59 | | | | | | | | % 71.81/10.59 | | | | | | | | BETA: splitting (640) gives: % 71.81/10.59 | | | | | | | | % 71.81/10.59 | | | | | | | | Case 1: % 71.81/10.59 | | | | | | | | | % 71.81/10.59 | | | | | | | | | (641) all_10_21 = e2 % 71.81/10.59 | | | | | | | | | % 71.81/10.59 | | | | | | | | | COMBINE_EQS: (331), (641) imply: % 71.81/10.59 | | | | | | | | | (642) all_4_9 = e2 % 71.81/10.59 | | | | | | | | | % 71.81/10.59 | | | | | | | | | REDUCE: (622), (642) imply: % 71.81/10.59 | | | | | | | | | (643) $false % 71.81/10.59 | | | | | | | | | % 71.81/10.59 | | | | | | | | | CLOSE: (643) is inconsistent. % 71.81/10.59 | | | | | | | | | % 71.81/10.59 | | | | | | | | Case 2: % 71.81/10.59 | | | | | | | | | % 71.81/10.59 | | | | | | | | | (644) all_10_22 = e2 | all_10_23 = e2 | all_10_24 = e2 % 71.81/10.59 | | | | | | | | | % 71.81/10.59 | | | | | | | | | BETA: splitting (287) gives: % 71.81/10.59 | | | | | | | | | % 71.81/10.59 | | | | | | | | | Case 1: % 71.81/10.59 | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | (645) all_10_16 = e2 % 71.81/10.59 | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | COMBINE_EQS: (385), (645) imply: % 71.81/10.59 | | | | | | | | | | (646) all_4_20 = e2 % 71.81/10.59 | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | REDUCE: (514), (646) imply: % 71.81/10.59 | | | | | | | | | | (647) $false % 71.81/10.59 | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | CLOSE: (647) is inconsistent. % 71.81/10.59 | | | | | | | | | | % 71.81/10.59 | | | | | | | | | Case 2: % 71.81/10.59 | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | (648) all_10_17 = e2 | all_10_18 = e2 | all_10_19 = e2 | % 71.81/10.59 | | | | | | | | | | all_10_24 = e2 % 71.81/10.59 | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | BETA: splitting (648) gives: % 71.81/10.59 | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | Case 1: % 71.81/10.59 | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | (649) all_10_17 = e2 % 71.81/10.59 | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | COMBINE_EQS: (370), (649) imply: % 71.81/10.59 | | | | | | | | | | | (650) all_4_21 = e2 % 71.81/10.59 | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | REDUCE: (634), (650) imply: % 71.81/10.59 | | | | | | | | | | | (651) $false % 71.81/10.59 | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | CLOSE: (651) is inconsistent. % 71.81/10.59 | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | Case 2: % 71.81/10.59 | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | (652) all_10_18 = e2 | all_10_19 = e2 | all_10_24 = e2 % 71.81/10.59 | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | BETA: splitting (644) gives: % 71.81/10.59 | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | Case 1: % 71.81/10.59 | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | (653) all_10_22 = e2 % 71.81/10.59 | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | COMBINE_EQS: (328), (653) imply: % 71.81/10.59 | | | | | | | | | | | | (654) all_4_14 = e2 % 71.81/10.59 | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | REDUCE: (632), (654) imply: % 71.81/10.59 | | | | | | | | | | | | (655) $false % 71.81/10.59 | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | CLOSE: (655) is inconsistent. % 71.81/10.59 | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | Case 2: % 71.81/10.59 | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | (656) all_10_23 = e2 | all_10_24 = e2 % 71.81/10.59 | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | BETA: splitting (652) gives: % 71.81/10.59 | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | Case 1: % 71.81/10.59 | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | (657) all_10_18 = e2 % 71.81/10.59 | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | COMBINE_EQS: (495), (657) imply: % 71.81/10.59 | | | | | | | | | | | | | (658) all_4_22 = e2 % 71.81/10.59 | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | COMBINE_EQS: (584), (658) imply: % 71.81/10.59 | | | | | | | | | | | | | (659) all_8_33 = e2 % 71.81/10.59 | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | BETA: splitting (295) gives: % 71.81/10.59 | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | Case 1: % 71.81/10.59 | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | (660) all_10_9 = e2 % 71.81/10.59 | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | COMBINE_EQS: (388), (660) imply: % 71.81/10.59 | | | | | | | | | | | | | | (661) all_4_15 = e2 % 71.81/10.59 | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | REDUCE: (512), (661) imply: % 71.81/10.59 | | | | | | | | | | | | | | (662) $false % 71.81/10.59 | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | CLOSE: (662) is inconsistent. % 71.81/10.59 | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | Case 2: % 71.81/10.59 | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | (663) all_10_10 = e2 | all_10_11 = e2 | all_10_15 = e2 | % 71.81/10.59 | | | | | | | | | | | | | | all_10_23 = e2 % 71.81/10.59 | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | BETA: splitting (656) gives: % 71.81/10.59 | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | Case 1: % 71.81/10.59 | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | (664) all_10_23 = e2 % 71.81/10.59 | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | COMBINE_EQS: (325), (664) imply: % 71.81/10.59 | | | | | | | | | | | | | | | (665) all_4_19 = e2 % 71.81/10.59 | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | REDUCE: (35), (665) imply: % 71.81/10.59 | | | | | | | | | | | | | | | (666) ~ (all_4_16 = e2) % 71.81/10.59 | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | REDUCE: (32), (665) imply: % 71.81/10.59 | | | | | | | | | | | | | | | (667) ~ (all_4_17 = e2) % 71.81/10.59 | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | REDUCE: (542), (665) imply: % 71.81/10.59 | | | | | | | | | | | | | | | (668) ~ (e4 = e2) % 71.81/10.59 | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_30, % 71.81/10.59 | | | | | | | | | | | | | | | e2, e3, simplifying with (635), (636) gives: % 71.81/10.59 | | | | | | | | | | | | | | | (669) all_8_30 = e2 % 71.81/10.59 | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 71.81/10.59 | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | Case 1: % 71.81/10.59 | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | (670) (all_8_26 = e4 & ~ (all_8_27 = e2)) | (all_8_29 = % 71.81/10.59 | | | | | | | | | | | | | | | | e3 & ~ (all_8_30 = e2)) % 71.81/10.59 | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | BETA: splitting (670) gives: % 71.81/10.59 | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | Case 1: % 71.81/10.59 | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | (671) all_8_26 = e4 & ~ (all_8_27 = e2) % 71.81/10.59 | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | ALPHA: (671) implies: % 71.81/10.59 | | | | | | | | | | | | | | | | | (672) all_8_26 = e4 % 71.81/10.59 | | | | | | | | | | | | | | | | | (673) ~ (all_8_27 = e2) % 71.81/10.59 | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | REDUCE: (562), (672) imply: % 71.81/10.59 | | | | | | | | | | | | | | | | | (674) op(e2, all_4_10) = e4 % 71.81/10.59 | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 71.81/10.59 | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.59 | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | (675) all_6_2 = e2 % 71.81/10.59 | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (510), (675) are inconsistent by sub-proof % 71.81/10.59 | | | | | | | | | | | | | | | | | | #168. % 71.81/10.59 | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.59 | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | (676) ~ (all_6_2 = e2) % 71.81/10.59 | | | | | | | | | | | | | | | | | | (677) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | % 71.81/10.59 | | | | | | | | | | | | | | | | | | all_6_2 = e0 % 71.81/10.59 | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 71.81/10.59 | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | (678) all_10_4 = e1 % 71.81/10.59 | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (678) imply: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | (679) all_4_10 = e1 % 71.81/10.59 | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | REDUCE: (57), (679) imply: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | (680) ~ (all_4_15 = e1) % 71.81/10.59 | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | SIMP: (680) implies: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | (681) ~ (all_4_15 = e1) % 71.81/10.59 | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | REDUCE: (510), (679) imply: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | (682) ~ (e2 = e1) % 71.81/10.59 | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | REDUCE: (674), (679) imply: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | (683) op(e2, e1) = e4 % 71.81/10.59 | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | (684) all_10_9 = e1 % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (388), (684) imply: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | (685) all_4_15 = e1 % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (681), (685) imply: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | (686) $false % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | CLOSE: (686) is inconsistent. % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | (687) all_10_10 = e1 | all_10_11 = e1 | all_10_15 = e1 | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | all_10_23 = e1 % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | BETA: splitting (687) gives: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | (688) all_10_10 = e1 % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (688) imply: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | (689) all_4_16 = e1 % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | REDUCE: (611), (689) imply: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | (690) $false % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | CLOSE: (690) is inconsistent. % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | (691) all_10_11 = e1 | all_10_15 = e1 | all_10_23 = e1 % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (691) gives: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | | (692) all_10_11 = e1 % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (692) imply: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | | (693) all_4_17 = e1 % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (128), (540), (566), (683), (693), % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | | #167. % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | | (694) all_10_15 = e1 | all_10_23 = e1 % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (496), (664), (694) are inconsistent by % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | | sub-proof #166. % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.59 | | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.59 | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | (695) ~ (all_10_4 = e1) % 71.81/10.59 | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | REDUCE: (391), (695) imply: % 71.81/10.59 | | | | | | | | | | | | | | | | | | | (696) ~ (all_4_10 = e1) % 71.81/10.59 | | | | | | | | | | | | | | | | | | | % 71.81/10.59 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (303), (391), (461), (521), (522), (550), % 71.81/10.59 | | | | | | | | | | | | | | | | | | | (673), (677), (696), (function-axioms) are % 71.81/10.59 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #160. % 71.81/10.59 | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | End of split % 71.81/10.60 | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | End of split % 71.81/10.60 | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | Case 2: % 71.81/10.60 | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | (697) all_8_29 = e3 & ~ (all_8_30 = e2) % 71.81/10.60 | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | ALPHA: (697) implies: % 71.81/10.60 | | | | | | | | | | | | | | | | | (698) ~ (all_8_30 = e2) % 71.81/10.60 | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | REDUCE: (669), (698) imply: % 71.81/10.60 | | | | | | | | | | | | | | | | | (699) $false % 71.81/10.60 | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | CLOSE: (699) is inconsistent. % 71.81/10.60 | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | End of split % 71.81/10.60 | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | Case 2: % 71.81/10.60 | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | (700) (all_8_33 = e1 & ~ (all_8_34 = e2)) | (all_8_36 = % 71.81/10.60 | | | | | | | | | | | | | | | | e0 & ~ (all_8_37 = e2)) % 71.81/10.60 | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | BETA: splitting (700) gives: % 71.81/10.60 | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | Case 1: % 71.81/10.60 | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | (701) all_8_33 = e1 & ~ (all_8_34 = e2) % 71.81/10.60 | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | ALPHA: (701) implies: % 71.81/10.60 | | | | | | | | | | | | | | | | | (702) all_8_33 = e1 % 71.81/10.60 | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | COMBINE_EQS: (659), (702) imply: % 71.81/10.60 | | | | | | | | | | | | | | | | | (703) e2 = e1 % 71.81/10.60 | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | SIMP: (703) implies: % 71.81/10.60 | | | | | | | | | | | | | | | | | (704) e2 = e1 % 71.81/10.60 | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | REDUCE: (6), (704) imply: % 71.81/10.60 | | | | | | | | | | | | | | | | | (705) $false % 71.81/10.60 | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | CLOSE: (705) is inconsistent. % 71.81/10.60 | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | Case 2: % 71.81/10.60 | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | (706) all_8_36 = e0 & ~ (all_8_37 = e2) % 71.81/10.60 | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | ALPHA: (706) implies: % 71.81/10.60 | | | | | | | | | | | | | | | | | (707) all_8_36 = e0 % 71.81/10.60 | | | | | | | | | | | | | | | | | (708) ~ (all_8_37 = e2) % 71.81/10.60 | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | REDUCE: (565), (707) imply: % 71.81/10.60 | | | | | | | | | | | | | | | | | (709) op(e2, all_4_14) = e0 % 71.81/10.60 | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 71.81/10.60 | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.60 | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | (710) all_6_2 = e2 % 71.81/10.60 | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (510), (710) are inconsistent by sub-proof % 71.81/10.60 | | | | | | | | | | | | | | | | | | #168. % 71.81/10.60 | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.60 | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | (711) ~ (all_6_2 = e2) % 71.81/10.60 | | | | | | | | | | | | | | | | | | (712) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | % 71.81/10.60 | | | | | | | | | | | | | | | | | | all_6_2 = e0 % 71.81/10.60 | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives: % 71.81/10.60 | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | (713) all_6_11 = e2 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (456), (620), (713) are inconsistent by sub-proof % 71.81/10.60 | | | | | | | | | | | | | | | | | | | #159. % 71.81/10.60 | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | (714) all_6_11 = e4 | all_6_11 = e3 | all_6_11 = e1 | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | all_6_11 = e0 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | (715) all_6_9 = e2 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (475), (634), (715) are inconsistent by sub-proof % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | #158. % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | (716) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e1 | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | all_6_9 = e0 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | (717) all_6_21 = e2 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (460), (622), (717) are inconsistent by sub-proof % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | #157. % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | (718) ~ (all_6_21 = e2) % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | (719) all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e1 | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | all_6_21 = e0 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | (720) all_6_22 = e2 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (466), (632), (720) are inconsistent by sub-proof % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | #156. % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | (721) all_6_22 = e4 | all_6_22 = e3 | all_6_22 = e1 | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | all_6_22 = e0 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | (722) all_6_1 = e2 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (454), (508), (722) are inconsistent by sub-proof % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | #155. % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | (723) ~ (all_6_1 = e2) % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | (724) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | all_6_1 = e0 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (170) gives: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | (725) all_6_20 = e2 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (725) imply: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | (726) all_4_4 = e2 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (506), (726) imply: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | (727) $false % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (727) is inconsistent. % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | (728) ~ (all_6_20 = e2) % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | (729) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e1 | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | all_6_20 = e0 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | (730) all_6_4 = e2 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (474), (514), (730) are inconsistent by sub-proof % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | #154. % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | (731) ~ (all_6_4 = e2) % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | (732) all_6_4 = e4 | all_6_4 = e3 | all_6_4 = e1 | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | all_6_4 = e0 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (733) all_6_5 = e2 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (450), (500), (733) are inconsistent by sub-proof % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | #153. % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (734) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_5 = e0 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (735) all_6_3 = e2 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (468), (512), (735) are inconsistent by sub-proof % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | #152. % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (736) ~ (all_6_3 = e2) % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (737) all_6_3 = e4 | all_6_3 = e3 | all_6_3 = e1 | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_3 = e0 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (738) (all_8_1 = e3 & ~ (all_8_2 = e4)) | (all_8_4 = e2 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_5 = e4)) % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (738) gives: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (739) all_8_1 = e3 & ~ (all_8_2 = e4) % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (739) implies: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (740) all_8_1 = e3 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (740) imply: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (741) op(e4, all_4_1) = e3 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (742) all_10_4 = e1 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (742) imply: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (743) all_4_10 = e1 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (743) imply: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (744) ~ (all_4_14 = e1) % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (744) implies: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (745) ~ (all_4_14 = e1) % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (57), (743) imply: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (746) ~ (all_4_15 = e1) % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (746) implies: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (747) ~ (all_4_15 = e1) % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (743) imply: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (748) ~ (all_4_20 = e1) % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (748) implies: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (749) ~ (all_4_20 = e1) % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (750) all_10_20 = e1 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (750) imply: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (751) all_4_4 = e1 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (751) implies: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (752) all_4_4 = e1 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (106), (752) imply: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (753) ~ (all_4_1 = e1) % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (95), (752) imply: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (754) ~ (all_4_3 = e1) % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (506), (752) imply: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (755) ~ (e2 = e1) % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (756) all_10_12 = e3 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (756) imply: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (757) all_4_3 = e3 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (757) implies: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (758) all_4_3 = e3 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (758) imply: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (759) ~ (all_4_1 = e3) % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (760) all_10_20 = e3 % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (750), (760) are inconsistent by sub-proof % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #151. % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (761) ~ (all_10_20 = e3) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (762) all_10_21 = e3 | all_10_22 = e3 | all_10_23 = e3 | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_24 = e3 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (750), (761) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (763) ~ (e3 = e1) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (762) gives: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (764) all_10_21 = e3 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (331), (764) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (765) all_4_9 = e3 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (765) implies: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766) all_4_9 = e3 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (83), (766) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (767) ~ (all_4_5 = e3) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (721) gives: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (768) all_6_22 = e4 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (466), (768) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (769) all_4_14 = e4 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (709), (769) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (770) op(e2, e4) = e0 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e0, % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e2, simplifying with (131), (770) gives: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (771) all_4_2 = e0 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (367), (771) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (772) all_10_6 = e0 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (771) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (773) ~ (all_4_1 = e0) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (99), (771) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774) ~ (all_4_7 = e0) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (774) implies: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (775) ~ (all_4_7 = e0) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (300) gives: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (776) all_10_6 = e4 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (535), (772), (776) are inconsistent by sub-proof % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #150. % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (777) all_10_7 = e4 | all_10_8 = e4 | all_10_11 = e4 | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_18 = e4 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (777) gives: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (778) all_10_7 = e4 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (497), (778) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (779) all_4_7 = e4 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (779) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (780) ~ (all_4_5 = e4) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781) all_10_1 = e0 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15), (38), (80), (81), (289), (296), (385), % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388), (394), (450), (468), (474), (538), (552), % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (732), (734), (737), (741), (747), (749), (753), % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (759), (773), (781), (function-axioms) are % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #139. % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (782) ~ (all_10_1 = e0) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (782) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (783) ~ (all_4_5 = e0) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (454), (601), (724), (767), (780), (783) are % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #134. % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (784) ~ (all_10_7 = e4) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (497), (784) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (785) ~ (all_4_7 = e4) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (456), (518), (603), (714), (775), (785) are % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #132. % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (786) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (466), (527), (533), (745), (786) are inconsistent % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #130. % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (787) ~ (all_10_21 = e3) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (331), (787) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788) ~ (all_4_9 = e3) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (58), (64), (118), (183), (295), % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301), (303), (325), (328), (345), (357), (361), % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373), (388), (391), (460), (461), (466), (496), % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510), (512), (521), (522), (527), (533), (577), % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589), (607), (630), (666), (667), (708), (719), % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (721), (788), (function-axioms) are inconsistent % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #125. % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (789) ~ (all_10_12 = e3) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (351), (452), (516), (517), (616), (754), (789) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #123. % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (790) ~ (all_10_20 = e1) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (89), (90), (334), (453), (460), (466), % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527), (533), (588), (589), (607), (719), (721), % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (729), (745), (790) are inconsistent by sub-proof % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #121. % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (791) ~ (all_10_4 = e1) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (58), (118), (183), (301), (303), % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (328), (345), (357), (361), (373), (391), % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (466), (496), (510), (521), (522), (527), % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533), (577), (630), (663), (666), (667), (708), % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (712), (721), (791), (function-axioms) are % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #120. % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (792) all_8_4 = e2 & ~ (all_8_5 = e4) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (792) implies: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (793) all_8_4 = e2 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (793) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (794) op(e4, all_4_2) = e2 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (795) all_10_4 = e1 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (795) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (796) all_4_10 = e1 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (796) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797) ~ (all_4_14 = e1) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (797) implies: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (798) ~ (all_4_14 = e1) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (57), (796) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (799) ~ (all_4_15 = e1) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (799) implies: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (800) ~ (all_4_15 = e1) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (796) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (801) ~ (all_4_20 = e1) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (801) implies: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (802) ~ (all_4_20 = e1) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (521), (796) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (803) ~ (e3 = e1) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (804) all_10_4 = e4 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (795), (804) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (805) e4 = e1 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (805) implies: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (806) e4 = e1 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (806) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (807) $false % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (807) is inconsistent. % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (808) all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_22 = e4 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (808) gives: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (809) all_10_5 = e4 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (630), (809) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (810) e4 = e2 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (810) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (811) $false % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (811) is inconsistent. % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (812) all_10_8 = e4 | all_10_14 = e4 | all_10_22 = e4 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (813) all_10_20 = e1 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (813) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (814) all_4_4 = e1 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (814) implies: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (815) all_4_4 = e1 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (506), (815) imply: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (816) ~ (e2 = e1) % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (817) all_10_20 = e3 % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (813), (817) are inconsistent by sub-proof % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #151. % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (818) ~ (all_10_20 = e3) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (819) all_10_21 = e3 | all_10_22 = e3 | all_10_23 = e3 | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_24 = e3 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (819) gives: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (820) all_10_21 = e3 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (331), (820) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (821) all_4_9 = e3 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (821) implies: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (822) all_4_9 = e3 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (83), (822) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (823) ~ (all_4_5 = e3) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (721) gives: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (824) all_6_22 = e4 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (466), (824) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (825) all_4_14 = e4 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (825) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (826) all_10_22 = e4 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (709), (825) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (827) op(e2, e4) = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e0, % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e2, simplifying with (131), (827) gives: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (828) all_4_2 = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (367), (828) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (829) all_10_6 = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (828) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (830) ~ (all_4_1 = e0) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (99), (828) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (831) ~ (all_4_7 = e0) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (831) implies: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (832) ~ (all_4_7 = e0) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (794), (828) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (833) op(e4, e0) = e2 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (300) gives: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (834) all_10_6 = e4 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (535), (829), (834) are inconsistent by sub-proof % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #150. % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (835) all_10_7 = e4 | all_10_8 = e4 | all_10_11 = e4 | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_18 = e4 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (835) gives: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (836) all_10_7 = e4 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (497), (836) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (837) all_4_7 = e4 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (837) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (838) ~ (all_4_5 = e4) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (839) all_10_1 = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (394), (839) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (840) all_4_5 = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (840) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (841) ~ (all_4_15 = e0) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (841) implies: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (842) ~ (all_4_15 = e0) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (80), (840) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (843) ~ (all_4_20 = e0) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (508), (840) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (844) ~ (e2 = e0) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (601), (840) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (845) ~ (e1 = e0) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (549), (840) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (846) op(e4, e0) = all_8_14 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (847) all_10_2 = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (382), (830), (847) are inconsistent by sub-proof % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #119. % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (848) all_10_3 = e0 | all_10_5 = e0 | all_10_10 = e0 | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_17 = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (848) gives: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (849) all_10_3 = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (600), (849) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (850) e1 = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (850) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (851) $false % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (851) is inconsistent. % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (852) all_10_5 = e0 | all_10_10 = e0 | all_10_17 = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (853) all_10_16 = e4 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (853) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (854) all_4_20 = e4 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (854) implies: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (855) all_4_20 = e4 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (27), (855) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (856) ~ (all_4_21 = e4) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (856) implies: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (857) ~ (all_4_21 = e4) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (855) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (858) op(e4, e0) = e4 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (859) all_10_16 = e3 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (853), (859) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (860) e4 = e3 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (860) implies: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (861) e4 = e3 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (861) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (862) $false % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (862) is inconsistent. % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (863) all_10_17 = e3 | all_10_18 = e3 | all_10_19 = e3 | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_24 = e3 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (863) gives: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (864) all_10_17 = e3 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (864) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (865) all_4_21 = e3 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (865) implies: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (866) all_4_21 = e3 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (857), (866) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (867) ~ (e4 = e3) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (852) gives: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (868) all_10_5 = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (630), (868) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (869) e2 = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (869) implies: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (870) e2 = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (664), (870) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (871) all_10_23 = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (357), (373), (496), (663), (666), % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (667), (871) are inconsistent by sub-proof #116. % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (872) all_10_10 = e0 | all_10_17 = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (872) gives: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (873) all_10_10 = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (873) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (874) all_4_16 = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (874) implies: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (875) all_4_16 = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, all_8_14, % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e4, simplifying with (846), (858) gives: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (876) all_8_14 = e4 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_14, % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e4, simplifying with (833), (846) gives: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (877) all_8_14 = e2 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (876), (877) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (878) e4 = e2 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (878) implies: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (879) e4 = e2 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (826), (879) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (880) all_10_22 = e2 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (11), (345), (361), (535), (812), (880) are % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #115. % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (881) all_10_17 = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (864), (881) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (882) e3 = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (882) implies: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (883) e3 = e0 % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (525), (883) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (884) $false % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (884) is inconsistent. % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (885) ~ (all_10_17 = e3) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (885) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (886) ~ (all_4_21 = e3) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (475), (592), (613), (716), (857), (886) are % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #110. % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (887) ~ (all_10_16 = e4) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (887) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (888) ~ (all_4_20 = e4) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (296), (388), (468), (474), (538), (591), % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (732), (737), (800), (802), (842), (888) are % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #143. % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (889) ~ (all_10_1 = e0) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (889) imply: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (890) ~ (all_4_5 = e0) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (454), (601), (724), (823), (838), (890) are % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #134. % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (891) ~ (all_10_7 = e4) % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (497), (891) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (892) ~ (all_4_7 = e4) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (456), (518), (603), (714), (832), (892) are % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #132. % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (893) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (466), (527), (533), (798), (893) are inconsistent % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #130. % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (894) ~ (all_10_21 = e3) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (331), (894) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (895) ~ (all_4_9 = e3) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (58), (64), (118), (183), (295), % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301), (303), (325), (328), (345), (357), (361), % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373), (388), (391), (460), (461), (466), (496), % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510), (512), (521), (522), (527), (533), (577), % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589), (607), (630), (666), (667), (708), (719), % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (721), (895), (function-axioms) are inconsistent % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #125. % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (896) ~ (all_10_20 = e1) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (89), (90), (334), (453), (460), (466), % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527), (533), (588), (589), (607), (719), (721), % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (729), (798), (896) are inconsistent by sub-proof % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #121. % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (897) ~ (all_10_4 = e1) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (58), (118), (183), (301), (303), % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (328), (345), (357), (361), (373), (391), % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (466), (496), (510), (521), (522), (527), % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533), (577), (630), (663), (666), (667), (708), % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (712), (721), (897), (function-axioms) are % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #120. % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (898) (all_8_7 = e1 & ~ (all_8_8 = e4)) | (all_8_10 = % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_11 = e4)) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (898) gives: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (899) all_8_7 = e1 & ~ (all_8_8 = e4) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (899) implies: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (900) all_8_7 = e1 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (547), (900) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (901) op(e4, all_4_3) = e1 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (902) all_10_4 = e1 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (902) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (903) all_4_10 = e1 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (903) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (904) ~ (all_4_14 = e1) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (904) implies: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (905) ~ (all_4_14 = e1) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (906) all_10_20 = e1 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (906) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (907) all_4_4 = e1 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (907) implies: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (908) all_4_4 = e1 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (95), (908) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (909) ~ (all_4_3 = e1) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (910) all_10_12 = e3 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (910) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (911) all_4_3 = e3 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (911) implies: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (912) all_4_3 = e3 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (901), (912) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (913) op(e4, e3) = e1 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_5, e1, % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e4, simplifying with (140), (913) gives: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (914) all_4_5 = e1 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (601), (914) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (915) $false % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (915) is inconsistent. % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (916) ~ (all_10_12 = e3) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (351), (452), (516), (517), (616), (909), (916) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #123. % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (917) ~ (all_10_20 = e1) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (89), (90), (334), (453), (460), (466), % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527), (533), (588), (589), (607), (719), (721), % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (729), (905), (917) are inconsistent by sub-proof % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #121. % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (918) ~ (all_10_4 = e1) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (58), (118), (183), (301), (303), % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (328), (345), (357), (361), (373), (391), % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (466), (496), (510), (521), (522), (527), % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533), (577), (630), (663), (666), (667), (708), % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (712), (721), (918), (function-axioms) are % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #120. % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (919) all_8_10 = e0 & ~ (all_8_11 = e4) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (919) implies: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (920) all_8_10 = e0 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (920) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (921) op(e4, all_4_4) = e0 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (922) all_10_4 = e1 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (922) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (923) all_4_10 = e1 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (923) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (924) ~ (all_4_14 = e1) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (924) implies: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (925) ~ (all_4_14 = e1) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (57), (923) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (926) ~ (all_4_15 = e1) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (926) implies: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (927) ~ (all_4_15 = e1) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (521), (923) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (928) ~ (e3 = e1) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (550), (923) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (929) op(e4, e1) = all_8_27 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (930) all_10_20 = e1 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (930) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (931) all_4_4 = e1 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (931) implies: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (932) all_4_4 = e1 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (506), (932) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (933) ~ (e2 = e1) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (921), (932) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (934) op(e4, e1) = e0 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (935) all_10_9 = e1 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (388), (935) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (936) all_4_15 = e1 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (927), (936) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (937) $false % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (937) is inconsistent. % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (938) all_10_10 = e1 | all_10_11 = e1 | all_10_15 = e1 | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_23 = e1 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (939) all_10_20 = e3 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (930), (939) are inconsistent by sub-proof % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #151. % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (940) ~ (all_10_20 = e3) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (941) all_10_21 = e3 | all_10_22 = e3 | all_10_23 = e3 | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_24 = e3 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (941) gives: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (942) all_10_21 = e3 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (331), (942) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (943) all_4_9 = e3 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (943) implies: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (944) all_4_9 = e3 % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (83), (944) imply: % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (945) ~ (all_4_5 = e3) % 71.81/10.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (721) gives: % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (946) all_6_22 = e4 % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (466), (946) imply: % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (947) all_4_14 = e4 % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (709), (947) imply: % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (948) op(e2, e4) = e0 % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (938) gives: % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (949) all_10_10 = e1 % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (949) imply: % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (950) all_4_16 = e1 % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (611), (950) imply: % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (951) $false % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (951) is inconsistent. % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (952) all_10_11 = e1 | all_10_15 = e1 | all_10_23 = e1 % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (952) gives: % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (953) all_10_11 = e1 % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (953) imply: % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (954) all_4_17 = e1 % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (954) implies: % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (955) all_4_17 = e1 % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e0, % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e2, simplifying with (131), (948) gives: % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (956) all_4_2 = e0 % 71.81/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_15, % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_27, e1, e4, simplifying with (138), (929) % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (957) all_8_27 = all_4_15 % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_8_27, % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e4, simplifying with (929), (934) gives: % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (958) all_8_27 = e0 % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (957), (958) imply: % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (959) all_4_15 = e0 % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (99), (956) imply: % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (960) ~ (all_4_7 = e0) % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (960) implies: % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (961) ~ (all_4_7 = e0) % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (959) imply: % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (962) ~ (all_4_5 = e0) % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (454), (456), (518), (601), (603), (714), % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (724), (945), (961), (962) are inconsistent by % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #109. % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (963) all_10_15 = e1 | all_10_23 = e1 % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (496), (664), (963) are inconsistent by % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #166. % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (964) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (466), (527), (533), (925), (964) are inconsistent % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #130. % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (965) ~ (all_10_21 = e3) % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (331), (965) imply: % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (966) ~ (all_4_9 = e3) % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (58), (64), (118), (183), (295), % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301), (303), (325), (328), (345), (357), (361), % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373), (388), (391), (460), (461), (466), (496), % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510), (512), (521), (522), (527), (533), (577), % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589), (607), (630), (666), (667), (708), (719), % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (721), (966), (function-axioms) are inconsistent % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #125. % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (967) ~ (all_10_20 = e1) % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (89), (90), (334), (453), (460), (466), % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527), (533), (588), (589), (607), (719), (721), % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (729), (925), (967) are inconsistent by sub-proof % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #121. % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (968) ~ (all_10_4 = e1) % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (58), (118), (183), (301), (303), % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (328), (345), (357), (361), (373), (391), % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (466), (496), (510), (521), (522), (527), % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533), (577), (630), (663), (666), (667), (708), % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (712), (721), (968), (function-axioms) are % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #120. % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | Case 2: % 72.73/10.64 | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | (969) all_10_24 = e2 % 72.73/10.64 | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | COMBINE_EQS: (585), (969) imply: % 72.73/10.64 | | | | | | | | | | | | | | | (970) e2 = e0 % 72.73/10.64 | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | REDUCE: (5), (970) imply: % 72.73/10.64 | | | | | | | | | | | | | | | (971) $false % 72.73/10.64 | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | CLOSE: (971) is inconsistent. % 72.73/10.64 | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | Case 2: % 72.73/10.64 | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | (972) all_10_19 = e2 | all_10_24 = e2 % 72.73/10.64 | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | BETA: splitting (656) gives: % 72.73/10.64 | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | Case 1: % 72.73/10.64 | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | (973) all_10_23 = e2 % 72.73/10.64 | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | COMBINE_EQS: (325), (973) imply: % 72.73/10.64 | | | | | | | | | | | | | | (974) all_4_19 = e2 % 72.73/10.64 | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | SIMP: (974) implies: % 72.73/10.64 | | | | | | | | | | | | | | (975) all_4_19 = e2 % 72.73/10.64 | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | REDUCE: (35), (975) imply: % 72.73/10.64 | | | | | | | | | | | | | | (976) ~ (all_4_16 = e2) % 72.73/10.64 | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | REDUCE: (32), (975) imply: % 72.73/10.64 | | | | | | | | | | | | | | (977) ~ (all_4_17 = e2) % 72.73/10.64 | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | REDUCE: (542), (975) imply: % 72.73/10.64 | | | | | | | | | | | | | | (978) ~ (e4 = e2) % 72.73/10.64 | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | BETA: splitting (972) gives: % 72.73/10.64 | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | Case 1: % 72.73/10.64 | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | (979) all_10_19 = e2 % 72.73/10.64 | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | COMBINE_EQS: (337), (979) imply: % 72.73/10.64 | | | | | | | | | | | | | | | (980) all_4_23 = e2 % 72.73/10.64 | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | REDUCE: (624), (980) imply: % 72.73/10.64 | | | | | | | | | | | | | | | (981) $false % 72.73/10.64 | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | CLOSE: (981) is inconsistent. % 72.73/10.64 | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | Case 2: % 72.73/10.64 | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | (982) all_10_24 = e2 % 72.73/10.64 | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | COMBINE_EQS: (585), (982) imply: % 72.73/10.64 | | | | | | | | | | | | | | | (983) e2 = e0 % 72.73/10.64 | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | COMBINE_EQS: (973), (983) imply: % 72.73/10.64 | | | | | | | | | | | | | | | (984) all_10_23 = e0 % 72.73/10.64 | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (295), (357), (373), (388), (496), % 72.73/10.64 | | | | | | | | | | | | | | | (512), (976), (977), (984) are inconsistent by % 72.73/10.64 | | | | | | | | | | | | | | | sub-proof #108. % 72.73/10.64 | | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | Case 2: % 72.73/10.64 | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | (985) all_10_24 = e2 % 72.73/10.64 | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | COMBINE_EQS: (585), (985) imply: % 72.73/10.64 | | | | | | | | | | | | | | (986) e2 = e0 % 72.73/10.64 | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | REDUCE: (5), (986) imply: % 72.73/10.64 | | | | | | | | | | | | | | (987) $false % 72.73/10.64 | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | | CLOSE: (987) is inconsistent. % 72.73/10.64 | | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | | % 72.73/10.64 | | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | | % 72.73/10.64 | | | | | | | | | End of split % 72.73/10.64 | | | | | | | | | % 72.73/10.64 | | | | | | | | End of split % 72.73/10.64 | | | | | | | | % 72.73/10.64 | | | | | | | End of split % 72.73/10.64 | | | | | | | % 72.73/10.64 | | | | | | Case 2: % 72.73/10.64 | | | | | | | % 72.73/10.64 | | | | | | | (988) ~ (all_6_7 = e2) % 72.73/10.64 | | | | | | | (989) all_6_7 = e4 | all_6_7 = e3 | all_6_7 = e1 | all_6_7 = e0 % 72.73/10.64 | | | | | | | % 72.73/10.64 | | | | | | | REDUCE: (462), (988) imply: % 72.73/10.64 | | | | | | | (990) ~ (all_4_11 = e2) % 72.73/10.64 | | | | | | | % 72.73/10.64 | | | | | | | BETA: splitting (302) gives: % 72.73/10.64 | | | | | | | % 72.73/10.64 | | | | | | | Case 1: % 72.73/10.64 | | | | | | | | % 72.73/10.64 | | | | | | | | (991) all_10_4 = e2 % 72.73/10.64 | | | | | | | | % 72.73/10.64 | | | | | | | | COMBINE_EQS: (391), (991) imply: % 72.73/10.64 | | | | | | | | (992) all_4_10 = e2 % 72.73/10.64 | | | | | | | | % 72.73/10.64 | | | | | | | | REDUCE: (510), (992) imply: % 72.73/10.64 | | | | | | | | (993) $false % 72.73/10.64 | | | | | | | | % 72.73/10.64 | | | | | | | | CLOSE: (993) is inconsistent. % 72.73/10.64 | | | | | | | | % 72.73/10.64 | | | | | | | Case 2: % 72.73/10.64 | | | | | | | | % 72.73/10.64 | | | | | | | | (994) all_10_5 = e2 | all_10_8 = e2 | all_10_14 = e2 | % 72.73/10.64 | | | | | | | | all_10_22 = e2 % 72.73/10.64 | | | | | | | | % 72.73/10.64 | | | | | | | | BETA: splitting (994) gives: % 72.73/10.64 | | | | | | | | % 72.73/10.64 | | | | | | | | Case 1: % 72.73/10.64 | | | | | | | | | % 72.73/10.64 | | | | | | | | | (995) all_10_5 = e2 % 72.73/10.64 | | | | | | | | | % 72.73/10.64 | | | | | | | | | COMBINE_EQS: (498), (995) imply: % 72.73/10.64 | | | | | | | | | (996) all_4_11 = e2 % 72.73/10.64 | | | | | | | | | % 72.73/10.64 | | | | | | | | | REDUCE: (990), (996) imply: % 72.73/10.64 | | | | | | | | | (997) $false % 72.73/10.64 | | | | | | | | | % 72.73/10.64 | | | | | | | | | CLOSE: (997) is inconsistent. % 72.73/10.64 | | | | | | | | | % 72.73/10.64 | | | | | | | | Case 2: % 72.73/10.64 | | | | | | | | | % 72.73/10.64 | | | | | | | | | (998) all_10_8 = e2 | all_10_14 = e2 | all_10_22 = e2 % 72.73/10.64 | | | | | | | | | % 72.73/10.64 | | | | | | | | | BETA: splitting (998) gives: % 72.73/10.64 | | | | | | | | | % 72.73/10.64 | | | | | | | | | Case 1: % 72.73/10.64 | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | (999) all_10_8 = e2 % 72.73/10.65 | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | COMBINE_EQS: (361), (999) imply: % 72.73/10.65 | | | | | | | | | | (1000) e3 = e2 % 72.73/10.65 | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | REDUCE: (8), (1000) imply: % 72.73/10.65 | | | | | | | | | | (1001) $false % 72.73/10.65 | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | CLOSE: (1001) is inconsistent. % 72.73/10.65 | | | | | | | | | | % 72.73/10.65 | | | | | | | | | Case 2: % 72.73/10.65 | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | (1002) all_10_14 = e2 | all_10_22 = e2 % 72.73/10.65 | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | BETA: splitting (1002) gives: % 72.73/10.65 | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | Case 1: % 72.73/10.65 | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | (1003) all_10_14 = e2 % 72.73/10.65 | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | COMBINE_EQS: (345), (1003) imply: % 72.73/10.65 | | | | | | | | | | | (1004) e2 = e0 % 72.73/10.65 | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | REDUCE: (5), (1004) imply: % 72.73/10.65 | | | | | | | | | | | (1005) $false % 72.73/10.65 | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | CLOSE: (1005) is inconsistent. % 72.73/10.65 | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | Case 2: % 72.73/10.65 | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | (1006) all_10_22 = e2 % 72.73/10.65 | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | COMBINE_EQS: (328), (1006) imply: % 72.73/10.65 | | | | | | | | | | | (1007) all_4_14 = e2 % 72.73/10.65 | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | REDUCE: (527), (1007) imply: % 72.73/10.65 | | | | | | | | | | | (1008) ~ (e3 = e2) % 72.73/10.65 | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | REDUCE: (565), (1007) imply: % 72.73/10.65 | | | | | | | | | | | (1009) op(e2, e2) = all_8_36 % 72.73/10.65 | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | REDUCE: (577), (1007) imply: % 72.73/10.65 | | | | | | | | | | | (1010) op(e0, e2) = all_8_37 % 72.73/10.65 | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | REDUCE: (119), (1007) imply: % 72.73/10.65 | | | | | | | | | | | (1011) op(e0, e2) = e2 % 72.73/10.65 | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | BETA: splitting (301) gives: % 72.73/10.65 | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | Case 1: % 72.73/10.65 | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | (1012) all_10_4 = e1 % 72.73/10.65 | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | COMBINE_EQS: (391), (1012) imply: % 72.73/10.65 | | | | | | | | | | | | (1013) all_4_10 = e1 % 72.73/10.65 | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | REDUCE: (550), (1013) imply: % 72.73/10.65 | | | | | | | | | | | | (1014) op(e4, e1) = all_8_27 % 72.73/10.65 | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | REDUCE: (562), (1013) imply: % 72.73/10.65 | | | | | | | | | | | | (1015) op(e2, e1) = all_8_26 % 72.73/10.65 | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | BETA: splitting (989) gives: % 72.73/10.65 | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | Case 1: % 72.73/10.65 | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | (1016) all_6_7 = e4 % 72.73/10.65 | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | COMBINE_EQS: (462), (1016) imply: % 72.73/10.65 | | | | | | | | | | | | | (1017) all_4_11 = e4 % 72.73/10.65 | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | SIMP: (1017) implies: % 72.73/10.65 | | | | | | | | | | | | | (1018) all_4_11 = e4 % 72.73/10.65 | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | REDUCE: (51), (1018) imply: % 72.73/10.65 | | | | | | | | | | | | | (1019) ~ (all_4_21 = e4) % 72.73/10.65 | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | SIMP: (1019) implies: % 72.73/10.65 | | | | | | | | | | | | | (1020) ~ (all_4_21 = e4) % 72.73/10.65 | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | REDUCE: (563), (1018) imply: % 72.73/10.65 | | | | | | | | | | | | | (1021) op(e2, e4) = all_8_29 % 72.73/10.65 | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_37, % 72.73/10.65 | | | | | | | | | | | | | e2, e0, simplifying with (1010), (1011) gives: % 72.73/10.65 | | | | | | | | | | | | | (1022) all_8_37 = e2 % 72.73/10.65 | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_17, % 72.73/10.65 | | | | | | | | | | | | | all_8_26, e1, e2, simplifying with (128), (1015) % 72.73/10.65 | | | | | | | | | | | | | gives: % 72.73/10.65 | | | | | | | | | | | | | (1023) all_8_26 = all_4_17 % 72.73/10.65 | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_8_36, % 72.73/10.65 | | | | | | | | | | | | | e2, e2, simplifying with (14), (1009) gives: % 72.73/10.65 | | | | | | | | | | | | | (1024) all_8_36 = e3 % 72.73/10.65 | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 72.73/10.65 | | | | | | | | | | | | | all_8_29, e4, e2, simplifying with (131), (1021) % 72.73/10.65 | | | | | | | | | | | | | gives: % 72.73/10.65 | | | | | | | | | | | | | (1025) all_8_29 = all_4_2 % 72.73/10.65 | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_15, % 72.73/10.65 | | | | | | | | | | | | | all_8_27, e1, e4, simplifying with (138), (1014) % 72.73/10.65 | | | | | | | | | | | | | gives: % 72.73/10.65 | | | | | | | | | | | | | (1026) all_8_27 = all_4_15 % 72.73/10.65 | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | BETA: splitting (251) gives: % 72.73/10.65 | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | Case 1: % 72.73/10.65 | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | (1027) (all_8_26 = e4 & ~ (all_8_27 = e2)) | (all_8_29 = % 72.73/10.65 | | | | | | | | | | | | | | e3 & ~ (all_8_30 = e2)) % 72.73/10.65 | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | BETA: splitting (1027) gives: % 72.73/10.65 | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | Case 1: % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | (1028) all_8_26 = e4 & ~ (all_8_27 = e2) % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | ALPHA: (1028) implies: % 72.73/10.65 | | | | | | | | | | | | | | | (1029) all_8_26 = e4 % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | COMBINE_EQS: (1023), (1029) imply: % 72.73/10.65 | | | | | | | | | | | | | | | (1030) all_4_17 = e4 % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | SIMP: (1030) implies: % 72.73/10.65 | | | | | | | | | | | | | | | (1031) all_4_17 = e4 % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | REDUCE: (540), (1031) imply: % 72.73/10.65 | | | | | | | | | | | | | | | (1032) $false % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | CLOSE: (1032) is inconsistent. % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | Case 2: % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | (1033) all_8_29 = e3 & ~ (all_8_30 = e2) % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | ALPHA: (1033) implies: % 72.73/10.65 | | | | | | | | | | | | | | | (1034) all_8_29 = e3 % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | COMBINE_EQS: (1025), (1034) imply: % 72.73/10.65 | | | | | | | | | | | | | | | (1035) all_4_2 = e3 % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | SIMP: (1035) implies: % 72.73/10.65 | | | | | | | | | | | | | | | (1036) all_4_2 = e3 % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | REDUCE: (515), (1036) imply: % 72.73/10.65 | | | | | | | | | | | | | | | (1037) $false % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | CLOSE: (1037) is inconsistent. % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | End of split % 72.73/10.65 | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | Case 2: % 72.73/10.65 | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | (1038) (all_8_33 = e1 & ~ (all_8_34 = e2)) | (all_8_36 = % 72.73/10.65 | | | | | | | | | | | | | | e0 & ~ (all_8_37 = e2)) % 72.73/10.65 | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | BETA: splitting (1038) gives: % 72.73/10.65 | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | Case 1: % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | (1039) all_8_33 = e1 & ~ (all_8_34 = e2) % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | ALPHA: (1039) implies: % 72.73/10.65 | | | | | | | | | | | | | | | (1040) all_8_33 = e1 % 72.73/10.65 | | | | | | | | | | | | | | | (1041) ~ (all_8_34 = e2) % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | COMBINE_EQS: (584), (1040) imply: % 72.73/10.65 | | | | | | | | | | | | | | | (1042) all_4_22 = e1 % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | SIMP: (1042) implies: % 72.73/10.65 | | | | | | | | | | | | | | | (1043) all_4_22 = e1 % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | COMBINE_EQS: (495), (1043) imply: % 72.73/10.65 | | | | | | | | | | | | | | | (1044) all_10_18 = e1 % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | REDUCE: (31), (1043) imply: % 72.73/10.65 | | | | | | | | | | | | | | | (1045) ~ (all_4_17 = e1) % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | REDUCE: (26), (1043) imply: % 72.73/10.65 | | | | | | | | | | | | | | | (1046) ~ (all_4_20 = e1) % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | REDUCE: (20), (1043) imply: % 72.73/10.65 | | | | | | | | | | | | | | | (1047) ~ (all_4_23 = e1) % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | SIMP: (1047) implies: % 72.73/10.65 | | | | | | | | | | | | | | | (1048) ~ (all_4_23 = e1) % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | REDUCE: (581), (1043) imply: % 72.73/10.65 | | | | | | | | | | | | | | | (1049) op(e0, e1) = all_8_58 % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 72.73/10.65 | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | Case 1: % 72.73/10.65 | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | (1050) all_10_6 = e2 % 72.73/10.65 | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | COMBINE_EQS: (367), (1050) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | (1051) all_4_2 = e2 % 72.73/10.65 | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | REDUCE: (502), (1051) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | (1052) $false % 72.73/10.65 | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | CLOSE: (1052) is inconsistent. % 72.73/10.65 | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | Case 2: % 72.73/10.65 | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | (1053) all_10_7 = e2 | all_10_8 = e2 | all_10_11 = e2 | % 72.73/10.65 | | | | | | | | | | | | | | | | all_10_18 = e2 % 72.73/10.65 | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 72.73/10.65 | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | Case 1: % 72.73/10.65 | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | (1054) all_6_19 = e2 % 72.73/10.65 | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | COMBINE_EQS: (479), (1054) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | (1055) all_4_23 = e2 % 72.73/10.65 | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | SIMP: (1055) implies: % 72.73/10.65 | | | | | | | | | | | | | | | | | (1056) all_4_23 = e2 % 72.73/10.65 | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | REDUCE: (624), (1056) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | (1057) $false % 72.73/10.65 | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | CLOSE: (1057) is inconsistent. % 72.73/10.65 | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | Case 2: % 72.73/10.65 | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | (1058) all_6_19 = e4 | all_6_19 = e3 | all_6_19 = e1 | % 72.73/10.65 | | | | | | | | | | | | | | | | | all_6_19 = e0 % 72.73/10.65 | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | BETA: splitting (1058) gives: % 72.73/10.65 | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.65 | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | (1059) all_6_19 = e4 % 72.73/10.65 | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (479), (1059) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | | (1060) all_4_23 = e4 % 72.73/10.65 | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | SIMP: (1060) implies: % 72.73/10.65 | | | | | | | | | | | | | | | | | | (1061) all_4_23 = e4 % 72.73/10.65 | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | REDUCE: (544), (1061) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | | (1062) $false % 72.73/10.65 | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | CLOSE: (1062) is inconsistent. % 72.73/10.65 | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.65 | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | (1063) all_6_19 = e3 | all_6_19 = e1 | all_6_19 = e0 % 72.73/10.65 | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | BETA: splitting (1053) gives: % 72.73/10.65 | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | (1064) all_10_7 = e2 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (497), (1064) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | (1065) all_4_7 = e2 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | REDUCE: (620), (1065) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | (1066) $false % 72.73/10.65 | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | CLOSE: (1066) is inconsistent. % 72.73/10.65 | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | (1067) all_10_8 = e2 | all_10_11 = e2 | all_10_18 = e2 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | BETA: splitting (1067) gives: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | (1068) all_10_8 = e2 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (1068) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | (1069) e3 = e2 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (1069) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | (1070) $false % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | CLOSE: (1070) is inconsistent. % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | (1071) all_10_11 = e2 | all_10_18 = e2 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1063) gives: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | (1072) all_6_19 = e1 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (479), (1072) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | (1073) all_4_23 = e1 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | SIMP: (1073) implies: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | (1074) all_4_23 = e1 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1048), (1074) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | (1075) $false % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1075) is inconsistent. % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | (1076) all_6_19 = e3 | all_6_19 = e0 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1076) gives: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | (1077) all_6_19 = e3 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (479), (1077) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | (1078) all_4_23 = e3 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1078) implies: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | (1079) all_4_23 = e3 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (1079) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | (1080) ~ (all_4_3 = e3) % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (25), (1079) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | (1081) ~ (all_4_20 = e3) % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22), (1079) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | (1082) ~ (all_4_21 = e3) % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (1079) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | (1083) op(e0, e3) = all_8_61 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | (1084) all_6_9 = e2 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (475), (1084) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | (1085) all_4_21 = e2 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (1085) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | (1086) op(e0, e2) = all_8_55 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (616) gives: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | (1087) all_6_15 = e4 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (452), (517), (1087) are inconsistent by sub-proof % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | #107. % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | (1088) all_6_15 = e3 | all_6_15 = e1 | all_6_15 = e0 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1088) gives: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | | (1089) all_6_15 = e1 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (452), (1089) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | | (1090) all_4_3 = e1 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1090) implies: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | | (1091) all_4_3 = e1 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (1091) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | | (1092) all_10_12 = e1 % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (1091) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | | (1093) ~ (all_4_1 = e1) % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (101), (1091) imply: % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | | (1094) ~ (all_4_2 = e1) % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.65 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (95), (1091) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | (1095) ~ (all_4_4 = e1) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1095) implies: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | (1096) ~ (all_4_4 = e1) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1080), (1091) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | (1097) ~ (e3 = e1) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (504), (1091) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | (1098) ~ (e2 = e1) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (547), (1091) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | (1099) op(e4, e1) = all_8_7 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (1100) all_6_4 = e2 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (474), (514), (1100) are inconsistent by sub-proof % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | #154. % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (1101) all_6_4 = e4 | all_6_4 = e3 | all_6_4 = e1 | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_4 = e0 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1101) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1102) all_6_4 = e4 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (474), (1102) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1103) all_4_20 = e4 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1103) implies: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1104) all_4_20 = e4 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (80), (1104) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1105) ~ (all_4_5 = e4) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (552), (1104) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1106) op(e4, e4) = all_8_53 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (1104) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1107) op(e4, e0) = e4 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (579), (1104) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1108) op(e0, e4) = all_8_52 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1071) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1109) all_10_11 = e2 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (1109) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1110) all_4_17 = e2 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (32), (1110) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1111) ~ (all_4_19 = e2) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1111) implies: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1112) ~ (all_4_19 = e2) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1113) all_10_20 = e1 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (1113) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1114) all_4_4 = e1 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1096), (1114) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1115) $false % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1115) is inconsistent. % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1116) all_10_21 = e1 | all_10_22 = e1 | all_10_23 = e1 | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_24 = e1 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1116) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1117) all_10_21 = e1 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (331), (1117) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1118) all_4_9 = e1 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (607), (1118) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1119) $false % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1119) is inconsistent. % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1120) all_10_22 = e1 | all_10_23 = e1 | all_10_24 = e1 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1120) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1121) all_10_22 = e1 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1006), (1121) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1122) e2 = e1 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (1122) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1123) $false % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1123) is inconsistent. % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1124) all_10_23 = e1 | all_10_24 = e1 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1124) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125) all_10_23 = e1 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (325), (1125) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1126) all_4_19 = e1 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (1126) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1127) ~ (all_4_15 = e1) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (578), (1126) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1128) op(e0, e1) = all_8_50 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (1126) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1129) op(e0, e1) = e1 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_58, % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_50, e1, e0, simplifying with (1049), (1128) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1130) all_8_50 = all_8_58 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_8_50, % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, simplifying with (1128), (1129) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1131) all_8_50 = e1 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_55, % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (1011), (1086) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1132) all_8_55 = e2 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_9, % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_61, e3, e0, simplifying with (120), (1083) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1133) all_8_61 = all_4_9 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_4, % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_52, e4, e0, simplifying with (121), (1108) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1134) all_8_52 = all_4_4 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_15, % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_7, e1, e4, simplifying with (138), (1099) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1135) all_8_7 = all_4_15 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_53, % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e4, simplifying with (15), (1106) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1136) all_8_53 = e2 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1130), (1131) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1137) all_8_58 = e1 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1137) implies: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1138) all_8_58 = e1 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1139) (all_8_52 = e4 & ~ (all_8_53 = e0)) | (all_8_55 = % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ~ (all_8_56 = e0)) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1139) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1140) all_8_52 = e4 & ~ (all_8_53 = e0) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1140) implies: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1141) all_8_52 = e4 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1134), (1141) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1142) all_4_4 = e4 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1142) implies: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1143) all_4_4 = e4 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (1143) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1144) all_10_20 = e4 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (106), (1143) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1145) ~ (all_4_1 = e4) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (100), (1143) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1146) ~ (all_4_2 = e4) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (1143) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1147) op(e4, e4) = all_8_10 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1148) all_6_10 = e2 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (451), (502), (1148) are inconsistent by sub-proof % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #106. % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1149) all_6_10 = e4 | all_6_10 = e3 | all_6_10 = e1 | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_10 = e0 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1149) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1150) all_6_10 = e4 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (451), (1146), (1150) are inconsistent by % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #105. % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1151) all_6_10 = e3 | all_6_10 = e1 | all_6_10 = e0 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1152) all_10_0 = e3 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (398), (1152) are inconsistent by sub-proof % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #104. % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1153) all_10_2 = e3 | all_10_6 = e3 | all_10_12 = e3 | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_20 = e3 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1151) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1154) all_6_10 = e1 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (451), (1094), (1154) are inconsistent by % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #103. % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1155) all_6_10 = e3 | all_6_10 = e0 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1155) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1156) all_6_10 = e3 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (451), (515), (1156) are inconsistent by sub-proof % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #102. % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1157) all_6_10 = e0 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (451), (1157) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1158) all_4_2 = e0 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1158) implies: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1159) all_4_2 = e0 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (1159) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1160) op(e4, e0) = all_8_4 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1153) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1161) all_10_2 = e3 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (382), (1161) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1162) all_4_1 = e3 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1162) implies: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1163) all_4_1 = e3 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (103), (1163) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1164) ~ (all_4_16 = e3) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1164) implies: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1165) ~ (all_4_16 = e3) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1145), (1163) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1166) ~ (e4 = e3) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (1163) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1167) op(e4, e3) = all_8_1 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1168) all_6_1 = e2 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (454), (508), (1168) are inconsistent by sub-proof % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #155. % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1169) ~ (all_6_1 = e2) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1170) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_1 = e0 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1170) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1171) all_6_1 = e4 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (454), (1105), (1171) are inconsistent by % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #138. % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1172) all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1173) all_10_9 = e3 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (388), (1173) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1174) all_4_15 = e3 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1135), (1174) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1175) all_8_7 = e3 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (1174) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1176) ~ (all_4_5 = e3) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (551), (1174) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1177) op(e4, e3) = all_8_40 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1178) all_10_1 = e0 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (394), (1178) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1179) all_4_5 = e0 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1176), (1179) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1180) ~ (e3 = e0) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (508), (1179) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1181) ~ (e2 = e0) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (549), (1179) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1182) op(e4, e0) = all_8_14 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (1179) imply: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1183) op(e4, e3) = e0 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, all_8_4, % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e4, simplifying with (1107), (1160) gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1184) all_8_4 = e4 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_14, % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_4, e0, e4, simplifying with (1160), (1182) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1185) all_8_4 = all_8_14 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_40, % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_1, e3, e4, simplifying with (1167), (1177) % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1186) all_8_1 = all_8_40 % 72.73/10.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_8_1, % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e4, simplifying with (1167), (1183) gives: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1187) all_8_1 = e0 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_10, % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e4, simplifying with (15), (1147) gives: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1188) all_8_10 = e2 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1186), (1187) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1189) all_8_40 = e0 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1184), (1185) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1190) all_8_14 = e4 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1191) (all_8_1 = e3 & ~ (all_8_2 = e4)) | (all_8_4 = e2 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_5 = e4)) % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1191) gives: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1192) all_8_1 = e3 & ~ (all_8_2 = e4) % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1192) implies: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1193) all_8_1 = e3 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1187), (1193) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1194) e3 = e0 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (525), (1194) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1195) $false % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1195) is inconsistent. % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1196) all_8_4 = e2 & ~ (all_8_5 = e4) % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1196) implies: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1197) all_8_4 = e2 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1184), (1197) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1198) e4 = e2 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1198) implies: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1199) e4 = e2 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (1199) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1200) $false % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1200) is inconsistent. % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1201) (all_8_7 = e1 & ~ (all_8_8 = e4)) | (all_8_10 = % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_11 = e4)) % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1201) gives: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1202) all_8_7 = e1 & ~ (all_8_8 = e4) % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1175), (1202) are inconsistent by sub-proof % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #101. % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1203) all_8_10 = e0 & ~ (all_8_11 = e4) % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1203) implies: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1204) all_8_10 = e0 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1188), (1204) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1205) e2 = e0 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (1205) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1206) $false % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1206) is inconsistent. % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1207) ~ (all_10_1 = e0) % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (1207) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1208) ~ (all_4_5 = e0) % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1172) gives: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1209) all_6_1 = e1 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (454), (601), (1209) are inconsistent by sub-proof % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #137. % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1210) all_6_1 = e3 | all_6_1 = e0 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (454), (1176), (1208), (1210) are inconsistent by % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #136. % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1211) all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_23 = e3 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1211) gives: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1212) all_10_10 = e3 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (1212) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1213) all_4_16 = e3 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1213) implies: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1214) all_4_16 = e3 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1165), (1214) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1215) $false % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1215) is inconsistent. % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1216) all_10_11 = e3 | all_10_15 = e3 | all_10_23 = e3 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1216) gives: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1217) all_10_11 = e3 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1109), (1217) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1218) e3 = e2 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (1218) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1219) $false % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1219) is inconsistent. % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1220) all_10_15 = e3 | all_10_23 = e3 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1220) gives: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1221) all_10_15 = e3 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (496), (1221) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1222) e4 = e3 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (1222) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1223) $false % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1223) is inconsistent. % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1224) all_10_23 = e3 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1125), (1224) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1225) e3 = e1 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (1225) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1226) $false % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1226) is inconsistent. % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1227) all_10_6 = e3 | all_10_12 = e3 | all_10_20 = e3 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (367), (515), (1092), (1144), (1227) % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #98. % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1228) all_8_55 = e3 & ~ (all_8_56 = e0) % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1132), (1228) are inconsistent by sub-proof % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #97. % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1229) (all_8_58 = e2 & ~ (all_8_59 = e0)) | (all_8_61 = % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_8_62 = e0)) % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1229) gives: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1230) all_8_58 = e2 & ~ (all_8_59 = e0) % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1230) implies: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1231) all_8_58 = e2 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1138), (1231) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1232) e2 = e1 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (1232) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1233) $false % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1233) is inconsistent. % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1234) all_8_61 = e1 & ~ (all_8_62 = e0) % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (607), (1133), (1234) are inconsistent by % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #96. % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1235) all_10_24 = e1 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (585), (1235) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1236) e1 = e0 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1236) implies: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1237) e1 = e0 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (1237) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1238) $false % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1238) is inconsistent. % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1239) all_10_18 = e2 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1044), (1239) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1240) e2 = e1 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1240) implies: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1241) e2 = e1 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (1241) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1242) $false % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1242) is inconsistent. % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1243) all_6_4 = e3 | all_6_4 = e1 | all_6_4 = e0 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (474), (591), (1046), (1081), (1243) are % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #95. % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | (1244) all_6_15 = e3 | all_6_15 = e0 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (452), (479), (516), (537), (1076), (1244) % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #94. % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | (1245) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e1 | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | all_6_9 = e0 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (475), (592), (613), (1020), (1082), (1245) are % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #110. % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | (1246) all_6_19 = e0 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (479), (1246) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | (1247) all_4_23 = e0 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1247) implies: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | (1248) all_4_23 = e0 % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (537), (1248) imply: % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | (1249) $false % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1249) is inconsistent. % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | (1250) all_8_36 = e0 & ~ (all_8_37 = e2) % 72.73/10.67 | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | | REF_CLOSE: (525), (1024), (1250) are inconsistent by % 72.73/10.67 | | | | | | | | | | | | | | | sub-proof #93. % 72.73/10.67 | | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | (1251) all_6_7 = e3 | all_6_7 = e1 | all_6_7 = e0 % 72.73/10.67 | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | REF_CLOSE: (462), (523), (524), (609), (1251) are % 72.73/10.67 | | | | | | | | | | | | | inconsistent by sub-proof #91. % 72.73/10.67 | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | End of split % 72.73/10.67 | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | (1252) ~ (all_10_4 = e1) % 72.73/10.67 | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | REDUCE: (391), (1252) imply: % 72.73/10.67 | | | | | | | | | | | | (1253) ~ (all_4_10 = e1) % 72.73/10.67 | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | BETA: splitting (183) gives: % 72.73/10.67 | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | Case 1: % 72.73/10.67 | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | (1254) all_6_2 = e2 % 72.73/10.67 | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | REF_CLOSE: (461), (510), (1254) are inconsistent by sub-proof % 72.73/10.67 | | | | | | | | | | | | | #168. % 72.73/10.67 | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | Case 2: % 72.73/10.67 | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | (1255) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | % 72.73/10.67 | | | | | | | | | | | | | all_6_2 = e0 % 72.73/10.67 | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | BETA: splitting (1255) gives: % 72.73/10.67 | | | | | | | | | | | | | % 72.73/10.67 | | | | | | | | | | | | | Case 1: % 72.73/10.67 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | (1256) all_6_2 = e4 % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | COMBINE_EQS: (461), (1256) imply: % 72.73/10.68 | | | | | | | | | | | | | | (1257) all_4_10 = e4 % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | SIMP: (1257) implies: % 72.73/10.68 | | | | | | | | | | | | | | (1258) all_4_10 = e4 % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | REDUCE: (61), (1258) imply: % 72.73/10.68 | | | | | | | | | | | | | | (1259) ~ (all_4_11 = e4) % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | SIMP: (1259) implies: % 72.73/10.68 | | | | | | | | | | | | | | (1260) ~ (all_4_11 = e4) % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | REF_CLOSE: (462), (523), (524), (609), (989), (1260) are % 72.73/10.68 | | | | | | | | | | | | | | inconsistent by sub-proof #90. % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | Case 2: % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | (1261) all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | REF_CLOSE: (461), (521), (522), (1253), (1261) are % 72.73/10.68 | | | | | | | | | | | | | | inconsistent by sub-proof #162. % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | End of split % 72.73/10.68 | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | End of split % 72.73/10.68 | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | End of split % 72.73/10.68 | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | End of split % 72.73/10.68 | | | | | | | | | | % 72.73/10.68 | | | | | | | | | End of split % 72.73/10.68 | | | | | | | | | % 72.73/10.68 | | | | | | | | End of split % 72.73/10.68 | | | | | | | | % 72.73/10.68 | | | | | | | End of split % 72.73/10.68 | | | | | | | % 72.73/10.68 | | | | | | End of split % 72.73/10.68 | | | | | | % 72.73/10.68 | | | | | Case 2: % 72.73/10.68 | | | | | | % 72.73/10.68 | | | | | | (1262) ~ (all_6_16 = e2) % 72.73/10.68 | | | | | | (1263) all_6_16 = e4 | all_6_16 = e3 | all_6_16 = e1 | all_6_16 = % 72.73/10.68 | | | | | | e0 % 72.73/10.68 | | | | | | % 72.73/10.68 | | | | | | REDUCE: (458), (1262) imply: % 72.73/10.68 | | | | | | (1264) ~ (all_4_8 = e2) % 72.73/10.68 | | | | | | % 72.73/10.68 | | | | | | BETA: splitting (291) gives: % 72.73/10.68 | | | | | | % 72.73/10.68 | | | | | | Case 1: % 72.73/10.68 | | | | | | | % 72.73/10.68 | | | | | | | (1265) all_10_12 = e2 % 72.73/10.68 | | | | | | | % 72.73/10.68 | | | | | | | REF_CLOSE: (351), (504), (1265) are inconsistent by sub-proof #89. % 72.73/10.68 | | | | | | | % 72.73/10.68 | | | | | | Case 2: % 72.73/10.68 | | | | | | | % 72.73/10.68 | | | | | | | (1266) all_10_13 = e2 | all_10_14 = e2 | all_10_15 = e2 | % 72.73/10.68 | | | | | | | all_10_19 = e2 % 72.73/10.68 | | | | | | | % 72.73/10.68 | | | | | | | BETA: splitting (1263) gives: % 72.73/10.68 | | | | | | | % 72.73/10.68 | | | | | | | Case 1: % 72.73/10.68 | | | | | | | | % 72.73/10.68 | | | | | | | | (1267) all_6_16 = e4 % 72.73/10.68 | | | | | | | | % 72.73/10.68 | | | | | | | | COMBINE_EQS: (458), (1267) imply: % 72.73/10.68 | | | | | | | | (1268) all_4_8 = e4 % 72.73/10.68 | | | | | | | | % 72.73/10.68 | | | | | | | | SIMP: (1268) implies: % 72.73/10.68 | | | | | | | | (1269) all_4_8 = e4 % 72.73/10.68 | | | | | | | | % 72.73/10.68 | | | | | | | | REDUCE: (520), (1269) imply: % 72.73/10.68 | | | | | | | | (1270) $false % 72.73/10.68 | | | | | | | | % 72.73/10.68 | | | | | | | | CLOSE: (1270) is inconsistent. % 72.73/10.68 | | | | | | | | % 72.73/10.68 | | | | | | | Case 2: % 72.73/10.68 | | | | | | | | % 72.73/10.68 | | | | | | | | (1271) all_6_16 = e3 | all_6_16 = e1 | all_6_16 = e0 % 72.73/10.68 | | | | | | | | % 72.73/10.68 | | | | | | | | BETA: splitting (1271) gives: % 72.73/10.68 | | | | | | | | % 72.73/10.68 | | | | | | | | Case 1: % 72.73/10.68 | | | | | | | | | % 72.73/10.68 | | | | | | | | | (1272) all_6_16 = e1 % 72.73/10.68 | | | | | | | | | % 72.73/10.68 | | | | | | | | | COMBINE_EQS: (458), (1272) imply: % 72.73/10.68 | | | | | | | | | (1273) all_4_8 = e1 % 72.73/10.68 | | | | | | | | | % 72.73/10.68 | | | | | | | | | SIMP: (1273) implies: % 72.73/10.68 | | | | | | | | | (1274) all_4_8 = e1 % 72.73/10.68 | | | | | | | | | % 72.73/10.68 | | | | | | | | | REDUCE: (605), (1274) imply: % 72.73/10.68 | | | | | | | | | (1275) $false % 72.73/10.68 | | | | | | | | | % 72.73/10.68 | | | | | | | | | CLOSE: (1275) is inconsistent. % 72.73/10.68 | | | | | | | | | % 72.73/10.68 | | | | | | | | Case 2: % 72.73/10.68 | | | | | | | | | % 72.73/10.68 | | | | | | | | | (1276) ~ (all_6_16 = e1) % 72.73/10.68 | | | | | | | | | (1277) all_6_16 = e3 | all_6_16 = e0 % 72.73/10.68 | | | | | | | | | % 72.73/10.68 | | | | | | | | | BETA: splitting (1266) gives: % 72.73/10.68 | | | | | | | | | % 72.73/10.68 | | | | | | | | | Case 1: % 72.73/10.68 | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | (1278) all_10_13 = e2 % 72.73/10.68 | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | REF_CLOSE: (348), (1264), (1278) are inconsistent by % 72.73/10.68 | | | | | | | | | | sub-proof #88. % 72.73/10.68 | | | | | | | | | | % 72.73/10.68 | | | | | | | | | Case 2: % 72.73/10.68 | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | (1279) ~ (all_10_13 = e2) % 72.73/10.68 | | | | | | | | | | (1280) all_10_14 = e2 | all_10_15 = e2 | all_10_19 = e2 % 72.73/10.68 | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | BETA: splitting (1277) gives: % 72.73/10.68 | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | Case 1: % 72.73/10.68 | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | (1281) all_6_16 = e3 % 72.73/10.68 | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | COMBINE_EQS: (458), (1281) imply: % 72.73/10.68 | | | | | | | | | | | (1282) all_4_8 = e3 % 72.73/10.68 | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | SIMP: (1282) implies: % 72.73/10.68 | | | | | | | | | | | (1283) all_4_8 = e3 % 72.73/10.68 | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | COMBINE_EQS: (348), (1283) imply: % 72.73/10.68 | | | | | | | | | | | (1284) all_10_13 = e3 % 72.73/10.68 | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | REDUCE: (94), (1283) imply: % 72.73/10.68 | | | | | | | | | | | (1285) ~ (all_4_3 = e3) % 72.73/10.68 | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | REDUCE: (84), (1283) imply: % 72.73/10.68 | | | | | | | | | | | (1286) ~ (all_4_5 = e3) % 72.73/10.68 | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | REDUCE: (68), (1283) imply: % 72.73/10.68 | | | | | | | | | | | (1287) ~ (all_4_9 = e3) % 72.73/10.68 | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | SIMP: (1287) implies: % 72.73/10.68 | | | | | | | | | | | (1288) ~ (all_4_9 = e3) % 72.73/10.68 | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | REDUCE: (65), (1283) imply: % 72.73/10.68 | | | | | | | | | | | (1289) ~ (all_4_23 = e3) % 72.73/10.68 | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | SIMP: (1289) implies: % 72.73/10.68 | | | | | | | | | | | (1290) ~ (all_4_23 = e3) % 72.73/10.68 | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | REDUCE: (569), (1283) imply: % 72.73/10.68 | | | | | | | | | | | (1291) op(e1, e3) = all_8_21 % 72.73/10.68 | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | REDUCE: (125), (1283) imply: % 72.73/10.68 | | | | | | | | | | | (1292) op(e1, e3) = e3 % 72.73/10.68 | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | BETA: splitting (1280) gives: % 72.73/10.68 | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | Case 1: % 72.73/10.68 | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | (1293) all_10_14 = e2 % 72.73/10.68 | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | COMBINE_EQS: (345), (1293) imply: % 72.73/10.68 | | | | | | | | | | | | (1294) e2 = e0 % 72.73/10.68 | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | REDUCE: (5), (1294) imply: % 72.73/10.68 | | | | | | | | | | | | (1295) $false % 72.73/10.68 | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | CLOSE: (1295) is inconsistent. % 72.73/10.68 | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | Case 2: % 72.73/10.68 | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | (1296) all_10_15 = e2 | all_10_19 = e2 % 72.73/10.68 | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | BETA: splitting (616) gives: % 72.73/10.68 | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | Case 1: % 72.73/10.68 | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | (1297) all_6_15 = e4 % 72.73/10.68 | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | REF_CLOSE: (452), (517), (1297) are inconsistent by sub-proof % 72.73/10.68 | | | | | | | | | | | | | #107. % 72.73/10.68 | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | Case 2: % 72.73/10.68 | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | (1298) all_6_15 = e3 | all_6_15 = e1 | all_6_15 = e0 % 72.73/10.68 | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | BETA: splitting (1298) gives: % 72.73/10.68 | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | Case 1: % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | (1299) all_6_15 = e1 % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | COMBINE_EQS: (452), (1299) imply: % 72.73/10.68 | | | | | | | | | | | | | | (1300) all_4_3 = e1 % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | SIMP: (1300) implies: % 72.73/10.68 | | | | | | | | | | | | | | (1301) all_4_3 = e1 % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | REDUCE: (107), (1301) imply: % 72.73/10.68 | | | | | | | | | | | | | | (1302) ~ (all_4_1 = e1) % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | REDUCE: (101), (1301) imply: % 72.73/10.68 | | | | | | | | | | | | | | (1303) ~ (all_4_2 = e1) % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | REDUCE: (95), (1301) imply: % 72.73/10.68 | | | | | | | | | | | | | | (1304) ~ (all_4_4 = e1) % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | SIMP: (1304) implies: % 72.73/10.68 | | | | | | | | | | | | | | (1305) ~ (all_4_4 = e1) % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | REDUCE: (91), (1301) imply: % 72.73/10.68 | | | | | | | | | | | | | | (1306) ~ (all_4_23 = e1) % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | SIMP: (1306) implies: % 72.73/10.68 | | | | | | | | | | | | | | (1307) ~ (all_4_23 = e1) % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | REDUCE: (1285), (1301) imply: % 72.73/10.68 | | | | | | | | | | | | | | (1308) ~ (e3 = e1) % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | REDUCE: (547), (1301) imply: % 72.73/10.68 | | | | | | | | | | | | | | (1309) op(e4, e1) = all_8_7 % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | REDUCE: (568), (1301) imply: % 72.73/10.68 | | | | | | | | | | | | | | (1310) op(e1, e1) = all_8_8 % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | BETA: splitting (171) gives: % 72.73/10.68 | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | Case 1: % 72.73/10.68 | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | (1311) all_6_19 = e2 % 72.73/10.68 | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | COMBINE_EQS: (479), (1311) imply: % 72.73/10.68 | | | | | | | | | | | | | | | (1312) all_4_23 = e2 % 72.73/10.68 | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | SIMP: (1312) implies: % 72.73/10.68 | | | | | | | | | | | | | | | (1313) all_4_23 = e2 % 72.73/10.68 | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | COMBINE_EQS: (583), (1313) imply: % 72.73/10.68 | | | | | | | | | | | | | | | (1314) all_8_34 = e2 % 72.73/10.68 | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | REDUCE: (22), (1313) imply: % 72.73/10.68 | | | | | | | | | | | | | | | (1315) ~ (all_4_21 = e2) % 72.73/10.68 | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | REDUCE: (544), (1313) imply: % 72.73/10.68 | | | | | | | | | | | | | | | (1316) ~ (e4 = e2) % 72.73/10.68 | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | REDUCE: (1290), (1313) imply: % 72.73/10.68 | | | | | | | | | | | | | | | (1317) ~ (e3 = e2) % 72.73/10.68 | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | REDUCE: (575), (1313) imply: % 72.73/10.68 | | | | | | | | | | | | | | | (1318) op(e1, e2) = all_8_62 % 72.73/10.68 | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | REDUCE: (122), (1313) imply: % 72.73/10.68 | | | | | | | | | | | | | | | (1319) op(e1, e0) = e2 % 72.73/10.68 | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, all_8_8, % 72.73/10.68 | | | | | | | | | | | | | | | e1, e1, simplifying with (12), (1310) gives: % 72.73/10.68 | | | | | | | | | | | | | | | (1320) all_8_8 = e4 % 72.73/10.68 | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_8_62, % 72.73/10.68 | | | | | | | | | | | | | | | e2, e1, simplifying with (13), (1318) gives: % 72.73/10.68 | | | | | | | | | | | | | | | (1321) all_8_62 = e0 % 72.73/10.68 | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_8_21, % 72.73/10.68 | | | | | | | | | | | | | | | e3, e1, simplifying with (1291), (1292) gives: % 72.73/10.68 | | | | | | | | | | | | | | | (1322) all_8_21 = e3 % 72.73/10.68 | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_15, % 72.73/10.68 | | | | | | | | | | | | | | | all_8_7, e1, e4, simplifying with (138), (1309) % 72.73/10.68 | | | | | | | | | | | | | | | gives: % 72.73/10.68 | | | | | | | | | | | | | | | (1323) all_8_7 = all_4_15 % 72.73/10.68 | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 72.73/10.68 | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | Case 1: % 72.73/10.68 | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | (1324) all_6_1 = e2 % 72.73/10.68 | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | REF_CLOSE: (454), (508), (1324) are inconsistent by sub-proof % 72.73/10.68 | | | | | | | | | | | | | | | | #155. % 72.73/10.68 | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | Case 2: % 72.73/10.68 | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | (1325) ~ (all_6_1 = e2) % 72.73/10.68 | | | | | | | | | | | | | | | | (1326) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | % 72.73/10.68 | | | | | | | | | | | | | | | | all_6_1 = e0 % 72.73/10.68 | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | BETA: splitting (179) gives: % 72.73/10.68 | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | Case 1: % 72.73/10.68 | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | (1327) all_6_7 = e2 % 72.73/10.68 | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | COMBINE_EQS: (462), (1327) imply: % 72.73/10.68 | | | | | | | | | | | | | | | | | (1328) all_4_11 = e2 % 72.73/10.68 | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | SIMP: (1328) implies: % 72.73/10.68 | | | | | | | | | | | | | | | | | (1329) all_4_11 = e2 % 72.73/10.68 | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | COMBINE_EQS: (498), (1329) imply: % 72.73/10.68 | | | | | | | | | | | | | | | | | (1330) all_10_5 = e2 % 72.73/10.68 | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | REDUCE: (53), (1329) imply: % 72.73/10.68 | | | | | | | | | | | | | | | | | (1331) ~ (all_4_14 = e2) % 72.73/10.68 | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | SIMP: (1331) implies: % 72.73/10.68 | | | | | | | | | | | | | | | | | (1332) ~ (all_4_14 = e2) % 72.73/10.68 | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | REDUCE: (52), (1329) imply: % 72.73/10.68 | | | | | | | | | | | | | | | | | (1333) ~ (all_4_16 = e2) % 72.73/10.68 | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | SIMP: (1333) implies: % 72.73/10.68 | | | | | | | | | | | | | | | | | (1334) ~ (all_4_16 = e2) % 72.73/10.68 | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | REDUCE: (51), (1329) imply: % 72.73/10.68 | | | | | | | | | | | | | | | | | (1335) ~ (all_4_21 = e2) % 72.73/10.68 | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | REDUCE: (558), (1329) imply: % 72.73/10.68 | | | | | | | | | | | | | | | | | (1336) op(e3, e2) = all_8_30 % 72.73/10.68 | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | REDUCE: (134), (1329) imply: % 72.73/10.68 | | | | | | | | | | | | | | | | | (1337) op(e3, e2) = e2 % 72.73/10.68 | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_30, % 72.73/10.68 | | | | | | | | | | | | | | | | | e2, e3, simplifying with (1336), (1337) gives: % 72.73/10.68 | | | | | | | | | | | | | | | | | (1338) all_8_30 = e2 % 72.73/10.68 | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 72.73/10.68 | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.68 | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | (1339) (all_8_26 = e4 & ~ (all_8_27 = e2)) | (all_8_29 = % 72.73/10.68 | | | | | | | | | | | | | | | | | | e3 & ~ (all_8_30 = e2)) % 72.73/10.68 | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | BETA: splitting (1339) gives: % 72.73/10.68 | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.68 | | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | | (1340) all_8_26 = e4 & ~ (all_8_27 = e2) % 72.73/10.68 | | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | | ALPHA: (1340) implies: % 72.73/10.68 | | | | | | | | | | | | | | | | | | | (1341) all_8_26 = e4 % 72.73/10.68 | | | | | | | | | | | | | | | | | | | (1342) ~ (all_8_27 = e2) % 72.73/10.68 | | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | | REDUCE: (562), (1341) imply: % 72.73/10.68 | | | | | | | | | | | | | | | | | | | (1343) op(e2, all_4_10) = e4 % 72.73/10.68 | | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 72.73/10.68 | | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | (1344) all_6_22 = e2 % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (466), (1332), (1344) are inconsistent by % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | sub-proof #156. % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | (1345) all_6_22 = e4 | all_6_22 = e3 | all_6_22 = e1 | % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | all_6_22 = e0 % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | | (1346) all_6_21 = e2 % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (460), (1346) imply: % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | | (1347) all_4_9 = e2 % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (1347) imply: % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | | (1348) ~ (all_4_19 = e2) % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | | SIMP: (1348) implies: % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | | (1349) ~ (all_4_19 = e2) % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.68 | | | | | | | | | | | | | | | | | | | | | | (1350) all_10_9 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (388), (1350) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | (1351) all_4_15 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (512), (1351) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | (1352) $false % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1352) is inconsistent. % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | (1353) all_10_10 = e2 | all_10_11 = e2 | all_10_15 = e2 | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | all_10_23 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1353) gives: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | (1354) all_10_10 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (1354) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | (1355) all_4_16 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1334), (1355) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | (1356) $false % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1356) is inconsistent. % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | (1357) all_10_11 = e2 | all_10_15 = e2 | all_10_23 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1357) gives: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | (1358) all_10_11 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (1358) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | (1359) all_4_17 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (1359) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | (1360) op(e2, e1) = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | (1361) all_6_2 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (1361) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | (1362) all_4_10 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (510), (1362) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | (1363) $false % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1363) is inconsistent. % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | (1364) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | all_6_2 = e0 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (1365) all_10_4 = e1 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (1365) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (1366) all_4_10 = e1 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1366) implies: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (1367) all_4_10 = e1 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1343), (1367) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (1368) op(e2, e1) = e4 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e4, e1, % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | e2, simplifying with (1360), (1368) gives: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (1369) e4 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (1369) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (1370) $false % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1370) is inconsistent. % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (1371) ~ (all_10_4 = e1) % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (1371) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (1372) ~ (all_4_10 = e1) % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (303), (391), (461), (521), (522), (550), % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (1342), (1364), (1372), (function-axioms) are % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #160. % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | (1373) all_10_15 = e2 | all_10_23 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (325), (496), (1349), (1373) are % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #87. % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | (1374) all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e1 | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | all_6_21 = e0 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1374) gives: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | (1375) all_6_21 = e4 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (460), (1375) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | (1376) all_4_9 = e4 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1376) implies: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | (1377) all_4_9 = e4 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (64), (1377) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | (1378) ~ (all_4_14 = e4) % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1378) implies: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | (1379) ~ (all_4_14 = e4) % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1345) gives: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | (1380) all_6_22 = e4 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (466), (1380) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | (1381) all_4_14 = e4 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1379), (1381) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | (1382) $false % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1382) is inconsistent. % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | (1383) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | (1384) all_10_4 = e4 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (391), (550), (1342), (1384), % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | #165. % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | (1385) ~ (all_10_4 = e4) % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (1385) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | (1386) ~ (all_4_10 = e4) % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (183), (461), (466), (510), (521), (522), % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | (527), (533), (1383), (1386) are inconsistent by % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #129. % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | (1387) all_6_21 = e3 | all_6_21 = e1 | all_6_21 = e0 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (460), (589), (607), (1288), (1387) are % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #126. % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | End of split % 72.73/10.69 | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | (1388) all_8_29 = e3 & ~ (all_8_30 = e2) % 72.73/10.69 | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | ALPHA: (1388) implies: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | (1389) ~ (all_8_30 = e2) % 72.73/10.69 | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | REDUCE: (1338), (1389) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | (1390) $false % 72.73/10.69 | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | CLOSE: (1390) is inconsistent. % 72.73/10.69 | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | End of split % 72.73/10.69 | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.69 | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | (1391) (all_8_33 = e1 & ~ (all_8_34 = e2)) | (all_8_36 = % 72.73/10.69 | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_37 = e2)) % 72.73/10.69 | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | BETA: splitting (1391) gives: % 72.73/10.69 | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | (1392) all_8_33 = e1 & ~ (all_8_34 = e2) % 72.73/10.69 | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | ALPHA: (1392) implies: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | (1393) ~ (all_8_34 = e2) % 72.73/10.69 | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | REDUCE: (1314), (1393) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | (1394) $false % 72.73/10.69 | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | CLOSE: (1394) is inconsistent. % 72.73/10.69 | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | (1395) all_8_36 = e0 & ~ (all_8_37 = e2) % 72.73/10.69 | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | ALPHA: (1395) implies: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | (1396) all_8_36 = e0 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | (1397) ~ (all_8_37 = e2) % 72.73/10.69 | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | REDUCE: (565), (1396) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | (1398) op(e2, all_4_14) = e0 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | (1399) all_6_22 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (466), (1332), (1399) are inconsistent by % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | sub-proof #156. % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | (1400) all_6_22 = e4 | all_6_22 = e3 | all_6_22 = e1 | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | all_6_22 = e0 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | (1401) all_6_21 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (460), (1401) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | (1402) all_4_9 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (331), (1402) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | (1403) all_10_21 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (1402) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | (1404) ~ (all_4_19 = e2) % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | SIMP: (1404) implies: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | (1405) ~ (all_4_19 = e2) % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (1402) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | (1406) op(e3, e2) = all_8_23 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | (1407) all_10_9 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (388), (1407) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | (1408) all_4_15 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (512), (1408) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | (1409) $false % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1409) is inconsistent. % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | (1410) all_10_10 = e2 | all_10_11 = e2 | all_10_15 = e2 | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | all_10_23 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1410) gives: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | (1411) all_10_10 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (1411) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | (1412) all_4_16 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1334), (1412) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | (1413) $false % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1413) is inconsistent. % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | (1414) all_10_11 = e2 | all_10_15 = e2 | all_10_23 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1414) gives: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | (1415) all_10_11 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (1415) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | (1416) all_4_17 = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (1416) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | (1417) ~ (all_4_7 = e2) % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (1416) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | (1418) ~ (all_4_22 = e2) % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1418) implies: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | (1419) ~ (all_4_22 = e2) % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (1416) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | (1420) op(e2, e1) = e2 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (573), (1416) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | (1421) op(e1, e2) = all_8_45 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | (1422) all_10_6 = e1 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (367), (1303), (1422) are inconsistent by % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #86. % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | (1423) all_10_7 = e1 | all_10_8 = e1 | all_10_11 = e1 | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | all_10_18 = e1 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1423) gives: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (1424) all_10_7 = e1 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (497), (1424) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (1425) all_4_7 = e1 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (603), (1425) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (1426) $false % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1426) is inconsistent. % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (1427) all_10_8 = e1 | all_10_11 = e1 | all_10_18 = e1 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1427) gives: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1428) all_10_8 = e1 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (1428) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1429) e3 = e1 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (1429) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1430) $false % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1430) is inconsistent. % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1431) all_10_11 = e1 | all_10_18 = e1 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1431) gives: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1432) all_10_11 = e1 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1415), (1432) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1433) e2 = e1 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (1433) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1434) $false % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1434) is inconsistent. % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1435) all_10_18 = e1 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (495), (1435) imply: % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1436) all_4_22 = e1 % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (26), (1436) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1437) ~ (all_4_20 = e1) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1419), (1436) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1438) ~ (e2 = e1) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (1436) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1439) op(e2, e1) = all_8_59 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_8_45, % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (13), (1421) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1440) all_8_45 = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_59, % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (1420), (1439) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1441) all_8_59 = e2 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_23, % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (1337), (1406) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1442) all_8_23 = e2 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1443) (all_8_13 = e4 & ~ (all_8_14 = e3)) | (all_8_17 = % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_8_18 = e3)) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1443) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1444) all_8_13 = e4 & ~ (all_8_14 = e3) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1444) implies: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1445) all_8_13 = e4 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (554), (1445) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1446) op(e3, all_4_5) = e4 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1447) all_6_4 = e2 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (474), (1447) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1448) all_4_20 = e2 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (514), (1448) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1449) $false % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1449) is inconsistent. % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1450) all_6_4 = e4 | all_6_4 = e3 | all_6_4 = e1 | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_4 = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (170) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1451) all_6_20 = e2 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (1451) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1452) all_4_4 = e2 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (506), (1452) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1453) $false % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1453) is inconsistent. % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1454) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e1 | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_20 = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1455) all_6_9 = e2 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (475), (1455) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1456) all_4_21 = e2 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1315), (1456) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1457) $false % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1457) is inconsistent. % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1458) ~ (all_6_9 = e2) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1459) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e1 | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_9 = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1460) all_6_2 = e2 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (1460) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1461) all_4_10 = e2 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (510), (1461) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1462) $false % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1462) is inconsistent. % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1463) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_2 = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1464) all_6_11 = e2 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (456), (1417), (1464) are inconsistent by % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #159. % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1465) all_6_11 = e4 | all_6_11 = e3 | all_6_11 = e1 | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_11 = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1466) (all_8_1 = e3 & ~ (all_8_2 = e4)) | (all_8_4 = e2 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_5 = e4)) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1466) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1467) all_8_1 = e3 & ~ (all_8_2 = e4) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (15), (27), (34), (35), % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (56), (57), (58), (80), (81), (82), (85), % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (99), (102), (103), (106), (108), (121), % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (131), (140), (180), (182), (285), (289), (293), % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294), (296), (301), (303), (307), (309), (316), % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318), (325), (334), (373), (382), (385), (388), % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391), (394), (398), (450), (453), (454), (456), % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (466), (468), (474), (475), (496), (500), % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512), (518), (521), (522), (527), (533), (538), % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542), (545), (552), (577), (588), (590), (601), % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (603), (613), (1286), (1302), (1305), (1326), % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1397), (1398), (1400), (1415), (1437), (1450), % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1454), (1459), (1463), (1465), (1467), % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #77. % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1468) all_8_4 = e2 & ~ (all_8_5 = e4) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1468) implies: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1469) all_8_4 = e2 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (1469) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1470) op(e4, all_4_2) = e2 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1471) all_6_5 = e2 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (450), (500), (1471) are inconsistent by sub-proof % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #153. % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1472) ~ (all_6_5 = e2) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1473) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_5 = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1474) all_6_3 = e2 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (468), (512), (1474) are inconsistent by sub-proof % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #152. % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1475) all_6_3 = e4 | all_6_3 = e3 | all_6_3 = e1 | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_3 = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1476) all_10_4 = e1 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (1476) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1477) all_4_10 = e1 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1477) implies: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1478) all_4_10 = e1 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (1478) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1479) ~ (all_4_14 = e1) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1479) implies: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1480) ~ (all_4_14 = e1) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (57), (1478) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1481) ~ (all_4_15 = e1) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1481) implies: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1482) ~ (all_4_15 = e1) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (1478) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1483) ~ (all_4_20 = e1) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1400) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1484) all_6_22 = e4 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (466), (1484) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1485) all_4_14 = e4 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1485) implies: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1486) all_4_14 = e4 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1398), (1486) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1487) op(e2, e4) = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e0, % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e2, simplifying with (131), (1487) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1488) all_4_2 = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (1488) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1489) ~ (all_4_1 = e0) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (99), (1488) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1490) ~ (all_4_7 = e0) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1490) implies: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1491) ~ (all_4_7 = e0) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1470), (1488) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1492) op(e4, e0) = e2 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1493) all_10_1 = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (394), (1493) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1494) all_4_5 = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (1494) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1495) ~ (all_4_15 = e0) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1495) implies: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1496) ~ (all_4_15 = e0) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (80), (1494) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1497) ~ (all_4_20 = e0) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (508), (1494) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1498) ~ (e2 = e0) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (601), (1494) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1499) ~ (e1 = e0) % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (549), (1494) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1500) op(e4, e0) = all_8_14 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1446), (1494) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1501) op(e3, e0) = e4 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1502) all_10_2 = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (382), (1502) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1503) all_4_1 = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1489), (1503) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1504) $false % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1504) is inconsistent. % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1505) all_10_3 = e0 | all_10_5 = e0 | all_10_10 = e0 | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_17 = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1505) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1506) all_10_3 = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (600), (1506) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1507) e1 = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (1507) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1508) $false % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1508) is inconsistent. % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1509) all_10_5 = e0 | all_10_10 = e0 | all_10_17 = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1509) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1510) all_10_5 = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1330), (1510) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1511) e2 = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (1511) imply: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1512) $false % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1512) is inconsistent. % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1513) all_10_10 = e0 | all_10_17 = e0 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1514) all_10_16 = e4 % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (1514) imply: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1515) all_4_20 = e4 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (27), (1515) imply: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1516) ~ (all_4_21 = e4) % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1516) implies: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1517) ~ (all_4_21 = e4) % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (1515) imply: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1518) op(e4, e0) = e4 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1519) all_10_16 = e3 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1514), (1519) imply: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1520) e4 = e3 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (1520) imply: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1521) $false % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1521) is inconsistent. % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1522) all_10_17 = e3 | all_10_18 = e3 | all_10_19 = e3 | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_24 = e3 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1513) gives: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1523) all_10_10 = e0 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (1523) imply: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1524) all_4_16 = e0 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (1524) imply: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1525) ~ (all_4_21 = e0) % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (1524) imply: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1526) op(e3, e0) = all_8_43 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1459) gives: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1527) all_6_9 = e4 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (475), (1517), (1527) are inconsistent by % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #114. % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1528) all_6_9 = e3 | all_6_9 = e1 | all_6_9 = e0 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1522) gives: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1529) all_10_17 = e3 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (1529) imply: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1530) all_4_21 = e3 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (1530) imply: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1531) op(e3, e0) = e3 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, all_8_43, % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e3, simplifying with (1501), (1526) gives: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1532) all_8_43 = e4 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_8_43, % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e3, simplifying with (1526), (1531) gives: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1533) all_8_43 = e3 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, all_8_14, % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e4, simplifying with (1500), (1518) gives: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1534) all_8_14 = e4 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_14, % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e4, simplifying with (1492), (1500) gives: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1535) all_8_14 = e2 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1534), (1535) imply: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1536) e4 = e2 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1536) implies: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1537) e4 = e2 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1532), (1533) imply: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1538) e4 = e3 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1538) implies: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1539) e4 = e3 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1537), (1539) imply: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1540) e3 = e2 % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (1540) imply: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1541) $false % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1541) is inconsistent. % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 72.73/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1542) ~ (all_10_17 = e3) % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (1542) imply: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1543) ~ (all_4_21 = e3) % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (475), (592), (613), (1528), (1543) are % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #111. % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1544) all_10_17 = e0 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (1544) imply: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1545) all_4_21 = e0 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (592), (1545) imply: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1546) $false % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1546) is inconsistent. % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1547) ~ (all_10_16 = e4) % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (1547) imply: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1548) ~ (all_4_20 = e4) % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (296), (388), (468), (474), (538), (591), % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1437), (1450), (1475), (1482), (1496), (1548) are % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #143. % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1549) ~ (all_10_1 = e0) % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (1549) imply: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1550) ~ (all_4_5 = e0) % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (454), (456), (518), (601), (603), (1286), % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1326), (1465), (1491), (1550) are inconsistent by % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #109. % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1551) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (466), (527), (533), (1480), (1551) are % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #130. % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1552) ~ (all_10_4 = e1) % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1553) all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_22 = e1 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (1552) imply: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1554) ~ (all_4_10 = e1) % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (27), (34), (35), (57), % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (81), (82), (88), (89), (102), (103), (106), % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (137), (286), (293), (294), (296), (303), (307), % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309), (313), (316), (318), (325), (328), (334), % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345), (351), (361), (367), (373), (382), (385), % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388), (391), (394), (398), (450), (453), (454), % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (475), (496), (500), (516), (521), (522), % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527), (533), (549), (588), (590), (601), (613), % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1286), (1302), (1326), (1330), (1334), (1398), % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1415), (1420), (1437), (1454), (1459), (1463), % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1470), (1473), (1553), (1554), (function-axioms) % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #71. % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1555) (all_8_7 = e1 & ~ (all_8_8 = e4)) | (all_8_10 = % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_11 = e4)) % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1555) gives: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1556) all_8_7 = e1 & ~ (all_8_8 = e4) % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1556) implies: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1557) ~ (all_8_8 = e4) % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1320), (1557) imply: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1558) $false % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1558) is inconsistent. % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1559) all_8_10 = e0 & ~ (all_8_11 = e4) % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1559) implies: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1560) all_8_10 = e0 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (1560) imply: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1561) op(e4, all_4_4) = e0 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1562) all_6_5 = e2 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (450), (500), (1562) are inconsistent by sub-proof % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #153. % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1563) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_5 = e0 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1564) all_10_4 = e1 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (1564) imply: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1565) all_4_10 = e1 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1565) implies: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1566) all_4_10 = e1 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (1566) imply: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1567) ~ (all_4_14 = e1) % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1567) implies: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1568) ~ (all_4_14 = e1) % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1400) gives: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1569) all_6_22 = e4 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (466), (1569) imply: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1570) all_4_14 = e4 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1570) implies: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1571) all_4_14 = e4 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (89), (1571) imply: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1572) ~ (all_4_4 = e4) % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (1571) imply: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1573) op(e0, e4) = all_8_37 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1454) gives: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1574) all_6_20 = e4 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (1574) imply: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1575) all_4_4 = e4 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1572), (1575) imply: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1576) $false % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1576) is inconsistent. % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1577) all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1577) gives: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1578) all_6_20 = e1 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (1578) imply: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1579) all_4_4 = e1 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1305), (1579) imply: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1580) $false % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1580) is inconsistent. % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1581) ~ (all_6_20 = e1) % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1582) all_6_20 = e3 | all_6_20 = e0 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1583) all_10_20 = e3 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (1583) imply: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1584) all_4_4 = e3 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1584) implies: % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1585) all_4_4 = e3 % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (106), (1585) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1586) ~ (all_4_1 = e3) % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1561), (1585) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1587) op(e4, e3) = e0 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (1585) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1588) op(e0, e4) = e3 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_8_37, % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e0, simplifying with (1573), (1588) gives: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1589) all_8_37 = e3 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_5, e0, % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e4, simplifying with (140), (1587) gives: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1590) all_4_5 = e0 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (1590) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1591) ~ (all_4_15 = e0) % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1591) implies: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1592) ~ (all_4_15 = e0) % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1286), (1590) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1593) ~ (e3 = e0) % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (508), (1590) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1594) ~ (e2 = e0) % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1446), (1590) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1595) op(e3, e0) = e4 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1596) all_10_9 = e0 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (388), (1596) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1597) all_4_15 = e0 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1592), (1597) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1598) $false % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1598) is inconsistent. % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1599) all_10_10 = e0 | all_10_11 = e0 | all_10_15 = e0 | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_23 = e0 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1599) gives: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1600) all_10_10 = e0 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (1600) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1601) all_4_16 = e0 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (103), (1601) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1602) ~ (all_4_1 = e0) % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (1601) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1603) op(e3, e0) = all_8_43 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1604) all_10_2 = e3 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (382), (1604) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1605) all_4_1 = e3 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1586), (1605) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1606) $false % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1606) is inconsistent. % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1607) ~ (all_10_2 = e3) % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1608) all_10_3 = e3 | all_10_5 = e3 | all_10_10 = e3 | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_17 = e3 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1608) gives: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1609) all_10_3 = e3 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (600), (1609) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1610) e3 = e1 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1610) implies: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1611) e3 = e1 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (1611) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1612) $false % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1612) is inconsistent. % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1613) all_10_5 = e3 | all_10_10 = e3 | all_10_17 = e3 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1613) gives: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1614) all_10_5 = e3 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1330), (1614) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1615) e3 = e2 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1615) implies: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1616) e3 = e2 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (1616) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1617) $false % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1617) is inconsistent. % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1618) all_10_10 = e3 | all_10_17 = e3 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1563) gives: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1619) all_6_5 = e4 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (450), (1619) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1620) all_4_1 = e4 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1620) implies: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1621) all_4_1 = e4 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (102), (1621) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1622) ~ (all_4_21 = e4) % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1622) implies: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1623) ~ (all_4_21 = e4) % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1618) gives: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1624) all_10_10 = e3 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (525), (1600), (1624) are inconsistent by % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #83. % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1625) all_10_17 = e3 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (1625) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1626) all_4_21 = e3 % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1623), (1626) imply: % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1627) ~ (e4 = e3) % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.08/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (1626) imply: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1628) op(e3, e0) = e3 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, all_8_43, % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e3, simplifying with (1595), (1603) gives: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1629) all_8_43 = e4 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_8_43, % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e3, simplifying with (1603), (1628) gives: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1630) all_8_43 = e3 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1629), (1630) imply: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1631) e4 = e3 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1631) implies: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1632) e4 = e3 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (1632) imply: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1633) $false % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1633) is inconsistent. % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1634) all_6_5 = e3 | all_6_5 = e1 | all_6_5 = e0 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (450), (1302), (1586), (1602), (1634) are % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #140. % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1635) all_10_11 = e0 | all_10_15 = e0 | all_10_23 = e0 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (325), (496), (535), (590), (1415), (1635) % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #79. % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1636) ~ (all_10_20 = e3) % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (334), (1636) imply: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1637) ~ (all_4_4 = e3) % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (453), (588), (1582), (1637) are inconsistent by % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #122. % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1638) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (466), (527), (533), (1568), (1638) are % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #130. % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1639) ~ (all_10_4 = e1) % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (15), (27), (34), (102), % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (103), (106), (286), (293), (303), (307), (316), % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318), (325), (334), (373), (382), (385), (391), % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394), (398), (450), (453), (461), (475), (496), % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521), (522), (550), (588), (590), (601), (613), % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1286), (1302), (1305), (1334), (1415), (1437), % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1454), (1459), (1463), (1561), (1563), (1639), % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #70. % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1640) all_8_17 = e2 & ~ (all_8_18 = e3) % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1640) implies: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1641) all_8_17 = e2 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (1641) imply: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1642) op(e3, all_4_7) = e2 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1643) all_6_4 = e2 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (474), (1643) imply: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1644) all_4_20 = e2 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (514), (1644) imply: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1645) $false % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1645) is inconsistent. % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1646) all_6_4 = e4 | all_6_4 = e3 | all_6_4 = e1 | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_4 = e0 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (170) gives: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1647) all_6_20 = e2 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (1647) imply: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1648) all_4_4 = e2 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (506), (1648) imply: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1649) $false % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1649) is inconsistent. % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1650) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e1 | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_20 = e0 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1651) all_6_9 = e2 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (475), (1651) imply: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1652) all_4_21 = e2 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1315), (1652) imply: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1653) $false % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1653) is inconsistent. % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1654) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e1 | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_9 = e0 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1655) all_6_2 = e2 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (1655) imply: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1656) all_4_10 = e2 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (510), (1656) imply: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1657) $false % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1657) is inconsistent. % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1658) ~ (all_6_2 = e2) % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1659) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_2 = e0 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1660) all_6_11 = e2 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (456), (1417), (1660) are inconsistent by % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #159. % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1661) all_6_11 = e4 | all_6_11 = e3 | all_6_11 = e1 | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_11 = e0 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1662) (all_8_39 = e4 & ~ (all_8_40 = e1)) | (all_8_42 = % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ~ (all_8_43 = e1)) % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1662) gives: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1663) all_8_39 = e4 & ~ (all_8_40 = e1) % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1663) implies: % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1664) all_8_39 = e4 % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (1664) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1665) op(e1, all_4_15) = e4 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1666) (all_8_1 = e3 & ~ (all_8_2 = e4)) | (all_8_4 = e2 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_5 = e4)) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1666) gives: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1667) all_8_1 = e3 & ~ (all_8_2 = e4) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (15), (27), (34), (35), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (56), (57), (58), (80), (81), (82), (85), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (99), (102), (103), (106), (108), (121), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (131), (140), (180), (182), (285), (289), (293), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294), (296), (301), (303), (307), (309), (316), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318), (325), (334), (373), (382), (385), (388), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391), (394), (398), (450), (453), (454), (456), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (466), (468), (474), (475), (496), (500), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512), (518), (521), (522), (527), (533), (538), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542), (545), (552), (577), (588), (590), (601), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (603), (613), (1286), (1302), (1305), (1326), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1397), (1398), (1400), (1415), (1437), (1646), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1650), (1654), (1659), (1661), (1667), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #77. % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1668) all_8_4 = e2 & ~ (all_8_5 = e4) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1668) implies: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1669) all_8_4 = e2 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (1669) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1670) op(e4, all_4_2) = e2 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1671) all_6_5 = e2 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (450), (500), (1671) are inconsistent by sub-proof % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #153. % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1672) ~ (all_6_5 = e2) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1673) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_5 = e0 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1674) all_6_3 = e2 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (468), (512), (1674) are inconsistent by sub-proof % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #152. % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1675) ~ (all_6_3 = e2) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1676) all_6_3 = e4 | all_6_3 = e3 | all_6_3 = e1 | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_3 = e0 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1677) all_10_4 = e1 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (1677) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1678) all_4_10 = e1 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1678) implies: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1679) all_4_10 = e1 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (1679) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1680) ~ (all_4_14 = e1) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1680) implies: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1681) ~ (all_4_14 = e1) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (57), (1679) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1682) ~ (all_4_15 = e1) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1682) implies: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1683) ~ (all_4_15 = e1) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1400) gives: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1684) all_6_22 = e4 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (466), (1684) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1685) all_4_14 = e4 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1685) implies: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1686) all_4_14 = e4 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (89), (1686) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1687) ~ (all_4_4 = e4) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1398), (1686) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1688) op(e2, e4) = e0 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1650) gives: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1689) all_6_20 = e4 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (1689) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1690) all_4_4 = e4 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1687), (1690) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1691) $false % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1691) is inconsistent. % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1692) all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1692) gives: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1693) all_6_20 = e1 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (1693) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1694) all_4_4 = e1 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1305), (1694) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1695) $false % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1695) is inconsistent. % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1696) all_6_20 = e3 | all_6_20 = e0 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1697) all_10_20 = e3 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (1697) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1698) all_4_4 = e3 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1698) implies: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1699) all_4_4 = e3 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (106), (1699) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1700) ~ (all_4_1 = e3) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e0, % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e2, simplifying with (131), (1688) gives: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1701) all_4_2 = e0 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (1701) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1702) ~ (all_4_1 = e0) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (99), (1701) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1703) ~ (all_4_7 = e0) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1703) implies: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1704) ~ (all_4_7 = e0) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1705) all_10_1 = e0 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (394), (1705) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1706) all_4_5 = e0 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (81), (85), (136), (296), (388), (450), (456), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468), (512), (518), (538), (553), (603), (1292), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1302), (1642), (1661), (1665), (1673), (1676), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1683), (1700), (1702), (1706), (function-axioms) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #68. % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1707) ~ (all_10_1 = e0) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (1707) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1708) ~ (all_4_5 = e0) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (454), (456), (518), (601), (603), (1286), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1326), (1661), (1704), (1708) are inconsistent by % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #109. % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1709) ~ (all_10_20 = e3) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (334), (1709) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1710) ~ (all_4_4 = e3) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (453), (588), (1696), (1710) are inconsistent by % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #122. % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1711) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (466), (527), (533), (1681), (1711) are % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #130. % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1712) ~ (all_10_4 = e1) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1713) all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_22 = e1 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (1712) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1714) ~ (all_4_10 = e1) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (27), (34), (35), (57), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (81), (82), (88), (89), (102), (103), (106), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (137), (286), (293), (294), (296), (303), (307), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309), (313), (316), (318), (325), (328), (334), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345), (351), (361), (367), (373), (382), (385), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388), (391), (394), (398), (450), (453), (454), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (475), (496), (500), (516), (521), (522), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527), (533), (549), (588), (590), (601), (613), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1286), (1302), (1326), (1330), (1334), (1398), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1415), (1420), (1437), (1650), (1654), (1659), % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1670), (1673), (1713), (1714), (function-axioms) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #71. % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1715) (all_8_7 = e1 & ~ (all_8_8 = e4)) | (all_8_10 = % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_11 = e4)) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1715) gives: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1716) all_8_7 = e1 & ~ (all_8_8 = e4) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1716) implies: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1717) ~ (all_8_8 = e4) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1320), (1717) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1718) $false % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1718) is inconsistent. % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1719) all_8_10 = e0 & ~ (all_8_11 = e4) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1719) implies: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1720) all_8_10 = e0 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (1720) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1721) op(e4, all_4_4) = e0 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1722) all_6_5 = e2 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (450), (500), (1722) are inconsistent by sub-proof % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #153. % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1723) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_5 = e0 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1724) all_6_3 = e2 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (468), (512), (1724) are inconsistent by sub-proof % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #152. % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1725) ~ (all_6_3 = e2) % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1726) all_6_3 = e4 | all_6_3 = e3 | all_6_3 = e1 | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_3 = e0 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1727) all_10_4 = e1 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (1727) imply: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1728) all_4_10 = e1 % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1728) implies: % 73.14/10.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1729) all_4_10 = e1 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (1729) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1730) ~ (all_4_14 = e1) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1730) implies: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1731) ~ (all_4_14 = e1) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (57), (1729) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1732) ~ (all_4_15 = e1) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1732) implies: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1733) ~ (all_4_15 = e1) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1400) gives: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1734) all_6_22 = e4 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (466), (1734) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1735) all_4_14 = e4 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1735) implies: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1736) all_4_14 = e4 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (89), (1736) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1737) ~ (all_4_4 = e4) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1398), (1736) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1738) op(e2, e4) = e0 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1650) gives: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1739) all_6_20 = e4 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (1739) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1740) all_4_4 = e4 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1737), (1740) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1741) $false % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1741) is inconsistent. % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1742) all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1742) gives: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1743) all_6_20 = e1 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (1743) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1744) all_4_4 = e1 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1305), (1744) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1745) $false % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1745) is inconsistent. % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1746) all_6_20 = e3 | all_6_20 = e0 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1747) all_10_20 = e3 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (1747) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1748) all_4_4 = e3 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1748) implies: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1749) all_4_4 = e3 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (106), (1749) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1750) ~ (all_4_1 = e3) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1721), (1749) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1751) op(e4, e3) = e0 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e0, % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e2, simplifying with (131), (1738) gives: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1752) all_4_2 = e0 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_5, e0, % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e4, simplifying with (140), (1751) gives: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1753) all_4_5 = e0 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (1752) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1754) ~ (all_4_1 = e0) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (81), (85), (136), (296), (388), (450), (456), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468), (512), (518), (538), (553), (603), (1292), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1302), (1642), (1661), (1665), (1723), (1726), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1733), (1750), (1753), (1754), (function-axioms) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #68. % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1755) ~ (all_10_20 = e3) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (334), (1755) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1756) ~ (all_4_4 = e3) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (453), (588), (1746), (1756) are inconsistent by % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #122. % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1757) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (466), (527), (533), (1731), (1757) are % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #130. % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1758) ~ (all_10_4 = e1) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (15), (27), (34), (102), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (103), (106), (286), (293), (303), (307), (316), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318), (325), (334), (373), (382), (385), (391), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394), (398), (450), (453), (461), (475), (496), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521), (522), (550), (588), (590), (601), (613), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1286), (1302), (1305), (1334), (1415), (1437), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1650), (1654), (1659), (1721), (1723), (1758), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #70. % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1759) all_8_42 = e3 & ~ (all_8_43 = e1) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1759) implies: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1760) all_8_42 = e3 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (572), (1760) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1761) op(e1, all_4_16) = e3 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1762) (all_8_1 = e3 & ~ (all_8_2 = e4)) | (all_8_4 = e2 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_5 = e4)) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1762) gives: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1763) all_8_1 = e3 & ~ (all_8_2 = e4) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (15), (27), (34), (35), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (56), (57), (58), (80), (81), (82), (85), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (99), (102), (103), (106), (108), (121), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (131), (140), (180), (182), (285), (289), (293), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294), (296), (301), (303), (307), (309), (316), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318), (325), (334), (373), (382), (385), (388), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391), (394), (398), (450), (453), (454), (456), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (466), (468), (474), (475), (496), (500), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512), (518), (521), (522), (527), (533), (538), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542), (545), (552), (577), (588), (590), (601), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (603), (613), (1286), (1302), (1305), (1326), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1397), (1398), (1400), (1415), (1437), (1646), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1650), (1654), (1659), (1661), (1763), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #77. % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1764) all_8_4 = e2 & ~ (all_8_5 = e4) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1764) implies: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1765) all_8_4 = e2 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (1765) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1766) op(e4, all_4_2) = e2 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1767) all_6_5 = e2 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (450), (500), (1767) are inconsistent by sub-proof % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #153. % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1768) ~ (all_6_5 = e2) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1769) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_5 = e0 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1770) all_10_4 = e1 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (1770) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1771) all_4_10 = e1 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1771) implies: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1772) all_4_10 = e1 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (1772) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1773) ~ (all_4_14 = e1) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1773) implies: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1774) ~ (all_4_14 = e1) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1400) gives: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1775) all_6_22 = e4 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (466), (1775) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1776) all_4_14 = e4 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1776) implies: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1777) all_4_14 = e4 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (89), (1777) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1778) ~ (all_4_4 = e4) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1398), (1777) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1779) op(e2, e4) = e0 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (1777) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1780) op(e0, e4) = all_8_37 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1650) gives: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1781) all_6_20 = e4 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (1781) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1782) all_4_4 = e4 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1778), (1782) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1783) $false % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1783) is inconsistent. % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1784) all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1784) gives: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1785) all_6_20 = e1 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (1785) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1786) all_4_4 = e1 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1305), (1786) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1787) $false % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1787) is inconsistent. % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1788) all_6_20 = e3 | all_6_20 = e0 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1789) all_10_20 = e3 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (1789) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1790) all_4_4 = e3 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1790) implies: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1791) all_4_4 = e3 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (1791) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1792) op(e0, e4) = e3 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_8_37, % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e0, simplifying with (1780), (1792) gives: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1793) all_8_37 = e3 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e0, % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e2, simplifying with (131), (1779) gives: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1794) all_4_2 = e0 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (99), (1794) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1795) ~ (all_4_7 = e0) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1795) implies: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1796) ~ (all_4_7 = e0) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1797) all_10_1 = e0 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (394), (1797) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1798) all_4_5 = e0 % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (81), (293), (325), (373), (388), (496), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508), (535), (590), (1319), (1415), (1761), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1798), (function-axioms) are inconsistent by % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #67. % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1799) ~ (all_10_1 = e0) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (1799) imply: % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1800) ~ (all_4_5 = e0) % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (454), (456), (518), (601), (603), (1286), % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1326), (1661), (1796), (1800) are inconsistent by % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #109. % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1801) ~ (all_10_20 = e3) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (334), (1801) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1802) ~ (all_4_4 = e3) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (453), (588), (1788), (1802) are inconsistent by % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #122. % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1803) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (466), (527), (533), (1774), (1803) are % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #130. % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1804) ~ (all_10_4 = e1) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1805) all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_22 = e1 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (1804) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1806) ~ (all_4_10 = e1) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (27), (34), (35), (57), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (81), (82), (88), (89), (102), (103), (106), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (137), (286), (293), (294), (296), (303), (307), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309), (313), (316), (318), (325), (328), (334), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345), (351), (361), (367), (373), (382), (385), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388), (391), (394), (398), (450), (453), (454), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (475), (496), (500), (516), (521), (522), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527), (533), (549), (588), (590), (601), (613), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1286), (1302), (1326), (1330), (1334), (1398), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1415), (1420), (1437), (1650), (1654), (1659), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1766), (1769), (1805), (1806), (function-axioms) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #71. % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1807) (all_8_7 = e1 & ~ (all_8_8 = e4)) | (all_8_10 = % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_11 = e4)) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1807) gives: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1808) all_8_7 = e1 & ~ (all_8_8 = e4) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1808) implies: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1809) ~ (all_8_8 = e4) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1320), (1809) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1810) $false % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1810) is inconsistent. % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1811) all_8_10 = e0 & ~ (all_8_11 = e4) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1811) implies: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1812) all_8_10 = e0 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (1812) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1813) op(e4, all_4_4) = e0 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1814) all_6_5 = e2 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (450), (500), (1814) are inconsistent by sub-proof % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #153. % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1815) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_5 = e0 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1816) all_10_4 = e1 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (1816) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1817) all_4_10 = e1 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1817) implies: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1818) all_4_10 = e1 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (1818) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1819) ~ (all_4_14 = e1) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1819) implies: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1820) ~ (all_4_14 = e1) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1400) gives: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1821) all_6_22 = e4 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (466), (1821) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1822) all_4_14 = e4 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1822) implies: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1823) all_4_14 = e4 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (89), (1823) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1824) ~ (all_4_4 = e4) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (1823) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1825) op(e0, e4) = all_8_37 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1650) gives: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1826) all_6_20 = e4 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (1826) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1827) all_4_4 = e4 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1824), (1827) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1828) $false % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1828) is inconsistent. % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1829) all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1829) gives: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1830) all_6_20 = e1 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (1830) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1831) all_4_4 = e1 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1305), (1831) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1832) $false % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1832) is inconsistent. % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1833) all_6_20 = e3 | all_6_20 = e0 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1834) all_10_20 = e3 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (1834) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1835) all_4_4 = e3 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1835) implies: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1836) all_4_4 = e3 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1813), (1836) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1837) op(e4, e3) = e0 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (1836) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1838) op(e0, e4) = e3 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_8_37, % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e0, simplifying with (1825), (1838) gives: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1839) all_8_37 = e3 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_5, e0, % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e4, simplifying with (140), (1837) gives: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1840) all_4_5 = e0 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (81), (293), (325), (373), (388), (496), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508), (535), (590), (1319), (1415), (1761), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1840), (function-axioms) are inconsistent by % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #67. % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1841) ~ (all_10_20 = e3) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (334), (1841) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1842) ~ (all_4_4 = e3) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (453), (588), (1833), (1842) are inconsistent by % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #122. % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1843) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (466), (527), (533), (1820), (1843) are % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #130. % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1844) ~ (all_10_4 = e1) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (15), (27), (34), (102), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (103), (106), (286), (293), (303), (307), (316), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318), (325), (334), (373), (382), (385), (391), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394), (398), (450), (453), (461), (475), (496), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521), (522), (550), (588), (590), (601), (613), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1286), (1302), (1305), (1334), (1415), (1437), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1650), (1654), (1659), (1813), (1815), (1844), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #70. % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1845) (all_8_45 = e2 & ~ (all_8_46 = e1)) | (all_8_49 = % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_50 = e1)) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1845) gives: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1846) all_8_45 = e2 & ~ (all_8_46 = e1) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1846) implies: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1847) all_8_45 = e2 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1440), (1847) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1848) e2 = e0 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (1848) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1849) $false % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1849) is inconsistent. % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1850) all_8_49 = e0 & ~ (all_8_50 = e1) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1850) implies: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1851) all_8_49 = e0 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (574), (1851) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1852) op(e1, all_4_19) = e0 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1853) (all_8_1 = e3 & ~ (all_8_2 = e4)) | (all_8_4 = e2 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_5 = e4)) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1853) gives: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1854) all_8_1 = e3 & ~ (all_8_2 = e4) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (15), (27), (34), (35), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (56), (57), (58), (80), (81), (82), (85), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (99), (102), (103), (106), (108), (121), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (131), (140), (180), (182), (285), (289), (293), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294), (296), (301), (303), (307), (309), (316), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318), (325), (334), (373), (382), (385), (388), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391), (394), (398), (450), (453), (454), (456), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (466), (468), (474), (475), (496), (500), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512), (518), (521), (522), (527), (533), (538), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542), (545), (552), (577), (588), (590), (601), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (603), (613), (1286), (1302), (1305), (1326), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1397), (1398), (1400), (1415), (1437), (1646), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1650), (1654), (1659), (1661), (1854), % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #77. % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1855) all_8_4 = e2 & ~ (all_8_5 = e4) % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1855) implies: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1856) all_8_4 = e2 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (1856) imply: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1857) op(e4, all_4_2) = e2 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1858) all_6_5 = e2 % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (450), (500), (1858) are inconsistent by sub-proof % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #153. % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1859) ~ (all_6_5 = e2) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1860) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_5 = e0 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1861) all_10_4 = e1 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (58), (283), (325), (328), (334), (391), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466), (510), (522), (527), (533), (585), (1305), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1400), (1403), (1852), (1861), (function-axioms) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #66. % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1862) ~ (all_10_4 = e1) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1863) all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_22 = e1 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (1862) imply: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1864) ~ (all_4_10 = e1) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (27), (34), (35), (57), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (81), (82), (88), (89), (102), (103), (106), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (137), (286), (293), (294), (296), (303), (307), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309), (313), (316), (318), (325), (328), (334), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345), (351), (361), (367), (373), (382), (385), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388), (391), (394), (398), (450), (453), (454), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (475), (496), (500), (516), (521), (522), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527), (533), (549), (588), (590), (601), (613), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1286), (1302), (1326), (1330), (1334), (1398), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1415), (1420), (1437), (1650), (1654), (1659), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1857), (1860), (1863), (1864), (function-axioms) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #71. % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1865) (all_8_7 = e1 & ~ (all_8_8 = e4)) | (all_8_10 = % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_11 = e4)) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1865) gives: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1866) all_8_7 = e1 & ~ (all_8_8 = e4) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1866) implies: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1867) ~ (all_8_8 = e4) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1320), (1867) imply: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1868) $false % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1868) is inconsistent. % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1869) all_8_10 = e0 & ~ (all_8_11 = e4) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1869) implies: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1870) all_8_10 = e0 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (1870) imply: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1871) op(e4, all_4_4) = e0 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1872) all_6_5 = e2 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (450), (500), (1872) are inconsistent by sub-proof % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #153. % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1873) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_5 = e0 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1874) all_10_4 = e1 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (58), (283), (325), (328), (334), (391), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466), (510), (522), (527), (533), (585), (1305), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1400), (1403), (1852), (1874), (function-axioms) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #66. % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1875) ~ (all_10_4 = e1) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (15), (27), (34), (102), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (103), (106), (286), (293), (303), (307), (316), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318), (325), (334), (373), (382), (385), (391), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394), (398), (450), (453), (461), (475), (496), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521), (522), (550), (588), (590), (601), (613), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1286), (1302), (1305), (1334), (1415), (1437), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1650), (1654), (1659), (1871), (1873), (1875), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #70. % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1876) (all_8_20 = e1 & ~ (all_8_21 = e3)) | (all_8_23 = % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_24 = e3)) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1876) gives: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1877) all_8_20 = e1 & ~ (all_8_21 = e3) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1877) implies: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1878) ~ (all_8_21 = e3) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1322), (1878) imply: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1879) $false % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1879) is inconsistent. % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1880) all_8_23 = e0 & ~ (all_8_24 = e3) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1880) implies: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1881) all_8_23 = e0 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1442), (1881) imply: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1882) e2 = e0 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1882) implies: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1883) e2 = e0 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (1883) imply: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1884) $false % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1884) is inconsistent. % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | (1885) all_10_15 = e2 | all_10_23 = e2 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (325), (496), (1405), (1885) are % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #87. % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | (1886) ~ (all_6_21 = e2) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | (1887) all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e1 | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | all_6_21 = e0 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | REDUCE: (460), (1886) imply: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | (1888) ~ (all_4_9 = e2) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | (1889) all_10_1 = e2 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (394), (1889) imply: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | (1890) all_4_5 = e2 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (508), (1890) imply: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | (1891) $false % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1891) is inconsistent. % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | (1892) all_10_3 = e2 | all_10_7 = e2 | all_10_13 = e2 | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | all_10_21 = e2 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1892) gives: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | (1893) all_10_3 = e2 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (600), (1893) are inconsistent by sub-proof % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | #65. % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | (1894) all_10_7 = e2 | all_10_13 = e2 | all_10_21 = e2 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1894) gives: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | (1895) all_10_7 = e2 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (497), (1895) imply: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | (1896) all_4_7 = e2 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (1896) imply: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | (1897) ~ (all_4_17 = e2) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1897) implies: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | (1898) ~ (all_4_17 = e2) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (58), (64), (118), (183), (295), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | (301), (303), (325), (328), (345), (357), (361), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | (373), (388), (391), (460), (461), (466), (496), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | (510), (512), (521), (522), (527), (533), (577), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | (589), (607), (1288), (1330), (1334), (1397), % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | (1400), (1887), (1898), (function-axioms) are % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #125. % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | (1899) all_10_13 = e2 | all_10_21 = e2 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (331), (348), (1264), (1888), (1899) are % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #64. % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | End of split % 73.14/10.76 | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | Case 2: % 73.14/10.76 | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | (1900) ~ (all_6_7 = e2) % 73.14/10.76 | | | | | | | | | | | | | | | | | (1901) all_6_7 = e4 | all_6_7 = e3 | all_6_7 = e1 | % 73.14/10.76 | | | | | | | | | | | | | | | | | all_6_7 = e0 % 73.14/10.76 | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | REDUCE: (462), (1900) imply: % 73.14/10.76 | | | | | | | | | | | | | | | | | (1902) ~ (all_4_11 = e2) % 73.14/10.76 | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | BETA: splitting (1901) gives: % 73.14/10.76 | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.76 | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | (1903) all_6_7 = e4 % 73.14/10.76 | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (462), (1903) imply: % 73.14/10.76 | | | | | | | | | | | | | | | | | | (1904) all_4_11 = e4 % 73.14/10.76 | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | SIMP: (1904) implies: % 73.14/10.76 | | | | | | | | | | | | | | | | | | (1905) all_4_11 = e4 % 73.14/10.76 | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (498), (1905) imply: % 73.14/10.76 | | | | | | | | | | | | | | | | | | (1906) all_10_5 = e4 % 73.14/10.76 | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | REDUCE: (61), (1905) imply: % 73.14/10.76 | | | | | | | | | | | | | | | | | | (1907) ~ (all_4_10 = e4) % 73.14/10.76 | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | REDUCE: (51), (1905) imply: % 73.14/10.76 | | | | | | | | | | | | | | | | | | (1908) ~ (all_4_21 = e4) % 73.14/10.76 | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | SIMP: (1908) implies: % 73.14/10.76 | | | | | | | | | | | | | | | | | | (1909) ~ (all_4_21 = e4) % 73.14/10.76 | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 73.14/10.76 | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | (1910) all_6_9 = e2 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (475), (1315), (1910) are inconsistent by % 73.14/10.76 | | | | | | | | | | | | | | | | | | | sub-proof #158. % 73.14/10.76 | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | (1911) ~ (all_6_9 = e2) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | (1912) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e1 | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | all_6_9 = e0 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | BETA: splitting (302) gives: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | (1913) all_10_4 = e2 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (1913) imply: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | (1914) all_4_10 = e2 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | REDUCE: (510), (1914) imply: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | (1915) $false % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | CLOSE: (1915) is inconsistent. % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | (1916) ~ (all_10_4 = e2) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | (1917) all_10_5 = e2 | all_10_8 = e2 | all_10_14 = e2 | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | all_10_22 = e2 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1917) gives: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | (1918) all_10_5 = e2 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1906), (1918) imply: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | (1919) e4 = e2 % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (1919) imply: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | (1920) $false % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1920) is inconsistent. % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | (1921) ~ (all_10_5 = e2) % 73.14/10.76 | | | | | | | | | | | | | | | | | | | | | (1922) all_10_8 = e2 | all_10_14 = e2 | all_10_22 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | (1923) all_10_2 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (382), (1923) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | (1924) all_4_1 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (500), (1924) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | (1925) $false % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1925) is inconsistent. % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | (1926) all_10_3 = e2 | all_10_5 = e2 | all_10_10 = e2 | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | all_10_17 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1926) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | (1927) all_10_3 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (600), (1927) are inconsistent by sub-proof % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | #65. % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | (1928) all_10_5 = e2 | all_10_10 = e2 | all_10_17 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1922) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | (1929) all_10_8 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (1929) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | (1930) e3 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (1930) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | (1931) $false % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1931) is inconsistent. % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | (1932) all_10_14 = e2 | all_10_22 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | (1933) all_6_2 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (1933) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | (1934) all_4_10 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (510), (1934) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | (1935) $false % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1935) is inconsistent. % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | (1936) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | all_6_2 = e0 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1928) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (1937) all_10_5 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1906), (1937) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (1938) e4 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (1938) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (1939) $false % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1939) is inconsistent. % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (1940) all_10_10 = e2 | all_10_17 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1940) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1941) all_10_10 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (1941) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1942) all_4_16 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (1942) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1943) ~ (all_4_21 = e2) % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1932) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1944) all_10_14 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (345), (1944) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1945) e2 = e0 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (1945) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1946) $false % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1946) is inconsistent. % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1947) all_10_22 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (1947) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1948) all_4_14 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (64), (1948) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1949) ~ (all_4_9 = e2) % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1950) all_6_21 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (460), (1949), (1950) are inconsistent by % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #157. % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1951) all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e1 | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_21 = e0 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1936) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1952) all_6_2 = e4 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (1907), (1952) are inconsistent by % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #164. % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1953) all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1912) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1954) all_6_9 = e4 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (475), (1909), (1954) are inconsistent by % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #114. % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1955) all_6_9 = e3 | all_6_9 = e1 | all_6_9 = e0 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1955) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1956) all_6_9 = e1 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (475), (613), (1956) are inconsistent by sub-proof % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #113. % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1957) all_6_9 = e3 | all_6_9 = e0 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1957) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1958) all_6_9 = e3 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (475), (1958) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1959) all_4_21 = e3 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1959) implies: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1960) all_4_21 = e3 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (1960) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1961) all_10_17 = e3 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (27), (1960) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1962) ~ (all_4_20 = e3) % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1963) all_10_2 = e0 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (382), (1963) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1964) all_4_1 = e0 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (1964) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1965) ~ (all_4_2 = e0) % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1965) implies: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1966) ~ (all_4_2 = e0) % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (106), (1964) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1967) ~ (all_4_4 = e0) % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (1964) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1968) op(e4, e0) = all_8_1 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1969) all_10_4 = e1 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (1969) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1970) all_4_10 = e1 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (57), (1970) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1971) ~ (all_4_15 = e1) % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1971) implies: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1972) ~ (all_4_15 = e1) % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (1970) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1973) ~ (all_4_20 = e1) % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1973) implies: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1974) ~ (all_4_20 = e1) % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1975) all_6_10 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (451), (1975) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1976) all_4_2 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (502), (1976) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1977) $false % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1977) is inconsistent. % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1978) all_6_10 = e4 | all_6_10 = e3 | all_6_10 = e1 | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_10 = e0 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1979) all_6_4 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (474), (514), (1979) are inconsistent by sub-proof % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #154. % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1980) all_6_4 = e4 | all_6_4 = e3 | all_6_4 = e1 | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_4 = e0 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1951) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1981) all_6_21 = e4 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (460), (1981) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1982) all_4_9 = e4 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (1982) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1983) op(e0, e3) = e4 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1980) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1984) all_6_4 = e4 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (474), (1984) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1985) all_4_20 = e4 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1985) implies: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1986) all_4_20 = e4 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (80), (1986) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1987) ~ (all_4_5 = e4) % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (1986) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1988) op(e4, e0) = e4 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1989) all_10_1 = e0 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (394), (1989) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1990) all_4_5 = e0 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (170) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1991) all_6_20 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (1991) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1992) all_4_4 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1992) implies: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1993) all_4_4 = e2 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (506), (1993) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1994) $false % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1994) is inconsistent. % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1995) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e1 | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_20 = e0 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (300) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1996) all_10_6 = e4 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (367), (1996) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1997) all_4_2 = e4 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (100), (1997) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1998) ~ (all_4_4 = e4) % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1998) implies: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1999) ~ (all_4_4 = e4) % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (560), (1997) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2000) op(e2, e4) = all_8_5 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (1997) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2001) op(e2, e4) = e4 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2002) all_10_0 = e3 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (398), (2002) are inconsistent by sub-proof % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #104. % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2003) all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_16 = e3 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1995) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2004) all_6_20 = e4 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (453), (1999), (2004) are inconsistent by % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #74. % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2005) all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2005) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2006) all_6_20 = e1 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (2006) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2007) all_4_4 = e1 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1305), (2007) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2008) $false % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2008) is inconsistent. % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2009) ~ (all_6_20 = e1) % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2010) all_6_20 = e3 | all_6_20 = e0 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2011) all_10_20 = e3 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (2011) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2012) all_4_4 = e3 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (576), (2012) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2013) op(e0, e3) = all_8_11 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2003) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2014) all_10_1 = e3 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1989), (2014) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2015) e3 = e0 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2015) implies: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2016) e3 = e0 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (525), (2016) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2017) $false % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2017) is inconsistent. % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2018) all_10_4 = e3 | all_10_9 = e3 | all_10_16 = e3 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2019) all_10_9 = e3 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (388), (2019) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2020) all_4_15 = e3 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1323), (2020) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2021) all_8_7 = e3 % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (538), (2020) imply: % 73.14/10.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2022) ~ (e4 = e3) % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, all_8_11, % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (1983), (2013) gives: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2023) all_8_11 = e4 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, all_8_5, % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e2, simplifying with (2000), (2001) gives: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2024) all_8_5 = e4 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, all_8_1, % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e4, simplifying with (1968), (1988) gives: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2025) all_8_1 = e4 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2026) (all_8_1 = e3 & ~ (all_8_2 = e4)) | (all_8_4 = e2 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_5 = e4)) % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2026) gives: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2027) all_8_1 = e3 & ~ (all_8_2 = e4) % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2027) implies: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2028) all_8_1 = e3 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2025), (2028) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2029) e4 = e3 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2029) implies: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2030) e4 = e3 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (2030) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2031) $false % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2031) is inconsistent. % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2032) all_8_4 = e2 & ~ (all_8_5 = e4) % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2032) implies: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2033) ~ (all_8_5 = e4) % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2024), (2033) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2034) $false % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2034) is inconsistent. % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2035) (all_8_7 = e1 & ~ (all_8_8 = e4)) | (all_8_10 = % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_11 = e4)) % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2035) gives: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2036) all_8_7 = e1 & ~ (all_8_8 = e4) % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2021), (2036) are inconsistent by sub-proof % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #101. % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2037) all_8_10 = e0 & ~ (all_8_11 = e4) % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2037) implies: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2038) ~ (all_8_11 = e4) % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2023), (2038) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2039) $false % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2039) is inconsistent. % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2040) ~ (all_10_9 = e3) % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (388), (2040) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2041) ~ (all_4_15 = e3) % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2018) gives: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2042) all_10_4 = e3 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1969), (2042) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2043) e3 = e1 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (2043) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2044) $false % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2044) is inconsistent. % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2045) all_10_9 = e3 | all_10_16 = e3 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (385), (388), (1962), (2041), (2045) are % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #63. % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2046) ~ (all_10_20 = e3) % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (334), (2046) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2047) ~ (all_4_4 = e3) % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (453), (588), (2010), (2047) are inconsistent by % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #122. % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2048) ~ (all_10_6 = e4) % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (2048) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2049) ~ (all_4_2 = e4) % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (451), (515), (1303), (1966), (1978), (2049) are % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #61. % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2050) ~ (all_10_1 = e0) % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (2050) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2051) ~ (all_4_5 = e0) % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (454), (601), (1286), (1326), (1987), (2051) are % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #134. % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2052) all_6_4 = e3 | all_6_4 = e1 | all_6_4 = e0 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (474), (591), (1962), (1974), (2052) are % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #95. % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2053) all_6_21 = e3 | all_6_21 = e1 | all_6_21 = e0 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (460), (589), (607), (1288), (2053) are % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #126. % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2054) ~ (all_10_4 = e1) % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (2054) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2055) ~ (all_4_10 = e1) % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (521), (522), (1953), (2055) are % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #162. % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2056) all_10_3 = e0 | all_10_5 = e0 | all_10_10 = e0 | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_17 = e0 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2056) gives: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2057) all_10_3 = e0 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (600), (2057) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2058) e1 = e0 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (2058) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2059) $false % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2059) is inconsistent. % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2060) all_10_5 = e0 | all_10_10 = e0 | all_10_17 = e0 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2060) gives: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2061) all_10_5 = e0 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1906), (2061) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2062) e4 = e0 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (535), (2062) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2063) $false % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2063) is inconsistent. % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2064) all_10_10 = e0 | all_10_17 = e0 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2064) gives: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2065) all_10_10 = e0 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1941), (2065) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2066) e2 = e0 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (2066) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2067) $false % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2067) is inconsistent. % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2068) all_10_17 = e0 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1961), (2068) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2069) e3 = e0 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (525), (2069) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2070) $false % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2070) is inconsistent. % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2071) all_6_9 = e0 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (475), (592), (2071) are inconsistent by sub-proof % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #112. % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2072) all_10_17 = e2 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (2072) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2073) all_4_21 = e2 % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1315), (2073) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2074) $false % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2074) is inconsistent. % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | (2075) all_6_7 = e3 | all_6_7 = e1 | all_6_7 = e0 % 73.14/10.78 | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | | REF_CLOSE: (462), (523), (524), (609), (2075) are % 73.14/10.78 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #91. % 73.14/10.78 | | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | (2076) ~ (all_6_19 = e2) % 73.14/10.78 | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | REDUCE: (479), (2076) imply: % 73.14/10.78 | | | | | | | | | | | | | | | (2077) ~ (all_4_23 = e2) % 73.14/10.78 | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | REF_CLOSE: (10), (337), (496), (1296), (2077) are % 73.14/10.78 | | | | | | | | | | | | | | | inconsistent by sub-proof #60. % 73.14/10.78 | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | (2078) ~ (all_6_15 = e1) % 73.14/10.78 | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | REDUCE: (452), (2078) imply: % 73.14/10.78 | | | | | | | | | | | | | | (2079) ~ (all_4_3 = e1) % 73.14/10.78 | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | BETA: splitting (1296) gives: % 73.14/10.78 | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | Case 1: % 73.14/10.78 | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | (2080) all_10_15 = e2 % 73.14/10.78 | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | COMBINE_EQS: (496), (2080) imply: % 73.14/10.78 | | | | | | | | | | | | | | | (2081) e4 = e2 % 73.14/10.78 | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | REDUCE: (10), (2081) imply: % 73.14/10.78 | | | | | | | | | | | | | | | (2082) $false % 73.14/10.78 | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | CLOSE: (2082) is inconsistent. % 73.14/10.78 | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | (2083) all_10_19 = e2 % 73.14/10.78 | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | COMBINE_EQS: (337), (2083) imply: % 73.14/10.78 | | | | | | | | | | | | | | | (2084) all_4_23 = e2 % 73.14/10.78 | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 73.14/10.78 | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | Case 1: % 73.14/10.78 | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | (2085) all_10_12 = e1 % 73.14/10.78 | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | REF_CLOSE: (351), (2079), (2085) are inconsistent by % 73.14/10.78 | | | | | | | | | | | | | | | | sub-proof #59. % 73.14/10.78 | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | (2086) all_10_13 = e1 | all_10_14 = e1 | all_10_15 = e1 | % 73.14/10.78 | | | | | | | | | | | | | | | | all_10_19 = e1 % 73.14/10.78 | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | BETA: splitting (2086) gives: % 73.14/10.78 | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | Case 1: % 73.14/10.78 | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | (2087) all_10_13 = e1 % 73.14/10.78 | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | COMBINE_EQS: (1284), (2087) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | (2088) e3 = e1 % 73.14/10.78 | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | SIMP: (2088) implies: % 73.14/10.78 | | | | | | | | | | | | | | | | | (2089) e3 = e1 % 73.14/10.78 | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | REDUCE: (7), (2089) imply: % 73.14/10.78 | | | | | | | | | | | | | | | | | (2090) $false % 73.14/10.78 | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | CLOSE: (2090) is inconsistent. % 73.14/10.78 | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | (2091) all_10_14 = e1 | all_10_15 = e1 | all_10_19 = e1 % 73.14/10.78 | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (345), (496), (2083), (2091) are % 73.14/10.78 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #58. % 73.14/10.78 | | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | Case 2: % 73.14/10.78 | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | (2092) all_6_16 = e0 % 73.14/10.78 | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | COMBINE_EQS: (458), (2092) imply: % 73.14/10.78 | | | | | | | | | | | (2093) all_4_8 = e0 % 73.14/10.78 | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | SIMP: (2093) implies: % 73.14/10.78 | | | | | | | | | | | (2094) all_4_8 = e0 % 73.14/10.78 | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | REDUCE: (519), (2094) imply: % 73.14/10.78 | | | | | | | | | | | (2095) $false % 73.14/10.78 | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | | CLOSE: (2095) is inconsistent. % 73.14/10.78 | | | | | | | | | | | % 73.14/10.78 | | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | | % 73.14/10.78 | | | | | | | | | End of split % 73.14/10.78 | | | | | | | | | % 73.14/10.78 | | | | | | | | End of split % 73.14/10.78 | | | | | | | | % 73.14/10.78 | | | | | | | End of split % 73.14/10.78 | | | | | | | % 73.14/10.78 | | | | | | End of split % 73.14/10.78 | | | | | | % 73.14/10.78 | | | | | End of split % 73.14/10.78 | | | | | % 73.14/10.78 | | | | End of split % 73.14/10.78 | | | | % 73.14/10.78 | | | Case 2: % 73.14/10.78 | | | | % 73.14/10.79 | | | | (2096) all_8_67 = e1 | all_8_68 = e1 | all_8_69 = e1 % 73.14/10.79 | | | | % 73.14/10.79 | | | | BETA: splitting (2096) gives: % 73.14/10.79 | | | | % 73.14/10.79 | | | | Case 1: % 73.14/10.79 | | | | | % 73.14/10.79 | | | | | (2097) all_8_67 = e1 % 73.14/10.79 | | | | | % 73.14/10.79 | | | | | REF_CLOSE: (7), (416), (2097) are inconsistent by sub-proof #57. % 73.14/10.79 | | | | | % 73.14/10.79 | | | | Case 2: % 73.14/10.79 | | | | | % 73.14/10.79 | | | | | (2098) all_8_68 = e1 | all_8_69 = e1 % 73.14/10.79 | | | | | % 73.14/10.79 | | | | | BETA: splitting (2098) gives: % 73.14/10.79 | | | | | % 73.14/10.79 | | | | | Case 1: % 73.14/10.79 | | | | | | % 73.14/10.79 | | | | | | (2099) all_8_68 = e1 % 73.14/10.79 | | | | | | % 73.14/10.79 | | | | | | REF_CLOSE: (9), (339), (2099) are inconsistent by sub-proof #56. % 73.14/10.79 | | | | | | % 73.14/10.79 | | | | | Case 2: % 73.14/10.79 | | | | | | % 73.14/10.79 | | | | | | (2100) all_8_69 = e1 % 73.14/10.79 | | | | | | % 73.14/10.79 | | | | | | COMBINE_EQS: (587), (2100) imply: % 73.14/10.79 | | | | | | (2101) e1 = e0 % 73.14/10.79 | | | | | | % 73.14/10.79 | | | | | | REDUCE: (4), (2101) imply: % 73.14/10.79 | | | | | | (2102) $false % 73.14/10.79 | | | | | | % 73.14/10.79 | | | | | | CLOSE: (2102) is inconsistent. % 73.14/10.79 | | | | | | % 73.14/10.79 | | | | | End of split % 73.14/10.79 | | | | | % 73.14/10.79 | | | | End of split % 73.14/10.79 | | | | % 73.14/10.79 | | | End of split % 73.14/10.79 | | | % 73.14/10.79 | | End of split % 73.14/10.79 | | % 73.14/10.79 | Case 2: % 73.14/10.79 | | % 73.14/10.79 | | (2103) ~ (all_10_24 = e0) % 73.14/10.79 | | (2104) (all_10_16 = e0 | all_10_17 = e0 | all_10_18 = e0 | all_10_19 = % 73.14/10.79 | | e0) & (all_10_20 = e0 | all_10_21 = e0 | all_10_22 = e0 | % 73.14/10.79 | | all_10_23 = e0) % 73.14/10.79 | | % 73.14/10.79 | | ALPHA: (2104) implies: % 73.14/10.79 | | (2105) all_10_20 = e0 | all_10_21 = e0 | all_10_22 = e0 | all_10_23 = e0 % 73.14/10.79 | | (2106) all_10_16 = e0 | all_10_17 = e0 | all_10_18 = e0 | all_10_19 = e0 % 73.14/10.79 | | % 73.14/10.79 | | REDUCE: (322), (2103) imply: % 73.14/10.79 | | (2107) ~ (all_4_24 = e0) % 73.14/10.79 | | % 73.14/10.79 | | BETA: splitting (254) gives: % 73.14/10.79 | | % 73.14/10.79 | | Case 1: % 73.14/10.79 | | | % 73.14/10.79 | | | (2108) all_8_65 = e0 % 73.14/10.79 | | | % 73.14/10.79 | | | COMBINE_EQS: (400), (2108) imply: % 73.14/10.79 | | | (2109) e2 = e0 % 73.14/10.79 | | | % 73.14/10.79 | | | SIMP: (2109) implies: % 73.14/10.79 | | | (2110) e2 = e0 % 73.14/10.79 | | | % 73.14/10.79 | | | REDUCE: (5), (2110) imply: % 73.14/10.79 | | | (2111) $false % 73.14/10.79 | | | % 73.14/10.79 | | | CLOSE: (2111) is inconsistent. % 73.14/10.79 | | | % 73.14/10.79 | | Case 2: % 73.14/10.79 | | | % 73.14/10.79 | | | (2112) all_8_66 = e0 | all_8_67 = e0 | all_8_68 = e0 | all_8_69 = e0 % 73.14/10.79 | | | % 73.14/10.79 | | | BETA: splitting (2112) gives: % 73.14/10.79 | | | % 73.14/10.79 | | | Case 1: % 73.14/10.79 | | | | % 73.14/10.79 | | | | (2113) all_8_66 = e0 % 73.14/10.79 | | | | % 73.14/10.79 | | | | COMBINE_EQS: (406), (2113) imply: % 73.14/10.79 | | | | (2114) all_4_6 = e0 % 73.14/10.79 | | | | % 73.14/10.79 | | | | SIMP: (2114) implies: % 73.14/10.79 | | | | (2115) all_4_6 = e0 % 73.14/10.79 | | | | % 73.14/10.79 | | | | COMBINE_EQS: (379), (2115) imply: % 73.14/10.79 | | | | (2116) all_10_3 = e0 % 73.14/10.79 | | | | % 73.14/10.79 | | | | REDUCE: (105), (2115) imply: % 73.14/10.79 | | | | (2117) ~ (all_4_1 = e0) % 73.14/10.79 | | | | % 73.14/10.79 | | | | REDUCE: (86), (2115) imply: % 73.14/10.79 | | | | (2118) ~ (all_4_5 = e0) % 73.14/10.79 | | | | % 73.14/10.79 | | | | REDUCE: (79), (2115) imply: % 73.14/10.79 | | | | (2119) ~ (all_4_7 = e0) % 73.14/10.79 | | | | % 73.14/10.79 | | | | SIMP: (2119) implies: % 73.14/10.79 | | | | (2120) ~ (all_4_7 = e0) % 73.14/10.79 | | | | % 73.14/10.79 | | | | REDUCE: (77), (2115) imply: % 73.14/10.79 | | | | (2121) ~ (all_4_9 = e0) % 73.14/10.79 | | | | % 73.14/10.79 | | | | SIMP: (2121) implies: % 73.14/10.79 | | | | (2122) ~ (all_4_9 = e0) % 73.14/10.79 | | | | % 73.14/10.79 | | | | REDUCE: (76), (2115) imply: % 73.14/10.79 | | | | (2123) ~ (all_4_11 = e0) % 73.14/10.79 | | | | % 73.14/10.79 | | | | REDUCE: (75), (2115) imply: % 73.14/10.79 | | | | (2124) ~ (all_4_16 = e0) % 73.14/10.79 | | | | % 73.14/10.79 | | | | SIMP: (2124) implies: % 73.14/10.79 | | | | (2125) ~ (all_4_16 = e0) % 73.14/10.79 | | | | % 73.14/10.79 | | | | REDUCE: (74), (2115) imply: % 73.14/10.79 | | | | (2126) ~ (all_4_21 = e0) % 73.14/10.79 | | | | % 73.14/10.79 | | | | SIMP: (2126) implies: % 73.14/10.79 | | | | (2127) ~ (all_4_21 = e0) % 73.14/10.79 | | | | % 73.14/10.79 | | | | REDUCE: (135), (2115) imply: % 73.14/10.79 | | | | (2128) op(e3, e3) = e0 % 73.14/10.79 | | | | % 73.14/10.79 | | | | BETA: splitting (255) gives: % 73.14/10.79 | | | | % 73.14/10.79 | | | | Case 1: % 73.14/10.79 | | | | | % 73.14/10.79 | | | | | (2129) all_8_65 = e1 % 73.14/10.79 | | | | | % 73.14/10.79 | | | | | REF_CLOSE: (6), (400), (2129) are inconsistent by sub-proof #170. % 73.14/10.79 | | | | | % 73.14/10.79 | | | | Case 2: % 73.14/10.79 | | | | | % 73.14/10.79 | | | | | (2130) all_8_66 = e1 | all_8_67 = e1 | all_8_68 = e1 | all_8_69 = % 73.14/10.79 | | | | | e1 % 73.14/10.79 | | | | | % 73.14/10.79 | | | | | BETA: splitting (2130) gives: % 73.14/10.79 | | | | | % 73.14/10.79 | | | | | Case 1: % 73.14/10.79 | | | | | | % 73.14/10.79 | | | | | | (2131) all_8_66 = e1 % 73.14/10.79 | | | | | | % 73.14/10.79 | | | | | | COMBINE_EQS: (2113), (2131) imply: % 73.14/10.79 | | | | | | (2132) e1 = e0 % 73.14/10.79 | | | | | | % 73.14/10.79 | | | | | | REDUCE: (4), (2132) imply: % 73.14/10.79 | | | | | | (2133) $false % 73.14/10.79 | | | | | | % 73.14/10.79 | | | | | | CLOSE: (2133) is inconsistent. % 73.14/10.79 | | | | | | % 73.14/10.79 | | | | | Case 2: % 73.14/10.79 | | | | | | % 73.14/10.79 | | | | | | (2134) all_8_67 = e1 | all_8_68 = e1 | all_8_69 = e1 % 73.14/10.79 | | | | | | % 73.14/10.79 | | | | | | BETA: splitting (2134) gives: % 73.14/10.79 | | | | | | % 73.14/10.79 | | | | | | Case 1: % 73.14/10.79 | | | | | | | % 73.14/10.79 | | | | | | | (2135) all_8_67 = e1 % 73.14/10.79 | | | | | | | % 73.14/10.79 | | | | | | | REF_CLOSE: (7), (416), (2135) are inconsistent by sub-proof #57. % 73.14/10.79 | | | | | | | % 73.14/10.79 | | | | | | Case 2: % 73.14/10.79 | | | | | | | % 73.14/10.79 | | | | | | | (2136) ~ (all_8_67 = e1) % 73.14/10.79 | | | | | | | (2137) all_8_68 = e1 | all_8_69 = e1 % 73.14/10.79 | | | | | | | % 73.14/10.79 | | | | | | | BETA: splitting (2137) gives: % 73.14/10.79 | | | | | | | % 73.14/10.79 | | | | | | | Case 1: % 73.14/10.79 | | | | | | | | % 73.14/10.79 | | | | | | | | (2138) all_8_68 = e1 % 73.14/10.79 | | | | | | | | % 73.14/10.79 | | | | | | | | REF_CLOSE: (9), (339), (2138) are inconsistent by sub-proof #56. % 73.14/10.79 | | | | | | | | % 73.14/10.79 | | | | | | | Case 2: % 73.14/10.79 | | | | | | | | % 73.14/10.79 | | | | | | | | (2139) all_8_69 = e1 % 73.14/10.79 | | | | | | | | (2140) ~ (all_8_68 = e1) % 73.14/10.79 | | | | | | | | % 73.14/10.79 | | | | | | | | COMBINE_EQS: (448), (2139) imply: % 73.14/10.79 | | | | | | | | (2141) all_4_24 = e1 % 73.14/10.79 | | | | | | | | % 73.14/10.79 | | | | | | | | SIMP: (2141) implies: % 73.14/10.79 | | | | | | | | (2142) all_4_24 = e1 % 73.14/10.79 | | | | | | | | % 73.14/10.79 | | | | | | | | COMBINE_EQS: (322), (2142) imply: % 73.14/10.79 | | | | | | | | (2143) all_10_24 = e1 % 73.14/10.79 | | | | | | | | % 73.14/10.79 | | | | | | | | REDUCE: (87), (2142) imply: % 73.14/10.79 | | | | | | | | (2144) ~ (all_4_4 = e1) % 73.14/10.79 | | | | | | | | % 73.14/10.79 | | | | | | | | REDUCE: (62), (2142) imply: % 73.14/10.79 | | | | | | | | (2145) ~ (all_4_9 = e1) % 73.14/10.79 | | | | | | | | % 73.14/10.79 | | | | | | | | REDUCE: (42), (2142) imply: % 73.14/10.79 | | | | | | | | (2146) ~ (all_4_14 = e1) % 73.14/10.79 | | | | | | | | % 73.14/10.79 | | | | | | | | REDUCE: (28), (2142) imply: % 73.14/10.79 | | | | | | | | (2147) ~ (all_4_19 = e1) % 73.14/10.79 | | | | | | | | % 73.14/10.79 | | | | | | | | REDUCE: (21), (2142) imply: % 73.14/10.79 | | | | | | | | (2148) ~ (all_4_21 = e1) % 73.14/10.79 | | | | | | | | % 73.14/10.79 | | | | | | | | REDUCE: (19), (2142) imply: % 73.14/10.79 | | | | | | | | (2149) ~ (all_4_22 = e1) % 73.14/10.79 | | | | | | | | % 73.14/10.79 | | | | | | | | REDUCE: (18), (2142) imply: % 73.14/10.79 | | | | | | | | (2150) ~ (all_4_23 = e1) % 73.14/10.79 | | | | | | | | % 73.14/10.79 | | | | | | | | REDUCE: (117), (2142) imply: % 73.14/10.79 | | | | | | | | (2151) op(e0, e0) = e1 % 73.14/10.79 | | | | | | | | % 73.14/10.79 | | | | | | | | BETA: splitting (173) gives: % 73.14/10.79 | | | | | | | | % 73.14/10.79 | | | | | | | | Case 1: % 73.14/10.79 | | | | | | | | | % 73.14/10.79 | | | | | | | | | (2152) all_6_15 = e2 % 73.14/10.79 | | | | | | | | | % 73.14/10.79 | | | | | | | | | REF_CLOSE: (452), (504), (2152) are inconsistent by sub-proof % 73.14/10.79 | | | | | | | | | #169. % 73.14/10.79 | | | | | | | | | % 73.14/10.79 | | | | | | | | Case 2: % 73.14/10.79 | | | | | | | | | % 73.14/10.79 | | | | | | | | | (2153) ~ (all_6_15 = e2) % 73.14/10.79 | | | | | | | | | (2154) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e1 | % 73.14/10.79 | | | | | | | | | all_6_15 = e0 % 73.14/10.79 | | | | | | | | | % 73.14/10.79 | | | | | | | | | BETA: splitting (168) gives: % 73.14/10.79 | | | | | | | | | % 73.14/10.79 | | | | | | | | | Case 1: % 73.14/10.79 | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | (2155) all_6_22 = e2 % 73.14/10.79 | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | COMBINE_EQS: (466), (2155) imply: % 73.14/10.79 | | | | | | | | | | (2156) all_4_14 = e2 % 73.14/10.79 | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | SIMP: (2156) implies: % 73.14/10.79 | | | | | | | | | | (2157) all_4_14 = e2 % 73.14/10.79 | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | COMBINE_EQS: (328), (2157) imply: % 73.14/10.79 | | | | | | | | | | (2158) all_10_22 = e2 % 73.14/10.79 | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | REDUCE: (64), (2157) imply: % 73.14/10.79 | | | | | | | | | | (2159) ~ (all_4_9 = e2) % 73.14/10.79 | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | REDUCE: (53), (2157) imply: % 73.14/10.79 | | | | | | | | | | (2160) ~ (all_4_11 = e2) % 73.14/10.79 | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | REDUCE: (43), (2157) imply: % 73.14/10.79 | | | | | | | | | | (2161) ~ (all_4_19 = e2) % 73.14/10.79 | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | SIMP: (2161) implies: % 73.14/10.79 | | | | | | | | | | (2162) ~ (all_4_19 = e2) % 73.14/10.79 | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | REDUCE: (565), (2157) imply: % 73.14/10.79 | | | | | | | | | | (2163) op(e2, e2) = all_8_36 % 73.14/10.79 | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | REDUCE: (577), (2157) imply: % 73.14/10.79 | | | | | | | | | | (2164) op(e0, e2) = all_8_37 % 73.14/10.79 | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | REDUCE: (119), (2157) imply: % 73.14/10.79 | | | | | | | | | | (2165) op(e0, e2) = e2 % 73.14/10.79 | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_37, % 73.14/10.79 | | | | | | | | | | e2, e0, simplifying with (2164), (2165) gives: % 73.14/10.79 | | | | | | | | | | (2166) all_8_37 = e2 % 73.14/10.79 | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_8_36, % 73.14/10.79 | | | | | | | | | | e2, e2, simplifying with (14), (2163) gives: % 73.14/10.79 | | | | | | | | | | (2167) all_8_36 = e3 % 73.14/10.79 | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | BETA: splitting (251) gives: % 73.14/10.79 | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | Case 1: % 73.14/10.79 | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | (2168) (all_8_26 = e4 & ~ (all_8_27 = e2)) | (all_8_29 = % 73.14/10.79 | | | | | | | | | | | e3 & ~ (all_8_30 = e2)) % 73.14/10.79 | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | BETA: splitting (2168) gives: % 73.14/10.79 | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | Case 1: % 73.14/10.79 | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | (2169) all_8_26 = e4 & ~ (all_8_27 = e2) % 73.14/10.79 | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | ALPHA: (2169) implies: % 73.14/10.79 | | | | | | | | | | | | (2170) all_8_26 = e4 % 73.14/10.79 | | | | | | | | | | | | (2171) ~ (all_8_27 = e2) % 73.14/10.79 | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | REDUCE: (562), (2170) imply: % 73.14/10.79 | | | | | | | | | | | | (2172) op(e2, all_4_10) = e4 % 73.14/10.79 | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | BETA: splitting (171) gives: % 73.14/10.79 | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | Case 1: % 73.14/10.79 | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | (2173) all_6_19 = e2 % 73.14/10.79 | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | COMBINE_EQS: (479), (2173) imply: % 73.14/10.79 | | | | | | | | | | | | | (2174) all_4_23 = e2 % 73.14/10.79 | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | COMBINE_EQS: (337), (2174) imply: % 73.14/10.79 | | | | | | | | | | | | | (2175) all_10_19 = e2 % 73.14/10.79 | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | REDUCE: (65), (2174) imply: % 73.14/10.79 | | | | | | | | | | | | | (2176) ~ (all_4_8 = e2) % 73.14/10.79 | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | REDUCE: (22), (2174) imply: % 73.14/10.79 | | | | | | | | | | | | | (2177) ~ (all_4_21 = e2) % 73.14/10.79 | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | BETA: splitting (310) gives: % 73.14/10.79 | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | Case 1: % 73.14/10.79 | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | (2178) all_10_1 = e2 % 73.14/10.79 | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | COMBINE_EQS: (394), (2178) imply: % 73.14/10.79 | | | | | | | | | | | | | | (2179) all_4_5 = e2 % 73.14/10.79 | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | REDUCE: (508), (2179) imply: % 73.14/10.79 | | | | | | | | | | | | | | (2180) $false % 73.14/10.79 | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | CLOSE: (2180) is inconsistent. % 73.14/10.79 | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | Case 2: % 73.14/10.79 | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | (2181) all_10_3 = e2 | all_10_7 = e2 | all_10_13 = e2 | % 73.14/10.79 | | | | | | | | | | | | | | all_10_21 = e2 % 73.14/10.79 | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | BETA: splitting (306) gives: % 73.14/10.79 | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | Case 1: % 73.14/10.79 | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | (2182) all_10_2 = e2 % 73.14/10.79 | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | REF_CLOSE: (382), (500), (2182) are inconsistent by sub-proof % 73.14/10.79 | | | | | | | | | | | | | | | #55. % 73.14/10.79 | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | Case 2: % 73.14/10.79 | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | (2183) all_10_3 = e2 | all_10_5 = e2 | all_10_10 = e2 | % 73.14/10.79 | | | | | | | | | | | | | | | all_10_17 = e2 % 73.14/10.79 | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | BETA: splitting (2183) gives: % 73.14/10.79 | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | Case 1: % 73.14/10.79 | | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | | (2184) all_10_3 = e2 % 73.14/10.79 | | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2116), (2184) are inconsistent by sub-proof % 73.14/10.79 | | | | | | | | | | | | | | | | #54. % 73.14/10.79 | | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | Case 2: % 73.14/10.79 | | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | | (2185) all_10_5 = e2 | all_10_10 = e2 | all_10_17 = e2 % 73.14/10.79 | | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | | BETA: splitting (2185) gives: % 73.14/10.79 | | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | | Case 1: % 73.14/10.79 | | | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | | | (2186) all_10_5 = e2 % 73.14/10.79 | | | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | | | REF_CLOSE: (498), (2160), (2186) are inconsistent by % 73.14/10.79 | | | | | | | | | | | | | | | | | sub-proof #53. % 73.14/10.79 | | | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | | Case 2: % 73.14/10.79 | | | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | | | (2187) all_10_10 = e2 | all_10_17 = e2 % 73.14/10.79 | | | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | | | BETA: splitting (2187) gives: % 73.14/10.79 | | | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.79 | | | | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | | | | (2188) all_10_10 = e2 % 73.14/10.79 | | | | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (2188) imply: % 73.14/10.79 | | | | | | | | | | | | | | | | | | (2189) all_4_16 = e2 % 73.14/10.79 | | | | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | | | | REDUCE: (34), (2189) imply: % 73.14/10.79 | | | | | | | | | | | | | | | | | | (2190) ~ (all_4_21 = e2) % 73.14/10.79 | | | | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | | | | REDUCE: (539), (2189) imply: % 73.14/10.79 | | | | | | | | | | | | | | | | | | (2191) ~ (e4 = e2) % 73.14/10.79 | | | | | | | | | | | | | | | | | | % 73.14/10.79 | | | | | | | | | | | | | | | | | | REDUCE: (559), (2189) imply: % 73.14/10.80 | | | | | | | | | | | | | | | | | | (2192) op(e3, e2) = all_8_43 % 73.14/10.80 | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | REDUCE: (133), (2189) imply: % 73.14/10.80 | | | | | | | | | | | | | | | | | | (2193) op(e3, e1) = e2 % 73.14/10.80 | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | BETA: splitting (2181) gives: % 73.14/10.80 | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | (2194) all_10_3 = e2 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2116), (2194) are inconsistent by sub-proof % 73.14/10.80 | | | | | | | | | | | | | | | | | | | #54. % 73.14/10.80 | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | (2195) all_10_7 = e2 | all_10_13 = e2 | all_10_21 = e2 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | BETA: splitting (2195) gives: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | (2196) all_10_7 = e2 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (497), (2196) imply: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | (2197) all_4_7 = e2 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (2197) imply: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | (2198) ~ (all_4_8 = e2) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (2197) imply: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | (2199) ~ (all_4_9 = e2) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (2197) imply: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | (2200) ~ (all_4_17 = e2) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | SIMP: (2200) implies: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | (2201) ~ (all_4_17 = e2) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (2197) imply: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | (2202) ~ (all_4_22 = e2) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | SIMP: (2202) implies: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | (2203) ~ (all_4_22 = e2) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | REDUCE: (518), (2197) imply: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | (2204) ~ (e3 = e2) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (2197) imply: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | (2205) op(e3, e2) = all_8_17 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_11, % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | all_8_17, e2, e3, simplifying with (134), (2205) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | gives: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | (2206) all_8_17 = all_4_11 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_43, % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | all_8_17, e2, e3, simplifying with (2192), (2205) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | gives: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | (2207) all_8_17 = all_8_43 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2206), (2207) imply: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | (2208) all_8_43 = all_4_11 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | (2209) all_6_9 = e2 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (475), (2177), (2209) are inconsistent by % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | sub-proof #158. % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | (2210) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e1 | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | all_6_9 = e0 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | (2211) all_6_21 = e2 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (460), (2159), (2211) are inconsistent by % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | sub-proof #157. % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | (2212) all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e1 | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | all_6_21 = e0 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | (2213) all_6_14 = e2 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (477), (2203), (2213) are inconsistent by % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #52. % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | (2214) all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e1 | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | all_6_14 = e0 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | (2215) all_6_13 = e2 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (470), (2215) imply: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | (2216) all_4_17 = e2 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2216) implies: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | (2217) all_4_17 = e2 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2201), (2217) imply: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | (2218) $false % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2218) is inconsistent. % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | (2219) all_6_13 = e4 | all_6_13 = e3 | all_6_13 = e1 | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | all_6_13 = e0 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | (2220) all_6_2 = e2 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (510), (2220) are inconsistent by sub-proof % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | #168. % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | (2221) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | all_6_2 = e0 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (2222) (all_8_13 = e4 & ~ (all_8_14 = e3)) | (all_8_17 = % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_8_18 = e3)) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2222) gives: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2223) all_8_13 = e4 & ~ (all_8_14 = e3) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2223) implies: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2224) all_8_13 = e4 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (554), (2224) imply: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2225) op(e3, all_4_5) = e4 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2226) all_6_1 = e2 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (454), (508), (2226) are inconsistent by sub-proof % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #155. % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2227) ~ (all_6_1 = e2) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2228) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_1 = e0 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2229) all_6_5 = e2 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (450), (500), (2229) are inconsistent by sub-proof % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #153. % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2230) ~ (all_6_5 = e2) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2231) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_5 = e0 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2232) all_10_20 = e4 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (2232) imply: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2233) all_4_4 = e4 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2233) implies: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2234) all_4_4 = e4 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (106), (2234) imply: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2235) ~ (all_4_1 = e4) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (100), (2234) imply: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2236) ~ (all_4_2 = e4) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (2234) imply: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2237) ~ (all_4_9 = e4) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2237) implies: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2238) ~ (all_4_9 = e4) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (11), (15), (27), (51), (61), (82), % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (83), (96), (102), (104), (108), (128), (285), % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288), (298), (301), (303), (305), (308), (312), % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313), (331), (345), (351), (357), (361), (367), % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370), (382), (385), (391), (394), (398), (450), % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454), (460), (461), (470), (475), (477), (495), % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (498), (500), (502), (508), (515), (516), (521), % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522), (524), (531), (535), (540), (550), (566), % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2106), (2116), (2117), (2118), (2122), (2127), % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2145), (2148), (2149), (2158), (2171), (2172), % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2175), (2196), (2210), (2212), (2214), (2219), % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2221), (2228), (2231), (2232), (2235), (2236), % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2238), (function-axioms) are inconsistent by % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #41. % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2239) all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_24 = e4 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2239) gives: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2240) all_10_21 = e4 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (331), (2240) imply: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2241) all_4_9 = e4 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2241) implies: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2242) all_4_9 = e4 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (83), (2242) imply: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2243) ~ (all_4_5 = e4) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2244) all_10_12 = e1 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (11), (15), (82), (84), (292), (301), % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303), (345), (348), (391), (454), (461), (496), % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521), (522), (525), (550), (2118), (2171), % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2175), (2221), (2228), (2243), (2244), % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #39. % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2245) all_10_13 = e1 | all_10_14 = e1 | all_10_15 = e1 | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_19 = e1 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (84), (311), (345), (348), (394), % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454), (496), (535), (2118), (2128), (2175), % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2225), (2228), (2243), (2245), (function-axioms) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #37. % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2246) all_10_22 = e4 | all_10_23 = e4 | all_10_24 = e4 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (325), (542), (2143), (2158), (2246) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #36. % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2247) all_8_17 = e2 & ~ (all_8_18 = e3) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2160), (2206), (2247) are inconsistent by % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #35. % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (2248) (all_8_20 = e1 & ~ (all_8_21 = e3)) | (all_8_23 = % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_24 = e3)) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2248) gives: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2249) all_8_20 = e1 & ~ (all_8_21 = e3) % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2249) implies: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2250) all_8_20 = e1 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (556), (2250) imply: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2251) op(e3, all_4_8) = e1 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2252) all_6_1 = e2 % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (454), (508), (2252) are inconsistent by sub-proof % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #155. % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2253) ~ (all_6_1 = e2) % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2254) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_1 = e0 % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2255) all_6_5 = e2 % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (450), (500), (2255) are inconsistent by sub-proof % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #153. % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2256) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_5 = e0 % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2257) all_10_20 = e4 % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (2257) imply: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2258) all_4_4 = e4 % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2258) implies: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2259) all_4_4 = e4 % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (106), (2259) imply: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2260) ~ (all_4_1 = e4) % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (100), (2259) imply: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2261) ~ (all_4_2 = e4) % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (2259) imply: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2262) ~ (all_4_9 = e4) % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2262) implies: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2263) ~ (all_4_9 = e4) % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2264) all_10_0 = e0 % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (398), (2264) imply: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2265) e2 = e0 % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (2265) imply: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2266) $false % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2266) is inconsistent. % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2267) all_10_2 = e0 | all_10_6 = e0 | all_10_12 = e0 | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_20 = e0 % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2268) all_10_1 = e4 % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (394), (2268) imply: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2269) all_4_5 = e4 % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (82), (2269) imply: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2270) ~ (all_4_10 = e4) % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2270) implies: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2271) ~ (all_4_10 = e4) % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (10), (11), (27), (51), % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (96), (102), (104), (108), (288), (290), (303), % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317), (345), (348), (351), (361), (367), (370), % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382), (385), (391), (398), (450), (475), (477), % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (495), (496), (498), (502), (515), (516), (523), % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524), (531), (535), (2106), (2117), (2127), % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2148), (2149), (2158), (2175), (2176), (2193), % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2210), (2214), (2251), (2256), (2257), (2261), % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2267), (2271), (function-axioms) are inconsistent % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #33. % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2272) ~ (all_10_1 = e4) % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (11), (15), (61), (82), (83), (285), (301), % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303), (308), (331), (345), (361), (382), (391), % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394), (454), (460), (461), (498), (521), (522), % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535), (550), (2116), (2118), (2122), (2145), % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2158), (2171), (2212), (2221), (2254), (2257), % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2260), (2263), (2272), (function-axioms) are % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #42. % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2273) all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_24 = e4 % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2273) gives: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2274) all_10_21 = e4 % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (331), (2274) imply: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2275) all_4_9 = e4 % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2275) implies: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2276) all_4_9 = e4 % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (83), (2276) imply: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2277) ~ (all_4_5 = e4) % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2278) all_10_12 = e1 % 73.14/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (11), (15), (82), (84), (292), (301), % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303), (345), (348), (391), (454), (461), (496), % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521), (522), (525), (550), (2118), (2171), % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2175), (2221), (2254), (2277), (2278), % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #39. % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2279) all_10_13 = e1 | all_10_14 = e1 | all_10_15 = e1 | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_19 = e1 % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (345), (348), (496), (2175), % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2176), (2193), (2251), (2279), (function-axioms) % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #34. % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2280) all_10_22 = e4 | all_10_23 = e4 | all_10_24 = e4 % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (325), (542), (2143), (2158), (2280) % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #36. % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2281) all_8_23 = e0 & ~ (all_8_24 = e3) % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2281) implies: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2282) all_8_23 = e0 % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (2282) imply: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2283) op(e3, all_4_9) = e0 % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2284) all_6_1 = e2 % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (454), (508), (2284) are inconsistent by sub-proof % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #155. % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2285) ~ (all_6_1 = e2) % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2286) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_1 = e0 % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2287) all_6_5 = e2 % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (450), (500), (2287) are inconsistent by sub-proof % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #153. % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2288) ~ (all_6_5 = e2) % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2289) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_5 = e0 % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2290) all_10_20 = e4 % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (2290) imply: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2291) all_4_4 = e4 % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2291) implies: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2292) all_4_4 = e4 % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (106), (2292) imply: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2293) ~ (all_4_1 = e4) % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (100), (2292) imply: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2294) ~ (all_4_2 = e4) % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (2292) imply: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2295) ~ (all_4_9 = e4) % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2295) implies: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2296) ~ (all_4_9 = e4) % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (11), (15), (27), (51), (61), (82), % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (83), (96), (102), (104), (108), (128), (285), % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288), (298), (301), (303), (305), (308), (312), % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313), (331), (345), (351), (357), (361), (367), % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370), (382), (385), (391), (394), (398), (450), % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454), (460), (461), (470), (475), (477), (495), % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (498), (500), (502), (508), (515), (516), (521), % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522), (524), (531), (535), (540), (550), (566), % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2106), (2116), (2117), (2118), (2122), (2127), % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2145), (2148), (2149), (2158), (2171), (2172), % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2175), (2196), (2210), (2212), (2214), (2219), % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2221), (2286), (2289), (2290), (2293), (2294), % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2296), (function-axioms) are inconsistent by % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #41. % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2297) all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_24 = e4 % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (136), (325), (331), (542), (2117), % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2143), (2158), (2283), (2297), (function-axioms) % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #32. % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | (2298) all_10_13 = e2 | all_10_21 = e2 % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (331), (348), (2159), (2176), (2298) are % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #64. % 73.57/10.81 | | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.81 | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | (2299) all_10_17 = e2 % 73.57/10.81 | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (2299) imply: % 73.57/10.81 | | | | | | | | | | | | | | | | | | (2300) all_4_21 = e2 % 73.57/10.81 | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | REDUCE: (2177), (2300) imply: % 73.57/10.81 | | | | | | | | | | | | | | | | | | (2301) $false % 73.57/10.81 | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | | CLOSE: (2301) is inconsistent. % 73.57/10.81 | | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | | End of split % 73.57/10.81 | | | | | | | | | | | | | % 73.57/10.81 | | | | | | | | | | | | Case 2: % 73.57/10.81 | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | (2302) ~ (all_6_19 = e2) % 73.57/10.82 | | | | | | | | | | | | | (2303) all_6_19 = e4 | all_6_19 = e3 | all_6_19 = e1 | % 73.57/10.82 | | | | | | | | | | | | | all_6_19 = e0 % 73.57/10.82 | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | REDUCE: (479), (2302) imply: % 73.57/10.82 | | | | | | | | | | | | | (2304) ~ (all_4_23 = e2) % 73.57/10.82 | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | BETA: splitting (291) gives: % 73.57/10.82 | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | Case 1: % 73.57/10.82 | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | (2305) all_10_12 = e2 % 73.57/10.82 | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | REF_CLOSE: (351), (504), (2305) are inconsistent by sub-proof % 73.57/10.82 | | | | | | | | | | | | | | #89. % 73.57/10.82 | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | Case 2: % 73.57/10.82 | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | (2306) all_10_13 = e2 | all_10_14 = e2 | all_10_15 = e2 | % 73.57/10.82 | | | | | | | | | | | | | | all_10_19 = e2 % 73.57/10.82 | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | BETA: splitting (2306) gives: % 73.57/10.82 | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | Case 1: % 73.57/10.82 | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | (2307) all_10_13 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | COMBINE_EQS: (348), (2307) imply: % 73.57/10.82 | | | | | | | | | | | | | | | (2308) all_4_8 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | SIMP: (2308) implies: % 73.57/10.82 | | | | | | | | | | | | | | | (2309) all_4_8 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | REDUCE: (68), (2309) imply: % 73.57/10.82 | | | | | | | | | | | | | | | (2310) ~ (all_4_9 = e2) % 73.57/10.82 | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | REDUCE: (520), (2309) imply: % 73.57/10.82 | | | | | | | | | | | | | | | (2311) ~ (e4 = e2) % 73.57/10.82 | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | REDUCE: (556), (2309) imply: % 73.57/10.82 | | | | | | | | | | | | | | | (2312) op(e3, e2) = all_8_20 % 73.57/10.82 | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | BETA: splitting (2303) gives: % 73.57/10.82 | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | Case 1: % 73.57/10.82 | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | (2313) all_6_19 = e4 % 73.57/10.82 | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | COMBINE_EQS: (479), (2313) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | (2314) all_4_23 = e4 % 73.57/10.82 | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | REDUCE: (544), (2314) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | (2315) $false % 73.57/10.82 | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | CLOSE: (2315) is inconsistent. % 73.57/10.82 | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | Case 2: % 73.57/10.82 | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | (2316) ~ (all_6_19 = e4) % 73.57/10.82 | | | | | | | | | | | | | | | | (2317) all_6_19 = e3 | all_6_19 = e1 | all_6_19 = e0 % 73.57/10.82 | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 73.57/10.82 | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | Case 1: % 73.57/10.82 | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | (2318) all_10_12 = e1 % 73.57/10.82 | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (2318) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | (2319) all_4_3 = e1 % 73.57/10.82 | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | SIMP: (2319) implies: % 73.57/10.82 | | | | | | | | | | | | | | | | | (2320) all_4_3 = e1 % 73.57/10.82 | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | REDUCE: (101), (2320) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | (2321) ~ (all_4_2 = e1) % 73.57/10.82 | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | REDUCE: (95), (2320) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | (2322) ~ (all_4_4 = e1) % 73.57/10.82 | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | REDUCE: (91), (2320) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | (2323) ~ (all_4_23 = e1) % 73.57/10.82 | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | REDUCE: (517), (2320) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | (2324) ~ (e4 = e1) % 73.57/10.82 | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | REDUCE: (568), (2320) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | (2325) op(e1, e1) = all_8_8 % 73.57/10.82 | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | BETA: splitting (2317) gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.82 | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | (2326) all_6_19 = e1 % 73.57/10.82 | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (479), (2326) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | (2327) all_4_23 = e1 % 73.57/10.82 | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | REDUCE: (2150), (2327) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | (2328) $false % 73.57/10.82 | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | CLOSE: (2328) is inconsistent. % 73.57/10.82 | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.82 | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | (2329) ~ (all_6_19 = e1) % 73.57/10.82 | | | | | | | | | | | | | | | | | | (2330) all_6_19 = e3 | all_6_19 = e0 % 73.57/10.82 | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | BETA: splitting (2330) gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | (2331) all_6_19 = e3 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (479), (2331) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | (2332) all_4_23 = e3 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | REDUCE: (25), (2332) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | (2333) ~ (all_4_20 = e3) % 73.57/10.82 | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | REDUCE: (22), (2332) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | (2334) ~ (all_4_21 = e3) % 73.57/10.82 | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | REDUCE: (544), (2332) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | (2335) ~ (e4 = e3) % 73.57/10.82 | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | REDUCE: (582), (2332) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | (2336) op(e0, e3) = all_8_61 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_9, % 73.57/10.82 | | | | | | | | | | | | | | | | | | | all_8_61, e3, e0, simplifying with (120), (2336) % 73.57/10.82 | | | | | | | | | | | | | | | | | | | gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | (2337) all_8_61 = all_4_9 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, all_8_8, % 73.57/10.82 | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (12), (2325) gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | (2338) all_8_8 = e4 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_11, % 73.57/10.82 | | | | | | | | | | | | | | | | | | | all_8_20, e2, e3, simplifying with (134), (2312) % 73.57/10.82 | | | | | | | | | | | | | | | | | | | gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | (2339) all_8_20 = all_4_11 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | (2340) all_6_2 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (510), (2340) are inconsistent by sub-proof % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | #168. % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | (2341) ~ (all_6_2 = e2) % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | (2342) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | all_6_2 = e0 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | (2343) all_6_10 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (451), (502), (2343) are inconsistent by sub-proof % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | #106. % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | (2344) all_6_10 = e4 | all_6_10 = e3 | all_6_10 = e1 | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | all_6_10 = e0 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | (2345) all_6_9 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (475), (2345) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | (2346) all_4_21 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2346) implies: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | (2347) all_4_21 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (2347) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | (2348) ~ (all_4_16 = e2) % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (2347) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | (2349) op(e0, e2) = all_8_55 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | (2350) all_10_9 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (388), (2350) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | (2351) all_4_15 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (512), (2351) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | (2352) $false % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2352) is inconsistent. % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | (2353) all_10_10 = e2 | all_10_11 = e2 | all_10_15 = e2 | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | all_10_23 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2353) gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | (2354) all_10_10 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (2354) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | (2355) all_4_16 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2348), (2355) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | (2356) $false % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2356) is inconsistent. % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | (2357) all_10_11 = e2 | all_10_15 = e2 | all_10_23 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2357) gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | (2358) all_10_11 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (2358) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | (2359) all_4_17 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (2359) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | (2360) ~ (all_4_22 = e2) % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2360) implies: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | (2361) ~ (all_4_22 = e2) % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (529), (2359) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | (2362) ~ (e3 = e2) % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (2359) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | (2363) op(e2, e1) = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (2364) all_10_6 = e1 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (367), (2321), (2364) are inconsistent by % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #86. % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (2365) all_10_7 = e1 | all_10_8 = e1 | all_10_11 = e1 | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_18 = e1 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2365) gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2366) all_10_7 = e1 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (497), (2366) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2367) all_4_7 = e1 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (2367) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2368) ~ (all_4_5 = e1) % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (2367) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2369) ~ (all_4_9 = e1) % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (2367) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2370) ~ (all_4_22 = e1) % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (518), (2367) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2371) ~ (e3 = e1) % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (2367) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2372) op(e3, e1) = all_8_17 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (2367) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2373) op(e2, e1) = all_8_18 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_55, % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (2165), (2349) gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2374) all_8_55 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_18, % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (2363), (2373) gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2375) all_8_18 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_16, % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_17, e1, e3, simplifying with (133), (2372) % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2376) all_8_17 = all_4_16 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2377) (all_8_52 = e4 & ~ (all_8_53 = e0)) | (all_8_55 = % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ~ (all_8_56 = e0)) % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2377) gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2378) all_8_52 = e4 & ~ (all_8_53 = e0) % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2378) implies: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2379) all_8_52 = e4 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (579), (2379) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2380) op(e0, all_4_20) = e4 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2381) all_6_21 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (460), (2381) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2382) all_4_9 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2159), (2382) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2383) $false % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2383) is inconsistent. % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2384) all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e1 | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_21 = e0 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2385) all_6_1 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (454), (2385) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2386) all_4_5 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (508), (2386) imply: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2387) $false % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2387) is inconsistent. % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2388) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_1 = e0 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2389) (all_8_1 = e3 & ~ (all_8_2 = e4)) | (all_8_4 = e2 % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_5 = e4)) % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2389) gives: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2390) all_8_1 = e3 & ~ (all_8_2 = e4) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2390) implies: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2391) all_8_1 = e3 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (2391) imply: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2392) op(e4, all_4_1) = e3 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2393) (all_8_13 = e4 & ~ (all_8_14 = e3)) | (all_8_17 = % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_8_18 = e3)) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2393) gives: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2394) all_8_13 = e4 & ~ (all_8_14 = e3) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2394) implies: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2395) all_8_13 = e4 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (554), (2395) imply: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2396) op(e3, all_4_5) = e4 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2397) all_10_20 = e4 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (2397) imply: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2398) all_4_4 = e4 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2398) implies: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2399) all_4_4 = e4 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (106), (2399) imply: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2400) ~ (all_4_1 = e4) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (2399) imply: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2401) ~ (all_4_9 = e4) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2401) implies: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2402) ~ (all_4_9 = e4) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (11), (39), (82), (83), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (140), (296), (301), (312), (314), (317), (318), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (331), (367), (382), (385), (388), (391), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394), (398), (460), (461), (500), (510), (515), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521), (522), (535), (542), (551), (578), (2105), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2116), (2118), (2122), (2145), (2147), (2151), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2158), (2172), (2307), (2318), (2333), (2342), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2363), (2366), (2380), (2384), (2392), (2397), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2400), (2402), (function-axioms) are inconsistent % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #27. % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2403) all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_24 = e4 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (83), (311), (325), (331), (394), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454), (542), (2118), (2122), (2128), (2143), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2158), (2368), (2388), (2396), (2403), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #26. % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2404) all_8_17 = e2 & ~ (all_8_18 = e3) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2348), (2376), (2404) are inconsistent by % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #25. % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2405) (all_8_20 = e1 & ~ (all_8_21 = e3)) | (all_8_23 = % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_24 = e3)) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2405) gives: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2406) all_8_20 = e1 & ~ (all_8_21 = e3) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (61), (303), (391), (461), (521), (522), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (550), (2171), (2339), (2342), (2406), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #24. % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2407) all_8_23 = e0 & ~ (all_8_24 = e3) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2407) implies: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2408) all_8_23 = e0 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (2408) imply: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2409) op(e3, all_4_9) = e0 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2410) all_10_20 = e4 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (2410) imply: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2411) all_4_4 = e4 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2411) implies: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2412) all_4_4 = e4 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (106), (2412) imply: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2413) ~ (all_4_1 = e4) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (2412) imply: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2414) ~ (all_4_9 = e4) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2414) implies: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2415) ~ (all_4_9 = e4) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (11), (39), (82), (83), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (140), (296), (301), (312), (314), (317), (318), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (331), (367), (382), (385), (388), (391), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394), (398), (460), (461), (500), (510), (515), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521), (522), (535), (542), (551), (578), (2105), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2116), (2118), (2122), (2145), (2147), (2151), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2158), (2172), (2307), (2318), (2333), (2342), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2363), (2366), (2380), (2384), (2392), (2410), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2413), (2415), (function-axioms) are inconsistent % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #27. % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2416) all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_24 = e4 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (136), (325), (331), (542), (2117), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2143), (2158), (2409), (2416), (function-axioms) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #32. % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2417) all_8_4 = e2 & ~ (all_8_5 = e4) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2417) implies: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2418) all_8_4 = e2 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (2418) imply: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2419) op(e4, all_4_2) = e2 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (10), (11), (15), (61), (82), (83), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (90), (100), (136), (137), (252), (286), (296), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297), (301), (303), (311), (312), (314), (318), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (331), (334), (367), (385), (388), (391), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394), (398), (451), (454), (461), (502), (506), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515), (521), (522), (525), (535), (542), (550), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552), (554), (557), (2116), (2117), (2118), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2122), (2128), (2143), (2144), (2158), (2171), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2307), (2321), (2333), (2339), (2342), (2344), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2348), (2366), (2368), (2376), (2388), (2419), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #20. % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2420) (all_8_7 = e1 & ~ (all_8_8 = e4)) | (all_8_10 = % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_11 = e4)) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2420) gives: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2421) all_8_7 = e1 & ~ (all_8_8 = e4) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2421) implies: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2422) ~ (all_8_8 = e4) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2338), (2422) imply: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2423) $false % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2423) is inconsistent. % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2424) all_8_10 = e0 & ~ (all_8_11 = e4) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2424) implies: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2425) all_8_10 = e0 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (2425) imply: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2426) op(e4, all_4_4) = e0 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (10), (15), (61), (83), (90), (136), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (286), (303), (311), (312), (325), (331), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (391), (394), (454), (461), (506), (521), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522), (535), (542), (549), (550), (554), (557), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2116), (2117), (2118), (2122), (2128), (2143), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2144), (2158), (2171), (2307), (2339), (2342), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2348), (2366), (2368), (2376), (2388), (2426), % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #16. % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2427) all_8_55 = e3 & ~ (all_8_56 = e0) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2374), (2427) are inconsistent by sub-proof % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #97. % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2428) (all_8_58 = e2 & ~ (all_8_59 = e0)) | (all_8_61 = % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_8_62 = e0)) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2428) gives: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2429) all_8_58 = e2 & ~ (all_8_59 = e0) % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2429) implies: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2430) all_8_58 = e2 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (2430) imply: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2431) op(e0, all_4_22) = e2 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2432) all_6_14 = e2 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (477), (2361), (2432) are inconsistent by % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #52. % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2433) all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e1 | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_14 = e0 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2434) all_6_1 = e2 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (454), (2434) imply: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2435) all_4_5 = e2 % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (508), (2435) imply: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2436) $false % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2436) is inconsistent. % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2437) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_1 = e0 % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2438) (all_8_1 = e3 & ~ (all_8_2 = e4)) | (all_8_4 = e2 % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_5 = e4)) % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2438) gives: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2439) all_8_1 = e3 & ~ (all_8_2 = e4) % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2439) implies: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2440) all_8_1 = e3 % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (2440) imply: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2441) op(e4, all_4_1) = e3 % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2442) (all_8_13 = e4 & ~ (all_8_14 = e3)) | (all_8_17 = % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_8_18 = e3)) % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (11), (26), (82), (83), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (90), (106), (121), (140), (286), (296), (301), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311), (312), (314), (317), (318), (325), (331), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (367), (382), (385), (388), (391), (394), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398), (454), (461), (477), (500), (506), (512), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515), (521), (522), (531), (535), (542), (551), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (554), (576), (2116), (2117), (2118), (2122), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2128), (2143), (2144), (2149), (2158), (2307), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2318), (2333), (2342), (2348), (2366), (2368), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2376), (2431), (2433), (2437), (2441), (2442), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #14. % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2443) (all_8_20 = e1 & ~ (all_8_21 = e3)) | (all_8_23 = % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_24 = e3)) % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2443) gives: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2444) all_8_20 = e1 & ~ (all_8_21 = e3) % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2444) implies: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2445) all_8_20 = e1 % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2339), (2445) imply: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2446) all_4_11 = e1 % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2446) implies: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2447) all_4_11 = e1 % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (2447) imply: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2448) ~ (all_4_10 = e1) % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (303), (391), (461), (521), (522), (550), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2171), (2342), (2448), (function-axioms) are % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #160. % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2449) all_8_23 = e0 & ~ (all_8_24 = e3) % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (11), (26), (82), (90), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (106), (121), (136), (140), (286), (296), (301), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312), (314), (317), (318), (325), (331), (334), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367), (382), (385), (388), (391), (394), (398), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (477), (500), (506), (512), (515), (521), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522), (531), (535), (542), (551), (557), (576), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2116), (2117), (2118), (2143), (2144), (2149), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2158), (2307), (2318), (2333), (2342), (2366), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2431), (2433), (2441), (2449), (function-axioms) % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #13. % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2450) all_8_4 = e2 & ~ (all_8_5 = e4) % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2450) implies: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2451) all_8_4 = e2 % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (2451) imply: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2452) op(e4, all_4_2) = e2 % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (10), (11), (15), (61), (82), (83), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (90), (100), (136), (137), (252), (286), (296), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297), (301), (303), (311), (312), (314), (318), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (331), (334), (367), (385), (388), (391), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394), (398), (451), (454), (461), (502), (506), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515), (521), (522), (525), (535), (542), (550), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552), (554), (557), (2116), (2117), (2118), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2122), (2128), (2143), (2144), (2158), (2171), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2307), (2321), (2333), (2339), (2342), (2344), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2348), (2366), (2368), (2376), (2437), (2452), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #20. % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2453) (all_8_7 = e1 & ~ (all_8_8 = e4)) | (all_8_10 = % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_11 = e4)) % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2453) gives: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2454) all_8_7 = e1 & ~ (all_8_8 = e4) % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2454) implies: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2455) ~ (all_8_8 = e4) % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2338), (2455) imply: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2456) $false % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2456) is inconsistent. % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2457) all_8_10 = e0 & ~ (all_8_11 = e4) % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2457) implies: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2458) all_8_10 = e0 % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (2458) imply: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2459) op(e4, all_4_4) = e0 % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (10), (15), (61), (83), (90), (136), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (286), (303), (311), (312), (325), (331), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (391), (394), (454), (461), (506), (521), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522), (535), (542), (549), (550), (554), (557), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2116), (2117), (2118), (2122), (2128), (2143), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2144), (2158), (2171), (2307), (2339), (2342), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2348), (2366), (2368), (2376), (2437), (2459), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #16. % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2460) all_8_61 = e1 & ~ (all_8_62 = e0) % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2145), (2337), (2460) are inconsistent by % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #96. % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2461) all_10_8 = e1 | all_10_11 = e1 | all_10_18 = e1 % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (361), (495), (2149), (2358), (2461) are % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #12. % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | (2462) all_10_15 = e2 | all_10_23 = e2 % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (325), (496), (2162), (2462) are % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #87. % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | (2463) ~ (all_6_9 = e2) % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | (2464) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e1 | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | all_6_9 = e0 % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (475), (2463) imply: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | (2465) ~ (all_4_21 = e2) % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2464) gives: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | (2466) all_6_9 = e4 % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (475), (2466) imply: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | (2467) all_4_21 = e4 % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2467) implies: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | (2468) all_4_21 = e4 % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (2468) imply: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | (2469) ~ (all_4_11 = e4) % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (11), (15), (303), (345), (361), (391), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | (498), (535), (550), (2158), (2171), (2469), % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | #43. % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | (2470) all_6_9 = e3 | all_6_9 = e1 | all_6_9 = e0 % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (475), (2127), (2148), (2334), (2470) are % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #111. % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | (2471) all_6_19 = e0 % 73.57/10.84 | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (479), (2471) imply: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | (2472) all_4_23 = e0 % 73.57/10.84 | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | REDUCE: (537), (2472) imply: % 73.57/10.84 | | | | | | | | | | | | | | | | | | | (2473) $false % 73.57/10.84 | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | | CLOSE: (2473) is inconsistent. % 73.57/10.84 | | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | Case 2: % 73.57/10.84 | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | (2474) ~ (all_10_12 = e1) % 73.57/10.84 | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (351), (452), (479), (516), (517), (537), % 73.57/10.84 | | | | | | | | | | | | | | | | | (2150), (2154), (2317), (2474) are inconsistent by % 73.57/10.84 | | | | | | | | | | | | | | | | | sub-proof #11. % 73.57/10.84 | | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | Case 2: % 73.57/10.84 | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | (2475) all_10_14 = e2 | all_10_15 = e2 | all_10_19 = e2 % 73.57/10.84 | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (337), (345), (496), (2304), (2475) are % 73.57/10.84 | | | | | | | | | | | | | | | inconsistent by sub-proof #10. % 73.57/10.84 | | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | End of split % 73.57/10.84 | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | Case 2: % 73.57/10.84 | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | (2476) all_8_29 = e3 & ~ (all_8_30 = e2) % 73.57/10.84 | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | ALPHA: (2476) implies: % 73.57/10.84 | | | | | | | | | | | | (2477) all_8_29 = e3 % 73.57/10.84 | | | | | | | | | | | | % 73.57/10.84 | | | | | | | | | | | | REDUCE: (563), (2477) imply: % 73.57/10.84 | | | | | | | | | | | | (2478) op(e2, all_4_11) = e3 % 73.57/10.84 | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | BETA: splitting (171) gives: % 73.57/10.85 | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | (2479) all_6_19 = e2 % 73.57/10.85 | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | COMBINE_EQS: (479), (2479) imply: % 73.57/10.85 | | | | | | | | | | | | | (2480) all_4_23 = e2 % 73.57/10.85 | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | COMBINE_EQS: (337), (2480) imply: % 73.57/10.85 | | | | | | | | | | | | | (2481) all_10_19 = e2 % 73.57/10.85 | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | REDUCE: (65), (2480) imply: % 73.57/10.85 | | | | | | | | | | | | | (2482) ~ (all_4_8 = e2) % 73.57/10.85 | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | REDUCE: (22), (2480) imply: % 73.57/10.85 | | | | | | | | | | | | | (2483) ~ (all_4_21 = e2) % 73.57/10.85 | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | BETA: splitting (310) gives: % 73.57/10.85 | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | (2484) all_10_1 = e2 % 73.57/10.85 | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | COMBINE_EQS: (394), (2484) imply: % 73.57/10.85 | | | | | | | | | | | | | | (2485) all_4_5 = e2 % 73.57/10.85 | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | REDUCE: (508), (2485) imply: % 73.57/10.85 | | | | | | | | | | | | | | (2486) $false % 73.57/10.85 | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | CLOSE: (2486) is inconsistent. % 73.57/10.85 | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | Case 2: % 73.57/10.85 | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | (2487) all_10_3 = e2 | all_10_7 = e2 | all_10_13 = e2 | % 73.57/10.85 | | | | | | | | | | | | | | all_10_21 = e2 % 73.57/10.85 | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | BETA: splitting (306) gives: % 73.57/10.85 | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | (2488) all_10_2 = e2 % 73.57/10.85 | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | REF_CLOSE: (382), (500), (2488) are inconsistent by sub-proof % 73.57/10.85 | | | | | | | | | | | | | | | #55. % 73.57/10.85 | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | Case 2: % 73.57/10.85 | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | (2489) all_10_3 = e2 | all_10_5 = e2 | all_10_10 = e2 | % 73.57/10.85 | | | | | | | | | | | | | | | all_10_17 = e2 % 73.57/10.85 | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | BETA: splitting (2489) gives: % 73.57/10.85 | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | (2490) all_10_3 = e2 % 73.57/10.85 | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2116), (2490) are inconsistent by sub-proof % 73.57/10.85 | | | | | | | | | | | | | | | | #54. % 73.57/10.85 | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | Case 2: % 73.57/10.85 | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | (2491) all_10_5 = e2 | all_10_10 = e2 | all_10_17 = e2 % 73.57/10.85 | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | BETA: splitting (2491) gives: % 73.57/10.85 | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | (2492) all_10_5 = e2 % 73.57/10.85 | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | REF_CLOSE: (498), (2160), (2492) are inconsistent by % 73.57/10.85 | | | | | | | | | | | | | | | | | sub-proof #53. % 73.57/10.85 | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | Case 2: % 73.57/10.85 | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | (2493) all_10_10 = e2 | all_10_17 = e2 % 73.57/10.85 | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | BETA: splitting (2493) gives: % 73.57/10.85 | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | (2494) all_10_10 = e2 % 73.57/10.85 | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (2494) imply: % 73.57/10.85 | | | | | | | | | | | | | | | | | | (2495) all_4_16 = e2 % 73.57/10.85 | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | REDUCE: (34), (2495) imply: % 73.57/10.85 | | | | | | | | | | | | | | | | | | (2496) ~ (all_4_21 = e2) % 73.57/10.85 | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | REDUCE: (539), (2495) imply: % 73.57/10.85 | | | | | | | | | | | | | | | | | | (2497) ~ (e4 = e2) % 73.57/10.85 | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | REDUCE: (559), (2495) imply: % 73.57/10.85 | | | | | | | | | | | | | | | | | | (2498) op(e3, e2) = all_8_43 % 73.57/10.85 | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | REDUCE: (133), (2495) imply: % 73.57/10.85 | | | | | | | | | | | | | | | | | | (2499) op(e3, e1) = e2 % 73.57/10.85 | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | BETA: splitting (2487) gives: % 73.57/10.85 | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | (2500) all_10_3 = e2 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2116), (2500) are inconsistent by sub-proof % 73.57/10.85 | | | | | | | | | | | | | | | | | | | #54. % 73.57/10.85 | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | (2501) all_10_7 = e2 | all_10_13 = e2 | all_10_21 = e2 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | BETA: splitting (2501) gives: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | (2502) all_10_7 = e2 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (497), (2502) imply: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | (2503) all_4_7 = e2 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (2503) imply: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | (2504) ~ (all_4_8 = e2) % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (2503) imply: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | (2505) ~ (all_4_9 = e2) % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (2503) imply: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | (2506) ~ (all_4_22 = e2) % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | SIMP: (2506) implies: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | (2507) ~ (all_4_22 = e2) % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | REDUCE: (518), (2503) imply: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | (2508) ~ (e3 = e2) % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (2503) imply: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | (2509) op(e3, e2) = all_8_17 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_11, % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | all_8_17, e2, e3, simplifying with (134), (2509) % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | gives: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | (2510) all_8_17 = all_4_11 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_43, % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | all_8_17, e2, e3, simplifying with (2498), (2509) % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | gives: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | (2511) all_8_17 = all_8_43 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2510), (2511) imply: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | (2512) all_8_43 = all_4_11 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | (2513) all_6_9 = e2 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (475), (2483), (2513) are inconsistent by % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | sub-proof #158. % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | (2514) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e1 | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | all_6_9 = e0 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | (2515) all_6_21 = e2 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (460), (2159), (2515) are inconsistent by % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | sub-proof #157. % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | (2516) all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e1 | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | all_6_21 = e0 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | (2517) all_6_14 = e2 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (477), (2507), (2517) are inconsistent by % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #52. % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | (2518) all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e1 | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | all_6_14 = e0 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | (2519) all_6_7 = e2 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (462), (2160), (2519) are inconsistent by % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #9. % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | (2520) ~ (all_6_7 = e2) % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | (2521) all_6_7 = e4 | all_6_7 = e3 | all_6_7 = e1 | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | all_6_7 = e0 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | (2522) all_6_2 = e2 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (510), (2522) are inconsistent by sub-proof % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | #168. % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | (2523) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | all_6_2 = e0 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (2524) (all_8_13 = e4 & ~ (all_8_14 = e3)) | (all_8_17 = % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_8_18 = e3)) % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2524) gives: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2525) all_8_13 = e4 & ~ (all_8_14 = e3) % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2525) implies: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2526) all_8_13 = e4 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (554), (2526) imply: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2527) op(e3, all_4_5) = e4 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2528) all_6_1 = e2 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (454), (508), (2528) are inconsistent by sub-proof % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #155. % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2529) ~ (all_6_1 = e2) % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2530) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_1 = e0 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2531) all_6_5 = e2 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (450), (500), (2531) are inconsistent by sub-proof % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #153. % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2532) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_5 = e0 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2533) all_6_10 = e2 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (451), (502), (2533) are inconsistent by sub-proof % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #106. % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2534) ~ (all_6_10 = e2) % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2535) all_6_10 = e4 | all_6_10 = e3 | all_6_10 = e1 | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_10 = e0 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2536) all_10_20 = e4 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (2536) imply: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2537) all_4_4 = e4 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2537) implies: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2538) all_4_4 = e4 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (100), (2538) imply: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2539) ~ (all_4_2 = e4) % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (2538) imply: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2540) ~ (all_4_9 = e4) % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2540) implies: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2541) ~ (all_4_9 = e4) % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11), (27), (51), (61), (80), (82), (83), % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (96), (102), (104), (108), (128), (131), (285), % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288), (289), (301), (303), (305), (312), (313), % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331), (345), (351), (361), (367), (370), (382), % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385), (391), (394), (398), (450), (451), (454), % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460), (461), (462), (475), (477), (495), (498), % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502), (508), (515), (516), (521), (522), (523), % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524), (529), (531), (567), (2106), (2117), % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2118), (2122), (2127), (2145), (2148), (2149), % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2158), (2478), (2481), (2514), (2516), (2518), % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2521), (2523), (2530), (2532), (2535), (2536), % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2539), (2541), (function-axioms) are inconsistent % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #5. % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2542) all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_24 = e4 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2542) gives: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2543) all_10_21 = e4 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (331), (2543) imply: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2544) all_4_9 = e4 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2544) implies: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2545) all_4_9 = e4 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (83), (2545) imply: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2546) ~ (all_4_5 = e4) % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2547) all_10_12 = e1 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (11), (61), (82), (84), (128), (292), % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301), (345), (348), (391), (454), (461), (462), % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (496), (521), (522), (523), (524), (525), (529), % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2118), (2478), (2481), (2521), (2523), (2530), % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2546), (2547), (function-axioms) are inconsistent % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #4. % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2548) all_10_13 = e1 | all_10_14 = e1 | all_10_15 = e1 | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_19 = e1 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (84), (311), (345), (348), (394), % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454), (496), (535), (2118), (2128), (2481), % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2527), (2530), (2546), (2548), (function-axioms) % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #37. % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2549) all_10_22 = e4 | all_10_23 = e4 | all_10_24 = e4 % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (325), (542), (2143), (2158), (2549) % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #36. % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2550) all_8_17 = e2 & ~ (all_8_18 = e3) % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2160), (2510), (2550) are inconsistent by % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #35. % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (2551) (all_8_20 = e1 & ~ (all_8_21 = e3)) | (all_8_23 = % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_24 = e3)) % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2551) gives: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2552) all_8_20 = e1 & ~ (all_8_21 = e3) % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2552) implies: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2553) all_8_20 = e1 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (556), (2553) imply: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2554) op(e3, all_4_8) = e1 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2555) all_6_1 = e2 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (454), (508), (2555) are inconsistent by sub-proof % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #155. % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2556) ~ (all_6_1 = e2) % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2557) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_1 = e0 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2558) all_6_5 = e2 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (450), (500), (2558) are inconsistent by sub-proof % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #153. % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2559) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_5 = e0 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2560) all_10_20 = e4 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (2560) imply: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2561) all_4_4 = e4 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2561) implies: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2562) all_4_4 = e4 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (100), (2562) imply: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2563) ~ (all_4_2 = e4) % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2564) all_10_0 = e0 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (398), (2564) imply: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2565) e2 = e0 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (2565) imply: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2566) $false % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2566) is inconsistent. % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2567) all_10_2 = e0 | all_10_6 = e0 | all_10_12 = e0 | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_20 = e0 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2568) all_10_1 = e4 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (394), (2568) imply: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2569) all_4_5 = e4 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (82), (2569) imply: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2570) ~ (all_4_10 = e4) % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2570) implies: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2571) ~ (all_4_10 = e4) % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (10), (11), (27), (51), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (96), (102), (104), (108), (288), (290), (303), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317), (345), (348), (351), (361), (367), (370), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382), (385), (391), (398), (450), (475), (477), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (495), (496), (498), (502), (515), (516), (523), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524), (531), (535), (2106), (2117), (2127), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2148), (2149), (2158), (2481), (2482), (2499), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2514), (2518), (2554), (2559), (2560), (2563), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2567), (2571), (function-axioms) are inconsistent % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #33. % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2572) ~ (all_10_1 = e4) % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (2572) imply: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2573) ~ (all_4_5 = e4) % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (11), (61), (82), (84), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (128), (290), (292), (301), (345), (348), (391), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454), (461), (462), (496), (521), (522), (523), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524), (525), (529), (2118), (2478), (2481), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2482), (2499), (2521), (2523), (2554), (2557), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2573), (function-axioms) are inconsistent by % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #3. % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2574) all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_24 = e4 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2574) gives: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2575) all_10_21 = e4 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (331), (2575) imply: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2576) all_4_9 = e4 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2576) implies: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2577) all_4_9 = e4 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (83), (2577) imply: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2578) ~ (all_4_5 = e4) % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (11), (61), (82), (84), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (128), (290), (292), (301), (345), (348), (391), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454), (461), (462), (496), (521), (522), (523), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524), (525), (529), (2118), (2478), (2481), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2482), (2499), (2521), (2523), (2554), (2557), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2578), (function-axioms) are inconsistent by % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #3. % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2579) all_10_22 = e4 | all_10_23 = e4 | all_10_24 = e4 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (325), (542), (2143), (2158), (2579) % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #36. % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2580) all_8_23 = e0 & ~ (all_8_24 = e3) % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2580) implies: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2581) all_8_23 = e0 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (2581) imply: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2582) op(e3, all_4_9) = e0 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2583) all_6_1 = e2 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (454), (508), (2583) are inconsistent by sub-proof % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #155. % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2584) ~ (all_6_1 = e2) % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2585) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_1 = e0 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2586) all_6_5 = e2 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (450), (500), (2586) are inconsistent by sub-proof % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #153. % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2587) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_5 = e0 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2588) all_6_10 = e2 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (451), (502), (2588) are inconsistent by sub-proof % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #106. % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2589) ~ (all_6_10 = e2) % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2590) all_6_10 = e4 | all_6_10 = e3 | all_6_10 = e1 | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_10 = e0 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2591) all_10_20 = e4 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (2591) imply: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2592) all_4_4 = e4 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2592) implies: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2593) all_4_4 = e4 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (100), (2593) imply: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2594) ~ (all_4_2 = e4) % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (2593) imply: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2595) ~ (all_4_9 = e4) % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2595) implies: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2596) ~ (all_4_9 = e4) % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11), (27), (51), (61), (80), (82), (83), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (96), (102), (104), (108), (128), (131), (285), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288), (289), (301), (303), (305), (312), (313), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331), (345), (351), (361), (367), (370), (382), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385), (391), (394), (398), (450), (451), (454), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460), (461), (462), (475), (477), (495), (498), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502), (508), (515), (516), (521), (522), (523), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524), (529), (531), (567), (2106), (2117), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2118), (2122), (2127), (2145), (2148), (2149), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2158), (2478), (2481), (2514), (2516), (2518), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2521), (2523), (2585), (2587), (2590), (2591), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2594), (2596), (function-axioms) are inconsistent % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #5. % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2597) all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_24 = e4 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (136), (325), (331), (542), (2117), % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2143), (2158), (2582), (2597), (function-axioms) % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #32. % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | (2598) all_10_13 = e2 | all_10_21 = e2 % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (331), (348), (2159), (2482), (2598) are % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #64. % 73.57/10.86 | | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.86 | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | (2599) all_10_17 = e2 % 73.57/10.86 | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (2599) imply: % 73.57/10.86 | | | | | | | | | | | | | | | | | | (2600) all_4_21 = e2 % 73.57/10.86 | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | REDUCE: (2483), (2600) imply: % 73.57/10.86 | | | | | | | | | | | | | | | | | | (2601) $false % 73.57/10.86 | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | | CLOSE: (2601) is inconsistent. % 73.57/10.86 | | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | End of split % 73.57/10.86 | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | Case 2: % 73.57/10.86 | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | (2602) ~ (all_6_19 = e2) % 73.57/10.86 | | | | | | | | | | | | | (2603) all_6_19 = e4 | all_6_19 = e3 | all_6_19 = e1 | % 73.57/10.86 | | | | | | | | | | | | | all_6_19 = e0 % 73.57/10.86 | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | REDUCE: (479), (2602) imply: % 73.57/10.86 | | | | | | | | | | | | | (2604) ~ (all_4_23 = e2) % 73.57/10.86 | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | BETA: splitting (291) gives: % 73.57/10.86 | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | Case 1: % 73.57/10.86 | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | (2605) all_10_12 = e2 % 73.57/10.86 | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | REF_CLOSE: (351), (504), (2605) are inconsistent by sub-proof % 73.57/10.86 | | | | | | | | | | | | | | #89. % 73.57/10.86 | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | Case 2: % 73.57/10.86 | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | (2606) all_10_13 = e2 | all_10_14 = e2 | all_10_15 = e2 | % 73.57/10.86 | | | | | | | | | | | | | | all_10_19 = e2 % 73.57/10.86 | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | BETA: splitting (2606) gives: % 73.57/10.86 | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | Case 1: % 73.57/10.86 | | | | | | | | | | | | | | | % 73.57/10.86 | | | | | | | | | | | | | | | (2607) all_10_13 = e2 % 73.57/10.86 | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | COMBINE_EQS: (348), (2607) imply: % 73.57/10.87 | | | | | | | | | | | | | | | (2608) all_4_8 = e2 % 73.57/10.87 | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | SIMP: (2608) implies: % 73.57/10.87 | | | | | | | | | | | | | | | (2609) all_4_8 = e2 % 73.57/10.87 | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | REDUCE: (68), (2609) imply: % 73.57/10.87 | | | | | | | | | | | | | | | (2610) ~ (all_4_9 = e2) % 73.57/10.87 | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | REDUCE: (520), (2609) imply: % 73.57/10.87 | | | | | | | | | | | | | | | (2611) ~ (e4 = e2) % 73.57/10.87 | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | REDUCE: (556), (2609) imply: % 73.57/10.87 | | | | | | | | | | | | | | | (2612) op(e3, e2) = all_8_20 % 73.57/10.87 | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | BETA: splitting (2603) gives: % 73.57/10.87 | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | Case 1: % 73.57/10.87 | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | (2613) all_6_19 = e4 % 73.57/10.87 | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | COMBINE_EQS: (479), (2613) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | (2614) all_4_23 = e4 % 73.57/10.87 | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | REDUCE: (544), (2614) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | (2615) $false % 73.57/10.87 | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | CLOSE: (2615) is inconsistent. % 73.57/10.87 | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | Case 2: % 73.57/10.87 | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | (2616) ~ (all_6_19 = e4) % 73.57/10.87 | | | | | | | | | | | | | | | | (2617) all_6_19 = e3 | all_6_19 = e1 | all_6_19 = e0 % 73.57/10.87 | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | Case 1: % 73.57/10.87 | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | (2618) all_10_12 = e1 % 73.57/10.87 | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (2618) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | (2619) all_4_3 = e1 % 73.57/10.87 | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | SIMP: (2619) implies: % 73.57/10.87 | | | | | | | | | | | | | | | | | (2620) all_4_3 = e1 % 73.57/10.87 | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | REDUCE: (101), (2620) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | (2621) ~ (all_4_2 = e1) % 73.57/10.87 | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | REDUCE: (95), (2620) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | (2622) ~ (all_4_4 = e1) % 73.57/10.87 | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | REDUCE: (91), (2620) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | (2623) ~ (all_4_23 = e1) % 73.57/10.87 | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | REDUCE: (517), (2620) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | (2624) ~ (e4 = e1) % 73.57/10.87 | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | REDUCE: (568), (2620) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | (2625) op(e1, e1) = all_8_8 % 73.57/10.87 | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | BETA: splitting (2617) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.87 | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | (2626) all_6_19 = e1 % 73.57/10.87 | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (479), (2626) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | (2627) all_4_23 = e1 % 73.57/10.87 | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | REDUCE: (2150), (2627) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | (2628) $false % 73.57/10.87 | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | CLOSE: (2628) is inconsistent. % 73.57/10.87 | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.87 | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | (2629) ~ (all_6_19 = e1) % 73.57/10.87 | | | | | | | | | | | | | | | | | | (2630) all_6_19 = e3 | all_6_19 = e0 % 73.57/10.87 | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | BETA: splitting (2630) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | (2631) all_6_19 = e3 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (479), (2631) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | (2632) all_4_23 = e3 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | REDUCE: (25), (2632) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | (2633) ~ (all_4_20 = e3) % 73.57/10.87 | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | REDUCE: (22), (2632) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | (2634) ~ (all_4_21 = e3) % 73.57/10.87 | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | REDUCE: (544), (2632) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | (2635) ~ (e4 = e3) % 73.57/10.87 | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | REDUCE: (582), (2632) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | (2636) op(e0, e3) = all_8_61 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_9, % 73.57/10.87 | | | | | | | | | | | | | | | | | | | all_8_61, e3, e0, simplifying with (120), (2636) % 73.57/10.87 | | | | | | | | | | | | | | | | | | | gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | (2637) all_8_61 = all_4_9 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, all_8_8, % 73.57/10.87 | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (12), (2625) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | (2638) all_8_8 = e4 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_11, % 73.57/10.87 | | | | | | | | | | | | | | | | | | | all_8_20, e2, e3, simplifying with (134), (2612) % 73.57/10.87 | | | | | | | | | | | | | | | | | | | gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | (2639) all_8_20 = all_4_11 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | (2640) all_6_2 = e2 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (461), (510), (2640) are inconsistent by sub-proof % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | #168. % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | (2641) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | all_6_2 = e0 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | (2642) all_6_10 = e2 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (451), (502), (2642) are inconsistent by sub-proof % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | #106. % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | (2643) all_6_10 = e4 | all_6_10 = e3 | all_6_10 = e1 | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | all_6_10 = e0 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | (2644) all_6_9 = e2 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (475), (2644) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | (2645) all_4_21 = e2 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2645) implies: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | (2646) all_4_21 = e2 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (2646) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | (2647) ~ (all_4_16 = e2) % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (2646) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | (2648) op(e0, e2) = all_8_55 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | (2649) all_10_9 = e2 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (388), (2649) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | (2650) all_4_15 = e2 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (512), (2650) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | (2651) $false % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2651) is inconsistent. % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | (2652) all_10_10 = e2 | all_10_11 = e2 | all_10_15 = e2 | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | all_10_23 = e2 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2652) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | (2653) all_10_10 = e2 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (2653) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | (2654) all_4_16 = e2 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2647), (2654) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | (2655) $false % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2655) is inconsistent. % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | (2656) all_10_11 = e2 | all_10_15 = e2 | all_10_23 = e2 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2656) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | (2657) all_10_11 = e2 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (2657) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | (2658) all_4_17 = e2 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (2658) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | (2659) ~ (all_4_22 = e2) % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2659) implies: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | (2660) ~ (all_4_22 = e2) % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (529), (2658) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | (2661) ~ (e3 = e2) % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (2662) all_10_6 = e1 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (367), (2621), (2662) are inconsistent by % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #86. % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (2663) all_10_7 = e1 | all_10_8 = e1 | all_10_11 = e1 | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_18 = e1 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2663) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2664) all_10_7 = e1 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (497), (2664) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2665) all_4_7 = e1 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (2665) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2666) ~ (all_4_5 = e1) % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (2665) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2667) ~ (all_4_9 = e1) % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (2665) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2668) ~ (all_4_22 = e1) % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (518), (2665) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2669) ~ (e3 = e1) % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (2665) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2670) op(e3, e1) = all_8_17 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_55, % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (2165), (2648) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2671) all_8_55 = e2 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_16, % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_17, e1, e3, simplifying with (133), (2670) % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2672) all_8_17 = all_4_16 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2673) (all_8_52 = e4 & ~ (all_8_53 = e0)) | (all_8_55 = % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ~ (all_8_56 = e0)) % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2673) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2674) all_8_52 = e4 & ~ (all_8_53 = e0) % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2674) implies: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2675) all_8_52 = e4 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (579), (2675) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2676) op(e0, all_4_20) = e4 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2677) all_6_21 = e2 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (460), (2677) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2678) all_4_9 = e2 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2159), (2678) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2679) $false % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2679) is inconsistent. % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2680) all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e1 | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_21 = e0 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2681) all_6_1 = e2 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (454), (2681) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2682) all_4_5 = e2 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (508), (2682) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2683) $false % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2683) is inconsistent. % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2684) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_1 = e0 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2685) (all_8_13 = e4 & ~ (all_8_14 = e3)) | (all_8_17 = % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_8_18 = e3)) % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2685) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2686) all_8_13 = e4 & ~ (all_8_14 = e3) % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2686) implies: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2687) all_8_13 = e4 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (554), (2687) imply: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2688) op(e3, all_4_5) = e4 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2689) all_10_20 = e4 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (11), (39), (82), (83), (88), (90), % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296), (301), (312), (314), (318), (325), (331), % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (385), (388), (391), (394), (398), (460), % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (506), (521), (522), (535), (578), (2105), % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2116), (2118), (2122), (2144), (2145), (2147), % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2151), (2158), (2607), (2633), (2641), (2664), % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2676), (2680), (2689), (function-axioms) are % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #2. % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2690) all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_24 = e4 % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (83), (311), (325), (331), (394), % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454), (542), (2118), (2122), (2128), (2143), % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2158), (2666), (2684), (2688), (2690), % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #26. % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2691) all_8_17 = e2 & ~ (all_8_18 = e3) % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2647), (2672), (2691) are inconsistent by % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #25. % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2692) (all_8_20 = e1 & ~ (all_8_21 = e3)) | (all_8_23 = % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_24 = e3)) % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2692) gives: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2693) all_8_20 = e1 & ~ (all_8_21 = e3) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2693) implies: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2694) all_8_20 = e1 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2639), (2694) imply: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2695) all_4_11 = e1 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (128), (529), (2478), (2695), (function-axioms) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #8. % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2696) all_8_23 = e0 & ~ (all_8_24 = e3) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2696) implies: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2697) all_8_23 = e0 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (2697) imply: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2698) op(e3, all_4_9) = e0 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2699) all_10_20 = e4 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (11), (39), (82), (83), (88), (90), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296), (301), (312), (314), (318), (325), (331), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (385), (388), (391), (394), (398), (460), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (506), (521), (522), (535), (578), (2105), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2116), (2118), (2122), (2144), (2145), (2147), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2151), (2158), (2607), (2633), (2641), (2664), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2676), (2680), (2699), (function-axioms) are % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #2. % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2700) all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_24 = e4 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (136), (325), (331), (542), (2117), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2143), (2158), (2698), (2700), (function-axioms) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #32. % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2701) all_8_55 = e3 & ~ (all_8_56 = e0) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2671), (2701) are inconsistent by sub-proof % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #97. % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2702) (all_8_58 = e2 & ~ (all_8_59 = e0)) | (all_8_61 = % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_8_62 = e0)) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2702) gives: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2703) all_8_58 = e2 & ~ (all_8_59 = e0) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2703) implies: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2704) all_8_58 = e2 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (2704) imply: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2705) op(e0, all_4_22) = e2 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2706) all_6_14 = e2 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (477), (2660), (2706) are inconsistent by % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #52. % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2707) all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e1 | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_14 = e0 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2708) all_6_1 = e2 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (454), (2708) imply: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2709) all_4_5 = e2 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (508), (2709) imply: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2710) $false % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2710) is inconsistent. % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2711) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_1 = e0 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2712) (all_8_1 = e3 & ~ (all_8_2 = e4)) | (all_8_4 = e2 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_5 = e4)) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2712) gives: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2713) all_8_1 = e3 & ~ (all_8_2 = e4) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2713) implies: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2714) all_8_1 = e3 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (2714) imply: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2715) op(e4, all_4_1) = e3 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2716) (all_8_13 = e4 & ~ (all_8_14 = e3)) | (all_8_17 = % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_8_18 = e3)) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (11), (26), (82), (83), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (90), (106), (121), (140), (286), (296), (301), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311), (312), (314), (317), (318), (325), (331), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (367), (382), (385), (388), (391), (394), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398), (454), (461), (477), (500), (506), (512), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515), (521), (522), (531), (535), (542), (551), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (554), (576), (2116), (2117), (2118), (2122), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2128), (2143), (2144), (2149), (2158), (2607), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2618), (2633), (2641), (2647), (2664), (2666), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2672), (2705), (2707), (2711), (2715), (2716), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #14. % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2717) (all_8_20 = e1 & ~ (all_8_21 = e3)) | (all_8_23 = % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_24 = e3)) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2717) gives: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2718) all_8_20 = e1 & ~ (all_8_21 = e3) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2718) implies: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2719) all_8_20 = e1 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2639), (2719) imply: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2720) all_4_11 = e1 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (128), (529), (2478), (2720), (function-axioms) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #8. % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2721) all_8_23 = e0 & ~ (all_8_24 = e3) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (11), (26), (82), (90), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (106), (121), (136), (140), (286), (296), (301), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312), (314), (317), (318), (325), (331), (334), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367), (382), (385), (388), (391), (394), (398), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (477), (500), (506), (512), (515), (521), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522), (531), (535), (542), (551), (557), (576), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2116), (2117), (2118), (2143), (2144), (2149), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2158), (2607), (2618), (2633), (2641), (2664), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2705), (2707), (2715), (2721), (function-axioms) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #13. % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2722) all_8_4 = e2 & ~ (all_8_5 = e4) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2722) implies: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2723) all_8_4 = e2 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (2723) imply: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2724) op(e4, all_4_2) = e2 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2725) (all_8_13 = e4 & ~ (all_8_14 = e3)) | (all_8_17 = % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_8_18 = e3)) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (10), (11), (82), (83), (90), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (100), (137), (286), (296), (297), (301), (311), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312), (314), (318), (325), (331), (334), (367), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385), (388), (391), (394), (398), (451), (454), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (502), (506), (515), (521), (522), (525), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535), (542), (552), (554), (2116), (2118), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2122), (2128), (2143), (2144), (2158), (2607), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2621), (2633), (2641), (2643), (2647), (2664), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2666), (2672), (2711), (2724), (2725), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #22. % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2726) (all_8_20 = e1 & ~ (all_8_21 = e3)) | (all_8_23 = % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_24 = e3)) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2726) gives: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2727) all_8_20 = e1 & ~ (all_8_21 = e3) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2727) implies: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2728) all_8_20 = e1 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2639), (2728) imply: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2729) all_4_11 = e1 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (128), (529), (2478), (2729), (function-axioms) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #8. % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2730) all_8_23 = e0 & ~ (all_8_24 = e3) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (10), (11), (82), (90), (100), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (136), (137), (286), (296), (297), (301), (312), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314), (318), (325), (331), (334), (367), (385), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388), (391), (394), (398), (451), (461), (502), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506), (515), (521), (522), (525), (535), (542), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552), (557), (2116), (2117), (2118), (2143), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2144), (2158), (2607), (2621), (2633), (2641), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2643), (2664), (2724), (2730), (function-axioms) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #21. % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2731) (all_8_7 = e1 & ~ (all_8_8 = e4)) | (all_8_10 = % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_11 = e4)) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2731) gives: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2732) all_8_7 = e1 & ~ (all_8_8 = e4) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2732) implies: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2733) ~ (all_8_8 = e4) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2638), (2733) imply: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2734) $false % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2734) is inconsistent. % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2735) all_8_10 = e0 & ~ (all_8_11 = e4) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2735) implies: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2736) all_8_10 = e0 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (2736) imply: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2737) op(e4, all_4_4) = e0 % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2738) (all_8_13 = e4 & ~ (all_8_14 = e3)) | (all_8_17 = % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_8_18 = e3)) % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (10), (15), (83), (90), (286), (311), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312), (325), (331), (334), (394), (454), (506), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535), (542), (549), (554), (2116), (2118), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2122), (2128), (2143), (2144), (2158), (2607), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2647), (2664), (2666), (2672), (2711), (2737), % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2738), (function-axioms) are inconsistent by % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #18. % 73.57/10.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2739) (all_8_20 = e1 & ~ (all_8_21 = e3)) | (all_8_23 = % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_24 = e3)) % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2739) gives: % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2740) all_8_20 = e1 & ~ (all_8_21 = e3) % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2740) implies: % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2741) all_8_20 = e1 % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2639), (2741) imply: % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2742) all_4_11 = e1 % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (128), (529), (2478), (2742), (function-axioms) % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #8. % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2743) all_8_23 = e0 & ~ (all_8_24 = e3) % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (10), (15), (90), (136), (286), (312), % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (331), (334), (394), (506), (535), (542), % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549), (557), (2116), (2117), (2143), (2144), % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2158), (2607), (2664), (2737), (2743), % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #17. % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2744) all_8_61 = e1 & ~ (all_8_62 = e0) % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2145), (2637), (2744) are inconsistent by % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #96. % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2745) all_10_8 = e1 | all_10_11 = e1 | all_10_18 = e1 % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (361), (495), (2149), (2657), (2745) are % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #12. % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (2746) all_10_15 = e2 | all_10_23 = e2 % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (325), (496), (2162), (2746) are % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #87. % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | End of split % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | (2747) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e1 | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | all_6_9 = e0 % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2747) gives: % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.57/10.89 | | | | | | | | | | | | | | | | | | | | | | | (2748) all_6_9 = e4 % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (475), (2748) imply: % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | (2749) all_4_21 = e4 % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2749) implies: % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | (2750) all_4_21 = e4 % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (2750) imply: % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | (2751) ~ (all_4_11 = e4) % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives: % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (2752) all_6_7 = e2 % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (462), (2160), (2752) are inconsistent by % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #9. % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (2753) all_6_7 = e4 | all_6_7 = e3 | all_6_7 = e1 | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | | all_6_7 = e0 % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (128), (462), (523), (524), (529), (2478), (2751), % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (2753), (function-axioms) are inconsistent by % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #7. % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | (2754) all_6_9 = e3 | all_6_9 = e1 | all_6_9 = e0 % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (475), (2127), (2148), (2634), (2754) are % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #111. % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.89 | | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.89 | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.89 | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | (2755) all_6_19 = e0 % 73.93/10.89 | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (479), (2755) imply: % 73.93/10.89 | | | | | | | | | | | | | | | | | | | (2756) all_4_23 = e0 % 73.93/10.89 | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | REDUCE: (537), (2756) imply: % 73.93/10.89 | | | | | | | | | | | | | | | | | | | (2757) $false % 73.93/10.89 | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | | CLOSE: (2757) is inconsistent. % 73.93/10.89 | | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | | End of split % 73.93/10.89 | | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | End of split % 73.93/10.89 | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | Case 2: % 73.93/10.89 | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | (2758) ~ (all_10_12 = e1) % 73.93/10.89 | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (351), (452), (479), (516), (517), (537), % 73.93/10.89 | | | | | | | | | | | | | | | | | (2150), (2154), (2617), (2758) are inconsistent by % 73.93/10.89 | | | | | | | | | | | | | | | | | sub-proof #11. % 73.93/10.89 | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | End of split % 73.93/10.89 | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | End of split % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | Case 2: % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | (2759) all_10_14 = e2 | all_10_15 = e2 | all_10_19 = e2 % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (337), (345), (496), (2604), (2759) are % 73.93/10.89 | | | | | | | | | | | | | | | inconsistent by sub-proof #10. % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | End of split % 73.93/10.89 | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | End of split % 73.93/10.89 | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | End of split % 73.93/10.89 | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | End of split % 73.93/10.89 | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | Case 2: % 73.93/10.89 | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | (2760) (all_8_33 = e1 & ~ (all_8_34 = e2)) | (all_8_36 = % 73.93/10.89 | | | | | | | | | | | e0 & ~ (all_8_37 = e2)) % 73.93/10.89 | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | BETA: splitting (2760) gives: % 73.93/10.89 | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | Case 1: % 73.93/10.89 | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | (2761) all_8_33 = e1 & ~ (all_8_34 = e2) % 73.93/10.89 | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | REF_CLOSE: (584), (2149), (2761) are inconsistent by % 73.93/10.89 | | | | | | | | | | | | sub-proof #1. % 73.93/10.89 | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | Case 2: % 73.93/10.89 | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | (2762) all_8_36 = e0 & ~ (all_8_37 = e2) % 73.93/10.89 | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | REF_CLOSE: (525), (2167), (2762) are inconsistent by % 73.93/10.89 | | | | | | | | | | | | sub-proof #93. % 73.93/10.89 | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | End of split % 73.93/10.89 | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | End of split % 73.93/10.89 | | | | | | | | | | % 73.93/10.89 | | | | | | | | | Case 2: % 73.93/10.89 | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | (2763) all_6_22 = e4 | all_6_22 = e3 | all_6_22 = e1 | % 73.93/10.89 | | | | | | | | | | all_6_22 = e0 % 73.93/10.89 | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | BETA: splitting (2763) gives: % 73.93/10.89 | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | Case 1: % 73.93/10.89 | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | (2764) all_6_22 = e4 % 73.93/10.89 | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | COMBINE_EQS: (466), (2764) imply: % 73.93/10.89 | | | | | | | | | | | (2765) all_4_14 = e4 % 73.93/10.89 | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | SIMP: (2765) implies: % 73.93/10.89 | | | | | | | | | | | (2766) all_4_14 = e4 % 73.93/10.89 | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | COMBINE_EQS: (328), (2766) imply: % 73.93/10.89 | | | | | | | | | | | (2767) all_10_22 = e4 % 73.93/10.89 | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | REDUCE: (58), (2766) imply: % 73.93/10.89 | | | | | | | | | | | (2768) ~ (all_4_10 = e4) % 73.93/10.89 | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | REDUCE: (53), (2766) imply: % 73.93/10.89 | | | | | | | | | | | (2769) ~ (all_4_11 = e4) % 73.93/10.89 | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | REDUCE: (565), (2766) imply: % 73.93/10.89 | | | | | | | | | | | (2770) op(e2, e4) = all_8_36 % 73.93/10.89 | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | REDUCE: (577), (2766) imply: % 73.93/10.89 | | | | | | | | | | | (2771) op(e0, e4) = all_8_37 % 73.93/10.89 | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | BETA: splitting (183) gives: % 73.93/10.89 | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | Case 1: % 73.93/10.89 | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | (2772) all_6_2 = e2 % 73.93/10.89 | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | REF_CLOSE: (461), (510), (2772) are inconsistent by sub-proof % 73.93/10.89 | | | | | | | | | | | | #168. % 73.93/10.89 | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | Case 2: % 73.93/10.89 | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | (2773) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | % 73.93/10.89 | | | | | | | | | | | | all_6_2 = e0 % 73.93/10.89 | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | BETA: splitting (2773) gives: % 73.93/10.89 | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | Case 1: % 73.93/10.89 | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | (2774) all_6_2 = e4 % 73.93/10.89 | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | REF_CLOSE: (461), (2768), (2774) are inconsistent by % 73.93/10.89 | | | | | | | | | | | | | sub-proof #164. % 73.93/10.89 | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | Case 2: % 73.93/10.89 | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | (2775) ~ (all_6_2 = e4) % 73.93/10.89 | | | | | | | | | | | | | (2776) all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 73.93/10.89 | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | BETA: splitting (2776) gives: % 73.93/10.89 | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | Case 1: % 73.93/10.89 | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | (2777) all_6_2 = e1 % 73.93/10.89 | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | COMBINE_EQS: (461), (2777) imply: % 73.93/10.89 | | | | | | | | | | | | | | (2778) all_4_10 = e1 % 73.93/10.89 | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | SIMP: (2778) implies: % 73.93/10.89 | | | | | | | | | | | | | | (2779) all_4_10 = e1 % 73.93/10.89 | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | REDUCE: (82), (2779) imply: % 73.93/10.89 | | | | | | | | | | | | | | (2780) ~ (all_4_5 = e1) % 73.93/10.89 | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | REDUCE: (61), (2779) imply: % 73.93/10.89 | | | | | | | | | | | | | | (2781) ~ (all_4_11 = e1) % 73.93/10.89 | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | SIMP: (2781) implies: % 73.93/10.89 | | | | | | | | | | | | | | (2782) ~ (all_4_11 = e1) % 73.93/10.89 | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | REDUCE: (57), (2779) imply: % 73.93/10.89 | | | | | | | | | | | | | | (2783) ~ (all_4_15 = e1) % 73.93/10.89 | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | SIMP: (2783) implies: % 73.93/10.89 | | | | | | | | | | | | | | (2784) ~ (all_4_15 = e1) % 73.93/10.89 | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | REDUCE: (56), (2779) imply: % 73.93/10.89 | | | | | | | | | | | | | | (2785) ~ (all_4_20 = e1) % 73.93/10.89 | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | SIMP: (2785) implies: % 73.93/10.89 | | | | | | | | | | | | | | (2786) ~ (all_4_20 = e1) % 73.93/10.89 | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | REDUCE: (2768), (2779) imply: % 73.93/10.89 | | | | | | | | | | | | | | (2787) ~ (e4 = e1) % 73.93/10.89 | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | REDUCE: (550), (2779) imply: % 73.93/10.89 | | | | | | | | | | | | | | (2788) op(e4, e1) = all_8_27 % 73.93/10.89 | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | REDUCE: (562), (2779) imply: % 73.93/10.89 | | | | | | | | | | | | | | (2789) op(e2, e1) = all_8_26 % 73.93/10.89 | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | BETA: splitting (179) gives: % 73.93/10.89 | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | Case 1: % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | (2790) all_6_7 = e2 % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | COMBINE_EQS: (462), (2790) imply: % 73.93/10.89 | | | | | | | | | | | | | | | (2791) all_4_11 = e2 % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | COMBINE_EQS: (498), (2791) imply: % 73.93/10.89 | | | | | | | | | | | | | | | (2792) all_10_5 = e2 % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | REDUCE: (52), (2791) imply: % 73.93/10.89 | | | | | | | | | | | | | | | (2793) ~ (all_4_16 = e2) % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | SIMP: (2793) implies: % 73.93/10.89 | | | | | | | | | | | | | | | (2794) ~ (all_4_16 = e2) % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | REDUCE: (51), (2791) imply: % 73.93/10.89 | | | | | | | | | | | | | | | (2795) ~ (all_4_21 = e2) % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | SIMP: (2795) implies: % 73.93/10.89 | | | | | | | | | | | | | | | (2796) ~ (all_4_21 = e2) % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | REDUCE: (2769), (2791) imply: % 73.93/10.89 | | | | | | | | | | | | | | | (2797) ~ (e4 = e2) % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | REDUCE: (558), (2791) imply: % 73.93/10.89 | | | | | | | | | | | | | | | (2798) op(e3, e2) = all_8_30 % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | REDUCE: (134), (2791) imply: % 73.93/10.89 | | | | | | | | | | | | | | | (2799) op(e3, e2) = e2 % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_4, % 73.93/10.89 | | | | | | | | | | | | | | | all_8_37, e4, e0, simplifying with (121), (2771) % 73.93/10.89 | | | | | | | | | | | | | | | gives: % 73.93/10.89 | | | | | | | | | | | | | | | (2800) all_8_37 = all_4_4 % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_17, % 73.93/10.89 | | | | | | | | | | | | | | | all_8_26, e1, e2, simplifying with (128), (2789) % 73.93/10.89 | | | | | | | | | | | | | | | gives: % 73.93/10.89 | | | | | | | | | | | | | | | (2801) all_8_26 = all_4_17 % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 73.93/10.89 | | | | | | | | | | | | | | | all_8_36, e4, e2, simplifying with (131), (2770) % 73.93/10.89 | | | | | | | | | | | | | | | gives: % 73.93/10.89 | | | | | | | | | | | | | | | (2802) all_8_36 = all_4_2 % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_30, % 73.93/10.89 | | | | | | | | | | | | | | | e2, e3, simplifying with (2798), (2799) gives: % 73.93/10.89 | | | | | | | | | | | | | | | (2803) all_8_30 = e2 % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_15, % 73.93/10.89 | | | | | | | | | | | | | | | all_8_27, e1, e4, simplifying with (138), (2788) % 73.93/10.89 | | | | | | | | | | | | | | | gives: % 73.93/10.89 | | | | | | | | | | | | | | | (2804) all_8_27 = all_4_15 % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 73.93/10.89 | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | Case 1: % 73.93/10.89 | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | (2805) (all_8_26 = e4 & ~ (all_8_27 = e2)) | (all_8_29 = % 73.93/10.89 | | | | | | | | | | | | | | | | e3 & ~ (all_8_30 = e2)) % 73.93/10.89 | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | BETA: splitting (2805) gives: % 73.93/10.89 | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | Case 1: % 73.93/10.89 | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | (2806) all_8_26 = e4 & ~ (all_8_27 = e2) % 73.93/10.89 | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | ALPHA: (2806) implies: % 73.93/10.89 | | | | | | | | | | | | | | | | | (2807) all_8_26 = e4 % 73.93/10.89 | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | COMBINE_EQS: (2801), (2807) imply: % 73.93/10.89 | | | | | | | | | | | | | | | | | (2808) all_4_17 = e4 % 73.93/10.89 | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | REDUCE: (540), (2808) imply: % 73.93/10.89 | | | | | | | | | | | | | | | | | (2809) $false % 73.93/10.89 | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | CLOSE: (2809) is inconsistent. % 73.93/10.89 | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | Case 2: % 73.93/10.89 | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | (2810) all_8_29 = e3 & ~ (all_8_30 = e2) % 73.93/10.89 | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | ALPHA: (2810) implies: % 73.93/10.89 | | | | | | | | | | | | | | | | | (2811) ~ (all_8_30 = e2) % 73.93/10.89 | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | REDUCE: (2803), (2811) imply: % 73.93/10.89 | | | | | | | | | | | | | | | | | (2812) $false % 73.93/10.89 | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | | CLOSE: (2812) is inconsistent. % 73.93/10.89 | | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | | End of split % 73.93/10.89 | | | | | | | | | | | | | | | | % 73.93/10.89 | | | | | | | | | | | | | | | Case 2: % 73.93/10.89 | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | (2813) (all_8_33 = e1 & ~ (all_8_34 = e2)) | (all_8_36 = % 73.93/10.90 | | | | | | | | | | | | | | | | e0 & ~ (all_8_37 = e2)) % 73.93/10.90 | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | BETA: splitting (2813) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | (2814) all_8_33 = e1 & ~ (all_8_34 = e2) % 73.93/10.90 | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | REF_CLOSE: (584), (2149), (2814) are inconsistent by % 73.93/10.90 | | | | | | | | | | | | | | | | | sub-proof #1. % 73.93/10.90 | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | Case 2: % 73.93/10.90 | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | (2815) all_8_36 = e0 & ~ (all_8_37 = e2) % 73.93/10.90 | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | ALPHA: (2815) implies: % 73.93/10.90 | | | | | | | | | | | | | | | | | (2816) all_8_36 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | (2817) ~ (all_8_37 = e2) % 73.93/10.90 | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | COMBINE_EQS: (2802), (2816) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | (2818) all_4_2 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | SIMP: (2818) implies: % 73.93/10.90 | | | | | | | | | | | | | | | | | (2819) all_4_2 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | COMBINE_EQS: (367), (2819) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | (2820) all_10_6 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | REDUCE: (100), (2819) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | (2821) ~ (all_4_4 = e0) % 73.93/10.90 | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | SIMP: (2821) implies: % 73.93/10.90 | | | | | | | | | | | | | | | | | (2822) ~ (all_4_4 = e0) % 73.93/10.90 | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | REDUCE: (96), (2819) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | (2823) ~ (all_4_22 = e0) % 73.93/10.90 | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | SIMP: (2823) implies: % 73.93/10.90 | | | | | | | | | | | | | | | | | (2824) ~ (all_4_22 = e0) % 73.93/10.90 | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | REDUCE: (502), (2819) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | (2825) ~ (e2 = e0) % 73.93/10.90 | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | REDUCE: (546), (2819) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | (2826) op(e4, e0) = all_8_4 % 73.93/10.90 | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | (2827) all_10_0 = e4 % 73.93/10.90 | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (398), (2827) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | (2828) e4 = e2 % 73.93/10.90 | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | SIMP: (2828) implies: % 73.93/10.90 | | | | | | | | | | | | | | | | | | (2829) e4 = e2 % 73.93/10.90 | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | REDUCE: (10), (2829) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | (2830) $false % 73.93/10.90 | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | CLOSE: (2830) is inconsistent. % 73.93/10.90 | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.90 | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | (2831) ~ (all_10_0 = e4) % 73.93/10.90 | | | | | | | | | | | | | | | | | | (2832) all_10_2 = e4 | all_10_6 = e4 | all_10_12 = e4 | % 73.93/10.90 | | | | | | | | | | | | | | | | | | all_10_20 = e4 % 73.93/10.90 | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | BETA: splitting (170) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | (2833) all_6_20 = e2 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (2833) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | (2834) all_4_4 = e2 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | REDUCE: (506), (2834) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | (2835) $false % 73.93/10.90 | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | CLOSE: (2835) is inconsistent. % 73.93/10.90 | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | (2836) ~ (all_6_20 = e2) % 73.93/10.90 | | | | | | | | | | | | | | | | | | | (2837) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e1 | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | all_6_20 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | BETA: splitting (2105) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | (2838) all_10_20 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (2838) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | (2839) all_4_4 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | REDUCE: (2822), (2839) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | (2840) $false % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | CLOSE: (2840) is inconsistent. % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | (2841) all_10_21 = e0 | all_10_22 = e0 | all_10_23 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2841) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | (2842) all_10_21 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (331), (2842) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | (2843) all_4_9 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2122), (2843) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | (2844) $false % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | CLOSE: (2844) is inconsistent. % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | (2845) all_10_22 = e0 | all_10_23 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2832) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | (2846) all_10_2 = e4 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (382), (2846) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | (2847) all_4_1 = e4 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (2847) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | (2848) ~ (all_4_3 = e4) % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (106), (2847) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | (2849) ~ (all_4_4 = e4) % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2849) implies: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | (2850) ~ (all_4_4 = e4) % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (102), (2847) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | (2851) ~ (all_4_21 = e4) % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2851) implies: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | (2852) ~ (all_4_21 = e4) % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (2847) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | (2853) op(e4, e4) = all_8_1 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2837) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | (2854) all_6_20 = e4 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (453), (2850), (2854) are inconsistent by % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #74. % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | (2855) all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2855) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | (2856) all_6_20 = e1 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (453), (2144), (2856) are inconsistent by % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #73. % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | (2857) ~ (all_6_20 = e1) % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | (2858) all_6_20 = e3 | all_6_20 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2845) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | (2859) all_10_22 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2767), (2859) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | (2860) e4 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (535), (2860) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | (2861) $false % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2861) is inconsistent. % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | (2862) all_10_23 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (325), (2862) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | (2863) all_4_19 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (2863) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | (2864) ~ (all_4_15 = e0) % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (32), (2863) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | (2865) ~ (all_4_17 = e0) % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (2866) all_6_9 = e2 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (475), (2796), (2866) are inconsistent by % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #158. % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (2867) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e1 | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_9 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2868) all_10_0 = e1 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (398), (2868) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2869) e2 = e1 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (2869) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2870) $false % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2870) is inconsistent. % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2871) ~ (all_10_0 = e1) % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2872) all_10_2 = e1 | all_10_6 = e1 | all_10_12 = e1 | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_20 = e1 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2872) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2873) all_10_2 = e1 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2846), (2873) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2874) e4 = e1 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (2874) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2875) $false % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2875) is inconsistent. % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2876) all_10_6 = e1 | all_10_12 = e1 | all_10_20 = e1 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2877) all_6_3 = e2 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (468), (512), (2877) are inconsistent by sub-proof % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #152. % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2878) all_6_3 = e4 | all_6_3 = e3 | all_6_3 = e1 | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_3 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2878) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2879) all_6_3 = e4 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (468), (538), (2879) are inconsistent by sub-proof % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #149. % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2880) all_6_3 = e3 | all_6_3 = e1 | all_6_3 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (284) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2881) all_10_20 = e2 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (2881) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2882) all_4_4 = e2 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (506), (2882) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2883) $false % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2883) is inconsistent. % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2884) all_10_21 = e2 | all_10_22 = e2 | all_10_23 = e2 | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_24 = e2 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2884) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2885) all_10_21 = e2 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (331), (2885) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2886) all_4_9 = e2 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (2886) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2887) ~ (all_4_8 = e2) % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2880) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2888) all_6_3 = e1 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (468), (2784), (2888) are inconsistent by % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #146. % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2889) all_6_3 = e3 | all_6_3 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2889) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2890) all_6_3 = e3 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (468), (2890) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2891) all_4_15 = e3 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2891) implies: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2892) all_4_15 = e3 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (388), (2892) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2893) all_10_9 = e3 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (2892) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2894) ~ (all_4_5 = e3) % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (2892) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2895) op(e4, e1) = e3 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2858) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2896) all_6_20 = e3 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (2896) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2897) all_4_4 = e3 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2897) implies: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2898) all_4_4 = e3 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (2898) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2899) all_10_20 = e3 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (95), (2898) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2900) ~ (all_4_3 = e3) % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (2898) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2901) op(e4, e3) = all_8_10 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2902) all_6_1 = e2 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (454), (508), (2902) are inconsistent by sub-proof % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #155. % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2903) ~ (all_6_1 = e2) % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2904) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_1 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2905) all_10_12 = e2 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (351), (2905) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2906) all_4_3 = e2 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (504), (2906) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2907) $false % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2907) is inconsistent. % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2908) all_10_13 = e2 | all_10_14 = e2 | all_10_15 = e2 | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_19 = e2 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2904) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2909) all_6_1 = e4 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (454), (2909) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2910) all_4_5 = e4 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2910) implies: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2911) all_4_5 = e4 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (80), (2911) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2912) ~ (all_4_20 = e4) % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2912) implies: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2913) ~ (all_4_20 = e4) % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (549), (2911) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2914) op(e4, e4) = all_8_14 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (2911) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2915) op(e4, e3) = e4 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2106) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2916) all_10_16 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (2916) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2917) all_4_20 = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2786), (2917) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2918) ~ (e1 = e0) % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (2917) imply: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2919) op(e4, e0) = e0 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2154) gives: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2920) all_6_15 = e4 % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (452), (517), (2920) are inconsistent by sub-proof % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #107. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2921) all_6_15 = e3 | all_6_15 = e1 | all_6_15 = e0 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2921) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2922) all_6_15 = e1 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (452), (2922) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2923) all_4_3 = e1 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2923) implies: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2924) all_4_3 = e1 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2900), (2924) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2925) ~ (e3 = e1) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (547), (2924) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2926) op(e4, e1) = all_8_7 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_8_4, % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e4, simplifying with (2826), (2919) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2927) all_8_4 = e0 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_8_7, % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e4, simplifying with (2895), (2926) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2928) all_8_7 = e3 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, all_8_10, % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e4, simplifying with (2901), (2915) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2929) all_8_10 = e4 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_1, % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e4, simplifying with (15), (2853) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2930) all_8_1 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_14, % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_1, e4, e4, simplifying with (2853), (2914) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2931) all_8_1 = all_8_14 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2930), (2931) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2932) all_8_14 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2933) (all_8_1 = e3 & ~ (all_8_2 = e4)) | (all_8_4 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_5 = e4)) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2933) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2934) all_8_1 = e3 & ~ (all_8_2 = e4) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2934) implies: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2935) all_8_1 = e3 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2930), (2935) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2936) e3 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2936) implies: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2937) e3 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (2937) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2938) $false % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2938) is inconsistent. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2939) all_8_4 = e2 & ~ (all_8_5 = e4) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2939) implies: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2940) all_8_4 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2927), (2940) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2941) e2 = e0 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (2941) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2942) $false % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2942) is inconsistent. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2943) (all_8_7 = e1 & ~ (all_8_8 = e4)) | (all_8_10 = % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ~ (all_8_11 = e4)) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2943) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2944) all_8_7 = e1 & ~ (all_8_8 = e4) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2928), (2944) are inconsistent by sub-proof % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #101. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2945) all_8_10 = e0 & ~ (all_8_11 = e4) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2945) implies: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2946) all_8_10 = e0 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2929), (2946) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2947) e4 = e0 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (535), (2947) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2948) $false % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2948) is inconsistent. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2949) ~ (all_6_15 = e1) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (452), (2949) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2950) ~ (all_4_3 = e1) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2876) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2951) all_10_6 = e1 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2820), (2951) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2952) e1 = e0 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (2952) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2953) $false % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2953) is inconsistent. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2954) all_10_12 = e1 | all_10_20 = e1 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2954) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2955) all_10_12 = e1 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (351), (2950), (2955) are inconsistent by % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #59. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2956) all_10_20 = e1 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2899), (2956) are inconsistent by sub-proof % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #151. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2957) all_10_17 = e0 | all_10_18 = e0 | all_10_19 = e0 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2958) all_10_9 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2893), (2958) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2959) e3 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (2959) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2960) $false % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2960) is inconsistent. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2961) all_10_10 = e2 | all_10_11 = e2 | all_10_15 = e2 | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_23 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2961) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2962) all_10_10 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (2962) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2963) all_4_16 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2794), (2963) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2964) $false % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2964) is inconsistent. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2965) all_10_11 = e2 | all_10_15 = e2 | all_10_23 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2867) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2966) all_6_9 = e4 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (475), (2852), (2966) are inconsistent by % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #114. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2967) all_6_9 = e3 | all_6_9 = e1 | all_6_9 = e0 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2968) all_6_13 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (470), (2968) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2969) all_4_17 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2969) implies: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2970) all_4_17 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (2970) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2971) ~ (all_4_22 = e2) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2971) implies: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2972) ~ (all_4_22 = e2) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2973) all_6_14 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (477), (2972), (2973) are inconsistent by % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #52. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2974) ~ (all_6_14 = e2) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2975) all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e1 | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_14 = e0 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2908) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2976) all_10_13 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (348), (2887), (2976) are inconsistent by % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #88. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2977) all_10_14 = e2 | all_10_15 = e2 | all_10_19 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2975) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2978) all_6_14 = e4 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (477), (2978) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2979) all_4_22 = e4 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2979) implies: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2980) all_4_22 = e4 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (495), (2980) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2981) all_10_18 = e4 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2977) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2982) all_10_14 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (345), (2982) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2983) e2 = e0 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (2983) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2984) $false % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2984) is inconsistent. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2985) ~ (all_10_14 = e2) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2986) all_10_15 = e2 | all_10_19 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2967) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2987) all_6_9 = e1 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (475), (2148), (2987) are inconsistent by % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #113. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2988) all_6_9 = e3 | all_6_9 = e0 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2989) all_6_19 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (479), (2989) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2990) all_4_23 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2990) implies: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2991) all_4_23 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (337), (2991) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2992) all_10_19 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (370), (475), (535), (2127), (2957), (2981), % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2988), (2992) are inconsistent by sub-proof #51. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2993) ~ (all_6_19 = e2) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (479), (2993) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2994) ~ (all_4_23 = e2) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (337), (496), (2986), (2994) are % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #60. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2995) all_6_14 = e3 | all_6_14 = e1 | all_6_14 = e0 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (477), (531), (2149), (2824), (2995) are % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #48. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2996) ~ (all_6_13 = e2) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (470), (2996) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2997) ~ (all_4_17 = e2) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (357), (496), (2862), (2965), (2997) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #117. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2998) all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (454), (2118), (2780), (2894), (2998) are % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #135. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2999) all_6_20 = e0 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (2999) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3000) all_4_4 = e0 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3000) implies: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3001) all_4_4 = e0 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2822), (3001) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3002) $false % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3002) is inconsistent. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3003) all_6_3 = e0 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (468), (2864), (3003) are inconsistent by % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #145. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3004) all_10_22 = e2 | all_10_23 = e2 | all_10_24 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3004) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3005) all_10_22 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2767), (3005) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3006) e4 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (3006) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3007) $false % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3007) is inconsistent. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3008) all_10_23 = e2 | all_10_24 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3008) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3009) all_10_23 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2862), (3009) are inconsistent by sub-proof % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #118. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3010) all_10_24 = e2 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2143), (3010) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3011) e2 = e1 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3011) implies: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3012) e2 = e1 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (3012) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3013) $false % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3013) is inconsistent. % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | (3014) ~ (all_10_2 = e4) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (382), (3014) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | (3015) ~ (all_4_1 = e4) % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (308) gives: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | (3016) all_10_2 = e4 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (382), (3016) imply: % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | (3017) all_4_1 = e4 % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.91 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3015), (3017) imply: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | (3018) $false % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3018) is inconsistent. % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | (3019) all_10_3 = e4 | all_10_5 = e4 | all_10_10 = e4 | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | all_10_17 = e4 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3019) gives: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | (3020) all_10_3 = e4 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (535), (2116), (3020) are inconsistent by % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #45. % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | (3021) ~ (all_10_3 = e4) % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | (3022) all_10_5 = e4 | all_10_10 = e4 | all_10_17 = e4 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3022) gives: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | (3023) all_10_5 = e4 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2792), (3023) imply: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | (3024) e4 = e2 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3024) implies: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | (3025) e4 = e2 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (3025) imply: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | (3026) $false % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3026) is inconsistent. % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | (3027) all_10_10 = e4 | all_10_17 = e4 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2845) gives: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (3028) all_10_22 = e0 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2767), (3028) imply: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (3029) e4 = e0 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (535), (3029) imply: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (3030) $false % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3030) is inconsistent. % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (3031) all_10_23 = e0 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (325), (3031) imply: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (3032) all_4_19 = e0 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3027) gives: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3033) all_10_10 = e4 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (3033) imply: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3034) all_4_16 = e4 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (539), (3034) imply: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3035) $false % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3035) is inconsistent. % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3036) all_10_17 = e4 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (3036) imply: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3037) all_4_21 = e4 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23), (3037) imply: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3038) ~ (all_4_22 = e4) % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3038) implies: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3039) ~ (all_4_22 = e4) % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3040) all_6_14 = e2 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (477), (3040) imply: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3041) all_4_22 = e2 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (3041) imply: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3042) ~ (all_4_17 = e2) % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (295), (357), (373), (388), (496), % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512), (2794), (3031), (3042) are inconsistent by % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #108. % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3043) all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e1 | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_14 = e0 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3043) gives: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3044) all_6_14 = e4 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (477), (3044) imply: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3045) all_4_22 = e4 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3039), (3045) imply: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3046) $false % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3046) is inconsistent. % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3047) all_6_14 = e3 | all_6_14 = e1 | all_6_14 = e0 % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (477), (531), (2149), (2824), (3047) are % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #48. % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.92 | | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | | End of split % 73.93/10.92 | | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | | End of split % 73.93/10.92 | | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | | End of split % 73.93/10.92 | | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | | End of split % 73.93/10.92 | | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | End of split % 73.93/10.92 | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | Case 2: % 73.93/10.92 | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | (3048) all_6_7 = e4 | all_6_7 = e3 | all_6_7 = e1 | % 73.93/10.92 | | | | | | | | | | | | | | | all_6_7 = e0 % 73.93/10.92 | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | | REF_CLOSE: (462), (523), (524), (2769), (2782), (3048) are % 73.93/10.92 | | | | | | | | | | | | | | | inconsistent by sub-proof #90. % 73.93/10.92 | | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | End of split % 73.93/10.92 | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | Case 2: % 73.93/10.92 | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | (3049) all_6_2 = e3 | all_6_2 = e0 % 73.93/10.92 | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | | REF_CLOSE: (461), (521), (522), (3049) are inconsistent by % 73.93/10.92 | | | | | | | | | | | | | | sub-proof #163. % 73.93/10.92 | | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | | End of split % 73.93/10.92 | | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | | End of split % 73.93/10.92 | | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | End of split % 73.93/10.92 | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | Case 2: % 73.93/10.92 | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | (3050) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 73.93/10.92 | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | | REF_CLOSE: (466), (527), (533), (2146), (3050) are % 73.93/10.92 | | | | | | | | | | | inconsistent by sub-proof #130. % 73.93/10.92 | | | | | | | | | | | % 73.93/10.92 | | | | | | | | | | End of split % 73.93/10.92 | | | | | | | | | | % 73.93/10.92 | | | | | | | | | End of split % 73.93/10.92 | | | | | | | | | % 73.93/10.92 | | | | | | | | End of split % 73.93/10.92 | | | | | | | | % 73.93/10.92 | | | | | | | End of split % 73.93/10.92 | | | | | | | % 73.93/10.92 | | | | | | End of split % 73.93/10.92 | | | | | | % 73.93/10.92 | | | | | End of split % 73.93/10.92 | | | | | % 73.93/10.92 | | | | End of split % 73.93/10.92 | | | | % 73.93/10.92 | | | Case 2: % 73.93/10.92 | | | | % 73.93/10.92 | | | | (3051) all_8_67 = e0 | all_8_68 = e0 | all_8_69 = e0 % 73.93/10.92 | | | | % 73.93/10.92 | | | | BETA: splitting (3051) gives: % 73.93/10.92 | | | | % 73.93/10.92 | | | | Case 1: % 73.93/10.92 | | | | | % 73.93/10.92 | | | | | (3052) all_8_67 = e0 % 73.93/10.92 | | | | | % 73.93/10.92 | | | | | COMBINE_EQS: (416), (3052) imply: % 73.93/10.92 | | | | | (3053) e3 = e0 % 73.93/10.92 | | | | | % 73.93/10.92 | | | | | SIMP: (3053) implies: % 73.93/10.92 | | | | | (3054) e3 = e0 % 73.93/10.92 | | | | | % 73.93/10.92 | | | | | REDUCE: (525), (3054) imply: % 73.93/10.92 | | | | | (3055) $false % 73.93/10.92 | | | | | % 73.93/10.92 | | | | | CLOSE: (3055) is inconsistent. % 73.93/10.92 | | | | | % 73.93/10.92 | | | | Case 2: % 73.93/10.92 | | | | | % 73.93/10.92 | | | | | (3056) all_8_68 = e0 | all_8_69 = e0 % 73.93/10.92 | | | | | % 73.93/10.92 | | | | | BETA: splitting (3056) gives: % 73.93/10.92 | | | | | % 73.93/10.92 | | | | | Case 1: % 73.93/10.92 | | | | | | % 73.93/10.92 | | | | | | (3057) all_8_68 = e0 % 73.93/10.92 | | | | | | % 73.93/10.92 | | | | | | COMBINE_EQS: (339), (3057) imply: % 73.93/10.92 | | | | | | (3058) e4 = e0 % 73.93/10.92 | | | | | | % 73.93/10.92 | | | | | | SIMP: (3058) implies: % 73.93/10.92 | | | | | | (3059) e4 = e0 % 73.93/10.92 | | | | | | % 73.93/10.92 | | | | | | REDUCE: (535), (3059) imply: % 73.93/10.92 | | | | | | (3060) $false % 73.93/10.92 | | | | | | % 73.93/10.92 | | | | | | CLOSE: (3060) is inconsistent. % 73.93/10.92 | | | | | | % 73.93/10.92 | | | | | Case 2: % 73.93/10.92 | | | | | | % 73.93/10.92 | | | | | | (3061) all_8_69 = e0 % 73.93/10.92 | | | | | | % 73.93/10.92 | | | | | | COMBINE_EQS: (448), (3061) imply: % 73.93/10.92 | | | | | | (3062) all_4_24 = e0 % 73.93/10.92 | | | | | | % 73.93/10.92 | | | | | | SIMP: (3062) implies: % 73.93/10.92 | | | | | | (3063) all_4_24 = e0 % 73.93/10.92 | | | | | | % 73.93/10.92 | | | | | | REDUCE: (2107), (3063) imply: % 73.93/10.92 | | | | | | (3064) $false % 73.93/10.92 | | | | | | % 73.93/10.92 | | | | | | CLOSE: (3064) is inconsistent. % 73.93/10.92 | | | | | | % 73.93/10.92 | | | | | End of split % 73.93/10.92 | | | | | % 73.93/10.92 | | | | End of split % 73.93/10.92 | | | | % 73.93/10.92 | | | End of split % 73.93/10.92 | | | % 73.93/10.92 | | End of split % 73.93/10.92 | | % 73.93/10.92 | End of split % 73.93/10.92 | % 73.93/10.92 End of proof % 73.93/10.92 % 73.93/10.92 Sub-proof #1 shows that the following formulas are inconsistent: % 73.93/10.92 ---------------------------------------------------------------- % 73.93/10.92 (1) all_8_33 = e1 & ~ (all_8_34 = e2) % 73.93/10.92 (2) all_8_33 = all_4_22 % 73.93/10.92 (3) ~ (all_4_22 = e1) % 73.93/10.92 % 73.93/10.92 Begin of proof % 73.93/10.92 | % 73.93/10.92 | ALPHA: (1) implies: % 73.93/10.92 | (4) all_8_33 = e1 % 73.93/10.92 | % 73.93/10.92 | COMBINE_EQS: (2), (4) imply: % 73.93/10.92 | (5) all_4_22 = e1 % 73.93/10.92 | % 73.93/10.92 | SIMP: (5) implies: % 73.93/10.92 | (6) all_4_22 = e1 % 73.93/10.92 | % 73.93/10.92 | REDUCE: (3), (6) imply: % 73.93/10.92 | (7) $false % 73.93/10.92 | % 73.93/10.92 | CLOSE: (7) is inconsistent. % 73.93/10.92 | % 73.93/10.92 End of proof % 73.93/10.92 % 73.93/10.92 Sub-proof #2 shows that the following formulas are inconsistent: % 73.93/10.92 ---------------------------------------------------------------- % 73.93/10.92 (1) all_10_1 = e4 | all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | % 73.93/10.92 all_10_21 = e4 % 73.93/10.92 (2) ~ (all_4_9 = e0) % 73.93/10.92 (3) ~ (all_4_10 = e3) % 73.93/10.92 (4) all_10_20 = e0 | all_10_21 = e0 | all_10_22 = e0 | all_10_23 = e0 % 73.93/10.92 (5) ~ (e3 = e2) % 73.93/10.92 (6) all_10_4 = all_4_10 % 73.93/10.92 (7) all_10_22 = e2 % 73.93/10.92 (8) all_10_20 = e4 % 73.93/10.92 (9) ~ (all_4_20 = e3) % 73.93/10.92 (10) all_10_1 = all_4_5 % 73.93/10.92 (11) ~ (all_4_4 = e2) % 73.93/10.92 (12) op(e0, e0) = e1 % 73.93/10.92 (13) ~ (e2 = e0) % 73.93/10.92 (14) all_10_16 = all_4_20 % 73.93/10.92 (15) ~ (e4 = e0) % 73.93/10.92 (16) all_10_3 = e0 % 73.93/10.92 (17) ~ (all_4_4 = all_4_9) % 73.93/10.92 (18) all_10_23 = all_4_19 % 73.93/10.92 (19) all_10_21 = all_4_9 % 73.93/10.92 (20) ~ (all_4_10 = e0) % 73.93/10.92 (21) op(e0, all_4_19) = all_8_50 % 73.93/10.92 (22) all_6_21 = all_4_9 % 73.93/10.92 (23) all_10_9 = e3 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 73.93/10.92 all_10_23 = e3 % 73.93/10.92 (24) all_10_20 = all_4_4 % 73.93/10.92 (25) all_10_0 = e3 | all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | % 73.93/10.92 all_10_16 = e3 % 73.93/10.92 (26) ~ (e4 = e3) % 73.93/10.92 (27) ~ (all_4_5 = e0) % 73.93/10.92 (28) ~ (all_4_15 = all_4_19) % 73.93/10.92 (29) op(e0, all_4_20) = e4 % 73.93/10.92 (30) ~ (all_4_19 = e1) % 73.93/10.92 (31) all_10_9 = all_4_15 % 73.93/10.92 (32) ~ (all_4_9 = e1) % 73.93/10.92 (33) all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e1 | all_6_21 = e0 % 73.93/10.92 (34) ~ (all_4_5 = all_4_10) % 73.93/10.92 (35) all_10_13 = e2 % 73.93/10.92 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 73.93/10.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 73.93/10.92 (37) all_6_2 = all_4_10 % 73.93/10.92 (38) ~ (all_4_4 = e1) % 73.93/10.92 (39) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 73.93/10.92 (40) all_10_0 = e2 % 73.93/10.92 (41) all_10_0 = e0 | all_10_1 = e0 | all_10_4 = e0 | all_10_9 = e0 | % 73.93/10.92 all_10_16 = e0 % 73.93/10.92 (42) ~ (all_4_5 = all_4_9) % 73.93/10.92 (43) ~ (all_4_4 = all_4_19) % 73.93/10.92 (44) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 73.93/10.92 all_10_22 = e1 % 73.93/10.92 (45) all_10_7 = e1 % 73.93/10.92 % 73.93/10.92 Begin of proof % 73.93/10.92 | % 73.93/10.92 | COMBINE_EQS: (8), (24) imply: % 73.93/10.92 | (46) all_4_4 = e4 % 73.93/10.92 | % 73.93/10.92 | SIMP: (46) implies: % 73.93/10.93 | (47) all_4_4 = e4 % 73.93/10.93 | % 73.93/10.93 | REDUCE: (17), (47) imply: % 73.93/10.93 | (48) ~ (all_4_9 = e4) % 73.93/10.93 | % 73.93/10.93 | SIMP: (48) implies: % 73.93/10.93 | (49) ~ (all_4_9 = e4) % 73.93/10.93 | % 73.93/10.93 | REDUCE: (43), (47) imply: % 73.93/10.93 | (50) ~ (all_4_19 = e4) % 73.93/10.93 | % 73.93/10.93 | SIMP: (50) implies: % 73.93/10.93 | (51) ~ (all_4_19 = e4) % 73.93/10.93 | % 73.93/10.93 | REDUCE: (11), (47) imply: % 73.93/10.93 | (52) ~ (e4 = e2) % 73.93/10.93 | % 73.93/10.93 | REDUCE: (38), (47) imply: % 73.93/10.93 | (53) ~ (e4 = e1) % 73.93/10.93 | % 73.93/10.93 | BETA: splitting (1) gives: % 73.93/10.93 | % 73.93/10.93 | Case 1: % 73.93/10.93 | | % 73.93/10.93 | | (54) all_10_1 = e4 % 73.93/10.93 | | % 73.93/10.93 | | COMBINE_EQS: (10), (54) imply: % 73.93/10.93 | | (55) all_4_5 = e4 % 73.93/10.93 | | % 73.93/10.93 | | REDUCE: (34), (55) imply: % 73.93/10.93 | | (56) ~ (all_4_10 = e4) % 73.93/10.93 | | % 73.93/10.93 | | SIMP: (56) implies: % 73.93/10.93 | | (57) ~ (all_4_10 = e4) % 73.93/10.93 | | % 73.93/10.93 | | BETA: splitting (25) gives: % 73.93/10.93 | | % 73.93/10.93 | | Case 1: % 73.93/10.93 | | | % 73.93/10.93 | | | (58) all_10_0 = e3 % 73.93/10.93 | | | % 73.93/10.93 | | | REF_CLOSE: (5), (40), (58) are inconsistent by sub-proof #104. % 73.93/10.93 | | | % 73.93/10.93 | | Case 2: % 73.93/10.93 | | | % 73.93/10.93 | | | (59) all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | all_10_16 = e3 % 73.93/10.93 | | | % 73.93/10.93 | | | BETA: splitting (4) gives: % 73.93/10.93 | | | % 73.93/10.93 | | | Case 1: % 73.93/10.93 | | | | % 73.93/10.93 | | | | (60) all_10_20 = e0 % 73.93/10.93 | | | | % 73.93/10.93 | | | | REF_CLOSE: (8), (15), (60) are inconsistent by sub-proof #76. % 73.93/10.93 | | | | % 73.93/10.93 | | | Case 2: % 73.93/10.93 | | | | % 73.93/10.93 | | | | (61) all_10_21 = e0 | all_10_22 = e0 | all_10_23 = e0 % 73.93/10.93 | | | | % 73.93/10.93 | | | | BETA: splitting (44) gives: % 73.93/10.93 | | | | % 73.93/10.93 | | | | Case 1: % 73.93/10.93 | | | | | % 73.93/10.93 | | | | | (62) all_10_4 = e1 % 73.93/10.93 | | | | | % 73.93/10.93 | | | | | COMBINE_EQS: (6), (62) imply: % 73.93/10.93 | | | | | (63) all_4_10 = e1 % 73.93/10.93 | | | | | % 73.93/10.93 | | | | | REDUCE: (57), (63) imply: % 73.93/10.93 | | | | | (64) ~ (e4 = e1) % 73.93/10.93 | | | | | % 73.93/10.93 | | | | | REDUCE: (3), (63) imply: % 73.93/10.93 | | | | | (65) ~ (e3 = e1) % 73.93/10.93 | | | | | % 73.93/10.93 | | | | | SIMP: (65) implies: % 73.93/10.93 | | | | | (66) ~ (e3 = e1) % 73.93/10.93 | | | | | % 73.93/10.93 | | | | | BETA: splitting (59) gives: % 73.93/10.93 | | | | | % 73.93/10.93 | | | | | Case 1: % 73.93/10.93 | | | | | | % 73.93/10.93 | | | | | | (67) all_10_1 = e3 % 73.93/10.93 | | | | | | % 73.93/10.93 | | | | | | COMBINE_EQS: (54), (67) imply: % 73.93/10.93 | | | | | | (68) e4 = e3 % 73.93/10.93 | | | | | | % 73.93/10.93 | | | | | | REDUCE: (26), (68) imply: % 73.93/10.93 | | | | | | (69) $false % 73.93/10.93 | | | | | | % 73.93/10.93 | | | | | | CLOSE: (69) is inconsistent. % 73.93/10.93 | | | | | | % 73.93/10.93 | | | | | Case 2: % 73.93/10.93 | | | | | | % 73.93/10.93 | | | | | | (70) all_10_4 = e3 | all_10_9 = e3 | all_10_16 = e3 % 73.93/10.93 | | | | | | % 73.93/10.93 | | | | | | BETA: splitting (70) gives: % 73.93/10.93 | | | | | | % 73.93/10.93 | | | | | | Case 1: % 73.93/10.93 | | | | | | | % 73.93/10.93 | | | | | | | (71) all_10_4 = e3 % 73.93/10.93 | | | | | | | % 73.93/10.93 | | | | | | | REF_CLOSE: (62), (66), (71) are inconsistent by sub-proof #31. % 73.93/10.93 | | | | | | | % 73.93/10.93 | | | | | | Case 2: % 73.93/10.93 | | | | | | | % 73.93/10.93 | | | | | | | (72) all_10_9 = e3 | all_10_16 = e3 % 73.93/10.93 | | | | | | | % 73.93/10.93 | | | | | | | BETA: splitting (33) gives: % 73.93/10.93 | | | | | | | % 73.93/10.93 | | | | | | | Case 1: % 73.93/10.93 | | | | | | | | % 73.93/10.93 | | | | | | | | (73) all_6_21 = e4 % 73.93/10.93 | | | | | | | | % 73.93/10.93 | | | | | | | | COMBINE_EQS: (22), (73) imply: % 73.93/10.93 | | | | | | | | (74) all_4_9 = e4 % 73.93/10.93 | | | | | | | | % 73.93/10.93 | | | | | | | | REDUCE: (49), (74) imply: % 73.93/10.93 | | | | | | | | (75) $false % 73.93/10.93 | | | | | | | | % 73.93/10.93 | | | | | | | | CLOSE: (75) is inconsistent. % 73.93/10.93 | | | | | | | | % 73.93/10.93 | | | | | | | Case 2: % 73.93/10.93 | | | | | | | | % 73.93/10.93 | | | | | | | | (76) all_6_21 = e3 | all_6_21 = e1 | all_6_21 = e0 % 73.93/10.93 | | | | | | | | % 73.93/10.93 | | | | | | | | BETA: splitting (76) gives: % 73.93/10.93 | | | | | | | | % 73.93/10.93 | | | | | | | | Case 1: % 73.93/10.93 | | | | | | | | | % 73.93/10.93 | | | | | | | | | (77) all_6_21 = e1 % 73.93/10.93 | | | | | | | | | % 73.93/10.93 | | | | | | | | | COMBINE_EQS: (22), (77) imply: % 73.93/10.93 | | | | | | | | | (78) all_4_9 = e1 % 73.93/10.93 | | | | | | | | | % 73.93/10.93 | | | | | | | | | REDUCE: (32), (78) imply: % 73.93/10.93 | | | | | | | | | (79) $false % 73.93/10.93 | | | | | | | | | % 73.93/10.93 | | | | | | | | | CLOSE: (79) is inconsistent. % 73.93/10.93 | | | | | | | | | % 73.93/10.93 | | | | | | | | Case 2: % 73.93/10.93 | | | | | | | | | % 73.93/10.93 | | | | | | | | | (80) all_6_21 = e3 | all_6_21 = e0 % 73.93/10.93 | | | | | | | | | % 73.93/10.93 | | | | | | | | | BETA: splitting (80) gives: % 73.93/10.93 | | | | | | | | | % 73.93/10.93 | | | | | | | | | Case 1: % 73.93/10.93 | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | (81) all_6_21 = e3 % 73.93/10.93 | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | COMBINE_EQS: (22), (81) imply: % 73.93/10.93 | | | | | | | | | | (82) all_4_9 = e3 % 73.93/10.93 | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | COMBINE_EQS: (19), (82) imply: % 73.93/10.93 | | | | | | | | | | (83) all_10_21 = e3 % 73.93/10.93 | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | REDUCE: (2), (82) imply: % 73.93/10.93 | | | | | | | | | | (84) ~ (e3 = e0) % 73.93/10.93 | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | BETA: splitting (23) gives: % 73.93/10.93 | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | Case 1: % 73.93/10.93 | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | (85) all_10_9 = e3 % 73.93/10.93 | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | COMBINE_EQS: (31), (85) imply: % 73.93/10.93 | | | | | | | | | | | (86) all_4_15 = e3 % 73.93/10.93 | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | REDUCE: (28), (86) imply: % 73.93/10.93 | | | | | | | | | | | (87) ~ (all_4_19 = e3) % 73.93/10.93 | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | SIMP: (87) implies: % 73.93/10.93 | | | | | | | | | | | (88) ~ (all_4_19 = e3) % 73.93/10.93 | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | BETA: splitting (41) gives: % 73.93/10.93 | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | Case 1: % 73.93/10.93 | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | (89) all_10_0 = e0 % 73.93/10.93 | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | COMBINE_EQS: (40), (89) imply: % 73.93/10.93 | | | | | | | | | | | | (90) e2 = e0 % 73.93/10.93 | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | REDUCE: (13), (90) imply: % 73.93/10.93 | | | | | | | | | | | | (91) $false % 73.93/10.93 | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | CLOSE: (91) is inconsistent. % 73.93/10.93 | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | Case 2: % 73.93/10.93 | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | (92) ~ (all_10_0 = e0) % 73.93/10.93 | | | | | | | | | | | | (93) all_10_1 = e0 | all_10_4 = e0 | all_10_9 = e0 | % 73.93/10.93 | | | | | | | | | | | | all_10_16 = e0 % 73.93/10.93 | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | BETA: splitting (61) gives: % 73.93/10.93 | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | Case 1: % 73.93/10.93 | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | (94) all_10_21 = e0 % 73.93/10.93 | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | REF_CLOSE: (83), (84), (94) are inconsistent by sub-proof % 73.93/10.93 | | | | | | | | | | | | | #30. % 73.93/10.93 | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | Case 2: % 73.93/10.93 | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | (95) all_10_22 = e0 | all_10_23 = e0 % 73.93/10.93 | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | BETA: splitting (95) gives: % 73.93/10.93 | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | Case 1: % 73.93/10.93 | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | (96) all_10_22 = e0 % 73.93/10.93 | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | REF_CLOSE: (7), (13), (96) are inconsistent by sub-proof #29. % 73.93/10.93 | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | Case 2: % 73.93/10.93 | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | (97) all_10_23 = e0 % 73.93/10.93 | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | COMBINE_EQS: (18), (97) imply: % 73.93/10.93 | | | | | | | | | | | | | | (98) all_4_19 = e0 % 73.93/10.93 | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | SIMP: (98) implies: % 73.93/10.93 | | | | | | | | | | | | | | (99) all_4_19 = e0 % 73.93/10.93 | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | REDUCE: (51), (99) imply: % 73.93/10.93 | | | | | | | | | | | | | | (100) ~ (e4 = e0) % 73.93/10.93 | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | REDUCE: (88), (99) imply: % 73.93/10.93 | | | | | | | | | | | | | | (101) ~ (e3 = e0) % 73.93/10.93 | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | REDUCE: (30), (99) imply: % 73.93/10.93 | | | | | | | | | | | | | | (102) ~ (e1 = e0) % 73.93/10.93 | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | SIMP: (102) implies: % 73.93/10.93 | | | | | | | | | | | | | | (103) ~ (e1 = e0) % 73.93/10.93 | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | REDUCE: (21), (99) imply: % 73.93/10.93 | | | | | | | | | | | | | | (104) op(e0, e0) = all_8_50 % 73.93/10.93 | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | BETA: splitting (93) gives: % 73.93/10.93 | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | Case 1: % 73.93/10.93 | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | (105) all_10_1 = e0 % 73.93/10.93 | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | COMBINE_EQS: (54), (105) imply: % 73.93/10.93 | | | | | | | | | | | | | | | (106) e4 = e0 % 73.93/10.93 | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | REDUCE: (15), (106) imply: % 73.93/10.93 | | | | | | | | | | | | | | | (107) $false % 73.93/10.93 | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | CLOSE: (107) is inconsistent. % 73.93/10.93 | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | Case 2: % 73.93/10.93 | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | (108) all_10_4 = e0 | all_10_9 = e0 | all_10_16 = e0 % 73.93/10.93 | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | BETA: splitting (108) gives: % 73.93/10.93 | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | Case 1: % 73.93/10.93 | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | (109) all_10_4 = e0 % 73.93/10.93 | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (109) imply: % 73.93/10.93 | | | | | | | | | | | | | | | | (110) e1 = e0 % 73.93/10.93 | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | REDUCE: (103), (110) imply: % 73.93/10.93 | | | | | | | | | | | | | | | | (111) $false % 73.93/10.93 | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | CLOSE: (111) is inconsistent. % 73.93/10.93 | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | Case 2: % 73.93/10.93 | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | (112) all_10_9 = e0 | all_10_16 = e0 % 73.93/10.93 | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | BETA: splitting (112) gives: % 73.93/10.93 | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | Case 1: % 73.93/10.93 | | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | | (113) all_10_9 = e0 % 73.93/10.93 | | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (113) imply: % 73.93/10.93 | | | | | | | | | | | | | | | | | (114) e3 = e0 % 73.93/10.93 | | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | | REDUCE: (84), (114) imply: % 73.93/10.93 | | | | | | | | | | | | | | | | | (115) $false % 73.93/10.93 | | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | | CLOSE: (115) is inconsistent. % 73.93/10.93 | | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | Case 2: % 73.93/10.93 | | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | | (116) all_10_16 = e0 % 73.93/10.93 | | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (116) imply: % 73.93/10.93 | | | | | | | | | | | | | | | | | (117) all_4_20 = e0 % 73.93/10.93 | | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | | REDUCE: (29), (117) imply: % 73.93/10.93 | | | | | | | | | | | | | | | | | (118) op(e0, e0) = e4 % 73.93/10.93 | | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with e1, all_8_50, e0, e0, % 73.93/10.93 | | | | | | | | | | | | | | | | | simplifying with (12), (104) gives: % 73.93/10.93 | | | | | | | | | | | | | | | | | (119) all_8_50 = e1 % 73.93/10.93 | | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with e4, all_8_50, e0, e0, % 73.93/10.93 | | | | | | | | | | | | | | | | | simplifying with (104), (118) gives: % 73.93/10.93 | | | | | | | | | | | | | | | | | (120) all_8_50 = e4 % 73.93/10.93 | | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | | COMBINE_EQS: (119), (120) imply: % 73.93/10.93 | | | | | | | | | | | | | | | | | (121) e4 = e1 % 73.93/10.93 | | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | | SIMP: (121) implies: % 73.93/10.93 | | | | | | | | | | | | | | | | | (122) e4 = e1 % 73.93/10.93 | | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | | REDUCE: (53), (122) imply: % 73.93/10.93 | | | | | | | | | | | | | | | | | (123) $false % 73.93/10.93 | | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | | CLOSE: (123) is inconsistent. % 73.93/10.93 | | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | | End of split % 73.93/10.93 | | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | | End of split % 73.93/10.93 | | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | | End of split % 73.93/10.93 | | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | | End of split % 73.93/10.93 | | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | | End of split % 73.93/10.93 | | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | End of split % 73.93/10.93 | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | Case 2: % 73.93/10.93 | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | (124) ~ (all_10_9 = e3) % 73.93/10.93 | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | REDUCE: (31), (124) imply: % 73.93/10.93 | | | | | | | | | | | (125) ~ (all_4_15 = e3) % 73.93/10.93 | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | | REF_CLOSE: (9), (14), (31), (72), (125) are inconsistent by % 73.93/10.93 | | | | | | | | | | | sub-proof #63. % 73.93/10.93 | | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | End of split % 73.93/10.93 | | | | | | | | | | % 73.93/10.93 | | | | | | | | | Case 2: % 73.93/10.93 | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | (126) all_6_21 = e0 % 73.93/10.93 | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | COMBINE_EQS: (22), (126) imply: % 73.93/10.93 | | | | | | | | | | (127) all_4_9 = e0 % 73.93/10.93 | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | REDUCE: (2), (127) imply: % 73.93/10.93 | | | | | | | | | | (128) $false % 73.93/10.93 | | | | | | | | | | % 73.93/10.93 | | | | | | | | | | CLOSE: (128) is inconsistent. % 73.93/10.93 | | | | | | | | | | % 73.93/10.93 | | | | | | | | | End of split % 73.93/10.93 | | | | | | | | | % 73.93/10.93 | | | | | | | | End of split % 73.93/10.93 | | | | | | | | % 73.93/10.93 | | | | | | | End of split % 73.93/10.93 | | | | | | | % 73.93/10.93 | | | | | | End of split % 73.93/10.93 | | | | | | % 73.93/10.93 | | | | | End of split % 73.93/10.93 | | | | | % 73.93/10.93 | | | | Case 2: % 73.93/10.93 | | | | | % 73.93/10.93 | | | | | (129) ~ (all_10_4 = e1) % 73.93/10.93 | | | | | % 73.93/10.93 | | | | | REDUCE: (6), (129) imply: % 73.93/10.93 | | | | | (130) ~ (all_4_10 = e1) % 73.93/10.93 | | | | | % 73.93/10.93 | | | | | REF_CLOSE: (3), (20), (37), (39), (57), (130) are inconsistent by % 73.93/10.93 | | | | | sub-proof #161. % 73.93/10.93 | | | | | % 73.93/10.93 | | | | End of split % 73.93/10.93 | | | | % 73.93/10.93 | | | End of split % 73.93/10.93 | | | % 73.93/10.93 | | End of split % 73.93/10.93 | | % 73.93/10.93 | Case 2: % 73.93/10.93 | | % 73.93/10.93 | | (131) all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | all_10_21 = e4 % 73.93/10.93 | | % 73.93/10.93 | | REF_CLOSE: (15), (16), (19), (35), (45), (49), (52), (53), (131) are % 73.93/10.93 | | inconsistent by sub-proof #28. % 73.93/10.93 | | % 73.93/10.93 | End of split % 73.93/10.93 | % 73.93/10.93 End of proof % 73.93/10.93 % 73.93/10.93 Sub-proof #3 shows that the following formulas are inconsistent: % 73.93/10.93 ---------------------------------------------------------------- % 73.93/10.93 (1) all_10_14 = e0 % 73.93/10.93 (2) op(e3, all_4_8) = e1 % 73.93/10.93 (3) ~ (all_4_11 = e0) % 73.93/10.93 (4) ~ (all_4_11 = e3) % 73.93/10.93 (5) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 73.93/10.93 (6) ~ (all_4_10 = e3) % 73.93/10.93 (7) ~ (e3 = e2) % 73.93/10.93 (8) all_10_4 = all_4_10 % 73.93/10.93 (9) all_10_15 = e4 % 73.93/10.93 (10) ~ (e3 = e1) % 73.93/10.93 (11) ~ (all_4_10 = e0) % 73.93/10.93 (12) op(e2, e1) = all_4_17 % 73.93/10.93 (13) all_10_12 = e1 | all_10_13 = e1 | all_10_14 = e1 | all_10_15 = e1 | % 73.93/10.93 all_10_19 = e1 % 73.93/10.93 (14) ~ (e2 = e1) % 73.93/10.93 (15) ~ (e4 = e3) % 73.93/10.93 (16) ~ (all_4_5 = e0) % 73.93/10.93 (17) all_10_13 = all_4_8 % 73.93/10.93 (18) all_10_12 = e3 | all_10_13 = e3 | all_10_14 = e3 | all_10_15 = e3 | % 73.93/10.93 all_10_19 = e3 % 73.93/10.93 (19) all_10_19 = e2 % 73.93/10.93 (20) ~ (all_4_10 = all_4_11) % 73.93/10.93 (21) ~ (e1 = e0) % 73.93/10.93 (22) ~ (all_4_5 = e4) % 73.93/10.93 (23) all_6_1 = all_4_5 % 73.93/10.93 (24) ~ (all_4_5 = all_4_10) % 73.93/10.93 (25) all_6_7 = all_4_11 % 73.93/10.93 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 73.93/10.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 73.93/10.93 (27) all_6_2 = all_4_10 % 73.93/10.93 (28) all_6_7 = e4 | all_6_7 = e3 | all_6_7 = e1 | all_6_7 = e0 % 73.93/10.93 (29) ~ (e4 = e1) % 73.93/10.93 (30) ~ (e3 = e0) % 73.93/10.93 (31) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 73.93/10.94 (32) ~ (all_4_17 = e3) % 73.93/10.94 (33) op(e2, all_4_11) = e3 % 73.93/10.95 (34) ~ (all_4_5 = all_4_8) % 73.93/10.95 (35) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 73.93/10.95 all_10_22 = e1 % 73.93/10.95 (36) ~ (all_4_8 = e2) % 73.93/10.95 (37) op(e3, e1) = e2 % 73.93/10.95 % 73.93/10.95 Begin of proof % 73.93/10.95 | % 73.93/10.95 | BETA: splitting (13) gives: % 73.93/10.95 | % 73.93/10.95 | Case 1: % 73.93/10.95 | | % 73.93/10.95 | | (38) all_10_12 = e1 % 73.93/10.95 | | % 73.93/10.95 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (15), % 73.93/10.95 | | (16), (17), (18), (19), (20), (22), (23), (24), (25), (26), (27), % 73.93/10.95 | | (28), (30), (31), (32), (33), (34), (35), (38) are inconsistent % 73.93/10.95 | | by sub-proof #4. % 73.93/10.95 | | % 73.93/10.95 | Case 2: % 73.93/10.95 | | % 73.93/10.95 | | (39) all_10_13 = e1 | all_10_14 = e1 | all_10_15 = e1 | all_10_19 = e1 % 73.93/10.95 | | % 73.93/10.95 | | REF_CLOSE: (1), (2), (9), (14), (17), (19), (21), (26), (29), (36), (37), % 73.93/10.95 | | (39) are inconsistent by sub-proof #34. % 73.93/10.95 | | % 73.93/10.95 | End of split % 73.93/10.95 | % 73.93/10.95 End of proof % 73.93/10.95 % 73.93/10.95 Sub-proof #4 shows that the following formulas are inconsistent: % 73.93/10.95 ---------------------------------------------------------------- % 73.93/10.95 (1) all_10_14 = e0 % 73.93/10.95 (2) ~ (all_4_11 = e0) % 73.93/10.95 (3) ~ (all_4_11 = e3) % 73.93/10.95 (4) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 73.93/10.95 (5) ~ (all_4_10 = e3) % 73.93/10.95 (6) ~ (e3 = e2) % 73.93/10.95 (7) all_10_4 = all_4_10 % 73.93/10.95 (8) all_10_15 = e4 % 73.93/10.95 (9) ~ (e3 = e1) % 73.93/10.95 (10) ~ (all_4_10 = e0) % 73.93/10.95 (11) op(e2, e1) = all_4_17 % 73.93/10.95 (12) ~ (e4 = e3) % 73.93/10.95 (13) ~ (all_4_5 = e0) % 73.93/10.95 (14) all_10_13 = all_4_8 % 73.93/10.95 (15) all_10_12 = e3 | all_10_13 = e3 | all_10_14 = e3 | all_10_15 = e3 | % 73.93/10.95 all_10_19 = e3 % 73.93/10.95 (16) all_10_19 = e2 % 73.93/10.95 (17) ~ (all_4_10 = all_4_11) % 73.93/10.95 (18) all_10_12 = e1 % 73.93/10.95 (19) ~ (all_4_5 = e4) % 73.93/10.95 (20) all_6_1 = all_4_5 % 73.93/10.95 (21) ~ (all_4_5 = all_4_10) % 73.93/10.95 (22) all_6_7 = all_4_11 % 73.93/10.95 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 73.93/10.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 73.93/10.95 (24) all_6_2 = all_4_10 % 73.93/10.95 (25) all_6_7 = e4 | all_6_7 = e3 | all_6_7 = e1 | all_6_7 = e0 % 73.93/10.95 (26) ~ (e3 = e0) % 73.93/10.95 (27) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 73.93/10.95 (28) ~ (all_4_17 = e3) % 73.93/10.95 (29) op(e2, all_4_11) = e3 % 73.93/10.95 (30) ~ (all_4_5 = all_4_8) % 73.93/10.95 (31) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 73.93/10.95 all_10_22 = e1 % 73.93/10.95 % 73.93/10.95 Begin of proof % 73.93/10.95 | % 73.93/10.95 | BETA: splitting (15) gives: % 73.93/10.95 | % 73.93/10.95 | Case 1: % 73.93/10.95 | | % 73.93/10.95 | | (32) all_10_12 = e3 % 73.93/10.95 | | % 73.93/10.95 | | COMBINE_EQS: (18), (32) imply: % 73.93/10.95 | | (33) e3 = e1 % 73.93/10.95 | | % 73.93/10.95 | | REDUCE: (9), (33) imply: % 73.93/10.95 | | (34) $false % 73.93/10.95 | | % 73.93/10.95 | | CLOSE: (34) is inconsistent. % 73.93/10.95 | | % 73.93/10.95 | Case 2: % 73.93/10.95 | | % 73.93/10.95 | | (35) all_10_13 = e3 | all_10_14 = e3 | all_10_15 = e3 | all_10_19 = e3 % 73.93/10.95 | | % 73.93/10.95 | | BETA: splitting (35) gives: % 73.93/10.95 | | % 73.93/10.95 | | Case 1: % 73.93/10.95 | | | % 73.93/10.95 | | | (36) all_10_13 = e3 % 73.93/10.95 | | | % 73.93/10.95 | | | COMBINE_EQS: (14), (36) imply: % 73.93/10.95 | | | (37) all_4_8 = e3 % 73.93/10.95 | | | % 73.93/10.95 | | | SIMP: (37) implies: % 73.93/10.95 | | | (38) all_4_8 = e3 % 73.93/10.95 | | | % 73.93/10.95 | | | REDUCE: (30), (38) imply: % 73.93/10.95 | | | (39) ~ (all_4_5 = e3) % 73.93/10.95 | | | % 73.93/10.95 | | | REF_CLOSE: (2), (3), (4), (5), (7), (10), (11), (13), (17), (19), (20), % 73.93/10.95 | | | (21), (22), (23), (24), (25), (27), (28), (29), (31), (39) are % 73.93/10.95 | | | inconsistent by sub-proof #6. % 73.93/10.95 | | | % 73.93/10.95 | | Case 2: % 73.93/10.95 | | | % 73.93/10.95 | | | (40) all_10_14 = e3 | all_10_15 = e3 | all_10_19 = e3 % 73.93/10.95 | | | % 73.93/10.95 | | | REF_CLOSE: (1), (6), (8), (12), (16), (26), (40) are inconsistent by % 73.93/10.95 | | | sub-proof #40. % 73.93/10.95 | | | % 73.93/10.95 | | End of split % 73.93/10.95 | | % 73.93/10.95 | End of split % 73.93/10.95 | % 73.93/10.95 End of proof % 73.93/10.95 % 73.93/10.95 Sub-proof #5 shows that the following formulas are inconsistent: % 73.93/10.95 ---------------------------------------------------------------- % 73.93/10.95 (1) ~ (all_4_5 = e2) % 73.93/10.95 (2) ~ (all_4_1 = e0) % 73.93/10.95 (3) all_10_1 = e4 | all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | % 73.93/10.95 all_10_21 = e4 % 73.93/10.95 (4) all_10_8 = e3 % 73.93/10.95 (5) ~ (all_4_1 = all_4_2) % 73.93/10.95 (6) all_10_14 = e0 % 73.93/10.95 (7) ~ (all_4_9 = e0) % 73.93/10.95 (8) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | all_6_5 = e0 % 73.93/10.95 (9) ~ (all_4_11 = e0) % 73.93/10.95 (10) ~ (all_4_11 = e3) % 73.93/10.95 (11) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 73.93/10.95 (12) ~ (all_4_10 = e3) % 73.93/10.95 (13) all_10_4 = all_4_10 % 73.93/10.95 (14) all_10_22 = e2 % 73.93/10.95 (15) all_10_20 = e4 % 73.93/10.95 (16) all_10_1 = all_4_5 % 73.93/10.95 (17) ~ (all_4_20 = all_4_21) % 73.93/10.95 (18) ~ (e2 = e0) % 73.93/10.95 (19) all_6_9 = all_4_21 % 73.93/10.95 (20) all_10_16 = e4 | all_10_17 = e4 | all_10_18 = e4 | all_10_19 = e4 | % 73.93/10.95 all_10_24 = e4 % 73.93/10.95 (21) all_10_12 = all_4_3 % 73.93/10.95 (22) ~ (all_4_2 = e3) % 73.93/10.95 (23) all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e1 | all_6_14 = e0 % 73.93/10.95 (24) all_10_16 = all_4_20 % 73.93/10.95 (25) ~ (all_4_2 = all_4_22) % 73.93/10.95 (26) all_10_21 = all_4_9 % 73.93/10.95 (27) ~ (all_4_10 = e0) % 73.93/10.95 (28) op(e2, e4) = all_4_2 % 73.93/10.95 (29) ~ (all_4_22 = e1) % 73.93/10.95 (30) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e1 | all_6_9 = e0 % 73.93/10.95 (31) all_10_17 = all_4_21 % 73.93/10.95 (32) all_6_21 = all_4_9 % 73.93/10.95 (33) op(e2, e1) = all_4_17 % 73.93/10.95 (34) ~ (all_4_5 = all_4_20) % 73.93/10.95 (35) all_6_5 = all_4_1 % 73.93/10.95 (36) ~ (all_4_1 = all_4_11) % 73.93/10.95 (37) ~ (all_4_1 = all_4_21) % 73.93/10.95 (38) all_10_0 = e0 | all_10_2 = e0 | all_10_6 = e0 | all_10_12 = e0 | % 73.93/10.95 all_10_20 = e0 % 73.93/10.95 (39) all_6_10 = all_4_2 % 73.93/10.95 (40) op(e2, all_4_22) = all_8_59 % 73.93/10.95 (41) ~ (e4 = e3) % 73.93/10.95 (42) all_10_2 = all_4_1 % 73.93/10.95 (43) ~ (all_4_3 = e0) % 73.93/10.95 (44) ~ (all_4_5 = e0) % 73.93/10.95 (45) ~ (all_4_22 = e3) % 73.93/10.95 (46) ~ (all_4_21 = e1) % 73.93/10.95 (47) all_6_14 = all_4_22 % 73.93/10.95 (48) ~ (all_4_9 = e1) % 73.93/10.95 (49) all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e1 | all_6_21 = e0 % 73.93/10.95 (50) ~ (all_4_2 = e2) % 73.93/10.95 (51) ~ (all_4_9 = e4) % 73.93/10.95 (52) ~ (all_4_2 = e4) % 73.93/10.95 (53) all_10_19 = e2 % 73.93/10.95 (54) ~ (all_4_10 = all_4_11) % 73.93/10.95 (55) ~ (all_4_21 = e0) % 73.93/10.95 (56) all_6_1 = all_4_5 % 73.93/10.95 (57) ~ (all_4_5 = all_4_10) % 73.93/10.95 (58) all_6_7 = all_4_11 % 73.93/10.95 (59) ~ (all_4_11 = all_4_21) % 73.93/10.95 (60) all_10_20 = e3 | all_10_21 = e3 | all_10_22 = e3 | all_10_23 = e3 | % 73.93/10.95 all_10_24 = e3 % 73.93/10.95 (61) all_10_6 = all_4_2 % 73.93/10.95 (62) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 73.93/10.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 73.93/10.95 (63) all_10_5 = all_4_11 % 73.93/10.95 (64) all_6_2 = all_4_10 % 73.93/10.95 (65) all_6_7 = e4 | all_6_7 = e3 | all_6_7 = e1 | all_6_7 = e0 % 73.93/10.95 (66) all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | % 73.93/10.95 all_10_22 = e4 % 73.93/10.95 (67) all_6_10 = e4 | all_6_10 = e3 | all_6_10 = e1 | all_6_10 = e0 % 73.93/10.95 (68) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 73.93/10.95 (69) all_10_0 = e2 % 73.93/10.95 (70) ~ (all_4_17 = e3) % 73.93/10.95 (71) all_10_18 = all_4_22 % 73.93/10.95 (72) ~ (all_4_5 = all_4_9) % 73.93/10.95 (73) all_10_2 = e1 | all_10_3 = e1 | all_10_5 = e1 | all_10_10 = e1 | % 73.93/10.95 all_10_17 = e1 % 73.93/10.95 (74) op(e2, all_4_11) = e3 % 73.93/10.95 (75) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 73.93/10.95 all_10_22 = e1 % 73.93/10.96 (76) all_10_16 = e0 | all_10_17 = e0 | all_10_18 = e0 | all_10_19 = e0 % 73.93/10.96 (77) all_10_16 = e3 | all_10_17 = e3 | all_10_18 = e3 | all_10_19 = e3 | % 73.93/10.96 all_10_24 = e3 % 73.93/10.96 % 73.93/10.96 Begin of proof % 73.93/10.96 | % 73.93/10.96 | BETA: splitting (38) gives: % 73.93/10.96 | % 73.93/10.96 | Case 1: % 73.93/10.96 | | % 73.93/10.96 | | (78) all_10_0 = e0 % 73.93/10.96 | | % 73.93/10.96 | | COMBINE_EQS: (69), (78) imply: % 73.93/10.96 | | (79) e2 = e0 % 73.93/10.96 | | % 73.93/10.96 | | REDUCE: (18), (79) imply: % 73.93/10.96 | | (80) $false % 73.93/10.96 | | % 73.93/10.96 | | CLOSE: (80) is inconsistent. % 73.93/10.96 | | % 73.93/10.96 | Case 2: % 73.93/10.96 | | % 73.93/10.96 | | (81) all_10_2 = e0 | all_10_6 = e0 | all_10_12 = e0 | all_10_20 = e0 % 73.93/10.96 | | % 73.93/10.96 | | BETA: splitting (3) gives: % 73.93/10.96 | | % 73.93/10.96 | | Case 1: % 73.93/10.96 | | | % 73.93/10.96 | | | (82) all_10_1 = e4 % 73.93/10.96 | | | % 73.93/10.96 | | | COMBINE_EQS: (16), (82) imply: % 73.93/10.96 | | | (83) all_4_5 = e4 % 73.93/10.96 | | | % 73.93/10.96 | | | REDUCE: (57), (83) imply: % 73.93/10.96 | | | (84) ~ (all_4_10 = e4) % 73.93/10.96 | | | % 73.93/10.96 | | | SIMP: (84) implies: % 73.93/10.96 | | | (85) ~ (all_4_10 = e4) % 73.93/10.96 | | | % 73.93/10.96 | | | REDUCE: (34), (83) imply: % 73.93/10.96 | | | (86) ~ (all_4_20 = e4) % 73.93/10.96 | | | % 73.93/10.96 | | | SIMP: (86) implies: % 73.93/10.96 | | | (87) ~ (all_4_20 = e4) % 73.93/10.96 | | | % 73.93/10.96 | | | REDUCE: (1), (83) imply: % 73.93/10.96 | | | (88) ~ (e4 = e2) % 73.93/10.96 | | | % 73.93/10.96 | | | REDUCE: (44), (83) imply: % 73.93/10.96 | | | (89) ~ (e4 = e0) % 73.93/10.96 | | | % 73.93/10.96 | | | BETA: splitting (66) gives: % 73.93/10.96 | | | % 73.93/10.96 | | | Case 1: % 73.93/10.96 | | | | % 73.93/10.96 | | | | (90) all_10_4 = e4 % 73.93/10.96 | | | | % 73.93/10.96 | | | | COMBINE_EQS: (13), (90) imply: % 73.93/10.96 | | | | (91) all_4_10 = e4 % 73.93/10.96 | | | | % 73.93/10.96 | | | | REDUCE: (85), (91) imply: % 73.93/10.96 | | | | (92) $false % 73.93/10.96 | | | | % 73.93/10.96 | | | | CLOSE: (92) is inconsistent. % 73.93/10.96 | | | | % 73.93/10.96 | | | Case 2: % 73.93/10.96 | | | | % 73.93/10.96 | | | | (93) all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | all_10_22 = e4 % 73.93/10.96 | | | | % 73.93/10.96 | | | | BETA: splitting (93) gives: % 73.93/10.96 | | | | % 73.93/10.96 | | | | Case 1: % 73.93/10.96 | | | | | % 73.93/10.96 | | | | | (94) all_10_5 = e4 % 73.93/10.96 | | | | | % 73.93/10.96 | | | | | COMBINE_EQS: (63), (94) imply: % 73.93/10.96 | | | | | (95) all_4_11 = e4 % 73.93/10.96 | | | | | % 73.93/10.96 | | | | | SIMP: (95) implies: % 73.93/10.96 | | | | | (96) all_4_11 = e4 % 73.93/10.96 | | | | | % 73.93/10.96 | | | | | REDUCE: (36), (96) imply: % 73.93/10.96 | | | | | (97) ~ (all_4_1 = e4) % 73.93/10.96 | | | | | % 73.93/10.96 | | | | | REDUCE: (59), (96) imply: % 73.93/10.96 | | | | | (98) ~ (all_4_21 = e4) % 73.93/10.96 | | | | | % 73.93/10.96 | | | | | SIMP: (98) implies: % 73.93/10.96 | | | | | (99) ~ (all_4_21 = e4) % 73.93/10.96 | | | | | % 73.93/10.96 | | | | | REDUCE: (74), (96) imply: % 73.93/10.96 | | | | | (100) op(e2, e4) = e3 % 73.93/10.96 | | | | | % 73.93/10.96 | | | | | BETA: splitting (20) gives: % 73.93/10.96 | | | | | % 73.93/10.96 | | | | | Case 1: % 73.93/10.96 | | | | | | % 73.93/10.96 | | | | | | (101) all_10_16 = e4 % 73.93/10.96 | | | | | | % 73.93/10.96 | | | | | | COMBINE_EQS: (24), (101) imply: % 73.93/10.96 | | | | | | (102) all_4_20 = e4 % 73.93/10.96 | | | | | | % 73.93/10.96 | | | | | | REDUCE: (87), (102) imply: % 73.93/10.96 | | | | | | (103) $false % 73.93/10.96 | | | | | | % 73.93/10.96 | | | | | | CLOSE: (103) is inconsistent. % 73.93/10.96 | | | | | | % 73.93/10.96 | | | | | Case 2: % 73.93/10.96 | | | | | | % 73.93/10.96 | | | | | | (104) all_10_17 = e4 | all_10_18 = e4 | all_10_19 = e4 | % 73.93/10.96 | | | | | | all_10_24 = e4 % 73.93/10.96 | | | | | | % 73.93/10.96 | | | | | | BETA: splitting (81) gives: % 73.93/10.96 | | | | | | % 73.93/10.96 | | | | | | Case 1: % 73.93/10.96 | | | | | | | % 73.93/10.96 | | | | | | | (105) all_10_2 = e0 % 73.93/10.96 | | | | | | | % 73.93/10.96 | | | | | | | REF_CLOSE: (2), (42), (105) are inconsistent by sub-proof #119. % 73.93/10.96 | | | | | | | % 73.93/10.96 | | | | | | Case 2: % 73.93/10.96 | | | | | | | % 73.93/10.96 | | | | | | | (106) all_10_6 = e0 | all_10_12 = e0 | all_10_20 = e0 % 73.93/10.96 | | | | | | | % 73.93/10.96 | | | | | | | BETA: splitting (73) gives: % 73.93/10.96 | | | | | | | % 73.93/10.96 | | | | | | | Case 1: % 73.93/10.96 | | | | | | | | % 73.93/10.96 | | | | | | | | (107) all_10_2 = e1 % 73.93/10.96 | | | | | | | | % 73.93/10.96 | | | | | | | | COMBINE_EQS: (42), (107) imply: % 73.93/10.96 | | | | | | | | (108) all_4_1 = e1 % 73.93/10.96 | | | | | | | | % 73.93/10.96 | | | | | | | | SIMP: (108) implies: % 73.93/10.96 | | | | | | | | (109) all_4_1 = e1 % 73.93/10.96 | | | | | | | | % 73.93/10.96 | | | | | | | | REDUCE: (5), (109) imply: % 73.93/10.96 | | | | | | | | (110) ~ (all_4_2 = e1) % 73.93/10.96 | | | | | | | | % 73.93/10.96 | | | | | | | | SIMP: (110) implies: % 73.93/10.96 | | | | | | | | (111) ~ (all_4_2 = e1) % 73.93/10.96 | | | | | | | | % 73.93/10.96 | | | | | | | | BETA: splitting (104) gives: % 73.93/10.96 | | | | | | | | % 73.93/10.96 | | | | | | | | Case 1: % 73.93/10.96 | | | | | | | | | % 73.93/10.96 | | | | | | | | | (112) all_10_17 = e4 % 73.93/10.96 | | | | | | | | | % 73.93/10.96 | | | | | | | | | COMBINE_EQS: (31), (112) imply: % 73.93/10.96 | | | | | | | | | (113) all_4_21 = e4 % 73.93/10.96 | | | | | | | | | % 73.93/10.96 | | | | | | | | | REDUCE: (99), (113) imply: % 73.93/10.96 | | | | | | | | | (114) $false % 73.93/10.96 | | | | | | | | | % 73.93/10.96 | | | | | | | | | CLOSE: (114) is inconsistent. % 73.93/10.96 | | | | | | | | | % 73.93/10.96 | | | | | | | | Case 2: % 73.93/10.96 | | | | | | | | | % 73.93/10.96 | | | | | | | | | (115) all_10_18 = e4 | all_10_19 = e4 | all_10_24 = e4 % 73.93/10.96 | | | | | | | | | % 73.93/10.96 | | | | | | | | | BETA: splitting (115) gives: % 73.93/10.96 | | | | | | | | | % 73.93/10.96 | | | | | | | | | Case 1: % 73.93/10.96 | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | (116) all_10_18 = e4 % 73.93/10.96 | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | COMBINE_EQS: (71), (116) imply: % 73.93/10.96 | | | | | | | | | | (117) all_4_22 = e4 % 73.93/10.96 | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | REDUCE: (40), (117) imply: % 73.93/10.96 | | | | | | | | | | (118) op(e2, e4) = all_8_59 % 73.93/10.96 | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | BETA: splitting (106) gives: % 73.93/10.96 | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | Case 1: % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | (119) all_10_6 = e0 % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | COMBINE_EQS: (61), (119) imply: % 73.93/10.96 | | | | | | | | | | | (120) all_4_2 = e0 % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | SIMP: (120) implies: % 73.93/10.96 | | | | | | | | | | | (121) all_4_2 = e0 % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | REDUCE: (22), (121) imply: % 73.93/10.96 | | | | | | | | | | | (122) ~ (e3 = e0) % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | SIMP: (122) implies: % 73.93/10.96 | | | | | | | | | | | (123) ~ (e3 = e0) % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | REDUCE: (28), (121) imply: % 73.93/10.96 | | | | | | | | | | | (124) op(e2, e4) = e0 % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | GROUND_INST: instantiating (62) with e3, all_8_59, e4, e2, % 73.93/10.96 | | | | | | | | | | | simplifying with (100), (118) gives: % 73.93/10.96 | | | | | | | | | | | (125) all_8_59 = e3 % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | GROUND_INST: instantiating (62) with e0, all_8_59, e4, e2, % 73.93/10.96 | | | | | | | | | | | simplifying with (118), (124) gives: % 73.93/10.96 | | | | | | | | | | | (126) all_8_59 = e0 % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | COMBINE_EQS: (125), (126) imply: % 73.93/10.96 | | | | | | | | | | | (127) e3 = e0 % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | REDUCE: (123), (127) imply: % 73.93/10.96 | | | | | | | | | | | (128) $false % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | CLOSE: (128) is inconsistent. % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | Case 2: % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | (129) all_10_12 = e0 | all_10_20 = e0 % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | REF_CLOSE: (15), (21), (43), (89), (129) are inconsistent by % 73.93/10.96 | | | | | | | | | | | sub-proof #75. % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | End of split % 73.93/10.96 | | | | | | | | | | % 73.93/10.96 | | | | | | | | | Case 2: % 73.93/10.96 | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | (130) ~ (all_10_18 = e4) % 73.93/10.96 | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | REDUCE: (71), (130) imply: % 73.93/10.96 | | | | | | | | | | (131) ~ (all_4_22 = e4) % 73.93/10.96 | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | BETA: splitting (23) gives: % 73.93/10.96 | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | Case 1: % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | (132) all_6_14 = e4 % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | COMBINE_EQS: (47), (132) imply: % 73.93/10.96 | | | | | | | | | | | (133) all_4_22 = e4 % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | SIMP: (133) implies: % 73.93/10.96 | | | | | | | | | | | (134) all_4_22 = e4 % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | REDUCE: (131), (134) imply: % 73.93/10.96 | | | | | | | | | | | (135) $false % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | CLOSE: (135) is inconsistent. % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | Case 2: % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | (136) all_6_14 = e3 | all_6_14 = e1 | all_6_14 = e0 % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | BETA: splitting (136) gives: % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | Case 1: % 73.93/10.96 | | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | | (137) all_6_14 = e1 % 73.93/10.96 | | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | | REF_CLOSE: (29), (47), (137) are inconsistent by sub-proof % 73.93/10.96 | | | | | | | | | | | | #50. % 73.93/10.96 | | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | Case 2: % 73.93/10.96 | | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | | (138) all_6_14 = e3 | all_6_14 = e0 % 73.93/10.96 | | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | | BETA: splitting (138) gives: % 73.93/10.96 | | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | | Case 1: % 73.93/10.96 | | | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | | | (139) all_6_14 = e3 % 73.93/10.96 | | | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | | | REF_CLOSE: (45), (47), (139) are inconsistent by sub-proof % 73.93/10.96 | | | | | | | | | | | | | #49. % 73.93/10.96 | | | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | | Case 2: % 73.93/10.96 | | | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | | | (140) all_6_14 = e0 % 73.93/10.96 | | | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | | | COMBINE_EQS: (47), (140) imply: % 73.93/10.96 | | | | | | | | | | | | | (141) all_4_22 = e0 % 73.93/10.96 | | | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | | | SIMP: (141) implies: % 73.93/10.96 | | | | | | | | | | | | | (142) all_4_22 = e0 % 73.93/10.96 | | | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | | | REDUCE: (25), (142) imply: % 73.93/10.96 | | | | | | | | | | | | | (143) ~ (all_4_2 = e0) % 73.93/10.96 | | | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | | | REF_CLOSE: (22), (39), (52), (67), (111), (143) are % 73.93/10.96 | | | | | | | | | | | | | inconsistent by sub-proof #61. % 73.93/10.96 | | | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | | End of split % 73.93/10.96 | | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | | End of split % 73.93/10.96 | | | | | | | | | | | % 73.93/10.96 | | | | | | | | | | End of split % 73.93/10.96 | | | | | | | | | | % 73.93/10.96 | | | | | | | | | End of split % 73.93/10.96 | | | | | | | | | % 73.93/10.96 | | | | | | | | End of split % 73.93/10.96 | | | | | | | | % 73.93/10.96 | | | | | | | Case 2: % 73.93/10.96 | | | | | | | | % 73.93/10.96 | | | | | | | | (144) ~ (all_10_2 = e1) % 73.93/10.96 | | | | | | | | % 73.93/10.96 | | | | | | | | REF_CLOSE: (5), (8), (15), (17), (19), (21), (22), (23), (24), % 73.93/10.96 | | | | | | | | (25), (29), (30), (31), (35), (37), (42), (43), (45), % 73.93/10.96 | | | | | | | | (46), (47), (50), (52), (53), (55), (61), (71), (76), % 73.93/10.96 | | | | | | | | (77), (89), (97), (99), (106), (144) are inconsistent % 73.93/10.96 | | | | | | | | by sub-proof #46. % 73.93/10.96 | | | | | | | | % 73.93/10.96 | | | | | | | End of split % 73.93/10.96 | | | | | | | % 73.93/10.96 | | | | | | End of split % 73.93/10.96 | | | | | | % 73.93/10.96 | | | | | End of split % 73.93/10.96 | | | | | % 73.93/10.96 | | | | Case 2: % 73.93/10.96 | | | | | % 73.93/10.96 | | | | | (145) all_10_8 = e4 | all_10_14 = e4 | all_10_22 = e4 % 73.93/10.96 | | | | | % 73.93/10.96 | | | | | REF_CLOSE: (4), (6), (14), (41), (88), (89), (145) are inconsistent by % 73.93/10.96 | | | | | sub-proof #115. % 73.93/10.96 | | | | | % 73.93/10.96 | | | | End of split % 73.93/10.96 | | | | % 73.93/10.96 | | | End of split % 73.93/10.96 | | | % 73.93/10.96 | | Case 2: % 73.93/10.96 | | | % 73.93/10.96 | | | (146) ~ (all_10_1 = e4) % 73.93/10.96 | | | % 73.93/10.96 | | | REDUCE: (16), (146) imply: % 73.93/10.96 | | | (147) ~ (all_4_5 = e4) % 73.93/10.96 | | | % 73.93/10.96 | | | BETA: splitting (49) gives: % 73.93/10.96 | | | % 73.93/10.96 | | | Case 1: % 73.93/10.96 | | | | % 73.93/10.96 | | | | (148) all_6_21 = e4 % 73.93/10.96 | | | | % 73.93/10.96 | | | | COMBINE_EQS: (32), (148) imply: % 73.93/10.96 | | | | (149) all_4_9 = e4 % 73.93/10.96 | | | | % 73.93/10.96 | | | | REDUCE: (51), (149) imply: % 73.93/10.96 | | | | (150) $false % 73.93/10.96 | | | | % 73.93/10.96 | | | | CLOSE: (150) is inconsistent. % 73.93/10.96 | | | | % 73.93/10.96 | | | Case 2: % 73.93/10.96 | | | | % 73.93/10.96 | | | | (151) all_6_21 = e3 | all_6_21 = e1 | all_6_21 = e0 % 73.93/10.96 | | | | % 73.93/10.96 | | | | BETA: splitting (60) gives: % 73.93/10.96 | | | | % 73.93/10.96 | | | | Case 1: % 73.93/10.96 | | | | | % 73.93/10.96 | | | | | (152) all_10_20 = e3 % 73.93/10.96 | | | | | % 73.93/10.96 | | | | | COMBINE_EQS: (15), (152) imply: % 73.93/10.96 | | | | | (153) e4 = e3 % 73.93/10.96 | | | | | % 73.93/10.96 | | | | | REDUCE: (41), (153) imply: % 73.93/10.96 | | | | | (154) $false % 73.93/10.96 | | | | | % 73.93/10.96 | | | | | CLOSE: (154) is inconsistent. % 73.93/10.96 | | | | | % 73.93/10.96 | | | | Case 2: % 73.93/10.96 | | | | | % 73.93/10.96 | | | | | (155) all_10_21 = e3 | all_10_22 = e3 | all_10_23 = e3 | all_10_24 % 73.93/10.96 | | | | | = e3 % 73.93/10.96 | | | | | % 73.93/10.96 | | | | | BETA: splitting (155) gives: % 73.93/10.96 | | | | | % 73.93/10.96 | | | | | Case 1: % 73.93/10.96 | | | | | | % 73.93/10.96 | | | | | | (156) all_10_21 = e3 % 73.93/10.96 | | | | | | % 73.93/10.96 | | | | | | COMBINE_EQS: (26), (156) imply: % 73.93/10.96 | | | | | | (157) all_4_9 = e3 % 73.93/10.96 | | | | | | % 73.93/10.96 | | | | | | REDUCE: (72), (157) imply: % 73.93/10.96 | | | | | | (158) ~ (all_4_5 = e3) % 73.93/10.96 | | | | | | % 73.93/10.96 | | | | | | REF_CLOSE: (9), (10), (11), (12), (13), (27), (33), (44), (54), % 73.93/10.96 | | | | | | (56), (57), (58), (62), (64), (65), (68), (70), (74), % 73.93/10.96 | | | | | | (75), (147), (158) are inconsistent by sub-proof #6. % 73.93/10.96 | | | | | | % 73.93/10.96 | | | | | Case 2: % 73.93/10.96 | | | | | | % 73.93/10.96 | | | | | | (159) ~ (all_10_21 = e3) % 73.93/10.96 | | | | | | % 73.93/10.96 | | | | | | REDUCE: (26), (159) imply: % 73.93/10.96 | | | | | | (160) ~ (all_4_9 = e3) % 73.93/10.96 | | | | | | % 73.93/10.96 | | | | | | REF_CLOSE: (7), (32), (48), (151), (160) are inconsistent by % 73.93/10.96 | | | | | | sub-proof #126. % 73.93/10.96 | | | | | | % 73.93/10.96 | | | | | End of split % 73.93/10.96 | | | | | % 73.93/10.96 | | | | End of split % 73.93/10.96 | | | | % 73.93/10.96 | | | End of split % 73.93/10.96 | | | % 73.93/10.96 | | End of split % 73.93/10.96 | | % 73.93/10.96 | End of split % 73.93/10.96 | % 73.93/10.96 End of proof % 73.93/10.96 % 73.93/10.96 Sub-proof #6 shows that the following formulas are inconsistent: % 73.93/10.96 ---------------------------------------------------------------- % 73.93/10.96 (1) ~ (all_4_11 = e0) % 73.93/10.96 (2) ~ (all_4_11 = e3) % 73.93/10.96 (3) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 73.93/10.96 (4) ~ (all_4_10 = e3) % 73.93/10.96 (5) all_10_4 = all_4_10 % 73.93/10.96 (6) ~ (all_4_10 = e0) % 73.93/10.96 (7) ~ (all_4_5 = e3) % 73.93/10.96 (8) op(e2, e1) = all_4_17 % 73.93/10.96 (9) ~ (all_4_5 = e0) % 73.93/10.96 (10) ~ (all_4_10 = all_4_11) % 73.93/10.96 (11) ~ (all_4_5 = e4) % 73.93/10.96 (12) all_6_1 = all_4_5 % 73.93/10.96 (13) ~ (all_4_5 = all_4_10) % 73.93/10.96 (14) all_6_7 = all_4_11 % 73.93/10.96 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 73.93/10.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 73.93/10.96 (16) all_6_2 = all_4_10 % 73.93/10.96 (17) all_6_7 = e4 | all_6_7 = e3 | all_6_7 = e1 | all_6_7 = e0 % 73.93/10.96 (18) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 73.93/10.96 (19) ~ (all_4_17 = e3) % 73.93/10.96 (20) op(e2, all_4_11) = e3 % 73.93/10.96 (21) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 73.93/10.96 all_10_22 = e1 % 73.93/10.96 % 73.93/10.96 Begin of proof % 73.93/10.96 | % 73.93/10.96 | BETA: splitting (18) gives: % 73.93/10.96 | % 73.93/10.96 | Case 1: % 73.93/10.96 | | % 73.93/10.96 | | (22) all_6_2 = e4 % 73.93/10.96 | | % 73.93/10.96 | | COMBINE_EQS: (16), (22) imply: % 73.93/10.96 | | (23) all_4_10 = e4 % 73.93/10.96 | | % 73.93/10.96 | | SIMP: (23) implies: % 73.93/10.96 | | (24) all_4_10 = e4 % 73.93/10.96 | | % 73.93/10.96 | | REDUCE: (10), (24) imply: % 73.93/10.96 | | (25) ~ (all_4_11 = e4) % 73.93/10.96 | | % 73.93/10.96 | | SIMP: (25) implies: % 73.93/10.96 | | (26) ~ (all_4_11 = e4) % 73.93/10.96 | | % 73.93/10.97 | | REF_CLOSE: (1), (2), (8), (14), (15), (17), (19), (20), (26) are % 73.93/10.97 | | inconsistent by sub-proof #7. % 73.93/10.97 | | % 73.93/10.97 | Case 2: % 73.93/10.97 | | % 73.93/10.97 | | (27) all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 73.93/10.97 | | % 73.93/10.97 | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (11), (12), (13), (16), (21), (27) % 73.93/10.97 | | are inconsistent by sub-proof #44. % 73.93/10.97 | | % 73.93/10.97 | End of split % 73.93/10.97 | % 73.93/10.97 End of proof % 73.93/10.97 % 73.93/10.97 Sub-proof #7 shows that the following formulas are inconsistent: % 73.93/10.97 ---------------------------------------------------------------- % 73.93/10.97 (1) ~ (all_4_11 = e0) % 73.93/10.97 (2) ~ (all_4_11 = e3) % 73.93/10.97 (3) ~ (all_4_11 = e4) % 73.93/10.97 (4) op(e2, e1) = all_4_17 % 73.93/10.97 (5) all_6_7 = all_4_11 % 73.93/10.97 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 73.93/10.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 73.93/10.97 (7) all_6_7 = e4 | all_6_7 = e3 | all_6_7 = e1 | all_6_7 = e0 % 73.93/10.97 (8) ~ (all_4_17 = e3) % 73.93/10.97 (9) op(e2, all_4_11) = e3 % 73.93/10.97 % 73.93/10.97 Begin of proof % 73.93/10.97 | % 73.93/10.97 | BETA: splitting (7) gives: % 73.93/10.97 | % 73.93/10.97 | Case 1: % 73.93/10.97 | | % 73.93/10.97 | | (10) all_6_7 = e4 % 73.93/10.97 | | % 73.93/10.97 | | COMBINE_EQS: (5), (10) imply: % 73.93/10.97 | | (11) all_4_11 = e4 % 73.93/10.97 | | % 73.93/10.97 | | SIMP: (11) implies: % 73.93/10.97 | | (12) all_4_11 = e4 % 73.93/10.97 | | % 73.93/10.97 | | REDUCE: (3), (12) imply: % 73.93/10.97 | | (13) $false % 73.93/10.97 | | % 73.93/10.97 | | CLOSE: (13) is inconsistent. % 73.93/10.97 | | % 73.93/10.97 | Case 2: % 73.93/10.97 | | % 73.93/10.97 | | (14) all_6_7 = e3 | all_6_7 = e1 | all_6_7 = e0 % 73.93/10.97 | | % 73.93/10.97 | | BETA: splitting (14) gives: % 73.93/10.97 | | % 73.93/10.97 | | Case 1: % 73.93/10.97 | | | % 73.93/10.97 | | | (15) all_6_7 = e1 % 73.93/10.97 | | | % 73.93/10.97 | | | COMBINE_EQS: (5), (15) imply: % 73.93/10.97 | | | (16) all_4_11 = e1 % 73.93/10.97 | | | % 73.93/10.97 | | | REF_CLOSE: (4), (6), (8), (9), (16) are inconsistent by sub-proof #8. % 73.93/10.97 | | | % 73.93/10.97 | | Case 2: % 73.93/10.97 | | | % 73.93/10.97 | | | (17) all_6_7 = e3 | all_6_7 = e0 % 73.93/10.97 | | | % 73.93/10.97 | | | REF_CLOSE: (1), (2), (5), (17) are inconsistent by sub-proof #92. % 73.93/10.97 | | | % 73.93/10.97 | | End of split % 73.93/10.97 | | % 73.93/10.97 | End of split % 73.93/10.97 | % 73.93/10.97 End of proof % 73.93/10.97 % 73.93/10.97 Sub-proof #8 shows that the following formulas are inconsistent: % 73.93/10.97 ---------------------------------------------------------------- % 73.93/10.97 (1) op(e2, e1) = all_4_17 % 73.93/10.97 (2) all_4_11 = e1 % 73.93/10.97 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 73.93/10.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 73.93/10.97 (4) ~ (all_4_17 = e3) % 73.93/10.97 (5) op(e2, all_4_11) = e3 % 73.93/10.97 % 73.93/10.97 Begin of proof % 73.93/10.97 | % 73.93/10.97 | SIMP: (2) implies: % 73.93/10.97 | (6) all_4_11 = e1 % 73.93/10.97 | % 73.93/10.97 | REDUCE: (5), (6) imply: % 73.93/10.97 | (7) op(e2, e1) = e3 % 73.93/10.97 | % 73.93/10.97 | GROUND_INST: instantiating (3) with all_4_17, e3, e1, e2, simplifying with % 73.93/10.97 | (1), (7) gives: % 73.93/10.97 | (8) all_4_17 = e3 % 73.93/10.97 | % 73.93/10.97 | REDUCE: (4), (8) imply: % 73.93/10.97 | (9) $false % 73.93/10.97 | % 73.93/10.97 | CLOSE: (9) is inconsistent. % 73.93/10.97 | % 73.93/10.97 End of proof % 73.93/10.97 % 73.93/10.97 Sub-proof #9 shows that the following formulas are inconsistent: % 73.93/10.97 ---------------------------------------------------------------- % 73.93/10.97 (1) all_6_7 = all_4_11 % 73.93/10.97 (2) all_6_7 = e2 % 73.93/10.97 (3) ~ (all_4_11 = e2) % 73.93/10.97 % 73.93/10.97 Begin of proof % 73.93/10.97 | % 73.93/10.97 | COMBINE_EQS: (1), (2) imply: % 73.93/10.97 | (4) all_4_11 = e2 % 73.93/10.97 | % 73.93/10.97 | SIMP: (4) implies: % 73.93/10.97 | (5) all_4_11 = e2 % 73.93/10.97 | % 73.93/10.97 | REDUCE: (3), (5) imply: % 73.93/10.97 | (6) $false % 73.93/10.97 | % 73.93/10.97 | CLOSE: (6) is inconsistent. % 73.93/10.97 | % 73.93/10.97 End of proof % 73.93/10.97 % 73.93/10.97 Sub-proof #10 shows that the following formulas are inconsistent: % 73.93/10.97 ---------------------------------------------------------------- % 73.93/10.97 (1) all_10_14 = e0 % 73.93/10.97 (2) all_10_15 = e4 % 73.93/10.97 (3) ~ (e2 = e0) % 73.93/10.97 (4) all_10_19 = all_4_23 % 73.93/10.97 (5) all_10_14 = e2 | all_10_15 = e2 | all_10_19 = e2 % 73.93/10.97 (6) ~ (e4 = e2) % 73.93/10.97 (7) ~ (all_4_23 = e2) % 73.93/10.97 % 73.93/10.97 Begin of proof % 73.93/10.97 | % 73.93/10.97 | BETA: splitting (5) gives: % 73.93/10.97 | % 73.93/10.97 | Case 1: % 73.93/10.97 | | % 73.93/10.97 | | (8) all_10_14 = e2 % 73.93/10.97 | | % 73.93/10.97 | | COMBINE_EQS: (1), (8) imply: % 73.93/10.97 | | (9) e2 = e0 % 73.93/10.97 | | % 73.93/10.97 | | REDUCE: (3), (9) imply: % 73.93/10.97 | | (10) $false % 73.93/10.97 | | % 73.93/10.97 | | CLOSE: (10) is inconsistent. % 73.93/10.97 | | % 73.93/10.97 | Case 2: % 73.93/10.97 | | % 73.93/10.97 | | (11) all_10_15 = e2 | all_10_19 = e2 % 73.93/10.97 | | % 73.93/10.97 | | REF_CLOSE: (2), (4), (6), (7), (11) are inconsistent by sub-proof #60. % 73.93/10.97 | | % 73.93/10.97 | End of split % 73.93/10.97 | % 73.93/10.97 End of proof % 73.93/10.97 % 73.93/10.97 Sub-proof #11 shows that the following formulas are inconsistent: % 73.93/10.97 ---------------------------------------------------------------- % 73.93/10.97 (1) ~ (all_4_3 = e4) % 73.93/10.97 (2) all_6_19 = all_4_23 % 73.93/10.97 (3) all_10_12 = all_4_3 % 73.93/10.97 (4) ~ (all_4_23 = e1) % 73.93/10.97 (5) ~ (all_4_3 = all_4_23) % 73.93/10.97 (6) ~ (all_4_3 = e0) % 73.93/10.97 (7) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e1 | all_6_15 = e0 % 73.93/10.97 (8) all_6_15 = all_4_3 % 73.93/10.97 (9) ~ (all_10_12 = e1) % 73.93/10.97 (10) all_6_19 = e3 | all_6_19 = e1 | all_6_19 = e0 % 73.93/10.97 (11) ~ (all_4_23 = e0) % 73.93/10.97 % 73.93/10.97 Begin of proof % 73.93/10.97 | % 73.93/10.97 | REDUCE: (3), (9) imply: % 73.93/10.97 | (12) ~ (all_4_3 = e1) % 73.93/10.97 | % 73.93/10.97 | BETA: splitting (7) gives: % 73.93/10.97 | % 73.93/10.97 | Case 1: % 73.93/10.97 | | % 73.93/10.97 | | (13) all_6_15 = e4 % 73.93/10.97 | | % 73.93/10.97 | | REF_CLOSE: (1), (8), (13) are inconsistent by sub-proof #107. % 73.93/10.97 | | % 73.93/10.97 | Case 2: % 73.93/10.97 | | % 73.93/10.97 | | (14) all_6_15 = e3 | all_6_15 = e1 | all_6_15 = e0 % 73.93/10.97 | | % 73.93/10.97 | | BETA: splitting (10) gives: % 73.93/10.97 | | % 73.93/10.97 | | Case 1: % 73.93/10.97 | | | % 73.93/10.97 | | | (15) all_6_19 = e1 % 73.93/10.97 | | | % 73.93/10.97 | | | COMBINE_EQS: (2), (15) imply: % 73.93/10.97 | | | (16) all_4_23 = e1 % 73.93/10.97 | | | % 73.93/10.97 | | | REDUCE: (4), (16) imply: % 73.93/10.97 | | | (17) $false % 73.93/10.97 | | | % 73.93/10.97 | | | CLOSE: (17) is inconsistent. % 73.93/10.97 | | | % 73.93/10.97 | | Case 2: % 73.93/10.97 | | | % 73.93/10.97 | | | (18) all_6_19 = e3 | all_6_19 = e0 % 73.93/10.97 | | | % 73.93/10.97 | | | BETA: splitting (14) gives: % 73.93/10.97 | | | % 73.93/10.97 | | | Case 1: % 73.93/10.97 | | | | % 73.93/10.97 | | | | (19) all_6_15 = e1 % 73.93/10.97 | | | | % 73.93/10.97 | | | | COMBINE_EQS: (8), (19) imply: % 73.93/10.97 | | | | (20) all_4_3 = e1 % 73.93/10.97 | | | | % 73.93/10.97 | | | | SIMP: (20) implies: % 73.93/10.97 | | | | (21) all_4_3 = e1 % 73.93/10.97 | | | | % 73.93/10.97 | | | | REDUCE: (12), (21) imply: % 73.93/10.97 | | | | (22) $false % 73.93/10.97 | | | | % 73.93/10.97 | | | | CLOSE: (22) is inconsistent. % 73.93/10.97 | | | | % 73.93/10.97 | | | Case 2: % 73.93/10.97 | | | | % 73.93/10.97 | | | | (23) all_6_15 = e3 | all_6_15 = e0 % 73.93/10.97 | | | | % 73.93/10.97 | | | | REF_CLOSE: (2), (5), (6), (8), (11), (18), (23) are inconsistent by % 73.93/10.97 | | | | sub-proof #94. % 73.93/10.97 | | | | % 73.93/10.97 | | | End of split % 73.93/10.97 | | | % 73.93/10.97 | | End of split % 73.93/10.97 | | % 73.93/10.97 | End of split % 73.93/10.97 | % 73.93/10.97 End of proof % 73.93/10.97 % 73.93/10.97 Sub-proof #12 shows that the following formulas are inconsistent: % 73.93/10.97 ---------------------------------------------------------------- % 73.93/10.97 (1) all_10_8 = e3 % 73.93/10.97 (2) ~ (e3 = e1) % 73.93/10.97 (3) ~ (all_4_22 = e1) % 73.93/10.97 (4) ~ (e2 = e1) % 73.93/10.97 (5) all_10_11 = e2 % 73.93/10.97 (6) all_10_8 = e1 | all_10_11 = e1 | all_10_18 = e1 % 73.93/10.97 (7) all_10_18 = all_4_22 % 73.93/10.97 % 73.93/10.97 Begin of proof % 73.93/10.97 | % 73.93/10.97 | BETA: splitting (6) gives: % 73.93/10.97 | % 73.93/10.97 | Case 1: % 73.93/10.97 | | % 73.93/10.97 | | (8) all_10_8 = e1 % 73.93/10.97 | | % 73.93/10.97 | | COMBINE_EQS: (1), (8) imply: % 73.93/10.97 | | (9) e3 = e1 % 73.93/10.97 | | % 73.93/10.97 | | REDUCE: (2), (9) imply: % 73.93/10.97 | | (10) $false % 73.93/10.97 | | % 73.93/10.97 | | CLOSE: (10) is inconsistent. % 73.93/10.97 | | % 73.93/10.97 | Case 2: % 73.93/10.97 | | % 73.93/10.97 | | (11) all_10_11 = e1 | all_10_18 = e1 % 73.93/10.97 | | % 73.93/10.97 | | BETA: splitting (11) gives: % 73.93/10.97 | | % 73.93/10.97 | | Case 1: % 73.93/10.97 | | | % 73.93/10.97 | | | (12) all_10_11 = e1 % 73.93/10.97 | | | % 73.93/10.97 | | | COMBINE_EQS: (5), (12) imply: % 73.93/10.97 | | | (13) e2 = e1 % 73.93/10.97 | | | % 73.93/10.97 | | | REDUCE: (4), (13) imply: % 73.93/10.97 | | | (14) $false % 73.93/10.97 | | | % 73.93/10.97 | | | CLOSE: (14) is inconsistent. % 73.93/10.97 | | | % 73.93/10.97 | | Case 2: % 73.93/10.97 | | | % 73.93/10.97 | | | (15) all_10_18 = e1 % 73.93/10.97 | | | % 73.93/10.97 | | | COMBINE_EQS: (7), (15) imply: % 73.93/10.97 | | | (16) all_4_22 = e1 % 73.93/10.97 | | | % 73.93/10.97 | | | REDUCE: (3), (16) imply: % 73.93/10.97 | | | (17) $false % 73.93/10.97 | | | % 73.93/10.97 | | | CLOSE: (17) is inconsistent. % 73.93/10.97 | | | % 73.93/10.97 | | End of split % 73.93/10.97 | | % 73.93/10.97 | End of split % 73.93/10.97 | % 73.93/10.97 End of proof % 73.93/10.97 % 73.93/10.97 Sub-proof #13 shows that the following formulas are inconsistent: % 73.93/10.97 ---------------------------------------------------------------- % 73.93/10.97 (1) ~ (all_4_19 = e4) % 73.93/10.97 (2) ~ (all_4_1 = e0) % 73.93/10.97 (3) all_10_1 = e4 | all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | % 73.93/10.97 all_10_21 = e4 % 73.93/10.97 (4) ~ (all_4_20 = all_4_22) % 73.93/10.97 (5) ~ (all_4_10 = e3) % 73.93/10.97 (6) ~ (e3 = e2) % 73.93/10.97 (7) op(e0, e4) = all_4_4 % 73.93/10.97 (8) all_10_4 = all_4_10 % 73.93/10.97 (9) all_10_22 = e2 % 73.93/10.97 (10) ~ (all_4_20 = e3) % 73.93/10.97 (11) all_10_1 = all_4_5 % 73.93/10.97 (12) ~ (all_4_4 = e2) % 73.93/10.97 (13) all_10_24 = e1 % 73.93/10.97 (14) ~ (e2 = e0) % 73.93/10.97 (15) ~ (all_4_2 = e3) % 73.93/10.97 (16) op(e3, e4) = all_4_1 % 73.93/10.97 (17) op(e4, all_4_15) = all_8_40 % 73.93/10.97 (18) ~ (e3 = e1) % 73.93/10.97 (19) all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e1 | all_6_14 = e0 % 73.93/10.97 (20) all_10_16 = all_4_20 % 73.93/10.97 (21) ~ (e4 = e0) % 73.93/10.97 (22) all_10_3 = e0 % 73.93/10.97 (23) ~ (all_4_4 = all_4_9) % 73.93/10.97 (24) all_10_23 = all_4_19 % 73.93/10.97 (25) all_10_21 = all_4_9 % 73.93/10.97 (26) ~ (all_4_10 = e0) % 73.93/10.97 (27) ~ (all_4_22 = e1) % 73.93/10.97 (28) all_10_9 = e3 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 73.93/10.97 all_10_23 = e3 % 73.93/10.97 (29) all_10_20 = all_4_4 % 73.93/10.97 (30) all_10_0 = e3 | all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | % 73.93/10.97 all_10_16 = e3 % 73.93/10.97 (31) op(e0, all_4_4) = all_8_11 % 73.93/10.97 (32) ~ (e4 = e3) % 73.93/10.97 (33) all_10_2 = all_4_1 % 73.93/10.97 (34) ~ (all_4_5 = e0) % 73.93/10.97 (35) ~ (all_4_22 = e3) % 73.93/10.97 (36) ~ (all_4_15 = e2) % 73.93/10.97 (37) all_6_14 = all_4_22 % 73.93/10.97 (38) all_10_9 = all_4_15 % 74.32/10.97 (39) all_10_20 = e4 | all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 74.32/10.97 all_10_24 = e4 % 74.32/10.97 (40) op(e0, all_4_22) = e2 % 74.32/10.98 (41) all_10_0 = e3 | all_10_2 = e3 | all_10_6 = e3 | all_10_12 = e3 | % 74.32/10.98 all_10_20 = e3 % 74.32/10.98 (42) op(e3, all_4_9) = all_8_23 % 74.32/10.98 (43) all_10_12 = e1 % 74.32/10.98 (44) op(e4, all_4_1) = e3 % 74.32/10.98 (45) ~ (all_4_5 = all_4_10) % 74.32/10.98 (46) all_10_13 = e2 % 74.32/10.98 (47) ~ (e4 = e2) % 74.32/10.98 (48) all_8_23 = e0 & ~ (all_8_24 = e3) % 74.32/10.98 (49) all_10_6 = all_4_2 % 74.32/10.98 (50) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.32/10.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.32/10.98 (51) all_6_2 = all_4_10 % 74.32/10.98 (52) ~ (all_4_1 = all_4_4) % 74.32/10.98 (53) ~ (e4 = e1) % 74.32/10.98 (54) ~ (all_4_4 = e1) % 74.32/10.98 (55) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.32/10.98 (56) all_10_0 = e2 % 74.32/10.98 (57) all_10_0 = e0 | all_10_1 = e0 | all_10_4 = e0 | all_10_9 = e0 | % 74.32/10.98 all_10_16 = e0 % 74.32/10.98 (58) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 74.32/10.98 all_10_22 = e1 % 74.32/10.98 (59) all_10_7 = e1 % 74.32/10.98 (60) ~ (all_4_1 = e2) % 74.32/10.98 (61) op(e4, e3) = all_4_5 % 74.32/10.98 % 74.32/10.98 Begin of proof % 74.32/10.98 | % 74.32/10.98 | ALPHA: (48) implies: % 74.32/10.98 | (62) all_8_23 = e0 % 74.32/10.98 | % 74.32/10.98 | REDUCE: (42), (62) imply: % 74.32/10.98 | (63) op(e3, all_4_9) = e0 % 74.32/10.98 | % 74.32/10.98 | BETA: splitting (39) gives: % 74.32/10.98 | % 74.32/10.98 | Case 1: % 74.32/10.98 | | % 74.32/10.98 | | (64) all_10_20 = e4 % 74.32/10.98 | | % 74.32/10.98 | | COMBINE_EQS: (29), (64) imply: % 74.32/10.98 | | (65) all_4_4 = e4 % 74.32/10.98 | | % 74.32/10.98 | | SIMP: (65) implies: % 74.32/10.98 | | (66) all_4_4 = e4 % 74.32/10.98 | | % 74.32/10.98 | | REDUCE: (52), (66) imply: % 74.32/10.98 | | (67) ~ (all_4_1 = e4) % 74.32/10.98 | | % 74.32/10.98 | | REDUCE: (23), (66) imply: % 74.32/10.98 | | (68) ~ (all_4_9 = e4) % 74.32/10.98 | | % 74.32/10.98 | | SIMP: (68) implies: % 74.32/10.98 | | (69) ~ (all_4_9 = e4) % 74.32/10.98 | | % 74.32/10.98 | | REDUCE: (31), (66) imply: % 74.32/10.98 | | (70) op(e0, e4) = all_8_11 % 74.32/10.98 | | % 74.32/10.98 | | REDUCE: (7), (66) imply: % 74.32/10.98 | | (71) op(e0, e4) = e4 % 74.32/10.98 | | % 74.32/10.98 | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (10), (11), (14), (15), (17), (18), % 74.32/10.98 | | (19), (20), (21), (22), (25), (26), (27), (28), (30), (32), (33), % 74.32/10.98 | | (34), (35), (36), (37), (38), (40), (41), (43), (44), (45), (46), % 74.32/10.98 | | (47), (49), (50), (51), (53), (55), (56), (57), (58), (59), (60), % 74.32/10.98 | | (61), (64), (67), (69), (70), (71) are inconsistent by sub-proof % 74.32/10.98 | | #15. % 74.32/10.98 | | % 74.32/10.98 | Case 2: % 74.32/10.98 | | % 74.32/10.98 | | (72) all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | all_10_24 = e4 % 74.32/10.98 | | % 74.32/10.98 | | REF_CLOSE: (1), (2), (9), (13), (16), (24), (25), (47), (50), (53), (63), % 74.32/10.98 | | (72) are inconsistent by sub-proof #32. % 74.32/10.98 | | % 74.32/10.98 | End of split % 74.32/10.98 | % 74.32/10.98 End of proof % 74.32/10.98 % 74.32/10.98 Sub-proof #14 shows that the following formulas are inconsistent: % 74.32/10.98 ---------------------------------------------------------------- % 74.32/10.98 (1) all_8_17 = all_4_16 % 74.32/10.98 (2) ~ (all_4_19 = e4) % 74.32/10.98 (3) ~ (all_4_1 = e0) % 74.32/10.98 (4) all_10_1 = e4 | all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | % 74.32/10.98 all_10_21 = e4 % 74.32/10.98 (5) ~ (all_4_9 = e0) % 74.32/10.98 (6) ~ (all_4_20 = all_4_22) % 74.32/10.98 (7) (all_8_13 = e4 & ~ (all_8_14 = e3)) | (all_8_17 = e2 & ~ (all_8_18 = % 74.32/10.98 e3)) % 74.32/10.98 (8) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 74.32/10.98 (9) ~ (all_4_10 = e3) % 74.32/10.98 (10) ~ (e3 = e2) % 74.32/10.98 (11) op(e0, e4) = all_4_4 % 74.32/10.98 (12) all_10_4 = all_4_10 % 74.32/10.98 (13) all_10_22 = e2 % 74.32/10.98 (14) ~ (all_4_16 = e2) % 74.32/10.98 (15) ~ (all_4_20 = e3) % 74.32/10.98 (16) all_10_1 = all_4_5 % 74.32/10.98 (17) ~ (all_4_4 = e2) % 74.32/10.98 (18) all_10_24 = e1 % 74.32/10.98 (19) ~ (e2 = e0) % 74.32/10.98 (20) ~ (all_4_2 = e3) % 74.32/10.98 (21) op(e4, all_4_15) = all_8_40 % 74.32/10.98 (22) ~ (e3 = e1) % 74.32/10.98 (23) all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e1 | all_6_14 = e0 % 74.32/10.98 (24) all_10_16 = all_4_20 % 74.32/10.98 (25) ~ (e4 = e0) % 74.32/10.98 (26) all_10_3 = e0 % 74.32/10.98 (27) ~ (all_4_4 = all_4_9) % 74.32/10.98 (28) all_10_23 = all_4_19 % 74.32/10.98 (29) all_10_21 = all_4_9 % 74.32/10.98 (30) ~ (all_4_10 = e0) % 74.32/10.98 (31) ~ (all_4_22 = e1) % 74.32/10.98 (32) ~ (all_4_5 = e1) % 74.32/10.98 (33) all_10_9 = e3 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 74.32/10.98 all_10_23 = e3 % 74.32/10.98 (34) all_10_20 = all_4_4 % 74.32/10.98 (35) all_10_0 = e3 | all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | % 74.32/10.98 all_10_16 = e3 % 74.32/10.98 (36) op(e0, all_4_4) = all_8_11 % 74.32/10.98 (37) ~ (e4 = e3) % 74.32/10.98 (38) all_10_2 = all_4_1 % 74.32/10.98 (39) ~ (all_4_5 = e0) % 74.32/10.98 (40) ~ (all_4_22 = e3) % 74.32/10.98 (41) ~ (all_4_15 = e2) % 74.32/10.98 (42) all_10_1 = e3 | all_10_3 = e3 | all_10_7 = e3 | all_10_13 = e3 | % 74.32/10.98 all_10_21 = e3 % 74.32/10.98 (43) all_6_14 = all_4_22 % 74.32/10.98 (44) all_10_9 = all_4_15 % 74.32/10.98 (45) all_10_20 = e4 | all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 74.32/10.98 all_10_24 = e4 % 74.32/10.98 (46) op(e0, all_4_22) = e2 % 74.32/10.98 (47) all_10_0 = e3 | all_10_2 = e3 | all_10_6 = e3 | all_10_12 = e3 | % 74.32/10.98 all_10_20 = e3 % 74.32/10.98 (48) all_10_12 = e1 % 74.32/10.98 (49) op(e4, all_4_1) = e3 % 74.32/10.98 (50) all_6_1 = all_4_5 % 74.32/10.98 (51) ~ (all_4_5 = all_4_10) % 74.32/10.98 (52) all_10_13 = e2 % 74.32/10.98 (53) ~ (e4 = e2) % 74.32/10.98 (54) all_10_6 = all_4_2 % 74.32/10.98 (55) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.32/10.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.32/10.98 (56) all_6_2 = all_4_10 % 74.32/10.98 (57) ~ (all_4_1 = all_4_4) % 74.32/10.98 (58) op(e3, e3) = e0 % 74.32/10.98 (59) ~ (e4 = e1) % 74.32/10.98 (60) ~ (all_4_4 = e1) % 74.32/10.98 (61) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.32/10.98 (62) all_10_0 = e2 % 74.32/10.98 (63) all_10_0 = e0 | all_10_1 = e0 | all_10_4 = e0 | all_10_9 = e0 | % 74.32/10.98 all_10_16 = e0 % 74.32/10.98 (64) ~ (all_4_5 = all_4_9) % 74.32/10.98 (65) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 74.32/10.98 all_10_22 = e1 % 74.32/10.98 (66) all_10_7 = e1 % 74.32/10.98 (67) ~ (all_4_1 = e2) % 74.32/10.98 (68) op(e3, all_4_5) = all_8_13 % 74.32/10.98 (69) op(e4, e3) = all_4_5 % 74.32/10.98 % 74.32/10.98 Begin of proof % 74.32/10.98 | % 74.32/10.98 | BETA: splitting (7) gives: % 74.32/10.98 | % 74.32/10.98 | Case 1: % 74.32/10.98 | | % 74.32/10.98 | | (70) all_8_13 = e4 & ~ (all_8_14 = e3) % 74.32/10.98 | | % 74.32/10.98 | | ALPHA: (70) implies: % 74.32/10.98 | | (71) all_8_13 = e4 % 74.32/10.98 | | % 74.32/10.98 | | REDUCE: (68), (71) imply: % 74.32/10.98 | | (72) op(e3, all_4_5) = e4 % 74.32/10.98 | | % 74.32/10.98 | | BETA: splitting (45) gives: % 74.32/10.98 | | % 74.32/10.98 | | Case 1: % 74.32/10.98 | | | % 74.32/10.98 | | | (73) all_10_20 = e4 % 74.32/10.98 | | | % 74.32/10.98 | | | COMBINE_EQS: (34), (73) imply: % 74.32/10.98 | | | (74) all_4_4 = e4 % 74.32/10.98 | | | % 74.32/10.98 | | | SIMP: (74) implies: % 74.32/10.98 | | | (75) all_4_4 = e4 % 74.32/10.98 | | | % 74.32/10.98 | | | REDUCE: (57), (75) imply: % 74.32/10.98 | | | (76) ~ (all_4_1 = e4) % 74.32/10.98 | | | % 74.32/10.98 | | | REDUCE: (27), (75) imply: % 74.32/10.98 | | | (77) ~ (all_4_9 = e4) % 74.32/10.98 | | | % 74.32/10.98 | | | SIMP: (77) implies: % 74.32/10.98 | | | (78) ~ (all_4_9 = e4) % 74.32/10.98 | | | % 74.32/10.98 | | | REDUCE: (36), (75) imply: % 74.32/10.98 | | | (79) op(e0, e4) = all_8_11 % 74.32/10.98 | | | % 74.32/10.98 | | | REDUCE: (11), (75) imply: % 74.32/10.98 | | | (80) op(e0, e4) = e4 % 74.32/10.98 | | | % 74.32/10.98 | | | REF_CLOSE: (3), (4), (6), (9), (10), (12), (15), (16), (19), (20), (21), % 74.32/10.98 | | | (22), (23), (24), (25), (26), (29), (30), (31), (33), (35), % 74.32/10.98 | | | (37), (38), (39), (40), (41), (43), (44), (46), (47), (48), % 74.32/10.98 | | | (49), (51), (52), (53), (54), (55), (56), (59), (61), (62), % 74.32/10.98 | | | (63), (65), (66), (67), (69), (73), (76), (78), (79), (80) are % 74.32/10.98 | | | inconsistent by sub-proof #15. % 74.32/10.98 | | | % 74.32/10.98 | | Case 2: % 74.32/10.98 | | | % 74.32/10.98 | | | (81) all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | all_10_24 = e4 % 74.32/10.98 | | | % 74.36/10.98 | | | REF_CLOSE: (2), (5), (8), (13), (16), (18), (28), (29), (32), (39), (42), % 74.36/10.98 | | | (50), (53), (55), (58), (59), (64), (72), (81) are inconsistent % 74.36/10.98 | | | by sub-proof #26. % 74.36/10.98 | | | % 74.36/10.98 | | End of split % 74.36/10.98 | | % 74.36/10.98 | Case 2: % 74.36/10.98 | | % 74.36/10.98 | | (82) all_8_17 = e2 & ~ (all_8_18 = e3) % 74.36/10.98 | | % 74.36/10.98 | | REF_CLOSE: (1), (14), (82) are inconsistent by sub-proof #25. % 74.36/10.98 | | % 74.36/10.98 | End of split % 74.36/10.98 | % 74.36/10.98 End of proof % 74.36/10.98 % 74.36/10.98 Sub-proof #15 shows that the following formulas are inconsistent: % 74.36/10.98 ---------------------------------------------------------------- % 74.36/10.98 (1) ~ (all_4_1 = e0) % 74.36/10.98 (2) all_10_1 = e4 | all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | % 74.36/10.98 all_10_21 = e4 % 74.36/10.98 (3) op(e0, e4) = all_8_11 % 74.36/10.98 (4) ~ (all_4_20 = all_4_22) % 74.36/10.98 (5) ~ (all_4_10 = e3) % 74.36/10.98 (6) ~ (e3 = e2) % 74.36/10.99 (7) all_10_4 = all_4_10 % 74.36/10.99 (8) all_10_20 = e4 % 74.36/10.99 (9) ~ (all_4_20 = e3) % 74.36/10.99 (10) all_10_1 = all_4_5 % 74.36/10.99 (11) ~ (e2 = e0) % 74.36/10.99 (12) ~ (all_4_2 = e3) % 74.36/10.99 (13) op(e4, all_4_15) = all_8_40 % 74.36/10.99 (14) ~ (e3 = e1) % 74.36/10.99 (15) all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e1 | all_6_14 = e0 % 74.36/10.99 (16) all_10_16 = all_4_20 % 74.36/10.99 (17) ~ (e4 = e0) % 74.36/10.99 (18) all_10_3 = e0 % 74.36/10.99 (19) all_10_21 = all_4_9 % 74.36/10.99 (20) ~ (all_4_10 = e0) % 74.36/10.99 (21) ~ (all_4_22 = e1) % 74.36/10.99 (22) all_10_9 = e3 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 74.36/10.99 all_10_23 = e3 % 74.36/10.99 (23) all_10_0 = e3 | all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | % 74.36/10.99 all_10_16 = e3 % 74.36/10.99 (24) ~ (e4 = e3) % 74.36/10.99 (25) all_10_2 = all_4_1 % 74.36/10.99 (26) ~ (all_4_5 = e0) % 74.36/10.99 (27) ~ (all_4_22 = e3) % 74.36/10.99 (28) ~ (all_4_15 = e2) % 74.36/10.99 (29) op(e0, e4) = e4 % 74.36/10.99 (30) all_6_14 = all_4_22 % 74.36/10.99 (31) all_10_9 = all_4_15 % 74.36/10.99 (32) op(e0, all_4_22) = e2 % 74.36/10.99 (33) ~ (all_4_9 = e4) % 74.36/10.99 (34) all_10_0 = e3 | all_10_2 = e3 | all_10_6 = e3 | all_10_12 = e3 | % 74.36/10.99 all_10_20 = e3 % 74.36/10.99 (35) all_10_12 = e1 % 74.36/10.99 (36) op(e4, all_4_1) = e3 % 74.36/10.99 (37) ~ (all_4_5 = all_4_10) % 74.36/10.99 (38) all_10_13 = e2 % 74.36/10.99 (39) ~ (e4 = e2) % 74.36/10.99 (40) all_10_6 = all_4_2 % 74.36/10.99 (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.36/10.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.36/10.99 (42) all_6_2 = all_4_10 % 74.36/10.99 (43) ~ (e4 = e1) % 74.36/10.99 (44) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.36/10.99 (45) all_10_0 = e2 % 74.36/10.99 (46) all_10_0 = e0 | all_10_1 = e0 | all_10_4 = e0 | all_10_9 = e0 | % 74.36/10.99 all_10_16 = e0 % 74.36/10.99 (47) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 74.36/10.99 all_10_22 = e1 % 74.36/10.99 (48) all_10_7 = e1 % 74.36/10.99 (49) ~ (all_4_1 = e2) % 74.36/10.99 (50) op(e4, e3) = all_4_5 % 74.36/10.99 (51) ~ (all_4_1 = e4) % 74.36/10.99 % 74.36/10.99 Begin of proof % 74.36/10.99 | % 74.36/10.99 | BETA: splitting (34) gives: % 74.36/10.99 | % 74.36/10.99 | Case 1: % 74.36/10.99 | | % 74.36/10.99 | | (52) all_10_0 = e3 % 74.36/10.99 | | % 74.36/10.99 | | REF_CLOSE: (6), (45), (52) are inconsistent by sub-proof #104. % 74.36/10.99 | | % 74.36/10.99 | Case 2: % 74.36/10.99 | | % 74.36/10.99 | | (53) all_10_2 = e3 | all_10_6 = e3 | all_10_12 = e3 | all_10_20 = e3 % 74.36/10.99 | | % 74.36/10.99 | | BETA: splitting (53) gives: % 74.36/10.99 | | % 74.36/10.99 | | Case 1: % 74.36/10.99 | | | % 74.36/10.99 | | | (54) all_10_2 = e3 % 74.36/10.99 | | | % 74.36/10.99 | | | COMBINE_EQS: (25), (54) imply: % 74.36/10.99 | | | (55) all_4_1 = e3 % 74.36/10.99 | | | % 74.36/10.99 | | | SIMP: (55) implies: % 74.36/10.99 | | | (56) all_4_1 = e3 % 74.36/10.99 | | | % 74.36/10.99 | | | REDUCE: (51), (56) imply: % 74.36/10.99 | | | (57) ~ (e4 = e3) % 74.36/10.99 | | | % 74.36/10.99 | | | REDUCE: (1), (56) imply: % 74.36/10.99 | | | (58) ~ (e3 = e0) % 74.36/10.99 | | | % 74.36/10.99 | | | REDUCE: (36), (56) imply: % 74.36/10.99 | | | (59) op(e4, e3) = e3 % 74.36/10.99 | | | % 74.36/10.99 | | | BETA: splitting (2) gives: % 74.36/10.99 | | | % 74.36/10.99 | | | Case 1: % 74.36/10.99 | | | | % 74.36/10.99 | | | | (60) all_10_1 = e4 % 74.36/10.99 | | | | % 74.36/10.99 | | | | COMBINE_EQS: (10), (60) imply: % 74.36/10.99 | | | | (61) all_4_5 = e4 % 74.36/10.99 | | | | % 74.36/10.99 | | | | REDUCE: (37), (61) imply: % 74.36/10.99 | | | | (62) ~ (all_4_10 = e4) % 74.36/10.99 | | | | % 74.36/10.99 | | | | SIMP: (62) implies: % 74.36/10.99 | | | | (63) ~ (all_4_10 = e4) % 74.36/10.99 | | | | % 74.36/10.99 | | | | REDUCE: (50), (61) imply: % 74.36/10.99 | | | | (64) op(e4, e3) = e4 % 74.36/10.99 | | | | % 74.36/10.99 | | | | BETA: splitting (23) gives: % 74.36/10.99 | | | | % 74.36/10.99 | | | | Case 1: % 74.36/10.99 | | | | | % 74.36/10.99 | | | | | (65) all_10_0 = e3 % 74.36/10.99 | | | | | % 74.36/10.99 | | | | | REF_CLOSE: (6), (45), (65) are inconsistent by sub-proof #104. % 74.36/10.99 | | | | | % 74.36/10.99 | | | | Case 2: % 74.36/10.99 | | | | | % 74.36/10.99 | | | | | (66) all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | all_10_16 = e3 % 74.36/10.99 | | | | | % 74.36/10.99 | | | | | BETA: splitting (47) gives: % 74.36/10.99 | | | | | % 74.36/10.99 | | | | | Case 1: % 74.36/10.99 | | | | | | % 74.36/10.99 | | | | | | (67) all_10_4 = e1 % 74.36/10.99 | | | | | | % 74.36/10.99 | | | | | | COMBINE_EQS: (7), (67) imply: % 74.36/10.99 | | | | | | (68) all_4_10 = e1 % 74.36/10.99 | | | | | | % 74.36/10.99 | | | | | | REDUCE: (5), (68) imply: % 74.36/10.99 | | | | | | (69) ~ (e3 = e1) % 74.36/10.99 | | | | | | % 74.36/10.99 | | | | | | REDUCE: (20), (68) imply: % 74.36/10.99 | | | | | | (70) ~ (e1 = e0) % 74.36/10.99 | | | | | | % 74.36/10.99 | | | | | | BETA: splitting (66) gives: % 74.36/10.99 | | | | | | % 74.36/10.99 | | | | | | Case 1: % 74.36/10.99 | | | | | | | % 74.36/10.99 | | | | | | | (71) all_10_1 = e3 % 74.36/10.99 | | | | | | | % 74.36/10.99 | | | | | | | COMBINE_EQS: (60), (71) imply: % 74.36/10.99 | | | | | | | (72) e4 = e3 % 74.36/10.99 | | | | | | | % 74.36/10.99 | | | | | | | REDUCE: (24), (72) imply: % 74.36/10.99 | | | | | | | (73) $false % 74.36/10.99 | | | | | | | % 74.36/10.99 | | | | | | | CLOSE: (73) is inconsistent. % 74.36/10.99 | | | | | | | % 74.36/10.99 | | | | | | Case 2: % 74.36/10.99 | | | | | | | % 74.36/10.99 | | | | | | | (74) all_10_4 = e3 | all_10_9 = e3 | all_10_16 = e3 % 74.36/10.99 | | | | | | | % 74.36/10.99 | | | | | | | BETA: splitting (74) gives: % 74.36/10.99 | | | | | | | % 74.36/10.99 | | | | | | | Case 1: % 74.36/10.99 | | | | | | | | % 74.36/10.99 | | | | | | | | (75) all_10_4 = e3 % 74.36/10.99 | | | | | | | | % 74.36/10.99 | | | | | | | | REF_CLOSE: (14), (67), (75) are inconsistent by sub-proof #31. % 74.36/10.99 | | | | | | | | % 74.36/10.99 | | | | | | | Case 2: % 74.36/10.99 | | | | | | | | % 74.36/10.99 | | | | | | | | (76) all_10_9 = e3 | all_10_16 = e3 % 74.36/10.99 | | | | | | | | % 74.36/10.99 | | | | | | | | BETA: splitting (22) gives: % 74.36/10.99 | | | | | | | | % 74.36/10.99 | | | | | | | | Case 1: % 74.36/10.99 | | | | | | | | | % 74.36/10.99 | | | | | | | | | (77) all_10_9 = e3 % 74.36/10.99 | | | | | | | | | % 74.36/10.99 | | | | | | | | | COMBINE_EQS: (31), (77) imply: % 74.36/10.99 | | | | | | | | | (78) all_4_15 = e3 % 74.36/10.99 | | | | | | | | | % 74.36/10.99 | | | | | | | | | REDUCE: (13), (78) imply: % 74.36/10.99 | | | | | | | | | (79) op(e4, e3) = all_8_40 % 74.36/10.99 | | | | | | | | | % 74.36/10.99 | | | | | | | | | BETA: splitting (46) gives: % 74.36/10.99 | | | | | | | | | % 74.36/10.99 | | | | | | | | | Case 1: % 74.36/10.99 | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | (80) all_10_0 = e0 % 74.36/10.99 | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | COMBINE_EQS: (45), (80) imply: % 74.36/10.99 | | | | | | | | | | (81) e2 = e0 % 74.36/10.99 | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | REDUCE: (11), (81) imply: % 74.36/10.99 | | | | | | | | | | (82) $false % 74.36/10.99 | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | CLOSE: (82) is inconsistent. % 74.36/10.99 | | | | | | | | | | % 74.36/10.99 | | | | | | | | | Case 2: % 74.36/10.99 | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | (83) all_10_1 = e0 | all_10_4 = e0 | all_10_9 = e0 | % 74.36/10.99 | | | | | | | | | | all_10_16 = e0 % 74.36/10.99 | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | BETA: splitting (83) gives: % 74.36/10.99 | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | Case 1: % 74.36/10.99 | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | (84) all_10_1 = e0 % 74.36/10.99 | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | COMBINE_EQS: (60), (84) imply: % 74.36/10.99 | | | | | | | | | | | (85) e4 = e0 % 74.36/10.99 | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | REDUCE: (17), (85) imply: % 74.36/10.99 | | | | | | | | | | | (86) $false % 74.36/10.99 | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | CLOSE: (86) is inconsistent. % 74.36/10.99 | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | Case 2: % 74.36/10.99 | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | (87) all_10_4 = e0 | all_10_9 = e0 | all_10_16 = e0 % 74.36/10.99 | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | BETA: splitting (87) gives: % 74.36/10.99 | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | Case 1: % 74.36/10.99 | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | (88) all_10_4 = e0 % 74.36/10.99 | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | COMBINE_EQS: (67), (88) imply: % 74.36/10.99 | | | | | | | | | | | | (89) e1 = e0 % 74.36/10.99 | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | REDUCE: (70), (89) imply: % 74.36/10.99 | | | | | | | | | | | | (90) $false % 74.36/10.99 | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | CLOSE: (90) is inconsistent. % 74.36/10.99 | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | Case 2: % 74.36/10.99 | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | (91) all_10_9 = e0 | all_10_16 = e0 % 74.36/10.99 | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | BETA: splitting (91) gives: % 74.36/10.99 | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | Case 1: % 74.36/10.99 | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | (92) all_10_9 = e0 % 74.36/10.99 | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | COMBINE_EQS: (77), (92) imply: % 74.36/10.99 | | | | | | | | | | | | | (93) e3 = e0 % 74.36/10.99 | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | REDUCE: (58), (93) imply: % 74.36/10.99 | | | | | | | | | | | | | (94) $false % 74.36/10.99 | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | CLOSE: (94) is inconsistent. % 74.36/10.99 | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | Case 2: % 74.36/10.99 | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | (95) all_10_16 = e0 % 74.36/10.99 | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | COMBINE_EQS: (16), (95) imply: % 74.36/10.99 | | | | | | | | | | | | | (96) all_4_20 = e0 % 74.36/10.99 | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | REDUCE: (4), (96) imply: % 74.36/10.99 | | | | | | | | | | | | | (97) ~ (all_4_22 = e0) % 74.36/10.99 | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | SIMP: (97) implies: % 74.36/10.99 | | | | | | | | | | | | | (98) ~ (all_4_22 = e0) % 74.36/10.99 | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | BETA: splitting (15) gives: % 74.36/10.99 | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | Case 1: % 74.36/10.99 | | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | | (99) all_6_14 = e4 % 74.36/10.99 | | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | | COMBINE_EQS: (30), (99) imply: % 74.36/10.99 | | | | | | | | | | | | | | (100) all_4_22 = e4 % 74.36/10.99 | | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | | SIMP: (100) implies: % 74.36/10.99 | | | | | | | | | | | | | | (101) all_4_22 = e4 % 74.36/10.99 | | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | | REDUCE: (32), (101) imply: % 74.36/10.99 | | | | | | | | | | | | | | (102) op(e0, e4) = e2 % 74.36/10.99 | | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | | GROUND_INST: instantiating (41) with e4, all_8_11, e4, e0, % 74.36/10.99 | | | | | | | | | | | | | | simplifying with (3), (29) gives: % 74.36/10.99 | | | | | | | | | | | | | | (103) all_8_11 = e4 % 74.36/10.99 | | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | | GROUND_INST: instantiating (41) with e2, all_8_11, e4, e0, % 74.36/10.99 | | | | | | | | | | | | | | simplifying with (3), (102) gives: % 74.36/10.99 | | | | | | | | | | | | | | (104) all_8_11 = e2 % 74.36/10.99 | | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | | GROUND_INST: instantiating (41) with e4, all_8_40, e3, e4, % 74.36/10.99 | | | | | | | | | | | | | | simplifying with (64), (79) gives: % 74.36/10.99 | | | | | | | | | | | | | | (105) all_8_40 = e4 % 74.36/10.99 | | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | | GROUND_INST: instantiating (41) with e3, all_8_40, e3, e4, % 74.36/10.99 | | | | | | | | | | | | | | simplifying with (59), (79) gives: % 74.36/10.99 | | | | | | | | | | | | | | (106) all_8_40 = e3 % 74.36/10.99 | | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | | COMBINE_EQS: (103), (104) imply: % 74.36/10.99 | | | | | | | | | | | | | | (107) e4 = e2 % 74.36/10.99 | | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | | SIMP: (107) implies: % 74.36/10.99 | | | | | | | | | | | | | | (108) e4 = e2 % 74.36/10.99 | | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | | COMBINE_EQS: (105), (106) imply: % 74.36/10.99 | | | | | | | | | | | | | | (109) e4 = e3 % 74.36/10.99 | | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | | REF_CLOSE: (6), (108), (109) are inconsistent by sub-proof % 74.36/10.99 | | | | | | | | | | | | | | #69. % 74.36/10.99 | | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | Case 2: % 74.36/10.99 | | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | | (110) all_6_14 = e3 | all_6_14 = e1 | all_6_14 = e0 % 74.36/10.99 | | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | | REF_CLOSE: (21), (27), (30), (98), (110) are inconsistent by % 74.36/10.99 | | | | | | | | | | | | | | sub-proof #48. % 74.36/10.99 | | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | | End of split % 74.36/10.99 | | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | | End of split % 74.36/10.99 | | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | | End of split % 74.36/10.99 | | | | | | | | | | | % 74.36/10.99 | | | | | | | | | | End of split % 74.36/10.99 | | | | | | | | | | % 74.36/10.99 | | | | | | | | | End of split % 74.36/10.99 | | | | | | | | | % 74.36/10.99 | | | | | | | | Case 2: % 74.36/10.99 | | | | | | | | | % 74.36/10.99 | | | | | | | | | (111) ~ (all_10_9 = e3) % 74.36/10.99 | | | | | | | | | % 74.36/10.99 | | | | | | | | | REDUCE: (31), (111) imply: % 74.36/10.99 | | | | | | | | | (112) ~ (all_4_15 = e3) % 74.36/10.99 | | | | | | | | | % 74.36/10.99 | | | | | | | | | REF_CLOSE: (9), (16), (31), (76), (112) are inconsistent by % 74.36/10.99 | | | | | | | | | sub-proof #63. % 74.36/10.99 | | | | | | | | | % 74.36/10.99 | | | | | | | | End of split % 74.36/10.99 | | | | | | | | % 74.36/10.99 | | | | | | | End of split % 74.36/10.99 | | | | | | | % 74.36/10.99 | | | | | | End of split % 74.36/10.99 | | | | | | % 74.36/10.99 | | | | | Case 2: % 74.36/10.99 | | | | | | % 74.36/10.99 | | | | | | (113) ~ (all_10_4 = e1) % 74.36/10.99 | | | | | | % 74.36/10.99 | | | | | | REDUCE: (7), (113) imply: % 74.36/10.99 | | | | | | (114) ~ (all_4_10 = e1) % 74.36/10.99 | | | | | | % 74.36/10.99 | | | | | | REF_CLOSE: (5), (20), (42), (44), (63), (114) are inconsistent by % 74.36/10.99 | | | | | | sub-proof #161. % 74.36/10.99 | | | | | | % 74.36/10.99 | | | | | End of split % 74.36/10.99 | | | | | % 74.36/10.99 | | | | End of split % 74.36/10.99 | | | | % 74.36/10.99 | | | Case 2: % 74.36/10.99 | | | | % 74.36/10.99 | | | | (115) all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | all_10_21 = e4 % 74.36/10.99 | | | | % 74.36/10.99 | | | | REF_CLOSE: (17), (18), (19), (33), (38), (39), (43), (48), (115) are % 74.36/10.99 | | | | inconsistent by sub-proof #28. % 74.36/10.99 | | | | % 74.36/10.99 | | | End of split % 74.36/10.99 | | | % 74.36/10.99 | | Case 2: % 74.36/10.99 | | | % 74.36/10.99 | | | (116) all_10_6 = e3 | all_10_12 = e3 | all_10_20 = e3 % 74.36/10.99 | | | % 74.36/10.99 | | | REF_CLOSE: (8), (12), (14), (24), (35), (40), (116) are inconsistent by % 74.36/10.99 | | | sub-proof #98. % 74.36/10.99 | | | % 74.36/10.99 | | End of split % 74.36/10.99 | | % 74.36/10.99 | End of split % 74.36/10.99 | % 74.36/10.99 End of proof % 74.36/10.99 % 74.36/10.99 Sub-proof #16 shows that the following formulas are inconsistent: % 74.36/10.99 ---------------------------------------------------------------- % 74.36/10.99 (1) all_8_17 = all_4_16 % 74.36/10.99 (2) ~ (all_4_19 = e4) % 74.36/10.99 (3) ~ (all_4_1 = e0) % 74.36/10.99 (4) all_10_1 = e4 | all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | % 74.36/10.99 all_10_21 = e4 % 74.36/10.99 (5) ~ (all_4_9 = e0) % 74.36/10.99 (6) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 74.36/10.99 (7) ~ (all_4_10 = e3) % 74.36/10.99 (8) all_10_4 = all_4_10 % 74.36/10.99 (9) all_10_22 = e2 % 74.36/10.99 (10) ~ (all_4_16 = e2) % 74.36/11.00 (11) (all_8_13 = e4 & ~ (all_8_14 = e3)) | (all_8_17 = e2 & ~ (all_8_18 = % 74.36/11.00 e3)) | (all_8_20 = e1 & ~ (all_8_21 = e3)) | (all_8_23 = e0 & ~ % 74.36/11.00 (all_8_24 = e3)) % 74.36/11.00 (12) all_10_1 = all_4_5 % 74.36/11.00 (13) ~ (all_4_4 = e2) % 74.36/11.00 (14) all_10_24 = e1 % 74.36/11.00 (15) ~ (e2 = e0) % 74.36/11.00 (16) op(e3, e4) = all_4_1 % 74.36/11.00 (17) ~ (e4 = e0) % 74.36/11.00 (18) all_10_3 = e0 % 74.36/11.00 (19) ~ (all_4_4 = all_4_9) % 74.36/11.00 (20) all_10_23 = all_4_19 % 74.36/11.00 (21) all_10_21 = all_4_9 % 74.36/11.00 (22) ~ (all_4_10 = e0) % 74.36/11.00 (23) op(e4, all_4_5) = all_8_14 % 74.36/11.00 (24) op(e4, e4) = e2 % 74.36/11.00 (25) ~ (all_8_27 = e2) % 74.36/11.00 (26) ~ (all_4_5 = e1) % 74.36/11.00 (27) all_8_20 = all_4_11 % 74.36/11.00 (28) all_10_20 = all_4_4 % 74.36/11.00 (29) ~ (all_4_5 = e0) % 74.36/11.00 (30) all_10_1 = e3 | all_10_3 = e3 | all_10_7 = e3 | all_10_13 = e3 | % 74.36/11.00 all_10_21 = e3 % 74.36/11.00 (31) all_10_20 = e4 | all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 74.36/11.00 all_10_24 = e4 % 74.36/11.00 (32) ~ (all_4_10 = all_4_11) % 74.36/11.00 (33) op(e3, all_4_9) = all_8_23 % 74.36/11.00 (34) all_6_1 = all_4_5 % 74.36/11.00 (35) all_10_13 = e2 % 74.36/11.00 (36) ~ (e4 = e2) % 74.36/11.00 (37) op(e4, all_4_10) = all_8_27 % 74.36/11.00 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.36/11.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.36/11.00 (39) op(e4, all_4_4) = e0 % 74.36/11.00 (40) all_6_2 = all_4_10 % 74.36/11.00 (41) op(e3, e3) = e0 % 74.36/11.00 (42) ~ (e4 = e1) % 74.36/11.00 (43) all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | % 74.36/11.00 all_10_22 = e4 % 74.36/11.00 (44) ~ (all_4_4 = e1) % 74.36/11.00 (45) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.36/11.00 (46) ~ (all_4_5 = all_4_9) % 74.36/11.00 (47) all_10_7 = e1 % 74.36/11.00 (48) op(e3, all_4_5) = all_8_13 % 74.36/11.00 % 74.36/11.00 Begin of proof % 74.36/11.00 | % 74.36/11.00 | BETA: splitting (11) gives: % 74.36/11.00 | % 74.36/11.00 | Case 1: % 74.36/11.00 | | % 74.36/11.00 | | (49) (all_8_13 = e4 & ~ (all_8_14 = e3)) | (all_8_17 = e2 & ~ (all_8_18 % 74.36/11.00 | | = e3)) % 74.36/11.00 | | % 74.36/11.00 | | REF_CLOSE: (1), (2), (4), (5), (6), (9), (10), (12), (13), (14), (15), (17), % 74.36/11.00 | | (18), (19), (20), (21), (23), (24), (26), (28), (29), (30), (31), % 74.36/11.00 | | (34), (35), (36), (38), (39), (41), (42), (44), (46), (47), (48), % 74.36/11.00 | | (49) are inconsistent by sub-proof #18. % 74.36/11.00 | | % 74.36/11.00 | Case 2: % 74.36/11.00 | | % 74.36/11.00 | | (50) (all_8_20 = e1 & ~ (all_8_21 = e3)) | (all_8_23 = e0 & ~ (all_8_24 % 74.36/11.00 | | = e3)) % 74.36/11.00 | | % 74.36/11.00 | | BETA: splitting (50) gives: % 74.36/11.00 | | % 74.36/11.00 | | Case 1: % 74.36/11.00 | | | % 74.36/11.00 | | | (51) all_8_20 = e1 & ~ (all_8_21 = e3) % 74.36/11.00 | | | % 74.36/11.00 | | | REF_CLOSE: (7), (8), (22), (24), (25), (27), (32), (37), (38), (40), (43), % 74.36/11.00 | | | (45), (51) are inconsistent by sub-proof #24. % 74.36/11.00 | | | % 74.36/11.00 | | Case 2: % 74.36/11.00 | | | % 74.36/11.00 | | | (52) all_8_23 = e0 & ~ (all_8_24 = e3) % 74.36/11.00 | | | % 74.36/11.00 | | | REF_CLOSE: (2), (3), (4), (9), (12), (13), (14), (15), (16), (17), (18), % 74.36/11.00 | | | (19), (20), (21), (23), (24), (28), (31), (33), (35), (36), % 74.36/11.00 | | | (38), (39), (42), (44), (47), (52) are inconsistent by % 74.36/11.00 | | | sub-proof #17. % 74.36/11.00 | | | % 74.36/11.00 | | End of split % 74.36/11.00 | | % 74.36/11.00 | End of split % 74.36/11.00 | % 74.36/11.00 End of proof % 74.36/11.00 % 74.36/11.00 Sub-proof #17 shows that the following formulas are inconsistent: % 74.36/11.00 ---------------------------------------------------------------- % 74.36/11.00 (1) ~ (all_4_19 = e4) % 74.36/11.00 (2) ~ (all_4_1 = e0) % 74.36/11.00 (3) all_10_1 = e4 | all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | % 74.36/11.00 all_10_21 = e4 % 74.36/11.00 (4) all_10_22 = e2 % 74.36/11.00 (5) all_10_1 = all_4_5 % 74.36/11.00 (6) ~ (all_4_4 = e2) % 74.36/11.00 (7) all_10_24 = e1 % 74.36/11.00 (8) ~ (e2 = e0) % 74.36/11.00 (9) op(e3, e4) = all_4_1 % 74.36/11.00 (10) ~ (e4 = e0) % 74.36/11.00 (11) all_10_3 = e0 % 74.36/11.00 (12) ~ (all_4_4 = all_4_9) % 74.36/11.00 (13) all_10_23 = all_4_19 % 74.36/11.00 (14) all_10_21 = all_4_9 % 74.36/11.00 (15) op(e4, all_4_5) = all_8_14 % 74.36/11.00 (16) op(e4, e4) = e2 % 74.36/11.00 (17) all_10_20 = all_4_4 % 74.36/11.00 (18) all_10_20 = e4 | all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 74.36/11.00 all_10_24 = e4 % 74.36/11.00 (19) op(e3, all_4_9) = all_8_23 % 74.36/11.00 (20) all_10_13 = e2 % 74.36/11.00 (21) ~ (e4 = e2) % 74.36/11.00 (22) all_8_23 = e0 & ~ (all_8_24 = e3) % 74.36/11.00 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.36/11.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.36/11.00 (24) op(e4, all_4_4) = e0 % 74.36/11.00 (25) ~ (e4 = e1) % 74.36/11.00 (26) ~ (all_4_4 = e1) % 74.36/11.00 (27) all_10_7 = e1 % 74.36/11.00 % 74.36/11.00 Begin of proof % 74.36/11.00 | % 74.36/11.00 | ALPHA: (22) implies: % 74.36/11.00 | (28) all_8_23 = e0 % 74.36/11.00 | % 74.36/11.00 | REDUCE: (19), (28) imply: % 74.36/11.00 | (29) op(e3, all_4_9) = e0 % 74.36/11.00 | % 74.36/11.00 | BETA: splitting (18) gives: % 74.36/11.00 | % 74.36/11.00 | Case 1: % 74.36/11.00 | | % 74.36/11.00 | | (30) all_10_20 = e4 % 74.36/11.00 | | % 74.36/11.00 | | REF_CLOSE: (3), (5), (6), (8), (10), (11), (12), (14), (15), (16), (17), % 74.36/11.00 | | (20), (23), (24), (26), (27), (30) are inconsistent by sub-proof % 74.36/11.00 | | #19. % 74.36/11.00 | | % 74.36/11.00 | Case 2: % 74.36/11.00 | | % 74.36/11.00 | | (31) all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | all_10_24 = e4 % 74.36/11.00 | | % 74.36/11.00 | | REF_CLOSE: (1), (2), (4), (7), (9), (13), (14), (21), (23), (25), (29), (31) % 74.36/11.00 | | are inconsistent by sub-proof #32. % 74.36/11.00 | | % 74.36/11.00 | End of split % 74.36/11.00 | % 74.36/11.00 End of proof % 74.36/11.00 % 74.36/11.00 Sub-proof #18 shows that the following formulas are inconsistent: % 74.36/11.00 ---------------------------------------------------------------- % 74.36/11.00 (1) all_8_17 = all_4_16 % 74.36/11.00 (2) ~ (all_4_19 = e4) % 74.36/11.00 (3) all_10_1 = e4 | all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | % 74.36/11.00 all_10_21 = e4 % 74.36/11.00 (4) ~ (all_4_9 = e0) % 74.36/11.00 (5) (all_8_13 = e4 & ~ (all_8_14 = e3)) | (all_8_17 = e2 & ~ (all_8_18 = % 74.36/11.00 e3)) % 74.36/11.00 (6) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 74.36/11.00 (7) all_10_22 = e2 % 74.36/11.00 (8) ~ (all_4_16 = e2) % 74.36/11.00 (9) all_10_1 = all_4_5 % 74.36/11.00 (10) ~ (all_4_4 = e2) % 74.36/11.00 (11) all_10_24 = e1 % 74.36/11.00 (12) ~ (e2 = e0) % 74.36/11.00 (13) ~ (e4 = e0) % 74.36/11.00 (14) all_10_3 = e0 % 74.36/11.00 (15) ~ (all_4_4 = all_4_9) % 74.36/11.00 (16) all_10_23 = all_4_19 % 74.36/11.00 (17) all_10_21 = all_4_9 % 74.36/11.00 (18) op(e4, all_4_5) = all_8_14 % 74.36/11.00 (19) op(e4, e4) = e2 % 74.36/11.00 (20) ~ (all_4_5 = e1) % 74.36/11.00 (21) all_10_20 = all_4_4 % 74.36/11.00 (22) ~ (all_4_5 = e0) % 74.36/11.00 (23) all_10_1 = e3 | all_10_3 = e3 | all_10_7 = e3 | all_10_13 = e3 | % 74.36/11.00 all_10_21 = e3 % 74.36/11.00 (24) all_10_20 = e4 | all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 74.36/11.00 all_10_24 = e4 % 74.36/11.00 (25) all_6_1 = all_4_5 % 74.36/11.00 (26) all_10_13 = e2 % 74.36/11.00 (27) ~ (e4 = e2) % 74.36/11.00 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.36/11.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.36/11.00 (29) op(e4, all_4_4) = e0 % 74.36/11.00 (30) op(e3, e3) = e0 % 74.36/11.00 (31) ~ (e4 = e1) % 74.36/11.00 (32) ~ (all_4_4 = e1) % 74.36/11.00 (33) ~ (all_4_5 = all_4_9) % 74.36/11.00 (34) all_10_7 = e1 % 74.36/11.00 (35) op(e3, all_4_5) = all_8_13 % 74.36/11.00 % 74.36/11.00 Begin of proof % 74.36/11.00 | % 74.36/11.00 | BETA: splitting (5) gives: % 74.36/11.00 | % 74.36/11.00 | Case 1: % 74.36/11.00 | | % 74.36/11.00 | | (36) all_8_13 = e4 & ~ (all_8_14 = e3) % 74.36/11.00 | | % 74.36/11.00 | | ALPHA: (36) implies: % 74.36/11.00 | | (37) all_8_13 = e4 % 74.36/11.00 | | % 74.36/11.00 | | REDUCE: (35), (37) imply: % 74.36/11.00 | | (38) op(e3, all_4_5) = e4 % 74.36/11.00 | | % 74.36/11.00 | | BETA: splitting (24) gives: % 74.36/11.00 | | % 74.36/11.00 | | Case 1: % 74.36/11.00 | | | % 74.36/11.00 | | | (39) all_10_20 = e4 % 74.36/11.00 | | | % 74.36/11.00 | | | REF_CLOSE: (3), (9), (10), (12), (13), (14), (15), (17), (18), (19), (21), % 74.36/11.00 | | | (26), (28), (29), (32), (34), (39) are inconsistent by % 74.36/11.00 | | | sub-proof #19. % 74.36/11.00 | | | % 74.36/11.00 | | Case 2: % 74.36/11.00 | | | % 74.36/11.00 | | | (40) all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | all_10_24 = e4 % 74.36/11.00 | | | % 74.36/11.00 | | | REF_CLOSE: (2), (4), (6), (7), (9), (11), (16), (17), (20), (22), (23), % 74.36/11.00 | | | (25), (27), (28), (30), (31), (33), (38), (40) are inconsistent % 74.36/11.00 | | | by sub-proof #26. % 74.36/11.00 | | | % 74.36/11.00 | | End of split % 74.36/11.00 | | % 74.36/11.00 | Case 2: % 74.36/11.00 | | % 74.36/11.00 | | (41) all_8_17 = e2 & ~ (all_8_18 = e3) % 74.36/11.00 | | % 74.36/11.00 | | REF_CLOSE: (1), (8), (41) are inconsistent by sub-proof #25. % 74.36/11.00 | | % 74.36/11.00 | End of split % 74.36/11.00 | % 74.36/11.00 End of proof % 74.36/11.00 % 74.36/11.00 Sub-proof #19 shows that the following formulas are inconsistent: % 74.36/11.00 ---------------------------------------------------------------- % 74.36/11.00 (1) all_10_1 = e4 | all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | % 74.36/11.00 all_10_21 = e4 % 74.36/11.00 (2) all_10_20 = e4 % 74.36/11.00 (3) all_10_1 = all_4_5 % 74.36/11.00 (4) ~ (all_4_4 = e2) % 74.36/11.00 (5) ~ (e2 = e0) % 74.36/11.00 (6) ~ (e4 = e0) % 74.36/11.00 (7) all_10_3 = e0 % 74.36/11.00 (8) ~ (all_4_4 = all_4_9) % 74.36/11.00 (9) all_10_21 = all_4_9 % 74.36/11.00 (10) op(e4, all_4_5) = all_8_14 % 74.36/11.00 (11) op(e4, e4) = e2 % 74.36/11.01 (12) all_10_20 = all_4_4 % 74.36/11.01 (13) all_10_13 = e2 % 74.36/11.01 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.36/11.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.36/11.01 (15) op(e4, all_4_4) = e0 % 74.36/11.01 (16) ~ (all_4_4 = e1) % 74.36/11.01 (17) all_10_7 = e1 % 74.36/11.01 % 74.36/11.01 Begin of proof % 74.36/11.01 | % 74.36/11.01 | COMBINE_EQS: (2), (12) imply: % 74.36/11.01 | (18) all_4_4 = e4 % 74.36/11.01 | % 74.36/11.01 | SIMP: (18) implies: % 74.36/11.01 | (19) all_4_4 = e4 % 74.36/11.01 | % 74.36/11.01 | REDUCE: (8), (19) imply: % 74.36/11.01 | (20) ~ (all_4_9 = e4) % 74.36/11.01 | % 74.36/11.01 | SIMP: (20) implies: % 74.36/11.01 | (21) ~ (all_4_9 = e4) % 74.36/11.01 | % 74.36/11.01 | REDUCE: (4), (19) imply: % 74.36/11.01 | (22) ~ (e4 = e2) % 74.36/11.01 | % 74.36/11.01 | REDUCE: (16), (19) imply: % 74.36/11.01 | (23) ~ (e4 = e1) % 74.36/11.01 | % 74.36/11.01 | REDUCE: (15), (19) imply: % 74.36/11.01 | (24) op(e4, e4) = e0 % 74.36/11.01 | % 74.36/11.01 | BETA: splitting (1) gives: % 74.36/11.01 | % 74.36/11.01 | Case 1: % 74.36/11.01 | | % 74.36/11.01 | | (25) all_10_1 = e4 % 74.36/11.01 | | % 74.36/11.01 | | COMBINE_EQS: (3), (25) imply: % 74.36/11.01 | | (26) all_4_5 = e4 % 74.36/11.01 | | % 74.36/11.01 | | REDUCE: (10), (26) imply: % 74.45/11.01 | | (27) op(e4, e4) = all_8_14 % 74.45/11.01 | | % 74.45/11.01 | | GROUND_INST: instantiating (14) with e2, all_8_14, e4, e4, simplifying with % 74.45/11.01 | | (11), (27) gives: % 74.45/11.01 | | (28) all_8_14 = e2 % 74.45/11.01 | | % 74.45/11.01 | | GROUND_INST: instantiating (14) with e0, all_8_14, e4, e4, simplifying with % 74.45/11.01 | | (24), (27) gives: % 74.45/11.01 | | (29) all_8_14 = e0 % 74.45/11.01 | | % 74.45/11.01 | | COMBINE_EQS: (28), (29) imply: % 74.45/11.01 | | (30) e2 = e0 % 74.45/11.01 | | % 74.45/11.01 | | SIMP: (30) implies: % 74.45/11.01 | | (31) e2 = e0 % 74.45/11.01 | | % 74.45/11.01 | | REDUCE: (5), (31) imply: % 74.45/11.01 | | (32) $false % 74.45/11.01 | | % 74.45/11.01 | | CLOSE: (32) is inconsistent. % 74.45/11.01 | | % 74.45/11.01 | Case 2: % 74.45/11.01 | | % 74.45/11.01 | | (33) all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | all_10_21 = e4 % 74.45/11.01 | | % 74.45/11.01 | | REF_CLOSE: (6), (7), (9), (13), (17), (21), (22), (23), (33) are % 74.45/11.01 | | inconsistent by sub-proof #28. % 74.45/11.01 | | % 74.45/11.01 | End of split % 74.45/11.01 | % 74.45/11.01 End of proof % 74.45/11.01 % 74.45/11.01 Sub-proof #20 shows that the following formulas are inconsistent: % 74.45/11.01 ---------------------------------------------------------------- % 74.45/11.01 (1) all_8_17 = all_4_16 % 74.45/11.01 (2) ~ (all_4_19 = e4) % 74.45/11.01 (3) ~ (all_4_1 = e0) % 74.45/11.01 (4) all_10_1 = e4 | all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | % 74.45/11.01 all_10_21 = e4 % 74.45/11.01 (5) ~ (all_4_9 = e0) % 74.45/11.01 (6) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 74.45/11.01 (7) ~ (all_4_2 = e1) % 74.45/11.01 (8) ~ (all_4_10 = e3) % 74.45/11.01 (9) ~ (e3 = e2) % 74.45/11.01 (10) all_10_4 = all_4_10 % 74.45/11.01 (11) all_10_22 = e2 % 74.45/11.01 (12) ~ (all_4_16 = e2) % 74.45/11.01 (13) (all_8_13 = e4 & ~ (all_8_14 = e3)) | (all_8_17 = e2 & ~ (all_8_18 = % 74.45/11.01 e3)) | (all_8_20 = e1 & ~ (all_8_21 = e3)) | (all_8_23 = e0 & ~ % 74.45/11.01 (all_8_24 = e3)) % 74.45/11.01 (14) ~ (all_4_20 = e3) % 74.45/11.01 (15) all_10_1 = all_4_5 % 74.45/11.01 (16) ~ (all_4_4 = e2) % 74.45/11.01 (17) all_10_24 = e1 % 74.45/11.01 (18) ~ (e2 = e0) % 74.45/11.01 (19) ~ (all_4_2 = e3) % 74.45/11.01 (20) op(e3, e4) = all_4_1 % 74.45/11.01 (21) all_10_16 = all_4_20 % 74.45/11.01 (22) ~ (e4 = e0) % 74.45/11.01 (23) all_10_3 = e0 % 74.45/11.01 (24) ~ (all_4_4 = all_4_9) % 74.45/11.01 (25) all_10_6 = e0 | all_10_7 = e0 | all_10_8 = e0 | all_10_11 = e0 | % 74.45/11.01 all_10_18 = e0 % 74.45/11.01 (26) all_10_23 = all_4_19 % 74.45/11.01 (27) all_10_21 = all_4_9 % 74.45/11.01 (28) ~ (all_4_10 = e0) % 74.45/11.01 (29) ~ (all_4_2 = all_4_4) % 74.45/11.01 (30) op(e4, e4) = e2 % 74.45/11.01 (31) ~ (all_8_27 = e2) % 74.45/11.01 (32) ~ (all_4_5 = e1) % 74.45/11.01 (33) all_8_20 = all_4_11 % 74.45/11.01 (34) all_10_9 = e3 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 74.45/11.01 all_10_23 = e3 % 74.45/11.01 (35) all_10_20 = all_4_4 % 74.45/11.01 (36) all_10_0 = e3 | all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | % 74.45/11.01 all_10_16 = e3 % 74.45/11.01 (37) all_6_10 = all_4_2 % 74.45/11.01 (38) ~ (e4 = e3) % 74.45/11.01 (39) ~ (all_4_5 = e0) % 74.45/11.01 (40) op(e4, all_4_20) = all_8_53 % 74.45/11.01 (41) all_10_1 = e3 | all_10_3 = e3 | all_10_7 = e3 | all_10_13 = e3 | % 74.45/11.01 all_10_21 = e3 % 74.45/11.01 (42) all_10_9 = all_4_15 % 74.45/11.01 (43) all_10_20 = e4 | all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 74.45/11.01 all_10_24 = e4 % 74.45/11.01 (44) ~ (all_4_2 = e2) % 74.45/11.01 (45) ~ (all_4_10 = all_4_11) % 74.45/11.01 (46) op(e3, all_4_9) = all_8_23 % 74.45/11.01 (47) all_6_1 = all_4_5 % 74.45/11.01 (48) ~ (all_4_5 = all_4_10) % 74.45/11.01 (49) all_10_13 = e2 % 74.45/11.01 (50) ~ (e4 = e2) % 74.45/11.01 (51) all_10_6 = all_4_2 % 74.45/11.01 (52) op(e4, all_4_10) = all_8_27 % 74.45/11.01 (53) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.45/11.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.45/11.01 (54) all_6_2 = all_4_10 % 74.45/11.01 (55) op(e3, e3) = e0 % 74.45/11.01 (56) ~ (e4 = e1) % 74.45/11.01 (57) op(e4, e0) = all_4_20 % 74.45/11.01 (58) all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | % 74.45/11.01 all_10_22 = e4 % 74.45/11.01 (59) ~ (e3 = e0) % 74.45/11.01 (60) op(e4, all_4_2) = e2 % 74.45/11.01 (61) ~ (all_4_4 = e1) % 74.45/11.01 (62) all_6_10 = e4 | all_6_10 = e3 | all_6_10 = e1 | all_6_10 = e0 % 74.45/11.01 (63) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.45/11.01 (64) all_10_0 = e2 % 74.45/11.01 (65) all_10_0 = e0 | all_10_1 = e0 | all_10_4 = e0 | all_10_9 = e0 | % 74.45/11.01 all_10_16 = e0 % 74.45/11.01 (66) ~ (all_4_5 = all_4_9) % 74.45/11.01 (67) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 74.45/11.01 all_10_22 = e1 % 74.45/11.01 (68) all_10_7 = e1 % 74.45/11.01 (69) op(e3, all_4_5) = all_8_13 % 74.45/11.01 % 74.45/11.01 Begin of proof % 74.45/11.01 | % 74.45/11.01 | BETA: splitting (13) gives: % 74.45/11.01 | % 74.45/11.01 | Case 1: % 74.45/11.01 | | % 74.45/11.01 | | (70) (all_8_13 = e4 & ~ (all_8_14 = e3)) | (all_8_17 = e2 & ~ (all_8_18 % 74.45/11.01 | | = e3)) % 74.45/11.01 | | % 74.45/11.01 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14), % 74.45/11.01 | | (15), (16), (17), (18), (19), (21), (22), (23), (24), (25), (26), % 74.45/11.01 | | (27), (28), (29), (32), (34), (35), (36), (37), (38), (39), (40), % 74.45/11.01 | | (41), (42), (43), (44), (47), (48), (49), (50), (51), (53), (54), % 74.45/11.01 | | (55), (56), (57), (59), (60), (61), (62), (63), (64), (65), (66), % 74.45/11.01 | | (67), (68), (69), (70) are inconsistent by sub-proof #22. % 74.45/11.01 | | % 74.45/11.01 | Case 2: % 74.45/11.01 | | % 74.45/11.01 | | (71) (all_8_20 = e1 & ~ (all_8_21 = e3)) | (all_8_23 = e0 & ~ (all_8_24 % 74.45/11.01 | | = e3)) % 74.45/11.01 | | % 74.45/11.01 | | BETA: splitting (71) gives: % 74.45/11.01 | | % 74.45/11.01 | | Case 1: % 74.45/11.01 | | | % 74.45/11.01 | | | (72) all_8_20 = e1 & ~ (all_8_21 = e3) % 74.45/11.01 | | | % 74.45/11.01 | | | REF_CLOSE: (8), (10), (28), (30), (31), (33), (45), (52), (53), (54), % 74.45/11.01 | | | (58), (63), (72) are inconsistent by sub-proof #24. % 74.45/11.01 | | | % 74.45/11.01 | | Case 2: % 74.45/11.01 | | | % 74.45/11.01 | | | (73) all_8_23 = e0 & ~ (all_8_24 = e3) % 74.45/11.01 | | | % 74.45/11.01 | | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (10), (11), (14), (15), (16), % 74.45/11.01 | | | (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), % 74.45/11.01 | | | (27), (28), (29), (34), (35), (36), (37), (38), (39), (40), % 74.45/11.01 | | | (42), (43), (44), (46), (48), (49), (50), (51), (53), (54), % 74.45/11.01 | | | (56), (57), (59), (60), (61), (62), (63), (64), (65), (67), % 74.45/11.01 | | | (68), (73) are inconsistent by sub-proof #21. % 74.45/11.01 | | | % 74.45/11.01 | | End of split % 74.45/11.01 | | % 74.45/11.01 | End of split % 74.45/11.01 | % 74.45/11.01 End of proof % 74.45/11.01 % 74.45/11.01 Sub-proof #21 shows that the following formulas are inconsistent: % 74.45/11.01 ---------------------------------------------------------------- % 74.45/11.01 (1) ~ (all_4_19 = e4) % 74.45/11.01 (2) ~ (all_4_1 = e0) % 74.45/11.01 (3) all_10_1 = e4 | all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | % 74.45/11.01 all_10_21 = e4 % 74.45/11.01 (4) ~ (all_4_2 = e1) % 74.45/11.01 (5) ~ (all_4_10 = e3) % 74.45/11.01 (6) ~ (e3 = e2) % 74.45/11.01 (7) all_10_4 = all_4_10 % 74.45/11.01 (8) all_10_22 = e2 % 74.45/11.01 (9) ~ (all_4_20 = e3) % 74.45/11.01 (10) all_10_1 = all_4_5 % 74.45/11.01 (11) ~ (all_4_4 = e2) % 74.45/11.01 (12) all_10_24 = e1 % 74.45/11.01 (13) ~ (e2 = e0) % 74.45/11.01 (14) ~ (all_4_2 = e3) % 74.45/11.01 (15) op(e3, e4) = all_4_1 % 74.45/11.01 (16) all_10_16 = all_4_20 % 74.45/11.01 (17) ~ (e4 = e0) % 74.45/11.01 (18) all_10_3 = e0 % 74.45/11.01 (19) ~ (all_4_4 = all_4_9) % 74.45/11.01 (20) all_10_6 = e0 | all_10_7 = e0 | all_10_8 = e0 | all_10_11 = e0 | % 74.45/11.01 all_10_18 = e0 % 74.45/11.01 (21) all_10_23 = all_4_19 % 74.45/11.01 (22) all_10_21 = all_4_9 % 74.45/11.01 (23) ~ (all_4_10 = e0) % 74.45/11.01 (24) ~ (all_4_2 = all_4_4) % 74.45/11.01 (25) all_10_9 = e3 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 74.45/11.01 all_10_23 = e3 % 74.45/11.01 (26) all_10_20 = all_4_4 % 74.45/11.01 (27) all_10_0 = e3 | all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | % 74.45/11.01 all_10_16 = e3 % 74.45/11.01 (28) all_6_10 = all_4_2 % 74.45/11.01 (29) ~ (e4 = e3) % 74.45/11.01 (30) ~ (all_4_5 = e0) % 74.45/11.01 (31) op(e4, all_4_20) = all_8_53 % 74.45/11.01 (32) all_10_9 = all_4_15 % 74.45/11.01 (33) all_10_20 = e4 | all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 74.45/11.01 all_10_24 = e4 % 74.45/11.01 (34) ~ (all_4_2 = e2) % 74.45/11.02 (35) op(e3, all_4_9) = all_8_23 % 74.45/11.02 (36) ~ (all_4_5 = all_4_10) % 74.45/11.02 (37) all_10_13 = e2 % 74.45/11.02 (38) ~ (e4 = e2) % 74.45/11.02 (39) all_8_23 = e0 & ~ (all_8_24 = e3) % 74.45/11.02 (40) all_10_6 = all_4_2 % 74.45/11.02 (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.45/11.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.45/11.02 (42) all_6_2 = all_4_10 % 74.45/11.02 (43) ~ (e4 = e1) % 74.45/11.02 (44) op(e4, e0) = all_4_20 % 74.45/11.02 (45) ~ (e3 = e0) % 74.45/11.02 (46) op(e4, all_4_2) = e2 % 74.45/11.02 (47) ~ (all_4_4 = e1) % 74.45/11.02 (48) all_6_10 = e4 | all_6_10 = e3 | all_6_10 = e1 | all_6_10 = e0 % 74.45/11.02 (49) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.45/11.02 (50) all_10_0 = e2 % 74.45/11.02 (51) all_10_0 = e0 | all_10_1 = e0 | all_10_4 = e0 | all_10_9 = e0 | % 74.45/11.02 all_10_16 = e0 % 74.45/11.02 (52) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 74.45/11.02 all_10_22 = e1 % 74.45/11.02 (53) all_10_7 = e1 % 74.45/11.02 % 74.45/11.02 Begin of proof % 74.45/11.02 | % 74.45/11.02 | ALPHA: (39) implies: % 74.45/11.02 | (54) all_8_23 = e0 % 74.45/11.02 | % 74.45/11.02 | REDUCE: (35), (54) imply: % 74.45/11.02 | (55) op(e3, all_4_9) = e0 % 74.45/11.02 | % 74.45/11.02 | BETA: splitting (33) gives: % 74.45/11.02 | % 74.45/11.02 | Case 1: % 74.45/11.02 | | % 74.45/11.02 | | (56) all_10_20 = e4 % 74.45/11.02 | | % 74.45/11.02 | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (10), (11), (13), (14), (16), (17), % 74.45/11.02 | | (18), (19), (20), (22), (23), (24), (25), (26), (27), (28), (29), % 74.45/11.02 | | (30), (31), (32), (34), (36), (37), (40), (41), (42), (44), (45), % 74.45/11.02 | | (46), (47), (48), (49), (50), (51), (52), (53), (56) are % 74.45/11.02 | | inconsistent by sub-proof #23. % 74.45/11.02 | | % 74.45/11.02 | Case 2: % 74.45/11.02 | | % 74.45/11.02 | | (57) all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | all_10_24 = e4 % 74.45/11.02 | | % 74.45/11.02 | | REF_CLOSE: (1), (2), (8), (12), (15), (21), (22), (38), (41), (43), (55), % 74.45/11.02 | | (57) are inconsistent by sub-proof #32. % 74.45/11.02 | | % 74.45/11.02 | End of split % 74.45/11.02 | % 74.45/11.02 End of proof % 74.45/11.02 % 74.45/11.02 Sub-proof #22 shows that the following formulas are inconsistent: % 74.45/11.02 ---------------------------------------------------------------- % 74.45/11.02 (1) all_8_17 = all_4_16 % 74.45/11.02 (2) ~ (all_4_19 = e4) % 74.45/11.02 (3) all_10_1 = e4 | all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | % 74.45/11.02 all_10_21 = e4 % 74.45/11.02 (4) ~ (all_4_9 = e0) % 74.45/11.02 (5) (all_8_13 = e4 & ~ (all_8_14 = e3)) | (all_8_17 = e2 & ~ (all_8_18 = % 74.45/11.02 e3)) % 74.45/11.02 (6) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 74.45/11.02 (7) ~ (all_4_2 = e1) % 74.45/11.02 (8) ~ (all_4_10 = e3) % 74.45/11.02 (9) ~ (e3 = e2) % 74.45/11.02 (10) all_10_4 = all_4_10 % 74.45/11.02 (11) all_10_22 = e2 % 74.45/11.02 (12) ~ (all_4_16 = e2) % 74.45/11.02 (13) ~ (all_4_20 = e3) % 74.45/11.02 (14) all_10_1 = all_4_5 % 74.45/11.02 (15) ~ (all_4_4 = e2) % 74.45/11.02 (16) all_10_24 = e1 % 74.45/11.02 (17) ~ (e2 = e0) % 74.45/11.02 (18) ~ (all_4_2 = e3) % 74.45/11.02 (19) all_10_16 = all_4_20 % 74.45/11.02 (20) ~ (e4 = e0) % 74.45/11.02 (21) all_10_3 = e0 % 74.45/11.02 (22) ~ (all_4_4 = all_4_9) % 74.50/11.02 (23) all_10_6 = e0 | all_10_7 = e0 | all_10_8 = e0 | all_10_11 = e0 | % 74.50/11.02 all_10_18 = e0 % 74.50/11.02 (24) all_10_23 = all_4_19 % 74.50/11.02 (25) all_10_21 = all_4_9 % 74.50/11.02 (26) ~ (all_4_10 = e0) % 74.50/11.02 (27) ~ (all_4_2 = all_4_4) % 74.50/11.02 (28) ~ (all_4_5 = e1) % 74.50/11.02 (29) all_10_9 = e3 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 74.50/11.02 all_10_23 = e3 % 74.50/11.02 (30) all_10_20 = all_4_4 % 74.50/11.02 (31) all_10_0 = e3 | all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | % 74.50/11.02 all_10_16 = e3 % 74.50/11.02 (32) all_6_10 = all_4_2 % 74.50/11.02 (33) ~ (e4 = e3) % 74.50/11.02 (34) ~ (all_4_5 = e0) % 74.50/11.02 (35) op(e4, all_4_20) = all_8_53 % 74.50/11.02 (36) all_10_1 = e3 | all_10_3 = e3 | all_10_7 = e3 | all_10_13 = e3 | % 74.50/11.02 all_10_21 = e3 % 74.50/11.02 (37) all_10_9 = all_4_15 % 74.50/11.02 (38) all_10_20 = e4 | all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 74.50/11.02 all_10_24 = e4 % 74.50/11.02 (39) ~ (all_4_2 = e2) % 74.50/11.02 (40) all_6_1 = all_4_5 % 74.50/11.02 (41) ~ (all_4_5 = all_4_10) % 74.50/11.02 (42) all_10_13 = e2 % 74.50/11.02 (43) ~ (e4 = e2) % 74.50/11.02 (44) all_10_6 = all_4_2 % 74.50/11.02 (45) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.50/11.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.50/11.02 (46) all_6_2 = all_4_10 % 74.50/11.02 (47) op(e3, e3) = e0 % 74.50/11.02 (48) ~ (e4 = e1) % 74.50/11.02 (49) op(e4, e0) = all_4_20 % 74.50/11.02 (50) ~ (e3 = e0) % 74.50/11.02 (51) op(e4, all_4_2) = e2 % 74.50/11.02 (52) ~ (all_4_4 = e1) % 74.50/11.02 (53) all_6_10 = e4 | all_6_10 = e3 | all_6_10 = e1 | all_6_10 = e0 % 74.50/11.02 (54) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.50/11.02 (55) all_10_0 = e2 % 74.50/11.02 (56) all_10_0 = e0 | all_10_1 = e0 | all_10_4 = e0 | all_10_9 = e0 | % 74.50/11.02 all_10_16 = e0 % 74.50/11.02 (57) ~ (all_4_5 = all_4_9) % 74.50/11.02 (58) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 74.50/11.02 all_10_22 = e1 % 74.50/11.02 (59) all_10_7 = e1 % 74.50/11.02 (60) op(e3, all_4_5) = all_8_13 % 74.50/11.02 % 74.50/11.02 Begin of proof % 74.50/11.02 | % 74.50/11.02 | BETA: splitting (5) gives: % 74.50/11.02 | % 74.50/11.02 | Case 1: % 74.50/11.02 | | % 74.50/11.02 | | (61) all_8_13 = e4 & ~ (all_8_14 = e3) % 74.50/11.02 | | % 74.50/11.02 | | ALPHA: (61) implies: % 74.50/11.02 | | (62) all_8_13 = e4 % 74.50/11.02 | | % 74.50/11.02 | | REDUCE: (60), (62) imply: % 74.50/11.02 | | (63) op(e3, all_4_5) = e4 % 74.50/11.02 | | % 74.50/11.02 | | BETA: splitting (38) gives: % 74.50/11.02 | | % 74.50/11.02 | | Case 1: % 74.50/11.02 | | | % 74.50/11.02 | | | (64) all_10_20 = e4 % 74.50/11.02 | | | % 74.50/11.02 | | | REF_CLOSE: (3), (7), (8), (9), (10), (13), (14), (15), (17), (18), (19), % 74.50/11.02 | | | (20), (21), (22), (23), (25), (26), (27), (29), (30), (31), % 74.50/11.02 | | | (32), (33), (34), (35), (37), (39), (41), (42), (44), (45), % 74.50/11.02 | | | (46), (49), (50), (51), (52), (53), (54), (55), (56), (58), % 74.50/11.02 | | | (59), (64) are inconsistent by sub-proof #23. % 74.50/11.02 | | | % 74.50/11.02 | | Case 2: % 74.50/11.02 | | | % 74.50/11.02 | | | (65) all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | all_10_24 = e4 % 74.50/11.02 | | | % 74.50/11.02 | | | REF_CLOSE: (2), (4), (6), (11), (14), (16), (24), (25), (28), (34), (36), % 74.50/11.02 | | | (40), (43), (45), (47), (48), (57), (63), (65) are inconsistent % 74.50/11.02 | | | by sub-proof #26. % 74.50/11.02 | | | % 74.50/11.02 | | End of split % 74.50/11.02 | | % 74.50/11.02 | Case 2: % 74.50/11.02 | | % 74.50/11.02 | | (66) all_8_17 = e2 & ~ (all_8_18 = e3) % 74.50/11.02 | | % 74.50/11.02 | | REF_CLOSE: (1), (12), (66) are inconsistent by sub-proof #25. % 74.50/11.02 | | % 74.50/11.02 | End of split % 74.50/11.02 | % 74.50/11.02 End of proof % 74.50/11.02 % 74.50/11.02 Sub-proof #23 shows that the following formulas are inconsistent: % 74.50/11.02 ---------------------------------------------------------------- % 74.50/11.02 (1) all_10_1 = e4 | all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | % 74.50/11.02 all_10_21 = e4 % 74.50/11.02 (2) ~ (all_4_2 = e1) % 74.50/11.02 (3) ~ (all_4_10 = e3) % 74.50/11.02 (4) ~ (e3 = e2) % 74.50/11.02 (5) all_10_4 = all_4_10 % 74.50/11.02 (6) all_10_20 = e4 % 74.50/11.02 (7) ~ (all_4_20 = e3) % 74.50/11.02 (8) all_10_1 = all_4_5 % 74.50/11.02 (9) ~ (all_4_4 = e2) % 74.50/11.02 (10) ~ (e2 = e0) % 74.50/11.02 (11) ~ (all_4_2 = e3) % 74.50/11.02 (12) all_10_16 = all_4_20 % 74.50/11.02 (13) ~ (e4 = e0) % 74.50/11.02 (14) all_10_3 = e0 % 74.50/11.02 (15) ~ (all_4_4 = all_4_9) % 74.50/11.02 (16) all_10_6 = e0 | all_10_7 = e0 | all_10_8 = e0 | all_10_11 = e0 | % 74.50/11.02 all_10_18 = e0 % 74.50/11.02 (17) all_10_21 = all_4_9 % 74.50/11.02 (18) ~ (all_4_10 = e0) % 74.50/11.02 (19) ~ (all_4_2 = all_4_4) % 74.50/11.02 (20) all_10_9 = e3 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 74.50/11.02 all_10_23 = e3 % 74.50/11.02 (21) all_10_20 = all_4_4 % 74.50/11.02 (22) all_10_0 = e3 | all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | % 74.50/11.02 all_10_16 = e3 % 74.50/11.02 (23) all_6_10 = all_4_2 % 74.50/11.02 (24) ~ (e4 = e3) % 74.50/11.02 (25) ~ (all_4_5 = e0) % 74.50/11.02 (26) op(e4, all_4_20) = all_8_53 % 74.50/11.02 (27) all_10_9 = all_4_15 % 74.50/11.02 (28) ~ (all_4_2 = e2) % 74.50/11.02 (29) ~ (all_4_5 = all_4_10) % 74.50/11.02 (30) all_10_13 = e2 % 74.50/11.02 (31) all_10_6 = all_4_2 % 74.50/11.02 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.50/11.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.50/11.02 (33) all_6_2 = all_4_10 % 74.50/11.02 (34) op(e4, e0) = all_4_20 % 74.50/11.02 (35) ~ (e3 = e0) % 74.50/11.02 (36) op(e4, all_4_2) = e2 % 74.50/11.02 (37) ~ (all_4_4 = e1) % 74.50/11.02 (38) all_6_10 = e4 | all_6_10 = e3 | all_6_10 = e1 | all_6_10 = e0 % 74.50/11.02 (39) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.50/11.03 (40) all_10_0 = e2 % 74.50/11.03 (41) all_10_0 = e0 | all_10_1 = e0 | all_10_4 = e0 | all_10_9 = e0 | % 74.50/11.03 all_10_16 = e0 % 74.50/11.03 (42) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 74.50/11.03 all_10_22 = e1 % 74.50/11.03 (43) all_10_7 = e1 % 74.50/11.03 % 74.50/11.03 Begin of proof % 74.50/11.03 | % 74.50/11.03 | COMBINE_EQS: (6), (21) imply: % 74.50/11.03 | (44) all_4_4 = e4 % 74.50/11.03 | % 74.50/11.03 | SIMP: (44) implies: % 74.50/11.03 | (45) all_4_4 = e4 % 74.50/11.03 | % 74.50/11.03 | REDUCE: (19), (45) imply: % 74.50/11.03 | (46) ~ (all_4_2 = e4) % 74.50/11.03 | % 74.50/11.03 | REDUCE: (15), (45) imply: % 74.50/11.03 | (47) ~ (all_4_9 = e4) % 74.50/11.03 | % 74.50/11.03 | SIMP: (47) implies: % 74.50/11.03 | (48) ~ (all_4_9 = e4) % 74.50/11.03 | % 74.50/11.03 | REDUCE: (9), (45) imply: % 74.50/11.03 | (49) ~ (e4 = e2) % 74.50/11.03 | % 74.50/11.03 | REDUCE: (37), (45) imply: % 74.50/11.03 | (50) ~ (e4 = e1) % 74.50/11.03 | % 74.50/11.03 | BETA: splitting (1) gives: % 74.50/11.03 | % 74.50/11.03 | Case 1: % 74.50/11.03 | | % 74.50/11.03 | | (51) all_10_1 = e4 % 74.50/11.03 | | % 74.50/11.03 | | COMBINE_EQS: (8), (51) imply: % 74.50/11.03 | | (52) all_4_5 = e4 % 74.50/11.03 | | % 74.50/11.03 | | REDUCE: (29), (52) imply: % 74.50/11.03 | | (53) ~ (all_4_10 = e4) % 74.50/11.03 | | % 74.50/11.03 | | SIMP: (53) implies: % 74.50/11.03 | | (54) ~ (all_4_10 = e4) % 74.50/11.03 | | % 74.50/11.03 | | BETA: splitting (22) gives: % 74.50/11.03 | | % 74.50/11.03 | | Case 1: % 74.50/11.03 | | | % 74.50/11.03 | | | (55) all_10_0 = e3 % 74.50/11.03 | | | % 74.50/11.03 | | | REF_CLOSE: (4), (40), (55) are inconsistent by sub-proof #104. % 74.50/11.03 | | | % 74.50/11.03 | | Case 2: % 74.50/11.03 | | | % 74.50/11.03 | | | (56) all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | all_10_16 = e3 % 74.50/11.03 | | | % 74.50/11.03 | | | BETA: splitting (38) gives: % 74.50/11.03 | | | % 74.50/11.03 | | | Case 1: % 74.50/11.03 | | | | % 74.50/11.03 | | | | (57) all_6_10 = e4 % 74.50/11.03 | | | | % 74.50/11.03 | | | | REF_CLOSE: (23), (46), (57) are inconsistent by sub-proof #105. % 74.50/11.03 | | | | % 74.50/11.03 | | | Case 2: % 74.50/11.03 | | | | % 74.50/11.03 | | | | (58) all_6_10 = e3 | all_6_10 = e1 | all_6_10 = e0 % 74.50/11.03 | | | | % 74.50/11.03 | | | | BETA: splitting (42) gives: % 74.50/11.03 | | | | % 74.50/11.03 | | | | Case 1: % 74.50/11.03 | | | | | % 74.50/11.03 | | | | | (59) all_10_4 = e1 % 74.50/11.03 | | | | | % 74.50/11.03 | | | | | COMBINE_EQS: (5), (59) imply: % 74.50/11.03 | | | | | (60) all_4_10 = e1 % 74.50/11.03 | | | | | % 74.50/11.03 | | | | | REDUCE: (3), (60) imply: % 74.50/11.03 | | | | | (61) ~ (e3 = e1) % 74.50/11.03 | | | | | % 74.50/11.03 | | | | | SIMP: (61) implies: % 74.50/11.03 | | | | | (62) ~ (e3 = e1) % 74.50/11.03 | | | | | % 74.50/11.03 | | | | | REDUCE: (18), (60) imply: % 74.50/11.03 | | | | | (63) ~ (e1 = e0) % 74.50/11.03 | | | | | % 74.50/11.03 | | | | | BETA: splitting (56) gives: % 74.50/11.03 | | | | | % 74.50/11.03 | | | | | Case 1: % 74.50/11.03 | | | | | | % 74.50/11.03 | | | | | | (64) all_10_1 = e3 % 74.50/11.03 | | | | | | % 74.50/11.03 | | | | | | COMBINE_EQS: (51), (64) imply: % 74.50/11.03 | | | | | | (65) e4 = e3 % 74.50/11.03 | | | | | | % 74.50/11.03 | | | | | | REDUCE: (24), (65) imply: % 74.50/11.03 | | | | | | (66) $false % 74.50/11.03 | | | | | | % 74.50/11.03 | | | | | | CLOSE: (66) is inconsistent. % 74.50/11.03 | | | | | | % 74.50/11.03 | | | | | Case 2: % 74.50/11.03 | | | | | | % 74.50/11.03 | | | | | | (67) all_10_4 = e3 | all_10_9 = e3 | all_10_16 = e3 % 74.50/11.03 | | | | | | % 74.50/11.03 | | | | | | BETA: splitting (67) gives: % 74.50/11.03 | | | | | | % 74.50/11.03 | | | | | | Case 1: % 74.50/11.03 | | | | | | | % 74.50/11.03 | | | | | | | (68) all_10_4 = e3 % 74.50/11.03 | | | | | | | % 74.50/11.03 | | | | | | | REF_CLOSE: (59), (62), (68) are inconsistent by sub-proof #31. % 74.50/11.03 | | | | | | | % 74.50/11.03 | | | | | | Case 2: % 74.50/11.03 | | | | | | | % 74.50/11.03 | | | | | | | (69) all_10_9 = e3 | all_10_16 = e3 % 74.50/11.03 | | | | | | | % 74.50/11.03 | | | | | | | BETA: splitting (20) gives: % 74.50/11.03 | | | | | | | % 74.50/11.03 | | | | | | | Case 1: % 74.50/11.03 | | | | | | | | % 74.50/11.03 | | | | | | | | (70) all_10_9 = e3 % 74.50/11.03 | | | | | | | | % 74.50/11.03 | | | | | | | | COMBINE_EQS: (27), (70) imply: % 74.50/11.03 | | | | | | | | (71) all_4_15 = e3 % 74.50/11.03 | | | | | | | | % 74.50/11.03 | | | | | | | | BETA: splitting (41) gives: % 74.50/11.03 | | | | | | | | % 74.50/11.03 | | | | | | | | Case 1: % 74.50/11.03 | | | | | | | | | % 74.50/11.03 | | | | | | | | | (72) all_10_0 = e0 % 74.50/11.03 | | | | | | | | | % 74.50/11.03 | | | | | | | | | COMBINE_EQS: (40), (72) imply: % 74.50/11.03 | | | | | | | | | (73) e2 = e0 % 74.50/11.03 | | | | | | | | | % 74.50/11.03 | | | | | | | | | REDUCE: (10), (73) imply: % 74.50/11.03 | | | | | | | | | (74) $false % 74.50/11.03 | | | | | | | | | % 74.50/11.03 | | | | | | | | | CLOSE: (74) is inconsistent. % 74.50/11.03 | | | | | | | | | % 74.50/11.03 | | | | | | | | Case 2: % 74.50/11.03 | | | | | | | | | % 74.50/11.03 | | | | | | | | | (75) all_10_1 = e0 | all_10_4 = e0 | all_10_9 = e0 | % 74.50/11.03 | | | | | | | | | all_10_16 = e0 % 74.50/11.03 | | | | | | | | | % 74.50/11.03 | | | | | | | | | BETA: splitting (75) gives: % 74.50/11.03 | | | | | | | | | % 74.50/11.03 | | | | | | | | | Case 1: % 74.50/11.03 | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | (76) all_10_1 = e0 % 74.50/11.03 | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | COMBINE_EQS: (51), (76) imply: % 74.50/11.03 | | | | | | | | | | (77) e4 = e0 % 74.50/11.03 | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | REDUCE: (13), (77) imply: % 74.50/11.03 | | | | | | | | | | (78) $false % 74.50/11.03 | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | CLOSE: (78) is inconsistent. % 74.50/11.03 | | | | | | | | | | % 74.50/11.03 | | | | | | | | | Case 2: % 74.50/11.03 | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | (79) all_10_4 = e0 | all_10_9 = e0 | all_10_16 = e0 % 74.50/11.03 | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | BETA: splitting (79) gives: % 74.50/11.03 | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | Case 1: % 74.50/11.03 | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | (80) all_10_4 = e0 % 74.50/11.03 | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | COMBINE_EQS: (59), (80) imply: % 74.50/11.03 | | | | | | | | | | | (81) e1 = e0 % 74.50/11.03 | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | REDUCE: (63), (81) imply: % 74.50/11.03 | | | | | | | | | | | (82) $false % 74.50/11.03 | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | CLOSE: (82) is inconsistent. % 74.50/11.03 | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | Case 2: % 74.50/11.03 | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | (83) all_10_9 = e0 | all_10_16 = e0 % 74.50/11.03 | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | BETA: splitting (58) gives: % 74.50/11.03 | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | Case 1: % 74.50/11.03 | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | (84) all_6_10 = e1 % 74.50/11.03 | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | REF_CLOSE: (2), (23), (84) are inconsistent by sub-proof % 74.50/11.03 | | | | | | | | | | | | #103. % 74.50/11.03 | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | Case 2: % 74.50/11.03 | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | (85) all_6_10 = e3 | all_6_10 = e0 % 74.50/11.03 | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | BETA: splitting (83) gives: % 74.50/11.03 | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | Case 1: % 74.50/11.03 | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | (86) all_10_9 = e0 % 74.50/11.03 | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | COMBINE_EQS: (70), (86) imply: % 74.50/11.03 | | | | | | | | | | | | | (87) e3 = e0 % 74.50/11.03 | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | REDUCE: (35), (87) imply: % 74.50/11.03 | | | | | | | | | | | | | (88) $false % 74.50/11.03 | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | CLOSE: (88) is inconsistent. % 74.50/11.03 | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | Case 2: % 74.50/11.03 | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | (89) all_10_16 = e0 % 74.50/11.03 | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | COMBINE_EQS: (12), (89) imply: % 74.50/11.03 | | | | | | | | | | | | | (90) all_4_20 = e0 % 74.50/11.03 | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | REDUCE: (26), (90) imply: % 74.50/11.03 | | | | | | | | | | | | | (91) op(e4, e0) = all_8_53 % 74.50/11.03 | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | REDUCE: (34), (90) imply: % 74.50/11.03 | | | | | | | | | | | | | (92) op(e4, e0) = e0 % 74.50/11.03 | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | BETA: splitting (16) gives: % 74.50/11.03 | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | Case 1: % 74.50/11.03 | | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | | (93) all_10_6 = e0 % 74.50/11.03 | | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | | COMBINE_EQS: (31), (93) imply: % 74.50/11.03 | | | | | | | | | | | | | | (94) all_4_2 = e0 % 74.50/11.03 | | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | | SIMP: (94) implies: % 74.50/11.03 | | | | | | | | | | | | | | (95) all_4_2 = e0 % 74.50/11.03 | | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | | REDUCE: (28), (95) imply: % 74.50/11.03 | | | | | | | | | | | | | | (96) ~ (e2 = e0) % 74.50/11.03 | | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | | REDUCE: (36), (95) imply: % 74.50/11.03 | | | | | | | | | | | | | | (97) op(e4, e0) = e2 % 74.50/11.03 | | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with e2, all_8_53, e0, e4, % 74.50/11.03 | | | | | | | | | | | | | | simplifying with (91), (97) gives: % 74.50/11.03 | | | | | | | | | | | | | | (98) all_8_53 = e2 % 74.50/11.03 | | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with e0, all_8_53, e0, e4, % 74.50/11.03 | | | | | | | | | | | | | | simplifying with (91), (92) gives: % 74.50/11.03 | | | | | | | | | | | | | | (99) all_8_53 = e0 % 74.50/11.03 | | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | | COMBINE_EQS: (98), (99) imply: % 74.50/11.03 | | | | | | | | | | | | | | (100) e2 = e0 % 74.50/11.03 | | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | | REDUCE: (10), (100) imply: % 74.50/11.03 | | | | | | | | | | | | | | (101) $false % 74.50/11.03 | | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | | CLOSE: (101) is inconsistent. % 74.50/11.03 | | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | Case 2: % 74.50/11.03 | | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | | (102) ~ (all_10_6 = e0) % 74.50/11.03 | | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | | REDUCE: (31), (102) imply: % 74.50/11.03 | | | | | | | | | | | | | | (103) ~ (all_4_2 = e0) % 74.50/11.03 | | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | | REF_CLOSE: (11), (23), (85), (103) are inconsistent by % 74.50/11.03 | | | | | | | | | | | | | | sub-proof #62. % 74.50/11.03 | | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | | End of split % 74.50/11.03 | | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | | End of split % 74.50/11.03 | | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | | End of split % 74.50/11.03 | | | | | | | | | | | % 74.50/11.03 | | | | | | | | | | End of split % 74.50/11.03 | | | | | | | | | | % 74.50/11.03 | | | | | | | | | End of split % 74.50/11.03 | | | | | | | | | % 74.50/11.03 | | | | | | | | End of split % 74.50/11.03 | | | | | | | | % 74.50/11.03 | | | | | | | Case 2: % 74.50/11.03 | | | | | | | | % 74.50/11.03 | | | | | | | | (104) ~ (all_10_9 = e3) % 74.50/11.03 | | | | | | | | % 74.50/11.03 | | | | | | | | REDUCE: (27), (104) imply: % 74.50/11.03 | | | | | | | | (105) ~ (all_4_15 = e3) % 74.50/11.03 | | | | | | | | % 74.50/11.03 | | | | | | | | REF_CLOSE: (7), (12), (27), (69), (105) are inconsistent by % 74.50/11.03 | | | | | | | | sub-proof #63. % 74.50/11.03 | | | | | | | | % 74.50/11.03 | | | | | | | End of split % 74.50/11.03 | | | | | | | % 74.50/11.03 | | | | | | End of split % 74.50/11.03 | | | | | | % 74.50/11.03 | | | | | End of split % 74.50/11.03 | | | | | % 74.50/11.03 | | | | Case 2: % 74.50/11.03 | | | | | % 74.50/11.03 | | | | | (106) ~ (all_10_4 = e1) % 74.50/11.03 | | | | | % 74.50/11.03 | | | | | REDUCE: (5), (106) imply: % 74.50/11.03 | | | | | (107) ~ (all_4_10 = e1) % 74.50/11.03 | | | | | % 74.50/11.03 | | | | | REF_CLOSE: (3), (18), (33), (39), (54), (107) are inconsistent by % 74.50/11.03 | | | | | sub-proof #161. % 74.50/11.03 | | | | | % 74.50/11.03 | | | | End of split % 74.50/11.03 | | | | % 74.50/11.03 | | | End of split % 74.50/11.03 | | | % 74.50/11.03 | | End of split % 74.50/11.03 | | % 74.50/11.03 | Case 2: % 74.50/11.03 | | % 74.50/11.03 | | (108) all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | all_10_21 = e4 % 74.50/11.03 | | % 74.50/11.03 | | REF_CLOSE: (13), (14), (17), (30), (43), (48), (49), (50), (108) are % 74.50/11.03 | | inconsistent by sub-proof #28. % 74.50/11.03 | | % 74.50/11.03 | End of split % 74.50/11.03 | % 74.50/11.03 End of proof % 74.50/11.03 % 74.50/11.03 Sub-proof #24 shows that the following formulas are inconsistent: % 74.50/11.03 ---------------------------------------------------------------- % 74.50/11.03 (1) all_8_20 = e1 & ~ (all_8_21 = e3) % 74.50/11.03 (2) ~ (all_4_10 = e3) % 74.50/11.03 (3) all_10_4 = all_4_10 % 74.50/11.03 (4) ~ (all_4_10 = e0) % 74.50/11.03 (5) op(e4, e4) = e2 % 74.50/11.03 (6) ~ (all_8_27 = e2) % 74.50/11.03 (7) all_8_20 = all_4_11 % 74.50/11.03 (8) ~ (all_4_10 = all_4_11) % 74.50/11.03 (9) op(e4, all_4_10) = all_8_27 % 74.50/11.03 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.50/11.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.50/11.03 (11) all_6_2 = all_4_10 % 74.50/11.03 (12) all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | % 74.50/11.03 all_10_22 = e4 % 74.50/11.03 (13) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.50/11.03 % 74.50/11.03 Begin of proof % 74.50/11.03 | % 74.50/11.03 | ALPHA: (1) implies: % 74.50/11.03 | (14) all_8_20 = e1 % 74.50/11.03 | % 74.50/11.03 | COMBINE_EQS: (7), (14) imply: % 74.50/11.03 | (15) all_4_11 = e1 % 74.50/11.03 | % 74.50/11.03 | SIMP: (15) implies: % 74.50/11.03 | (16) all_4_11 = e1 % 74.50/11.03 | % 74.50/11.03 | REDUCE: (8), (16) imply: % 74.50/11.03 | (17) ~ (all_4_10 = e1) % 74.50/11.03 | % 74.50/11.03 | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (11), (12), (13), (17) are % 74.50/11.03 | inconsistent by sub-proof #160. % 74.50/11.03 | % 74.50/11.03 End of proof % 74.50/11.03 % 74.50/11.03 Sub-proof #25 shows that the following formulas are inconsistent: % 74.50/11.03 ---------------------------------------------------------------- % 74.50/11.03 (1) all_8_17 = e2 & ~ (all_8_18 = e3) % 74.50/11.03 (2) all_8_17 = all_4_16 % 74.50/11.03 (3) ~ (all_4_16 = e2) % 74.50/11.03 % 74.50/11.03 Begin of proof % 74.50/11.03 | % 74.50/11.03 | ALPHA: (1) implies: % 74.50/11.03 | (4) all_8_17 = e2 % 74.50/11.03 | % 74.50/11.03 | COMBINE_EQS: (2), (4) imply: % 74.50/11.03 | (5) all_4_16 = e2 % 74.50/11.03 | % 74.50/11.03 | SIMP: (5) implies: % 74.50/11.03 | (6) all_4_16 = e2 % 74.50/11.03 | % 74.50/11.03 | REDUCE: (3), (6) imply: % 74.50/11.03 | (7) $false % 74.50/11.03 | % 74.50/11.03 | CLOSE: (7) is inconsistent. % 74.50/11.03 | % 74.50/11.03 End of proof % 74.50/11.03 % 74.50/11.03 Sub-proof #26 shows that the following formulas are inconsistent: % 74.50/11.03 ---------------------------------------------------------------- % 74.50/11.03 (1) ~ (all_4_19 = e4) % 74.50/11.03 (2) ~ (all_4_9 = e0) % 74.50/11.03 (3) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 74.50/11.03 (4) all_10_22 = e2 % 74.50/11.03 (5) all_10_1 = all_4_5 % 74.50/11.03 (6) all_10_24 = e1 % 74.50/11.03 (7) op(e3, all_4_5) = e4 % 74.50/11.03 (8) all_10_23 = all_4_19 % 74.50/11.03 (9) all_10_21 = all_4_9 % 74.50/11.03 (10) ~ (all_4_5 = e1) % 74.50/11.03 (11) ~ (all_4_5 = e0) % 74.50/11.03 (12) all_10_1 = e3 | all_10_3 = e3 | all_10_7 = e3 | all_10_13 = e3 | % 74.50/11.03 all_10_21 = e3 % 74.50/11.03 (13) all_6_1 = all_4_5 % 74.50/11.03 (14) ~ (e4 = e2) % 74.50/11.03 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.50/11.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.50/11.03 (16) all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | all_10_24 = e4 % 74.50/11.03 (17) op(e3, e3) = e0 % 74.50/11.03 (18) ~ (e4 = e1) % 74.50/11.03 (19) ~ (all_4_5 = all_4_9) % 74.50/11.03 % 74.50/11.03 Begin of proof % 74.50/11.03 | % 74.50/11.03 | BETA: splitting (16) gives: % 74.50/11.03 | % 74.50/11.03 | Case 1: % 74.50/11.03 | | % 74.50/11.03 | | (20) all_10_21 = e4 % 74.50/11.03 | | % 74.50/11.03 | | COMBINE_EQS: (9), (20) imply: % 74.50/11.03 | | (21) all_4_9 = e4 % 74.50/11.03 | | % 74.50/11.04 | | SIMP: (21) implies: % 74.50/11.04 | | (22) all_4_9 = e4 % 74.50/11.04 | | % 74.50/11.04 | | REDUCE: (19), (22) imply: % 74.50/11.04 | | (23) ~ (all_4_5 = e4) % 74.50/11.04 | | % 74.50/11.04 | | REDUCE: (2), (22) imply: % 74.50/11.04 | | (24) ~ (e4 = e0) % 74.50/11.04 | | % 74.50/11.04 | | REF_CLOSE: (3), (5), (7), (10), (11), (12), (13), (15), (17), (23), (24) are % 74.50/11.04 | | inconsistent by sub-proof #38. % 74.50/11.04 | | % 74.50/11.04 | Case 2: % 74.50/11.04 | | % 74.50/11.04 | | (25) all_10_22 = e4 | all_10_23 = e4 | all_10_24 = e4 % 74.50/11.04 | | % 74.50/11.04 | | REF_CLOSE: (1), (4), (6), (8), (14), (18), (25) are inconsistent by % 74.50/11.04 | | sub-proof #36. % 74.50/11.04 | | % 74.50/11.04 | End of split % 74.50/11.04 | % 74.50/11.04 End of proof % 74.50/11.04 % 74.50/11.04 Sub-proof #27 shows that the following formulas are inconsistent: % 74.50/11.04 ---------------------------------------------------------------- % 74.50/11.04 (1) ~ (all_4_19 = e4) % 74.50/11.04 (2) all_10_1 = e4 | all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | % 74.50/11.04 all_10_21 = e4 % 74.50/11.04 (3) ~ (all_4_9 = e0) % 74.50/11.04 (4) ~ (all_4_10 = e3) % 74.50/11.04 (5) all_10_20 = e0 | all_10_21 = e0 | all_10_22 = e0 | all_10_23 = e0 % 74.50/11.04 (6) ~ (e3 = e2) % 74.50/11.04 (7) all_10_4 = all_4_10 % 74.50/11.04 (8) all_10_22 = e2 % 74.50/11.04 (9) all_10_20 = e4 % 74.50/11.04 (10) ~ (all_4_20 = e3) % 74.50/11.04 (11) all_10_1 = all_4_5 % 74.50/11.04 (12) op(e0, e0) = e1 % 74.50/11.04 (13) ~ (e2 = e0) % 74.50/11.04 (14) ~ (all_4_2 = e3) % 74.50/11.04 (15) op(e4, all_4_15) = all_8_40 % 74.50/11.04 (16) ~ (e3 = e1) % 74.50/11.04 (17) all_10_16 = all_4_20 % 74.50/11.04 (18) op(e2, e1) = e2 % 74.50/11.04 (19) ~ (e4 = e0) % 74.50/11.04 (20) all_10_3 = e0 % 74.50/11.04 (21) all_10_23 = all_4_19 % 74.50/11.04 (22) all_10_21 = all_4_9 % 74.50/11.04 (23) ~ (all_4_10 = e0) % 74.50/11.04 (24) op(e0, all_4_19) = all_8_50 % 74.50/11.04 (25) all_6_21 = all_4_9 % 74.50/11.04 (26) all_10_9 = e3 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 74.50/11.04 all_10_23 = e3 % 74.50/11.04 (27) all_10_0 = e3 | all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | % 74.50/11.04 all_10_16 = e3 % 74.50/11.04 (28) ~ (e4 = e3) % 74.50/11.04 (29) all_10_2 = all_4_1 % 74.50/11.04 (30) ~ (all_4_5 = e0) % 74.50/11.04 (31) ~ (all_4_15 = all_4_19) % 74.50/11.04 (32) op(e0, all_4_20) = e4 % 74.50/11.04 (33) ~ (all_4_19 = e1) % 74.50/11.04 (34) op(e2, all_4_10) = e4 % 74.50/11.04 (35) all_10_9 = all_4_15 % 74.50/11.04 (36) ~ (all_4_9 = e1) % 74.50/11.04 (37) all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e1 | all_6_21 = e0 % 74.50/11.04 (38) ~ (all_4_9 = e4) % 74.50/11.04 (39) all_10_0 = e3 | all_10_2 = e3 | all_10_6 = e3 | all_10_12 = e3 | % 74.50/11.04 all_10_20 = e3 % 74.50/11.04 (40) all_10_12 = e1 % 74.50/11.04 (41) op(e4, all_4_1) = e3 % 74.50/11.04 (42) ~ (all_4_5 = all_4_10) % 74.50/11.04 (43) all_10_13 = e2 % 74.50/11.04 (44) ~ (e4 = e2) % 74.50/11.04 (45) all_10_6 = all_4_2 % 74.50/11.04 (46) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.50/11.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.50/11.04 (47) all_6_2 = all_4_10 % 74.50/11.04 (48) ~ (e4 = e1) % 74.50/11.04 (49) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.50/11.04 (50) all_10_0 = e2 % 74.50/11.04 (51) all_10_0 = e0 | all_10_1 = e0 | all_10_4 = e0 | all_10_9 = e0 | % 74.50/11.04 all_10_16 = e0 % 74.50/11.04 (52) ~ (all_4_10 = e2) % 74.50/11.04 (53) ~ (all_4_5 = all_4_9) % 74.50/11.04 (54) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 74.50/11.04 all_10_22 = e1 % 74.50/11.04 (55) all_10_7 = e1 % 74.50/11.04 (56) ~ (all_4_1 = e2) % 74.50/11.04 (57) op(e4, e3) = all_4_5 % 74.50/11.04 (58) ~ (all_4_1 = e4) % 74.50/11.04 % 74.50/11.04 Begin of proof % 74.50/11.04 | % 74.50/11.04 | BETA: splitting (39) gives: % 74.50/11.04 | % 74.50/11.04 | Case 1: % 74.50/11.04 | | % 74.50/11.04 | | (59) all_10_0 = e3 % 74.50/11.04 | | % 74.50/11.04 | | REF_CLOSE: (6), (50), (59) are inconsistent by sub-proof #104. % 74.50/11.04 | | % 74.50/11.04 | Case 2: % 74.50/11.04 | | % 74.50/11.04 | | (60) all_10_2 = e3 | all_10_6 = e3 | all_10_12 = e3 | all_10_20 = e3 % 74.50/11.04 | | % 74.50/11.04 | | BETA: splitting (60) gives: % 74.50/11.04 | | % 74.50/11.04 | | Case 1: % 74.50/11.04 | | | % 74.50/11.04 | | | (61) all_10_2 = e3 % 74.50/11.04 | | | % 74.50/11.04 | | | COMBINE_EQS: (29), (61) imply: % 74.50/11.04 | | | (62) all_4_1 = e3 % 74.50/11.04 | | | % 74.50/11.04 | | | SIMP: (62) implies: % 74.50/11.04 | | | (63) all_4_1 = e3 % 74.50/11.04 | | | % 74.50/11.04 | | | REDUCE: (58), (63) imply: % 74.50/11.04 | | | (64) ~ (e4 = e3) % 74.50/11.04 | | | % 74.50/11.04 | | | REDUCE: (41), (63) imply: % 74.50/11.04 | | | (65) op(e4, e3) = e3 % 74.50/11.04 | | | % 74.50/11.04 | | | BETA: splitting (2) gives: % 74.50/11.04 | | | % 74.50/11.04 | | | Case 1: % 74.50/11.04 | | | | % 74.50/11.04 | | | | (66) all_10_1 = e4 % 74.50/11.04 | | | | % 74.50/11.04 | | | | COMBINE_EQS: (11), (66) imply: % 74.50/11.04 | | | | (67) all_4_5 = e4 % 74.50/11.04 | | | | % 74.50/11.04 | | | | REDUCE: (53), (67) imply: % 74.50/11.04 | | | | (68) ~ (all_4_9 = e4) % 74.50/11.04 | | | | % 74.50/11.04 | | | | REDUCE: (42), (67) imply: % 74.50/11.04 | | | | (69) ~ (all_4_10 = e4) % 74.50/11.04 | | | | % 74.50/11.04 | | | | SIMP: (69) implies: % 74.50/11.04 | | | | (70) ~ (all_4_10 = e4) % 74.50/11.04 | | | | % 74.50/11.04 | | | | REDUCE: (57), (67) imply: % 74.50/11.04 | | | | (71) op(e4, e3) = e4 % 74.50/11.04 | | | | % 74.50/11.04 | | | | BETA: splitting (27) gives: % 74.50/11.04 | | | | % 74.50/11.04 | | | | Case 1: % 74.50/11.04 | | | | | % 74.50/11.04 | | | | | (72) all_10_0 = e3 % 74.50/11.04 | | | | | % 74.50/11.04 | | | | | REF_CLOSE: (6), (50), (72) are inconsistent by sub-proof #104. % 74.50/11.04 | | | | | % 74.50/11.04 | | | | Case 2: % 74.50/11.04 | | | | | % 74.50/11.04 | | | | | (73) all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | all_10_16 = e3 % 74.50/11.04 | | | | | % 74.50/11.04 | | | | | BETA: splitting (5) gives: % 74.50/11.04 | | | | | % 74.50/11.04 | | | | | Case 1: % 74.50/11.04 | | | | | | % 74.50/11.04 | | | | | | (74) all_10_20 = e0 % 74.50/11.04 | | | | | | % 74.50/11.04 | | | | | | REF_CLOSE: (9), (19), (74) are inconsistent by sub-proof #76. % 74.50/11.04 | | | | | | % 74.50/11.04 | | | | | Case 2: % 74.50/11.04 | | | | | | % 74.50/11.04 | | | | | | (75) all_10_21 = e0 | all_10_22 = e0 | all_10_23 = e0 % 74.50/11.04 | | | | | | % 74.50/11.04 | | | | | | BETA: splitting (54) gives: % 74.50/11.04 | | | | | | % 74.50/11.04 | | | | | | Case 1: % 74.50/11.04 | | | | | | | % 74.50/11.04 | | | | | | | (76) all_10_4 = e1 % 74.50/11.04 | | | | | | | % 74.50/11.04 | | | | | | | COMBINE_EQS: (7), (76) imply: % 74.50/11.04 | | | | | | | (77) all_4_10 = e1 % 74.50/11.04 | | | | | | | % 74.50/11.04 | | | | | | | REDUCE: (4), (77) imply: % 74.50/11.04 | | | | | | | (78) ~ (e3 = e1) % 74.50/11.04 | | | | | | | % 74.50/11.04 | | | | | | | REDUCE: (52), (77) imply: % 74.50/11.04 | | | | | | | (79) ~ (e2 = e1) % 74.50/11.04 | | | | | | | % 74.50/11.04 | | | | | | | SIMP: (79) implies: % 74.50/11.04 | | | | | | | (80) ~ (e2 = e1) % 74.50/11.04 | | | | | | | % 74.50/11.04 | | | | | | | REDUCE: (34), (77) imply: % 74.50/11.04 | | | | | | | (81) op(e2, e1) = e4 % 74.50/11.04 | | | | | | | % 74.50/11.04 | | | | | | | BETA: splitting (73) gives: % 74.50/11.04 | | | | | | | % 74.50/11.04 | | | | | | | Case 1: % 74.50/11.04 | | | | | | | | % 74.50/11.04 | | | | | | | | (82) all_10_1 = e3 % 74.50/11.04 | | | | | | | | % 74.50/11.04 | | | | | | | | COMBINE_EQS: (66), (82) imply: % 74.50/11.04 | | | | | | | | (83) e4 = e3 % 74.50/11.04 | | | | | | | | % 74.50/11.04 | | | | | | | | REDUCE: (28), (83) imply: % 74.50/11.04 | | | | | | | | (84) $false % 74.50/11.04 | | | | | | | | % 74.50/11.04 | | | | | | | | CLOSE: (84) is inconsistent. % 74.50/11.04 | | | | | | | | % 74.50/11.04 | | | | | | | Case 2: % 74.50/11.04 | | | | | | | | % 74.50/11.04 | | | | | | | | (85) all_10_4 = e3 | all_10_9 = e3 | all_10_16 = e3 % 74.50/11.04 | | | | | | | | % 74.50/11.04 | | | | | | | | BETA: splitting (85) gives: % 74.50/11.04 | | | | | | | | % 74.50/11.04 | | | | | | | | Case 1: % 74.50/11.04 | | | | | | | | | % 74.50/11.04 | | | | | | | | | (86) all_10_4 = e3 % 74.50/11.04 | | | | | | | | | % 74.50/11.04 | | | | | | | | | REF_CLOSE: (16), (76), (86) are inconsistent by sub-proof #31. % 74.50/11.04 | | | | | | | | | % 74.50/11.04 | | | | | | | | Case 2: % 74.50/11.04 | | | | | | | | | % 74.50/11.04 | | | | | | | | | (87) all_10_9 = e3 | all_10_16 = e3 % 74.50/11.04 | | | | | | | | | % 74.50/11.04 | | | | | | | | | BETA: splitting (37) gives: % 74.50/11.04 | | | | | | | | | % 74.50/11.04 | | | | | | | | | Case 1: % 74.50/11.04 | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | (88) all_6_21 = e4 % 74.50/11.04 | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | COMBINE_EQS: (25), (88) imply: % 74.50/11.04 | | | | | | | | | | (89) all_4_9 = e4 % 74.50/11.04 | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | REDUCE: (38), (89) imply: % 74.50/11.04 | | | | | | | | | | (90) $false % 74.50/11.04 | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | CLOSE: (90) is inconsistent. % 74.50/11.04 | | | | | | | | | | % 74.50/11.04 | | | | | | | | | Case 2: % 74.50/11.04 | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | (91) all_6_21 = e3 | all_6_21 = e1 | all_6_21 = e0 % 74.50/11.04 | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | BETA: splitting (91) gives: % 74.50/11.04 | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | Case 1: % 74.50/11.04 | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | (92) all_6_21 = e1 % 74.50/11.04 | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | COMBINE_EQS: (25), (92) imply: % 74.50/11.04 | | | | | | | | | | | (93) all_4_9 = e1 % 74.50/11.04 | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | REDUCE: (36), (93) imply: % 74.50/11.04 | | | | | | | | | | | (94) $false % 74.50/11.04 | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | CLOSE: (94) is inconsistent. % 74.50/11.04 | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | Case 2: % 74.50/11.04 | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | (95) all_6_21 = e3 | all_6_21 = e0 % 74.50/11.04 | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | BETA: splitting (95) gives: % 74.50/11.04 | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | Case 1: % 74.50/11.04 | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | (96) all_6_21 = e3 % 74.50/11.04 | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | COMBINE_EQS: (25), (96) imply: % 74.50/11.04 | | | | | | | | | | | | (97) all_4_9 = e3 % 74.50/11.04 | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | COMBINE_EQS: (22), (97) imply: % 74.50/11.04 | | | | | | | | | | | | (98) all_10_21 = e3 % 74.50/11.04 | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | REDUCE: (3), (97) imply: % 74.50/11.04 | | | | | | | | | | | | (99) ~ (e3 = e0) % 74.50/11.04 | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | BETA: splitting (26) gives: % 74.50/11.04 | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | Case 1: % 74.50/11.04 | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | (100) all_10_9 = e3 % 74.50/11.04 | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | COMBINE_EQS: (35), (100) imply: % 74.50/11.04 | | | | | | | | | | | | | (101) all_4_15 = e3 % 74.50/11.04 | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | REDUCE: (31), (101) imply: % 74.50/11.04 | | | | | | | | | | | | | (102) ~ (all_4_19 = e3) % 74.50/11.04 | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | SIMP: (102) implies: % 74.50/11.04 | | | | | | | | | | | | | (103) ~ (all_4_19 = e3) % 74.50/11.04 | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | REDUCE: (15), (101) imply: % 74.50/11.04 | | | | | | | | | | | | | (104) op(e4, e3) = all_8_40 % 74.50/11.04 | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | BETA: splitting (51) gives: % 74.50/11.04 | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | Case 1: % 74.50/11.04 | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | (105) all_10_0 = e0 % 74.50/11.04 | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | COMBINE_EQS: (50), (105) imply: % 74.50/11.04 | | | | | | | | | | | | | | (106) e2 = e0 % 74.50/11.04 | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | REDUCE: (13), (106) imply: % 74.50/11.04 | | | | | | | | | | | | | | (107) $false % 74.50/11.04 | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | CLOSE: (107) is inconsistent. % 74.50/11.04 | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | Case 2: % 74.50/11.04 | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | (108) ~ (all_10_0 = e0) % 74.50/11.04 | | | | | | | | | | | | | | (109) all_10_1 = e0 | all_10_4 = e0 | all_10_9 = e0 | % 74.50/11.04 | | | | | | | | | | | | | | all_10_16 = e0 % 74.50/11.04 | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | BETA: splitting (75) gives: % 74.50/11.04 | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | Case 1: % 74.50/11.04 | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | (110) all_10_21 = e0 % 74.50/11.04 | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | REF_CLOSE: (98), (99), (110) are inconsistent by sub-proof % 74.50/11.04 | | | | | | | | | | | | | | | #30. % 74.50/11.04 | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | Case 2: % 74.50/11.04 | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | (111) all_10_22 = e0 | all_10_23 = e0 % 74.50/11.04 | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | BETA: splitting (111) gives: % 74.50/11.04 | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | Case 1: % 74.50/11.04 | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | (112) all_10_22 = e0 % 74.50/11.04 | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13), (112) are inconsistent by sub-proof % 74.50/11.04 | | | | | | | | | | | | | | | | #29. % 74.50/11.04 | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | Case 2: % 74.50/11.04 | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | (113) all_10_23 = e0 % 74.50/11.04 | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (113) imply: % 74.50/11.04 | | | | | | | | | | | | | | | | (114) all_4_19 = e0 % 74.50/11.04 | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | SIMP: (114) implies: % 74.50/11.04 | | | | | | | | | | | | | | | | (115) all_4_19 = e0 % 74.50/11.04 | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | REDUCE: (1), (115) imply: % 74.50/11.04 | | | | | | | | | | | | | | | | (116) ~ (e4 = e0) % 74.50/11.04 | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | REDUCE: (103), (115) imply: % 74.50/11.04 | | | | | | | | | | | | | | | | (117) ~ (e3 = e0) % 74.50/11.04 | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | REDUCE: (33), (115) imply: % 74.50/11.04 | | | | | | | | | | | | | | | | (118) ~ (e1 = e0) % 74.50/11.04 | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | SIMP: (118) implies: % 74.50/11.04 | | | | | | | | | | | | | | | | (119) ~ (e1 = e0) % 74.50/11.04 | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | REDUCE: (24), (115) imply: % 74.50/11.04 | | | | | | | | | | | | | | | | (120) op(e0, e0) = all_8_50 % 74.50/11.04 | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | BETA: splitting (109) gives: % 74.50/11.04 | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | Case 1: % 74.50/11.04 | | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | | (121) all_10_1 = e0 % 74.50/11.04 | | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (121) imply: % 74.50/11.04 | | | | | | | | | | | | | | | | | (122) e4 = e0 % 74.50/11.04 | | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | | REDUCE: (19), (122) imply: % 74.50/11.04 | | | | | | | | | | | | | | | | | (123) $false % 74.50/11.04 | | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | | CLOSE: (123) is inconsistent. % 74.50/11.04 | | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | Case 2: % 74.50/11.04 | | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | | (124) all_10_4 = e0 | all_10_9 = e0 | all_10_16 = e0 % 74.50/11.04 | | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | | BETA: splitting (124) gives: % 74.50/11.04 | | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | | Case 1: % 74.50/11.04 | | | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | | | (125) all_10_4 = e0 % 74.50/11.04 | | | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (125) imply: % 74.50/11.04 | | | | | | | | | | | | | | | | | | (126) e1 = e0 % 74.50/11.04 | | | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | | | REDUCE: (119), (126) imply: % 74.50/11.04 | | | | | | | | | | | | | | | | | | (127) $false % 74.50/11.04 | | | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | | | CLOSE: (127) is inconsistent. % 74.50/11.04 | | | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | | Case 2: % 74.50/11.04 | | | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | | | (128) all_10_9 = e0 | all_10_16 = e0 % 74.50/11.04 | | | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives: % 74.50/11.04 | | | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | | | Case 1: % 74.50/11.04 | | | | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | | | | (129) all_10_9 = e0 % 74.50/11.04 | | | | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (129) imply: % 74.50/11.04 | | | | | | | | | | | | | | | | | | | (130) e3 = e0 % 74.50/11.04 | | | | | | | | | | | | | | | | | | | % 74.50/11.04 | | | | | | | | | | | | | | | | | | | REDUCE: (99), (130) imply: % 74.50/11.04 | | | | | | | | | | | | | | | | | | | (131) $false % 74.50/11.05 | | | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | | | | CLOSE: (131) is inconsistent. % 74.50/11.05 | | | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | | | Case 2: % 74.50/11.05 | | | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | | | | (132) all_10_16 = e0 % 74.50/11.05 | | | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (132) imply: % 74.50/11.05 | | | | | | | | | | | | | | | | | | | (133) all_4_20 = e0 % 74.50/11.05 | | | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | | | | REDUCE: (32), (133) imply: % 74.50/11.05 | | | | | | | | | | | | | | | | | | | (134) op(e0, e0) = e4 % 74.50/11.05 | | | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (46) with e1, all_8_50, e0, e0, % 74.50/11.05 | | | | | | | | | | | | | | | | | | | simplifying with (12), (120) gives: % 74.50/11.05 | | | | | | | | | | | | | | | | | | | (135) all_8_50 = e1 % 74.50/11.05 | | | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (46) with e4, all_8_50, e0, e0, % 74.50/11.05 | | | | | | | | | | | | | | | | | | | simplifying with (120), (134) gives: % 74.50/11.05 | | | | | | | | | | | | | | | | | | | (136) all_8_50 = e4 % 74.50/11.05 | | | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (46) with e2, e4, e1, e2, % 74.50/11.05 | | | | | | | | | | | | | | | | | | | simplifying with (18), (81) gives: % 74.50/11.05 | | | | | | | | | | | | | | | | | | | (137) e4 = e2 % 74.50/11.05 | | | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (46) with e4, all_8_40, e3, e4, % 74.50/11.05 | | | | | | | | | | | | | | | | | | | simplifying with (71), (104) gives: % 74.50/11.05 | | | | | | | | | | | | | | | | | | | (138) all_8_40 = e4 % 74.50/11.05 | | | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (46) with e3, all_8_40, e3, e4, % 74.50/11.05 | | | | | | | | | | | | | | | | | | | simplifying with (65), (104) gives: % 74.50/11.05 | | | | | | | | | | | | | | | | | | | (139) all_8_40 = e3 % 74.50/11.05 | | | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (138), (139) imply: % 74.50/11.05 | | | | | | | | | | | | | | | | | | | (140) e4 = e3 % 74.50/11.05 | | | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (135), (136) imply: % 74.50/11.05 | | | | | | | | | | | | | | | | | | | (141) e4 = e1 % 74.50/11.05 | | | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (137), (140) imply: % 74.50/11.05 | | | | | | | | | | | | | | | | | | | (142) e3 = e2 % 74.50/11.05 | | | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (141) imply: % 74.50/11.05 | | | | | | | | | | | | | | | | | | | (143) e3 = e1 % 74.50/11.05 | | | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (142), (143) imply: % 74.50/11.05 | | | | | | | | | | | | | | | | | | | (144) e2 = e1 % 74.50/11.05 | | | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | | | | SIMP: (144) implies: % 74.50/11.05 | | | | | | | | | | | | | | | | | | | (145) e2 = e1 % 74.50/11.05 | | | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | | | | REDUCE: (80), (145) imply: % 74.50/11.05 | | | | | | | | | | | | | | | | | | | (146) $false % 74.50/11.05 | | | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | | | | CLOSE: (146) is inconsistent. % 74.50/11.05 | | | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | | | End of split % 74.50/11.05 | | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | | End of split % 74.50/11.05 | | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | | End of split % 74.50/11.05 | | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | | End of split % 74.50/11.05 | | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | | End of split % 74.50/11.05 | | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | End of split % 74.50/11.05 | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | Case 2: % 74.50/11.05 | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | (147) ~ (all_10_9 = e3) % 74.50/11.05 | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | REDUCE: (35), (147) imply: % 74.50/11.05 | | | | | | | | | | | | | (148) ~ (all_4_15 = e3) % 74.50/11.05 | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | | REF_CLOSE: (10), (17), (35), (87), (148) are inconsistent by % 74.50/11.05 | | | | | | | | | | | | | sub-proof #63. % 74.50/11.05 | | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | End of split % 74.50/11.05 | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | Case 2: % 74.50/11.05 | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | (149) all_6_21 = e0 % 74.50/11.05 | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | COMBINE_EQS: (25), (149) imply: % 74.50/11.05 | | | | | | | | | | | | (150) all_4_9 = e0 % 74.50/11.05 | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | REDUCE: (3), (150) imply: % 74.50/11.05 | | | | | | | | | | | | (151) $false % 74.50/11.05 | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | | CLOSE: (151) is inconsistent. % 74.50/11.05 | | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | | End of split % 74.50/11.05 | | | | | | | | | | | % 74.50/11.05 | | | | | | | | | | End of split % 74.50/11.05 | | | | | | | | | | % 74.50/11.05 | | | | | | | | | End of split % 74.50/11.05 | | | | | | | | | % 74.50/11.05 | | | | | | | | End of split % 74.50/11.05 | | | | | | | | % 74.50/11.05 | | | | | | | End of split % 74.50/11.05 | | | | | | | % 74.50/11.05 | | | | | | Case 2: % 74.50/11.05 | | | | | | | % 74.50/11.05 | | | | | | | (152) ~ (all_10_4 = e1) % 74.50/11.05 | | | | | | | % 74.50/11.05 | | | | | | | REDUCE: (7), (152) imply: % 74.50/11.05 | | | | | | | (153) ~ (all_4_10 = e1) % 74.50/11.05 | | | | | | | % 74.50/11.05 | | | | | | | REF_CLOSE: (4), (23), (47), (49), (70), (153) are inconsistent by % 74.50/11.05 | | | | | | | sub-proof #161. % 74.50/11.05 | | | | | | | % 74.50/11.05 | | | | | | End of split % 74.50/11.05 | | | | | | % 74.50/11.05 | | | | | End of split % 74.50/11.05 | | | | | % 74.50/11.05 | | | | End of split % 74.50/11.05 | | | | % 74.50/11.05 | | | Case 2: % 74.50/11.05 | | | | % 74.50/11.05 | | | | (154) all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | all_10_21 = e4 % 74.50/11.05 | | | | % 74.50/11.05 | | | | REF_CLOSE: (19), (20), (22), (38), (43), (44), (48), (55), (154) are % 74.50/11.05 | | | | inconsistent by sub-proof #28. % 74.50/11.05 | | | | % 74.50/11.05 | | | End of split % 74.50/11.05 | | | % 74.50/11.05 | | Case 2: % 74.50/11.05 | | | % 74.50/11.05 | | | (155) all_10_6 = e3 | all_10_12 = e3 | all_10_20 = e3 % 74.50/11.05 | | | % 74.50/11.05 | | | REF_CLOSE: (9), (14), (16), (28), (40), (45), (155) are inconsistent by % 74.50/11.05 | | | sub-proof #98. % 74.50/11.05 | | | % 74.50/11.05 | | End of split % 74.50/11.05 | | % 74.50/11.05 | End of split % 74.50/11.05 | % 74.50/11.05 End of proof % 74.50/11.05 % 74.50/11.05 Sub-proof #28 shows that the following formulas are inconsistent: % 74.50/11.05 ---------------------------------------------------------------- % 74.50/11.05 (1) ~ (e4 = e0) % 74.50/11.05 (2) all_10_3 = e0 % 74.50/11.05 (3) all_10_21 = all_4_9 % 74.50/11.05 (4) ~ (all_4_9 = e4) % 74.50/11.05 (5) all_10_13 = e2 % 74.50/11.05 (6) ~ (e4 = e2) % 74.50/11.05 (7) ~ (e4 = e1) % 74.50/11.05 (8) all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | all_10_21 = e4 % 74.50/11.05 (9) all_10_7 = e1 % 74.50/11.05 % 74.50/11.05 Begin of proof % 74.50/11.05 | % 74.50/11.05 | BETA: splitting (8) gives: % 74.50/11.05 | % 74.50/11.05 | Case 1: % 74.50/11.05 | | % 74.50/11.05 | | (10) all_10_3 = e4 % 74.50/11.05 | | % 74.50/11.05 | | REF_CLOSE: (1), (2), (10) are inconsistent by sub-proof #45. % 74.50/11.05 | | % 74.50/11.05 | Case 2: % 74.50/11.05 | | % 74.50/11.05 | | (11) all_10_7 = e4 | all_10_13 = e4 | all_10_21 = e4 % 74.50/11.05 | | % 74.50/11.05 | | BETA: splitting (11) gives: % 74.50/11.05 | | % 74.50/11.05 | | Case 1: % 74.50/11.05 | | | % 74.50/11.05 | | | (12) all_10_7 = e4 % 74.50/11.05 | | | % 74.50/11.05 | | | COMBINE_EQS: (9), (12) imply: % 74.50/11.05 | | | (13) e4 = e1 % 74.50/11.05 | | | % 74.50/11.05 | | | SIMP: (13) implies: % 74.50/11.05 | | | (14) e4 = e1 % 74.50/11.05 | | | % 74.50/11.05 | | | REDUCE: (7), (14) imply: % 74.50/11.05 | | | (15) $false % 74.50/11.05 | | | % 74.50/11.05 | | | CLOSE: (15) is inconsistent. % 74.50/11.05 | | | % 74.50/11.05 | | Case 2: % 74.50/11.05 | | | % 74.50/11.05 | | | (16) all_10_13 = e4 | all_10_21 = e4 % 74.50/11.05 | | | % 74.50/11.05 | | | BETA: splitting (16) gives: % 74.50/11.05 | | | % 74.50/11.05 | | | Case 1: % 74.50/11.05 | | | | % 74.50/11.05 | | | | (17) all_10_13 = e4 % 74.50/11.05 | | | | % 74.50/11.05 | | | | COMBINE_EQS: (5), (17) imply: % 74.50/11.05 | | | | (18) e4 = e2 % 74.50/11.05 | | | | % 74.50/11.05 | | | | REDUCE: (6), (18) imply: % 74.50/11.05 | | | | (19) $false % 74.50/11.05 | | | | % 74.50/11.05 | | | | CLOSE: (19) is inconsistent. % 74.50/11.05 | | | | % 74.50/11.05 | | | Case 2: % 74.50/11.05 | | | | % 74.50/11.05 | | | | (20) all_10_21 = e4 % 74.50/11.05 | | | | % 74.50/11.05 | | | | COMBINE_EQS: (3), (20) imply: % 74.50/11.05 | | | | (21) all_4_9 = e4 % 74.50/11.05 | | | | % 74.50/11.05 | | | | SIMP: (21) implies: % 74.50/11.05 | | | | (22) all_4_9 = e4 % 74.50/11.05 | | | | % 74.50/11.05 | | | | REDUCE: (4), (22) imply: % 74.50/11.05 | | | | (23) $false % 74.50/11.05 | | | | % 74.50/11.05 | | | | CLOSE: (23) is inconsistent. % 74.50/11.05 | | | | % 74.50/11.05 | | | End of split % 74.50/11.05 | | | % 74.50/11.05 | | End of split % 74.50/11.05 | | % 74.50/11.05 | End of split % 74.50/11.05 | % 74.50/11.05 End of proof % 74.50/11.05 % 74.50/11.05 Sub-proof #29 shows that the following formulas are inconsistent: % 74.50/11.05 ---------------------------------------------------------------- % 74.50/11.05 (1) all_10_22 = e2 % 74.50/11.05 (2) all_10_22 = e0 % 74.50/11.05 (3) ~ (e2 = e0) % 74.50/11.05 % 74.50/11.05 Begin of proof % 74.50/11.05 | % 74.50/11.05 | COMBINE_EQS: (1), (2) imply: % 74.50/11.05 | (4) e2 = e0 % 74.50/11.05 | % 74.50/11.05 | SIMP: (4) implies: % 74.50/11.05 | (5) e2 = e0 % 74.50/11.05 | % 74.50/11.05 | REDUCE: (3), (5) imply: % 74.50/11.05 | (6) $false % 74.50/11.05 | % 74.50/11.05 | CLOSE: (6) is inconsistent. % 74.50/11.05 | % 74.50/11.05 End of proof % 74.50/11.05 % 74.50/11.05 Sub-proof #30 shows that the following formulas are inconsistent: % 74.50/11.05 ---------------------------------------------------------------- % 74.50/11.05 (1) all_10_21 = e3 % 74.50/11.05 (2) all_10_21 = e0 % 74.50/11.05 (3) ~ (e3 = e0) % 74.50/11.05 % 74.50/11.05 Begin of proof % 74.50/11.05 | % 74.50/11.05 | COMBINE_EQS: (1), (2) imply: % 74.50/11.05 | (4) e3 = e0 % 74.50/11.05 | % 74.50/11.05 | SIMP: (4) implies: % 74.50/11.05 | (5) e3 = e0 % 74.50/11.05 | % 74.50/11.05 | REDUCE: (3), (5) imply: % 74.50/11.05 | (6) $false % 74.50/11.05 | % 74.50/11.05 | CLOSE: (6) is inconsistent. % 74.50/11.05 | % 74.50/11.05 End of proof % 74.50/11.05 % 74.50/11.05 Sub-proof #31 shows that the following formulas are inconsistent: % 74.50/11.05 ---------------------------------------------------------------- % 74.50/11.05 (1) all_10_4 = e3 % 74.50/11.05 (2) all_10_4 = e1 % 74.50/11.05 (3) ~ (e3 = e1) % 74.50/11.05 % 74.50/11.05 Begin of proof % 74.50/11.05 | % 74.50/11.05 | COMBINE_EQS: (1), (2) imply: % 74.50/11.05 | (4) e3 = e1 % 74.50/11.05 | % 74.50/11.05 | SIMP: (4) implies: % 74.50/11.05 | (5) e3 = e1 % 74.50/11.05 | % 74.50/11.05 | REDUCE: (3), (5) imply: % 74.50/11.05 | (6) $false % 74.50/11.05 | % 74.50/11.05 | CLOSE: (6) is inconsistent. % 74.50/11.05 | % 74.50/11.05 End of proof % 74.50/11.05 % 74.50/11.05 Sub-proof #32 shows that the following formulas are inconsistent: % 74.50/11.05 ---------------------------------------------------------------- % 74.50/11.05 (1) ~ (all_4_19 = e4) % 74.50/11.05 (2) ~ (all_4_1 = e0) % 74.50/11.05 (3) all_10_22 = e2 % 74.50/11.05 (4) all_10_24 = e1 % 74.50/11.05 (5) op(e3, e4) = all_4_1 % 74.50/11.05 (6) op(e3, all_4_9) = e0 % 74.50/11.05 (7) all_10_23 = all_4_19 % 74.50/11.05 (8) all_10_21 = all_4_9 % 74.50/11.05 (9) ~ (e4 = e2) % 74.50/11.05 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.50/11.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.50/11.05 (11) all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | all_10_24 = e4 % 74.50/11.05 (12) ~ (e4 = e1) % 74.50/11.05 % 74.50/11.05 Begin of proof % 74.50/11.05 | % 74.50/11.05 | BETA: splitting (11) gives: % 74.50/11.05 | % 74.50/11.05 | Case 1: % 74.50/11.05 | | % 74.50/11.05 | | (13) all_10_21 = e4 % 74.50/11.05 | | % 74.50/11.05 | | COMBINE_EQS: (8), (13) imply: % 74.50/11.05 | | (14) all_4_9 = e4 % 74.50/11.05 | | % 74.50/11.05 | | SIMP: (14) implies: % 74.50/11.05 | | (15) all_4_9 = e4 % 74.50/11.05 | | % 74.50/11.05 | | REDUCE: (6), (15) imply: % 74.50/11.05 | | (16) op(e3, e4) = e0 % 74.50/11.05 | | % 74.50/11.05 | | GROUND_INST: instantiating (10) with all_4_1, e0, e4, e3, simplifying with % 74.50/11.05 | | (5), (16) gives: % 74.50/11.05 | | (17) all_4_1 = e0 % 74.50/11.05 | | % 74.50/11.05 | | REDUCE: (2), (17) imply: % 74.50/11.05 | | (18) $false % 74.50/11.05 | | % 74.50/11.05 | | CLOSE: (18) is inconsistent. % 74.50/11.05 | | % 74.50/11.05 | Case 2: % 74.50/11.05 | | % 74.50/11.05 | | (19) all_10_22 = e4 | all_10_23 = e4 | all_10_24 = e4 % 74.50/11.05 | | % 74.50/11.05 | | REF_CLOSE: (1), (3), (4), (7), (9), (12), (19) are inconsistent by sub-proof % 74.50/11.05 | | #36. % 74.50/11.05 | | % 74.50/11.05 | End of split % 74.50/11.05 | % 74.50/11.05 End of proof % 74.50/11.05 % 74.50/11.05 Sub-proof #33 shows that the following formulas are inconsistent: % 74.50/11.05 ---------------------------------------------------------------- % 74.50/11.05 (1) ~ (all_4_1 = e0) % 74.50/11.05 (2) all_10_8 = e3 % 74.50/11.05 (3) ~ (all_4_1 = all_4_2) % 74.50/11.05 (4) all_10_14 = e0 % 74.50/11.05 (5) op(e3, all_4_8) = e1 % 74.50/11.05 (6) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | all_6_5 = e0 % 74.50/11.05 (7) ~ (all_4_11 = e0) % 74.50/11.05 (8) ~ (all_4_11 = e3) % 74.50/11.05 (9) ~ (e3 = e2) % 74.50/11.05 (10) all_10_4 = all_4_10 % 74.50/11.05 (11) all_10_22 = e2 % 74.50/11.05 (12) all_10_20 = e4 % 74.50/11.05 (13) all_10_15 = e4 % 74.50/11.05 (14) ~ (all_4_20 = all_4_21) % 74.50/11.05 (15) all_6_9 = all_4_21 % 74.50/11.05 (16) all_10_2 = e0 | all_10_6 = e0 | all_10_12 = e0 | all_10_20 = e0 % 74.50/11.05 (17) all_10_12 = all_4_3 % 74.50/11.05 (18) ~ (all_4_2 = e3) % 74.50/11.05 (19) ~ (e3 = e1) % 74.50/11.05 (20) all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e1 | all_6_14 = e0 % 74.50/11.05 (21) all_10_16 = all_4_20 % 74.50/11.05 (22) ~ (e4 = e0) % 74.50/11.05 (23) ~ (all_4_2 = all_4_22) % 74.50/11.05 (24) ~ (all_4_22 = e1) % 74.50/11.05 (25) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e1 | all_6_9 = e0 % 74.50/11.05 (26) all_10_17 = all_4_21 % 74.50/11.05 (27) all_10_12 = e1 | all_10_13 = e1 | all_10_14 = e1 | all_10_15 = e1 | % 74.50/11.05 all_10_19 = e1 % 74.50/11.05 (28) all_6_5 = all_4_1 % 74.50/11.05 (29) ~ (e2 = e1) % 74.50/11.05 (30) ~ (all_4_1 = all_4_11) % 74.50/11.05 (31) ~ (all_4_1 = all_4_21) % 74.50/11.05 (32) ~ (e4 = e3) % 74.50/11.05 (33) all_10_2 = all_4_1 % 74.50/11.05 (34) ~ (all_4_3 = e0) % 74.50/11.05 (35) ~ (all_4_22 = e3) % 74.50/11.05 (36) ~ (all_4_21 = e1) % 74.50/11.05 (37) ~ (all_4_10 = e4) % 74.50/11.05 (38) all_10_13 = all_4_8 % 74.50/11.05 (39) all_6_14 = all_4_22 % 74.50/11.05 (40) ~ (all_4_2 = e2) % 74.50/11.05 (41) ~ (all_4_2 = e4) % 74.50/11.05 (42) all_10_19 = e2 % 74.50/11.05 (43) all_10_0 = e3 | all_10_2 = e3 | all_10_6 = e3 | all_10_12 = e3 | % 74.50/11.05 all_10_20 = e3 % 74.50/11.05 (44) ~ (e1 = e0) % 74.50/11.05 (45) ~ (all_4_21 = e0) % 74.50/11.05 (46) ~ (e4 = e2) % 74.50/11.05 (47) ~ (all_4_11 = all_4_21) % 74.50/11.05 (48) all_10_6 = all_4_2 % 74.50/11.05 (49) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.50/11.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.50/11.05 (50) all_10_5 = all_4_11 % 74.50/11.05 (51) ~ (e4 = e1) % 74.50/11.06 (52) all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | % 74.50/11.06 all_10_22 = e4 % 74.50/11.06 (53) all_10_0 = e2 % 74.50/11.06 (54) all_10_18 = all_4_22 % 74.50/11.06 (55) ~ (all_4_8 = e2) % 74.50/11.06 (56) all_10_16 = e0 | all_10_17 = e0 | all_10_18 = e0 | all_10_19 = e0 % 74.50/11.06 (57) op(e3, e1) = e2 % 74.50/11.06 (58) all_10_16 = e3 | all_10_17 = e3 | all_10_18 = e3 | all_10_19 = e3 | % 74.50/11.06 all_10_24 = e3 % 74.50/11.06 % 74.50/11.06 Begin of proof % 74.50/11.06 | % 74.50/11.06 | BETA: splitting (52) gives: % 74.50/11.06 | % 74.50/11.06 | Case 1: % 74.50/11.06 | | % 74.50/11.06 | | (59) all_10_4 = e4 % 74.50/11.06 | | % 74.50/11.06 | | COMBINE_EQS: (10), (59) imply: % 74.50/11.06 | | (60) all_4_10 = e4 % 74.50/11.06 | | % 74.50/11.06 | | REDUCE: (37), (60) imply: % 74.50/11.06 | | (61) $false % 74.50/11.06 | | % 74.50/11.06 | | CLOSE: (61) is inconsistent. % 74.50/11.06 | | % 74.50/11.06 | Case 2: % 74.50/11.06 | | % 74.50/11.06 | | (62) all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | all_10_22 = e4 % 74.50/11.06 | | % 74.50/11.06 | | BETA: splitting (62) gives: % 74.50/11.06 | | % 74.50/11.06 | | Case 1: % 74.50/11.06 | | | % 74.50/11.06 | | | (63) all_10_5 = e4 % 74.50/11.06 | | | % 74.50/11.06 | | | COMBINE_EQS: (50), (63) imply: % 74.50/11.06 | | | (64) all_4_11 = e4 % 74.50/11.06 | | | % 74.50/11.06 | | | SIMP: (64) implies: % 74.50/11.06 | | | (65) all_4_11 = e4 % 74.50/11.06 | | | % 74.50/11.06 | | | REDUCE: (30), (65) imply: % 74.50/11.06 | | | (66) ~ (all_4_1 = e4) % 74.50/11.06 | | | % 74.50/11.06 | | | REDUCE: (47), (65) imply: % 74.50/11.06 | | | (67) ~ (all_4_21 = e4) % 74.50/11.06 | | | % 74.50/11.06 | | | SIMP: (67) implies: % 74.50/11.06 | | | (68) ~ (all_4_21 = e4) % 74.50/11.06 | | | % 74.50/11.06 | | | BETA: splitting (16) gives: % 74.50/11.06 | | | % 74.50/11.06 | | | Case 1: % 74.50/11.06 | | | | % 74.50/11.06 | | | | (69) all_10_2 = e0 % 74.50/11.06 | | | | % 74.50/11.06 | | | | REF_CLOSE: (1), (33), (69) are inconsistent by sub-proof #119. % 74.50/11.06 | | | | % 74.50/11.06 | | | Case 2: % 74.50/11.06 | | | | % 74.50/11.06 | | | | (70) all_10_6 = e0 | all_10_12 = e0 | all_10_20 = e0 % 74.50/11.06 | | | | % 74.50/11.06 | | | | BETA: splitting (6) gives: % 74.50/11.06 | | | | % 74.50/11.06 | | | | Case 1: % 74.50/11.06 | | | | | % 74.50/11.06 | | | | | (71) all_6_5 = e4 % 74.50/11.06 | | | | | % 74.50/11.06 | | | | | REF_CLOSE: (28), (66), (71) are inconsistent by sub-proof #81. % 74.50/11.06 | | | | | % 74.50/11.06 | | | | Case 2: % 74.50/11.06 | | | | | % 74.50/11.06 | | | | | (72) all_6_5 = e3 | all_6_5 = e1 | all_6_5 = e0 % 74.50/11.06 | | | | | % 74.50/11.06 | | | | | BETA: splitting (72) gives: % 74.50/11.06 | | | | | % 74.50/11.06 | | | | | Case 1: % 74.50/11.06 | | | | | | % 74.50/11.06 | | | | | | (73) all_6_5 = e1 % 74.50/11.06 | | | | | | % 74.50/11.06 | | | | | | COMBINE_EQS: (28), (73) imply: % 74.50/11.06 | | | | | | (74) all_4_1 = e1 % 74.50/11.06 | | | | | | % 74.50/11.06 | | | | | | SIMP: (74) implies: % 74.50/11.06 | | | | | | (75) all_4_1 = e1 % 74.50/11.06 | | | | | | % 74.50/11.06 | | | | | | COMBINE_EQS: (33), (75) imply: % 74.50/11.06 | | | | | | (76) all_10_2 = e1 % 74.50/11.06 | | | | | | % 74.50/11.06 | | | | | | BETA: splitting (43) gives: % 74.50/11.06 | | | | | | % 74.50/11.06 | | | | | | Case 1: % 74.50/11.06 | | | | | | | % 74.50/11.06 | | | | | | | (77) all_10_0 = e3 % 74.50/11.06 | | | | | | | % 74.50/11.06 | | | | | | | REF_CLOSE: (9), (53), (77) are inconsistent by sub-proof #104. % 74.50/11.06 | | | | | | | % 74.50/11.06 | | | | | | Case 2: % 74.50/11.06 | | | | | | | % 74.50/11.06 | | | | | | | (78) all_10_2 = e3 | all_10_6 = e3 | all_10_12 = e3 | all_10_20 % 74.50/11.06 | | | | | | | = e3 % 74.50/11.06 | | | | | | | % 74.50/11.06 | | | | | | | BETA: splitting (78) gives: % 74.50/11.06 | | | | | | | % 74.50/11.06 | | | | | | | Case 1: % 74.50/11.06 | | | | | | | | % 74.50/11.06 | | | | | | | | (79) all_10_2 = e3 % 74.50/11.06 | | | | | | | | % 74.50/11.06 | | | | | | | | COMBINE_EQS: (76), (79) imply: % 74.50/11.06 | | | | | | | | (80) e3 = e1 % 74.50/11.06 | | | | | | | | % 74.50/11.06 | | | | | | | | REDUCE: (19), (80) imply: % 74.50/11.06 | | | | | | | | (81) $false % 74.50/11.06 | | | | | | | | % 74.50/11.06 | | | | | | | | CLOSE: (81) is inconsistent. % 74.50/11.06 | | | | | | | | % 74.50/11.06 | | | | | | | Case 2: % 74.50/11.06 | | | | | | | | % 74.50/11.06 | | | | | | | | (82) ~ (all_10_2 = e3) % 74.50/11.06 | | | | | | | | (83) all_10_6 = e3 | all_10_12 = e3 | all_10_20 = e3 % 74.50/11.06 | | | | | | | | % 74.50/11.06 | | | | | | | | REDUCE: (76), (82) imply: % 74.50/11.06 | | | | | | | | (84) ~ (e3 = e1) % 74.50/11.06 | | | | | | | | % 74.50/11.06 | | | | | | | | BETA: splitting (83) gives: % 74.50/11.06 | | | | | | | | % 74.50/11.06 | | | | | | | | Case 1: % 74.50/11.06 | | | | | | | | | % 74.50/11.06 | | | | | | | | | (85) all_10_6 = e3 % 74.50/11.06 | | | | | | | | | % 74.50/11.06 | | | | | | | | | REF_CLOSE: (18), (48), (85) are inconsistent by sub-proof % 74.50/11.06 | | | | | | | | | #100. % 74.50/11.06 | | | | | | | | | % 74.50/11.06 | | | | | | | | Case 2: % 74.50/11.06 | | | | | | | | | % 74.50/11.06 | | | | | | | | | (86) all_10_12 = e3 | all_10_20 = e3 % 74.50/11.06 | | | | | | | | | % 74.50/11.06 | | | | | | | | | BETA: splitting (27) gives: % 74.50/11.06 | | | | | | | | | % 74.50/11.06 | | | | | | | | | Case 1: % 74.50/11.06 | | | | | | | | | | % 74.50/11.06 | | | | | | | | | | (87) all_10_12 = e1 % 74.50/11.06 | | | | | | | | | | % 74.50/11.06 | | | | | | | | | | REF_CLOSE: (12), (19), (32), (86), (87) are inconsistent by % 74.50/11.06 | | | | | | | | | | sub-proof #99. % 74.50/11.06 | | | | | | | | | | % 74.50/11.06 | | | | | | | | | Case 2: % 74.50/11.06 | | | | | | | | | | % 74.50/11.06 | | | | | | | | | | (88) all_10_13 = e1 | all_10_14 = e1 | all_10_15 = e1 | % 74.50/11.06 | | | | | | | | | | all_10_19 = e1 % 74.50/11.06 | | | | | | | | | | % 74.50/11.06 | | | | | | | | | | REF_CLOSE: (4), (5), (13), (29), (38), (42), (44), (49), % 74.50/11.06 | | | | | | | | | | (51), (55), (57), (88) are inconsistent by % 74.50/11.06 | | | | | | | | | | sub-proof #34. % 74.50/11.06 | | | | | | | | | | % 74.50/11.06 | | | | | | | | | End of split % 74.50/11.06 | | | | | | | | | % 74.50/11.06 | | | | | | | | End of split % 74.50/11.06 | | | | | | | | % 74.50/11.06 | | | | | | | End of split % 74.50/11.06 | | | | | | | % 74.50/11.06 | | | | | | End of split % 74.50/11.06 | | | | | | % 74.50/11.06 | | | | | Case 2: % 74.50/11.06 | | | | | | % 74.50/11.06 | | | | | | (89) all_6_5 = e3 | all_6_5 = e0 % 74.50/11.06 | | | | | | % 74.50/11.06 | | | | | | REF_CLOSE: (3), (12), (14), (15), (17), (18), (20), (21), (22), % 74.50/11.06 | | | | | | (23), (24), (25), (26), (28), (31), (34), (35), (36), % 74.50/11.06 | | | | | | (39), (40), (41), (42), (45), (48), (54), (56), (58), % 74.50/11.06 | | | | | | (68), (70), (89) are inconsistent by sub-proof #47. % 74.50/11.06 | | | | | | % 74.50/11.06 | | | | | End of split % 74.50/11.06 | | | | | % 74.50/11.06 | | | | End of split % 74.50/11.06 | | | | % 74.50/11.06 | | | End of split % 74.50/11.06 | | | % 74.50/11.06 | | Case 2: % 74.50/11.06 | | | % 74.50/11.06 | | | (90) all_10_8 = e4 | all_10_14 = e4 | all_10_22 = e4 % 74.50/11.06 | | | % 74.50/11.06 | | | REF_CLOSE: (2), (4), (11), (22), (32), (46), (90) are inconsistent by % 74.50/11.06 | | | sub-proof #115. % 74.50/11.06 | | | % 74.50/11.06 | | End of split % 74.50/11.06 | | % 74.50/11.06 | End of split % 74.50/11.06 | % 74.50/11.06 End of proof % 74.50/11.06 % 74.50/11.06 Sub-proof #34 shows that the following formulas are inconsistent: % 74.50/11.06 ---------------------------------------------------------------- % 74.50/11.06 (1) all_10_14 = e0 % 74.50/11.06 (2) op(e3, all_4_8) = e1 % 74.50/11.06 (3) all_10_15 = e4 % 74.50/11.06 (4) all_10_13 = e1 | all_10_14 = e1 | all_10_15 = e1 | all_10_19 = e1 % 74.50/11.06 (5) ~ (e2 = e1) % 74.50/11.06 (6) all_10_13 = all_4_8 % 74.50/11.06 (7) all_10_19 = e2 % 74.50/11.06 (8) ~ (e1 = e0) % 74.50/11.06 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.50/11.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.50/11.06 (10) ~ (e4 = e1) % 74.50/11.06 (11) ~ (all_4_8 = e2) % 74.50/11.06 (12) op(e3, e1) = e2 % 74.50/11.06 % 74.50/11.06 Begin of proof % 74.50/11.06 | % 74.50/11.06 | BETA: splitting (4) gives: % 74.50/11.06 | % 74.50/11.06 | Case 1: % 74.50/11.06 | | % 74.50/11.06 | | (13) all_10_13 = e1 % 74.50/11.06 | | % 74.50/11.06 | | COMBINE_EQS: (6), (13) imply: % 74.50/11.06 | | (14) all_4_8 = e1 % 74.50/11.06 | | % 74.50/11.06 | | SIMP: (14) implies: % 74.50/11.06 | | (15) all_4_8 = e1 % 74.50/11.06 | | % 74.50/11.06 | | REDUCE: (11), (15) imply: % 74.50/11.06 | | (16) ~ (e2 = e1) % 74.50/11.06 | | % 74.50/11.06 | | REDUCE: (2), (15) imply: % 74.50/11.06 | | (17) op(e3, e1) = e1 % 74.50/11.06 | | % 74.50/11.06 | | GROUND_INST: instantiating (9) with e2, e1, e1, e3, simplifying with (12), % 74.50/11.06 | | (17) gives: % 74.50/11.06 | | (18) e2 = e1 % 74.50/11.06 | | % 74.50/11.06 | | REDUCE: (5), (18) imply: % 74.50/11.06 | | (19) $false % 74.50/11.06 | | % 74.50/11.06 | | CLOSE: (19) is inconsistent. % 74.50/11.06 | | % 74.50/11.06 | Case 2: % 74.50/11.06 | | % 74.50/11.06 | | (20) all_10_14 = e1 | all_10_15 = e1 | all_10_19 = e1 % 74.50/11.06 | | % 74.50/11.06 | | REF_CLOSE: (1), (3), (5), (7), (8), (10), (20) are inconsistent by sub-proof % 74.50/11.06 | | #58. % 74.50/11.06 | | % 74.50/11.06 | End of split % 74.50/11.06 | % 74.50/11.06 End of proof % 74.50/11.06 % 74.50/11.06 Sub-proof #35 shows that the following formulas are inconsistent: % 74.50/11.06 ---------------------------------------------------------------- % 74.50/11.06 (1) all_8_17 = e2 & ~ (all_8_18 = e3) % 74.50/11.06 (2) all_8_17 = all_4_11 % 74.50/11.06 (3) ~ (all_4_11 = e2) % 74.50/11.06 % 74.50/11.06 Begin of proof % 74.50/11.06 | % 74.50/11.06 | ALPHA: (1) implies: % 74.50/11.06 | (4) all_8_17 = e2 % 74.50/11.06 | % 74.50/11.06 | COMBINE_EQS: (2), (4) imply: % 74.50/11.06 | (5) all_4_11 = e2 % 74.50/11.06 | % 74.50/11.06 | SIMP: (5) implies: % 74.50/11.06 | (6) all_4_11 = e2 % 74.50/11.06 | % 74.50/11.06 | REDUCE: (3), (6) imply: % 74.50/11.06 | (7) $false % 74.50/11.06 | % 74.50/11.06 | CLOSE: (7) is inconsistent. % 74.50/11.06 | % 74.50/11.06 End of proof % 74.50/11.06 % 74.50/11.06 Sub-proof #36 shows that the following formulas are inconsistent: % 74.50/11.06 ---------------------------------------------------------------- % 74.50/11.06 (1) ~ (all_4_19 = e4) % 74.50/11.06 (2) all_10_22 = e2 % 74.50/11.06 (3) all_10_24 = e1 % 74.50/11.06 (4) all_10_23 = all_4_19 % 74.50/11.06 (5) all_10_22 = e4 | all_10_23 = e4 | all_10_24 = e4 % 74.50/11.06 (6) ~ (e4 = e2) % 74.50/11.06 (7) ~ (e4 = e1) % 74.50/11.06 % 74.50/11.06 Begin of proof % 74.50/11.06 | % 74.50/11.06 | BETA: splitting (5) gives: % 74.50/11.06 | % 74.50/11.06 | Case 1: % 74.50/11.06 | | % 74.50/11.06 | | (8) all_10_22 = e4 % 74.50/11.06 | | % 74.50/11.06 | | COMBINE_EQS: (2), (8) imply: % 74.50/11.06 | | (9) e4 = e2 % 74.50/11.06 | | % 74.50/11.06 | | REDUCE: (6), (9) imply: % 74.50/11.06 | | (10) $false % 74.50/11.06 | | % 74.50/11.06 | | CLOSE: (10) is inconsistent. % 74.50/11.06 | | % 74.50/11.06 | Case 2: % 74.50/11.06 | | % 74.50/11.06 | | (11) all_10_23 = e4 | all_10_24 = e4 % 74.50/11.06 | | % 74.50/11.06 | | BETA: splitting (11) gives: % 74.50/11.06 | | % 74.50/11.06 | | Case 1: % 74.50/11.06 | | | % 74.50/11.06 | | | (12) all_10_23 = e4 % 74.50/11.06 | | | % 74.50/11.06 | | | COMBINE_EQS: (4), (12) imply: % 74.50/11.06 | | | (13) all_4_19 = e4 % 74.50/11.06 | | | % 74.50/11.06 | | | SIMP: (13) implies: % 74.50/11.06 | | | (14) all_4_19 = e4 % 74.50/11.06 | | | % 74.50/11.06 | | | REDUCE: (1), (14) imply: % 74.50/11.06 | | | (15) $false % 74.50/11.06 | | | % 74.50/11.06 | | | CLOSE: (15) is inconsistent. % 74.50/11.06 | | | % 74.50/11.06 | | Case 2: % 74.50/11.06 | | | % 74.50/11.06 | | | (16) all_10_24 = e4 % 74.50/11.06 | | | % 74.50/11.06 | | | COMBINE_EQS: (3), (16) imply: % 74.50/11.06 | | | (17) e4 = e1 % 74.50/11.06 | | | % 74.50/11.06 | | | REDUCE: (7), (17) imply: % 74.50/11.06 | | | (18) $false % 74.50/11.06 | | | % 74.50/11.06 | | | CLOSE: (18) is inconsistent. % 74.50/11.06 | | | % 74.50/11.06 | | End of split % 74.50/11.06 | | % 74.50/11.06 | End of split % 74.50/11.06 | % 74.50/11.06 End of proof % 74.50/11.06 % 74.50/11.06 Sub-proof #37 shows that the following formulas are inconsistent: % 74.50/11.06 ---------------------------------------------------------------- % 74.50/11.06 (1) all_10_14 = e0 % 74.50/11.06 (2) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 74.50/11.06 (3) all_10_1 = all_4_5 % 74.50/11.06 (4) all_10_15 = e4 % 74.50/11.06 (5) op(e3, all_4_5) = e4 % 74.50/11.06 (6) ~ (e4 = e0) % 74.50/11.06 (7) all_10_13 = e1 | all_10_14 = e1 | all_10_15 = e1 | all_10_19 = e1 % 74.50/11.06 (8) ~ (e2 = e1) % 74.50/11.06 (9) ~ (all_4_5 = e0) % 74.50/11.06 (10) all_10_13 = all_4_8 % 74.50/11.06 (11) all_10_1 = e3 | all_10_3 = e3 | all_10_7 = e3 | all_10_13 = e3 | % 74.50/11.06 all_10_21 = e3 % 74.50/11.06 (12) all_10_19 = e2 % 74.50/11.06 (13) ~ (e1 = e0) % 74.50/11.06 (14) ~ (all_4_5 = e4) % 74.50/11.06 (15) all_6_1 = all_4_5 % 74.50/11.06 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.50/11.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.50/11.06 (17) op(e3, e3) = e0 % 74.50/11.06 (18) ~ (e4 = e1) % 74.50/11.06 (19) ~ (all_4_5 = all_4_8) % 74.50/11.06 % 74.50/11.06 Begin of proof % 74.50/11.06 | % 74.50/11.06 | BETA: splitting (7) gives: % 74.50/11.06 | % 74.50/11.06 | Case 1: % 74.50/11.06 | | % 74.50/11.06 | | (20) all_10_13 = e1 % 74.50/11.06 | | % 74.50/11.06 | | COMBINE_EQS: (10), (20) imply: % 74.50/11.06 | | (21) all_4_8 = e1 % 74.50/11.06 | | % 74.50/11.06 | | SIMP: (21) implies: % 74.50/11.06 | | (22) all_4_8 = e1 % 74.50/11.06 | | % 74.50/11.06 | | REDUCE: (19), (22) imply: % 74.50/11.06 | | (23) ~ (all_4_5 = e1) % 74.50/11.06 | | % 74.50/11.06 | | REF_CLOSE: (2), (3), (5), (6), (9), (11), (14), (15), (16), (17), (23) are % 74.50/11.06 | | inconsistent by sub-proof #38. % 74.50/11.06 | | % 74.50/11.06 | Case 2: % 74.50/11.06 | | % 74.50/11.06 | | (24) all_10_14 = e1 | all_10_15 = e1 | all_10_19 = e1 % 74.50/11.06 | | % 74.50/11.06 | | REF_CLOSE: (1), (4), (8), (12), (13), (18), (24) are inconsistent by % 74.50/11.06 | | sub-proof #58. % 74.50/11.06 | | % 74.50/11.06 | End of split % 74.50/11.06 | % 74.50/11.06 End of proof % 74.50/11.06 % 74.50/11.06 Sub-proof #38 shows that the following formulas are inconsistent: % 74.50/11.06 ---------------------------------------------------------------- % 74.50/11.06 (1) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 74.50/11.06 (2) all_10_1 = all_4_5 % 74.50/11.06 (3) op(e3, all_4_5) = e4 % 74.50/11.06 (4) ~ (e4 = e0) % 74.50/11.06 (5) ~ (all_4_5 = e1) % 74.50/11.06 (6) ~ (all_4_5 = e0) % 74.50/11.06 (7) all_10_1 = e3 | all_10_3 = e3 | all_10_7 = e3 | all_10_13 = e3 | % 74.50/11.06 all_10_21 = e3 % 74.50/11.06 (8) ~ (all_4_5 = e4) % 74.50/11.06 (9) all_6_1 = all_4_5 % 74.50/11.07 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.50/11.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.50/11.07 (11) op(e3, e3) = e0 % 74.50/11.07 % 74.50/11.07 Begin of proof % 74.50/11.07 | % 74.50/11.07 | BETA: splitting (7) gives: % 74.50/11.07 | % 74.50/11.07 | Case 1: % 74.50/11.07 | | % 74.50/11.07 | | (12) all_10_1 = e3 % 74.50/11.07 | | % 74.50/11.07 | | COMBINE_EQS: (2), (12) imply: % 74.50/11.07 | | (13) all_4_5 = e3 % 74.50/11.07 | | % 74.50/11.07 | | REDUCE: (3), (13) imply: % 74.50/11.07 | | (14) op(e3, e3) = e4 % 74.50/11.07 | | % 74.50/11.07 | | GROUND_INST: instantiating (10) with e0, e4, e3, e3, simplifying with (11), % 74.50/11.07 | | (14) gives: % 74.50/11.07 | | (15) e4 = e0 % 74.50/11.07 | | % 74.50/11.07 | | REDUCE: (4), (15) imply: % 74.50/11.07 | | (16) $false % 74.50/11.07 | | % 74.50/11.07 | | CLOSE: (16) is inconsistent. % 74.50/11.07 | | % 74.50/11.07 | Case 2: % 74.50/11.07 | | % 74.50/11.07 | | (17) ~ (all_10_1 = e3) % 74.50/11.07 | | % 74.50/11.07 | | REDUCE: (2), (17) imply: % 74.50/11.07 | | (18) ~ (all_4_5 = e3) % 74.50/11.07 | | % 74.50/11.07 | | REF_CLOSE: (1), (5), (6), (8), (9), (18) are inconsistent by sub-proof #134. % 74.50/11.07 | | % 74.50/11.07 | End of split % 74.50/11.07 | % 74.50/11.07 End of proof % 74.50/11.07 % 74.50/11.07 Sub-proof #39 shows that the following formulas are inconsistent: % 74.50/11.07 ---------------------------------------------------------------- % 74.50/11.07 (1) all_10_14 = e0 % 74.50/11.07 (2) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 74.50/11.07 (3) ~ (all_4_10 = e3) % 74.50/11.07 (4) ~ (e3 = e2) % 74.50/11.07 (5) all_10_4 = all_4_10 % 74.50/11.07 (6) all_10_15 = e4 % 74.50/11.07 (7) ~ (e3 = e1) % 74.50/11.07 (8) ~ (all_4_10 = e0) % 74.50/11.07 (9) op(e4, e4) = e2 % 74.50/11.07 (10) ~ (all_8_27 = e2) % 74.50/11.07 (11) ~ (e4 = e3) % 74.50/11.07 (12) ~ (all_4_5 = e0) % 74.50/11.07 (13) all_10_13 = all_4_8 % 74.50/11.07 (14) all_10_12 = e3 | all_10_13 = e3 | all_10_14 = e3 | all_10_15 = e3 | % 74.50/11.07 all_10_19 = e3 % 74.50/11.07 (15) all_10_19 = e2 % 74.50/11.07 (16) all_10_12 = e1 % 74.50/11.07 (17) ~ (all_4_5 = e4) % 74.50/11.07 (18) all_6_1 = all_4_5 % 74.50/11.07 (19) ~ (all_4_5 = all_4_10) % 74.50/11.07 (20) op(e4, all_4_10) = all_8_27 % 74.50/11.07 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.50/11.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.50/11.07 (22) all_6_2 = all_4_10 % 74.50/11.07 (23) all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | % 74.50/11.07 all_10_22 = e4 % 74.50/11.07 (24) ~ (e3 = e0) % 74.50/11.07 (25) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.50/11.07 (26) ~ (all_4_5 = all_4_8) % 74.50/11.07 (27) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 74.50/11.07 all_10_22 = e1 % 74.50/11.07 % 74.50/11.07 Begin of proof % 74.50/11.07 | % 74.50/11.07 | BETA: splitting (14) gives: % 74.50/11.07 | % 74.50/11.07 | Case 1: % 74.50/11.07 | | % 74.50/11.07 | | (28) all_10_12 = e3 % 74.50/11.07 | | % 74.50/11.07 | | COMBINE_EQS: (16), (28) imply: % 74.50/11.07 | | (29) e3 = e1 % 74.50/11.07 | | % 74.50/11.07 | | REDUCE: (7), (29) imply: % 74.50/11.07 | | (30) $false % 74.50/11.07 | | % 74.50/11.07 | | CLOSE: (30) is inconsistent. % 74.50/11.07 | | % 74.50/11.07 | Case 2: % 74.50/11.07 | | % 74.50/11.07 | | (31) all_10_13 = e3 | all_10_14 = e3 | all_10_15 = e3 | all_10_19 = e3 % 74.50/11.07 | | % 74.50/11.07 | | BETA: splitting (31) gives: % 74.50/11.07 | | % 74.50/11.07 | | Case 1: % 74.50/11.07 | | | % 74.50/11.07 | | | (32) all_10_13 = e3 % 74.50/11.07 | | | % 74.50/11.07 | | | COMBINE_EQS: (13), (32) imply: % 74.50/11.07 | | | (33) all_4_8 = e3 % 74.50/11.07 | | | % 74.50/11.07 | | | SIMP: (33) implies: % 74.50/11.07 | | | (34) all_4_8 = e3 % 74.50/11.07 | | | % 74.50/11.07 | | | REDUCE: (26), (34) imply: % 74.50/11.07 | | | (35) ~ (all_4_5 = e3) % 74.50/11.07 | | | % 74.50/11.07 | | | BETA: splitting (27) gives: % 74.50/11.07 | | | % 74.50/11.07 | | | Case 1: % 74.50/11.07 | | | | % 74.50/11.07 | | | | (36) all_10_4 = e1 % 74.50/11.07 | | | | % 74.50/11.07 | | | | COMBINE_EQS: (5), (36) imply: % 74.50/11.07 | | | | (37) all_4_10 = e1 % 74.50/11.07 | | | | % 74.50/11.07 | | | | REDUCE: (19), (37) imply: % 74.50/11.07 | | | | (38) ~ (all_4_5 = e1) % 74.50/11.07 | | | | % 74.50/11.07 | | | | REF_CLOSE: (2), (12), (17), (18), (35), (38) are inconsistent by % 74.50/11.07 | | | | sub-proof #134. % 74.50/11.07 | | | | % 74.50/11.07 | | | Case 2: % 74.50/11.07 | | | | % 74.50/11.07 | | | | (39) ~ (all_10_4 = e1) % 74.50/11.07 | | | | % 74.50/11.07 | | | | REDUCE: (5), (39) imply: % 74.50/11.07 | | | | (40) ~ (all_4_10 = e1) % 74.50/11.07 | | | | % 74.50/11.07 | | | | REF_CLOSE: (3), (5), (8), (9), (10), (20), (21), (22), (23), (25), (40) % 74.50/11.07 | | | | are inconsistent by sub-proof #160. % 74.50/11.07 | | | | % 74.50/11.07 | | | End of split % 74.50/11.07 | | | % 74.50/11.07 | | Case 2: % 74.50/11.07 | | | % 74.50/11.07 | | | (41) all_10_14 = e3 | all_10_15 = e3 | all_10_19 = e3 % 74.50/11.07 | | | % 74.50/11.07 | | | REF_CLOSE: (1), (4), (6), (11), (15), (24), (41) are inconsistent by % 74.50/11.07 | | | sub-proof #40. % 74.50/11.07 | | | % 74.50/11.07 | | End of split % 74.50/11.07 | | % 74.50/11.07 | End of split % 74.50/11.07 | % 74.50/11.07 End of proof % 74.50/11.07 % 74.50/11.07 Sub-proof #40 shows that the following formulas are inconsistent: % 74.50/11.07 ---------------------------------------------------------------- % 74.50/11.07 (1) all_10_14 = e0 % 74.50/11.07 (2) ~ (e3 = e2) % 74.50/11.07 (3) all_10_15 = e4 % 74.50/11.07 (4) all_10_14 = e3 | all_10_15 = e3 | all_10_19 = e3 % 74.50/11.07 (5) ~ (e4 = e3) % 74.50/11.07 (6) all_10_19 = e2 % 74.50/11.07 (7) ~ (e3 = e0) % 74.50/11.07 % 74.50/11.07 Begin of proof % 74.50/11.07 | % 74.50/11.07 | BETA: splitting (4) gives: % 74.50/11.07 | % 74.50/11.07 | Case 1: % 74.50/11.07 | | % 74.50/11.07 | | (8) all_10_14 = e3 % 74.50/11.07 | | % 74.50/11.07 | | COMBINE_EQS: (1), (8) imply: % 74.50/11.07 | | (9) e3 = e0 % 74.50/11.07 | | % 74.50/11.07 | | REDUCE: (7), (9) imply: % 74.50/11.07 | | (10) $false % 74.50/11.07 | | % 74.50/11.07 | | CLOSE: (10) is inconsistent. % 74.50/11.07 | | % 74.50/11.07 | Case 2: % 74.50/11.07 | | % 74.50/11.07 | | (11) all_10_15 = e3 | all_10_19 = e3 % 74.50/11.07 | | % 74.50/11.07 | | BETA: splitting (11) gives: % 74.50/11.07 | | % 74.50/11.07 | | Case 1: % 74.50/11.07 | | | % 74.50/11.07 | | | (12) all_10_15 = e3 % 74.50/11.07 | | | % 74.50/11.07 | | | COMBINE_EQS: (3), (12) imply: % 74.50/11.07 | | | (13) e4 = e3 % 74.50/11.07 | | | % 74.50/11.07 | | | REDUCE: (5), (13) imply: % 74.50/11.07 | | | (14) $false % 74.50/11.07 | | | % 74.50/11.07 | | | CLOSE: (14) is inconsistent. % 74.50/11.07 | | | % 74.50/11.07 | | Case 2: % 74.50/11.07 | | | % 74.50/11.07 | | | (15) all_10_19 = e3 % 74.50/11.07 | | | % 74.50/11.07 | | | COMBINE_EQS: (6), (15) imply: % 74.50/11.07 | | | (16) e3 = e2 % 74.50/11.07 | | | % 74.50/11.07 | | | REDUCE: (2), (16) imply: % 74.50/11.07 | | | (17) $false % 74.50/11.07 | | | % 74.50/11.07 | | | CLOSE: (17) is inconsistent. % 74.50/11.07 | | | % 74.50/11.07 | | End of split % 74.50/11.07 | | % 74.50/11.07 | End of split % 74.50/11.07 | % 74.50/11.07 End of proof % 74.50/11.07 % 74.50/11.07 Sub-proof #41 shows that the following formulas are inconsistent: % 74.50/11.07 ---------------------------------------------------------------- % 74.50/11.07 (1) ~ (all_4_5 = e2) % 74.50/11.07 (2) ~ (all_4_1 = e0) % 74.50/11.07 (3) all_10_1 = e4 | all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | % 74.50/11.07 all_10_21 = e4 % 74.50/11.07 (4) all_10_8 = e3 % 74.50/11.07 (5) ~ (all_4_1 = all_4_2) % 74.50/11.07 (6) all_10_14 = e0 % 74.50/11.07 (7) ~ (all_4_9 = e0) % 74.50/11.07 (8) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | all_6_5 = e0 % 74.50/11.07 (9) ~ (all_4_11 = e0) % 74.50/11.07 (10) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 74.50/11.07 (11) ~ (all_4_10 = e3) % 74.50/11.07 (12) all_6_13 = all_4_17 % 74.50/11.07 (13) all_10_4 = all_4_10 % 74.50/11.07 (14) all_10_22 = e2 % 74.50/11.07 (15) all_10_20 = e4 % 74.50/11.07 (16) all_10_1 = all_4_5 % 74.50/11.07 (17) ~ (all_4_20 = all_4_21) % 74.50/11.07 (18) ~ (e2 = e0) % 74.50/11.07 (19) all_6_9 = all_4_21 % 74.50/11.07 (20) all_10_12 = all_4_3 % 74.50/11.07 (21) op(e2, all_4_17) = all_8_46 % 74.50/11.07 (22) ~ (all_4_2 = e3) % 74.50/11.07 (23) all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e1 | all_6_14 = e0 % 74.50/11.07 (24) all_10_16 = all_4_20 % 74.50/11.07 (25) ~ (e4 = e0) % 74.50/11.07 (26) all_10_3 = e0 % 74.50/11.07 (27) ~ (all_4_2 = all_4_22) % 74.50/11.07 (28) all_10_21 = all_4_9 % 74.50/11.07 (29) ~ (all_4_10 = e0) % 74.50/11.07 (30) ~ (all_4_22 = e1) % 74.50/11.07 (31) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e1 | all_6_9 = e0 % 74.50/11.07 (32) op(e4, e4) = e2 % 74.50/11.07 (33) all_10_17 = all_4_21 % 74.50/11.07 (34) all_6_21 = all_4_9 % 74.50/11.07 (35) ~ (all_8_27 = e2) % 74.50/11.07 (36) op(e2, e1) = all_4_17 % 74.50/11.07 (37) all_6_5 = all_4_1 % 74.50/11.07 (38) ~ (all_4_1 = all_4_11) % 74.50/11.07 (39) ~ (all_4_1 = all_4_21) % 74.50/11.07 (40) all_10_0 = e0 | all_10_2 = e0 | all_10_6 = e0 | all_10_12 = e0 | % 74.50/11.07 all_10_20 = e0 % 74.50/11.07 (41) all_10_6 = e1 | all_10_7 = e1 | all_10_8 = e1 | all_10_11 = e1 | % 74.50/11.07 all_10_18 = e1 % 74.50/11.07 (42) ~ (e4 = e3) % 74.50/11.07 (43) all_10_2 = all_4_1 % 74.50/11.07 (44) ~ (all_4_3 = e0) % 74.50/11.07 (45) ~ (all_4_5 = e0) % 74.50/11.07 (46) ~ (all_4_22 = e3) % 74.50/11.07 (47) ~ (all_4_17 = e4) % 74.50/11.07 (48) ~ (all_4_21 = e1) % 74.50/11.07 (49) op(e2, all_4_10) = e4 % 74.50/11.07 (50) all_6_14 = all_4_22 % 74.50/11.07 (51) ~ (all_4_9 = e1) % 74.50/11.07 (52) all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e1 | all_6_21 = e0 % 74.50/11.07 (53) ~ (all_4_2 = e2) % 74.50/11.07 (54) ~ (all_4_9 = e4) % 74.50/11.07 (55) ~ (all_4_2 = e4) % 74.50/11.07 (56) all_10_19 = e2 % 74.50/11.07 (57) ~ (all_4_10 = all_4_11) % 74.50/11.07 (58) all_10_2 = e4 | all_10_3 = e4 | all_10_5 = e4 | all_10_10 = e4 | % 74.50/11.07 all_10_17 = e4 % 74.50/11.07 (59) ~ (all_4_21 = e0) % 74.50/11.07 (60) all_6_1 = all_4_5 % 74.50/11.07 (61) ~ (all_4_5 = all_4_10) % 74.50/11.07 (62) ~ (e4 = e2) % 74.50/11.07 (63) all_6_13 = e4 | all_6_13 = e3 | all_6_13 = e1 | all_6_13 = e0 % 74.50/11.07 (64) ~ (all_4_11 = all_4_21) % 74.50/11.07 (65) all_10_20 = e3 | all_10_21 = e3 | all_10_22 = e3 | all_10_23 = e3 | % 74.50/11.07 all_10_24 = e3 % 74.50/11.07 (66) all_10_6 = all_4_2 % 74.50/11.07 (67) op(e4, all_4_10) = all_8_27 % 74.50/11.07 (68) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.50/11.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.50/11.07 (69) all_10_5 = all_4_11 % 74.50/11.07 (70) all_10_7 = e2 % 74.50/11.07 (71) all_6_2 = all_4_10 % 74.50/11.07 (72) all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | % 74.50/11.07 all_10_22 = e4 % 74.50/11.07 (73) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.50/11.07 (74) all_10_0 = e2 % 74.50/11.07 (75) all_10_18 = all_4_22 % 74.50/11.07 (76) ~ (all_4_5 = all_4_9) % 74.50/11.07 (77) all_10_2 = e1 | all_10_3 = e1 | all_10_5 = e1 | all_10_10 = e1 | % 74.50/11.07 all_10_17 = e1 % 74.50/11.07 (78) all_10_11 = all_4_17 % 74.50/11.07 (79) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 74.50/11.07 all_10_22 = e1 % 74.50/11.07 (80) all_10_16 = e0 | all_10_17 = e0 | all_10_18 = e0 | all_10_19 = e0 % 74.50/11.07 (81) ~ (all_4_1 = e2) % 74.50/11.07 (82) ~ (all_4_1 = e4) % 74.50/11.07 (83) all_10_16 = e3 | all_10_17 = e3 | all_10_18 = e3 | all_10_19 = e3 | % 74.50/11.07 all_10_24 = e3 % 74.50/11.07 % 74.50/11.07 Begin of proof % 74.50/11.07 | % 74.50/11.08 | BETA: splitting (40) gives: % 74.50/11.08 | % 74.50/11.08 | Case 1: % 74.50/11.08 | | % 74.50/11.08 | | (84) all_10_0 = e0 % 74.50/11.08 | | % 74.50/11.08 | | COMBINE_EQS: (74), (84) imply: % 74.50/11.08 | | (85) e2 = e0 % 74.50/11.08 | | % 74.50/11.08 | | REDUCE: (18), (85) imply: % 74.50/11.08 | | (86) $false % 74.50/11.08 | | % 74.50/11.08 | | CLOSE: (86) is inconsistent. % 74.50/11.08 | | % 74.50/11.08 | Case 2: % 74.50/11.08 | | % 74.50/11.08 | | (87) all_10_2 = e0 | all_10_6 = e0 | all_10_12 = e0 | all_10_20 = e0 % 74.50/11.08 | | % 74.50/11.08 | | BETA: splitting (3) gives: % 74.50/11.08 | | % 74.50/11.08 | | Case 1: % 74.50/11.08 | | | % 74.50/11.08 | | | (88) all_10_1 = e4 % 74.50/11.08 | | | % 74.50/11.08 | | | COMBINE_EQS: (16), (88) imply: % 74.50/11.08 | | | (89) all_4_5 = e4 % 74.50/11.08 | | | % 74.50/11.08 | | | REDUCE: (61), (89) imply: % 74.50/11.08 | | | (90) ~ (all_4_10 = e4) % 74.50/11.08 | | | % 74.50/11.08 | | | SIMP: (90) implies: % 74.50/11.08 | | | (91) ~ (all_4_10 = e4) % 74.50/11.08 | | | % 74.50/11.08 | | | BETA: splitting (72) gives: % 74.50/11.08 | | | % 74.50/11.08 | | | Case 1: % 74.50/11.08 | | | | % 74.50/11.08 | | | | (92) all_10_4 = e4 % 74.50/11.08 | | | | % 74.50/11.08 | | | | COMBINE_EQS: (13), (92) imply: % 74.50/11.08 | | | | (93) all_4_10 = e4 % 74.50/11.08 | | | | % 74.50/11.08 | | | | REDUCE: (91), (93) imply: % 74.50/11.08 | | | | (94) $false % 74.50/11.08 | | | | % 74.50/11.08 | | | | CLOSE: (94) is inconsistent. % 74.50/11.08 | | | | % 74.50/11.08 | | | Case 2: % 74.50/11.08 | | | | % 74.50/11.08 | | | | (95) ~ (all_10_4 = e4) % 74.50/11.08 | | | | (96) all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | all_10_22 = e4 % 74.50/11.08 | | | | % 74.50/11.08 | | | | BETA: splitting (73) gives: % 74.50/11.08 | | | | % 74.50/11.08 | | | | Case 1: % 74.50/11.08 | | | | | % 74.50/11.08 | | | | | (97) all_6_2 = e4 % 74.50/11.08 | | | | | % 74.50/11.08 | | | | | COMBINE_EQS: (71), (97) imply: % 74.50/11.08 | | | | | (98) all_4_10 = e4 % 74.50/11.08 | | | | | % 74.50/11.08 | | | | | REDUCE: (91), (98) imply: % 74.50/11.08 | | | | | (99) $false % 74.50/11.08 | | | | | % 74.50/11.08 | | | | | CLOSE: (99) is inconsistent. % 74.50/11.08 | | | | | % 74.50/11.08 | | | | Case 2: % 74.50/11.08 | | | | | % 74.50/11.08 | | | | | (100) all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.50/11.08 | | | | | % 74.50/11.08 | | | | | BETA: splitting (96) gives: % 74.50/11.08 | | | | | % 74.50/11.08 | | | | | Case 1: % 74.50/11.08 | | | | | | % 74.50/11.08 | | | | | | (101) all_10_5 = e4 % 74.50/11.08 | | | | | | % 74.50/11.08 | | | | | | COMBINE_EQS: (69), (101) imply: % 74.50/11.08 | | | | | | (102) all_4_11 = e4 % 74.50/11.08 | | | | | | % 74.50/11.08 | | | | | | SIMP: (102) implies: % 74.50/11.08 | | | | | | (103) all_4_11 = e4 % 74.50/11.08 | | | | | | % 74.50/11.08 | | | | | | REDUCE: (64), (103) imply: % 74.50/11.08 | | | | | | (104) ~ (all_4_21 = e4) % 74.50/11.08 | | | | | | % 74.50/11.08 | | | | | | SIMP: (104) implies: % 74.50/11.08 | | | | | | (105) ~ (all_4_21 = e4) % 74.50/11.08 | | | | | | % 74.50/11.08 | | | | | | BETA: splitting (87) gives: % 74.50/11.08 | | | | | | % 74.50/11.08 | | | | | | Case 1: % 74.50/11.08 | | | | | | | % 74.50/11.08 | | | | | | | (106) all_10_2 = e0 % 74.50/11.08 | | | | | | | % 74.50/11.08 | | | | | | | REF_CLOSE: (2), (43), (106) are inconsistent by sub-proof #119. % 74.50/11.08 | | | | | | | % 74.50/11.08 | | | | | | Case 2: % 74.50/11.08 | | | | | | | % 74.50/11.08 | | | | | | | (107) all_10_6 = e0 | all_10_12 = e0 | all_10_20 = e0 % 74.50/11.08 | | | | | | | % 74.50/11.08 | | | | | | | BETA: splitting (79) gives: % 74.50/11.08 | | | | | | | % 74.50/11.08 | | | | | | | Case 1: % 74.50/11.08 | | | | | | | | % 74.50/11.08 | | | | | | | | (108) all_10_4 = e1 % 74.50/11.08 | | | | | | | | % 74.50/11.08 | | | | | | | | COMBINE_EQS: (13), (108) imply: % 74.50/11.08 | | | | | | | | (109) all_4_10 = e1 % 74.50/11.08 | | | | | | | | % 74.50/11.08 | | | | | | | | REDUCE: (11), (109) imply: % 74.50/11.08 | | | | | | | | (110) ~ (e3 = e1) % 74.50/11.08 | | | | | | | | % 74.50/11.08 | | | | | | | | SIMP: (110) implies: % 74.50/11.08 | | | | | | | | (111) ~ (e3 = e1) % 74.50/11.08 | | | | | | | | % 74.50/11.08 | | | | | | | | REDUCE: (49), (109) imply: % 74.50/11.08 | | | | | | | | (112) op(e2, e1) = e4 % 74.50/11.08 | | | | | | | | % 74.50/11.08 | | | | | | | | BETA: splitting (77) gives: % 74.50/11.08 | | | | | | | | % 74.50/11.08 | | | | | | | | Case 1: % 74.50/11.08 | | | | | | | | | % 74.50/11.08 | | | | | | | | | (113) all_10_2 = e1 % 74.50/11.08 | | | | | | | | | % 74.50/11.08 | | | | | | | | | COMBINE_EQS: (43), (113) imply: % 74.50/11.08 | | | | | | | | | (114) all_4_1 = e1 % 74.50/11.08 | | | | | | | | | % 74.50/11.08 | | | | | | | | | SIMP: (114) implies: % 74.50/11.08 | | | | | | | | | (115) all_4_1 = e1 % 74.50/11.08 | | | | | | | | | % 74.50/11.08 | | | | | | | | | REDUCE: (5), (115) imply: % 74.50/11.08 | | | | | | | | | (116) ~ (all_4_2 = e1) % 74.50/11.08 | | | | | | | | | % 74.50/11.08 | | | | | | | | | SIMP: (116) implies: % 74.50/11.08 | | | | | | | | | (117) ~ (all_4_2 = e1) % 74.50/11.08 | | | | | | | | | % 74.50/11.08 | | | | | | | | | REDUCE: (81), (115) imply: % 74.50/11.08 | | | | | | | | | (118) ~ (e2 = e1) % 74.50/11.08 | | | | | | | | | % 74.50/11.08 | | | | | | | | | SIMP: (118) implies: % 74.50/11.08 | | | | | | | | | (119) ~ (e2 = e1) % 74.50/11.08 | | | | | | | | | % 74.50/11.08 | | | | | | | | | BETA: splitting (41) gives: % 74.50/11.08 | | | | | | | | | % 74.50/11.08 | | | | | | | | | Case 1: % 74.50/11.08 | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | (120) all_10_6 = e1 % 74.50/11.08 | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | REF_CLOSE: (66), (117), (120) are inconsistent by sub-proof % 74.50/11.08 | | | | | | | | | | #86. % 74.50/11.08 | | | | | | | | | | % 74.50/11.08 | | | | | | | | | Case 2: % 74.50/11.08 | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | (121) all_10_7 = e1 | all_10_8 = e1 | all_10_11 = e1 | % 74.50/11.08 | | | | | | | | | | all_10_18 = e1 % 74.50/11.08 | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | BETA: splitting (63) gives: % 74.50/11.08 | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | Case 1: % 74.50/11.08 | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | (122) all_6_13 = e4 % 74.50/11.08 | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | COMBINE_EQS: (12), (122) imply: % 74.50/11.08 | | | | | | | | | | | (123) all_4_17 = e4 % 74.50/11.08 | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | SIMP: (123) implies: % 74.50/11.08 | | | | | | | | | | | (124) all_4_17 = e4 % 74.50/11.08 | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | REDUCE: (47), (124) imply: % 74.50/11.08 | | | | | | | | | | | (125) $false % 74.50/11.08 | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | CLOSE: (125) is inconsistent. % 74.50/11.08 | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | Case 2: % 74.50/11.08 | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | (126) ~ (all_6_13 = e4) % 74.50/11.08 | | | | | | | | | | | (127) all_6_13 = e3 | all_6_13 = e1 | all_6_13 = e0 % 74.50/11.08 | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | BETA: splitting (127) gives: % 74.50/11.08 | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | Case 1: % 74.50/11.08 | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | (128) all_6_13 = e1 % 74.50/11.08 | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | COMBINE_EQS: (12), (128) imply: % 74.50/11.08 | | | | | | | | | | | | (129) all_4_17 = e1 % 74.50/11.08 | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | REF_CLOSE: (21), (36), (47), (68), (112), (129) are % 74.50/11.08 | | | | | | | | | | | | inconsistent by sub-proof #167. % 74.50/11.08 | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | Case 2: % 74.50/11.08 | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | (130) ~ (all_6_13 = e1) % 74.50/11.08 | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | REDUCE: (12), (130) imply: % 74.50/11.08 | | | | | | | | | | | | (131) ~ (all_4_17 = e1) % 74.50/11.08 | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | BETA: splitting (121) gives: % 74.50/11.08 | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | Case 1: % 74.50/11.08 | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | (132) all_10_7 = e1 % 74.50/11.08 | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | COMBINE_EQS: (70), (132) imply: % 74.50/11.08 | | | | | | | | | | | | | (133) e2 = e1 % 74.50/11.08 | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | REDUCE: (119), (133) imply: % 74.50/11.08 | | | | | | | | | | | | | (134) $false % 74.50/11.08 | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | CLOSE: (134) is inconsistent. % 74.50/11.08 | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | Case 2: % 74.50/11.08 | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | (135) all_10_8 = e1 | all_10_11 = e1 | all_10_18 = e1 % 74.50/11.08 | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | BETA: splitting (135) gives: % 74.50/11.08 | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | Case 1: % 74.50/11.08 | | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | | (136) all_10_8 = e1 % 74.50/11.08 | | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | | COMBINE_EQS: (4), (136) imply: % 74.50/11.08 | | | | | | | | | | | | | | (137) e3 = e1 % 74.50/11.08 | | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | | REDUCE: (111), (137) imply: % 74.50/11.08 | | | | | | | | | | | | | | (138) $false % 74.50/11.08 | | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | | CLOSE: (138) is inconsistent. % 74.50/11.08 | | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | Case 2: % 74.50/11.08 | | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | | (139) all_10_11 = e1 | all_10_18 = e1 % 74.50/11.08 | | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | | BETA: splitting (139) gives: % 74.50/11.08 | | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | | Case 1: % 74.50/11.08 | | | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | | | (140) all_10_11 = e1 % 74.50/11.08 | | | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | | | COMBINE_EQS: (78), (140) imply: % 74.50/11.08 | | | | | | | | | | | | | | | (141) all_4_17 = e1 % 74.50/11.08 | | | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | | | SIMP: (141) implies: % 74.50/11.08 | | | | | | | | | | | | | | | (142) all_4_17 = e1 % 74.50/11.08 | | | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | | | REDUCE: (131), (142) imply: % 74.50/11.08 | | | | | | | | | | | | | | | (143) $false % 74.50/11.08 | | | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | | | CLOSE: (143) is inconsistent. % 74.50/11.08 | | | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | | Case 2: % 74.50/11.08 | | | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | | | (144) all_10_18 = e1 % 74.50/11.08 | | | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | | | COMBINE_EQS: (75), (144) imply: % 74.50/11.08 | | | | | | | | | | | | | | | (145) all_4_22 = e1 % 74.50/11.08 | | | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | | | REDUCE: (30), (145) imply: % 74.50/11.08 | | | | | | | | | | | | | | | (146) $false % 74.50/11.08 | | | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | | | CLOSE: (146) is inconsistent. % 74.50/11.08 | | | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | | End of split % 74.50/11.08 | | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | | End of split % 74.50/11.08 | | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | | End of split % 74.50/11.08 | | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | | End of split % 74.50/11.08 | | | | | | | | | | | % 74.50/11.08 | | | | | | | | | | End of split % 74.50/11.08 | | | | | | | | | | % 74.50/11.08 | | | | | | | | | End of split % 74.50/11.08 | | | | | | | | | % 74.50/11.08 | | | | | | | | Case 2: % 74.50/11.08 | | | | | | | | | % 74.50/11.08 | | | | | | | | | (147) ~ (all_10_2 = e1) % 74.50/11.08 | | | | | | | | | % 74.50/11.08 | | | | | | | | | REF_CLOSE: (5), (8), (15), (17), (19), (20), (22), (23), (24), % 74.50/11.08 | | | | | | | | | (25), (27), (30), (31), (33), (37), (39), (43), % 74.50/11.08 | | | | | | | | | (44), (46), (48), (50), (53), (55), (56), (59), % 74.50/11.08 | | | | | | | | | (66), (75), (80), (82), (83), (105), (107), (147) % 74.50/11.08 | | | | | | | | | are inconsistent by sub-proof #46. % 74.50/11.08 | | | | | | | | | % 74.50/11.08 | | | | | | | | End of split % 74.50/11.08 | | | | | | | | % 74.50/11.08 | | | | | | | Case 2: % 74.50/11.08 | | | | | | | | % 74.50/11.08 | | | | | | | | (148) ~ (all_10_4 = e1) % 74.50/11.08 | | | | | | | | % 74.50/11.08 | | | | | | | | REDUCE: (13), (148) imply: % 74.50/11.08 | | | | | | | | (149) ~ (all_4_10 = e1) % 74.50/11.08 | | | | | | | | % 74.50/11.08 | | | | | | | | REF_CLOSE: (11), (29), (71), (100), (149) are inconsistent by % 74.50/11.08 | | | | | | | | sub-proof #162. % 74.50/11.08 | | | | | | | | % 74.50/11.08 | | | | | | | End of split % 74.50/11.08 | | | | | | | % 74.50/11.08 | | | | | | End of split % 74.50/11.08 | | | | | | % 74.50/11.08 | | | | | Case 2: % 74.50/11.08 | | | | | | % 74.50/11.08 | | | | | | (150) all_10_8 = e4 | all_10_14 = e4 | all_10_22 = e4 % 74.50/11.08 | | | | | | % 74.50/11.08 | | | | | | REF_CLOSE: (4), (6), (14), (25), (42), (62), (150) are inconsistent % 74.50/11.08 | | | | | | by sub-proof #115. % 74.50/11.08 | | | | | | % 74.50/11.08 | | | | | End of split % 74.50/11.08 | | | | | % 74.50/11.08 | | | | End of split % 74.50/11.08 | | | | % 74.50/11.08 | | | End of split % 74.50/11.08 | | | % 74.50/11.08 | | Case 2: % 74.50/11.08 | | | % 74.50/11.08 | | | (151) ~ (all_10_1 = e4) % 74.50/11.08 | | | % 74.50/11.08 | | | REF_CLOSE: (4), (6), (7), (10), (11), (13), (14), (15), (16), (25), (26), % 74.50/11.08 | | | (28), (29), (32), (34), (35), (42), (43), (45), (51), (52), % 74.50/11.08 | | | (54), (57), (58), (60), (61), (62), (65), (67), (68), (69), % 74.50/11.08 | | | (71), (72), (73), (76), (79), (82), (151) are inconsistent by % 74.50/11.08 | | | sub-proof #42. % 74.50/11.08 | | | % 74.50/11.08 | | End of split % 74.50/11.08 | | % 74.50/11.08 | End of split % 74.50/11.08 | % 74.50/11.08 End of proof % 74.50/11.08 % 74.50/11.08 Sub-proof #42 shows that the following formulas are inconsistent: % 74.50/11.08 ---------------------------------------------------------------- % 74.50/11.08 (1) all_10_8 = e3 % 74.50/11.08 (2) all_10_14 = e0 % 74.50/11.08 (3) ~ (all_4_9 = e0) % 74.50/11.08 (4) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 74.50/11.08 (5) ~ (all_4_10 = e3) % 74.50/11.08 (6) all_10_4 = all_4_10 % 74.50/11.08 (7) all_10_22 = e2 % 74.50/11.08 (8) all_10_20 = e4 % 74.50/11.08 (9) all_10_1 = all_4_5 % 74.50/11.08 (10) ~ (e4 = e0) % 74.50/11.08 (11) all_10_3 = e0 % 74.50/11.08 (12) all_10_21 = all_4_9 % 74.50/11.08 (13) ~ (all_4_10 = e0) % 74.50/11.08 (14) op(e4, e4) = e2 % 74.50/11.08 (15) all_6_21 = all_4_9 % 74.50/11.08 (16) ~ (all_8_27 = e2) % 74.50/11.08 (17) ~ (all_10_1 = e4) % 74.50/11.08 (18) ~ (e4 = e3) % 74.50/11.08 (19) all_10_2 = all_4_1 % 74.50/11.08 (20) ~ (all_4_5 = e0) % 74.50/11.08 (21) ~ (all_4_9 = e1) % 74.50/11.08 (22) all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e1 | all_6_21 = e0 % 74.50/11.08 (23) ~ (all_4_9 = e4) % 74.50/11.08 (24) ~ (all_4_10 = all_4_11) % 74.50/11.08 (25) all_10_2 = e4 | all_10_3 = e4 | all_10_5 = e4 | all_10_10 = e4 | % 74.50/11.08 all_10_17 = e4 % 74.50/11.08 (26) all_6_1 = all_4_5 % 74.50/11.08 (27) ~ (all_4_5 = all_4_10) % 74.50/11.08 (28) ~ (e4 = e2) % 74.50/11.08 (29) all_10_20 = e3 | all_10_21 = e3 | all_10_22 = e3 | all_10_23 = e3 | % 74.50/11.08 all_10_24 = e3 % 74.50/11.08 (30) op(e4, all_4_10) = all_8_27 % 74.50/11.08 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.50/11.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.50/11.08 (32) all_10_5 = all_4_11 % 74.50/11.08 (33) all_6_2 = all_4_10 % 74.50/11.08 (34) all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | % 74.50/11.08 all_10_22 = e4 % 74.50/11.08 (35) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.50/11.08 (36) ~ (all_4_5 = all_4_9) % 74.50/11.08 (37) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 74.50/11.08 all_10_22 = e1 % 74.50/11.08 (38) ~ (all_4_1 = e4) % 74.50/11.08 % 74.50/11.08 Begin of proof % 74.50/11.08 | % 74.50/11.08 | REDUCE: (9), (17) imply: % 74.50/11.08 | (39) ~ (all_4_5 = e4) % 74.50/11.08 | % 74.50/11.08 | BETA: splitting (22) gives: % 74.50/11.08 | % 74.50/11.08 | Case 1: % 74.50/11.08 | | % 74.50/11.08 | | (40) all_6_21 = e4 % 74.50/11.08 | | % 74.50/11.08 | | COMBINE_EQS: (15), (40) imply: % 74.50/11.08 | | (41) all_4_9 = e4 % 74.50/11.08 | | % 74.50/11.08 | | REDUCE: (23), (41) imply: % 74.50/11.08 | | (42) $false % 74.50/11.08 | | % 74.50/11.08 | | CLOSE: (42) is inconsistent. % 74.50/11.08 | | % 74.50/11.08 | Case 2: % 74.50/11.08 | | % 74.50/11.08 | | (43) ~ (all_6_21 = e4) % 74.50/11.08 | | (44) all_6_21 = e3 | all_6_21 = e1 | all_6_21 = e0 % 74.50/11.08 | | % 74.50/11.08 | | BETA: splitting (25) gives: % 74.50/11.08 | | % 74.50/11.08 | | Case 1: % 74.50/11.08 | | | % 74.50/11.08 | | | (45) all_10_2 = e4 % 74.50/11.08 | | | % 74.50/11.08 | | | COMBINE_EQS: (19), (45) imply: % 74.50/11.08 | | | (46) all_4_1 = e4 % 74.50/11.08 | | | % 74.50/11.08 | | | SIMP: (46) implies: % 74.50/11.08 | | | (47) all_4_1 = e4 % 74.50/11.08 | | | % 74.50/11.08 | | | REDUCE: (38), (47) imply: % 74.50/11.08 | | | (48) $false % 74.50/11.08 | | | % 74.50/11.08 | | | CLOSE: (48) is inconsistent. % 74.50/11.08 | | | % 74.50/11.08 | | Case 2: % 74.50/11.08 | | | % 74.50/11.08 | | | (49) all_10_3 = e4 | all_10_5 = e4 | all_10_10 = e4 | all_10_17 = e4 % 74.50/11.08 | | | % 74.50/11.08 | | | BETA: splitting (29) gives: % 74.50/11.08 | | | % 74.50/11.08 | | | Case 1: % 74.50/11.08 | | | | % 74.50/11.08 | | | | (50) all_10_20 = e3 % 74.50/11.08 | | | | % 74.50/11.08 | | | | COMBINE_EQS: (8), (50) imply: % 74.50/11.08 | | | | (51) e4 = e3 % 74.50/11.08 | | | | % 74.50/11.08 | | | | REDUCE: (18), (51) imply: % 74.50/11.08 | | | | (52) $false % 74.50/11.08 | | | | % 74.50/11.08 | | | | CLOSE: (52) is inconsistent. % 74.50/11.08 | | | | % 74.50/11.08 | | | Case 2: % 74.50/11.08 | | | | % 74.50/11.08 | | | | (53) all_10_21 = e3 | all_10_22 = e3 | all_10_23 = e3 | all_10_24 = % 74.50/11.08 | | | | e3 % 74.50/11.08 | | | | % 74.50/11.08 | | | | BETA: splitting (53) gives: % 74.50/11.08 | | | | % 74.50/11.08 | | | | Case 1: % 74.50/11.08 | | | | | % 74.50/11.08 | | | | | (54) all_10_21 = e3 % 74.50/11.08 | | | | | % 74.50/11.08 | | | | | COMBINE_EQS: (12), (54) imply: % 74.50/11.08 | | | | | (55) all_4_9 = e3 % 74.50/11.08 | | | | | % 74.50/11.08 | | | | | REDUCE: (36), (55) imply: % 74.50/11.08 | | | | | (56) ~ (all_4_5 = e3) % 74.50/11.08 | | | | | % 74.50/11.08 | | | | | REDUCE: (23), (55) imply: % 74.50/11.08 | | | | | (57) ~ (e4 = e3) % 74.50/11.08 | | | | | % 74.50/11.08 | | | | | BETA: splitting (49) gives: % 74.50/11.08 | | | | | % 74.50/11.08 | | | | | Case 1: % 74.50/11.08 | | | | | | % 74.50/11.08 | | | | | | (58) all_10_3 = e4 % 74.50/11.08 | | | | | | % 74.50/11.09 | | | | | | REF_CLOSE: (10), (11), (58) are inconsistent by sub-proof #45. % 74.50/11.09 | | | | | | % 74.50/11.09 | | | | | Case 2: % 74.50/11.09 | | | | | | % 74.50/11.09 | | | | | | (59) ~ (all_10_3 = e4) % 74.50/11.09 | | | | | | (60) all_10_5 = e4 | all_10_10 = e4 | all_10_17 = e4 % 74.50/11.09 | | | | | | % 74.50/11.09 | | | | | | REDUCE: (11), (59) imply: % 74.50/11.09 | | | | | | (61) ~ (e4 = e0) % 74.50/11.09 | | | | | | % 74.50/11.09 | | | | | | BETA: splitting (60) gives: % 74.50/11.09 | | | | | | % 74.50/11.09 | | | | | | Case 1: % 74.50/11.09 | | | | | | | % 74.50/11.09 | | | | | | | (62) all_10_5 = e4 % 74.50/11.09 | | | | | | | % 74.50/11.09 | | | | | | | COMBINE_EQS: (32), (62) imply: % 74.50/11.09 | | | | | | | (63) all_4_11 = e4 % 74.50/11.09 | | | | | | | % 74.50/11.09 | | | | | | | REDUCE: (24), (63) imply: % 74.50/11.09 | | | | | | | (64) ~ (all_4_10 = e4) % 74.50/11.09 | | | | | | | % 74.50/11.09 | | | | | | | BETA: splitting (35) gives: % 74.50/11.09 | | | | | | | % 74.50/11.09 | | | | | | | Case 1: % 74.50/11.09 | | | | | | | | % 74.50/11.09 | | | | | | | | (65) all_6_2 = e4 % 74.50/11.09 | | | | | | | | % 74.50/11.09 | | | | | | | | REF_CLOSE: (33), (64), (65) are inconsistent by sub-proof #164. % 74.50/11.09 | | | | | | | | % 74.50/11.09 | | | | | | | Case 2: % 74.50/11.09 | | | | | | | | % 74.50/11.09 | | | | | | | | (66) all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.50/11.09 | | | | | | | | % 74.50/11.09 | | | | | | | | REF_CLOSE: (4), (5), (6), (13), (20), (26), (27), (33), (37), % 74.50/11.09 | | | | | | | | (39), (56), (66) are inconsistent by sub-proof #44. % 74.50/11.09 | | | | | | | | % 74.50/11.09 | | | | | | | End of split % 74.50/11.09 | | | | | | | % 74.50/11.09 | | | | | | Case 2: % 74.50/11.09 | | | | | | | % 74.50/11.09 | | | | | | | (67) ~ (all_10_5 = e4) % 74.50/11.09 | | | | | | | % 74.50/11.09 | | | | | | | REDUCE: (32), (67) imply: % 74.50/11.09 | | | | | | | (68) ~ (all_4_11 = e4) % 74.50/11.09 | | | | | | | % 74.50/11.09 | | | | | | | REF_CLOSE: (1), (2), (6), (7), (10), (14), (16), (18), (28), (30), % 74.50/11.09 | | | | | | | (31), (32), (34), (68) are inconsistent by sub-proof % 74.50/11.09 | | | | | | | #43. % 74.50/11.09 | | | | | | | % 74.50/11.09 | | | | | | End of split % 74.50/11.09 | | | | | | % 74.50/11.09 | | | | | End of split % 74.50/11.09 | | | | | % 74.50/11.09 | | | | Case 2: % 74.50/11.09 | | | | | % 74.50/11.09 | | | | | (69) ~ (all_10_21 = e3) % 74.50/11.09 | | | | | % 74.50/11.09 | | | | | REDUCE: (12), (69) imply: % 74.50/11.09 | | | | | (70) ~ (all_4_9 = e3) % 74.50/11.09 | | | | | % 74.50/11.09 | | | | | REF_CLOSE: (3), (15), (21), (44), (70) are inconsistent by sub-proof % 74.50/11.09 | | | | | #126. % 74.50/11.09 | | | | | % 74.50/11.09 | | | | End of split % 74.50/11.09 | | | | % 74.50/11.09 | | | End of split % 74.50/11.09 | | | % 74.50/11.09 | | End of split % 74.50/11.09 | | % 74.50/11.09 | End of split % 74.50/11.09 | % 74.50/11.09 End of proof % 74.50/11.09 % 74.50/11.09 Sub-proof #43 shows that the following formulas are inconsistent: % 74.50/11.09 ---------------------------------------------------------------- % 74.50/11.09 (1) all_10_8 = e3 % 74.50/11.09 (2) all_10_14 = e0 % 74.50/11.09 (3) all_10_4 = all_4_10 % 74.50/11.09 (4) all_10_22 = e2 % 74.50/11.09 (5) ~ (e4 = e0) % 74.50/11.09 (6) ~ (all_4_11 = e4) % 74.50/11.09 (7) op(e4, e4) = e2 % 74.50/11.09 (8) ~ (all_8_27 = e2) % 74.50/11.09 (9) ~ (e4 = e3) % 74.50/11.09 (10) ~ (e4 = e2) % 74.50/11.09 (11) op(e4, all_4_10) = all_8_27 % 74.50/11.09 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.50/11.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.50/11.09 (13) all_10_5 = all_4_11 % 74.50/11.09 (14) all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | % 74.50/11.09 all_10_22 = e4 % 74.50/11.09 % 74.50/11.09 Begin of proof % 74.50/11.09 | % 74.50/11.09 | BETA: splitting (14) gives: % 74.50/11.09 | % 74.50/11.09 | Case 1: % 74.50/11.09 | | % 74.50/11.09 | | (15) all_10_4 = e4 % 74.50/11.09 | | % 74.50/11.09 | | REF_CLOSE: (3), (7), (8), (11), (12), (15) are inconsistent by sub-proof % 74.50/11.09 | | #165. % 74.50/11.09 | | % 74.50/11.09 | Case 2: % 74.50/11.09 | | % 74.50/11.09 | | (16) all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | all_10_22 = e4 % 74.50/11.09 | | % 74.50/11.09 | | BETA: splitting (16) gives: % 74.50/11.09 | | % 74.50/11.09 | | Case 1: % 74.50/11.09 | | | % 74.50/11.09 | | | (17) all_10_5 = e4 % 74.50/11.09 | | | % 74.50/11.09 | | | COMBINE_EQS: (13), (17) imply: % 74.50/11.09 | | | (18) all_4_11 = e4 % 74.50/11.09 | | | % 74.50/11.09 | | | REDUCE: (6), (18) imply: % 74.50/11.09 | | | (19) $false % 74.50/11.09 | | | % 74.50/11.09 | | | CLOSE: (19) is inconsistent. % 74.50/11.09 | | | % 74.50/11.09 | | Case 2: % 74.50/11.09 | | | % 74.50/11.09 | | | (20) all_10_8 = e4 | all_10_14 = e4 | all_10_22 = e4 % 74.50/11.09 | | | % 74.50/11.09 | | | REF_CLOSE: (1), (2), (4), (5), (9), (10), (20) are inconsistent by % 74.50/11.09 | | | sub-proof #115. % 74.50/11.09 | | | % 74.50/11.09 | | End of split % 74.50/11.09 | | % 74.50/11.09 | End of split % 74.50/11.09 | % 74.50/11.09 End of proof % 74.50/11.09 % 74.50/11.09 Sub-proof #44 shows that the following formulas are inconsistent: % 74.50/11.09 ---------------------------------------------------------------- % 74.50/11.09 (1) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 74.50/11.09 (2) ~ (all_4_10 = e3) % 74.50/11.09 (3) all_10_4 = all_4_10 % 74.50/11.09 (4) ~ (all_4_10 = e0) % 74.50/11.09 (5) ~ (all_4_5 = e3) % 74.50/11.09 (6) ~ (all_4_5 = e0) % 74.50/11.09 (7) all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.50/11.09 (8) ~ (all_4_5 = e4) % 74.50/11.09 (9) all_6_1 = all_4_5 % 74.50/11.09 (10) ~ (all_4_5 = all_4_10) % 74.50/11.09 (11) all_6_2 = all_4_10 % 74.50/11.09 (12) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 74.50/11.09 all_10_22 = e1 % 74.50/11.09 % 74.50/11.09 Begin of proof % 74.50/11.09 | % 74.50/11.09 | BETA: splitting (12) gives: % 74.50/11.09 | % 74.50/11.09 | Case 1: % 74.50/11.09 | | % 74.50/11.09 | | (13) all_10_4 = e1 % 74.50/11.09 | | % 74.50/11.09 | | COMBINE_EQS: (3), (13) imply: % 74.50/11.09 | | (14) all_4_10 = e1 % 74.50/11.09 | | % 74.50/11.09 | | REDUCE: (10), (14) imply: % 74.50/11.09 | | (15) ~ (all_4_5 = e1) % 74.50/11.09 | | % 74.50/11.09 | | REF_CLOSE: (1), (5), (6), (8), (9), (15) are inconsistent by sub-proof #134. % 74.50/11.09 | | % 74.50/11.09 | Case 2: % 74.50/11.09 | | % 74.50/11.09 | | (16) ~ (all_10_4 = e1) % 74.50/11.09 | | % 74.50/11.09 | | REDUCE: (3), (16) imply: % 74.50/11.09 | | (17) ~ (all_4_10 = e1) % 74.50/11.09 | | % 74.50/11.09 | | REF_CLOSE: (2), (4), (7), (11), (17) are inconsistent by sub-proof #162. % 74.50/11.09 | | % 74.50/11.09 | End of split % 74.50/11.09 | % 74.50/11.09 End of proof % 74.50/11.09 % 74.50/11.09 Sub-proof #45 shows that the following formulas are inconsistent: % 74.50/11.09 ---------------------------------------------------------------- % 74.50/11.09 (1) all_10_3 = e4 % 74.50/11.09 (2) all_10_3 = e0 % 74.50/11.09 (3) ~ (e4 = e0) % 74.50/11.09 % 74.50/11.09 Begin of proof % 74.50/11.09 | % 74.50/11.09 | COMBINE_EQS: (1), (2) imply: % 74.50/11.09 | (4) e4 = e0 % 74.50/11.09 | % 74.50/11.09 | SIMP: (4) implies: % 74.50/11.09 | (5) e4 = e0 % 74.50/11.09 | % 74.50/11.09 | REDUCE: (3), (5) imply: % 74.50/11.09 | (6) $false % 74.50/11.09 | % 74.50/11.09 | CLOSE: (6) is inconsistent. % 74.50/11.09 | % 74.50/11.09 End of proof % 74.50/11.09 % 74.50/11.09 Sub-proof #46 shows that the following formulas are inconsistent: % 74.50/11.09 ---------------------------------------------------------------- % 74.50/11.09 (1) ~ (all_4_1 = all_4_2) % 74.50/11.09 (2) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | all_6_5 = e0 % 74.50/11.09 (3) all_10_20 = e4 % 74.50/11.09 (4) ~ (all_4_20 = all_4_21) % 74.50/11.09 (5) all_6_9 = all_4_21 % 74.50/11.09 (6) all_10_12 = all_4_3 % 74.50/11.09 (7) ~ (all_4_2 = e3) % 74.50/11.09 (8) all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e1 | all_6_14 = e0 % 74.50/11.09 (9) all_10_16 = all_4_20 % 74.50/11.09 (10) ~ (e4 = e0) % 74.50/11.09 (11) ~ (all_4_2 = all_4_22) % 74.50/11.09 (12) ~ (all_4_22 = e1) % 74.50/11.09 (13) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e1 | all_6_9 = e0 % 74.50/11.09 (14) all_10_17 = all_4_21 % 74.50/11.09 (15) all_6_5 = all_4_1 % 74.50/11.09 (16) ~ (all_4_1 = all_4_21) % 74.50/11.09 (17) all_10_2 = all_4_1 % 74.50/11.09 (18) ~ (all_4_3 = e0) % 74.50/11.09 (19) ~ (all_4_22 = e3) % 74.50/11.09 (20) ~ (all_4_21 = e4) % 74.50/11.09 (21) ~ (all_10_2 = e1) % 74.50/11.09 (22) ~ (all_4_21 = e1) % 74.50/11.09 (23) all_6_14 = all_4_22 % 74.50/11.09 (24) ~ (all_4_2 = e2) % 74.50/11.09 (25) ~ (all_4_2 = e4) % 74.50/11.09 (26) all_10_19 = e2 % 74.50/11.09 (27) all_10_6 = e0 | all_10_12 = e0 | all_10_20 = e0 % 74.50/11.09 (28) ~ (all_4_21 = e0) % 74.50/11.09 (29) all_10_6 = all_4_2 % 74.50/11.09 (30) all_10_18 = all_4_22 % 74.50/11.09 (31) all_10_16 = e0 | all_10_17 = e0 | all_10_18 = e0 | all_10_19 = e0 % 74.50/11.09 (32) ~ (all_4_1 = e4) % 74.50/11.09 (33) all_10_16 = e3 | all_10_17 = e3 | all_10_18 = e3 | all_10_19 = e3 | % 74.50/11.09 all_10_24 = e3 % 74.50/11.09 % 74.50/11.09 Begin of proof % 74.50/11.09 | % 74.50/11.09 | REDUCE: (17), (21) imply: % 74.50/11.09 | (34) ~ (all_4_1 = e1) % 74.50/11.09 | % 74.50/11.09 | BETA: splitting (2) gives: % 74.50/11.09 | % 74.50/11.09 | Case 1: % 74.50/11.09 | | % 74.50/11.09 | | (35) all_6_5 = e4 % 74.50/11.09 | | % 74.50/11.09 | | REF_CLOSE: (15), (32), (35) are inconsistent by sub-proof #81. % 74.50/11.09 | | % 74.50/11.09 | Case 2: % 74.50/11.09 | | % 74.50/11.09 | | (36) all_6_5 = e3 | all_6_5 = e1 | all_6_5 = e0 % 74.50/11.09 | | % 74.50/11.09 | | BETA: splitting (36) gives: % 74.50/11.09 | | % 74.50/11.09 | | Case 1: % 74.50/11.09 | | | % 74.50/11.09 | | | (37) all_6_5 = e1 % 74.50/11.09 | | | % 74.50/11.09 | | | REF_CLOSE: (15), (34), (37) are inconsistent by sub-proof #142. % 74.50/11.09 | | | % 74.50/11.09 | | Case 2: % 74.50/11.09 | | | % 74.50/11.09 | | | (38) all_6_5 = e3 | all_6_5 = e0 % 74.50/11.09 | | | % 74.50/11.09 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 74.50/11.09 | | | (14), (15), (16), (18), (19), (20), (22), (23), (24), (25), % 74.50/11.09 | | | (26), (27), (28), (29), (30), (31), (33), (38) are inconsistent % 74.50/11.09 | | | by sub-proof #47. % 74.50/11.09 | | | % 74.50/11.09 | | End of split % 74.50/11.09 | | % 74.50/11.09 | End of split % 74.50/11.09 | % 74.50/11.09 End of proof % 74.50/11.09 % 74.50/11.09 Sub-proof #47 shows that the following formulas are inconsistent: % 74.50/11.09 ---------------------------------------------------------------- % 74.50/11.09 (1) ~ (all_4_1 = all_4_2) % 74.50/11.09 (2) all_10_20 = e4 % 74.50/11.09 (3) ~ (all_4_20 = all_4_21) % 74.50/11.09 (4) all_6_9 = all_4_21 % 74.50/11.09 (5) all_10_12 = all_4_3 % 74.50/11.09 (6) ~ (all_4_2 = e3) % 74.50/11.09 (7) all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e1 | all_6_14 = e0 % 74.50/11.09 (8) all_10_16 = all_4_20 % 74.50/11.09 (9) ~ (e4 = e0) % 74.50/11.09 (10) ~ (all_4_2 = all_4_22) % 74.50/11.09 (11) ~ (all_4_22 = e1) % 74.50/11.09 (12) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e1 | all_6_9 = e0 % 74.50/11.09 (13) all_6_5 = e3 | all_6_5 = e0 % 74.50/11.09 (14) all_10_17 = all_4_21 % 74.50/11.09 (15) all_6_5 = all_4_1 % 74.50/11.09 (16) ~ (all_4_1 = all_4_21) % 74.50/11.09 (17) ~ (all_4_3 = e0) % 74.50/11.09 (18) ~ (all_4_22 = e3) % 74.50/11.09 (19) ~ (all_4_21 = e4) % 74.50/11.09 (20) ~ (all_4_21 = e1) % 74.50/11.09 (21) all_6_14 = all_4_22 % 74.50/11.09 (22) ~ (all_4_2 = e2) % 74.50/11.09 (23) ~ (all_4_2 = e4) % 74.50/11.09 (24) all_10_19 = e2 % 74.50/11.09 (25) all_10_6 = e0 | all_10_12 = e0 | all_10_20 = e0 % 74.50/11.09 (26) ~ (all_4_21 = e0) % 74.50/11.09 (27) all_10_6 = all_4_2 % 74.50/11.09 (28) all_10_18 = all_4_22 % 74.50/11.09 (29) all_10_16 = e0 | all_10_17 = e0 | all_10_18 = e0 | all_10_19 = e0 % 74.50/11.09 (30) all_10_16 = e3 | all_10_17 = e3 | all_10_18 = e3 | all_10_19 = e3 | % 74.50/11.09 all_10_24 = e3 % 74.50/11.09 % 74.50/11.09 Begin of proof % 74.50/11.09 | % 74.50/11.09 | BETA: splitting (25) gives: % 74.50/11.09 | % 74.50/11.09 | Case 1: % 74.50/11.09 | | % 74.50/11.09 | | (31) all_10_6 = e0 % 74.50/11.09 | | % 74.50/11.09 | | COMBINE_EQS: (27), (31) imply: % 74.50/11.09 | | (32) all_4_2 = e0 % 74.50/11.09 | | % 74.50/11.09 | | SIMP: (32) implies: % 74.50/11.09 | | (33) all_4_2 = e0 % 74.50/11.09 | | % 74.50/11.09 | | REDUCE: (1), (33) imply: % 74.50/11.09 | | (34) ~ (all_4_1 = e0) % 74.50/11.09 | | % 74.50/11.09 | | REDUCE: (10), (33) imply: % 74.50/11.09 | | (35) ~ (all_4_22 = e0) % 74.50/11.09 | | % 74.50/11.09 | | SIMP: (35) implies: % 74.50/11.09 | | (36) ~ (all_4_22 = e0) % 74.50/11.09 | | % 74.50/11.09 | | REDUCE: (23), (33) imply: % 74.50/11.09 | | (37) ~ (e4 = e0) % 74.50/11.09 | | % 74.50/11.09 | | REDUCE: (6), (33) imply: % 74.50/11.09 | | (38) ~ (e3 = e0) % 74.50/11.09 | | % 74.50/11.09 | | SIMP: (38) implies: % 74.50/11.09 | | (39) ~ (e3 = e0) % 74.50/11.09 | | % 74.50/11.09 | | REDUCE: (22), (33) imply: % 74.50/11.09 | | (40) ~ (e2 = e0) % 74.50/11.09 | | % 74.50/11.09 | | SIMP: (40) implies: % 74.50/11.09 | | (41) ~ (e2 = e0) % 74.50/11.09 | | % 74.50/11.09 | | BETA: splitting (12) gives: % 74.50/11.09 | | % 74.50/11.09 | | Case 1: % 74.50/11.09 | | | % 74.50/11.09 | | | (42) all_6_9 = e4 % 74.50/11.09 | | | % 74.50/11.09 | | | REF_CLOSE: (4), (19), (42) are inconsistent by sub-proof #114. % 74.50/11.09 | | | % 74.50/11.09 | | Case 2: % 74.50/11.09 | | | % 74.50/11.09 | | | (43) ~ (all_6_9 = e4) % 74.50/11.09 | | | (44) all_6_9 = e3 | all_6_9 = e1 | all_6_9 = e0 % 74.50/11.09 | | | % 74.50/11.09 | | | BETA: splitting (29) gives: % 74.50/11.09 | | | % 74.50/11.09 | | | Case 1: % 74.50/11.09 | | | | % 74.50/11.09 | | | | (45) all_10_16 = e0 % 74.50/11.09 | | | | % 74.50/11.09 | | | | COMBINE_EQS: (8), (45) imply: % 74.50/11.09 | | | | (46) all_4_20 = e0 % 74.50/11.09 | | | | % 74.50/11.09 | | | | REDUCE: (3), (46) imply: % 74.50/11.09 | | | | (47) ~ (all_4_21 = e0) % 74.50/11.09 | | | | % 74.50/11.09 | | | | BETA: splitting (30) gives: % 74.50/11.09 | | | | % 74.50/11.09 | | | | Case 1: % 74.50/11.09 | | | | | % 74.50/11.09 | | | | | (48) all_10_16 = e3 % 74.50/11.09 | | | | | % 74.50/11.09 | | | | | COMBINE_EQS: (45), (48) imply: % 74.50/11.09 | | | | | (49) e3 = e0 % 74.50/11.09 | | | | | % 74.50/11.09 | | | | | SIMP: (49) implies: % 74.50/11.09 | | | | | (50) e3 = e0 % 74.50/11.10 | | | | | % 74.50/11.10 | | | | | REDUCE: (39), (50) imply: % 74.50/11.10 | | | | | (51) $false % 74.50/11.10 | | | | | % 74.50/11.10 | | | | | CLOSE: (51) is inconsistent. % 74.50/11.10 | | | | | % 74.50/11.10 | | | | Case 2: % 74.50/11.10 | | | | | % 74.50/11.10 | | | | | (52) all_10_17 = e3 | all_10_18 = e3 | all_10_19 = e3 | all_10_24 = % 74.50/11.10 | | | | | e3 % 74.50/11.10 | | | | | % 74.50/11.10 | | | | | BETA: splitting (52) gives: % 74.50/11.10 | | | | | % 74.50/11.10 | | | | | Case 1: % 74.50/11.10 | | | | | | % 74.50/11.10 | | | | | | (53) all_10_17 = e3 % 74.50/11.10 | | | | | | % 74.50/11.10 | | | | | | COMBINE_EQS: (14), (53) imply: % 74.50/11.10 | | | | | | (54) all_4_21 = e3 % 74.50/11.10 | | | | | | % 74.50/11.10 | | | | | | REDUCE: (16), (54) imply: % 74.50/11.10 | | | | | | (55) ~ (all_4_1 = e3) % 74.50/11.10 | | | | | | % 74.50/11.10 | | | | | | REF_CLOSE: (13), (15), (34), (55) are inconsistent by sub-proof % 74.50/11.10 | | | | | | #141. % 74.50/11.10 | | | | | | % 74.50/11.10 | | | | | Case 2: % 74.50/11.10 | | | | | | % 74.50/11.10 | | | | | | (56) ~ (all_10_17 = e3) % 74.50/11.10 | | | | | | % 74.50/11.10 | | | | | | REDUCE: (14), (56) imply: % 74.50/11.10 | | | | | | (57) ~ (all_4_21 = e3) % 74.50/11.10 | | | | | | % 74.50/11.10 | | | | | | REF_CLOSE: (4), (20), (26), (44), (57) are inconsistent by sub-proof % 74.50/11.10 | | | | | | #111. % 74.50/11.10 | | | | | | % 74.50/11.10 | | | | | End of split % 74.50/11.10 | | | | | % 74.50/11.10 | | | | End of split % 74.50/11.10 | | | | % 74.50/11.10 | | | Case 2: % 74.50/11.10 | | | | % 74.50/11.10 | | | | (58) all_10_17 = e0 | all_10_18 = e0 | all_10_19 = e0 % 74.50/11.10 | | | | % 74.50/11.10 | | | | BETA: splitting (7) gives: % 74.50/11.10 | | | | % 74.50/11.10 | | | | Case 1: % 74.50/11.10 | | | | | % 74.50/11.10 | | | | | (59) all_6_14 = e4 % 74.50/11.10 | | | | | % 74.50/11.10 | | | | | COMBINE_EQS: (21), (59) imply: % 74.50/11.10 | | | | | (60) all_4_22 = e4 % 74.50/11.10 | | | | | % 74.50/11.10 | | | | | SIMP: (60) implies: % 74.50/11.10 | | | | | (61) all_4_22 = e4 % 74.50/11.10 | | | | | % 74.50/11.10 | | | | | COMBINE_EQS: (28), (61) imply: % 74.50/11.10 | | | | | (62) all_10_18 = e4 % 74.50/11.10 | | | | | % 74.50/11.10 | | | | | BETA: splitting (12) gives: % 74.50/11.10 | | | | | % 74.50/11.10 | | | | | Case 1: % 74.50/11.10 | | | | | | % 74.50/11.10 | | | | | | (63) all_6_9 = e4 % 74.50/11.10 | | | | | | % 74.50/11.10 | | | | | | REF_CLOSE: (4), (19), (63) are inconsistent by sub-proof #114. % 74.50/11.10 | | | | | | % 74.50/11.10 | | | | | Case 2: % 74.50/11.10 | | | | | | % 74.50/11.10 | | | | | | % 74.50/11.10 | | | | | | BETA: splitting (44) gives: % 74.50/11.10 | | | | | | % 74.50/11.10 | | | | | | Case 1: % 74.50/11.10 | | | | | | | % 74.50/11.10 | | | | | | | (64) all_6_9 = e1 % 74.50/11.10 | | | | | | | % 74.50/11.10 | | | | | | | REF_CLOSE: (4), (20), (64) are inconsistent by sub-proof #113. % 74.50/11.10 | | | | | | | % 74.50/11.10 | | | | | | Case 2: % 74.50/11.10 | | | | | | | % 74.50/11.10 | | | | | | | (65) all_6_9 = e3 | all_6_9 = e0 % 74.50/11.10 | | | | | | | % 74.50/11.10 | | | | | | | REF_CLOSE: (4), (9), (14), (24), (26), (41), (58), (62), (65) are % 74.50/11.10 | | | | | | | inconsistent by sub-proof #51. % 74.50/11.10 | | | | | | | % 74.50/11.10 | | | | | | End of split % 74.50/11.10 | | | | | | % 74.50/11.10 | | | | | End of split % 74.50/11.10 | | | | | % 74.50/11.10 | | | | Case 2: % 74.50/11.10 | | | | | % 74.50/11.10 | | | | | (66) all_6_14 = e3 | all_6_14 = e1 | all_6_14 = e0 % 74.50/11.10 | | | | | % 74.50/11.10 | | | | | REF_CLOSE: (11), (18), (21), (36), (66) are inconsistent by sub-proof % 74.50/11.10 | | | | | #48. % 74.50/11.10 | | | | | % 74.50/11.10 | | | | End of split % 74.50/11.10 | | | | % 74.50/11.10 | | | End of split % 74.50/11.10 | | | % 74.50/11.10 | | End of split % 74.50/11.10 | | % 74.50/11.10 | Case 2: % 74.50/11.10 | | % 74.50/11.10 | | (67) all_10_12 = e0 | all_10_20 = e0 % 74.50/11.10 | | % 74.50/11.10 | | REF_CLOSE: (2), (5), (9), (17), (67) are inconsistent by sub-proof #75. % 74.50/11.10 | | % 74.50/11.10 | End of split % 74.50/11.10 | % 74.50/11.10 End of proof % 74.50/11.10 % 74.50/11.10 Sub-proof #48 shows that the following formulas are inconsistent: % 74.50/11.10 ---------------------------------------------------------------- % 74.50/11.10 (1) ~ (all_4_22 = e0) % 74.50/11.10 (2) ~ (all_4_22 = e1) % 74.50/11.10 (3) all_6_14 = e3 | all_6_14 = e1 | all_6_14 = e0 % 74.50/11.10 (4) ~ (all_4_22 = e3) % 74.50/11.10 (5) all_6_14 = all_4_22 % 74.50/11.10 % 74.50/11.10 Begin of proof % 74.50/11.10 | % 74.50/11.10 | BETA: splitting (3) gives: % 74.50/11.10 | % 74.50/11.10 | Case 1: % 74.50/11.10 | | % 74.50/11.10 | | (6) all_6_14 = e1 % 74.50/11.10 | | % 74.50/11.10 | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #50. % 74.50/11.10 | | % 74.50/11.10 | Case 2: % 74.50/11.10 | | % 74.50/11.10 | | (7) all_6_14 = e3 | all_6_14 = e0 % 74.50/11.10 | | % 74.50/11.10 | | BETA: splitting (7) gives: % 74.50/11.10 | | % 74.50/11.10 | | Case 1: % 74.50/11.10 | | | % 74.50/11.10 | | | (8) all_6_14 = e3 % 74.50/11.10 | | | % 74.50/11.10 | | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #49. % 74.50/11.10 | | | % 74.50/11.10 | | Case 2: % 74.50/11.10 | | | % 74.50/11.10 | | | (9) all_6_14 = e0 % 74.50/11.10 | | | % 74.50/11.10 | | | COMBINE_EQS: (5), (9) imply: % 74.50/11.10 | | | (10) all_4_22 = e0 % 74.50/11.10 | | | % 74.50/11.10 | | | SIMP: (10) implies: % 74.50/11.10 | | | (11) all_4_22 = e0 % 74.50/11.10 | | | % 74.50/11.10 | | | REDUCE: (1), (11) imply: % 74.50/11.10 | | | (12) $false % 74.50/11.10 | | | % 74.50/11.10 | | | CLOSE: (12) is inconsistent. % 74.50/11.10 | | | % 74.50/11.10 | | End of split % 74.50/11.10 | | % 74.50/11.10 | End of split % 74.50/11.10 | % 74.50/11.10 End of proof % 74.50/11.10 % 74.50/11.10 Sub-proof #49 shows that the following formulas are inconsistent: % 74.50/11.10 ---------------------------------------------------------------- % 74.50/11.10 (1) all_6_14 = all_4_22 % 74.50/11.10 (2) all_6_14 = e3 % 74.50/11.10 (3) ~ (all_4_22 = e3) % 74.50/11.10 % 74.50/11.10 Begin of proof % 74.50/11.10 | % 74.50/11.10 | COMBINE_EQS: (1), (2) imply: % 74.50/11.10 | (4) all_4_22 = e3 % 74.50/11.10 | % 74.50/11.10 | SIMP: (4) implies: % 74.50/11.10 | (5) all_4_22 = e3 % 74.50/11.10 | % 74.50/11.10 | REDUCE: (3), (5) imply: % 74.50/11.10 | (6) $false % 74.50/11.10 | % 74.50/11.10 | CLOSE: (6) is inconsistent. % 74.50/11.10 | % 74.50/11.10 End of proof % 74.50/11.10 % 74.50/11.10 Sub-proof #50 shows that the following formulas are inconsistent: % 74.50/11.10 ---------------------------------------------------------------- % 74.50/11.10 (1) all_6_14 = all_4_22 % 74.50/11.10 (2) all_6_14 = e1 % 74.50/11.10 (3) ~ (all_4_22 = e1) % 74.50/11.10 % 74.50/11.10 Begin of proof % 74.50/11.10 | % 74.50/11.10 | COMBINE_EQS: (1), (2) imply: % 74.50/11.10 | (4) all_4_22 = e1 % 74.50/11.10 | % 74.50/11.10 | SIMP: (4) implies: % 74.50/11.10 | (5) all_4_22 = e1 % 74.50/11.10 | % 74.50/11.10 | REDUCE: (3), (5) imply: % 74.50/11.10 | (6) $false % 74.50/11.10 | % 74.50/11.10 | CLOSE: (6) is inconsistent. % 74.50/11.10 | % 74.50/11.10 End of proof % 74.50/11.10 % 74.50/11.10 Sub-proof #51 shows that the following formulas are inconsistent: % 74.50/11.10 ---------------------------------------------------------------- % 74.50/11.10 (1) ~ (e2 = e0) % 74.50/11.10 (2) all_6_9 = all_4_21 % 74.50/11.10 (3) ~ (e4 = e0) % 74.50/11.10 (4) all_10_18 = e4 % 74.50/11.10 (5) all_10_17 = all_4_21 % 74.50/11.10 (6) all_10_17 = e0 | all_10_18 = e0 | all_10_19 = e0 % 74.50/11.10 (7) all_6_9 = e3 | all_6_9 = e0 % 74.50/11.10 (8) all_10_19 = e2 % 74.50/11.10 (9) ~ (all_4_21 = e0) % 74.50/11.10 % 74.50/11.10 Begin of proof % 74.50/11.10 | % 74.50/11.10 | BETA: splitting (7) gives: % 74.50/11.10 | % 74.50/11.10 | Case 1: % 74.50/11.10 | | % 74.50/11.10 | | (10) all_6_9 = e3 % 74.50/11.10 | | % 74.50/11.10 | | COMBINE_EQS: (2), (10) imply: % 74.50/11.10 | | (11) all_4_21 = e3 % 74.50/11.10 | | % 74.50/11.10 | | SIMP: (11) implies: % 74.50/11.10 | | (12) all_4_21 = e3 % 74.50/11.10 | | % 74.50/11.10 | | COMBINE_EQS: (5), (12) imply: % 74.50/11.10 | | (13) all_10_17 = e3 % 74.50/11.10 | | % 74.50/11.10 | | REDUCE: (9), (12) imply: % 74.50/11.10 | | (14) ~ (e3 = e0) % 74.50/11.10 | | % 74.50/11.10 | | BETA: splitting (6) gives: % 74.50/11.10 | | % 74.50/11.10 | | Case 1: % 74.50/11.10 | | | % 74.50/11.10 | | | (15) all_10_17 = e0 % 74.50/11.10 | | | % 74.50/11.10 | | | COMBINE_EQS: (13), (15) imply: % 74.50/11.10 | | | (16) e3 = e0 % 74.50/11.10 | | | % 74.50/11.10 | | | REDUCE: (14), (16) imply: % 74.50/11.10 | | | (17) $false % 74.50/11.10 | | | % 74.50/11.10 | | | CLOSE: (17) is inconsistent. % 74.50/11.10 | | | % 74.50/11.10 | | Case 2: % 74.50/11.10 | | | % 74.50/11.10 | | | (18) all_10_18 = e0 | all_10_19 = e0 % 74.50/11.10 | | | % 74.50/11.10 | | | BETA: splitting (18) gives: % 74.50/11.10 | | | % 74.50/11.10 | | | Case 1: % 74.50/11.10 | | | | % 74.50/11.10 | | | | (19) all_10_18 = e0 % 74.50/11.10 | | | | % 74.50/11.10 | | | | COMBINE_EQS: (4), (19) imply: % 74.50/11.10 | | | | (20) e4 = e0 % 74.50/11.10 | | | | % 74.50/11.10 | | | | REDUCE: (3), (20) imply: % 74.50/11.10 | | | | (21) $false % 74.50/11.10 | | | | % 74.50/11.10 | | | | CLOSE: (21) is inconsistent. % 74.50/11.10 | | | | % 74.50/11.10 | | | Case 2: % 74.50/11.10 | | | | % 74.50/11.10 | | | | (22) all_10_19 = e0 % 74.50/11.10 | | | | % 74.50/11.10 | | | | COMBINE_EQS: (8), (22) imply: % 74.50/11.10 | | | | (23) e2 = e0 % 74.50/11.10 | | | | % 74.50/11.10 | | | | REDUCE: (1), (23) imply: % 74.50/11.10 | | | | (24) $false % 74.50/11.10 | | | | % 74.50/11.10 | | | | CLOSE: (24) is inconsistent. % 74.50/11.10 | | | | % 74.50/11.10 | | | End of split % 74.50/11.10 | | | % 74.50/11.10 | | End of split % 74.50/11.10 | | % 74.50/11.10 | Case 2: % 74.50/11.10 | | % 74.50/11.10 | | (25) all_6_9 = e0 % 74.50/11.10 | | % 74.50/11.10 | | REF_CLOSE: (2), (9), (25) are inconsistent by sub-proof #112. % 74.50/11.10 | | % 74.50/11.10 | End of split % 74.50/11.10 | % 74.50/11.10 End of proof % 74.50/11.10 % 74.50/11.10 Sub-proof #52 shows that the following formulas are inconsistent: % 74.50/11.10 ---------------------------------------------------------------- % 74.50/11.10 (1) all_6_14 = all_4_22 % 74.50/11.10 (2) all_6_14 = e2 % 74.50/11.10 (3) ~ (all_4_22 = e2) % 74.50/11.10 % 74.50/11.10 Begin of proof % 74.50/11.10 | % 74.50/11.10 | COMBINE_EQS: (1), (2) imply: % 74.50/11.10 | (4) all_4_22 = e2 % 74.50/11.10 | % 74.50/11.10 | SIMP: (4) implies: % 74.50/11.10 | (5) all_4_22 = e2 % 74.50/11.10 | % 74.50/11.10 | REDUCE: (3), (5) imply: % 74.50/11.10 | (6) $false % 74.50/11.10 | % 74.50/11.10 | CLOSE: (6) is inconsistent. % 74.50/11.10 | % 74.50/11.10 End of proof % 74.50/11.10 % 74.50/11.10 Sub-proof #53 shows that the following formulas are inconsistent: % 74.50/11.10 ---------------------------------------------------------------- % 74.50/11.10 (1) all_10_5 = all_4_11 % 74.50/11.10 (2) all_10_5 = e2 % 74.50/11.10 (3) ~ (all_4_11 = e2) % 74.50/11.10 % 74.50/11.10 Begin of proof % 74.50/11.10 | % 74.50/11.10 | COMBINE_EQS: (1), (2) imply: % 74.50/11.10 | (4) all_4_11 = e2 % 74.50/11.10 | % 74.50/11.10 | SIMP: (4) implies: % 74.50/11.10 | (5) all_4_11 = e2 % 74.50/11.10 | % 74.50/11.10 | REDUCE: (3), (5) imply: % 74.50/11.10 | (6) $false % 74.50/11.10 | % 74.50/11.10 | CLOSE: (6) is inconsistent. % 74.50/11.10 | % 74.50/11.10 End of proof % 74.50/11.10 % 74.50/11.10 Sub-proof #54 shows that the following formulas are inconsistent: % 74.50/11.10 ---------------------------------------------------------------- % 74.50/11.10 (1) all_10_3 = e2 % 74.50/11.10 (2) all_10_3 = e0 % 74.50/11.10 (3) ~ (e2 = e0) % 74.50/11.10 % 74.50/11.10 Begin of proof % 74.50/11.10 | % 74.50/11.10 | COMBINE_EQS: (1), (2) imply: % 74.50/11.10 | (4) e2 = e0 % 74.50/11.10 | % 74.50/11.10 | SIMP: (4) implies: % 74.50/11.10 | (5) e2 = e0 % 74.50/11.10 | % 74.50/11.10 | REDUCE: (3), (5) imply: % 74.50/11.10 | (6) $false % 74.50/11.10 | % 74.50/11.10 | CLOSE: (6) is inconsistent. % 74.50/11.10 | % 74.50/11.10 End of proof % 74.50/11.10 % 74.50/11.10 Sub-proof #55 shows that the following formulas are inconsistent: % 74.50/11.10 ---------------------------------------------------------------- % 74.50/11.10 (1) all_10_2 = all_4_1 % 74.50/11.10 (2) all_10_2 = e2 % 74.50/11.10 (3) ~ (all_4_1 = e2) % 74.50/11.10 % 74.50/11.10 Begin of proof % 74.50/11.10 | % 74.50/11.10 | COMBINE_EQS: (1), (2) imply: % 74.50/11.10 | (4) all_4_1 = e2 % 74.50/11.10 | % 74.50/11.10 | SIMP: (4) implies: % 74.50/11.10 | (5) all_4_1 = e2 % 74.50/11.10 | % 74.50/11.10 | REDUCE: (3), (5) imply: % 74.50/11.10 | (6) $false % 74.50/11.10 | % 74.50/11.10 | CLOSE: (6) is inconsistent. % 74.50/11.10 | % 74.50/11.10 End of proof % 74.50/11.10 % 74.50/11.10 Sub-proof #56 shows that the following formulas are inconsistent: % 74.50/11.10 ---------------------------------------------------------------- % 74.50/11.10 (1) all_8_68 = e4 % 74.50/11.10 (2) all_8_68 = e1 % 74.50/11.10 (3) ~ (e4 = e1) % 74.50/11.10 % 74.50/11.10 Begin of proof % 74.50/11.10 | % 74.50/11.10 | COMBINE_EQS: (1), (2) imply: % 74.50/11.10 | (4) e4 = e1 % 74.50/11.10 | % 74.50/11.10 | SIMP: (4) implies: % 74.50/11.10 | (5) e4 = e1 % 74.50/11.10 | % 74.50/11.10 | REDUCE: (3), (5) imply: % 74.50/11.10 | (6) $false % 74.50/11.10 | % 74.50/11.10 | CLOSE: (6) is inconsistent. % 74.50/11.10 | % 74.50/11.10 End of proof % 74.50/11.10 % 74.50/11.10 Sub-proof #57 shows that the following formulas are inconsistent: % 74.50/11.10 ---------------------------------------------------------------- % 74.50/11.10 (1) all_8_67 = e3 % 74.50/11.10 (2) all_8_67 = e1 % 74.50/11.10 (3) ~ (e3 = e1) % 74.50/11.10 % 74.50/11.10 Begin of proof % 74.50/11.10 | % 74.50/11.10 | COMBINE_EQS: (1), (2) imply: % 74.50/11.10 | (4) e3 = e1 % 74.50/11.10 | % 74.50/11.10 | SIMP: (4) implies: % 74.50/11.10 | (5) e3 = e1 % 74.50/11.10 | % 74.50/11.10 | REDUCE: (3), (5) imply: % 74.50/11.10 | (6) $false % 74.50/11.10 | % 74.50/11.10 | CLOSE: (6) is inconsistent. % 74.50/11.10 | % 74.50/11.10 End of proof % 74.50/11.10 % 74.50/11.10 Sub-proof #58 shows that the following formulas are inconsistent: % 74.50/11.10 ---------------------------------------------------------------- % 74.50/11.10 (1) all_10_14 = e0 % 74.50/11.10 (2) all_10_15 = e4 % 74.50/11.10 (3) ~ (e2 = e1) % 74.50/11.10 (4) all_10_14 = e1 | all_10_15 = e1 | all_10_19 = e1 % 74.50/11.10 (5) all_10_19 = e2 % 74.50/11.10 (6) ~ (e1 = e0) % 74.50/11.10 (7) ~ (e4 = e1) % 74.50/11.10 % 74.50/11.10 Begin of proof % 74.50/11.10 | % 74.50/11.10 | BETA: splitting (4) gives: % 74.50/11.10 | % 74.50/11.10 | Case 1: % 74.50/11.10 | | % 74.50/11.10 | | (8) all_10_14 = e1 % 74.50/11.10 | | % 74.50/11.10 | | COMBINE_EQS: (1), (8) imply: % 74.50/11.10 | | (9) e1 = e0 % 74.50/11.10 | | % 74.50/11.10 | | REDUCE: (6), (9) imply: % 74.50/11.10 | | (10) $false % 74.50/11.10 | | % 74.50/11.10 | | CLOSE: (10) is inconsistent. % 74.50/11.10 | | % 74.50/11.10 | Case 2: % 74.50/11.10 | | % 74.50/11.10 | | (11) all_10_15 = e1 | all_10_19 = e1 % 74.50/11.10 | | % 74.50/11.10 | | BETA: splitting (11) gives: % 74.50/11.10 | | % 74.50/11.10 | | Case 1: % 74.50/11.10 | | | % 74.50/11.10 | | | (12) all_10_15 = e1 % 74.50/11.10 | | | % 74.50/11.10 | | | COMBINE_EQS: (2), (12) imply: % 74.50/11.10 | | | (13) e4 = e1 % 74.50/11.10 | | | % 74.50/11.10 | | | REDUCE: (7), (13) imply: % 74.50/11.10 | | | (14) $false % 74.50/11.10 | | | % 74.50/11.10 | | | CLOSE: (14) is inconsistent. % 74.50/11.10 | | | % 74.50/11.10 | | Case 2: % 74.50/11.10 | | | % 74.50/11.10 | | | (15) all_10_19 = e1 % 74.50/11.10 | | | % 74.50/11.10 | | | COMBINE_EQS: (5), (15) imply: % 74.50/11.10 | | | (16) e2 = e1 % 74.50/11.10 | | | % 74.50/11.10 | | | SIMP: (16) implies: % 74.50/11.10 | | | (17) e2 = e1 % 74.50/11.10 | | | % 74.50/11.10 | | | REDUCE: (3), (17) imply: % 74.50/11.10 | | | (18) $false % 74.50/11.10 | | | % 74.50/11.10 | | | CLOSE: (18) is inconsistent. % 74.50/11.10 | | | % 74.50/11.10 | | End of split % 74.50/11.10 | | % 74.50/11.10 | End of split % 74.50/11.10 | % 74.50/11.10 End of proof % 74.50/11.10 % 74.50/11.10 Sub-proof #59 shows that the following formulas are inconsistent: % 74.50/11.10 ---------------------------------------------------------------- % 74.50/11.10 (1) all_10_12 = all_4_3 % 74.50/11.10 (2) all_10_12 = e1 % 74.50/11.10 (3) ~ (all_4_3 = e1) % 74.50/11.10 % 74.50/11.10 Begin of proof % 74.50/11.10 | % 74.50/11.10 | COMBINE_EQS: (1), (2) imply: % 74.50/11.10 | (4) all_4_3 = e1 % 74.50/11.10 | % 74.50/11.10 | SIMP: (4) implies: % 74.50/11.10 | (5) all_4_3 = e1 % 74.50/11.10 | % 74.50/11.10 | REDUCE: (3), (5) imply: % 74.50/11.10 | (6) $false % 74.50/11.10 | % 74.50/11.10 | CLOSE: (6) is inconsistent. % 74.50/11.10 | % 74.50/11.10 End of proof % 74.50/11.10 % 74.50/11.10 Sub-proof #60 shows that the following formulas are inconsistent: % 74.50/11.10 ---------------------------------------------------------------- % 74.50/11.10 (1) all_10_15 = e4 % 74.50/11.10 (2) all_10_19 = all_4_23 % 74.50/11.10 (3) ~ (e4 = e2) % 74.50/11.10 (4) ~ (all_4_23 = e2) % 74.50/11.10 (5) all_10_15 = e2 | all_10_19 = e2 % 74.50/11.10 % 74.50/11.10 Begin of proof % 74.50/11.10 | % 74.50/11.10 | BETA: splitting (5) gives: % 74.50/11.10 | % 74.50/11.10 | Case 1: % 74.50/11.10 | | % 74.50/11.10 | | (6) all_10_15 = e2 % 74.50/11.10 | | % 74.50/11.10 | | COMBINE_EQS: (1), (6) imply: % 74.50/11.10 | | (7) e4 = e2 % 74.50/11.10 | | % 74.50/11.10 | | REDUCE: (3), (7) imply: % 74.50/11.10 | | (8) $false % 74.50/11.10 | | % 74.50/11.10 | | CLOSE: (8) is inconsistent. % 74.50/11.10 | | % 74.50/11.10 | Case 2: % 74.50/11.10 | | % 74.50/11.10 | | (9) all_10_19 = e2 % 74.50/11.10 | | % 74.50/11.10 | | COMBINE_EQS: (2), (9) imply: % 74.50/11.10 | | (10) all_4_23 = e2 % 74.50/11.10 | | % 74.50/11.10 | | REDUCE: (4), (10) imply: % 74.50/11.10 | | (11) $false % 74.50/11.10 | | % 74.50/11.10 | | CLOSE: (11) is inconsistent. % 74.50/11.10 | | % 74.50/11.10 | End of split % 74.50/11.10 | % 74.50/11.10 End of proof % 74.50/11.10 % 74.50/11.10 Sub-proof #61 shows that the following formulas are inconsistent: % 74.50/11.10 ---------------------------------------------------------------- % 74.50/11.10 (1) ~ (all_4_2 = e1) % 74.50/11.10 (2) ~ (all_4_2 = e3) % 74.50/11.10 (3) all_6_10 = all_4_2 % 74.50/11.10 (4) ~ (all_4_2 = e0) % 74.50/11.10 (5) ~ (all_4_2 = e4) % 74.50/11.11 (6) all_6_10 = e4 | all_6_10 = e3 | all_6_10 = e1 | all_6_10 = e0 % 74.50/11.11 % 74.50/11.11 Begin of proof % 74.50/11.11 | % 74.50/11.11 | BETA: splitting (6) gives: % 74.50/11.11 | % 74.50/11.11 | Case 1: % 74.50/11.11 | | % 74.50/11.11 | | (7) all_6_10 = e4 % 74.50/11.11 | | % 74.50/11.11 | | COMBINE_EQS: (3), (7) imply: % 74.50/11.11 | | (8) all_4_2 = e4 % 74.50/11.11 | | % 74.50/11.11 | | REDUCE: (5), (8) imply: % 74.50/11.11 | | (9) $false % 74.50/11.11 | | % 74.50/11.11 | | CLOSE: (9) is inconsistent. % 74.50/11.11 | | % 74.50/11.11 | Case 2: % 74.50/11.11 | | % 74.50/11.11 | | (10) all_6_10 = e3 | all_6_10 = e1 | all_6_10 = e0 % 74.50/11.11 | | % 74.50/11.11 | | BETA: splitting (10) gives: % 74.50/11.11 | | % 74.50/11.11 | | Case 1: % 74.50/11.11 | | | % 74.50/11.11 | | | (11) all_6_10 = e1 % 74.50/11.11 | | | % 74.50/11.11 | | | REF_CLOSE: (1), (3), (11) are inconsistent by sub-proof #103. % 74.50/11.11 | | | % 74.50/11.11 | | Case 2: % 74.50/11.11 | | | % 74.50/11.11 | | | (12) all_6_10 = e3 | all_6_10 = e0 % 74.50/11.11 | | | % 74.50/11.11 | | | REF_CLOSE: (2), (3), (4), (12) are inconsistent by sub-proof #62. % 74.50/11.11 | | | % 74.50/11.11 | | End of split % 74.50/11.11 | | % 74.50/11.11 | End of split % 74.50/11.11 | % 74.50/11.11 End of proof % 74.50/11.11 % 74.50/11.11 Sub-proof #62 shows that the following formulas are inconsistent: % 74.50/11.11 ---------------------------------------------------------------- % 74.50/11.11 (1) all_6_10 = e3 | all_6_10 = e0 % 74.50/11.11 (2) all_6_10 = all_4_2 % 74.50/11.11 (3) ~ (all_4_2 = e3) % 74.50/11.11 (4) ~ (all_4_2 = e0) % 74.50/11.11 % 74.50/11.11 Begin of proof % 74.50/11.11 | % 74.50/11.11 | BETA: splitting (1) gives: % 74.50/11.11 | % 74.50/11.11 | Case 1: % 74.50/11.11 | | % 74.50/11.11 | | (5) all_6_10 = e3 % 74.50/11.11 | | % 74.50/11.11 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #102. % 74.50/11.11 | | % 74.50/11.11 | Case 2: % 74.50/11.11 | | % 74.50/11.11 | | (6) all_6_10 = e0 % 74.50/11.11 | | % 74.50/11.11 | | COMBINE_EQS: (2), (6) imply: % 74.50/11.11 | | (7) all_4_2 = e0 % 74.50/11.11 | | % 74.50/11.11 | | SIMP: (7) implies: % 74.50/11.11 | | (8) all_4_2 = e0 % 74.50/11.11 | | % 74.50/11.11 | | REDUCE: (4), (8) imply: % 74.50/11.11 | | (9) $false % 74.50/11.11 | | % 74.50/11.11 | | CLOSE: (9) is inconsistent. % 74.50/11.11 | | % 74.50/11.11 | End of split % 74.50/11.11 | % 74.50/11.11 End of proof % 74.50/11.11 % 74.50/11.11 Sub-proof #63 shows that the following formulas are inconsistent: % 74.50/11.11 ---------------------------------------------------------------- % 74.50/11.11 (1) ~ (all_4_20 = e3) % 74.50/11.11 (2) all_10_9 = e3 | all_10_16 = e3 % 74.50/11.11 (3) all_10_16 = all_4_20 % 74.50/11.11 (4) all_10_9 = all_4_15 % 74.50/11.11 (5) ~ (all_4_15 = e3) % 74.50/11.11 % 74.50/11.11 Begin of proof % 74.50/11.11 | % 74.50/11.11 | BETA: splitting (2) gives: % 74.50/11.11 | % 74.50/11.11 | Case 1: % 74.50/11.11 | | % 74.50/11.11 | | (6) all_10_9 = e3 % 74.50/11.11 | | % 74.50/11.11 | | COMBINE_EQS: (4), (6) imply: % 74.50/11.11 | | (7) all_4_15 = e3 % 74.50/11.11 | | % 74.50/11.11 | | REDUCE: (5), (7) imply: % 74.50/11.11 | | (8) $false % 74.50/11.11 | | % 74.50/11.11 | | CLOSE: (8) is inconsistent. % 74.50/11.11 | | % 74.50/11.11 | Case 2: % 74.50/11.11 | | % 74.50/11.11 | | (9) all_10_16 = e3 % 74.50/11.11 | | % 74.50/11.11 | | COMBINE_EQS: (3), (9) imply: % 74.50/11.11 | | (10) all_4_20 = e3 % 74.50/11.11 | | % 74.50/11.11 | | REDUCE: (1), (10) imply: % 74.50/11.11 | | (11) $false % 74.50/11.11 | | % 74.50/11.11 | | CLOSE: (11) is inconsistent. % 74.50/11.11 | | % 74.50/11.11 | End of split % 74.50/11.11 | % 74.50/11.11 End of proof % 74.50/11.11 % 74.50/11.11 Sub-proof #64 shows that the following formulas are inconsistent: % 74.50/11.11 ---------------------------------------------------------------- % 74.50/11.11 (1) all_10_21 = all_4_9 % 74.50/11.11 (2) ~ (all_4_9 = e2) % 74.50/11.11 (3) all_10_13 = e2 | all_10_21 = e2 % 74.50/11.11 (4) all_10_13 = all_4_8 % 74.50/11.11 (5) ~ (all_4_8 = e2) % 74.50/11.11 % 74.50/11.11 Begin of proof % 74.50/11.11 | % 74.50/11.11 | BETA: splitting (3) gives: % 74.50/11.11 | % 74.50/11.11 | Case 1: % 74.50/11.11 | | % 74.50/11.11 | | (6) all_10_13 = e2 % 74.50/11.11 | | % 74.50/11.11 | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #88. % 74.50/11.11 | | % 74.50/11.11 | Case 2: % 74.50/11.11 | | % 74.50/11.11 | | (7) all_10_21 = e2 % 74.50/11.11 | | % 74.50/11.11 | | COMBINE_EQS: (1), (7) imply: % 74.50/11.11 | | (8) all_4_9 = e2 % 74.50/11.11 | | % 74.50/11.11 | | REDUCE: (2), (8) imply: % 74.50/11.11 | | (9) $false % 74.50/11.11 | | % 74.50/11.11 | | CLOSE: (9) is inconsistent. % 74.50/11.11 | | % 74.50/11.11 | End of split % 74.50/11.11 | % 74.50/11.11 End of proof % 74.50/11.11 % 74.50/11.11 Sub-proof #65 shows that the following formulas are inconsistent: % 74.50/11.11 ---------------------------------------------------------------- % 74.50/11.11 (1) all_10_3 = e2 % 74.50/11.11 (2) all_10_3 = e1 % 74.50/11.11 (3) ~ (e2 = e1) % 74.50/11.11 % 74.50/11.11 Begin of proof % 74.50/11.11 | % 74.50/11.11 | COMBINE_EQS: (1), (2) imply: % 74.50/11.11 | (4) e2 = e1 % 74.50/11.11 | % 74.50/11.11 | SIMP: (4) implies: % 74.50/11.11 | (5) e2 = e1 % 74.50/11.11 | % 74.50/11.11 | REDUCE: (3), (5) imply: % 74.50/11.11 | (6) $false % 74.50/11.11 | % 74.50/11.11 | CLOSE: (6) is inconsistent. % 74.50/11.11 | % 74.50/11.11 End of proof % 74.50/11.11 % 74.50/11.11 Sub-proof #66 shows that the following formulas are inconsistent: % 74.50/11.11 ---------------------------------------------------------------- % 74.50/11.11 (1) ~ (all_4_14 = e3) % 74.50/11.11 (2) all_10_4 = all_4_10 % 74.50/11.11 (3) ~ (all_4_10 = all_4_14) % 74.50/11.11 (4) ~ (all_4_14 = e0) % 74.50/11.11 (5) all_6_22 = e4 | all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 74.50/11.11 (6) all_10_23 = all_4_19 % 74.50/11.11 (7) ~ (all_4_10 = e0) % 74.50/11.11 (8) all_10_20 = e1 | all_10_21 = e1 | all_10_22 = e1 | all_10_23 = e1 | % 74.50/11.11 all_10_24 = e1 % 74.50/11.11 (9) all_10_24 = e0 % 74.50/11.11 (10) all_10_20 = all_4_4 % 74.50/11.11 (11) all_10_22 = all_4_14 % 74.50/11.11 (12) all_10_4 = e1 % 74.50/11.11 (13) all_10_21 = e2 % 74.50/11.11 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.50/11.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.50/11.11 (15) op(e1, all_4_19) = e0 % 74.50/11.11 (16) all_6_22 = all_4_14 % 74.50/11.11 (17) ~ (all_4_4 = e1) % 74.50/11.11 (18) ~ (all_4_10 = e2) % 74.50/11.11 (19) op(e1, e1) = e4 % 74.50/11.11 % 74.50/11.11 Begin of proof % 74.50/11.11 | % 74.50/11.11 | COMBINE_EQS: (2), (12) imply: % 74.50/11.11 | (20) all_4_10 = e1 % 74.50/11.11 | % 74.50/11.11 | SIMP: (20) implies: % 74.87/11.11 | (21) all_4_10 = e1 % 74.87/11.11 | % 74.87/11.11 | REDUCE: (3), (21) imply: % 74.87/11.11 | (22) ~ (all_4_14 = e1) % 74.87/11.11 | % 74.87/11.11 | SIMP: (22) implies: % 74.87/11.11 | (23) ~ (all_4_14 = e1) % 74.87/11.11 | % 74.87/11.11 | REDUCE: (18), (21) imply: % 74.87/11.11 | (24) ~ (e2 = e1) % 74.87/11.11 | % 74.87/11.11 | SIMP: (24) implies: % 74.87/11.11 | (25) ~ (e2 = e1) % 74.87/11.11 | % 74.87/11.11 | REDUCE: (7), (21) imply: % 74.87/11.11 | (26) ~ (e1 = e0) % 74.87/11.11 | % 74.87/11.11 | BETA: splitting (5) gives: % 74.87/11.11 | % 74.87/11.11 | Case 1: % 74.87/11.11 | | % 74.87/11.11 | | (27) all_6_22 = e4 % 74.87/11.11 | | % 74.87/11.11 | | COMBINE_EQS: (16), (27) imply: % 74.87/11.11 | | (28) all_4_14 = e4 % 74.87/11.11 | | % 74.87/11.11 | | SIMP: (28) implies: % 74.87/11.11 | | (29) all_4_14 = e4 % 74.87/11.11 | | % 74.87/11.11 | | COMBINE_EQS: (11), (29) imply: % 74.87/11.11 | | (30) all_10_22 = e4 % 74.87/11.11 | | % 74.87/11.11 | | REDUCE: (23), (29) imply: % 74.87/11.11 | | (31) ~ (e4 = e1) % 74.87/11.11 | | % 74.87/11.11 | | REDUCE: (4), (29) imply: % 74.87/11.11 | | (32) ~ (e4 = e0) % 74.87/11.11 | | % 74.87/11.11 | | BETA: splitting (8) gives: % 74.87/11.11 | | % 74.87/11.11 | | Case 1: % 74.87/11.11 | | | % 74.87/11.11 | | | (33) all_10_20 = e1 % 74.87/11.11 | | | % 74.87/11.11 | | | COMBINE_EQS: (10), (33) imply: % 74.87/11.11 | | | (34) all_4_4 = e1 % 74.87/11.11 | | | % 74.87/11.11 | | | SIMP: (34) implies: % 74.87/11.11 | | | (35) all_4_4 = e1 % 74.87/11.11 | | | % 74.87/11.11 | | | REDUCE: (17), (35) imply: % 74.87/11.11 | | | (36) $false % 74.87/11.11 | | | % 74.87/11.11 | | | CLOSE: (36) is inconsistent. % 74.87/11.11 | | | % 74.87/11.11 | | Case 2: % 74.87/11.11 | | | % 74.87/11.11 | | | (37) all_10_21 = e1 | all_10_22 = e1 | all_10_23 = e1 | all_10_24 = e1 % 74.87/11.11 | | | % 74.87/11.11 | | | BETA: splitting (37) gives: % 74.87/11.11 | | | % 74.87/11.11 | | | Case 1: % 74.87/11.11 | | | | % 74.87/11.11 | | | | (38) all_10_21 = e1 % 74.87/11.11 | | | | % 74.87/11.11 | | | | COMBINE_EQS: (13), (38) imply: % 74.87/11.11 | | | | (39) e2 = e1 % 74.87/11.11 | | | | % 74.87/11.11 | | | | SIMP: (39) implies: % 74.87/11.11 | | | | (40) e2 = e1 % 74.87/11.11 | | | | % 74.87/11.11 | | | | REDUCE: (25), (40) imply: % 74.87/11.11 | | | | (41) $false % 74.87/11.11 | | | | % 74.87/11.11 | | | | CLOSE: (41) is inconsistent. % 74.87/11.11 | | | | % 74.87/11.11 | | | Case 2: % 74.87/11.11 | | | | % 74.87/11.11 | | | | (42) all_10_22 = e1 | all_10_23 = e1 | all_10_24 = e1 % 74.87/11.11 | | | | % 74.87/11.11 | | | | BETA: splitting (42) gives: % 74.87/11.11 | | | | % 74.87/11.11 | | | | Case 1: % 74.87/11.11 | | | | | % 74.87/11.11 | | | | | (43) all_10_22 = e1 % 74.87/11.11 | | | | | % 74.87/11.11 | | | | | COMBINE_EQS: (30), (43) imply: % 74.87/11.11 | | | | | (44) e4 = e1 % 74.87/11.11 | | | | | % 74.87/11.11 | | | | | SIMP: (44) implies: % 74.87/11.11 | | | | | (45) e4 = e1 % 74.87/11.11 | | | | | % 74.87/11.11 | | | | | REDUCE: (31), (45) imply: % 74.87/11.11 | | | | | (46) $false % 74.87/11.11 | | | | | % 74.87/11.11 | | | | | CLOSE: (46) is inconsistent. % 74.87/11.11 | | | | | % 74.87/11.11 | | | | Case 2: % 74.87/11.11 | | | | | % 74.87/11.11 | | | | | (47) all_10_23 = e1 | all_10_24 = e1 % 74.87/11.11 | | | | | % 74.87/11.11 | | | | | BETA: splitting (47) gives: % 74.87/11.11 | | | | | % 74.87/11.11 | | | | | Case 1: % 74.87/11.11 | | | | | | % 74.87/11.11 | | | | | | (48) all_10_23 = e1 % 74.87/11.11 | | | | | | % 74.87/11.11 | | | | | | COMBINE_EQS: (6), (48) imply: % 74.87/11.11 | | | | | | (49) all_4_19 = e1 % 74.87/11.11 | | | | | | % 74.87/11.11 | | | | | | SIMP: (49) implies: % 74.87/11.11 | | | | | | (50) all_4_19 = e1 % 74.87/11.11 | | | | | | % 74.87/11.11 | | | | | | REDUCE: (15), (50) imply: % 74.87/11.11 | | | | | | (51) op(e1, e1) = e0 % 74.87/11.11 | | | | | | % 74.87/11.11 | | | | | | GROUND_INST: instantiating (14) with e4, e0, e1, e1, simplifying % 74.87/11.11 | | | | | | with (19), (51) gives: % 74.87/11.11 | | | | | | (52) e4 = e0 % 74.87/11.11 | | | | | | % 74.87/11.11 | | | | | | REDUCE: (32), (52) imply: % 74.87/11.11 | | | | | | (53) $false % 74.87/11.11 | | | | | | % 74.87/11.11 | | | | | | CLOSE: (53) is inconsistent. % 74.87/11.11 | | | | | | % 74.87/11.11 | | | | | Case 2: % 74.87/11.11 | | | | | | % 74.87/11.11 | | | | | | (54) all_10_24 = e1 % 74.87/11.11 | | | | | | % 74.87/11.11 | | | | | | COMBINE_EQS: (9), (54) imply: % 74.87/11.11 | | | | | | (55) e1 = e0 % 74.87/11.11 | | | | | | % 74.87/11.11 | | | | | | REDUCE: (26), (55) imply: % 74.87/11.11 | | | | | | (56) $false % 74.87/11.11 | | | | | | % 74.87/11.11 | | | | | | CLOSE: (56) is inconsistent. % 74.87/11.11 | | | | | | % 74.87/11.11 | | | | | End of split % 74.87/11.11 | | | | | % 74.87/11.11 | | | | End of split % 74.87/11.11 | | | | % 74.87/11.11 | | | End of split % 74.87/11.11 | | | % 74.87/11.11 | | End of split % 74.87/11.11 | | % 74.87/11.11 | Case 2: % 74.87/11.11 | | % 74.87/11.11 | | (57) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 74.87/11.11 | | % 74.87/11.11 | | REF_CLOSE: (1), (4), (16), (23), (57) are inconsistent by sub-proof #130. % 74.87/11.11 | | % 74.87/11.11 | End of split % 74.87/11.11 | % 74.87/11.11 End of proof % 74.87/11.11 % 74.87/11.11 Sub-proof #67 shows that the following formulas are inconsistent: % 74.87/11.11 ---------------------------------------------------------------- % 74.87/11.11 (1) ~ (all_4_5 = e2) % 74.87/11.11 (2) ~ (all_4_19 = e0) % 74.87/11.11 (3) op(e1, e0) = e2 % 74.87/11.11 (4) ~ (e3 = e2) % 74.87/11.11 (5) all_10_15 = e4 % 74.87/11.11 (6) ~ (e4 = e0) % 74.87/11.11 (7) all_10_23 = all_4_19 % 74.87/11.11 (8) ~ (all_4_5 = all_4_15) % 74.87/11.11 (9) all_10_11 = e2 % 74.87/11.11 (10) op(e1, all_4_16) = e3 % 74.87/11.11 (11) all_4_5 = e0 % 74.87/11.11 (12) all_10_10 = all_4_16 % 74.87/11.11 (13) all_10_9 = all_4_15 % 74.87/11.11 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.87/11.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.87/11.11 (15) all_10_9 = e0 | all_10_10 = e0 | all_10_11 = e0 | all_10_15 = e0 | % 74.87/11.11 all_10_23 = e0 % 74.87/11.11 % 74.87/11.11 Begin of proof % 74.87/11.11 | % 74.87/11.11 | REDUCE: (8), (11) imply: % 74.87/11.11 | (16) ~ (all_4_15 = e0) % 74.87/11.11 | % 74.87/11.11 | SIMP: (16) implies: % 74.87/11.11 | (17) ~ (all_4_15 = e0) % 74.87/11.11 | % 74.87/11.11 | REDUCE: (1), (11) imply: % 74.87/11.11 | (18) ~ (e2 = e0) % 74.87/11.11 | % 74.87/11.11 | SIMP: (18) implies: % 74.87/11.11 | (19) ~ (e2 = e0) % 74.87/11.11 | % 74.87/11.11 | BETA: splitting (15) gives: % 74.87/11.11 | % 74.87/11.11 | Case 1: % 74.87/11.11 | | % 74.87/11.11 | | (20) all_10_9 = e0 % 74.87/11.11 | | % 74.87/11.11 | | COMBINE_EQS: (13), (20) imply: % 74.87/11.11 | | (21) all_4_15 = e0 % 74.87/11.11 | | % 74.87/11.11 | | REDUCE: (17), (21) imply: % 74.87/11.11 | | (22) $false % 74.87/11.11 | | % 74.87/11.11 | | CLOSE: (22) is inconsistent. % 74.87/11.11 | | % 74.87/11.11 | Case 2: % 74.87/11.11 | | % 74.87/11.11 | | (23) all_10_10 = e0 | all_10_11 = e0 | all_10_15 = e0 | all_10_23 = e0 % 74.87/11.11 | | % 74.87/11.11 | | BETA: splitting (23) gives: % 74.87/11.11 | | % 74.87/11.11 | | Case 1: % 74.87/11.11 | | | % 74.87/11.11 | | | (24) all_10_10 = e0 % 74.87/11.11 | | | % 74.87/11.11 | | | COMBINE_EQS: (12), (24) imply: % 74.87/11.11 | | | (25) all_4_16 = e0 % 74.87/11.11 | | | % 74.87/11.11 | | | REDUCE: (10), (25) imply: % 74.87/11.11 | | | (26) op(e1, e0) = e3 % 74.87/11.11 | | | % 74.87/11.11 | | | GROUND_INST: instantiating (14) with e2, e3, e0, e1, simplifying with (3), % 74.87/11.11 | | | (26) gives: % 74.87/11.11 | | | (27) e3 = e2 % 74.87/11.11 | | | % 74.87/11.11 | | | REDUCE: (4), (27) imply: % 74.87/11.11 | | | (28) $false % 74.87/11.11 | | | % 74.87/11.11 | | | CLOSE: (28) is inconsistent. % 74.87/11.11 | | | % 74.87/11.11 | | Case 2: % 74.87/11.11 | | | % 74.87/11.11 | | | (29) all_10_11 = e0 | all_10_15 = e0 | all_10_23 = e0 % 74.87/11.11 | | | % 74.87/11.11 | | | REF_CLOSE: (2), (5), (6), (7), (9), (19), (29) are inconsistent by % 74.87/11.11 | | | sub-proof #79. % 74.87/11.11 | | | % 74.87/11.11 | | End of split % 74.87/11.11 | | % 74.87/11.11 | End of split % 74.87/11.11 | % 74.87/11.11 End of proof % 74.87/11.11 % 74.87/11.11 Sub-proof #68 shows that the following formulas are inconsistent: % 74.87/11.11 ---------------------------------------------------------------- % 74.87/11.11 (1) ~ (all_4_1 = e0) % 74.87/11.11 (2) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | all_6_5 = e0 % 74.87/11.11 (3) ~ (all_4_7 = e3) % 74.87/11.11 (4) all_6_11 = e4 | all_6_11 = e3 | all_6_11 = e1 | all_6_11 = e0 % 74.87/11.11 (5) op(e3, e4) = all_4_1 % 74.87/11.11 (6) op(e1, all_4_15) = e4 % 74.87/11.11 (7) ~ (all_4_1 = e3) % 74.87/11.11 (8) ~ (all_4_5 = all_4_15) % 74.87/11.12 (9) all_6_5 = all_4_1 % 74.87/11.12 (10) all_10_9 = e3 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 74.87/11.12 all_10_23 = e3 % 74.87/11.12 (11) op(e3, all_4_1) = all_8_2 % 74.87/11.12 (12) ~ (all_4_1 = e1) % 74.87/11.12 (13) all_4_5 = e0 % 74.87/11.12 (14) all_6_3 = all_4_15 % 74.87/11.12 (15) all_6_3 = e4 | all_6_3 = e3 | all_6_3 = e1 | all_6_3 = e0 % 74.87/11.12 (16) ~ (all_4_15 = e2) % 74.87/11.12 (17) all_10_9 = all_4_15 % 74.87/11.12 (18) ~ (all_4_5 = all_4_7) % 74.87/11.12 (19) all_6_11 = all_4_7 % 74.87/11.12 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.87/11.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.87/11.12 (21) ~ (all_4_15 = e1) % 74.87/11.12 (22) ~ (all_4_7 = e1) % 74.87/11.12 (23) op(e1, e3) = e3 % 74.87/11.12 (24) ~ (all_4_15 = e4) % 74.87/11.12 (25) op(e3, all_4_7) = e2 % 74.87/11.12 % 74.87/11.12 Begin of proof % 74.87/11.12 | % 74.87/11.12 | REDUCE: (13), (18) imply: % 74.87/11.12 | (26) ~ (all_4_7 = e0) % 74.87/11.12 | % 74.87/11.12 | SIMP: (26) implies: % 74.87/11.12 | (27) ~ (all_4_7 = e0) % 74.87/11.12 | % 74.87/11.12 | REDUCE: (8), (13) imply: % 74.87/11.12 | (28) ~ (all_4_15 = e0) % 74.87/11.12 | % 74.87/11.12 | SIMP: (28) implies: % 74.87/11.12 | (29) ~ (all_4_15 = e0) % 74.87/11.12 | % 74.87/11.12 | BETA: splitting (4) gives: % 74.87/11.12 | % 74.87/11.12 | Case 1: % 74.87/11.12 | | % 74.87/11.12 | | (30) all_6_11 = e4 % 74.87/11.12 | | % 74.87/11.12 | | COMBINE_EQS: (19), (30) imply: % 74.87/11.12 | | (31) all_4_7 = e4 % 74.87/11.12 | | % 74.87/11.12 | | SIMP: (31) implies: % 74.87/11.12 | | (32) all_4_7 = e4 % 74.87/11.12 | | % 74.87/11.12 | | REDUCE: (25), (32) imply: % 74.87/11.12 | | (33) op(e3, e4) = e2 % 74.87/11.12 | | % 74.87/11.12 | | BETA: splitting (15) gives: % 74.87/11.12 | | % 74.87/11.12 | | Case 1: % 74.87/11.12 | | | % 74.87/11.12 | | | (34) all_6_3 = e4 % 74.87/11.12 | | | % 74.87/11.12 | | | REF_CLOSE: (14), (24), (34) are inconsistent by sub-proof #149. % 74.87/11.12 | | | % 74.87/11.12 | | Case 2: % 74.87/11.12 | | | % 74.87/11.12 | | | (35) all_6_3 = e3 | all_6_3 = e1 | all_6_3 = e0 % 74.87/11.12 | | | % 74.87/11.12 | | | BETA: splitting (10) gives: % 74.87/11.12 | | | % 74.87/11.12 | | | Case 1: % 74.87/11.12 | | | | % 74.87/11.12 | | | | (36) all_10_9 = e3 % 74.87/11.12 | | | | % 74.87/11.12 | | | | COMBINE_EQS: (17), (36) imply: % 74.87/11.12 | | | | (37) all_4_15 = e3 % 74.87/11.12 | | | | % 74.87/11.12 | | | | REDUCE: (16), (37) imply: % 74.87/11.12 | | | | (38) ~ (e3 = e2) % 74.87/11.12 | | | | % 74.87/11.12 | | | | REDUCE: (6), (37) imply: % 74.87/11.12 | | | | (39) op(e1, e3) = e4 % 74.87/11.12 | | | | % 74.87/11.12 | | | | BETA: splitting (2) gives: % 74.87/11.12 | | | | % 74.87/11.12 | | | | Case 1: % 74.87/11.12 | | | | | % 74.87/11.12 | | | | | (40) all_6_5 = e4 % 74.87/11.12 | | | | | % 74.87/11.12 | | | | | COMBINE_EQS: (9), (40) imply: % 74.87/11.12 | | | | | (41) all_4_1 = e4 % 74.87/11.12 | | | | | % 74.87/11.12 | | | | | SIMP: (41) implies: % 74.87/11.12 | | | | | (42) all_4_1 = e4 % 74.87/11.12 | | | | | % 74.87/11.12 | | | | | REDUCE: (11), (42) imply: % 74.87/11.12 | | | | | (43) op(e3, e4) = all_8_2 % 74.87/11.12 | | | | | % 74.87/11.12 | | | | | REDUCE: (5), (42) imply: % 74.87/11.12 | | | | | (44) op(e3, e4) = e4 % 74.87/11.12 | | | | | % 74.87/11.12 | | | | | GROUND_INST: instantiating (20) with e3, e4, e3, e1, simplifying with % 74.87/11.12 | | | | | (23), (39) gives: % 74.87/11.12 | | | | | (45) e4 = e3 % 74.87/11.12 | | | | | % 74.87/11.12 | | | | | GROUND_INST: instantiating (20) with e4, all_8_2, e4, e3, simplifying % 74.87/11.12 | | | | | with (43), (44) gives: % 74.87/11.12 | | | | | (46) all_8_2 = e4 % 74.87/11.12 | | | | | % 74.87/11.12 | | | | | GROUND_INST: instantiating (20) with e2, all_8_2, e4, e3, simplifying % 74.87/11.12 | | | | | with (33), (43) gives: % 74.87/11.12 | | | | | (47) all_8_2 = e2 % 74.87/11.12 | | | | | % 74.87/11.12 | | | | | COMBINE_EQS: (46), (47) imply: % 74.87/11.12 | | | | | (48) e4 = e2 % 74.87/11.12 | | | | | % 74.87/11.12 | | | | | SIMP: (48) implies: % 74.87/11.12 | | | | | (49) e4 = e2 % 74.87/11.12 | | | | | % 74.87/11.12 | | | | | REF_CLOSE: (38), (45), (49) are inconsistent by sub-proof #69. % 74.87/11.12 | | | | | % 74.87/11.12 | | | | Case 2: % 74.87/11.12 | | | | | % 74.87/11.12 | | | | | (50) all_6_5 = e3 | all_6_5 = e1 | all_6_5 = e0 % 74.87/11.12 | | | | | % 74.87/11.12 | | | | | REF_CLOSE: (1), (7), (9), (12), (50) are inconsistent by sub-proof % 74.87/11.12 | | | | | #140. % 74.87/11.12 | | | | | % 74.87/11.12 | | | | End of split % 74.87/11.12 | | | | % 74.87/11.12 | | | Case 2: % 74.87/11.12 | | | | % 74.87/11.12 | | | | (51) ~ (all_10_9 = e3) % 74.87/11.12 | | | | % 74.87/11.12 | | | | REF_CLOSE: (14), (17), (21), (29), (35), (51) are inconsistent by % 74.87/11.12 | | | | sub-proof #144. % 74.87/11.12 | | | | % 74.87/11.12 | | | End of split % 74.87/11.12 | | | % 74.87/11.12 | | End of split % 74.87/11.12 | | % 74.87/11.12 | Case 2: % 74.87/11.12 | | % 74.87/11.12 | | (52) all_6_11 = e3 | all_6_11 = e1 | all_6_11 = e0 % 74.87/11.12 | | % 74.87/11.12 | | REF_CLOSE: (3), (19), (22), (27), (52) are inconsistent by sub-proof #133. % 74.87/11.12 | | % 74.87/11.12 | End of split % 74.87/11.12 | % 74.87/11.12 End of proof % 74.87/11.12 % 74.87/11.12 Sub-proof #69 shows that the following formulas are inconsistent: % 74.87/11.12 ---------------------------------------------------------------- % 74.87/11.12 (1) e4 = e3 % 74.87/11.12 (2) e4 = e2 % 74.87/11.12 (3) ~ (e3 = e2) % 74.87/11.12 % 74.87/11.12 Begin of proof % 74.87/11.12 | % 74.87/11.12 | COMBINE_EQS: (1), (2) imply: % 74.87/11.12 | (4) e3 = e2 % 74.87/11.12 | % 74.87/11.12 | SIMP: (4) implies: % 74.87/11.12 | (5) e3 = e2 % 74.87/11.12 | % 74.87/11.12 | REDUCE: (3), (5) imply: % 74.87/11.12 | (6) $false % 74.87/11.12 | % 74.87/11.12 | CLOSE: (6) is inconsistent. % 74.87/11.12 | % 74.87/11.12 End of proof % 74.87/11.12 % 74.87/11.12 Sub-proof #70 shows that the following formulas are inconsistent: % 74.87/11.12 ---------------------------------------------------------------- % 74.87/11.12 (1) all_6_20 = all_4_4 % 74.87/11.12 (2) ~ (all_4_20 = e1) % 74.87/11.12 (3) ~ (all_4_19 = e0) % 74.87/11.12 (4) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | all_6_5 = e0 % 74.87/11.12 (5) ~ (all_4_10 = e3) % 74.87/11.12 (6) ~ (e3 = e2) % 74.87/11.12 (7) all_10_4 = all_4_10 % 74.87/11.12 (8) ~ (all_4_16 = e2) % 74.87/11.12 (9) all_10_1 = all_4_5 % 74.87/11.12 (10) all_10_15 = e4 % 74.87/11.12 (11) ~ (all_4_20 = all_4_21) % 74.87/11.12 (12) ~ (e2 = e0) % 74.87/11.12 (13) all_6_9 = all_4_21 % 74.87/11.12 (14) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 74.87/11.12 (15) ~ (all_4_16 = all_4_21) % 74.87/11.12 (16) ~ (e3 = e1) % 74.87/11.12 (17) all_10_16 = all_4_20 % 74.87/11.12 (18) all_10_0 = e1 | all_10_1 = e1 | all_10_4 = e1 | all_10_9 = e1 | % 74.87/11.12 all_10_16 = e1 % 74.87/11.12 (19) all_10_23 = all_4_19 % 74.87/11.12 (20) ~ (all_4_10 = e0) % 74.87/11.12 (21) ~ (all_4_5 = e3) % 74.87/11.12 (22) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e1 | all_6_9 = e0 % 74.87/11.12 (23) op(e4, e4) = e2 % 74.87/11.12 (24) ~ (all_4_5 = e1) % 74.87/11.12 (25) all_6_5 = all_4_1 % 74.87/11.12 (26) all_10_20 = all_4_4 % 74.87/11.12 (27) ~ (all_4_1 = e1) % 74.87/11.12 (28) ~ (e2 = e1) % 74.87/11.12 (29) ~ (all_4_1 = all_4_21) % 74.87/11.12 (30) all_10_11 = e2 % 74.87/11.12 (31) all_10_0 = e3 | all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | % 74.87/11.12 all_10_16 = e3 % 74.87/11.12 (32) ~ (all_4_4 = e0) % 74.87/11.12 (33) all_10_2 = e3 | all_10_3 = e3 | all_10_5 = e3 | all_10_10 = e3 | % 74.87/11.12 all_10_17 = e3 % 74.87/11.12 (34) all_10_2 = all_4_1 % 74.87/11.12 (35) all_10_10 = all_4_16 % 74.87/11.12 (36) ~ (all_10_4 = e1) % 74.87/11.12 (37) ~ (all_4_21 = e1) % 74.87/11.12 (38) all_10_20 = e4 | all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 74.87/11.12 all_10_24 = e4 % 74.87/11.12 (39) ~ (e1 = e0) % 74.87/11.12 (40) ~ (all_4_1 = all_4_16) % 74.87/11.12 (41) op(e4, all_4_10) = all_8_27 % 74.87/11.12 (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.87/11.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.87/11.12 (43) op(e4, all_4_4) = e0 % 74.87/11.12 (44) all_6_2 = all_4_10 % 74.87/11.12 (45) ~ (all_4_1 = all_4_4) % 74.87/11.12 (46) all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | % 74.87/11.12 all_10_22 = e4 % 74.87/11.12 (47) ~ (all_4_4 = e1) % 74.87/11.12 (48) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.87/11.12 (49) all_10_0 = e2 % 74.87/11.12 (50) all_10_9 = e0 | all_10_10 = e0 | all_10_11 = e0 | all_10_15 = e0 | % 74.87/11.12 all_10_23 = e0 % 74.87/11.12 % 74.87/11.12 Begin of proof % 74.87/11.12 | % 74.87/11.12 | REDUCE: (7), (36) imply: % 74.87/11.12 | (51) ~ (all_4_10 = e1) % 74.87/11.12 | % 74.87/11.12 | BETA: splitting (18) gives: % 74.87/11.12 | % 74.87/11.12 | Case 1: % 74.87/11.12 | | % 74.87/11.12 | | (52) all_10_0 = e1 % 74.87/11.12 | | % 74.87/11.12 | | COMBINE_EQS: (49), (52) imply: % 74.87/11.12 | | (53) e2 = e1 % 74.87/11.12 | | % 74.87/11.12 | | REDUCE: (28), (53) imply: % 74.87/11.12 | | (54) $false % 74.87/11.12 | | % 74.87/11.12 | | CLOSE: (54) is inconsistent. % 74.87/11.12 | | % 74.87/11.12 | Case 2: % 74.87/11.12 | | % 74.87/11.12 | | (55) all_10_1 = e1 | all_10_4 = e1 | all_10_9 = e1 | all_10_16 = e1 % 74.87/11.12 | | % 74.87/11.12 | | BETA: splitting (55) gives: % 74.87/11.12 | | % 74.87/11.12 | | Case 1: % 74.87/11.12 | | | % 74.87/11.12 | | | (56) all_10_1 = e1 % 74.87/11.12 | | | % 74.87/11.12 | | | COMBINE_EQS: (9), (56) imply: % 74.87/11.12 | | | (57) all_4_5 = e1 % 74.87/11.12 | | | % 74.87/11.12 | | | REDUCE: (24), (57) imply: % 74.87/11.12 | | | (58) $false % 74.87/11.12 | | | % 74.87/11.12 | | | CLOSE: (58) is inconsistent. % 74.87/11.12 | | | % 74.87/11.12 | | Case 2: % 74.87/11.12 | | | % 74.87/11.12 | | | (59) all_10_4 = e1 | all_10_9 = e1 | all_10_16 = e1 % 74.87/11.12 | | | % 74.87/11.12 | | | BETA: splitting (59) gives: % 74.87/11.12 | | | % 74.87/11.12 | | | Case 1: % 74.87/11.12 | | | | % 74.87/11.12 | | | | (60) all_10_4 = e1 % 74.87/11.12 | | | | % 74.87/11.12 | | | | REF_CLOSE: (7), (51), (60) are inconsistent by sub-proof #85. % 74.87/11.12 | | | | % 74.87/11.12 | | | Case 2: % 74.87/11.12 | | | | % 74.87/11.12 | | | | (61) all_10_9 = e1 | all_10_16 = e1 % 74.87/11.12 | | | | % 74.87/11.12 | | | | BETA: splitting (61) gives: % 74.87/11.12 | | | | % 74.87/11.12 | | | | Case 1: % 74.87/11.12 | | | | | % 74.87/11.12 | | | | | (62) all_10_9 = e1 % 74.87/11.12 | | | | | % 74.87/11.12 | | | | | BETA: splitting (31) gives: % 74.87/11.12 | | | | | % 74.87/11.12 | | | | | Case 1: % 74.87/11.12 | | | | | | % 74.87/11.12 | | | | | | (63) all_10_0 = e3 % 74.87/11.12 | | | | | | % 74.87/11.12 | | | | | | REF_CLOSE: (6), (49), (63) are inconsistent by sub-proof #104. % 74.87/11.12 | | | | | | % 74.87/11.12 | | | | | Case 2: % 74.87/11.12 | | | | | | % 74.87/11.12 | | | | | | (64) all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | all_10_16 = % 74.87/11.12 | | | | | | e3 % 74.87/11.12 | | | | | | % 74.87/11.12 | | | | | | BETA: splitting (64) gives: % 74.87/11.12 | | | | | | % 74.87/11.12 | | | | | | Case 1: % 74.87/11.12 | | | | | | | % 74.87/11.12 | | | | | | | (65) all_10_1 = e3 % 74.87/11.12 | | | | | | | % 74.87/11.12 | | | | | | | COMBINE_EQS: (9), (65) imply: % 74.87/11.12 | | | | | | | (66) all_4_5 = e3 % 74.87/11.12 | | | | | | | % 74.87/11.12 | | | | | | | REDUCE: (21), (66) imply: % 74.87/11.12 | | | | | | | (67) $false % 74.87/11.12 | | | | | | | % 74.87/11.12 | | | | | | | CLOSE: (67) is inconsistent. % 74.87/11.12 | | | | | | | % 74.87/11.12 | | | | | | Case 2: % 74.87/11.12 | | | | | | | % 74.87/11.12 | | | | | | | (68) all_10_4 = e3 | all_10_9 = e3 | all_10_16 = e3 % 74.87/11.12 | | | | | | | % 74.87/11.12 | | | | | | | BETA: splitting (46) gives: % 74.87/11.12 | | | | | | | % 74.87/11.12 | | | | | | | Case 1: % 74.87/11.12 | | | | | | | | % 74.87/11.12 | | | | | | | | (69) all_10_4 = e4 % 74.87/11.12 | | | | | | | | % 74.87/11.12 | | | | | | | | COMBINE_EQS: (7), (69) imply: % 74.87/11.12 | | | | | | | | (70) all_4_10 = e4 % 74.87/11.12 | | | | | | | | % 74.87/11.12 | | | | | | | | REDUCE: (5), (70) imply: % 74.87/11.12 | | | | | | | | (71) ~ (e4 = e3) % 74.87/11.12 | | | | | | | | % 74.87/11.12 | | | | | | | | REDUCE: (20), (70) imply: % 74.87/11.12 | | | | | | | | (72) ~ (e4 = e0) % 74.87/11.12 | | | | | | | | % 74.87/11.12 | | | | | | | | REDUCE: (41), (70) imply: % 74.87/11.12 | | | | | | | | (73) op(e4, e4) = all_8_27 % 74.87/11.12 | | | | | | | | % 74.87/11.12 | | | | | | | | BETA: splitting (68) gives: % 74.87/11.12 | | | | | | | | % 74.87/11.12 | | | | | | | | Case 1: % 74.87/11.12 | | | | | | | | | % 74.87/11.12 | | | | | | | | | (74) all_10_4 = e3 % 74.87/11.12 | | | | | | | | | % 74.87/11.12 | | | | | | | | | COMBINE_EQS: (69), (74) imply: % 74.87/11.12 | | | | | | | | | (75) e4 = e3 % 74.87/11.12 | | | | | | | | | % 74.87/11.12 | | | | | | | | | REDUCE: (71), (75) imply: % 74.87/11.12 | | | | | | | | | (76) $false % 74.87/11.12 | | | | | | | | | % 74.87/11.12 | | | | | | | | | CLOSE: (76) is inconsistent. % 74.87/11.12 | | | | | | | | | % 74.87/11.12 | | | | | | | | Case 2: % 74.87/11.12 | | | | | | | | | % 74.87/11.12 | | | | | | | | | (77) all_10_9 = e3 | all_10_16 = e3 % 74.87/11.12 | | | | | | | | | % 74.87/11.12 | | | | | | | | | BETA: splitting (50) gives: % 74.87/11.12 | | | | | | | | | % 74.87/11.12 | | | | | | | | | Case 1: % 74.87/11.12 | | | | | | | | | | % 74.87/11.12 | | | | | | | | | | (78) all_10_9 = e0 % 74.87/11.12 | | | | | | | | | | % 74.87/11.12 | | | | | | | | | | COMBINE_EQS: (62), (78) imply: % 74.87/11.12 | | | | | | | | | | (79) e1 = e0 % 74.87/11.12 | | | | | | | | | | % 74.87/11.12 | | | | | | | | | | REDUCE: (39), (79) imply: % 74.87/11.12 | | | | | | | | | | (80) $false % 74.87/11.12 | | | | | | | | | | % 74.87/11.12 | | | | | | | | | | CLOSE: (80) is inconsistent. % 74.87/11.12 | | | | | | | | | | % 74.87/11.12 | | | | | | | | | Case 2: % 74.87/11.12 | | | | | | | | | | % 74.87/11.12 | | | | | | | | | | (81) all_10_10 = e0 | all_10_11 = e0 | all_10_15 = e0 | % 74.87/11.12 | | | | | | | | | | all_10_23 = e0 % 74.87/11.12 | | | | | | | | | | % 74.87/11.12 | | | | | | | | | | BETA: splitting (81) gives: % 74.87/11.12 | | | | | | | | | | % 74.87/11.12 | | | | | | | | | | Case 1: % 74.87/11.12 | | | | | | | | | | | % 74.87/11.12 | | | | | | | | | | | (82) all_10_10 = e0 % 74.87/11.12 | | | | | | | | | | | % 74.87/11.12 | | | | | | | | | | | COMBINE_EQS: (35), (82) imply: % 74.87/11.12 | | | | | | | | | | | (83) all_4_16 = e0 % 74.87/11.12 | | | | | | | | | | | % 74.87/11.12 | | | | | | | | | | | SIMP: (83) implies: % 74.87/11.12 | | | | | | | | | | | (84) all_4_16 = e0 % 74.87/11.12 | | | | | | | | | | | % 74.87/11.12 | | | | | | | | | | | REDUCE: (40), (84) imply: % 74.87/11.12 | | | | | | | | | | | (85) ~ (all_4_1 = e0) % 74.87/11.12 | | | | | | | | | | | % 74.87/11.12 | | | | | | | | | | | REDUCE: (15), (84) imply: % 74.87/11.12 | | | | | | | | | | | (86) ~ (all_4_21 = e0) % 74.87/11.12 | | | | | | | | | | | % 74.87/11.12 | | | | | | | | | | | SIMP: (86) implies: % 74.87/11.12 | | | | | | | | | | | (87) ~ (all_4_21 = e0) % 74.87/11.12 | | | | | | | | | | | % 74.87/11.12 | | | | | | | | | | | REDUCE: (8), (84) imply: % 74.87/11.12 | | | | | | | | | | | (88) ~ (e2 = e0) % 74.87/11.12 | | | | | | | | | | | % 74.87/11.12 | | | | | | | | | | | BETA: splitting (77) gives: % 74.87/11.12 | | | | | | | | | | | % 74.87/11.12 | | | | | | | | | | | Case 1: % 74.87/11.12 | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | (89) all_10_9 = e3 % 74.87/11.13 | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | REF_CLOSE: (16), (62), (89) are inconsistent by sub-proof % 74.87/11.13 | | | | | | | | | | | | #84. % 74.87/11.13 | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | Case 2: % 74.87/11.13 | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | (90) all_10_16 = e3 % 74.87/11.13 | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | COMBINE_EQS: (17), (90) imply: % 74.87/11.13 | | | | | | | | | | | | (91) all_4_20 = e3 % 74.87/11.13 | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | REDUCE: (11), (91) imply: % 74.87/11.13 | | | | | | | | | | | | (92) ~ (all_4_21 = e3) % 74.87/11.13 | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | SIMP: (92) implies: % 74.87/11.13 | | | | | | | | | | | | (93) ~ (all_4_21 = e3) % 74.87/11.13 | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | BETA: splitting (33) gives: % 74.87/11.13 | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | Case 1: % 74.87/11.13 | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | (94) all_10_2 = e3 % 74.87/11.13 | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | COMBINE_EQS: (34), (94) imply: % 74.87/11.13 | | | | | | | | | | | | | (95) all_4_1 = e3 % 74.87/11.13 | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | SIMP: (95) implies: % 74.87/11.13 | | | | | | | | | | | | | (96) all_4_1 = e3 % 74.87/11.13 | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | REDUCE: (45), (96) imply: % 74.87/11.13 | | | | | | | | | | | | | (97) ~ (all_4_4 = e3) % 74.87/11.13 | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | SIMP: (97) implies: % 74.87/11.13 | | | | | | | | | | | | | (98) ~ (all_4_4 = e3) % 74.87/11.13 | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | BETA: splitting (38) gives: % 74.87/11.13 | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | Case 1: % 74.87/11.13 | | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | | (99) all_10_20 = e4 % 74.87/11.13 | | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | | COMBINE_EQS: (26), (99) imply: % 74.87/11.13 | | | | | | | | | | | | | | (100) all_4_4 = e4 % 74.87/11.13 | | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | | REDUCE: (43), (100) imply: % 74.87/11.13 | | | | | | | | | | | | | | (101) op(e4, e4) = e0 % 74.87/11.13 | | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | | GROUND_INST: instantiating (42) with e2, all_8_27, e4, e4, % 74.87/11.13 | | | | | | | | | | | | | | simplifying with (23), (73) gives: % 74.87/11.13 | | | | | | | | | | | | | | (102) all_8_27 = e2 % 74.87/11.13 | | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | | GROUND_INST: instantiating (42) with e0, all_8_27, e4, e4, % 74.87/11.13 | | | | | | | | | | | | | | simplifying with (73), (101) gives: % 74.87/11.13 | | | | | | | | | | | | | | (103) all_8_27 = e0 % 74.87/11.13 | | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | | COMBINE_EQS: (102), (103) imply: % 74.87/11.13 | | | | | | | | | | | | | | (104) e2 = e0 % 74.87/11.13 | | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | | SIMP: (104) implies: % 74.87/11.13 | | | | | | | | | | | | | | (105) e2 = e0 % 74.87/11.13 | | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | | REDUCE: (12), (105) imply: % 74.87/11.13 | | | | | | | | | | | | | | (106) $false % 74.87/11.13 | | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | | CLOSE: (106) is inconsistent. % 74.87/11.13 | | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | Case 2: % 74.87/11.13 | | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | | (107) ~ (all_10_20 = e4) % 74.87/11.13 | | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | | REF_CLOSE: (1), (14), (26), (32), (47), (98), (107) are % 74.87/11.13 | | | | | | | | | | | | | | inconsistent by sub-proof #72. % 74.87/11.13 | | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | End of split % 74.87/11.13 | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | Case 2: % 74.87/11.13 | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | (108) ~ (all_10_2 = e3) % 74.87/11.13 | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | | REF_CLOSE: (4), (13), (22), (25), (27), (29), (34), (37), % 74.87/11.13 | | | | | | | | | | | | | (85), (87), (93), (108) are inconsistent by % 74.87/11.13 | | | | | | | | | | | | | sub-proof #80. % 74.87/11.13 | | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | | End of split % 74.87/11.13 | | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | End of split % 74.87/11.13 | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | Case 2: % 74.87/11.13 | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | (109) all_10_11 = e0 | all_10_15 = e0 | all_10_23 = e0 % 74.87/11.13 | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | | REF_CLOSE: (3), (10), (12), (19), (30), (72), (109) are % 74.87/11.13 | | | | | | | | | | | inconsistent by sub-proof #79. % 74.87/11.13 | | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | End of split % 74.87/11.13 | | | | | | | | | | % 74.87/11.13 | | | | | | | | | End of split % 74.87/11.13 | | | | | | | | | % 74.87/11.13 | | | | | | | | End of split % 74.87/11.13 | | | | | | | | % 74.87/11.13 | | | | | | | Case 2: % 74.87/11.13 | | | | | | | | % 74.87/11.13 | | | | | | | | (110) ~ (all_10_4 = e4) % 74.87/11.13 | | | | | | | | % 74.87/11.13 | | | | | | | | REDUCE: (7), (110) imply: % 74.87/11.13 | | | | | | | | (111) ~ (all_4_10 = e4) % 74.87/11.13 | | | | | | | | % 74.87/11.13 | | | | | | | | REF_CLOSE: (5), (20), (44), (48), (51), (111) are inconsistent % 74.87/11.13 | | | | | | | | by sub-proof #161. % 74.87/11.13 | | | | | | | | % 74.87/11.13 | | | | | | | End of split % 74.87/11.13 | | | | | | | % 74.87/11.13 | | | | | | End of split % 74.87/11.13 | | | | | | % 74.87/11.13 | | | | | End of split % 74.87/11.13 | | | | | % 74.87/11.13 | | | | Case 2: % 74.87/11.13 | | | | | % 74.87/11.13 | | | | | (112) all_10_16 = e1 % 74.87/11.13 | | | | | % 74.87/11.13 | | | | | COMBINE_EQS: (17), (112) imply: % 74.87/11.13 | | | | | (113) all_4_20 = e1 % 74.87/11.13 | | | | | % 74.87/11.13 | | | | | REDUCE: (2), (113) imply: % 74.87/11.13 | | | | | (114) $false % 74.87/11.13 | | | | | % 74.87/11.13 | | | | | CLOSE: (114) is inconsistent. % 74.87/11.13 | | | | | % 74.87/11.13 | | | | End of split % 74.87/11.13 | | | | % 74.87/11.13 | | | End of split % 74.87/11.13 | | | % 74.87/11.13 | | End of split % 74.87/11.13 | | % 74.87/11.13 | End of split % 74.87/11.13 | % 74.87/11.13 End of proof % 74.87/11.13 % 74.87/11.13 Sub-proof #71 shows that the following formulas are inconsistent: % 74.87/11.13 ---------------------------------------------------------------- % 74.87/11.13 (1) all_10_8 = e3 % 74.87/11.13 (2) op(e2, all_4_14) = e0 % 74.87/11.13 (3) all_6_20 = all_4_4 % 74.87/11.13 (4) ~ (all_4_20 = e1) % 74.87/11.13 (5) all_10_14 = e0 % 74.87/11.13 (6) ~ (all_4_19 = e0) % 74.87/11.13 (7) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | all_6_5 = e0 % 74.87/11.13 (8) ~ (all_4_10 = e1) % 74.87/11.13 (9) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 74.87/11.13 (10) ~ (all_4_10 = e3) % 74.87/11.13 (11) ~ (e3 = e2) % 74.87/11.13 (12) ~ (all_4_16 = all_4_19) % 74.87/11.13 (13) ~ (all_4_14 = e3) % 74.87/11.13 (14) all_10_4 = all_4_10 % 74.87/11.13 (15) ~ (all_4_16 = e2) % 74.87/11.13 (16) all_10_1 = all_4_5 % 74.87/11.13 (17) all_10_15 = e4 % 74.87/11.13 (18) ~ (all_4_20 = all_4_21) % 74.87/11.13 (19) ~ (e2 = e0) % 74.87/11.13 (20) all_6_9 = all_4_21 % 74.87/11.13 (21) all_10_12 = all_4_3 % 74.87/11.13 (22) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 74.87/11.13 (23) all_10_5 = e2 % 74.87/11.13 (24) ~ (all_4_16 = all_4_21) % 74.87/11.13 (25) ~ (e3 = e1) % 74.87/11.13 (26) all_10_16 = all_4_20 % 74.87/11.13 (27) op(e2, e1) = e2 % 74.87/11.13 (28) ~ (all_4_14 = e0) % 74.87/11.13 (29) all_10_9 = e1 | all_10_10 = e1 | all_10_11 = e1 | all_10_15 = e1 | % 74.87/11.13 all_10_23 = e1 % 74.87/11.13 (30) all_10_0 = e1 | all_10_1 = e1 | all_10_4 = e1 | all_10_9 = e1 | % 74.87/11.13 all_10_16 = e1 % 74.87/11.13 (31) all_10_23 = all_4_19 % 74.87/11.13 (32) ~ (all_4_10 = e0) % 74.87/11.13 (33) op(e4, all_4_5) = all_8_14 % 74.87/11.13 (34) ~ (all_4_5 = all_4_15) % 74.87/11.13 (35) ~ (all_4_5 = e3) % 74.87/11.13 (36) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e1 | all_6_9 = e0 % 74.87/11.13 (37) ~ (all_4_5 = e1) % 74.87/11.13 (38) ~ (all_4_10 = all_4_15) % 74.87/11.13 (39) ~ (all_4_5 = all_4_20) % 74.87/11.13 (40) all_6_5 = all_4_1 % 74.87/11.13 (41) all_10_1 = e0 | all_10_3 = e0 | all_10_7 = e0 | all_10_13 = e0 | % 74.87/11.13 all_10_21 = e0 % 74.87/11.13 (42) all_10_9 = e3 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 74.87/11.13 all_10_23 = e3 % 74.87/11.13 (43) all_10_20 = all_4_4 % 74.87/11.13 (44) ~ (all_4_1 = e1) % 74.87/11.13 (45) ~ (e2 = e1) % 74.87/11.13 (46) ~ (all_4_1 = all_4_21) % 74.87/11.13 (47) all_10_11 = e2 % 74.87/11.13 (48) all_10_0 = e0 | all_10_2 = e0 | all_10_6 = e0 | all_10_12 = e0 | % 74.87/11.13 all_10_20 = e0 % 74.87/11.13 (49) all_10_0 = e3 | all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | % 74.87/11.13 all_10_16 = e3 % 74.87/11.13 (50) ~ (all_4_4 = e0) % 74.87/11.13 (51) all_10_2 = e3 | all_10_3 = e3 | all_10_5 = e3 | all_10_10 = e3 | % 74.87/11.13 all_10_17 = e3 % 74.87/11.13 (52) all_10_2 = all_4_1 % 74.87/11.13 (53) all_10_22 = all_4_14 % 74.87/11.13 (54) ~ (all_4_3 = e0) % 74.87/11.13 (55) all_10_10 = all_4_16 % 74.87/11.13 (56) ~ (all_4_21 = e1) % 74.87/11.13 (57) all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | all_10_22 = e1 % 74.87/11.13 (58) all_10_9 = all_4_15 % 74.87/11.13 (59) all_10_20 = e4 | all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | % 74.87/11.13 all_10_24 = e4 % 74.87/11.13 (60) ~ (all_4_4 = all_4_14) % 74.87/11.13 (61) ~ (e1 = e0) % 74.87/11.13 (62) ~ (all_4_1 = all_4_16) % 74.87/11.13 (63) all_6_1 = all_4_5 % 74.87/11.13 (64) ~ (all_4_5 = all_4_10) % 74.87/11.13 (65) all_10_6 = all_4_2 % 74.87/11.13 (66) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.87/11.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.87/11.13 (67) all_6_2 = all_4_10 % 74.87/11.13 (68) ~ (all_4_1 = all_4_4) % 74.87/11.13 (69) op(e4, e0) = all_4_20 % 74.87/11.13 (70) all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | % 74.87/11.13 all_10_22 = e4 % 74.87/11.13 (71) op(e4, all_4_2) = e2 % 74.87/11.13 (72) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.87/11.13 (73) all_10_0 = e2 % 74.87/11.13 (74) all_10_9 = e0 | all_10_10 = e0 | all_10_11 = e0 | all_10_15 = e0 | % 74.87/11.13 all_10_23 = e0 % 74.87/11.13 (75) ~ (all_4_4 = all_4_19) % 74.87/11.13 (76) ~ (all_4_1 = e2) % 74.87/11.13 % 74.87/11.13 Begin of proof % 74.87/11.13 | % 74.87/11.13 | BETA: splitting (57) gives: % 74.87/11.13 | % 74.87/11.13 | Case 1: % 74.87/11.13 | | % 74.87/11.13 | | (77) all_10_5 = e1 % 74.87/11.13 | | % 74.87/11.13 | | COMBINE_EQS: (23), (77) imply: % 74.87/11.13 | | (78) e2 = e1 % 74.87/11.13 | | % 74.87/11.13 | | SIMP: (78) implies: % 74.87/11.13 | | (79) e2 = e1 % 74.87/11.13 | | % 74.87/11.13 | | REDUCE: (45), (79) imply: % 74.87/11.13 | | (80) $false % 74.87/11.13 | | % 74.87/11.13 | | CLOSE: (80) is inconsistent. % 74.87/11.13 | | % 74.87/11.13 | Case 2: % 74.87/11.13 | | % 74.87/11.13 | | (81) ~ (all_10_5 = e1) % 74.87/11.13 | | (82) all_10_8 = e1 | all_10_14 = e1 | all_10_22 = e1 % 74.87/11.13 | | % 74.87/11.13 | | BETA: splitting (30) gives: % 74.87/11.13 | | % 74.87/11.13 | | Case 1: % 74.87/11.13 | | | % 74.87/11.13 | | | (83) all_10_0 = e1 % 74.87/11.13 | | | % 74.87/11.13 | | | COMBINE_EQS: (73), (83) imply: % 74.87/11.13 | | | (84) e2 = e1 % 74.87/11.13 | | | % 74.87/11.13 | | | REDUCE: (45), (84) imply: % 74.87/11.13 | | | (85) $false % 74.87/11.13 | | | % 74.87/11.13 | | | CLOSE: (85) is inconsistent. % 74.87/11.13 | | | % 74.87/11.13 | | Case 2: % 74.87/11.13 | | | % 74.87/11.13 | | | (86) all_10_1 = e1 | all_10_4 = e1 | all_10_9 = e1 | all_10_16 = e1 % 74.87/11.13 | | | % 74.87/11.13 | | | BETA: splitting (86) gives: % 74.87/11.13 | | | % 74.87/11.13 | | | Case 1: % 74.87/11.13 | | | | % 74.87/11.13 | | | | (87) all_10_1 = e1 % 74.87/11.13 | | | | % 74.87/11.13 | | | | COMBINE_EQS: (16), (87) imply: % 74.87/11.13 | | | | (88) all_4_5 = e1 % 74.87/11.13 | | | | % 74.87/11.13 | | | | REDUCE: (37), (88) imply: % 74.87/11.13 | | | | (89) $false % 74.87/11.13 | | | | % 74.87/11.13 | | | | CLOSE: (89) is inconsistent. % 74.87/11.13 | | | | % 74.87/11.13 | | | Case 2: % 74.87/11.13 | | | | % 74.87/11.13 | | | | (90) all_10_4 = e1 | all_10_9 = e1 | all_10_16 = e1 % 74.87/11.13 | | | | % 74.87/11.13 | | | | BETA: splitting (90) gives: % 74.87/11.13 | | | | % 74.87/11.13 | | | | Case 1: % 74.87/11.13 | | | | | % 74.87/11.13 | | | | | (91) all_10_4 = e1 % 74.87/11.13 | | | | | % 74.87/11.13 | | | | | REF_CLOSE: (8), (14), (91) are inconsistent by sub-proof #85. % 74.87/11.13 | | | | | % 74.87/11.13 | | | | Case 2: % 74.87/11.13 | | | | | % 74.87/11.13 | | | | | (92) all_10_9 = e1 | all_10_16 = e1 % 74.87/11.13 | | | | | % 74.87/11.13 | | | | | BETA: splitting (82) gives: % 74.87/11.13 | | | | | % 74.87/11.13 | | | | | Case 1: % 74.87/11.13 | | | | | | % 74.87/11.13 | | | | | | (93) all_10_8 = e1 % 74.87/11.13 | | | | | | % 74.87/11.13 | | | | | | COMBINE_EQS: (1), (93) imply: % 74.87/11.13 | | | | | | (94) e3 = e1 % 74.87/11.13 | | | | | | % 74.87/11.13 | | | | | | REDUCE: (25), (94) imply: % 74.87/11.13 | | | | | | (95) $false % 74.87/11.13 | | | | | | % 74.87/11.13 | | | | | | CLOSE: (95) is inconsistent. % 74.87/11.13 | | | | | | % 74.87/11.13 | | | | | Case 2: % 74.87/11.13 | | | | | | % 74.87/11.13 | | | | | | (96) all_10_14 = e1 | all_10_22 = e1 % 74.87/11.13 | | | | | | % 74.87/11.13 | | | | | | BETA: splitting (96) gives: % 74.87/11.13 | | | | | | % 74.87/11.13 | | | | | | Case 1: % 74.87/11.13 | | | | | | | % 74.87/11.13 | | | | | | | (97) all_10_14 = e1 % 74.87/11.13 | | | | | | | % 74.87/11.13 | | | | | | | COMBINE_EQS: (5), (97) imply: % 74.87/11.13 | | | | | | | (98) e1 = e0 % 74.87/11.13 | | | | | | | % 74.87/11.13 | | | | | | | REDUCE: (61), (98) imply: % 74.87/11.13 | | | | | | | (99) $false % 74.87/11.13 | | | | | | | % 74.87/11.13 | | | | | | | CLOSE: (99) is inconsistent. % 74.87/11.13 | | | | | | | % 74.87/11.13 | | | | | | Case 2: % 74.87/11.13 | | | | | | | % 74.87/11.13 | | | | | | | (100) all_10_22 = e1 % 74.87/11.13 | | | | | | | % 74.87/11.13 | | | | | | | COMBINE_EQS: (53), (100) imply: % 74.87/11.13 | | | | | | | (101) all_4_14 = e1 % 74.87/11.13 | | | | | | | % 74.87/11.13 | | | | | | | SIMP: (101) implies: % 74.87/11.13 | | | | | | | (102) all_4_14 = e1 % 74.87/11.13 | | | | | | | % 74.87/11.13 | | | | | | | REDUCE: (60), (102) imply: % 74.87/11.13 | | | | | | | (103) ~ (all_4_4 = e1) % 74.87/11.13 | | | | | | | % 74.87/11.13 | | | | | | | REDUCE: (13), (102) imply: % 74.87/11.13 | | | | | | | (104) ~ (e3 = e1) % 74.87/11.13 | | | | | | | % 74.87/11.13 | | | | | | | REDUCE: (2), (102) imply: % 74.87/11.13 | | | | | | | (105) op(e2, e1) = e0 % 74.87/11.13 | | | | | | | % 74.87/11.13 | | | | | | | BETA: splitting (29) gives: % 74.87/11.13 | | | | | | | % 74.87/11.13 | | | | | | | Case 1: % 74.87/11.13 | | | | | | | | % 74.87/11.13 | | | | | | | | (106) all_10_9 = e1 % 74.87/11.13 | | | | | | | | % 74.87/11.13 | | | | | | | | COMBINE_EQS: (58), (106) imply: % 74.87/11.13 | | | | | | | | (107) all_4_15 = e1 % 74.87/11.13 | | | | | | | | % 74.87/11.13 | | | | | | | | SIMP: (107) implies: % 74.87/11.13 | | | | | | | | (108) all_4_15 = e1 % 74.87/11.13 | | | | | | | | % 74.87/11.13 | | | | | | | | BETA: splitting (49) gives: % 74.87/11.13 | | | | | | | | % 74.87/11.13 | | | | | | | | Case 1: % 74.87/11.13 | | | | | | | | | % 74.87/11.13 | | | | | | | | | (109) all_10_0 = e3 % 74.87/11.13 | | | | | | | | | % 74.87/11.13 | | | | | | | | | REF_CLOSE: (11), (73), (109) are inconsistent by sub-proof % 74.87/11.13 | | | | | | | | | #104. % 74.87/11.13 | | | | | | | | | % 74.87/11.13 | | | | | | | | Case 2: % 74.87/11.13 | | | | | | | | | % 74.87/11.13 | | | | | | | | | (110) all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | % 74.87/11.13 | | | | | | | | | all_10_16 = e3 % 74.87/11.13 | | | | | | | | | % 74.87/11.13 | | | | | | | | | BETA: splitting (110) gives: % 74.87/11.13 | | | | | | | | | % 74.87/11.13 | | | | | | | | | Case 1: % 74.87/11.13 | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | (111) all_10_1 = e3 % 74.87/11.13 | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | COMBINE_EQS: (16), (111) imply: % 74.87/11.13 | | | | | | | | | | (112) all_4_5 = e3 % 74.87/11.13 | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | REDUCE: (35), (112) imply: % 74.87/11.13 | | | | | | | | | | (113) $false % 74.87/11.13 | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | CLOSE: (113) is inconsistent. % 74.87/11.13 | | | | | | | | | | % 74.87/11.13 | | | | | | | | | Case 2: % 74.87/11.13 | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | (114) all_10_4 = e3 | all_10_9 = e3 | all_10_16 = e3 % 74.87/11.13 | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | BETA: splitting (70) gives: % 74.87/11.13 | | | | | | | | | | % 74.87/11.13 | | | | | | | | | | Case 1: % 74.87/11.13 | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | (115) all_10_4 = e4 % 74.87/11.14 | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | COMBINE_EQS: (14), (115) imply: % 74.87/11.14 | | | | | | | | | | | (116) all_4_10 = e4 % 74.87/11.14 | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | REDUCE: (64), (116) imply: % 74.87/11.14 | | | | | | | | | | | (117) ~ (all_4_5 = e4) % 74.87/11.14 | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | REDUCE: (10), (116) imply: % 74.87/11.14 | | | | | | | | | | | (118) ~ (e4 = e3) % 74.87/11.14 | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | REDUCE: (32), (116) imply: % 74.87/11.14 | | | | | | | | | | | (119) ~ (e4 = e0) % 74.87/11.14 | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | BETA: splitting (114) gives: % 74.87/11.14 | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | Case 1: % 74.87/11.14 | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | (120) all_10_4 = e3 % 74.87/11.14 | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | COMBINE_EQS: (115), (120) imply: % 74.87/11.14 | | | | | | | | | | | | (121) e4 = e3 % 74.87/11.14 | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | REDUCE: (118), (121) imply: % 74.87/11.14 | | | | | | | | | | | | (122) $false % 74.87/11.14 | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | CLOSE: (122) is inconsistent. % 74.87/11.14 | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | Case 2: % 74.87/11.14 | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | (123) all_10_9 = e3 | all_10_16 = e3 % 74.87/11.14 | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | BETA: splitting (74) gives: % 74.87/11.14 | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | Case 1: % 74.87/11.14 | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | (124) all_10_9 = e0 % 74.87/11.14 | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | COMBINE_EQS: (106), (124) imply: % 74.87/11.14 | | | | | | | | | | | | | (125) e1 = e0 % 74.87/11.14 | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | REDUCE: (61), (125) imply: % 74.87/11.14 | | | | | | | | | | | | | (126) $false % 74.87/11.14 | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | CLOSE: (126) is inconsistent. % 74.87/11.14 | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | Case 2: % 74.87/11.14 | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | (127) all_10_10 = e0 | all_10_11 = e0 | all_10_15 = e0 | % 74.87/11.14 | | | | | | | | | | | | | all_10_23 = e0 % 74.87/11.14 | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | BETA: splitting (127) gives: % 74.87/11.14 | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | Case 1: % 74.87/11.14 | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | (128) all_10_10 = e0 % 74.87/11.14 | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | COMBINE_EQS: (55), (128) imply: % 74.87/11.14 | | | | | | | | | | | | | | (129) all_4_16 = e0 % 74.87/11.14 | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | SIMP: (129) implies: % 74.87/11.14 | | | | | | | | | | | | | | (130) all_4_16 = e0 % 74.87/11.14 | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | REDUCE: (62), (130) imply: % 74.87/11.14 | | | | | | | | | | | | | | (131) ~ (all_4_1 = e0) % 74.87/11.14 | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | REDUCE: (12), (130) imply: % 74.87/11.14 | | | | | | | | | | | | | | (132) ~ (all_4_19 = e0) % 74.87/11.14 | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | REDUCE: (24), (130) imply: % 74.87/11.14 | | | | | | | | | | | | | | (133) ~ (all_4_21 = e0) % 74.87/11.14 | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | SIMP: (133) implies: % 74.87/11.14 | | | | | | | | | | | | | | (134) ~ (all_4_21 = e0) % 74.87/11.14 | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | REDUCE: (15), (130) imply: % 74.87/11.14 | | | | | | | | | | | | | | (135) ~ (e2 = e0) % 74.87/11.14 | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | BETA: splitting (42) gives: % 74.87/11.14 | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | Case 1: % 74.87/11.14 | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | (136) all_10_9 = e3 % 74.87/11.14 | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | REF_CLOSE: (25), (106), (136) are inconsistent by sub-proof % 74.87/11.14 | | | | | | | | | | | | | | | #84. % 74.87/11.14 | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | Case 2: % 74.87/11.14 | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | (137) ~ (all_10_9 = e3) % 74.87/11.14 | | | | | | | | | | | | | | | (138) all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 74.87/11.14 | | | | | | | | | | | | | | | all_10_23 = e3 % 74.87/11.14 | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | BETA: splitting (48) gives: % 74.87/11.14 | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | Case 1: % 74.87/11.14 | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | (139) all_10_0 = e0 % 74.87/11.14 | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (73), (139) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | (140) e2 = e0 % 74.87/11.14 | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | REDUCE: (19), (140) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | (141) $false % 74.87/11.14 | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | CLOSE: (141) is inconsistent. % 74.87/11.14 | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | Case 2: % 74.87/11.14 | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | (142) all_10_2 = e0 | all_10_6 = e0 | all_10_12 = e0 | % 74.87/11.14 | | | | | | | | | | | | | | | | all_10_20 = e0 % 74.87/11.14 | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | BETA: splitting (142) gives: % 74.87/11.14 | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | Case 1: % 74.87/11.14 | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | (143) all_10_2 = e0 % 74.87/11.14 | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (131), (143) are inconsistent by sub-proof % 74.87/11.14 | | | | | | | | | | | | | | | | | #119. % 74.87/11.14 | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | Case 2: % 74.87/11.14 | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | (144) ~ (all_10_2 = e0) % 74.87/11.14 | | | | | | | | | | | | | | | | | (145) all_10_6 = e0 | all_10_12 = e0 | all_10_20 = e0 % 74.87/11.14 | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | BETA: splitting (9) gives: % 74.87/11.14 | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | Case 1: % 74.87/11.14 | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | (146) all_6_1 = e4 % 74.87/11.14 | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (117), (146) are inconsistent by sub-proof % 74.87/11.14 | | | | | | | | | | | | | | | | | | #138. % 74.87/11.14 | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | Case 2: % 74.87/11.14 | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | (147) all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 74.87/11.14 | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | BETA: splitting (123) gives: % 74.87/11.14 | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | Case 1: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | (148) all_10_9 = e3 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (106), (148) are inconsistent by sub-proof % 74.87/11.14 | | | | | | | | | | | | | | | | | | | #84. % 74.87/11.14 | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | Case 2: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | (149) all_10_16 = e3 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (149) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | (150) all_4_20 = e3 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | REDUCE: (18), (150) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | (151) ~ (all_4_21 = e3) % 74.87/11.14 | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | SIMP: (151) implies: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | (152) ~ (all_4_21 = e3) % 74.87/11.14 | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | REDUCE: (69), (150) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | (153) op(e4, e0) = e3 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | BETA: splitting (51) gives: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | Case 1: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | (154) all_10_2 = e3 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (154) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | (155) all_4_1 = e3 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | SIMP: (155) implies: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | (156) all_4_1 = e3 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (156) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | (157) ~ (all_4_4 = e3) % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | SIMP: (157) implies: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | (158) ~ (all_4_4 = e3) % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (156) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | (159) ~ (e3 = e0) % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | Case 1: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | (160) all_10_10 = e3 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (128), (159), (160) are inconsistent by sub-proof % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | #83. % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | Case 2: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | (161) all_10_11 = e3 | all_10_15 = e3 | all_10_23 = e3 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (59) gives: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | Case 1: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | (162) all_10_20 = e4 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (43), (162) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | (163) all_4_4 = e4 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (75), (163) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | (164) ~ (all_4_19 = e4) % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | SIMP: (164) implies: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | (165) ~ (all_4_19 = e4) % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | (166) all_10_11 = e3 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (166) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | (167) e3 = e2 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (167) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | (168) $false % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (168) is inconsistent. % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | (169) all_10_15 = e3 | all_10_23 = e3 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | (170) all_10_6 = e0 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (65), (170) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | (171) all_4_2 = e0 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (171) implies: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | (172) all_4_2 = e0 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (71), (172) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | (173) op(e4, e0) = e2 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (147) gives: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | (174) all_6_1 = e1 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (63), (174) are inconsistent by sub-proof % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | #137. % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | (175) all_6_1 = e3 | all_6_1 = e0 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (176) all_10_1 = e0 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (176) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (177) all_4_5 = e0 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (33), (177) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (178) op(e4, e0) = all_8_14 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (179) all_10_15 = e3 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (179) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (180) e4 = e3 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (180) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (181) $false % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (181) is inconsistent. % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (182) all_10_23 = e3 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (31), (182) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (183) all_4_19 = e3 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (183) implies: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (184) all_4_19 = e3 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (184) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (185) ~ (e4 = e3) % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (66) with e2, e0, e1, e2, % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (27), (105) gives: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (186) e2 = e0 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (66) with e3, all_8_14, e0, e4, % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (153), (178) gives: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (187) all_8_14 = e3 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (66) with e2, all_8_14, e0, e4, % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (173), (178) gives: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (188) all_8_14 = e2 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (187), (188) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (189) e3 = e2 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (189) implies: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (190) e3 = e2 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (186), (190) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (191) e3 = e0 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (118), (159), (169), (182), (191) are % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #82. % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (192) ~ (all_10_1 = e0) % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (192) imply: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (193) ~ (all_4_5 = e0) % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (63), (175), (193) are inconsistent by % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #136. % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | (194) all_10_12 = e0 | all_10_20 = e0 % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (54), (119), (162), (194) are inconsistent % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #75. % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | End of split % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | End of split % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | Case 2: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | (195) ~ (all_10_20 = e4) % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (22), (43), (50), (103), (158), (195) are % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #72. % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | End of split % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | End of split % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | Case 2: % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | (196) ~ (all_10_2 = e3) % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (20), (36), (40), (44), (46), (52), (56), % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | (131), (134), (152), (196) are inconsistent by % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | sub-proof #80. % 74.87/11.14 | | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | | End of split % 74.87/11.14 | | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | | End of split % 74.87/11.14 | | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | | End of split % 74.87/11.14 | | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | | End of split % 74.87/11.14 | | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | | End of split % 74.87/11.14 | | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | End of split % 74.87/11.14 | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | Case 2: % 74.87/11.14 | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | (197) all_10_11 = e0 | all_10_15 = e0 | all_10_23 = e0 % 74.87/11.14 | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | | REF_CLOSE: (6), (17), (19), (31), (47), (119), (197) are % 74.87/11.14 | | | | | | | | | | | | | | inconsistent by sub-proof #79. % 74.87/11.14 | | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | | End of split % 74.87/11.14 | | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | | End of split % 74.87/11.14 | | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | End of split % 74.87/11.14 | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | Case 2: % 74.87/11.14 | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | (198) ~ (all_10_4 = e4) % 74.87/11.14 | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | REDUCE: (14), (198) imply: % 74.87/11.14 | | | | | | | | | | | (199) ~ (all_4_10 = e4) % 74.87/11.14 | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | | REF_CLOSE: (8), (10), (32), (67), (72), (199) are % 74.87/11.14 | | | | | | | | | | | inconsistent by sub-proof #161. % 74.87/11.14 | | | | | | | | | | | % 74.87/11.14 | | | | | | | | | | End of split % 74.87/11.14 | | | | | | | | | | % 74.87/11.14 | | | | | | | | | End of split % 74.87/11.14 | | | | | | | | | % 74.87/11.14 | | | | | | | | End of split % 74.87/11.14 | | | | | | | | % 74.87/11.14 | | | | | | | Case 2: % 74.87/11.14 | | | | | | | | % 74.87/11.14 | | | | | | | | (200) ~ (all_10_9 = e1) % 74.87/11.14 | | | | | | | | % 74.87/11.14 | | | | | | | | REF_CLOSE: (4), (26), (58), (92), (200) are inconsistent by % 74.87/11.14 | | | | | | | | sub-proof #78. % 74.87/11.14 | | | | | | | | % 74.87/11.14 | | | | | | | End of split % 74.87/11.14 | | | | | | | % 74.87/11.14 | | | | | | End of split % 74.87/11.14 | | | | | | % 74.87/11.14 | | | | | End of split % 74.87/11.14 | | | | | % 74.87/11.14 | | | | End of split % 74.87/11.14 | | | | % 74.87/11.14 | | | End of split % 74.87/11.14 | | | % 74.87/11.14 | | End of split % 74.87/11.14 | | % 74.87/11.14 | End of split % 74.87/11.14 | % 74.87/11.14 End of proof % 74.87/11.14 % 74.87/11.14 Sub-proof #72 shows that the following formulas are inconsistent: % 74.87/11.14 ---------------------------------------------------------------- % 74.87/11.14 (1) all_6_20 = all_4_4 % 74.87/11.14 (2) ~ (all_10_20 = e4) % 74.87/11.14 (3) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 74.87/11.14 (4) ~ (all_4_4 = e3) % 74.87/11.14 (5) all_10_20 = all_4_4 % 74.87/11.14 (6) ~ (all_4_4 = e0) % 74.87/11.14 (7) ~ (all_4_4 = e1) % 74.87/11.14 % 74.87/11.14 Begin of proof % 74.87/11.14 | % 74.87/11.14 | REDUCE: (2), (5) imply: % 74.87/11.14 | (8) ~ (all_4_4 = e4) % 74.87/11.14 | % 74.87/11.14 | BETA: splitting (3) gives: % 74.87/11.14 | % 74.87/11.14 | Case 1: % 74.87/11.14 | | % 74.87/11.14 | | (9) all_6_20 = e4 % 74.87/11.14 | | % 74.87/11.14 | | REF_CLOSE: (1), (8), (9) are inconsistent by sub-proof #74. % 74.87/11.14 | | % 74.87/11.14 | Case 2: % 74.87/11.14 | | % 74.87/11.14 | | (10) all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 74.87/11.14 | | % 74.87/11.14 | | BETA: splitting (10) gives: % 74.87/11.14 | | % 74.87/11.14 | | Case 1: % 74.87/11.14 | | | % 74.87/11.14 | | | (11) all_6_20 = e1 % 74.87/11.14 | | | % 74.87/11.14 | | | REF_CLOSE: (1), (7), (11) are inconsistent by sub-proof #73. % 74.87/11.14 | | | % 74.87/11.14 | | Case 2: % 74.87/11.14 | | | % 74.87/11.14 | | | (12) all_6_20 = e3 | all_6_20 = e0 % 74.87/11.14 | | | % 74.87/11.14 | | | REF_CLOSE: (1), (4), (6), (12) are inconsistent by sub-proof #122. % 74.87/11.14 | | | % 74.87/11.14 | | End of split % 74.87/11.14 | | % 74.87/11.14 | End of split % 74.87/11.14 | % 74.87/11.14 End of proof % 74.87/11.14 % 74.87/11.14 Sub-proof #73 shows that the following formulas are inconsistent: % 74.87/11.14 ---------------------------------------------------------------- % 74.87/11.14 (1) all_6_20 = all_4_4 % 74.87/11.14 (2) all_6_20 = e1 % 74.87/11.14 (3) ~ (all_4_4 = e1) % 74.87/11.14 % 74.87/11.14 Begin of proof % 74.87/11.14 | % 74.87/11.14 | COMBINE_EQS: (1), (2) imply: % 74.87/11.14 | (4) all_4_4 = e1 % 74.87/11.14 | % 74.87/11.14 | SIMP: (4) implies: % 74.87/11.14 | (5) all_4_4 = e1 % 74.87/11.14 | % 74.87/11.14 | REDUCE: (3), (5) imply: % 74.87/11.14 | (6) $false % 74.87/11.14 | % 74.87/11.14 | CLOSE: (6) is inconsistent. % 74.87/11.14 | % 74.87/11.14 End of proof % 74.87/11.14 % 74.87/11.14 Sub-proof #74 shows that the following formulas are inconsistent: % 74.87/11.14 ---------------------------------------------------------------- % 74.87/11.14 (1) all_6_20 = all_4_4 % 74.87/11.14 (2) all_6_20 = e4 % 74.87/11.14 (3) ~ (all_4_4 = e4) % 74.87/11.14 % 74.87/11.14 Begin of proof % 74.87/11.14 | % 74.87/11.14 | COMBINE_EQS: (1), (2) imply: % 74.87/11.14 | (4) all_4_4 = e4 % 74.87/11.14 | % 74.87/11.14 | SIMP: (4) implies: % 74.87/11.14 | (5) all_4_4 = e4 % 74.87/11.14 | % 74.87/11.14 | REDUCE: (3), (5) imply: % 74.87/11.14 | (6) $false % 74.87/11.14 | % 74.87/11.14 | CLOSE: (6) is inconsistent. % 74.87/11.14 | % 74.87/11.14 End of proof % 74.87/11.14 % 74.87/11.14 Sub-proof #75 shows that the following formulas are inconsistent: % 74.87/11.14 ---------------------------------------------------------------- % 74.87/11.14 (1) all_10_20 = e4 % 74.87/11.14 (2) all_10_12 = all_4_3 % 74.87/11.14 (3) ~ (e4 = e0) % 74.87/11.14 (4) all_10_12 = e0 | all_10_20 = e0 % 74.87/11.14 (5) ~ (all_4_3 = e0) % 74.87/11.14 % 74.87/11.14 Begin of proof % 74.87/11.14 | % 74.87/11.14 | BETA: splitting (4) gives: % 74.87/11.14 | % 74.87/11.14 | Case 1: % 74.87/11.14 | | % 74.87/11.14 | | (6) all_10_12 = e0 % 74.87/11.14 | | % 74.87/11.14 | | COMBINE_EQS: (2), (6) imply: % 74.87/11.14 | | (7) all_4_3 = e0 % 74.87/11.14 | | % 74.87/11.14 | | SIMP: (7) implies: % 74.87/11.14 | | (8) all_4_3 = e0 % 74.87/11.14 | | % 74.87/11.14 | | REDUCE: (5), (8) imply: % 74.87/11.14 | | (9) $false % 74.87/11.14 | | % 74.87/11.14 | | CLOSE: (9) is inconsistent. % 74.87/11.14 | | % 74.87/11.14 | Case 2: % 74.87/11.14 | | % 74.87/11.14 | | (10) all_10_20 = e0 % 74.87/11.14 | | % 74.87/11.14 | | REF_CLOSE: (1), (3), (10) are inconsistent by sub-proof #76. % 74.87/11.14 | | % 74.87/11.14 | End of split % 74.87/11.14 | % 74.87/11.14 End of proof % 74.87/11.14 % 74.87/11.14 Sub-proof #76 shows that the following formulas are inconsistent: % 74.87/11.14 ---------------------------------------------------------------- % 74.87/11.14 (1) all_10_20 = e4 % 74.87/11.14 (2) all_10_20 = e0 % 74.87/11.14 (3) ~ (e4 = e0) % 74.87/11.14 % 74.87/11.14 Begin of proof % 74.87/11.14 | % 74.87/11.14 | COMBINE_EQS: (1), (2) imply: % 74.87/11.14 | (4) e4 = e0 % 74.87/11.14 | % 74.87/11.14 | SIMP: (4) implies: % 74.87/11.14 | (5) e4 = e0 % 74.87/11.14 | % 74.87/11.14 | REDUCE: (3), (5) imply: % 74.87/11.14 | (6) $false % 74.87/11.14 | % 74.87/11.14 | CLOSE: (6) is inconsistent. % 74.87/11.14 | % 74.87/11.14 End of proof % 74.87/11.14 % 74.87/11.14 Sub-proof #77 shows that the following formulas are inconsistent: % 74.87/11.14 ---------------------------------------------------------------- % 74.87/11.14 (1) ~ (all_4_19 = e4) % 74.87/11.14 (2) op(e2, all_4_14) = e0 % 74.87/11.14 (3) ~ (all_4_1 = all_4_2) % 74.87/11.14 (4) all_6_20 = all_4_4 % 74.87/11.14 (5) ~ (all_4_20 = e1) % 74.87/11.14 (6) ~ (all_4_15 = all_4_20) % 74.87/11.14 (7) ~ (all_4_19 = e0) % 74.87/11.14 (8) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 74.87/11.14 (9) ~ (all_4_10 = e3) % 74.87/11.15 (10) ~ (e3 = e2) % 74.87/11.15 (11) ~ (all_4_7 = e3) % 74.87/11.15 (12) ~ (all_4_16 = all_4_19) % 74.87/11.15 (13) op(e0, e4) = all_4_4 % 74.87/11.15 (14) ~ (all_4_14 = e3) % 74.87/11.15 (15) all_10_4 = all_4_10 % 74.87/11.15 (16) all_10_1 = all_4_5 % 74.87/11.15 (17) all_10_15 = e4 % 74.87/11.15 (18) all_6_11 = e4 | all_6_11 = e3 | all_6_11 = e1 | all_6_11 = e0 % 74.87/11.15 (19) ~ (all_4_20 = all_4_21) % 74.87/11.15 (20) ~ (e2 = e0) % 74.87/11.15 (21) all_6_9 = all_4_21 % 74.87/11.15 (22) all_10_16 = e4 | all_10_17 = e4 | all_10_18 = e4 | all_10_19 = e4 | % 74.87/11.15 all_10_24 = e4 % 74.87/11.15 (23) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 74.87/11.15 (24) ~ (all_4_16 = all_4_21) % 74.87/11.15 (25) ~ (e3 = e1) % 74.87/11.15 (26) ~ (all_4_10 = all_4_14) % 74.87/11.15 (27) all_8_1 = e3 & ~ (all_8_2 = e4) % 74.87/11.15 (28) all_10_16 = all_4_20 % 74.87/11.15 (29) ~ (all_4_14 = e0) % 74.87/11.15 (30) all_10_9 = e1 | all_10_10 = e1 | all_10_11 = e1 | all_10_15 = e1 | % 74.87/11.15 all_10_23 = e1 % 74.87/11.15 (31) all_10_0 = e1 | all_10_1 = e1 | all_10_4 = e1 | all_10_9 = e1 | % 74.87/11.15 all_10_16 = e1 % 74.87/11.15 (32) all_6_22 = e4 | all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 74.87/11.15 (33) all_10_23 = all_4_19 % 74.87/11.15 (34) ~ (all_4_10 = e0) % 74.87/11.15 (35) op(e2, e4) = all_4_2 % 74.87/11.15 (36) ~ (all_8_37 = e2) % 74.87/11.15 (37) all_6_3 = e4 | all_6_3 = e3 | all_6_3 = e2 | all_6_3 = e1 | all_6_3 = e0 % 74.87/11.15 (38) ~ (all_4_5 = all_4_15) % 74.87/11.15 (39) ~ (all_4_5 = e3) % 74.87/11.15 (40) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e1 | all_6_9 = e0 % 74.87/11.15 (41) op(e4, e4) = e2 % 74.87/11.15 (42) ~ (all_4_5 = e1) % 74.87/11.15 (43) ~ (all_4_10 = all_4_15) % 74.87/11.15 (44) ~ (all_4_5 = all_4_20) % 74.87/11.15 (45) all_6_5 = all_4_1 % 74.87/11.15 (46) all_10_1 = e0 | all_10_3 = e0 | all_10_7 = e0 | all_10_13 = e0 | % 74.87/11.15 all_10_21 = e0 % 74.87/11.15 (47) all_10_9 = e3 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 74.87/11.15 all_10_23 = e3 % 74.87/11.15 (48) op(e4, all_4_1) = all_8_1 % 74.87/11.15 (49) all_10_20 = all_4_4 % 74.87/11.15 (50) ~ (all_4_1 = e1) % 74.87/11.15 (51) ~ (e2 = e1) % 74.87/11.15 (52) ~ (all_4_2 = all_4_7) % 74.87/11.15 (53) ~ (all_4_1 = all_4_21) % 74.87/11.15 (54) all_10_11 = e2 % 74.87/11.15 (55) all_10_0 = e3 | all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | % 74.87/11.15 all_10_16 = e3 % 74.87/11.15 (56) ~ (all_4_4 = e0) % 74.87/11.15 (57) all_10_2 = e3 | all_10_3 = e3 | all_10_5 = e3 | all_10_10 = e3 | % 74.87/11.15 all_10_17 = e3 % 74.87/11.15 (58) all_10_2 = all_4_1 % 74.87/11.15 (59) all_10_10 = all_4_16 % 74.87/11.15 (60) all_6_3 = all_4_15 % 74.87/11.15 (61) ~ (all_4_21 = e1) % 74.87/11.15 (62) op(e4, all_4_20) = all_8_53 % 74.87/11.15 (63) all_6_4 = e4 | all_6_4 = e3 | all_6_4 = e1 | all_6_4 = e0 % 74.87/11.15 (64) ~ (all_4_15 = e2) % 74.87/11.15 (65) all_10_9 = all_4_15 % 74.87/11.15 (66) ~ (all_4_4 = all_4_14) % 74.87/11.15 (67) all_6_4 = all_4_20 % 74.87/11.15 (68) ~ (e1 = e0) % 74.87/11.15 (69) ~ (all_4_1 = all_4_16) % 74.87/11.15 (70) op(e0, all_4_14) = all_8_37 % 74.87/11.15 (71) all_6_1 = all_4_5 % 74.87/11.15 (72) ~ (all_4_5 = all_4_10) % 74.87/11.15 (73) ~ (all_4_5 = all_4_7) % 74.87/11.15 (74) all_10_20 = e3 | all_10_21 = e3 | all_10_22 = e3 | all_10_23 = e3 | % 74.87/11.15 all_10_24 = e3 % 74.87/11.15 (75) all_6_11 = all_4_7 % 74.87/11.15 (76) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.87/11.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.87/11.15 (77) all_6_2 = all_4_10 % 74.87/11.15 (78) ~ (all_4_1 = all_4_4) % 74.87/11.15 (79) all_6_22 = all_4_14 % 74.87/11.15 (80) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e2 | all_6_5 = e1 | all_6_5 = e0 % 74.87/11.15 (81) all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | % 74.87/11.15 all_10_22 = e4 % 74.87/11.15 (82) ~ (all_4_10 = all_4_20) % 74.87/11.15 (83) ~ (all_4_4 = e1) % 74.87/11.15 (84) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.87/11.15 (85) all_10_0 = e2 % 74.87/11.15 (86) all_10_9 = e0 | all_10_10 = e0 | all_10_11 = e0 | all_10_15 = e0 | % 74.87/11.15 all_10_23 = e0 % 74.87/11.15 (87) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 74.87/11.15 all_10_22 = e1 % 74.87/11.15 (88) ~ (all_4_7 = e1) % 74.87/11.15 (89) ~ (all_4_1 = e2) % 74.87/11.15 (90) ~ (all_4_15 = e4) % 74.87/11.15 (91) op(e4, e3) = all_4_5 % 74.87/11.15 % 74.87/11.15 Begin of proof % 74.87/11.15 | % 74.87/11.15 | ALPHA: (27) implies: % 74.87/11.15 | (92) all_8_1 = e3 % 74.87/11.15 | % 74.87/11.15 | REDUCE: (48), (92) imply: % 74.87/11.15 | (93) op(e4, all_4_1) = e3 % 74.87/11.15 | % 74.87/11.15 | BETA: splitting (80) gives: % 74.87/11.15 | % 74.87/11.15 | Case 1: % 74.87/11.15 | | % 74.87/11.15 | | (94) all_6_5 = e2 % 74.87/11.15 | | % 74.87/11.15 | | REF_CLOSE: (45), (89), (94) are inconsistent by sub-proof #153. % 74.87/11.15 | | % 74.87/11.15 | Case 2: % 74.87/11.15 | | % 74.87/11.15 | | (95) ~ (all_6_5 = e2) % 74.87/11.15 | | (96) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | all_6_5 = e0 % 74.87/11.15 | | % 74.87/11.15 | | BETA: splitting (37) gives: % 74.87/11.15 | | % 74.87/11.15 | | Case 1: % 74.87/11.15 | | | % 74.87/11.15 | | | (97) all_6_3 = e2 % 74.87/11.15 | | | % 74.87/11.15 | | | REF_CLOSE: (60), (64), (97) are inconsistent by sub-proof #152. % 74.87/11.15 | | | % 74.87/11.15 | | Case 2: % 74.87/11.15 | | | % 74.87/11.15 | | | (98) all_6_3 = e4 | all_6_3 = e3 | all_6_3 = e1 | all_6_3 = e0 % 74.87/11.15 | | | % 74.87/11.15 | | | BETA: splitting (87) gives: % 74.87/11.15 | | | % 74.87/11.15 | | | Case 1: % 74.87/11.15 | | | | % 74.87/11.15 | | | | (99) all_10_4 = e1 % 74.87/11.15 | | | | % 74.87/11.15 | | | | COMBINE_EQS: (15), (99) imply: % 74.87/11.15 | | | | (100) all_4_10 = e1 % 74.87/11.15 | | | | % 74.87/11.15 | | | | SIMP: (100) implies: % 74.87/11.15 | | | | (101) all_4_10 = e1 % 74.87/11.15 | | | | % 74.87/11.15 | | | | REDUCE: (26), (101) imply: % 74.87/11.15 | | | | (102) ~ (all_4_14 = e1) % 74.87/11.15 | | | | % 74.87/11.15 | | | | SIMP: (102) implies: % 74.87/11.15 | | | | (103) ~ (all_4_14 = e1) % 74.87/11.15 | | | | % 74.87/11.15 | | | | REDUCE: (43), (101) imply: % 74.87/11.15 | | | | (104) ~ (all_4_15 = e1) % 74.87/11.15 | | | | % 74.87/11.15 | | | | SIMP: (104) implies: % 74.87/11.15 | | | | (105) ~ (all_4_15 = e1) % 74.87/11.15 | | | | % 74.87/11.15 | | | | REDUCE: (82), (101) imply: % 74.87/11.15 | | | | (106) ~ (all_4_20 = e1) % 74.87/11.15 | | | | % 74.87/11.15 | | | | BETA: splitting (32) gives: % 74.87/11.15 | | | | % 74.87/11.15 | | | | Case 1: % 74.87/11.15 | | | | | % 74.87/11.15 | | | | | (107) all_6_22 = e4 % 74.87/11.15 | | | | | % 74.87/11.15 | | | | | COMBINE_EQS: (79), (107) imply: % 74.87/11.15 | | | | | (108) all_4_14 = e4 % 74.87/11.15 | | | | | % 74.87/11.15 | | | | | SIMP: (108) implies: % 74.87/11.15 | | | | | (109) all_4_14 = e4 % 74.87/11.15 | | | | | % 74.87/11.15 | | | | | REDUCE: (66), (109) imply: % 74.87/11.15 | | | | | (110) ~ (all_4_4 = e4) % 74.87/11.15 | | | | | % 74.87/11.15 | | | | | REDUCE: (2), (109) imply: % 74.87/11.15 | | | | | (111) op(e2, e4) = e0 % 74.87/11.15 | | | | | % 74.87/11.15 | | | | | REDUCE: (70), (109) imply: % 74.87/11.15 | | | | | (112) op(e0, e4) = all_8_37 % 74.87/11.15 | | | | | % 74.87/11.15 | | | | | BETA: splitting (23) gives: % 74.87/11.15 | | | | | % 74.87/11.15 | | | | | Case 1: % 74.87/11.15 | | | | | | % 74.87/11.15 | | | | | | (113) all_6_20 = e4 % 74.87/11.15 | | | | | | % 74.87/11.15 | | | | | | COMBINE_EQS: (4), (113) imply: % 74.87/11.15 | | | | | | (114) all_4_4 = e4 % 74.87/11.15 | | | | | | % 74.87/11.15 | | | | | | REDUCE: (110), (114) imply: % 74.87/11.15 | | | | | | (115) $false % 74.87/11.15 | | | | | | % 74.87/11.15 | | | | | | CLOSE: (115) is inconsistent. % 74.87/11.15 | | | | | | % 74.87/11.15 | | | | | Case 2: % 74.87/11.15 | | | | | | % 74.87/11.15 | | | | | | (116) all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 74.87/11.15 | | | | | | % 74.87/11.15 | | | | | | BETA: splitting (116) gives: % 74.87/11.15 | | | | | | % 74.87/11.15 | | | | | | Case 1: % 74.87/11.15 | | | | | | | % 74.87/11.15 | | | | | | | (117) all_6_20 = e1 % 74.87/11.15 | | | | | | | % 74.87/11.15 | | | | | | | COMBINE_EQS: (4), (117) imply: % 74.87/11.15 | | | | | | | (118) all_4_4 = e1 % 74.87/11.15 | | | | | | | % 74.87/11.15 | | | | | | | REDUCE: (83), (118) imply: % 74.87/11.15 | | | | | | | (119) $false % 74.87/11.15 | | | | | | | % 74.87/11.15 | | | | | | | CLOSE: (119) is inconsistent. % 74.87/11.15 | | | | | | | % 74.87/11.15 | | | | | | Case 2: % 74.87/11.15 | | | | | | | % 74.87/11.15 | | | | | | | (120) all_6_20 = e3 | all_6_20 = e0 % 74.87/11.15 | | | | | | | % 74.87/11.15 | | | | | | | BETA: splitting (74) gives: % 74.87/11.15 | | | | | | | % 74.87/11.15 | | | | | | | Case 1: % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | | (121) all_10_20 = e3 % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | | COMBINE_EQS: (49), (121) imply: % 74.87/11.15 | | | | | | | | (122) all_4_4 = e3 % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | | SIMP: (122) implies: % 74.87/11.15 | | | | | | | | (123) all_4_4 = e3 % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | | REDUCE: (78), (123) imply: % 74.87/11.15 | | | | | | | | (124) ~ (all_4_1 = e3) % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | | REDUCE: (13), (123) imply: % 74.87/11.15 | | | | | | | | (125) op(e0, e4) = e3 % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | | GROUND_INST: instantiating (76) with e3, all_8_37, e4, e0, % 74.87/11.15 | | | | | | | | simplifying with (112), (125) gives: % 74.87/11.15 | | | | | | | | (126) all_8_37 = e3 % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | | GROUND_INST: instantiating (76) with all_4_2, e0, e4, e2, % 74.87/11.15 | | | | | | | | simplifying with (35), (111) gives: % 74.87/11.15 | | | | | | | | (127) all_4_2 = e0 % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | | REDUCE: (3), (127) imply: % 74.87/11.15 | | | | | | | | (128) ~ (all_4_1 = e0) % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | | REDUCE: (52), (127) imply: % 74.87/11.15 | | | | | | | | (129) ~ (all_4_7 = e0) % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | | SIMP: (129) implies: % 74.87/11.15 | | | | | | | | (130) ~ (all_4_7 = e0) % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | | BETA: splitting (46) gives: % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | | Case 1: % 74.87/11.15 | | | | | | | | | % 74.87/11.15 | | | | | | | | | (131) all_10_1 = e0 % 74.87/11.15 | | | | | | | | | % 74.87/11.15 | | | | | | | | | REF_CLOSE: (5), (6), (10), (16), (22), (28), (38), (41), (44), % 74.87/11.15 | | | | | | | | | (45), (47), (50), (60), (62), (63), (65), (67), % 74.87/11.15 | | | | | | | | | (76), (90), (93), (96), (98), (105), (124), (128), % 74.87/11.15 | | | | | | | | | (131) are inconsistent by sub-proof #139. % 74.87/11.15 | | | | | | | | | % 74.87/11.15 | | | | | | | | Case 2: % 74.87/11.15 | | | | | | | | | % 74.87/11.15 | | | | | | | | | (132) ~ (all_10_1 = e0) % 74.87/11.15 | | | | | | | | | % 74.87/11.15 | | | | | | | | | REDUCE: (16), (132) imply: % 74.87/11.15 | | | | | | | | | (133) ~ (all_4_5 = e0) % 74.87/11.15 | | | | | | | | | % 74.87/11.15 | | | | | | | | | REF_CLOSE: (8), (11), (18), (39), (42), (71), (73), (75), % 74.87/11.15 | | | | | | | | | (88), (130), (133) are inconsistent by sub-proof % 74.87/11.15 | | | | | | | | | #109. % 74.87/11.15 | | | | | | | | | % 74.87/11.15 | | | | | | | | End of split % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | Case 2: % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | | (134) ~ (all_10_20 = e3) % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | | REDUCE: (49), (134) imply: % 74.87/11.15 | | | | | | | | (135) ~ (all_4_4 = e3) % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | | REF_CLOSE: (4), (56), (120), (135) are inconsistent by sub-proof % 74.87/11.15 | | | | | | | | #122. % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | End of split % 74.87/11.15 | | | | | | | % 74.87/11.15 | | | | | | End of split % 74.87/11.15 | | | | | | % 74.87/11.15 | | | | | End of split % 74.87/11.15 | | | | | % 74.87/11.15 | | | | Case 2: % 74.87/11.15 | | | | | % 74.87/11.15 | | | | | (136) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 74.87/11.15 | | | | | % 74.87/11.15 | | | | | REF_CLOSE: (14), (29), (79), (103), (136) are inconsistent by % 74.87/11.15 | | | | | sub-proof #130. % 74.87/11.15 | | | | | % 74.87/11.15 | | | | End of split % 74.87/11.15 | | | | % 74.87/11.15 | | | Case 2: % 74.87/11.15 | | | | % 74.87/11.15 | | | | (137) ~ (all_10_4 = e1) % 74.87/11.15 | | | | % 74.87/11.15 | | | | REDUCE: (15), (137) imply: % 74.87/11.15 | | | | (138) ~ (all_4_10 = e1) % 74.87/11.15 | | | | % 74.87/11.15 | | | | BETA: splitting (31) gives: % 74.87/11.15 | | | | % 74.87/11.15 | | | | Case 1: % 74.87/11.15 | | | | | % 74.87/11.15 | | | | | (139) all_10_0 = e1 % 74.87/11.15 | | | | | % 74.87/11.15 | | | | | COMBINE_EQS: (85), (139) imply: % 74.87/11.15 | | | | | (140) e2 = e1 % 74.87/11.15 | | | | | % 74.87/11.15 | | | | | REDUCE: (51), (140) imply: % 74.87/11.15 | | | | | (141) $false % 74.87/11.15 | | | | | % 74.87/11.15 | | | | | CLOSE: (141) is inconsistent. % 74.87/11.15 | | | | | % 74.87/11.15 | | | | Case 2: % 74.87/11.15 | | | | | % 74.87/11.15 | | | | | (142) all_10_1 = e1 | all_10_4 = e1 | all_10_9 = e1 | all_10_16 = % 74.87/11.15 | | | | | e1 % 74.87/11.15 | | | | | % 74.87/11.15 | | | | | BETA: splitting (142) gives: % 74.87/11.15 | | | | | % 74.87/11.15 | | | | | Case 1: % 74.87/11.15 | | | | | | % 74.87/11.15 | | | | | | (143) all_10_1 = e1 % 74.87/11.15 | | | | | | % 74.87/11.15 | | | | | | COMBINE_EQS: (16), (143) imply: % 74.87/11.15 | | | | | | (144) all_4_5 = e1 % 74.87/11.15 | | | | | | % 74.87/11.15 | | | | | | REDUCE: (42), (144) imply: % 74.87/11.15 | | | | | | (145) $false % 74.87/11.15 | | | | | | % 74.87/11.15 | | | | | | CLOSE: (145) is inconsistent. % 74.87/11.15 | | | | | | % 74.87/11.15 | | | | | Case 2: % 74.87/11.15 | | | | | | % 74.87/11.15 | | | | | | (146) all_10_4 = e1 | all_10_9 = e1 | all_10_16 = e1 % 74.87/11.15 | | | | | | % 74.87/11.15 | | | | | | BETA: splitting (146) gives: % 74.87/11.15 | | | | | | % 74.87/11.15 | | | | | | Case 1: % 74.87/11.15 | | | | | | | % 74.87/11.15 | | | | | | | (147) all_10_4 = e1 % 74.87/11.15 | | | | | | | % 74.87/11.15 | | | | | | | REF_CLOSE: (15), (138), (147) are inconsistent by sub-proof #85. % 74.87/11.15 | | | | | | | % 74.87/11.15 | | | | | | Case 2: % 74.87/11.15 | | | | | | | % 74.87/11.15 | | | | | | | (148) all_10_9 = e1 | all_10_16 = e1 % 74.87/11.15 | | | | | | | % 74.87/11.15 | | | | | | | BETA: splitting (30) gives: % 74.87/11.15 | | | | | | | % 74.87/11.15 | | | | | | | Case 1: % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | | (149) all_10_9 = e1 % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | | COMBINE_EQS: (65), (149) imply: % 74.87/11.15 | | | | | | | | (150) all_4_15 = e1 % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | | SIMP: (150) implies: % 74.87/11.15 | | | | | | | | (151) all_4_15 = e1 % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | | BETA: splitting (55) gives: % 74.87/11.15 | | | | | | | | % 74.87/11.15 | | | | | | | | Case 1: % 74.87/11.15 | | | | | | | | | % 74.87/11.15 | | | | | | | | | (152) all_10_0 = e3 % 74.87/11.15 | | | | | | | | | % 74.87/11.15 | | | | | | | | | REF_CLOSE: (10), (85), (152) are inconsistent by sub-proof % 74.87/11.16 | | | | | | | | | #104. % 74.87/11.16 | | | | | | | | | % 74.87/11.16 | | | | | | | | Case 2: % 74.87/11.16 | | | | | | | | | % 74.87/11.16 | | | | | | | | | (153) all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | % 74.87/11.16 | | | | | | | | | all_10_16 = e3 % 74.87/11.16 | | | | | | | | | % 74.87/11.16 | | | | | | | | | BETA: splitting (153) gives: % 74.87/11.16 | | | | | | | | | % 74.87/11.16 | | | | | | | | | Case 1: % 74.87/11.16 | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | (154) all_10_1 = e3 % 74.87/11.16 | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | COMBINE_EQS: (16), (154) imply: % 74.87/11.16 | | | | | | | | | | (155) all_4_5 = e3 % 74.87/11.16 | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | REDUCE: (39), (155) imply: % 74.87/11.16 | | | | | | | | | | (156) $false % 74.87/11.16 | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | CLOSE: (156) is inconsistent. % 74.87/11.16 | | | | | | | | | | % 74.87/11.16 | | | | | | | | | Case 2: % 74.87/11.16 | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | (157) all_10_4 = e3 | all_10_9 = e3 | all_10_16 = e3 % 74.87/11.16 | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | BETA: splitting (81) gives: % 74.87/11.16 | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | Case 1: % 74.87/11.16 | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | (158) all_10_4 = e4 % 74.87/11.16 | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | COMBINE_EQS: (15), (158) imply: % 74.87/11.16 | | | | | | | | | | | (159) all_4_10 = e4 % 74.87/11.16 | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | REDUCE: (72), (159) imply: % 74.87/11.16 | | | | | | | | | | | (160) ~ (all_4_5 = e4) % 74.87/11.16 | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | REDUCE: (82), (159) imply: % 74.87/11.16 | | | | | | | | | | | (161) ~ (all_4_20 = e4) % 74.87/11.16 | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | SIMP: (161) implies: % 74.87/11.16 | | | | | | | | | | | (162) ~ (all_4_20 = e4) % 74.87/11.16 | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | REDUCE: (9), (159) imply: % 74.87/11.16 | | | | | | | | | | | (163) ~ (e4 = e3) % 74.87/11.16 | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | REDUCE: (34), (159) imply: % 74.87/11.16 | | | | | | | | | | | (164) ~ (e4 = e0) % 74.87/11.16 | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | BETA: splitting (157) gives: % 74.87/11.16 | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | Case 1: % 74.87/11.16 | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | (165) all_10_4 = e3 % 74.87/11.16 | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | COMBINE_EQS: (158), (165) imply: % 74.87/11.16 | | | | | | | | | | | | (166) e4 = e3 % 74.87/11.16 | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | REDUCE: (163), (166) imply: % 74.87/11.16 | | | | | | | | | | | | (167) $false % 74.87/11.16 | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | CLOSE: (167) is inconsistent. % 74.87/11.16 | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | Case 2: % 74.87/11.16 | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | (168) all_10_9 = e3 | all_10_16 = e3 % 74.87/11.16 | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | BETA: splitting (86) gives: % 74.87/11.16 | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | Case 1: % 74.87/11.16 | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | (169) all_10_9 = e0 % 74.87/11.16 | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | COMBINE_EQS: (149), (169) imply: % 74.87/11.16 | | | | | | | | | | | | | (170) e1 = e0 % 74.87/11.16 | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | REDUCE: (68), (170) imply: % 74.87/11.16 | | | | | | | | | | | | | (171) $false % 74.87/11.16 | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | CLOSE: (171) is inconsistent. % 74.87/11.16 | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | Case 2: % 74.87/11.16 | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | (172) all_10_10 = e0 | all_10_11 = e0 | all_10_15 = e0 | % 74.87/11.16 | | | | | | | | | | | | | all_10_23 = e0 % 74.87/11.16 | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | BETA: splitting (172) gives: % 74.87/11.16 | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | Case 1: % 74.87/11.16 | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | (173) all_10_10 = e0 % 74.87/11.16 | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | COMBINE_EQS: (59), (173) imply: % 74.87/11.16 | | | | | | | | | | | | | | (174) all_4_16 = e0 % 74.87/11.16 | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | SIMP: (174) implies: % 74.87/11.16 | | | | | | | | | | | | | | (175) all_4_16 = e0 % 74.87/11.16 | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | REDUCE: (69), (175) imply: % 74.87/11.16 | | | | | | | | | | | | | | (176) ~ (all_4_1 = e0) % 74.87/11.16 | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | REDUCE: (12), (175) imply: % 74.87/11.16 | | | | | | | | | | | | | | (177) ~ (all_4_19 = e0) % 74.87/11.16 | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | REDUCE: (24), (175) imply: % 74.87/11.16 | | | | | | | | | | | | | | (178) ~ (all_4_21 = e0) % 74.87/11.16 | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | SIMP: (178) implies: % 74.87/11.16 | | | | | | | | | | | | | | (179) ~ (all_4_21 = e0) % 74.87/11.16 | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | BETA: splitting (47) gives: % 74.87/11.16 | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | Case 1: % 74.87/11.16 | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | (180) all_10_9 = e3 % 74.87/11.16 | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | REF_CLOSE: (25), (149), (180) are inconsistent by sub-proof % 74.87/11.16 | | | | | | | | | | | | | | | #84. % 74.87/11.16 | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | Case 2: % 74.87/11.16 | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | (181) ~ (all_10_9 = e3) % 74.87/11.16 | | | | | | | | | | | | | | | (182) all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 74.87/11.16 | | | | | | | | | | | | | | | all_10_23 = e3 % 74.87/11.16 | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | REDUCE: (149), (181) imply: % 74.87/11.16 | | | | | | | | | | | | | | | (183) ~ (e3 = e1) % 74.87/11.16 | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | BETA: splitting (8) gives: % 74.87/11.16 | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | Case 1: % 74.87/11.16 | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | (184) all_6_1 = e4 % 74.87/11.16 | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | REF_CLOSE: (71), (160), (184) are inconsistent by sub-proof % 74.87/11.16 | | | | | | | | | | | | | | | | #138. % 74.87/11.16 | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | Case 2: % 74.87/11.16 | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | (185) all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 74.87/11.16 | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 74.87/11.16 | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | Case 1: % 74.87/11.16 | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | (186) all_10_9 = e3 % 74.87/11.16 | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (149), (186) are inconsistent by sub-proof % 74.87/11.16 | | | | | | | | | | | | | | | | | #84. % 74.87/11.16 | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | Case 2: % 74.87/11.16 | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | (187) all_10_16 = e3 % 74.87/11.16 | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (187) imply: % 74.87/11.16 | | | | | | | | | | | | | | | | | (188) all_4_20 = e3 % 74.87/11.16 | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | REDUCE: (19), (188) imply: % 74.87/11.16 | | | | | | | | | | | | | | | | | (189) ~ (all_4_21 = e3) % 74.87/11.16 | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | SIMP: (189) implies: % 74.87/11.16 | | | | | | | | | | | | | | | | | (190) ~ (all_4_21 = e3) % 74.87/11.16 | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | REDUCE: (162), (188) imply: % 74.87/11.16 | | | | | | | | | | | | | | | | | (191) ~ (e4 = e3) % 74.87/11.16 | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | REDUCE: (62), (188) imply: % 74.87/11.16 | | | | | | | | | | | | | | | | | (192) op(e4, e3) = all_8_53 % 74.87/11.16 | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | BETA: splitting (57) gives: % 74.87/11.16 | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | Case 1: % 74.87/11.16 | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | (193) all_10_2 = e3 % 74.87/11.16 | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (193) imply: % 74.87/11.16 | | | | | | | | | | | | | | | | | | (194) all_4_1 = e3 % 74.87/11.16 | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | SIMP: (194) implies: % 74.87/11.16 | | | | | | | | | | | | | | | | | | (195) all_4_1 = e3 % 74.87/11.16 | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | REDUCE: (176), (195) imply: % 74.87/11.16 | | | | | | | | | | | | | | | | | | (196) ~ (e3 = e0) % 74.87/11.16 | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | REDUCE: (93), (195) imply: % 74.87/11.16 | | | | | | | | | | | | | | | | | | (197) op(e4, e3) = e3 % 74.87/11.16 | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives: % 74.87/11.16 | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | Case 1: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | (198) all_10_10 = e3 % 74.87/11.16 | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (196), (198) are inconsistent by sub-proof % 74.87/11.16 | | | | | | | | | | | | | | | | | | | #83. % 74.87/11.16 | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | Case 2: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | (199) all_10_11 = e3 | all_10_15 = e3 | all_10_23 = e3 % 74.87/11.16 | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | Case 1: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | (200) all_10_11 = e3 % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (200) imply: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | (201) e3 = e2 % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (201) imply: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | (202) $false % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | CLOSE: (202) is inconsistent. % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | Case 2: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | (203) all_10_15 = e3 | all_10_23 = e3 % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | Case 1: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | (204) all_6_1 = e1 % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (71), (204) are inconsistent by sub-proof % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | #137. % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | Case 2: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | (205) all_6_1 = e3 | all_6_1 = e0 % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | Case 1: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | (206) all_10_1 = e0 % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (206) imply: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | (207) all_4_5 = e0 % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (207) imply: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | (208) op(e4, e3) = e0 % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | (209) all_10_15 = e3 % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (209) imply: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | (210) e4 = e3 % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (210) imply: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | (211) $false % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (211) is inconsistent. % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | (212) all_10_23 = e3 % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (212) imply: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | (213) all_4_19 = e3 % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (213) implies: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | (214) all_4_19 = e3 % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (76) with e3, all_8_53, e3, e4, % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (192), (197) gives: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | (215) all_8_53 = e3 % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (76) with e0, all_8_53, e3, e4, % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (192), (208) gives: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | (216) all_8_53 = e0 % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (215), (216) imply: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | (217) e3 = e0 % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (163), (196), (203), (212), (217) are % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #82. % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | End of split % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | Case 2: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | (218) ~ (all_10_1 = e0) % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (218) imply: % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | (219) ~ (all_4_5 = e0) % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (71), (205), (219) are inconsistent by % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | sub-proof #136. % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | End of split % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | End of split % 74.87/11.16 | | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | | End of split % 74.87/11.16 | | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | End of split % 74.87/11.16 | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | Case 2: % 74.87/11.16 | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | (220) ~ (all_10_2 = e3) % 74.87/11.16 | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (40), (45), (50), (53), (58), (61), (96), % 74.87/11.16 | | | | | | | | | | | | | | | | | | (176), (179), (190), (220) are inconsistent by % 74.87/11.16 | | | | | | | | | | | | | | | | | | sub-proof #80. % 74.87/11.16 | | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | | End of split % 74.87/11.16 | | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | | End of split % 74.87/11.16 | | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | | End of split % 74.87/11.16 | | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | End of split % 74.87/11.16 | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | Case 2: % 74.87/11.16 | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | (221) all_10_11 = e0 | all_10_15 = e0 | all_10_23 = e0 % 74.87/11.16 | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | | REF_CLOSE: (7), (17), (20), (33), (54), (164), (221) are % 74.87/11.16 | | | | | | | | | | | | | | inconsistent by sub-proof #79. % 74.87/11.16 | | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | | End of split % 74.87/11.16 | | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | | End of split % 74.87/11.16 | | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | End of split % 74.87/11.16 | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | Case 2: % 74.87/11.16 | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | (222) ~ (all_10_4 = e4) % 74.87/11.16 | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | REDUCE: (15), (222) imply: % 74.87/11.16 | | | | | | | | | | | (223) ~ (all_4_10 = e4) % 74.87/11.16 | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | | REF_CLOSE: (9), (34), (77), (84), (138), (223) are % 74.87/11.16 | | | | | | | | | | | inconsistent by sub-proof #161. % 74.87/11.16 | | | | | | | | | | | % 74.87/11.16 | | | | | | | | | | End of split % 74.87/11.16 | | | | | | | | | | % 74.87/11.16 | | | | | | | | | End of split % 74.87/11.16 | | | | | | | | | % 74.87/11.16 | | | | | | | | End of split % 74.87/11.16 | | | | | | | | % 74.87/11.16 | | | | | | | Case 2: % 74.87/11.16 | | | | | | | | % 74.87/11.16 | | | | | | | | (224) ~ (all_10_9 = e1) % 74.87/11.16 | | | | | | | | % 74.87/11.16 | | | | | | | | REF_CLOSE: (5), (28), (65), (148), (224) are inconsistent by % 74.87/11.16 | | | | | | | | sub-proof #78. % 74.87/11.16 | | | | | | | | % 74.87/11.16 | | | | | | | End of split % 74.87/11.16 | | | | | | | % 74.87/11.16 | | | | | | End of split % 74.87/11.16 | | | | | | % 74.87/11.16 | | | | | End of split % 74.87/11.16 | | | | | % 74.87/11.16 | | | | End of split % 74.87/11.16 | | | | % 74.87/11.16 | | | End of split % 74.87/11.16 | | | % 74.87/11.16 | | End of split % 74.87/11.16 | | % 74.87/11.16 | End of split % 74.87/11.16 | % 74.87/11.16 End of proof % 74.87/11.16 % 74.87/11.16 Sub-proof #78 shows that the following formulas are inconsistent: % 74.87/11.16 ---------------------------------------------------------------- % 74.87/11.16 (1) ~ (all_4_20 = e1) % 74.87/11.16 (2) ~ (all_10_9 = e1) % 74.87/11.16 (3) all_10_16 = all_4_20 % 74.87/11.16 (4) all_10_9 = all_4_15 % 74.87/11.16 (5) all_10_9 = e1 | all_10_16 = e1 % 74.87/11.16 % 74.87/11.16 Begin of proof % 74.87/11.16 | % 74.87/11.16 | REDUCE: (2), (4) imply: % 74.87/11.16 | (6) ~ (all_4_15 = e1) % 74.87/11.16 | % 74.87/11.16 | BETA: splitting (5) gives: % 74.87/11.16 | % 74.87/11.16 | Case 1: % 74.87/11.16 | | % 74.87/11.16 | | (7) all_10_9 = e1 % 74.87/11.16 | | % 74.87/11.16 | | COMBINE_EQS: (4), (7) imply: % 74.87/11.16 | | (8) all_4_15 = e1 % 74.87/11.16 | | % 74.87/11.16 | | REDUCE: (6), (8) imply: % 74.87/11.16 | | (9) $false % 74.87/11.16 | | % 74.87/11.16 | | CLOSE: (9) is inconsistent. % 74.87/11.16 | | % 74.87/11.16 | Case 2: % 74.87/11.16 | | % 74.87/11.16 | | (10) all_10_16 = e1 % 74.87/11.16 | | % 74.87/11.16 | | COMBINE_EQS: (3), (10) imply: % 74.87/11.16 | | (11) all_4_20 = e1 % 74.87/11.16 | | % 74.87/11.16 | | REDUCE: (1), (11) imply: % 74.87/11.16 | | (12) $false % 74.87/11.16 | | % 74.87/11.16 | | CLOSE: (12) is inconsistent. % 74.87/11.16 | | % 74.87/11.16 | End of split % 74.87/11.16 | % 74.87/11.16 End of proof % 74.87/11.16 % 74.87/11.16 Sub-proof #79 shows that the following formulas are inconsistent: % 74.87/11.16 ---------------------------------------------------------------- % 74.87/11.16 (1) ~ (all_4_19 = e0) % 74.87/11.16 (2) all_10_15 = e4 % 74.87/11.16 (3) ~ (e2 = e0) % 74.87/11.16 (4) all_10_11 = e0 | all_10_15 = e0 | all_10_23 = e0 % 74.87/11.16 (5) ~ (e4 = e0) % 74.87/11.16 (6) all_10_23 = all_4_19 % 74.87/11.16 (7) all_10_11 = e2 % 74.87/11.16 % 74.87/11.16 Begin of proof % 74.87/11.16 | % 74.87/11.16 | BETA: splitting (4) gives: % 74.87/11.16 | % 74.87/11.16 | Case 1: % 74.87/11.16 | | % 74.87/11.16 | | (8) all_10_11 = e0 % 74.87/11.16 | | % 74.87/11.16 | | COMBINE_EQS: (7), (8) imply: % 74.87/11.16 | | (9) e2 = e0 % 74.87/11.16 | | % 74.87/11.16 | | SIMP: (9) implies: % 74.87/11.16 | | (10) e2 = e0 % 74.87/11.16 | | % 74.87/11.16 | | REDUCE: (3), (10) imply: % 74.87/11.16 | | (11) $false % 74.87/11.16 | | % 74.87/11.16 | | CLOSE: (11) is inconsistent. % 74.87/11.16 | | % 74.87/11.16 | Case 2: % 74.87/11.16 | | % 74.87/11.16 | | (12) all_10_15 = e0 | all_10_23 = e0 % 74.87/11.16 | | % 74.87/11.16 | | BETA: splitting (12) gives: % 74.87/11.16 | | % 74.87/11.16 | | Case 1: % 74.87/11.16 | | | % 74.87/11.16 | | | (13) all_10_15 = e0 % 74.87/11.16 | | | % 74.87/11.16 | | | COMBINE_EQS: (2), (13) imply: % 74.87/11.16 | | | (14) e4 = e0 % 74.87/11.16 | | | % 74.87/11.16 | | | REDUCE: (5), (14) imply: % 74.87/11.16 | | | (15) $false % 74.87/11.16 | | | % 74.87/11.16 | | | CLOSE: (15) is inconsistent. % 74.87/11.16 | | | % 74.87/11.16 | | Case 2: % 74.87/11.16 | | | % 74.87/11.16 | | | (16) all_10_23 = e0 % 74.87/11.16 | | | % 74.87/11.16 | | | COMBINE_EQS: (6), (16) imply: % 74.87/11.16 | | | (17) all_4_19 = e0 % 74.87/11.16 | | | % 74.87/11.16 | | | SIMP: (17) implies: % 74.87/11.16 | | | (18) all_4_19 = e0 % 74.87/11.16 | | | % 74.87/11.16 | | | REDUCE: (1), (18) imply: % 74.87/11.16 | | | (19) $false % 74.87/11.16 | | | % 74.87/11.16 | | | CLOSE: (19) is inconsistent. % 74.87/11.16 | | | % 74.87/11.16 | | End of split % 74.87/11.16 | | % 74.87/11.16 | End of split % 74.87/11.16 | % 74.87/11.16 End of proof % 74.87/11.16 % 74.87/11.16 Sub-proof #80 shows that the following formulas are inconsistent: % 74.87/11.16 ---------------------------------------------------------------- % 74.87/11.16 (1) ~ (all_4_1 = e0) % 74.87/11.16 (2) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | all_6_5 = e0 % 74.87/11.16 (3) all_6_9 = all_4_21 % 74.87/11.16 (4) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e1 | all_6_9 = e0 % 74.87/11.16 (5) all_6_5 = all_4_1 % 74.87/11.16 (6) ~ (all_4_1 = e1) % 74.87/11.16 (7) ~ (all_4_1 = all_4_21) % 74.87/11.16 (8) all_10_2 = all_4_1 % 74.87/11.16 (9) ~ (all_4_21 = e1) % 74.87/11.16 (10) ~ (all_4_21 = e3) % 74.87/11.16 (11) ~ (all_4_21 = e0) % 74.87/11.16 (12) ~ (all_10_2 = e3) % 74.87/11.16 % 74.87/11.16 Begin of proof % 74.87/11.16 | % 74.87/11.16 | REDUCE: (8), (12) imply: % 74.87/11.16 | (13) ~ (all_4_1 = e3) % 74.87/11.16 | % 74.87/11.16 | BETA: splitting (4) gives: % 74.87/11.16 | % 74.87/11.16 | Case 1: % 74.87/11.16 | | % 74.87/11.16 | | (14) all_6_9 = e4 % 74.87/11.16 | | % 74.87/11.16 | | COMBINE_EQS: (3), (14) imply: % 74.87/11.16 | | (15) all_4_21 = e4 % 74.87/11.16 | | % 74.87/11.16 | | SIMP: (15) implies: % 74.87/11.16 | | (16) all_4_21 = e4 % 74.87/11.16 | | % 74.87/11.16 | | REDUCE: (7), (16) imply: % 74.87/11.16 | | (17) ~ (all_4_1 = e4) % 74.87/11.16 | | % 74.87/11.16 | | BETA: splitting (2) gives: % 74.87/11.16 | | % 74.87/11.16 | | Case 1: % 74.87/11.16 | | | % 74.87/11.16 | | | (18) all_6_5 = e4 % 74.87/11.16 | | | % 74.87/11.16 | | | REF_CLOSE: (5), (17), (18) are inconsistent by sub-proof #81. % 74.87/11.16 | | | % 74.87/11.16 | | Case 2: % 74.87/11.16 | | | % 74.87/11.16 | | | (19) all_6_5 = e3 | all_6_5 = e1 | all_6_5 = e0 % 74.87/11.16 | | | % 74.87/11.16 | | | REF_CLOSE: (1), (5), (6), (13), (19) are inconsistent by sub-proof #140. % 74.87/11.16 | | | % 74.87/11.16 | | End of split % 74.87/11.16 | | % 74.87/11.16 | Case 2: % 74.87/11.16 | | % 74.87/11.16 | | (20) all_6_9 = e3 | all_6_9 = e1 | all_6_9 = e0 % 74.87/11.16 | | % 74.87/11.16 | | REF_CLOSE: (3), (9), (10), (11), (20) are inconsistent by sub-proof #111. % 74.87/11.16 | | % 74.87/11.16 | End of split % 74.87/11.16 | % 74.87/11.16 End of proof % 74.87/11.16 % 74.87/11.16 Sub-proof #81 shows that the following formulas are inconsistent: % 74.87/11.16 ---------------------------------------------------------------- % 74.87/11.16 (1) all_6_5 = all_4_1 % 74.87/11.16 (2) all_6_5 = e4 % 74.87/11.16 (3) ~ (all_4_1 = e4) % 74.87/11.16 % 74.87/11.16 Begin of proof % 74.87/11.16 | % 74.87/11.16 | COMBINE_EQS: (1), (2) imply: % 74.87/11.16 | (4) all_4_1 = e4 % 74.87/11.16 | % 74.87/11.16 | SIMP: (4) implies: % 74.87/11.16 | (5) all_4_1 = e4 % 74.87/11.16 | % 74.87/11.16 | REDUCE: (3), (5) imply: % 74.87/11.16 | (6) $false % 74.87/11.16 | % 74.87/11.16 | CLOSE: (6) is inconsistent. % 74.87/11.16 | % 74.87/11.16 End of proof % 74.87/11.16 % 74.87/11.16 Sub-proof #82 shows that the following formulas are inconsistent: % 74.87/11.16 ---------------------------------------------------------------- % 74.87/11.16 (1) all_10_23 = e3 % 74.87/11.16 (2) all_10_15 = e4 % 74.87/11.16 (3) all_10_15 = e3 | all_10_23 = e3 % 74.87/11.16 (4) ~ (e4 = e3) % 74.87/11.16 (5) ~ (e3 = e0) % 74.87/11.16 (6) e3 = e0 % 74.87/11.16 % 74.87/11.16 Begin of proof % 74.87/11.16 | % 74.87/11.16 | COMBINE_EQS: (1), (6) imply: % 74.87/11.17 | (7) all_10_23 = e0 % 74.87/11.17 | % 74.87/11.17 | BETA: splitting (3) gives: % 74.87/11.17 | % 74.87/11.17 | Case 1: % 74.87/11.17 | | % 74.87/11.17 | | (8) all_10_15 = e3 % 74.87/11.17 | | % 74.87/11.17 | | COMBINE_EQS: (2), (8) imply: % 74.87/11.17 | | (9) e4 = e3 % 74.87/11.17 | | % 74.87/11.17 | | REDUCE: (4), (9) imply: % 74.87/11.17 | | (10) $false % 74.87/11.17 | | % 74.87/11.17 | | CLOSE: (10) is inconsistent. % 74.87/11.17 | | % 74.87/11.17 | Case 2: % 74.87/11.17 | | % 74.87/11.17 | | % 74.87/11.17 | | COMBINE_EQS: (1), (7) imply: % 74.87/11.17 | | (11) e3 = e0 % 74.87/11.17 | | % 74.87/11.17 | | REDUCE: (5), (6) imply: % 74.87/11.17 | | (12) $false % 74.87/11.17 | | % 74.87/11.17 | | CLOSE: (12) is inconsistent. % 74.87/11.17 | | % 74.87/11.17 | End of split % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #83 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) all_10_10 = e3 % 74.87/11.17 (2) all_10_10 = e0 % 74.87/11.17 (3) ~ (e3 = e0) % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | COMBINE_EQS: (1), (2) imply: % 74.87/11.17 | (4) e3 = e0 % 74.87/11.17 | % 74.87/11.17 | SIMP: (4) implies: % 74.87/11.17 | (5) e3 = e0 % 74.87/11.17 | % 74.87/11.17 | REDUCE: (3), (5) imply: % 74.87/11.17 | (6) $false % 74.87/11.17 | % 74.87/11.17 | CLOSE: (6) is inconsistent. % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #84 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) all_10_9 = e3 % 74.87/11.17 (2) all_10_9 = e1 % 74.87/11.17 (3) ~ (e3 = e1) % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | COMBINE_EQS: (1), (2) imply: % 74.87/11.17 | (4) e3 = e1 % 74.87/11.17 | % 74.87/11.17 | SIMP: (4) implies: % 74.87/11.17 | (5) e3 = e1 % 74.87/11.17 | % 74.87/11.17 | REDUCE: (3), (5) imply: % 74.87/11.17 | (6) $false % 74.87/11.17 | % 74.87/11.17 | CLOSE: (6) is inconsistent. % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #85 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) all_10_4 = all_4_10 % 74.87/11.17 (2) all_10_4 = e1 % 74.87/11.17 (3) ~ (all_4_10 = e1) % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | COMBINE_EQS: (1), (2) imply: % 74.87/11.17 | (4) all_4_10 = e1 % 74.87/11.17 | % 74.87/11.17 | SIMP: (4) implies: % 74.87/11.17 | (5) all_4_10 = e1 % 74.87/11.17 | % 74.87/11.17 | REDUCE: (3), (5) imply: % 74.87/11.17 | (6) $false % 74.87/11.17 | % 74.87/11.17 | CLOSE: (6) is inconsistent. % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #86 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) all_10_6 = all_4_2 % 74.87/11.17 (2) all_10_6 = e1 % 74.87/11.17 (3) ~ (all_4_2 = e1) % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | COMBINE_EQS: (1), (2) imply: % 74.87/11.17 | (4) all_4_2 = e1 % 74.87/11.17 | % 74.87/11.17 | SIMP: (4) implies: % 74.87/11.17 | (5) all_4_2 = e1 % 74.87/11.17 | % 74.87/11.17 | REDUCE: (3), (5) imply: % 74.87/11.17 | (6) $false % 74.87/11.17 | % 74.87/11.17 | CLOSE: (6) is inconsistent. % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #87 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) ~ (all_4_19 = e2) % 74.87/11.17 (2) all_10_15 = e4 % 74.87/11.17 (3) all_10_23 = all_4_19 % 74.87/11.17 (4) all_10_15 = e2 | all_10_23 = e2 % 74.87/11.17 (5) ~ (e4 = e2) % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | BETA: splitting (4) gives: % 74.87/11.17 | % 74.87/11.17 | Case 1: % 74.87/11.17 | | % 74.87/11.17 | | (6) all_10_15 = e2 % 74.87/11.17 | | % 74.87/11.17 | | COMBINE_EQS: (2), (6) imply: % 74.87/11.17 | | (7) e4 = e2 % 74.87/11.17 | | % 74.87/11.17 | | REDUCE: (5), (7) imply: % 74.87/11.17 | | (8) $false % 74.87/11.17 | | % 74.87/11.17 | | CLOSE: (8) is inconsistent. % 74.87/11.17 | | % 74.87/11.17 | Case 2: % 74.87/11.17 | | % 74.87/11.17 | | (9) all_10_23 = e2 % 74.87/11.17 | | % 74.87/11.17 | | COMBINE_EQS: (3), (9) imply: % 74.87/11.17 | | (10) all_4_19 = e2 % 74.87/11.17 | | % 74.87/11.17 | | SIMP: (10) implies: % 74.87/11.17 | | (11) all_4_19 = e2 % 74.87/11.17 | | % 74.87/11.17 | | REDUCE: (1), (11) imply: % 74.87/11.17 | | (12) $false % 74.87/11.17 | | % 74.87/11.17 | | CLOSE: (12) is inconsistent. % 74.87/11.17 | | % 74.87/11.17 | End of split % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #88 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) all_10_13 = all_4_8 % 74.87/11.17 (2) all_10_13 = e2 % 74.87/11.17 (3) ~ (all_4_8 = e2) % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | COMBINE_EQS: (1), (2) imply: % 74.87/11.17 | (4) all_4_8 = e2 % 74.87/11.17 | % 74.87/11.17 | SIMP: (4) implies: % 74.87/11.17 | (5) all_4_8 = e2 % 74.87/11.17 | % 74.87/11.17 | REDUCE: (3), (5) imply: % 74.87/11.17 | (6) $false % 74.87/11.17 | % 74.87/11.17 | CLOSE: (6) is inconsistent. % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #89 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) all_10_12 = all_4_3 % 74.87/11.17 (2) all_10_12 = e2 % 74.87/11.17 (3) ~ (all_4_3 = e2) % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | COMBINE_EQS: (1), (2) imply: % 74.87/11.17 | (4) all_4_3 = e2 % 74.87/11.17 | % 74.87/11.17 | SIMP: (4) implies: % 74.87/11.17 | (5) all_4_3 = e2 % 74.87/11.17 | % 74.87/11.17 | REDUCE: (3), (5) imply: % 74.87/11.17 | (6) $false % 74.87/11.17 | % 74.87/11.17 | CLOSE: (6) is inconsistent. % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #90 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) ~ (all_4_11 = e0) % 74.87/11.17 (2) ~ (all_4_11 = e3) % 74.87/11.17 (3) ~ (all_4_11 = e1) % 74.87/11.17 (4) ~ (all_4_11 = e4) % 74.87/11.17 (5) all_6_7 = all_4_11 % 74.87/11.17 (6) all_6_7 = e4 | all_6_7 = e3 | all_6_7 = e1 | all_6_7 = e0 % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | BETA: splitting (6) gives: % 74.87/11.17 | % 74.87/11.17 | Case 1: % 74.87/11.17 | | % 74.87/11.17 | | (7) all_6_7 = e4 % 74.87/11.17 | | % 74.87/11.17 | | COMBINE_EQS: (5), (7) imply: % 74.87/11.17 | | (8) all_4_11 = e4 % 74.87/11.17 | | % 74.87/11.17 | | REDUCE: (4), (8) imply: % 74.87/11.17 | | (9) $false % 74.87/11.17 | | % 74.87/11.17 | | CLOSE: (9) is inconsistent. % 74.87/11.17 | | % 74.87/11.17 | Case 2: % 74.87/11.17 | | % 74.87/11.17 | | (10) all_6_7 = e3 | all_6_7 = e1 | all_6_7 = e0 % 74.87/11.17 | | % 74.87/11.17 | | REF_CLOSE: (1), (2), (3), (5), (10) are inconsistent by sub-proof #91. % 74.87/11.17 | | % 74.87/11.17 | End of split % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #91 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) ~ (all_4_11 = e0) % 74.87/11.17 (2) ~ (all_4_11 = e3) % 74.87/11.17 (3) all_6_7 = e3 | all_6_7 = e1 | all_6_7 = e0 % 74.87/11.17 (4) ~ (all_4_11 = e1) % 74.87/11.17 (5) all_6_7 = all_4_11 % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | BETA: splitting (3) gives: % 74.87/11.17 | % 74.87/11.17 | Case 1: % 74.87/11.17 | | % 74.87/11.17 | | (6) all_6_7 = e1 % 74.87/11.17 | | % 74.87/11.17 | | COMBINE_EQS: (5), (6) imply: % 74.87/11.17 | | (7) all_4_11 = e1 % 74.87/11.17 | | % 74.87/11.17 | | REDUCE: (4), (7) imply: % 74.87/11.17 | | (8) $false % 74.87/11.17 | | % 74.87/11.17 | | CLOSE: (8) is inconsistent. % 74.87/11.17 | | % 74.87/11.17 | Case 2: % 74.87/11.17 | | % 74.87/11.17 | | (9) all_6_7 = e3 | all_6_7 = e0 % 74.87/11.17 | | % 74.87/11.17 | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #92. % 74.87/11.17 | | % 74.87/11.17 | End of split % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #92 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) all_6_7 = e3 | all_6_7 = e0 % 74.87/11.17 (2) all_6_7 = all_4_11 % 74.87/11.17 (3) ~ (all_4_11 = e3) % 74.87/11.17 (4) ~ (all_4_11 = e0) % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | BETA: splitting (1) gives: % 74.87/11.17 | % 74.87/11.17 | Case 1: % 74.87/11.17 | | % 74.87/11.17 | | (5) all_6_7 = e3 % 74.87/11.17 | | % 74.87/11.17 | | COMBINE_EQS: (2), (5) imply: % 74.87/11.17 | | (6) all_4_11 = e3 % 74.87/11.17 | | % 74.87/11.17 | | REDUCE: (3), (6) imply: % 74.87/11.17 | | (7) $false % 74.87/11.17 | | % 74.87/11.17 | | CLOSE: (7) is inconsistent. % 74.87/11.17 | | % 74.87/11.17 | Case 2: % 74.87/11.17 | | % 74.87/11.17 | | (8) all_6_7 = e0 % 74.87/11.17 | | % 74.87/11.17 | | COMBINE_EQS: (2), (8) imply: % 74.87/11.17 | | (9) all_4_11 = e0 % 74.87/11.17 | | % 74.87/11.17 | | REDUCE: (4), (9) imply: % 74.87/11.17 | | (10) $false % 74.87/11.17 | | % 74.87/11.17 | | CLOSE: (10) is inconsistent. % 74.87/11.17 | | % 74.87/11.17 | End of split % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #93 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) all_8_36 = e0 & ~ (all_8_37 = e2) % 74.87/11.17 (2) all_8_36 = e3 % 74.87/11.17 (3) ~ (e3 = e0) % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | ALPHA: (1) implies: % 74.87/11.17 | (4) all_8_36 = e0 % 74.87/11.17 | % 74.87/11.17 | COMBINE_EQS: (2), (4) imply: % 74.87/11.17 | (5) e3 = e0 % 74.87/11.17 | % 74.87/11.17 | SIMP: (5) implies: % 74.87/11.17 | (6) e3 = e0 % 74.87/11.17 | % 74.87/11.17 | REDUCE: (3), (6) imply: % 74.87/11.17 | (7) $false % 74.87/11.17 | % 74.87/11.17 | CLOSE: (7) is inconsistent. % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #94 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) all_6_19 = all_4_23 % 74.87/11.17 (2) all_6_19 = e3 | all_6_19 = e0 % 74.87/11.17 (3) ~ (all_4_3 = all_4_23) % 74.87/11.17 (4) ~ (all_4_3 = e0) % 74.87/11.17 (5) all_6_15 = all_4_3 % 74.87/11.17 (6) all_6_15 = e3 | all_6_15 = e0 % 74.87/11.17 (7) ~ (all_4_23 = e0) % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | BETA: splitting (6) gives: % 74.87/11.17 | % 74.87/11.17 | Case 1: % 74.87/11.17 | | % 74.87/11.17 | | (8) all_6_15 = e3 % 74.87/11.17 | | % 74.87/11.17 | | COMBINE_EQS: (5), (8) imply: % 74.87/11.17 | | (9) all_4_3 = e3 % 74.87/11.17 | | % 74.87/11.17 | | SIMP: (9) implies: % 74.87/11.17 | | (10) all_4_3 = e3 % 74.87/11.17 | | % 74.87/11.17 | | REDUCE: (3), (10) imply: % 74.87/11.17 | | (11) ~ (all_4_23 = e3) % 74.87/11.17 | | % 74.87/11.17 | | SIMP: (11) implies: % 74.87/11.17 | | (12) ~ (all_4_23 = e3) % 74.87/11.17 | | % 74.87/11.17 | | BETA: splitting (2) gives: % 74.87/11.17 | | % 74.87/11.17 | | Case 1: % 74.87/11.17 | | | % 74.87/11.17 | | | (13) all_6_19 = e3 % 74.87/11.17 | | | % 74.87/11.17 | | | COMBINE_EQS: (1), (13) imply: % 74.87/11.17 | | | (14) all_4_23 = e3 % 74.87/11.17 | | | % 74.87/11.17 | | | REDUCE: (12), (14) imply: % 74.87/11.17 | | | (15) $false % 74.87/11.17 | | | % 74.87/11.17 | | | CLOSE: (15) is inconsistent. % 74.87/11.17 | | | % 74.87/11.17 | | Case 2: % 74.87/11.17 | | | % 74.87/11.17 | | | (16) all_6_19 = e0 % 74.87/11.17 | | | % 74.87/11.17 | | | COMBINE_EQS: (1), (16) imply: % 74.87/11.17 | | | (17) all_4_23 = e0 % 74.87/11.17 | | | % 74.87/11.17 | | | REDUCE: (7), (17) imply: % 74.87/11.17 | | | (18) $false % 74.87/11.17 | | | % 74.87/11.17 | | | CLOSE: (18) is inconsistent. % 74.87/11.17 | | | % 74.87/11.17 | | End of split % 74.87/11.17 | | % 74.87/11.17 | Case 2: % 74.87/11.17 | | % 74.87/11.17 | | (19) all_6_15 = e0 % 74.87/11.17 | | % 74.87/11.17 | | REF_CLOSE: (4), (5), (19) are inconsistent by sub-proof #124. % 74.87/11.17 | | % 74.87/11.17 | End of split % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #95 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) ~ (all_4_20 = e1) % 74.87/11.17 (2) ~ (all_4_20 = e3) % 74.87/11.17 (3) all_6_4 = e3 | all_6_4 = e1 | all_6_4 = e0 % 74.87/11.17 (4) all_6_4 = all_4_20 % 74.87/11.17 (5) ~ (all_4_20 = e0) % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | BETA: splitting (3) gives: % 74.87/11.17 | % 74.87/11.17 | Case 1: % 74.87/11.17 | | % 74.87/11.17 | | (6) all_6_4 = e1 % 74.87/11.17 | | % 74.87/11.17 | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #148. % 74.87/11.17 | | % 74.87/11.17 | Case 2: % 74.87/11.17 | | % 74.87/11.17 | | (7) all_6_4 = e3 | all_6_4 = e0 % 74.87/11.17 | | % 74.87/11.17 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #147. % 74.87/11.17 | | % 74.87/11.17 | End of split % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #96 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) all_8_61 = e1 & ~ (all_8_62 = e0) % 74.87/11.17 (2) all_8_61 = all_4_9 % 74.87/11.17 (3) ~ (all_4_9 = e1) % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | ALPHA: (1) implies: % 74.87/11.17 | (4) all_8_61 = e1 % 74.87/11.17 | % 74.87/11.17 | COMBINE_EQS: (2), (4) imply: % 74.87/11.17 | (5) all_4_9 = e1 % 74.87/11.17 | % 74.87/11.17 | SIMP: (5) implies: % 74.87/11.17 | (6) all_4_9 = e1 % 74.87/11.17 | % 74.87/11.17 | REDUCE: (3), (6) imply: % 74.87/11.17 | (7) $false % 74.87/11.17 | % 74.87/11.17 | CLOSE: (7) is inconsistent. % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #97 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) all_8_55 = e3 & ~ (all_8_56 = e0) % 74.87/11.17 (2) all_8_55 = e2 % 74.87/11.17 (3) ~ (e3 = e2) % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | ALPHA: (1) implies: % 74.87/11.17 | (4) all_8_55 = e3 % 74.87/11.17 | % 74.87/11.17 | COMBINE_EQS: (2), (4) imply: % 74.87/11.17 | (5) e3 = e2 % 74.87/11.17 | % 74.87/11.17 | REDUCE: (3), (5) imply: % 74.87/11.17 | (6) $false % 74.87/11.17 | % 74.87/11.17 | CLOSE: (6) is inconsistent. % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #98 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) all_10_6 = e3 | all_10_12 = e3 | all_10_20 = e3 % 74.87/11.17 (2) all_10_20 = e4 % 74.87/11.17 (3) ~ (all_4_2 = e3) % 74.87/11.17 (4) ~ (e3 = e1) % 74.87/11.17 (5) ~ (e4 = e3) % 74.87/11.17 (6) all_10_12 = e1 % 74.87/11.17 (7) all_10_6 = all_4_2 % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | BETA: splitting (1) gives: % 74.87/11.17 | % 74.87/11.17 | Case 1: % 74.87/11.17 | | % 74.87/11.17 | | (8) all_10_6 = e3 % 74.87/11.17 | | % 74.87/11.17 | | REF_CLOSE: (3), (7), (8) are inconsistent by sub-proof #100. % 74.87/11.17 | | % 74.87/11.17 | Case 2: % 74.87/11.17 | | % 74.87/11.17 | | (9) all_10_12 = e3 | all_10_20 = e3 % 74.87/11.17 | | % 74.87/11.17 | | REF_CLOSE: (2), (4), (5), (6), (9) are inconsistent by sub-proof #99. % 74.87/11.17 | | % 74.87/11.17 | End of split % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #99 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) all_10_20 = e4 % 74.87/11.17 (2) ~ (e3 = e1) % 74.87/11.17 (3) ~ (e4 = e3) % 74.87/11.17 (4) all_10_12 = e1 % 74.87/11.17 (5) all_10_12 = e3 | all_10_20 = e3 % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | BETA: splitting (5) gives: % 74.87/11.17 | % 74.87/11.17 | Case 1: % 74.87/11.17 | | % 74.87/11.17 | | (6) all_10_12 = e3 % 74.87/11.17 | | % 74.87/11.17 | | COMBINE_EQS: (4), (6) imply: % 74.87/11.17 | | (7) e3 = e1 % 74.87/11.17 | | % 74.87/11.17 | | REDUCE: (2), (7) imply: % 74.87/11.17 | | (8) $false % 74.87/11.17 | | % 74.87/11.17 | | CLOSE: (8) is inconsistent. % 74.87/11.17 | | % 74.87/11.17 | Case 2: % 74.87/11.17 | | % 74.87/11.17 | | (9) all_10_20 = e3 % 74.87/11.17 | | % 74.87/11.17 | | COMBINE_EQS: (1), (9) imply: % 74.87/11.17 | | (10) e4 = e3 % 74.87/11.17 | | % 74.87/11.17 | | SIMP: (10) implies: % 74.87/11.17 | | (11) e4 = e3 % 74.87/11.17 | | % 74.87/11.17 | | REDUCE: (3), (11) imply: % 74.87/11.17 | | (12) $false % 74.87/11.17 | | % 74.87/11.17 | | CLOSE: (12) is inconsistent. % 74.87/11.17 | | % 74.87/11.17 | End of split % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #100 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) all_10_6 = all_4_2 % 74.87/11.17 (2) all_10_6 = e3 % 74.87/11.17 (3) ~ (all_4_2 = e3) % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | COMBINE_EQS: (1), (2) imply: % 74.87/11.17 | (4) all_4_2 = e3 % 74.87/11.17 | % 74.87/11.17 | SIMP: (4) implies: % 74.87/11.17 | (5) all_4_2 = e3 % 74.87/11.17 | % 74.87/11.17 | REDUCE: (3), (5) imply: % 74.87/11.17 | (6) $false % 74.87/11.17 | % 74.87/11.17 | CLOSE: (6) is inconsistent. % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #101 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) all_8_7 = e1 & ~ (all_8_8 = e4) % 74.87/11.17 (2) all_8_7 = e3 % 74.87/11.17 (3) ~ (e3 = e1) % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | ALPHA: (1) implies: % 74.87/11.17 | (4) all_8_7 = e1 % 74.87/11.17 | % 74.87/11.17 | COMBINE_EQS: (2), (4) imply: % 74.87/11.17 | (5) e3 = e1 % 74.87/11.17 | % 74.87/11.17 | SIMP: (5) implies: % 74.87/11.17 | (6) e3 = e1 % 74.87/11.17 | % 74.87/11.17 | REDUCE: (3), (6) imply: % 74.87/11.17 | (7) $false % 74.87/11.17 | % 74.87/11.17 | CLOSE: (7) is inconsistent. % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #102 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) all_6_10 = all_4_2 % 74.87/11.17 (2) all_6_10 = e3 % 74.87/11.17 (3) ~ (all_4_2 = e3) % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | COMBINE_EQS: (1), (2) imply: % 74.87/11.17 | (4) all_4_2 = e3 % 74.87/11.17 | % 74.87/11.17 | SIMP: (4) implies: % 74.87/11.17 | (5) all_4_2 = e3 % 74.87/11.17 | % 74.87/11.17 | REDUCE: (3), (5) imply: % 74.87/11.17 | (6) $false % 74.87/11.17 | % 74.87/11.17 | CLOSE: (6) is inconsistent. % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #103 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.17 (1) all_6_10 = all_4_2 % 74.87/11.17 (2) all_6_10 = e1 % 74.87/11.17 (3) ~ (all_4_2 = e1) % 74.87/11.17 % 74.87/11.17 Begin of proof % 74.87/11.17 | % 74.87/11.17 | COMBINE_EQS: (1), (2) imply: % 74.87/11.17 | (4) all_4_2 = e1 % 74.87/11.17 | % 74.87/11.17 | SIMP: (4) implies: % 74.87/11.17 | (5) all_4_2 = e1 % 74.87/11.17 | % 74.87/11.17 | REDUCE: (3), (5) imply: % 74.87/11.17 | (6) $false % 74.87/11.17 | % 74.87/11.17 | CLOSE: (6) is inconsistent. % 74.87/11.17 | % 74.87/11.17 End of proof % 74.87/11.17 % 74.87/11.17 Sub-proof #104 shows that the following formulas are inconsistent: % 74.87/11.17 ---------------------------------------------------------------- % 74.87/11.18 (1) all_10_0 = e3 % 74.87/11.18 (2) all_10_0 = e2 % 74.87/11.18 (3) ~ (e3 = e2) % 74.87/11.18 % 74.87/11.18 Begin of proof % 74.87/11.18 | % 74.87/11.18 | COMBINE_EQS: (1), (2) imply: % 74.87/11.18 | (4) e3 = e2 % 74.87/11.18 | % 74.87/11.18 | SIMP: (4) implies: % 74.87/11.18 | (5) e3 = e2 % 74.87/11.18 | % 74.87/11.18 | REDUCE: (3), (5) imply: % 74.87/11.18 | (6) $false % 74.87/11.18 | % 74.87/11.18 | CLOSE: (6) is inconsistent. % 74.87/11.18 | % 74.87/11.18 End of proof % 74.87/11.18 % 74.87/11.18 Sub-proof #105 shows that the following formulas are inconsistent: % 74.87/11.18 ---------------------------------------------------------------- % 74.87/11.18 (1) all_6_10 = all_4_2 % 74.87/11.18 (2) all_6_10 = e4 % 74.87/11.18 (3) ~ (all_4_2 = e4) % 74.87/11.18 % 74.87/11.18 Begin of proof % 74.87/11.18 | % 74.87/11.18 | COMBINE_EQS: (1), (2) imply: % 74.87/11.18 | (4) all_4_2 = e4 % 74.87/11.18 | % 74.87/11.18 | SIMP: (4) implies: % 74.87/11.18 | (5) all_4_2 = e4 % 74.87/11.18 | % 74.87/11.18 | REDUCE: (3), (5) imply: % 74.87/11.18 | (6) $false % 74.87/11.18 | % 74.87/11.18 | CLOSE: (6) is inconsistent. % 74.87/11.18 | % 74.87/11.18 End of proof % 74.87/11.18 % 74.87/11.18 Sub-proof #106 shows that the following formulas are inconsistent: % 74.87/11.18 ---------------------------------------------------------------- % 74.87/11.18 (1) all_6_10 = all_4_2 % 74.87/11.18 (2) all_6_10 = e2 % 74.87/11.18 (3) ~ (all_4_2 = e2) % 74.87/11.18 % 74.87/11.18 Begin of proof % 74.87/11.18 | % 74.87/11.18 | COMBINE_EQS: (1), (2) imply: % 74.87/11.18 | (4) all_4_2 = e2 % 74.87/11.18 | % 74.87/11.18 | SIMP: (4) implies: % 74.87/11.18 | (5) all_4_2 = e2 % 74.87/11.18 | % 74.87/11.18 | REDUCE: (3), (5) imply: % 74.87/11.18 | (6) $false % 74.87/11.18 | % 74.87/11.18 | CLOSE: (6) is inconsistent. % 74.87/11.18 | % 74.87/11.18 End of proof % 74.87/11.18 % 74.87/11.18 Sub-proof #107 shows that the following formulas are inconsistent: % 74.87/11.18 ---------------------------------------------------------------- % 74.87/11.18 (1) all_6_15 = all_4_3 % 74.87/11.18 (2) all_6_15 = e4 % 74.87/11.18 (3) ~ (all_4_3 = e4) % 74.87/11.18 % 74.87/11.18 Begin of proof % 74.87/11.18 | % 74.87/11.18 | COMBINE_EQS: (1), (2) imply: % 74.87/11.18 | (4) all_4_3 = e4 % 74.87/11.18 | % 74.87/11.18 | SIMP: (4) implies: % 74.87/11.18 | (5) all_4_3 = e4 % 74.87/11.18 | % 74.87/11.18 | REDUCE: (3), (5) imply: % 74.87/11.18 | (6) $false % 74.87/11.18 | % 74.87/11.18 | CLOSE: (6) is inconsistent. % 74.87/11.18 | % 74.87/11.18 End of proof % 74.87/11.18 % 74.87/11.18 Sub-proof #108 shows that the following formulas are inconsistent: % 74.87/11.18 ---------------------------------------------------------------- % 74.87/11.18 (1) ~ (all_4_16 = e2) % 74.87/11.18 (2) all_10_15 = e4 % 74.87/11.18 (3) ~ (e2 = e0) % 74.87/11.18 (4) all_10_10 = all_4_16 % 74.87/11.18 (5) all_10_9 = e2 | all_10_10 = e2 | all_10_11 = e2 | all_10_15 = e2 | % 74.87/11.18 all_10_23 = e2 % 74.87/11.18 (6) ~ (all_4_15 = e2) % 74.87/11.18 (7) all_10_9 = all_4_15 % 74.87/11.18 (8) ~ (e4 = e2) % 74.87/11.18 (9) ~ (all_4_17 = e2) % 74.87/11.18 (10) all_10_11 = all_4_17 % 74.87/11.18 (11) all_10_23 = e0 % 74.87/11.18 % 74.87/11.18 Begin of proof % 74.87/11.18 | % 74.87/11.18 | BETA: splitting (5) gives: % 74.87/11.18 | % 74.87/11.18 | Case 1: % 74.87/11.18 | | % 74.87/11.18 | | (12) all_10_9 = e2 % 74.87/11.18 | | % 74.87/11.18 | | COMBINE_EQS: (7), (12) imply: % 74.87/11.18 | | (13) all_4_15 = e2 % 74.87/11.18 | | % 74.87/11.18 | | REDUCE: (6), (13) imply: % 74.87/11.18 | | (14) $false % 74.87/11.18 | | % 74.87/11.18 | | CLOSE: (14) is inconsistent. % 74.87/11.18 | | % 74.87/11.18 | Case 2: % 74.87/11.18 | | % 74.87/11.18 | | (15) all_10_10 = e2 | all_10_11 = e2 | all_10_15 = e2 | all_10_23 = e2 % 74.87/11.18 | | % 74.87/11.18 | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (10), (11), (15) are inconsistent % 74.87/11.18 | | by sub-proof #116. % 74.87/11.18 | | % 74.87/11.18 | End of split % 74.87/11.18 | % 74.87/11.18 End of proof % 74.87/11.18 % 74.87/11.18 Sub-proof #109 shows that the following formulas are inconsistent: % 74.87/11.18 ---------------------------------------------------------------- % 74.87/11.18 (1) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 74.87/11.18 (2) ~ (all_4_7 = e3) % 74.87/11.18 (3) ~ (all_4_7 = e0) % 74.87/11.18 (4) all_6_11 = e4 | all_6_11 = e3 | all_6_11 = e1 | all_6_11 = e0 % 74.87/11.18 (5) ~ (all_4_5 = e3) % 74.87/11.18 (6) ~ (all_4_5 = e1) % 74.87/11.18 (7) ~ (all_4_5 = e0) % 74.87/11.18 (8) all_6_1 = all_4_5 % 74.87/11.18 (9) ~ (all_4_5 = all_4_7) % 74.87/11.18 (10) all_6_11 = all_4_7 % 74.87/11.18 (11) ~ (all_4_7 = e1) % 74.87/11.18 % 74.87/11.18 Begin of proof % 74.87/11.18 | % 74.87/11.18 | BETA: splitting (1) gives: % 74.87/11.18 | % 74.87/11.18 | Case 1: % 74.87/11.18 | | % 74.87/11.18 | | (12) all_6_1 = e4 % 74.87/11.18 | | % 74.87/11.18 | | COMBINE_EQS: (8), (12) imply: % 74.87/11.18 | | (13) all_4_5 = e4 % 74.87/11.18 | | % 74.87/11.18 | | SIMP: (13) implies: % 74.87/11.18 | | (14) all_4_5 = e4 % 74.87/11.18 | | % 74.87/11.18 | | REDUCE: (9), (14) imply: % 74.87/11.18 | | (15) ~ (all_4_7 = e4) % 74.87/11.18 | | % 74.87/11.18 | | SIMP: (15) implies: % 74.87/11.18 | | (16) ~ (all_4_7 = e4) % 74.87/11.18 | | % 74.87/11.18 | | REF_CLOSE: (2), (3), (4), (10), (11), (16) are inconsistent by sub-proof % 74.87/11.18 | | #132. % 74.87/11.18 | | % 74.87/11.18 | Case 2: % 74.87/11.18 | | % 74.87/11.18 | | (17) all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 74.87/11.18 | | % 74.87/11.18 | | REF_CLOSE: (5), (6), (7), (8), (17) are inconsistent by sub-proof #135. % 74.87/11.18 | | % 74.87/11.18 | End of split % 74.87/11.18 | % 74.87/11.18 End of proof % 74.87/11.18 % 74.87/11.18 Sub-proof #110 shows that the following formulas are inconsistent: % 74.87/11.18 ---------------------------------------------------------------- % 74.87/11.18 (1) all_6_9 = all_4_21 % 74.87/11.18 (2) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e1 | all_6_9 = e0 % 74.87/11.18 (3) ~ (all_4_21 = e4) % 74.87/11.18 (4) ~ (all_4_21 = e1) % 74.87/11.18 (5) ~ (all_4_21 = e3) % 74.87/11.18 (6) ~ (all_4_21 = e0) % 74.87/11.18 % 74.87/11.18 Begin of proof % 74.87/11.18 | % 74.87/11.18 | BETA: splitting (2) gives: % 74.87/11.18 | % 74.87/11.18 | Case 1: % 74.87/11.18 | | % 74.87/11.18 | | (7) all_6_9 = e4 % 74.87/11.18 | | % 74.87/11.18 | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #114. % 74.87/11.18 | | % 74.87/11.18 | Case 2: % 74.87/11.18 | | % 74.87/11.18 | | (8) all_6_9 = e3 | all_6_9 = e1 | all_6_9 = e0 % 74.87/11.18 | | % 74.87/11.18 | | REF_CLOSE: (1), (4), (5), (6), (8) are inconsistent by sub-proof #111. % 74.87/11.18 | | % 74.87/11.18 | End of split % 74.87/11.18 | % 74.87/11.18 End of proof % 74.87/11.18 % 74.87/11.18 Sub-proof #111 shows that the following formulas are inconsistent: % 74.87/11.18 ---------------------------------------------------------------- % 74.87/11.18 (1) all_6_9 = all_4_21 % 74.87/11.18 (2) all_6_9 = e3 | all_6_9 = e1 | all_6_9 = e0 % 74.87/11.18 (3) ~ (all_4_21 = e1) % 74.87/11.18 (4) ~ (all_4_21 = e3) % 74.87/11.18 (5) ~ (all_4_21 = e0) % 74.87/11.18 % 74.87/11.18 Begin of proof % 74.87/11.18 | % 74.87/11.18 | BETA: splitting (2) gives: % 74.87/11.18 | % 74.87/11.18 | Case 1: % 74.87/11.18 | | % 74.87/11.18 | | (6) all_6_9 = e1 % 74.87/11.18 | | % 74.87/11.18 | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #113. % 74.87/11.18 | | % 74.87/11.18 | Case 2: % 74.87/11.18 | | % 74.87/11.18 | | (7) all_6_9 = e3 | all_6_9 = e0 % 74.87/11.18 | | % 74.87/11.18 | | BETA: splitting (7) gives: % 74.87/11.18 | | % 74.87/11.18 | | Case 1: % 74.87/11.18 | | | % 74.87/11.18 | | | (8) all_6_9 = e3 % 74.87/11.18 | | | % 74.87/11.18 | | | COMBINE_EQS: (1), (8) imply: % 74.87/11.18 | | | (9) all_4_21 = e3 % 74.87/11.18 | | | % 74.87/11.18 | | | SIMP: (9) implies: % 74.87/11.18 | | | (10) all_4_21 = e3 % 74.87/11.18 | | | % 74.87/11.18 | | | REDUCE: (4), (10) imply: % 74.87/11.18 | | | (11) $false % 74.87/11.18 | | | % 74.87/11.18 | | | CLOSE: (11) is inconsistent. % 74.87/11.18 | | | % 74.87/11.18 | | Case 2: % 74.87/11.18 | | | % 74.87/11.18 | | | (12) all_6_9 = e0 % 74.87/11.18 | | | % 74.87/11.18 | | | REF_CLOSE: (1), (5), (12) are inconsistent by sub-proof #112. % 74.87/11.18 | | | % 74.87/11.18 | | End of split % 74.87/11.18 | | % 74.87/11.18 | End of split % 74.87/11.18 | % 74.87/11.18 End of proof % 74.87/11.18 % 74.87/11.18 Sub-proof #112 shows that the following formulas are inconsistent: % 74.87/11.18 ---------------------------------------------------------------- % 74.87/11.18 (1) all_6_9 = all_4_21 % 74.87/11.18 (2) all_6_9 = e0 % 74.87/11.18 (3) ~ (all_4_21 = e0) % 74.87/11.18 % 74.87/11.18 Begin of proof % 74.87/11.18 | % 74.87/11.18 | COMBINE_EQS: (1), (2) imply: % 74.87/11.18 | (4) all_4_21 = e0 % 74.87/11.18 | % 74.87/11.18 | SIMP: (4) implies: % 74.87/11.18 | (5) all_4_21 = e0 % 74.87/11.18 | % 74.87/11.18 | REDUCE: (3), (5) imply: % 74.87/11.18 | (6) $false % 74.87/11.18 | % 74.87/11.18 | CLOSE: (6) is inconsistent. % 74.87/11.18 | % 74.87/11.18 End of proof % 74.87/11.18 % 74.87/11.18 Sub-proof #113 shows that the following formulas are inconsistent: % 74.87/11.18 ---------------------------------------------------------------- % 74.87/11.18 (1) all_6_9 = all_4_21 % 74.87/11.18 (2) all_6_9 = e1 % 74.87/11.18 (3) ~ (all_4_21 = e1) % 74.87/11.18 % 74.87/11.18 Begin of proof % 74.87/11.18 | % 74.87/11.18 | COMBINE_EQS: (1), (2) imply: % 74.87/11.18 | (4) all_4_21 = e1 % 74.87/11.18 | % 74.87/11.18 | SIMP: (4) implies: % 74.87/11.18 | (5) all_4_21 = e1 % 74.87/11.18 | % 74.87/11.18 | REDUCE: (3), (5) imply: % 74.87/11.18 | (6) $false % 74.87/11.18 | % 74.87/11.18 | CLOSE: (6) is inconsistent. % 74.87/11.18 | % 74.87/11.18 End of proof % 74.87/11.18 % 74.87/11.18 Sub-proof #114 shows that the following formulas are inconsistent: % 74.87/11.18 ---------------------------------------------------------------- % 74.87/11.18 (1) all_6_9 = all_4_21 % 74.87/11.18 (2) all_6_9 = e4 % 74.87/11.18 (3) ~ (all_4_21 = e4) % 74.87/11.18 % 74.87/11.18 Begin of proof % 74.87/11.18 | % 74.87/11.18 | COMBINE_EQS: (1), (2) imply: % 74.87/11.18 | (4) all_4_21 = e4 % 74.87/11.18 | % 74.87/11.18 | SIMP: (4) implies: % 74.87/11.18 | (5) all_4_21 = e4 % 74.87/11.18 | % 74.87/11.18 | REDUCE: (3), (5) imply: % 74.87/11.18 | (6) $false % 74.87/11.18 | % 74.87/11.18 | CLOSE: (6) is inconsistent. % 74.87/11.18 | % 74.87/11.18 End of proof % 74.87/11.18 % 74.87/11.18 Sub-proof #115 shows that the following formulas are inconsistent: % 74.87/11.18 ---------------------------------------------------------------- % 74.87/11.18 (1) all_10_8 = e3 % 74.87/11.18 (2) all_10_14 = e0 % 74.87/11.18 (3) all_10_22 = e2 % 74.87/11.18 (4) ~ (e4 = e0) % 74.87/11.18 (5) ~ (e4 = e3) % 74.87/11.18 (6) all_10_8 = e4 | all_10_14 = e4 | all_10_22 = e4 % 74.87/11.18 (7) ~ (e4 = e2) % 74.87/11.18 % 74.87/11.18 Begin of proof % 74.87/11.18 | % 74.87/11.18 | BETA: splitting (6) gives: % 74.87/11.18 | % 74.87/11.18 | Case 1: % 74.87/11.18 | | % 74.87/11.18 | | (8) all_10_8 = e4 % 74.87/11.18 | | % 74.87/11.18 | | COMBINE_EQS: (1), (8) imply: % 74.87/11.18 | | (9) e4 = e3 % 74.87/11.18 | | % 74.87/11.18 | | SIMP: (9) implies: % 74.87/11.18 | | (10) e4 = e3 % 74.87/11.18 | | % 74.87/11.18 | | REDUCE: (5), (10) imply: % 74.87/11.18 | | (11) $false % 74.87/11.18 | | % 74.87/11.18 | | CLOSE: (11) is inconsistent. % 74.87/11.18 | | % 74.87/11.18 | Case 2: % 74.87/11.18 | | % 74.87/11.18 | | (12) all_10_14 = e4 | all_10_22 = e4 % 74.87/11.18 | | % 74.87/11.18 | | BETA: splitting (12) gives: % 74.87/11.18 | | % 74.87/11.18 | | Case 1: % 74.87/11.18 | | | % 74.87/11.18 | | | (13) all_10_14 = e4 % 74.87/11.18 | | | % 74.87/11.18 | | | COMBINE_EQS: (2), (13) imply: % 74.87/11.18 | | | (14) e4 = e0 % 74.87/11.18 | | | % 74.87/11.18 | | | REDUCE: (4), (14) imply: % 74.87/11.18 | | | (15) $false % 74.87/11.18 | | | % 74.87/11.18 | | | CLOSE: (15) is inconsistent. % 74.87/11.18 | | | % 74.87/11.18 | | Case 2: % 74.87/11.18 | | | % 74.87/11.18 | | | (16) all_10_22 = e4 % 74.87/11.18 | | | % 74.87/11.18 | | | COMBINE_EQS: (3), (16) imply: % 74.87/11.18 | | | (17) e4 = e2 % 74.87/11.18 | | | % 74.87/11.18 | | | SIMP: (17) implies: % 74.87/11.18 | | | (18) e4 = e2 % 74.87/11.18 | | | % 74.87/11.18 | | | REDUCE: (7), (18) imply: % 74.87/11.18 | | | (19) $false % 74.87/11.18 | | | % 74.87/11.18 | | | CLOSE: (19) is inconsistent. % 74.87/11.18 | | | % 74.87/11.18 | | End of split % 74.87/11.18 | | % 74.87/11.18 | End of split % 74.87/11.18 | % 74.87/11.18 End of proof % 74.87/11.18 % 74.87/11.18 Sub-proof #116 shows that the following formulas are inconsistent: % 74.87/11.18 ---------------------------------------------------------------- % 74.87/11.18 (1) ~ (all_4_16 = e2) % 74.87/11.18 (2) all_10_15 = e4 % 74.87/11.18 (3) ~ (e2 = e0) % 74.87/11.18 (4) all_10_10 = all_4_16 % 74.87/11.18 (5) ~ (e4 = e2) % 74.87/11.18 (6) all_10_10 = e2 | all_10_11 = e2 | all_10_15 = e2 | all_10_23 = e2 % 74.87/11.18 (7) ~ (all_4_17 = e2) % 74.87/11.18 (8) all_10_11 = all_4_17 % 74.87/11.18 (9) all_10_23 = e0 % 74.87/11.18 % 74.87/11.18 Begin of proof % 74.87/11.18 | % 74.87/11.18 | BETA: splitting (6) gives: % 74.87/11.18 | % 74.87/11.18 | Case 1: % 74.87/11.18 | | % 74.87/11.18 | | (10) all_10_10 = e2 % 74.87/11.18 | | % 74.87/11.18 | | COMBINE_EQS: (4), (10) imply: % 74.87/11.18 | | (11) all_4_16 = e2 % 74.87/11.18 | | % 74.87/11.18 | | REDUCE: (1), (11) imply: % 74.87/11.18 | | (12) $false % 74.87/11.18 | | % 74.87/11.18 | | CLOSE: (12) is inconsistent. % 74.87/11.18 | | % 74.87/11.18 | Case 2: % 74.87/11.18 | | % 74.87/11.18 | | (13) all_10_11 = e2 | all_10_15 = e2 | all_10_23 = e2 % 74.87/11.18 | | % 74.87/11.18 | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (13) are inconsistent by sub-proof % 74.87/11.18 | | #117. % 74.87/11.18 | | % 74.87/11.18 | End of split % 74.87/11.18 | % 74.87/11.18 End of proof % 74.87/11.18 % 74.87/11.18 Sub-proof #117 shows that the following formulas are inconsistent: % 74.87/11.18 ---------------------------------------------------------------- % 74.87/11.18 (1) all_10_15 = e4 % 74.87/11.18 (2) ~ (e2 = e0) % 74.87/11.18 (3) all_10_11 = e2 | all_10_15 = e2 | all_10_23 = e2 % 74.87/11.18 (4) ~ (e4 = e2) % 74.87/11.18 (5) ~ (all_4_17 = e2) % 74.87/11.18 (6) all_10_11 = all_4_17 % 74.87/11.18 (7) all_10_23 = e0 % 74.87/11.18 % 74.87/11.18 Begin of proof % 74.87/11.18 | % 74.87/11.18 | BETA: splitting (3) gives: % 74.87/11.18 | % 74.87/11.18 | Case 1: % 74.87/11.18 | | % 74.87/11.18 | | (8) all_10_11 = e2 % 74.87/11.18 | | % 74.87/11.18 | | COMBINE_EQS: (6), (8) imply: % 74.87/11.18 | | (9) all_4_17 = e2 % 74.87/11.18 | | % 74.87/11.18 | | REDUCE: (5), (9) imply: % 74.87/11.18 | | (10) $false % 74.87/11.18 | | % 74.87/11.18 | | CLOSE: (10) is inconsistent. % 74.87/11.18 | | % 74.87/11.18 | Case 2: % 74.87/11.18 | | % 74.87/11.18 | | (11) all_10_15 = e2 | all_10_23 = e2 % 74.87/11.18 | | % 74.87/11.18 | | BETA: splitting (11) gives: % 74.87/11.18 | | % 74.87/11.18 | | Case 1: % 74.87/11.18 | | | % 74.87/11.18 | | | (12) all_10_15 = e2 % 74.87/11.18 | | | % 74.87/11.18 | | | COMBINE_EQS: (1), (12) imply: % 74.87/11.18 | | | (13) e4 = e2 % 74.87/11.18 | | | % 74.87/11.18 | | | REDUCE: (4), (13) imply: % 74.87/11.18 | | | (14) $false % 74.87/11.18 | | | % 74.87/11.18 | | | CLOSE: (14) is inconsistent. % 74.87/11.18 | | | % 74.87/11.18 | | Case 2: % 74.87/11.18 | | | % 74.87/11.18 | | | (15) all_10_23 = e2 % 74.87/11.18 | | | % 74.87/11.18 | | | REF_CLOSE: (2), (7), (15) are inconsistent by sub-proof #118. % 74.87/11.18 | | | % 74.87/11.18 | | End of split % 74.87/11.18 | | % 74.87/11.18 | End of split % 74.87/11.18 | % 74.87/11.18 End of proof % 74.87/11.18 % 74.87/11.18 Sub-proof #118 shows that the following formulas are inconsistent: % 74.87/11.18 ---------------------------------------------------------------- % 74.87/11.18 (1) all_10_23 = e2 % 74.87/11.18 (2) all_10_23 = e0 % 74.87/11.18 (3) ~ (e2 = e0) % 74.87/11.18 % 74.87/11.18 Begin of proof % 74.87/11.18 | % 74.87/11.18 | COMBINE_EQS: (1), (2) imply: % 74.87/11.18 | (4) e2 = e0 % 74.87/11.18 | % 74.87/11.18 | SIMP: (4) implies: % 74.87/11.18 | (5) e2 = e0 % 74.87/11.18 | % 74.87/11.18 | REDUCE: (3), (5) imply: % 74.87/11.18 | (6) $false % 74.87/11.18 | % 74.87/11.18 | CLOSE: (6) is inconsistent. % 74.87/11.18 | % 74.87/11.18 End of proof % 74.87/11.18 % 74.87/11.18 Sub-proof #119 shows that the following formulas are inconsistent: % 74.87/11.18 ---------------------------------------------------------------- % 74.87/11.18 (1) all_10_2 = all_4_1 % 74.87/11.18 (2) all_10_2 = e0 % 74.87/11.18 (3) ~ (all_4_1 = e0) % 74.87/11.18 % 74.87/11.18 Begin of proof % 74.87/11.18 | % 74.87/11.18 | COMBINE_EQS: (1), (2) imply: % 74.87/11.18 | (4) all_4_1 = e0 % 74.87/11.18 | % 74.87/11.18 | SIMP: (4) implies: % 74.87/11.18 | (5) all_4_1 = e0 % 74.87/11.18 | % 74.87/11.18 | REDUCE: (3), (5) imply: % 74.87/11.18 | (6) $false % 74.87/11.18 | % 74.87/11.18 | CLOSE: (6) is inconsistent. % 74.87/11.18 | % 74.87/11.18 End of proof % 74.87/11.18 % 74.87/11.18 Sub-proof #120 shows that the following formulas are inconsistent: % 74.87/11.18 ---------------------------------------------------------------- % 74.87/11.18 (1) all_10_8 = e3 % 74.87/11.18 (2) all_10_14 = e0 % 74.87/11.18 (3) ~ (all_4_10 = e3) % 74.87/11.18 (4) ~ (all_4_14 = e3) % 74.87/11.18 (5) all_10_4 = all_4_10 % 74.87/11.18 (6) ~ (all_4_16 = e2) % 74.87/11.18 (7) all_10_15 = e4 % 74.87/11.18 (8) all_10_5 = e2 % 74.87/11.18 (9) ~ (e3 = e1) % 74.87/11.18 (10) ~ (all_4_10 = all_4_14) % 74.87/11.18 (11) ~ (all_4_14 = e0) % 74.87/11.18 (12) all_6_22 = e4 | all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 74.87/11.18 (13) all_10_23 = all_4_19 % 74.87/11.18 (14) ~ (all_4_10 = e0) % 74.87/11.18 (15) ~ (all_8_37 = e2) % 74.87/11.18 (16) op(e0, e1) = all_4_19 % 74.87/11.18 (17) ~ (e2 = e1) % 74.87/11.18 (18) all_10_22 = all_4_14 % 74.87/11.19 (19) all_10_10 = all_4_16 % 74.87/11.19 (20) ~ (all_10_4 = e1) % 74.87/11.19 (21) ~ (e1 = e0) % 74.87/11.19 (22) op(e0, all_4_14) = all_8_37 % 74.87/11.19 (23) all_10_10 = e2 | all_10_11 = e2 | all_10_15 = e2 | all_10_23 = e2 % 74.87/11.19 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.87/11.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 74.87/11.19 (25) ~ (all_4_17 = e2) % 74.87/11.19 (26) all_6_2 = all_4_10 % 74.87/11.19 (27) all_6_22 = all_4_14 % 74.87/11.19 (28) all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | % 74.87/11.19 all_10_22 = e4 % 74.87/11.19 (29) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.87/11.19 (30) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | all_6_2 = e0 % 74.87/11.19 (31) ~ (all_4_10 = e2) % 74.87/11.19 (32) all_10_11 = all_4_17 % 74.87/11.19 (33) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 74.87/11.19 all_10_22 = e1 % 74.87/11.19 % 74.87/11.19 Begin of proof % 74.87/11.19 | % 74.87/11.19 | REDUCE: (5), (20) imply: % 74.87/11.19 | (34) ~ (all_4_10 = e1) % 74.87/11.19 | % 74.87/11.19 | BETA: splitting (29) gives: % 74.87/11.19 | % 74.87/11.19 | Case 1: % 74.87/11.19 | | % 74.87/11.19 | | (35) all_6_2 = e4 % 74.87/11.19 | | % 74.87/11.19 | | COMBINE_EQS: (26), (35) imply: % 74.87/11.19 | | (36) all_4_10 = e4 % 74.87/11.19 | | % 74.87/11.19 | | SIMP: (36) implies: % 74.87/11.19 | | (37) all_4_10 = e4 % 74.87/11.19 | | % 74.87/11.19 | | REDUCE: (10), (37) imply: % 74.87/11.19 | | (38) ~ (all_4_14 = e4) % 74.87/11.19 | | % 74.87/11.19 | | SIMP: (38) implies: % 74.87/11.19 | | (39) ~ (all_4_14 = e4) % 74.87/11.19 | | % 74.87/11.19 | | REDUCE: (34), (37) imply: % 74.87/11.19 | | (40) ~ (e4 = e1) % 74.87/11.19 | | % 74.87/11.19 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 74.87/11.19 | | (13), (14), (15), (16), (17), (18), (19), (21), (22), (23), (24), % 74.87/11.19 | | (25), (26), (27), (28), (30), (31), (32), (33), (39), (40) are % 74.87/11.19 | | inconsistent by sub-proof #128. % 74.87/11.19 | | % 74.87/11.19 | Case 2: % 74.87/11.19 | | % 74.87/11.19 | | (41) all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 74.87/11.19 | | % 74.87/11.19 | | REF_CLOSE: (3), (14), (26), (34), (41) are inconsistent by sub-proof #162. % 74.87/11.19 | | % 74.87/11.19 | End of split % 74.87/11.19 | % 74.87/11.19 End of proof % 74.87/11.19 % 74.87/11.19 Sub-proof #121 shows that the following formulas are inconsistent: % 74.87/11.19 ---------------------------------------------------------------- % 74.87/11.19 (1) all_6_20 = all_4_4 % 75.19/11.19 (2) ~ (all_4_9 = e0) % 75.19/11.19 (3) ~ (all_4_14 = e3) % 75.19/11.19 (4) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 75.19/11.19 (5) ~ (all_10_20 = e1) % 75.19/11.19 (6) ~ (all_4_14 = e0) % 75.19/11.19 (7) ~ (all_4_4 = all_4_9) % 75.19/11.19 (8) all_6_22 = e4 | all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 75.19/11.19 (9) all_6_21 = all_4_9 % 75.19/11.19 (10) all_10_20 = all_4_4 % 75.19/11.19 (11) ~ (all_4_9 = all_4_14) % 75.19/11.19 (12) ~ (all_4_4 = e0) % 75.19/11.19 (13) ~ (all_4_14 = e1) % 75.19/11.19 (14) ~ (all_4_4 = all_4_14) % 75.19/11.19 (15) ~ (all_4_9 = e1) % 75.19/11.19 (16) all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e1 | all_6_21 = e0 % 75.19/11.19 (17) all_6_22 = all_4_14 % 75.19/11.19 % 75.19/11.19 Begin of proof % 75.19/11.19 | % 75.19/11.19 | REDUCE: (5), (10) imply: % 75.19/11.19 | (18) ~ (all_4_4 = e1) % 75.19/11.19 | % 75.19/11.19 | BETA: splitting (8) gives: % 75.19/11.19 | % 75.19/11.19 | Case 1: % 75.19/11.19 | | % 75.19/11.19 | | (19) all_6_22 = e4 % 75.19/11.19 | | % 75.19/11.19 | | COMBINE_EQS: (17), (19) imply: % 75.19/11.19 | | (20) all_4_14 = e4 % 75.19/11.19 | | % 75.19/11.19 | | SIMP: (20) implies: % 75.19/11.19 | | (21) all_4_14 = e4 % 75.19/11.19 | | % 75.19/11.19 | | REDUCE: (14), (21) imply: % 75.19/11.19 | | (22) ~ (all_4_4 = e4) % 75.19/11.19 | | % 75.19/11.19 | | REDUCE: (11), (21) imply: % 75.19/11.19 | | (23) ~ (all_4_9 = e4) % 75.19/11.19 | | % 75.19/11.19 | | BETA: splitting (16) gives: % 75.19/11.19 | | % 75.19/11.19 | | Case 1: % 75.19/11.19 | | | % 75.19/11.19 | | | (24) all_6_21 = e4 % 75.19/11.19 | | | % 75.19/11.19 | | | COMBINE_EQS: (9), (24) imply: % 75.19/11.19 | | | (25) all_4_9 = e4 % 75.19/11.19 | | | % 75.19/11.19 | | | REDUCE: (23), (25) imply: % 75.19/11.19 | | | (26) $false % 75.19/11.19 | | | % 75.19/11.19 | | | CLOSE: (26) is inconsistent. % 75.19/11.19 | | | % 75.19/11.19 | | Case 2: % 75.19/11.19 | | | % 75.19/11.19 | | | (27) all_6_21 = e3 | all_6_21 = e1 | all_6_21 = e0 % 75.19/11.19 | | | % 75.19/11.19 | | | BETA: splitting (27) gives: % 75.19/11.19 | | | % 75.19/11.19 | | | Case 1: % 75.19/11.19 | | | | % 75.19/11.19 | | | | (28) all_6_21 = e1 % 75.19/11.19 | | | | % 75.19/11.19 | | | | COMBINE_EQS: (9), (28) imply: % 75.19/11.19 | | | | (29) all_4_9 = e1 % 75.19/11.19 | | | | % 75.19/11.19 | | | | REDUCE: (15), (29) imply: % 75.19/11.19 | | | | (30) $false % 75.19/11.19 | | | | % 75.19/11.19 | | | | CLOSE: (30) is inconsistent. % 75.19/11.19 | | | | % 75.19/11.19 | | | Case 2: % 75.19/11.19 | | | | % 75.19/11.19 | | | | (31) all_6_21 = e3 | all_6_21 = e0 % 75.19/11.19 | | | | % 75.19/11.19 | | | | BETA: splitting (4) gives: % 75.19/11.19 | | | | % 75.19/11.19 | | | | Case 1: % 75.19/11.19 | | | | | % 75.19/11.19 | | | | | (32) all_6_20 = e4 % 75.19/11.19 | | | | | % 75.19/11.19 | | | | | COMBINE_EQS: (1), (32) imply: % 75.19/11.19 | | | | | (33) all_4_4 = e4 % 75.19/11.19 | | | | | % 75.19/11.19 | | | | | REDUCE: (22), (33) imply: % 75.19/11.19 | | | | | (34) $false % 75.19/11.19 | | | | | % 75.19/11.19 | | | | | CLOSE: (34) is inconsistent. % 75.19/11.19 | | | | | % 75.19/11.19 | | | | Case 2: % 75.19/11.19 | | | | | % 75.19/11.19 | | | | | (35) all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 75.19/11.19 | | | | | % 75.19/11.19 | | | | | BETA: splitting (35) gives: % 75.19/11.19 | | | | | % 75.19/11.19 | | | | | Case 1: % 75.19/11.19 | | | | | | % 75.19/11.19 | | | | | | (36) all_6_20 = e1 % 75.19/11.19 | | | | | | % 75.19/11.19 | | | | | | COMBINE_EQS: (1), (36) imply: % 75.19/11.19 | | | | | | (37) all_4_4 = e1 % 75.19/11.19 | | | | | | % 75.19/11.19 | | | | | | REDUCE: (18), (37) imply: % 75.19/11.19 | | | | | | (38) $false % 75.19/11.19 | | | | | | % 75.19/11.19 | | | | | | CLOSE: (38) is inconsistent. % 75.19/11.19 | | | | | | % 75.19/11.19 | | | | | Case 2: % 75.19/11.19 | | | | | | % 75.19/11.19 | | | | | | (39) all_6_20 = e3 | all_6_20 = e0 % 75.19/11.19 | | | | | | % 75.19/11.19 | | | | | | BETA: splitting (31) gives: % 75.19/11.19 | | | | | | % 75.19/11.19 | | | | | | Case 1: % 75.19/11.19 | | | | | | | % 75.19/11.19 | | | | | | | (40) all_6_21 = e3 % 75.19/11.19 | | | | | | | % 75.19/11.19 | | | | | | | COMBINE_EQS: (9), (40) imply: % 75.19/11.19 | | | | | | | (41) all_4_9 = e3 % 75.19/11.19 | | | | | | | % 75.19/11.19 | | | | | | | SIMP: (41) implies: % 75.19/11.19 | | | | | | | (42) all_4_9 = e3 % 75.19/11.19 | | | | | | | % 75.19/11.19 | | | | | | | REDUCE: (7), (42) imply: % 75.19/11.19 | | | | | | | (43) ~ (all_4_4 = e3) % 75.19/11.19 | | | | | | | % 75.19/11.19 | | | | | | | REF_CLOSE: (1), (12), (39), (43) are inconsistent by sub-proof % 75.19/11.19 | | | | | | | #122. % 75.19/11.19 | | | | | | | % 75.19/11.19 | | | | | | Case 2: % 75.19/11.19 | | | | | | | % 75.19/11.19 | | | | | | | (44) all_6_21 = e0 % 75.19/11.19 | | | | | | | % 75.19/11.19 | | | | | | | REF_CLOSE: (2), (9), (44) are inconsistent by sub-proof #127. % 75.19/11.19 | | | | | | | % 75.19/11.19 | | | | | | End of split % 75.19/11.19 | | | | | | % 75.19/11.19 | | | | | End of split % 75.19/11.19 | | | | | % 75.19/11.19 | | | | End of split % 75.19/11.19 | | | | % 75.19/11.19 | | | End of split % 75.19/11.19 | | | % 75.19/11.19 | | End of split % 75.19/11.19 | | % 75.19/11.19 | Case 2: % 75.19/11.19 | | % 75.19/11.19 | | (45) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 75.19/11.19 | | % 75.19/11.19 | | REF_CLOSE: (3), (6), (13), (17), (45) are inconsistent by sub-proof #130. % 75.19/11.19 | | % 75.19/11.19 | End of split % 75.19/11.19 | % 75.19/11.19 End of proof % 75.19/11.19 % 75.19/11.19 Sub-proof #122 shows that the following formulas are inconsistent: % 75.19/11.19 ---------------------------------------------------------------- % 75.19/11.19 (1) all_6_20 = e3 | all_6_20 = e0 % 75.19/11.19 (2) all_6_20 = all_4_4 % 75.19/11.19 (3) ~ (all_4_4 = e3) % 75.19/11.19 (4) ~ (all_4_4 = e0) % 75.19/11.19 % 75.19/11.19 Begin of proof % 75.19/11.19 | % 75.19/11.19 | BETA: splitting (1) gives: % 75.19/11.19 | % 75.19/11.19 | Case 1: % 75.19/11.19 | | % 75.19/11.19 | | (5) all_6_20 = e3 % 75.19/11.19 | | % 75.19/11.19 | | COMBINE_EQS: (2), (5) imply: % 75.19/11.19 | | (6) all_4_4 = e3 % 75.19/11.19 | | % 75.19/11.19 | | REDUCE: (3), (6) imply: % 75.19/11.19 | | (7) $false % 75.19/11.19 | | % 75.19/11.19 | | CLOSE: (7) is inconsistent. % 75.19/11.19 | | % 75.19/11.19 | Case 2: % 75.19/11.19 | | % 75.19/11.19 | | (8) all_6_20 = e0 % 75.19/11.19 | | % 75.19/11.19 | | COMBINE_EQS: (2), (8) imply: % 75.19/11.19 | | (9) all_4_4 = e0 % 75.19/11.19 | | % 75.19/11.19 | | REDUCE: (4), (9) imply: % 75.19/11.19 | | (10) $false % 75.19/11.19 | | % 75.19/11.19 | | CLOSE: (10) is inconsistent. % 75.19/11.19 | | % 75.19/11.19 | End of split % 75.19/11.19 | % 75.19/11.19 End of proof % 75.19/11.19 % 75.19/11.19 Sub-proof #123 shows that the following formulas are inconsistent: % 75.19/11.19 ---------------------------------------------------------------- % 75.19/11.19 (1) ~ (all_4_3 = e4) % 75.19/11.19 (2) all_10_12 = all_4_3 % 75.19/11.19 (3) ~ (all_4_3 = e0) % 75.19/11.19 (4) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e1 | all_6_15 = e0 % 75.19/11.19 (5) all_6_15 = all_4_3 % 75.19/11.19 (6) ~ (all_10_12 = e3) % 75.19/11.19 (7) ~ (all_4_3 = e1) % 75.19/11.19 % 75.19/11.19 Begin of proof % 75.19/11.19 | % 75.19/11.19 | REDUCE: (2), (6) imply: % 75.19/11.19 | (8) ~ (all_4_3 = e3) % 75.19/11.19 | % 75.19/11.19 | BETA: splitting (4) gives: % 75.19/11.19 | % 75.19/11.19 | Case 1: % 75.19/11.19 | | % 75.19/11.19 | | (9) all_6_15 = e4 % 75.19/11.19 | | % 75.19/11.19 | | COMBINE_EQS: (5), (9) imply: % 75.19/11.19 | | (10) all_4_3 = e4 % 75.19/11.19 | | % 75.19/11.19 | | REDUCE: (1), (10) imply: % 75.19/11.19 | | (11) $false % 75.19/11.19 | | % 75.19/11.19 | | CLOSE: (11) is inconsistent. % 75.19/11.19 | | % 75.19/11.19 | Case 2: % 75.19/11.19 | | % 75.19/11.19 | | (12) all_6_15 = e3 | all_6_15 = e1 | all_6_15 = e0 % 75.19/11.19 | | % 75.19/11.19 | | BETA: splitting (12) gives: % 75.19/11.19 | | % 75.19/11.19 | | Case 1: % 75.19/11.19 | | | % 75.19/11.19 | | | (13) all_6_15 = e1 % 75.19/11.19 | | | % 75.19/11.19 | | | COMBINE_EQS: (5), (13) imply: % 75.19/11.19 | | | (14) all_4_3 = e1 % 75.19/11.19 | | | % 75.19/11.19 | | | REDUCE: (7), (14) imply: % 75.19/11.19 | | | (15) $false % 75.19/11.19 | | | % 75.19/11.19 | | | CLOSE: (15) is inconsistent. % 75.19/11.19 | | | % 75.19/11.19 | | Case 2: % 75.19/11.19 | | | % 75.19/11.19 | | | (16) all_6_15 = e3 | all_6_15 = e0 % 75.19/11.19 | | | % 75.19/11.19 | | | BETA: splitting (16) gives: % 75.19/11.19 | | | % 75.19/11.19 | | | Case 1: % 75.19/11.19 | | | | % 75.19/11.19 | | | | (17) all_6_15 = e3 % 75.19/11.19 | | | | % 75.19/11.19 | | | | COMBINE_EQS: (5), (17) imply: % 75.19/11.19 | | | | (18) all_4_3 = e3 % 75.19/11.19 | | | | % 75.19/11.19 | | | | SIMP: (18) implies: % 75.19/11.19 | | | | (19) all_4_3 = e3 % 75.19/11.19 | | | | % 75.19/11.19 | | | | REDUCE: (8), (19) imply: % 75.19/11.19 | | | | (20) $false % 75.19/11.19 | | | | % 75.19/11.19 | | | | CLOSE: (20) is inconsistent. % 75.19/11.19 | | | | % 75.19/11.19 | | | Case 2: % 75.19/11.19 | | | | % 75.19/11.19 | | | | (21) all_6_15 = e0 % 75.19/11.19 | | | | % 75.19/11.19 | | | | REF_CLOSE: (3), (5), (21) are inconsistent by sub-proof #124. % 75.19/11.19 | | | | % 75.19/11.19 | | | End of split % 75.19/11.19 | | | % 75.19/11.19 | | End of split % 75.19/11.19 | | % 75.19/11.19 | End of split % 75.19/11.19 | % 75.19/11.19 End of proof % 75.19/11.19 % 75.19/11.19 Sub-proof #124 shows that the following formulas are inconsistent: % 75.19/11.19 ---------------------------------------------------------------- % 75.19/11.19 (1) all_6_15 = all_4_3 % 75.19/11.19 (2) all_6_15 = e0 % 75.19/11.19 (3) ~ (all_4_3 = e0) % 75.19/11.19 % 75.19/11.19 Begin of proof % 75.19/11.19 | % 75.19/11.19 | COMBINE_EQS: (1), (2) imply: % 75.19/11.19 | (4) all_4_3 = e0 % 75.19/11.19 | % 75.19/11.19 | SIMP: (4) implies: % 75.19/11.19 | (5) all_4_3 = e0 % 75.19/11.19 | % 75.19/11.19 | REDUCE: (3), (5) imply: % 75.19/11.19 | (6) $false % 75.19/11.19 | % 75.19/11.19 | CLOSE: (6) is inconsistent. % 75.19/11.19 | % 75.19/11.19 End of proof % 75.19/11.19 % 75.19/11.19 Sub-proof #125 shows that the following formulas are inconsistent: % 75.19/11.19 ---------------------------------------------------------------- % 75.19/11.19 (1) all_10_8 = e3 % 75.19/11.19 (2) all_10_14 = e0 % 75.19/11.19 (3) ~ (all_4_9 = e0) % 75.19/11.19 (4) ~ (all_4_10 = e3) % 75.19/11.19 (5) ~ (all_4_14 = e3) % 75.19/11.19 (6) all_10_4 = all_4_10 % 75.19/11.19 (7) ~ (all_4_16 = e2) % 75.19/11.19 (8) all_10_15 = e4 % 75.19/11.19 (9) all_10_5 = e2 % 75.19/11.19 (10) ~ (e3 = e1) % 75.19/11.19 (11) ~ (all_4_10 = all_4_14) % 75.19/11.19 (12) ~ (all_4_14 = e0) % 75.19/11.19 (13) all_6_22 = e4 | all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 75.19/11.19 (14) all_10_23 = all_4_19 % 75.19/11.19 (15) ~ (all_4_10 = e0) % 75.19/11.19 (16) ~ (all_8_37 = e2) % 75.19/11.19 (17) ~ (all_4_9 = e3) % 75.19/11.19 (18) all_6_21 = all_4_9 % 75.19/11.19 (19) op(e0, e1) = all_4_19 % 75.19/11.19 (20) ~ (e2 = e1) % 75.19/11.19 (21) ~ (all_4_9 = all_4_14) % 75.19/11.19 (22) all_10_22 = all_4_14 % 75.19/11.19 (23) all_10_10 = all_4_16 % 75.19/11.19 (24) all_10_9 = e2 | all_10_10 = e2 | all_10_11 = e2 | all_10_15 = e2 | % 75.19/11.19 all_10_23 = e2 % 75.19/11.19 (25) ~ (all_4_15 = e2) % 75.19/11.19 (26) all_10_9 = all_4_15 % 75.19/11.19 (27) ~ (all_4_9 = e1) % 75.19/11.19 (28) all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e1 | all_6_21 = e0 % 75.19/11.19 (29) ~ (e1 = e0) % 75.19/11.19 (30) op(e0, all_4_14) = all_8_37 % 75.19/11.19 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 75.19/11.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 75.19/11.19 (32) ~ (all_4_17 = e2) % 75.19/11.19 (33) all_6_2 = all_4_10 % 75.19/11.19 (34) all_6_22 = all_4_14 % 75.19/11.19 (35) all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | % 75.19/11.19 all_10_22 = e4 % 75.19/11.19 (36) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | all_6_2 = e0 % 75.19/11.19 (37) ~ (all_4_10 = e2) % 75.19/11.19 (38) all_10_11 = all_4_17 % 75.19/11.19 (39) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 75.19/11.19 all_10_22 = e1 % 75.19/11.19 % 75.19/11.19 Begin of proof % 75.19/11.19 | % 75.19/11.19 | BETA: splitting (28) gives: % 75.19/11.19 | % 75.19/11.19 | Case 1: % 75.19/11.19 | | % 75.19/11.19 | | (40) all_6_21 = e4 % 75.19/11.19 | | % 75.19/11.19 | | COMBINE_EQS: (18), (40) imply: % 75.19/11.19 | | (41) all_4_9 = e4 % 75.19/11.19 | | % 75.19/11.19 | | SIMP: (41) implies: % 75.19/11.19 | | (42) all_4_9 = e4 % 75.19/11.19 | | % 75.19/11.19 | | REDUCE: (21), (42) imply: % 75.19/11.19 | | (43) ~ (all_4_14 = e4) % 75.19/11.19 | | % 75.19/11.19 | | SIMP: (43) implies: % 75.19/11.19 | | (44) ~ (all_4_14 = e4) % 75.19/11.19 | | % 75.19/11.19 | | REDUCE: (27), (42) imply: % 75.19/11.19 | | (45) ~ (e4 = e1) % 75.19/11.19 | | % 75.19/11.19 | | BETA: splitting (24) gives: % 75.19/11.20 | | % 75.19/11.20 | | Case 1: % 75.19/11.20 | | | % 75.19/11.20 | | | (46) all_10_9 = e2 % 75.19/11.20 | | | % 75.19/11.20 | | | COMBINE_EQS: (26), (46) imply: % 75.19/11.20 | | | (47) all_4_15 = e2 % 75.19/11.20 | | | % 75.19/11.20 | | | REDUCE: (25), (47) imply: % 75.19/11.20 | | | (48) $false % 75.19/11.20 | | | % 75.19/11.20 | | | CLOSE: (48) is inconsistent. % 75.19/11.20 | | | % 75.19/11.20 | | Case 2: % 75.19/11.20 | | | % 75.19/11.20 | | | (49) all_10_10 = e2 | all_10_11 = e2 | all_10_15 = e2 | all_10_23 = e2 % 75.19/11.20 | | | % 75.19/11.20 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 75.19/11.20 | | | (14), (15), (16), (19), (20), (22), (23), (29), (30), (31), % 75.19/11.20 | | | (32), (33), (34), (35), (36), (37), (38), (39), (44), (45), % 75.19/11.20 | | | (49) are inconsistent by sub-proof #128. % 75.19/11.20 | | | % 75.19/11.20 | | End of split % 75.19/11.20 | | % 75.19/11.20 | Case 2: % 75.19/11.20 | | % 75.19/11.20 | | (50) all_6_21 = e3 | all_6_21 = e1 | all_6_21 = e0 % 75.19/11.20 | | % 75.19/11.20 | | REF_CLOSE: (3), (17), (18), (27), (50) are inconsistent by sub-proof #126. % 75.19/11.20 | | % 75.19/11.20 | End of split % 75.19/11.20 | % 75.19/11.20 End of proof % 75.19/11.20 % 75.19/11.20 Sub-proof #126 shows that the following formulas are inconsistent: % 75.19/11.20 ---------------------------------------------------------------- % 75.19/11.20 (1) ~ (all_4_9 = e0) % 75.19/11.20 (2) ~ (all_4_9 = e3) % 75.19/11.20 (3) all_6_21 = all_4_9 % 75.19/11.20 (4) all_6_21 = e3 | all_6_21 = e1 | all_6_21 = e0 % 75.19/11.20 (5) ~ (all_4_9 = e1) % 75.19/11.20 % 75.19/11.20 Begin of proof % 75.19/11.20 | % 75.19/11.20 | BETA: splitting (4) gives: % 75.19/11.20 | % 75.19/11.20 | Case 1: % 75.19/11.20 | | % 75.19/11.20 | | (6) all_6_21 = e1 % 75.19/11.20 | | % 75.19/11.20 | | COMBINE_EQS: (3), (6) imply: % 75.19/11.20 | | (7) all_4_9 = e1 % 75.19/11.20 | | % 75.19/11.20 | | SIMP: (7) implies: % 75.19/11.20 | | (8) all_4_9 = e1 % 75.19/11.20 | | % 75.19/11.20 | | REDUCE: (5), (8) imply: % 75.19/11.20 | | (9) $false % 75.19/11.20 | | % 75.19/11.20 | | CLOSE: (9) is inconsistent. % 75.19/11.20 | | % 75.19/11.20 | Case 2: % 75.19/11.20 | | % 75.19/11.20 | | (10) all_6_21 = e3 | all_6_21 = e0 % 75.19/11.20 | | % 75.19/11.20 | | BETA: splitting (10) gives: % 75.19/11.20 | | % 75.19/11.20 | | Case 1: % 75.19/11.20 | | | % 75.19/11.20 | | | (11) all_6_21 = e3 % 75.19/11.20 | | | % 75.19/11.20 | | | COMBINE_EQS: (3), (11) imply: % 75.19/11.20 | | | (12) all_4_9 = e3 % 75.19/11.20 | | | % 75.19/11.20 | | | SIMP: (12) implies: % 75.19/11.20 | | | (13) all_4_9 = e3 % 75.19/11.20 | | | % 75.19/11.20 | | | REDUCE: (2), (13) imply: % 75.19/11.20 | | | (14) $false % 75.19/11.20 | | | % 75.19/11.20 | | | CLOSE: (14) is inconsistent. % 75.19/11.20 | | | % 75.19/11.20 | | Case 2: % 75.19/11.20 | | | % 75.19/11.20 | | | (15) all_6_21 = e0 % 75.19/11.20 | | | % 75.19/11.20 | | | REF_CLOSE: (1), (3), (15) are inconsistent by sub-proof #127. % 75.19/11.20 | | | % 75.19/11.20 | | End of split % 75.19/11.20 | | % 75.19/11.20 | End of split % 75.19/11.20 | % 75.19/11.20 End of proof % 75.19/11.20 % 75.19/11.20 Sub-proof #127 shows that the following formulas are inconsistent: % 75.19/11.20 ---------------------------------------------------------------- % 75.19/11.20 (1) all_6_21 = all_4_9 % 75.19/11.20 (2) all_6_21 = e0 % 75.19/11.20 (3) ~ (all_4_9 = e0) % 75.19/11.20 % 75.19/11.20 Begin of proof % 75.19/11.20 | % 75.19/11.20 | COMBINE_EQS: (1), (2) imply: % 75.19/11.20 | (4) all_4_9 = e0 % 75.19/11.20 | % 75.19/11.20 | SIMP: (4) implies: % 75.19/11.20 | (5) all_4_9 = e0 % 75.19/11.20 | % 75.19/11.20 | REDUCE: (3), (5) imply: % 75.19/11.20 | (6) $false % 75.19/11.20 | % 75.19/11.20 | CLOSE: (6) is inconsistent. % 75.19/11.20 | % 75.19/11.20 End of proof % 75.19/11.20 % 75.19/11.20 Sub-proof #128 shows that the following formulas are inconsistent: % 75.19/11.20 ---------------------------------------------------------------- % 75.19/11.20 (1) all_10_8 = e3 % 75.19/11.20 (2) all_10_14 = e0 % 75.19/11.20 (3) ~ (all_4_10 = e3) % 75.19/11.20 (4) ~ (all_4_14 = e3) % 75.19/11.20 (5) all_10_4 = all_4_10 % 75.19/11.20 (6) ~ (all_4_16 = e2) % 75.19/11.20 (7) all_10_15 = e4 % 75.19/11.20 (8) all_10_5 = e2 % 75.19/11.20 (9) ~ (e3 = e1) % 75.19/11.20 (10) ~ (all_4_10 = all_4_14) % 75.19/11.20 (11) ~ (all_4_14 = e0) % 75.19/11.20 (12) ~ (all_4_14 = e4) % 75.19/11.20 (13) all_6_22 = e4 | all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 75.19/11.20 (14) all_10_23 = all_4_19 % 75.19/11.20 (15) ~ (all_4_10 = e0) % 75.19/11.20 (16) ~ (all_8_37 = e2) % 75.19/11.20 (17) op(e0, e1) = all_4_19 % 75.19/11.20 (18) ~ (e2 = e1) % 75.19/11.20 (19) all_10_22 = all_4_14 % 75.19/11.20 (20) all_10_10 = all_4_16 % 75.19/11.20 (21) ~ (e1 = e0) % 75.19/11.20 (22) op(e0, all_4_14) = all_8_37 % 75.19/11.20 (23) all_10_10 = e2 | all_10_11 = e2 | all_10_15 = e2 | all_10_23 = e2 % 75.19/11.20 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 75.19/11.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 75.19/11.20 (25) ~ (all_4_17 = e2) % 75.19/11.20 (26) all_6_2 = all_4_10 % 75.19/11.20 (27) all_6_22 = all_4_14 % 75.19/11.20 (28) ~ (e4 = e1) % 75.19/11.20 (29) all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | % 75.19/11.20 all_10_22 = e4 % 75.19/11.20 (30) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | all_6_2 = e0 % 75.19/11.20 (31) ~ (all_4_10 = e2) % 75.19/11.20 (32) all_10_11 = all_4_17 % 75.19/11.20 (33) all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 75.19/11.20 all_10_22 = e1 % 75.19/11.20 % 75.19/11.20 Begin of proof % 75.19/11.20 | % 75.19/11.20 | BETA: splitting (23) gives: % 75.19/11.20 | % 75.19/11.20 | Case 1: % 75.19/11.20 | | % 75.19/11.20 | | (34) all_10_10 = e2 % 75.19/11.20 | | % 75.19/11.20 | | COMBINE_EQS: (20), (34) imply: % 75.19/11.20 | | (35) all_4_16 = e2 % 75.19/11.20 | | % 75.19/11.20 | | REDUCE: (6), (35) imply: % 75.19/11.20 | | (36) $false % 75.19/11.20 | | % 75.19/11.20 | | CLOSE: (36) is inconsistent. % 75.19/11.20 | | % 75.19/11.20 | Case 2: % 75.19/11.20 | | % 75.19/11.20 | | (37) all_10_11 = e2 | all_10_15 = e2 | all_10_23 = e2 % 75.19/11.20 | | % 75.19/11.20 | | BETA: splitting (37) gives: % 75.19/11.20 | | % 75.19/11.20 | | Case 1: % 75.19/11.20 | | | % 75.19/11.20 | | | (38) all_10_11 = e2 % 75.19/11.20 | | | % 75.19/11.20 | | | COMBINE_EQS: (32), (38) imply: % 75.19/11.20 | | | (39) all_4_17 = e2 % 75.19/11.20 | | | % 75.19/11.20 | | | REDUCE: (25), (39) imply: % 75.19/11.20 | | | (40) $false % 75.19/11.20 | | | % 75.19/11.20 | | | CLOSE: (40) is inconsistent. % 75.19/11.20 | | | % 75.19/11.20 | | Case 2: % 75.19/11.20 | | | % 75.19/11.20 | | | (41) all_10_15 = e2 | all_10_23 = e2 % 75.19/11.20 | | | % 75.19/11.20 | | | BETA: splitting (13) gives: % 75.19/11.20 | | | % 75.19/11.20 | | | Case 1: % 75.19/11.20 | | | | % 75.19/11.20 | | | | (42) all_6_22 = e4 % 75.19/11.20 | | | | % 75.19/11.20 | | | | COMBINE_EQS: (27), (42) imply: % 75.19/11.20 | | | | (43) all_4_14 = e4 % 75.19/11.20 | | | | % 75.19/11.20 | | | | REDUCE: (12), (43) imply: % 75.19/11.20 | | | | (44) $false % 75.19/11.20 | | | | % 75.19/11.20 | | | | CLOSE: (44) is inconsistent. % 75.19/11.20 | | | | % 75.19/11.20 | | | Case 2: % 75.19/11.20 | | | | % 75.19/11.20 | | | | (45) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 75.19/11.20 | | | | % 75.19/11.20 | | | | BETA: splitting (29) gives: % 75.19/11.20 | | | | % 75.19/11.20 | | | | Case 1: % 75.19/11.20 | | | | | % 75.19/11.20 | | | | | (46) all_10_4 = e4 % 75.19/11.20 | | | | | % 75.19/11.20 | | | | | COMBINE_EQS: (5), (46) imply: % 75.19/11.20 | | | | | (47) all_4_10 = e4 % 75.19/11.20 | | | | | % 75.19/11.20 | | | | | REDUCE: (31), (47) imply: % 75.19/11.20 | | | | | (48) ~ (e4 = e2) % 75.19/11.20 | | | | | % 75.19/11.20 | | | | | BETA: splitting (33) gives: % 75.19/11.20 | | | | | % 75.19/11.20 | | | | | Case 1: % 75.19/11.20 | | | | | | % 75.19/11.20 | | | | | | (49) all_10_4 = e1 % 75.19/11.20 | | | | | | % 75.19/11.20 | | | | | | COMBINE_EQS: (46), (49) imply: % 75.19/11.20 | | | | | | (50) e4 = e1 % 75.19/11.20 | | | | | | % 75.19/11.20 | | | | | | REDUCE: (28), (50) imply: % 75.19/11.20 | | | | | | (51) $false % 75.19/11.20 | | | | | | % 75.19/11.20 | | | | | | CLOSE: (51) is inconsistent. % 75.19/11.20 | | | | | | % 75.19/11.20 | | | | | Case 2: % 75.19/11.20 | | | | | | % 75.19/11.20 | | | | | | (52) all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | all_10_22 = % 75.19/11.20 | | | | | | e1 % 75.19/11.20 | | | | | | % 75.19/11.20 | | | | | | BETA: splitting (52) gives: % 75.19/11.20 | | | | | | % 75.19/11.20 | | | | | | Case 1: % 75.19/11.20 | | | | | | | % 75.19/11.20 | | | | | | | (53) all_10_5 = e1 % 75.19/11.20 | | | | | | | % 75.19/11.20 | | | | | | | COMBINE_EQS: (8), (53) imply: % 75.19/11.20 | | | | | | | (54) e2 = e1 % 75.19/11.20 | | | | | | | % 75.19/11.20 | | | | | | | REDUCE: (18), (54) imply: % 75.19/11.20 | | | | | | | (55) $false % 75.19/11.20 | | | | | | | % 75.19/11.20 | | | | | | | CLOSE: (55) is inconsistent. % 75.19/11.20 | | | | | | | % 75.19/11.20 | | | | | | Case 2: % 75.19/11.20 | | | | | | | % 75.19/11.20 | | | | | | | (56) all_10_8 = e1 | all_10_14 = e1 | all_10_22 = e1 % 75.19/11.20 | | | | | | | % 75.19/11.20 | | | | | | | BETA: splitting (56) gives: % 75.19/11.20 | | | | | | | % 75.19/11.20 | | | | | | | Case 1: % 75.19/11.20 | | | | | | | | % 75.19/11.20 | | | | | | | | (57) all_10_8 = e1 % 75.19/11.20 | | | | | | | | % 75.19/11.20 | | | | | | | | COMBINE_EQS: (1), (57) imply: % 75.19/11.20 | | | | | | | | (58) e3 = e1 % 75.19/11.20 | | | | | | | | % 75.19/11.20 | | | | | | | | REDUCE: (9), (58) imply: % 75.19/11.20 | | | | | | | | (59) $false % 75.19/11.20 | | | | | | | | % 75.19/11.20 | | | | | | | | CLOSE: (59) is inconsistent. % 75.19/11.20 | | | | | | | | % 75.19/11.20 | | | | | | | Case 2: % 75.19/11.20 | | | | | | | | % 75.19/11.20 | | | | | | | | (60) all_10_14 = e1 | all_10_22 = e1 % 75.19/11.20 | | | | | | | | % 75.19/11.20 | | | | | | | | BETA: splitting (41) gives: % 75.19/11.20 | | | | | | | | % 75.19/11.20 | | | | | | | | Case 1: % 75.19/11.20 | | | | | | | | | % 75.19/11.20 | | | | | | | | | (61) all_10_15 = e2 % 75.19/11.20 | | | | | | | | | % 75.19/11.20 | | | | | | | | | COMBINE_EQS: (7), (61) imply: % 75.19/11.20 | | | | | | | | | (62) e4 = e2 % 75.19/11.20 | | | | | | | | | % 75.19/11.20 | | | | | | | | | REDUCE: (48), (62) imply: % 75.19/11.20 | | | | | | | | | (63) $false % 75.19/11.20 | | | | | | | | | % 75.19/11.20 | | | | | | | | | CLOSE: (63) is inconsistent. % 75.19/11.20 | | | | | | | | | % 75.19/11.20 | | | | | | | | Case 2: % 75.19/11.20 | | | | | | | | | % 75.19/11.20 | | | | | | | | | (64) all_10_23 = e2 % 75.19/11.20 | | | | | | | | | % 75.19/11.20 | | | | | | | | | COMBINE_EQS: (14), (64) imply: % 75.19/11.20 | | | | | | | | | (65) all_4_19 = e2 % 75.19/11.20 | | | | | | | | | % 75.19/11.20 | | | | | | | | | REDUCE: (17), (65) imply: % 75.19/11.20 | | | | | | | | | (66) op(e0, e1) = e2 % 75.19/11.20 | | | | | | | | | % 75.19/11.20 | | | | | | | | | BETA: splitting (60) gives: % 75.19/11.20 | | | | | | | | | % 75.19/11.20 | | | | | | | | | Case 1: % 75.19/11.20 | | | | | | | | | | % 75.19/11.20 | | | | | | | | | | (67) all_10_14 = e1 % 75.19/11.20 | | | | | | | | | | % 75.19/11.20 | | | | | | | | | | COMBINE_EQS: (2), (67) imply: % 75.19/11.20 | | | | | | | | | | (68) e1 = e0 % 75.19/11.20 | | | | | | | | | | % 75.19/11.20 | | | | | | | | | | REDUCE: (21), (68) imply: % 75.19/11.20 | | | | | | | | | | (69) $false % 75.19/11.20 | | | | | | | | | | % 75.19/11.20 | | | | | | | | | | CLOSE: (69) is inconsistent. % 75.19/11.20 | | | | | | | | | | % 75.19/11.20 | | | | | | | | | Case 2: % 75.19/11.20 | | | | | | | | | | % 75.19/11.20 | | | | | | | | | | (70) all_10_22 = e1 % 75.19/11.20 | | | | | | | | | | % 75.19/11.20 | | | | | | | | | | COMBINE_EQS: (19), (70) imply: % 75.19/11.20 | | | | | | | | | | (71) all_4_14 = e1 % 75.19/11.20 | | | | | | | | | | % 75.19/11.20 | | | | | | | | | | REDUCE: (22), (71) imply: % 75.19/11.20 | | | | | | | | | | (72) op(e0, e1) = all_8_37 % 75.19/11.20 | | | | | | | | | | % 75.19/11.20 | | | | | | | | | | GROUND_INST: instantiating (24) with e2, all_8_37, e1, e0, % 75.19/11.20 | | | | | | | | | | simplifying with (66), (72) gives: % 75.19/11.20 | | | | | | | | | | (73) all_8_37 = e2 % 75.19/11.20 | | | | | | | | | | % 75.19/11.20 | | | | | | | | | | REDUCE: (16), (73) imply: % 75.19/11.20 | | | | | | | | | | (74) $false % 75.19/11.20 | | | | | | | | | | % 75.19/11.20 | | | | | | | | | | CLOSE: (74) is inconsistent. % 75.19/11.20 | | | | | | | | | | % 75.19/11.20 | | | | | | | | | End of split % 75.19/11.20 | | | | | | | | | % 75.19/11.20 | | | | | | | | End of split % 75.19/11.20 | | | | | | | | % 75.19/11.20 | | | | | | | End of split % 75.19/11.20 | | | | | | | % 75.19/11.20 | | | | | | End of split % 75.19/11.20 | | | | | | % 75.19/11.20 | | | | | End of split % 75.19/11.20 | | | | | % 75.19/11.20 | | | | Case 2: % 75.19/11.20 | | | | | % 75.19/11.20 | | | | | (75) ~ (all_10_4 = e4) % 75.19/11.20 | | | | | % 75.19/11.20 | | | | | REDUCE: (5), (75) imply: % 75.19/11.20 | | | | | (76) ~ (all_4_10 = e4) % 75.19/11.20 | | | | | % 75.19/11.20 | | | | | REF_CLOSE: (3), (4), (10), (11), (15), (26), (27), (30), (31), (45), % 75.19/11.20 | | | | | (76) are inconsistent by sub-proof #129. % 75.19/11.20 | | | | | % 75.19/11.20 | | | | End of split % 75.19/11.20 | | | | % 75.19/11.20 | | | End of split % 75.19/11.20 | | | % 75.19/11.20 | | End of split % 75.19/11.20 | | % 75.19/11.20 | End of split % 75.19/11.20 | % 75.19/11.20 End of proof % 75.19/11.20 % 75.19/11.20 Sub-proof #129 shows that the following formulas are inconsistent: % 75.19/11.20 ---------------------------------------------------------------- % 75.19/11.20 (1) ~ (all_4_10 = e3) % 75.19/11.20 (2) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 75.19/11.20 (3) ~ (all_4_14 = e3) % 75.19/11.20 (4) ~ (all_4_10 = all_4_14) % 75.19/11.20 (5) ~ (all_4_14 = e0) % 75.19/11.20 (6) ~ (all_4_10 = e0) % 75.19/11.20 (7) ~ (all_4_10 = e4) % 75.19/11.20 (8) all_6_2 = all_4_10 % 75.19/11.20 (9) all_6_22 = all_4_14 % 75.19/11.20 (10) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | all_6_2 = e0 % 75.19/11.20 (11) ~ (all_4_10 = e2) % 75.19/11.20 % 75.19/11.20 Begin of proof % 75.19/11.20 | % 75.19/11.20 | BETA: splitting (10) gives: % 75.19/11.20 | % 75.19/11.20 | Case 1: % 75.19/11.20 | | % 75.19/11.20 | | (12) all_6_2 = e2 % 75.19/11.20 | | % 75.19/11.20 | | REF_CLOSE: (8), (11), (12) are inconsistent by sub-proof #168. % 75.19/11.20 | | % 75.19/11.20 | Case 2: % 75.19/11.20 | | % 75.19/11.20 | | (13) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 75.19/11.20 | | % 75.19/11.20 | | BETA: splitting (2) gives: % 75.19/11.20 | | % 75.19/11.20 | | Case 1: % 75.19/11.20 | | | % 75.19/11.20 | | | (14) all_6_22 = e1 % 75.19/11.20 | | | % 75.19/11.20 | | | COMBINE_EQS: (9), (14) imply: % 75.19/11.20 | | | (15) all_4_14 = e1 % 75.19/11.20 | | | % 75.19/11.20 | | | REDUCE: (4), (15) imply: % 75.19/11.20 | | | (16) ~ (all_4_10 = e1) % 75.19/11.20 | | | % 75.19/11.20 | | | REF_CLOSE: (1), (6), (7), (8), (13), (16) are inconsistent by sub-proof % 75.19/11.20 | | | #161. % 75.19/11.20 | | | % 75.19/11.20 | | Case 2: % 75.19/11.20 | | | % 75.19/11.20 | | | (17) all_6_22 = e3 | all_6_22 = e0 % 75.19/11.20 | | | % 75.19/11.20 | | | REF_CLOSE: (3), (5), (9), (17) are inconsistent by sub-proof #131. % 75.19/11.20 | | | % 75.19/11.20 | | End of split % 75.19/11.20 | | % 75.19/11.20 | End of split % 75.19/11.20 | % 75.19/11.20 End of proof % 75.19/11.20 % 75.19/11.20 Sub-proof #130 shows that the following formulas are inconsistent: % 75.19/11.20 ---------------------------------------------------------------- % 75.19/11.20 (1) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 75.19/11.20 (2) ~ (all_4_14 = e3) % 75.19/11.20 (3) ~ (all_4_14 = e0) % 75.19/11.20 (4) ~ (all_4_14 = e1) % 75.19/11.20 (5) all_6_22 = all_4_14 % 75.19/11.20 % 75.19/11.20 Begin of proof % 75.19/11.20 | % 75.19/11.20 | BETA: splitting (1) gives: % 75.19/11.20 | % 75.19/11.20 | Case 1: % 75.19/11.20 | | % 75.19/11.20 | | (6) all_6_22 = e1 % 75.19/11.20 | | % 75.19/11.20 | | COMBINE_EQS: (5), (6) imply: % 75.19/11.20 | | (7) all_4_14 = e1 % 75.19/11.20 | | % 75.19/11.20 | | SIMP: (7) implies: % 75.19/11.20 | | (8) all_4_14 = e1 % 75.19/11.20 | | % 75.19/11.20 | | REDUCE: (4), (8) imply: % 75.19/11.20 | | (9) $false % 75.19/11.20 | | % 75.19/11.20 | | CLOSE: (9) is inconsistent. % 75.19/11.20 | | % 75.19/11.20 | Case 2: % 75.19/11.20 | | % 75.19/11.20 | | (10) all_6_22 = e3 | all_6_22 = e0 % 75.19/11.20 | | % 75.19/11.20 | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #131. % 75.19/11.20 | | % 75.19/11.20 | End of split % 75.19/11.20 | % 75.19/11.20 End of proof % 75.19/11.20 % 75.19/11.20 Sub-proof #131 shows that the following formulas are inconsistent: % 75.19/11.20 ---------------------------------------------------------------- % 75.19/11.20 (1) all_6_22 = e3 | all_6_22 = e0 % 75.19/11.20 (2) all_6_22 = all_4_14 % 75.19/11.20 (3) ~ (all_4_14 = e3) % 75.19/11.20 (4) ~ (all_4_14 = e0) % 75.19/11.20 % 75.19/11.20 Begin of proof % 75.19/11.20 | % 75.19/11.20 | BETA: splitting (1) gives: % 75.19/11.20 | % 75.19/11.20 | Case 1: % 75.19/11.20 | | % 75.19/11.20 | | (5) all_6_22 = e3 % 75.19/11.20 | | % 75.19/11.20 | | COMBINE_EQS: (2), (5) imply: % 75.19/11.20 | | (6) all_4_14 = e3 % 75.19/11.20 | | % 75.19/11.20 | | SIMP: (6) implies: % 75.19/11.20 | | (7) all_4_14 = e3 % 75.19/11.20 | | % 75.19/11.20 | | REDUCE: (3), (7) imply: % 75.19/11.20 | | (8) $false % 75.19/11.20 | | % 75.19/11.20 | | CLOSE: (8) is inconsistent. % 75.19/11.20 | | % 75.19/11.20 | Case 2: % 75.19/11.20 | | % 75.19/11.20 | | (9) all_6_22 = e0 % 75.19/11.20 | | % 75.19/11.20 | | COMBINE_EQS: (2), (9) imply: % 75.19/11.20 | | (10) all_4_14 = e0 % 75.19/11.20 | | % 75.19/11.20 | | SIMP: (10) implies: % 75.19/11.20 | | (11) all_4_14 = e0 % 75.19/11.20 | | % 75.19/11.20 | | REDUCE: (4), (11) imply: % 75.19/11.20 | | (12) $false % 75.19/11.20 | | % 75.19/11.20 | | CLOSE: (12) is inconsistent. % 75.19/11.20 | | % 75.19/11.20 | End of split % 75.19/11.20 | % 75.19/11.20 End of proof % 75.19/11.20 % 75.19/11.20 Sub-proof #132 shows that the following formulas are inconsistent: % 75.19/11.20 ---------------------------------------------------------------- % 75.19/11.20 (1) ~ (all_4_7 = e4) % 75.19/11.20 (2) ~ (all_4_7 = e3) % 75.19/11.20 (3) ~ (all_4_7 = e0) % 75.19/11.20 (4) all_6_11 = e4 | all_6_11 = e3 | all_6_11 = e1 | all_6_11 = e0 % 75.19/11.20 (5) all_6_11 = all_4_7 % 75.19/11.20 (6) ~ (all_4_7 = e1) % 75.19/11.20 % 75.19/11.20 Begin of proof % 75.19/11.20 | % 75.19/11.20 | BETA: splitting (4) gives: % 75.19/11.20 | % 75.19/11.20 | Case 1: % 75.19/11.20 | | % 75.19/11.20 | | (7) all_6_11 = e4 % 75.19/11.20 | | % 75.19/11.20 | | COMBINE_EQS: (5), (7) imply: % 75.19/11.20 | | (8) all_4_7 = e4 % 75.19/11.20 | | % 75.19/11.20 | | SIMP: (8) implies: % 75.19/11.20 | | (9) all_4_7 = e4 % 75.19/11.20 | | % 75.19/11.20 | | REDUCE: (1), (9) imply: % 75.19/11.20 | | (10) $false % 75.19/11.20 | | % 75.19/11.20 | | CLOSE: (10) is inconsistent. % 75.19/11.20 | | % 75.19/11.20 | Case 2: % 75.19/11.20 | | % 75.19/11.20 | | (11) all_6_11 = e3 | all_6_11 = e1 | all_6_11 = e0 % 75.19/11.20 | | % 75.19/11.20 | | REF_CLOSE: (2), (3), (5), (6), (11) are inconsistent by sub-proof #133. % 75.19/11.20 | | % 75.19/11.20 | End of split % 75.19/11.20 | % 75.19/11.20 End of proof % 75.19/11.20 % 75.19/11.20 Sub-proof #133 shows that the following formulas are inconsistent: % 75.19/11.20 ---------------------------------------------------------------- % 75.19/11.21 (1) ~ (all_4_7 = e3) % 75.19/11.21 (2) ~ (all_4_7 = e0) % 75.19/11.21 (3) all_6_11 = e3 | all_6_11 = e1 | all_6_11 = e0 % 75.19/11.21 (4) all_6_11 = all_4_7 % 75.19/11.21 (5) ~ (all_4_7 = e1) % 75.19/11.21 % 75.19/11.21 Begin of proof % 75.19/11.21 | % 75.19/11.21 | BETA: splitting (3) gives: % 75.19/11.21 | % 75.19/11.21 | Case 1: % 75.19/11.21 | | % 75.19/11.21 | | (6) all_6_11 = e1 % 75.19/11.21 | | % 75.19/11.21 | | COMBINE_EQS: (4), (6) imply: % 75.19/11.21 | | (7) all_4_7 = e1 % 75.19/11.21 | | % 75.19/11.21 | | SIMP: (7) implies: % 75.19/11.21 | | (8) all_4_7 = e1 % 75.19/11.21 | | % 75.19/11.21 | | REDUCE: (5), (8) imply: % 75.19/11.21 | | (9) $false % 75.19/11.21 | | % 75.19/11.21 | | CLOSE: (9) is inconsistent. % 75.19/11.21 | | % 75.19/11.21 | Case 2: % 75.19/11.21 | | % 75.19/11.21 | | (10) all_6_11 = e3 | all_6_11 = e0 % 75.19/11.21 | | % 75.19/11.21 | | BETA: splitting (10) gives: % 75.19/11.21 | | % 75.19/11.21 | | Case 1: % 75.19/11.21 | | | % 75.19/11.21 | | | (11) all_6_11 = e3 % 75.19/11.21 | | | % 75.19/11.21 | | | COMBINE_EQS: (4), (11) imply: % 75.19/11.21 | | | (12) all_4_7 = e3 % 75.19/11.21 | | | % 75.19/11.21 | | | SIMP: (12) implies: % 75.19/11.21 | | | (13) all_4_7 = e3 % 75.19/11.21 | | | % 75.19/11.21 | | | REDUCE: (1), (13) imply: % 75.19/11.21 | | | (14) $false % 75.19/11.21 | | | % 75.19/11.21 | | | CLOSE: (14) is inconsistent. % 75.19/11.21 | | | % 75.19/11.21 | | Case 2: % 75.19/11.21 | | | % 75.19/11.21 | | | (15) all_6_11 = e0 % 75.19/11.21 | | | % 75.19/11.21 | | | COMBINE_EQS: (4), (15) imply: % 75.19/11.21 | | | (16) all_4_7 = e0 % 75.19/11.21 | | | % 75.19/11.21 | | | SIMP: (16) implies: % 75.19/11.21 | | | (17) all_4_7 = e0 % 75.19/11.21 | | | % 75.19/11.21 | | | REDUCE: (2), (17) imply: % 75.19/11.21 | | | (18) $false % 75.19/11.21 | | | % 75.19/11.21 | | | CLOSE: (18) is inconsistent. % 75.19/11.21 | | | % 75.19/11.21 | | End of split % 75.19/11.21 | | % 75.19/11.21 | End of split % 75.19/11.21 | % 75.19/11.21 End of proof % 75.19/11.21 % 75.19/11.21 Sub-proof #134 shows that the following formulas are inconsistent: % 75.19/11.21 ---------------------------------------------------------------- % 75.19/11.21 (1) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 75.19/11.21 (2) ~ (all_4_5 = e3) % 75.19/11.21 (3) ~ (all_4_5 = e1) % 75.19/11.21 (4) ~ (all_4_5 = e0) % 75.19/11.21 (5) ~ (all_4_5 = e4) % 75.19/11.21 (6) all_6_1 = all_4_5 % 75.19/11.21 % 75.19/11.21 Begin of proof % 75.19/11.21 | % 75.19/11.21 | BETA: splitting (1) gives: % 75.19/11.21 | % 75.19/11.21 | Case 1: % 75.19/11.21 | | % 75.19/11.21 | | (7) all_6_1 = e4 % 75.19/11.21 | | % 75.19/11.21 | | REF_CLOSE: (5), (6), (7) are inconsistent by sub-proof #138. % 75.19/11.21 | | % 75.19/11.21 | Case 2: % 75.19/11.21 | | % 75.19/11.21 | | (8) all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 75.19/11.21 | | % 75.19/11.21 | | REF_CLOSE: (2), (3), (4), (6), (8) are inconsistent by sub-proof #135. % 75.19/11.21 | | % 75.19/11.21 | End of split % 75.19/11.21 | % 75.19/11.21 End of proof % 75.19/11.21 % 75.19/11.21 Sub-proof #135 shows that the following formulas are inconsistent: % 75.19/11.21 ---------------------------------------------------------------- % 75.19/11.21 (1) ~ (all_4_5 = e3) % 75.19/11.21 (2) ~ (all_4_5 = e1) % 75.19/11.21 (3) all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 75.19/11.21 (4) ~ (all_4_5 = e0) % 75.19/11.21 (5) all_6_1 = all_4_5 % 75.19/11.21 % 75.19/11.21 Begin of proof % 75.19/11.21 | % 75.19/11.21 | BETA: splitting (3) gives: % 75.19/11.21 | % 75.19/11.21 | Case 1: % 75.19/11.21 | | % 75.19/11.21 | | (6) all_6_1 = e1 % 75.19/11.21 | | % 75.19/11.21 | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #137. % 75.19/11.21 | | % 75.19/11.21 | Case 2: % 75.19/11.21 | | % 75.19/11.21 | | (7) all_6_1 = e3 | all_6_1 = e0 % 75.19/11.21 | | % 75.19/11.21 | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #136. % 75.19/11.21 | | % 75.19/11.21 | End of split % 75.19/11.21 | % 75.19/11.21 End of proof % 75.19/11.21 % 75.19/11.21 Sub-proof #136 shows that the following formulas are inconsistent: % 75.19/11.21 ---------------------------------------------------------------- % 75.19/11.21 (1) all_6_1 = e3 | all_6_1 = e0 % 75.19/11.21 (2) all_6_1 = all_4_5 % 75.19/11.21 (3) ~ (all_4_5 = e3) % 75.19/11.21 (4) ~ (all_4_5 = e0) % 75.19/11.21 % 75.19/11.21 Begin of proof % 75.19/11.21 | % 75.19/11.21 | BETA: splitting (1) gives: % 75.19/11.21 | % 75.19/11.21 | Case 1: % 75.19/11.21 | | % 75.19/11.21 | | (5) all_6_1 = e3 % 75.19/11.21 | | % 75.19/11.21 | | COMBINE_EQS: (2), (5) imply: % 75.19/11.21 | | (6) all_4_5 = e3 % 75.19/11.21 | | % 75.19/11.21 | | SIMP: (6) implies: % 75.19/11.21 | | (7) all_4_5 = e3 % 75.19/11.21 | | % 75.19/11.21 | | REDUCE: (3), (7) imply: % 75.19/11.21 | | (8) $false % 75.19/11.21 | | % 75.19/11.21 | | CLOSE: (8) is inconsistent. % 75.19/11.21 | | % 75.19/11.21 | Case 2: % 75.19/11.21 | | % 75.19/11.21 | | (9) all_6_1 = e0 % 75.19/11.21 | | % 75.19/11.21 | | COMBINE_EQS: (2), (9) imply: % 75.19/11.21 | | (10) all_4_5 = e0 % 75.19/11.21 | | % 75.19/11.21 | | SIMP: (10) implies: % 75.19/11.21 | | (11) all_4_5 = e0 % 75.19/11.21 | | % 75.19/11.21 | | REDUCE: (4), (11) imply: % 75.19/11.21 | | (12) $false % 75.19/11.21 | | % 75.19/11.21 | | CLOSE: (12) is inconsistent. % 75.19/11.21 | | % 75.19/11.21 | End of split % 75.19/11.21 | % 75.19/11.21 End of proof % 75.19/11.21 % 75.19/11.21 Sub-proof #137 shows that the following formulas are inconsistent: % 75.19/11.21 ---------------------------------------------------------------- % 75.19/11.21 (1) all_6_1 = all_4_5 % 75.19/11.21 (2) all_6_1 = e1 % 75.19/11.21 (3) ~ (all_4_5 = e1) % 75.19/11.21 % 75.19/11.21 Begin of proof % 75.19/11.21 | % 75.19/11.21 | COMBINE_EQS: (1), (2) imply: % 75.19/11.21 | (4) all_4_5 = e1 % 75.19/11.21 | % 75.19/11.21 | SIMP: (4) implies: % 75.19/11.21 | (5) all_4_5 = e1 % 75.19/11.21 | % 75.19/11.21 | REDUCE: (3), (5) imply: % 75.19/11.21 | (6) $false % 75.19/11.21 | % 75.19/11.21 | CLOSE: (6) is inconsistent. % 75.19/11.21 | % 75.19/11.21 End of proof % 75.19/11.21 % 75.19/11.21 Sub-proof #138 shows that the following formulas are inconsistent: % 75.19/11.21 ---------------------------------------------------------------- % 75.19/11.21 (1) all_6_1 = all_4_5 % 75.19/11.21 (2) all_6_1 = e4 % 75.19/11.21 (3) ~ (all_4_5 = e4) % 75.19/11.21 % 75.19/11.21 Begin of proof % 75.19/11.21 | % 75.19/11.21 | COMBINE_EQS: (1), (2) imply: % 75.19/11.21 | (4) all_4_5 = e4 % 75.19/11.21 | % 75.19/11.21 | SIMP: (4) implies: % 75.19/11.21 | (5) all_4_5 = e4 % 75.19/11.21 | % 75.19/11.21 | REDUCE: (3), (5) imply: % 75.19/11.21 | (6) $false % 75.19/11.21 | % 75.19/11.21 | CLOSE: (6) is inconsistent. % 75.19/11.21 | % 75.19/11.21 End of proof % 75.19/11.21 % 75.19/11.21 Sub-proof #139 shows that the following formulas are inconsistent: % 75.19/11.21 ---------------------------------------------------------------- % 75.19/11.21 (1) ~ (all_4_1 = e0) % 75.19/11.21 (2) ~ (all_4_20 = e1) % 75.19/11.21 (3) ~ (all_4_15 = all_4_20) % 75.19/11.21 (4) all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e1 | all_6_5 = e0 % 75.19/11.21 (5) ~ (e3 = e2) % 75.19/11.21 (6) all_10_1 = all_4_5 % 75.19/11.21 (7) all_10_16 = e4 | all_10_17 = e4 | all_10_18 = e4 | all_10_19 = e4 | % 75.19/11.21 all_10_24 = e4 % 75.19/11.21 (8) all_10_1 = e0 % 75.19/11.21 (9) ~ (all_4_1 = e3) % 75.19/11.21 (10) all_10_16 = all_4_20 % 75.19/11.21 (11) ~ (all_4_5 = all_4_15) % 75.19/11.21 (12) op(e4, e4) = e2 % 75.19/11.21 (13) ~ (all_4_5 = all_4_20) % 75.19/11.21 (14) all_6_5 = all_4_1 % 75.19/11.21 (15) all_10_9 = e3 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 75.19/11.21 all_10_23 = e3 % 75.19/11.21 (16) ~ (all_4_1 = e1) % 75.19/11.21 (17) all_6_3 = all_4_15 % 75.19/11.21 (18) all_6_3 = e4 | all_6_3 = e3 | all_6_3 = e1 | all_6_3 = e0 % 75.19/11.21 (19) op(e4, all_4_20) = all_8_53 % 75.19/11.21 (20) all_6_4 = e4 | all_6_4 = e3 | all_6_4 = e1 | all_6_4 = e0 % 75.19/11.21 (21) all_10_9 = all_4_15 % 75.19/11.21 (22) all_6_4 = all_4_20 % 75.19/11.21 (23) op(e4, all_4_1) = e3 % 75.19/11.21 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 75.19/11.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 75.19/11.21 (25) ~ (all_4_15 = e1) % 75.19/11.21 (26) ~ (all_4_15 = e4) % 75.19/11.21 % 75.19/11.21 Begin of proof % 75.19/11.21 | % 75.19/11.21 | COMBINE_EQS: (6), (8) imply: % 75.19/11.21 | (27) all_4_5 = e0 % 75.19/11.21 | % 75.19/11.21 | REDUCE: (11), (27) imply: % 75.19/11.21 | (28) ~ (all_4_15 = e0) % 75.19/11.21 | % 75.19/11.21 | SIMP: (28) implies: % 75.19/11.21 | (29) ~ (all_4_15 = e0) % 75.19/11.21 | % 75.19/11.21 | REDUCE: (13), (27) imply: % 75.19/11.21 | (30) ~ (all_4_20 = e0) % 75.19/11.21 | % 75.19/11.21 | SIMP: (30) implies: % 75.19/11.21 | (31) ~ (all_4_20 = e0) % 75.19/11.21 | % 75.19/11.21 | BETA: splitting (4) gives: % 75.19/11.21 | % 75.19/11.21 | Case 1: % 75.19/11.21 | | % 75.19/11.21 | | (32) all_6_5 = e4 % 75.19/11.21 | | % 75.19/11.21 | | COMBINE_EQS: (14), (32) imply: % 75.19/11.21 | | (33) all_4_1 = e4 % 75.19/11.21 | | % 75.19/11.21 | | SIMP: (33) implies: % 75.19/11.21 | | (34) all_4_1 = e4 % 75.19/11.21 | | % 75.19/11.21 | | REDUCE: (23), (34) imply: % 75.19/11.21 | | (35) op(e4, e4) = e3 % 75.19/11.21 | | % 75.19/11.21 | | BETA: splitting (7) gives: % 75.19/11.21 | | % 75.19/11.21 | | Case 1: % 75.19/11.21 | | | % 75.19/11.21 | | | (36) all_10_16 = e4 % 75.19/11.21 | | | % 75.19/11.21 | | | COMBINE_EQS: (10), (36) imply: % 75.19/11.21 | | | (37) all_4_20 = e4 % 75.19/11.21 | | | % 75.19/11.21 | | | REDUCE: (19), (37) imply: % 75.19/11.21 | | | (38) op(e4, e4) = all_8_53 % 75.19/11.21 | | | % 75.19/11.21 | | | GROUND_INST: instantiating (24) with e2, all_8_53, e4, e4, simplifying % 75.19/11.21 | | | with (12), (38) gives: % 75.19/11.21 | | | (39) all_8_53 = e2 % 75.19/11.21 | | | % 75.19/11.21 | | | GROUND_INST: instantiating (24) with e3, all_8_53, e4, e4, simplifying % 75.19/11.21 | | | with (35), (38) gives: % 75.19/11.21 | | | (40) all_8_53 = e3 % 75.19/11.21 | | | % 75.19/11.21 | | | COMBINE_EQS: (39), (40) imply: % 75.19/11.21 | | | (41) e3 = e2 % 75.19/11.21 | | | % 75.19/11.21 | | | SIMP: (41) implies: % 75.19/11.21 | | | (42) e3 = e2 % 75.19/11.21 | | | % 75.19/11.21 | | | REDUCE: (5), (42) imply: % 75.19/11.21 | | | (43) $false % 75.19/11.21 | | | % 75.19/11.21 | | | CLOSE: (43) is inconsistent. % 75.19/11.21 | | | % 75.19/11.21 | | Case 2: % 75.19/11.21 | | | % 75.19/11.21 | | | (44) ~ (all_10_16 = e4) % 75.19/11.21 | | | % 75.19/11.21 | | | REDUCE: (10), (44) imply: % 75.19/11.21 | | | (45) ~ (all_4_20 = e4) % 75.19/11.21 | | | % 75.19/11.21 | | | REF_CLOSE: (2), (3), (15), (17), (18), (20), (21), (22), (25), (26), (29), % 75.19/11.21 | | | (31), (45) are inconsistent by sub-proof #143. % 75.19/11.21 | | | % 75.19/11.21 | | End of split % 75.19/11.21 | | % 75.19/11.21 | Case 2: % 75.19/11.21 | | % 75.19/11.21 | | (46) all_6_5 = e3 | all_6_5 = e1 | all_6_5 = e0 % 75.19/11.21 | | % 75.19/11.21 | | REF_CLOSE: (1), (9), (14), (16), (46) are inconsistent by sub-proof #140. % 75.19/11.21 | | % 75.19/11.21 | End of split % 75.19/11.21 | % 75.19/11.21 End of proof % 75.19/11.21 % 75.19/11.21 Sub-proof #140 shows that the following formulas are inconsistent: % 75.19/11.21 ---------------------------------------------------------------- % 75.19/11.21 (1) ~ (all_4_1 = e0) % 75.19/11.21 (2) ~ (all_4_1 = e3) % 75.19/11.21 (3) all_6_5 = all_4_1 % 75.19/11.21 (4) ~ (all_4_1 = e1) % 75.19/11.21 (5) all_6_5 = e3 | all_6_5 = e1 | all_6_5 = e0 % 75.19/11.21 % 75.19/11.21 Begin of proof % 75.19/11.21 | % 75.19/11.21 | BETA: splitting (5) gives: % 75.19/11.21 | % 75.19/11.21 | Case 1: % 75.19/11.21 | | % 75.19/11.21 | | (6) all_6_5 = e1 % 75.19/11.21 | | % 75.19/11.21 | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #142. % 75.19/11.21 | | % 75.19/11.21 | Case 2: % 75.19/11.21 | | % 75.19/11.21 | | (7) all_6_5 = e3 | all_6_5 = e0 % 75.19/11.21 | | % 75.19/11.21 | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #141. % 75.19/11.21 | | % 75.19/11.21 | End of split % 75.19/11.21 | % 75.19/11.21 End of proof % 75.19/11.21 % 75.19/11.21 Sub-proof #141 shows that the following formulas are inconsistent: % 75.19/11.21 ---------------------------------------------------------------- % 75.19/11.21 (1) all_6_5 = e3 | all_6_5 = e0 % 75.19/11.21 (2) all_6_5 = all_4_1 % 75.19/11.21 (3) ~ (all_4_1 = e3) % 75.19/11.21 (4) ~ (all_4_1 = e0) % 75.19/11.21 % 75.19/11.21 Begin of proof % 75.19/11.21 | % 75.19/11.21 | BETA: splitting (1) gives: % 75.19/11.21 | % 75.19/11.21 | Case 1: % 75.19/11.21 | | % 75.19/11.21 | | (5) all_6_5 = e3 % 75.19/11.21 | | % 75.19/11.21 | | COMBINE_EQS: (2), (5) imply: % 75.19/11.21 | | (6) all_4_1 = e3 % 75.19/11.21 | | % 75.19/11.21 | | SIMP: (6) implies: % 75.19/11.21 | | (7) all_4_1 = e3 % 75.19/11.21 | | % 75.19/11.21 | | REDUCE: (3), (7) imply: % 75.19/11.21 | | (8) $false % 75.19/11.21 | | % 75.19/11.21 | | CLOSE: (8) is inconsistent. % 75.19/11.21 | | % 75.19/11.21 | Case 2: % 75.19/11.21 | | % 75.19/11.21 | | (9) all_6_5 = e0 % 75.19/11.21 | | % 75.19/11.21 | | COMBINE_EQS: (2), (9) imply: % 75.19/11.21 | | (10) all_4_1 = e0 % 75.19/11.21 | | % 75.19/11.21 | | SIMP: (10) implies: % 75.19/11.21 | | (11) all_4_1 = e0 % 75.19/11.21 | | % 75.19/11.21 | | REDUCE: (4), (11) imply: % 75.19/11.21 | | (12) $false % 75.19/11.21 | | % 75.19/11.21 | | CLOSE: (12) is inconsistent. % 75.19/11.21 | | % 75.19/11.21 | End of split % 75.19/11.21 | % 75.19/11.21 End of proof % 75.19/11.21 % 75.19/11.21 Sub-proof #142 shows that the following formulas are inconsistent: % 75.19/11.21 ---------------------------------------------------------------- % 75.19/11.21 (1) all_6_5 = all_4_1 % 75.19/11.21 (2) all_6_5 = e1 % 75.19/11.21 (3) ~ (all_4_1 = e1) % 75.19/11.21 % 75.19/11.21 Begin of proof % 75.19/11.21 | % 75.19/11.21 | COMBINE_EQS: (1), (2) imply: % 75.19/11.21 | (4) all_4_1 = e1 % 75.19/11.21 | % 75.19/11.21 | SIMP: (4) implies: % 75.19/11.21 | (5) all_4_1 = e1 % 75.19/11.21 | % 75.19/11.21 | REDUCE: (3), (5) imply: % 75.19/11.21 | (6) $false % 75.19/11.21 | % 75.19/11.21 | CLOSE: (6) is inconsistent. % 75.19/11.21 | % 75.19/11.21 End of proof % 75.19/11.21 % 75.19/11.21 Sub-proof #143 shows that the following formulas are inconsistent: % 75.19/11.21 ---------------------------------------------------------------- % 75.19/11.21 (1) ~ (all_4_20 = e1) % 75.19/11.21 (2) ~ (all_4_15 = all_4_20) % 75.19/11.21 (3) ~ (all_4_15 = e0) % 75.19/11.21 (4) ~ (all_4_20 = e4) % 75.19/11.21 (5) all_10_9 = e3 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 75.19/11.21 all_10_23 = e3 % 75.19/11.21 (6) all_6_3 = all_4_15 % 75.19/11.21 (7) all_6_3 = e4 | all_6_3 = e3 | all_6_3 = e1 | all_6_3 = e0 % 75.19/11.21 (8) all_6_4 = e4 | all_6_4 = e3 | all_6_4 = e1 | all_6_4 = e0 % 75.19/11.21 (9) all_10_9 = all_4_15 % 75.19/11.21 (10) all_6_4 = all_4_20 % 75.19/11.21 (11) ~ (all_4_20 = e0) % 75.19/11.21 (12) ~ (all_4_15 = e1) % 75.19/11.21 (13) ~ (all_4_15 = e4) % 75.19/11.21 % 75.19/11.21 Begin of proof % 75.19/11.21 | % 75.19/11.21 | BETA: splitting (7) gives: % 75.19/11.21 | % 75.19/11.21 | Case 1: % 75.19/11.21 | | % 75.19/11.21 | | (14) all_6_3 = e4 % 75.19/11.21 | | % 75.19/11.21 | | REF_CLOSE: (6), (13), (14) are inconsistent by sub-proof #149. % 75.19/11.21 | | % 75.19/11.21 | Case 2: % 75.19/11.21 | | % 75.19/11.21 | | (15) all_6_3 = e3 | all_6_3 = e1 | all_6_3 = e0 % 75.19/11.21 | | % 75.19/11.21 | | BETA: splitting (8) gives: % 75.19/11.21 | | % 75.19/11.21 | | Case 1: % 75.19/11.21 | | | % 75.19/11.21 | | | (16) all_6_4 = e4 % 75.19/11.21 | | | % 75.19/11.21 | | | COMBINE_EQS: (10), (16) imply: % 75.19/11.21 | | | (17) all_4_20 = e4 % 75.19/11.21 | | | % 75.19/11.21 | | | SIMP: (17) implies: % 75.19/11.21 | | | (18) all_4_20 = e4 % 75.19/11.21 | | | % 75.19/11.21 | | | REDUCE: (4), (18) imply: % 75.19/11.21 | | | (19) $false % 75.19/11.21 | | | % 75.19/11.21 | | | CLOSE: (19) is inconsistent. % 75.19/11.21 | | | % 75.19/11.21 | | Case 2: % 75.19/11.21 | | | % 75.19/11.21 | | | (20) all_6_4 = e3 | all_6_4 = e1 | all_6_4 = e0 % 75.19/11.21 | | | % 75.19/11.21 | | | BETA: splitting (20) gives: % 75.19/11.21 | | | % 75.19/11.21 | | | Case 1: % 75.19/11.21 | | | | % 75.19/11.21 | | | | (21) all_6_4 = e1 % 75.19/11.21 | | | | % 75.19/11.21 | | | | REF_CLOSE: (1), (10), (21) are inconsistent by sub-proof #148. % 75.19/11.21 | | | | % 75.19/11.21 | | | Case 2: % 75.19/11.21 | | | | % 75.19/11.21 | | | | (22) all_6_4 = e3 | all_6_4 = e0 % 75.19/11.21 | | | | % 75.19/11.21 | | | | BETA: splitting (5) gives: % 75.19/11.21 | | | | % 75.19/11.21 | | | | Case 1: % 75.19/11.21 | | | | | % 75.19/11.21 | | | | | (23) all_10_9 = e3 % 75.19/11.21 | | | | | % 75.19/11.21 | | | | | COMBINE_EQS: (9), (23) imply: % 75.19/11.21 | | | | | (24) all_4_15 = e3 % 75.19/11.21 | | | | | % 75.19/11.21 | | | | | REDUCE: (2), (24) imply: % 75.19/11.21 | | | | | (25) ~ (all_4_20 = e3) % 75.19/11.21 | | | | | % 75.19/11.21 | | | | | SIMP: (25) implies: % 75.19/11.21 | | | | | (26) ~ (all_4_20 = e3) % 75.19/11.21 | | | | | % 75.19/11.21 | | | | | REF_CLOSE: (10), (11), (22), (26) are inconsistent by sub-proof #147. % 75.19/11.21 | | | | | % 75.19/11.21 | | | | Case 2: % 75.19/11.21 | | | | | % 75.19/11.21 | | | | | (27) ~ (all_10_9 = e3) % 75.19/11.21 | | | | | % 75.19/11.21 | | | | | REF_CLOSE: (3), (6), (9), (12), (15), (27) are inconsistent by % 75.19/11.21 | | | | | sub-proof #144. % 75.19/11.21 | | | | | % 75.19/11.21 | | | | End of split % 75.19/11.21 | | | | % 75.19/11.21 | | | End of split % 75.19/11.21 | | | % 75.19/11.21 | | End of split % 75.19/11.21 | | % 75.19/11.21 | End of split % 75.19/11.21 | % 75.19/11.21 End of proof % 75.19/11.21 % 75.19/11.21 Sub-proof #144 shows that the following formulas are inconsistent: % 75.19/11.21 ---------------------------------------------------------------- % 75.19/11.21 (1) ~ (all_4_15 = e0) % 75.19/11.21 (2) all_6_3 = e3 | all_6_3 = e1 | all_6_3 = e0 % 75.19/11.21 (3) all_6_3 = all_4_15 % 75.19/11.21 (4) all_10_9 = all_4_15 % 75.19/11.21 (5) ~ (all_10_9 = e3) % 75.19/11.21 (6) ~ (all_4_15 = e1) % 75.19/11.21 % 75.19/11.21 Begin of proof % 75.19/11.21 | % 75.19/11.21 | REDUCE: (4), (5) imply: % 75.19/11.21 | (7) ~ (all_4_15 = e3) % 75.19/11.21 | % 75.19/11.21 | BETA: splitting (2) gives: % 75.19/11.21 | % 75.19/11.21 | Case 1: % 75.19/11.21 | | % 75.19/11.21 | | (8) all_6_3 = e1 % 75.19/11.21 | | % 75.19/11.21 | | REF_CLOSE: (3), (6), (8) are inconsistent by sub-proof #146. % 75.19/11.21 | | % 75.19/11.21 | Case 2: % 75.19/11.21 | | % 75.19/11.22 | | (9) all_6_3 = e3 | all_6_3 = e0 % 75.19/11.22 | | % 75.19/11.22 | | BETA: splitting (9) gives: % 75.19/11.22 | | % 75.19/11.22 | | Case 1: % 75.19/11.22 | | | % 75.19/11.22 | | | (10) all_6_3 = e3 % 75.19/11.22 | | | % 75.19/11.22 | | | COMBINE_EQS: (3), (10) imply: % 75.19/11.22 | | | (11) all_4_15 = e3 % 75.19/11.22 | | | % 75.19/11.22 | | | SIMP: (11) implies: % 75.19/11.22 | | | (12) all_4_15 = e3 % 75.19/11.22 | | | % 75.19/11.22 | | | REDUCE: (7), (12) imply: % 75.19/11.22 | | | (13) $false % 75.19/11.22 | | | % 75.19/11.22 | | | CLOSE: (13) is inconsistent. % 75.19/11.22 | | | % 75.19/11.22 | | Case 2: % 75.19/11.22 | | | % 75.19/11.22 | | | (14) all_6_3 = e0 % 75.19/11.22 | | | % 75.19/11.22 | | | REF_CLOSE: (1), (3), (14) are inconsistent by sub-proof #145. % 75.19/11.22 | | | % 75.19/11.22 | | End of split % 75.19/11.22 | | % 75.19/11.22 | End of split % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #145 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) all_6_3 = all_4_15 % 75.19/11.22 (2) all_6_3 = e0 % 75.19/11.22 (3) ~ (all_4_15 = e0) % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | COMBINE_EQS: (1), (2) imply: % 75.19/11.22 | (4) all_4_15 = e0 % 75.19/11.22 | % 75.19/11.22 | SIMP: (4) implies: % 75.19/11.22 | (5) all_4_15 = e0 % 75.19/11.22 | % 75.19/11.22 | REDUCE: (3), (5) imply: % 75.19/11.22 | (6) $false % 75.19/11.22 | % 75.19/11.22 | CLOSE: (6) is inconsistent. % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #146 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) all_6_3 = all_4_15 % 75.19/11.22 (2) all_6_3 = e1 % 75.19/11.22 (3) ~ (all_4_15 = e1) % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | COMBINE_EQS: (1), (2) imply: % 75.19/11.22 | (4) all_4_15 = e1 % 75.19/11.22 | % 75.19/11.22 | SIMP: (4) implies: % 75.19/11.22 | (5) all_4_15 = e1 % 75.19/11.22 | % 75.19/11.22 | REDUCE: (3), (5) imply: % 75.19/11.22 | (6) $false % 75.19/11.22 | % 75.19/11.22 | CLOSE: (6) is inconsistent. % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #147 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) all_6_4 = e3 | all_6_4 = e0 % 75.19/11.22 (2) all_6_4 = all_4_20 % 75.19/11.22 (3) ~ (all_4_20 = e3) % 75.19/11.22 (4) ~ (all_4_20 = e0) % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | BETA: splitting (1) gives: % 75.19/11.22 | % 75.19/11.22 | Case 1: % 75.19/11.22 | | % 75.19/11.22 | | (5) all_6_4 = e3 % 75.19/11.22 | | % 75.19/11.22 | | COMBINE_EQS: (2), (5) imply: % 75.19/11.22 | | (6) all_4_20 = e3 % 75.19/11.22 | | % 75.19/11.22 | | SIMP: (6) implies: % 75.19/11.22 | | (7) all_4_20 = e3 % 75.19/11.22 | | % 75.19/11.22 | | REDUCE: (3), (7) imply: % 75.19/11.22 | | (8) $false % 75.19/11.22 | | % 75.19/11.22 | | CLOSE: (8) is inconsistent. % 75.19/11.22 | | % 75.19/11.22 | Case 2: % 75.19/11.22 | | % 75.19/11.22 | | (9) all_6_4 = e0 % 75.19/11.22 | | % 75.19/11.22 | | COMBINE_EQS: (2), (9) imply: % 75.19/11.22 | | (10) all_4_20 = e0 % 75.19/11.22 | | % 75.19/11.22 | | SIMP: (10) implies: % 75.19/11.22 | | (11) all_4_20 = e0 % 75.19/11.22 | | % 75.19/11.22 | | REDUCE: (4), (11) imply: % 75.19/11.22 | | (12) $false % 75.19/11.22 | | % 75.19/11.22 | | CLOSE: (12) is inconsistent. % 75.19/11.22 | | % 75.19/11.22 | End of split % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #148 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) all_6_4 = all_4_20 % 75.19/11.22 (2) all_6_4 = e1 % 75.19/11.22 (3) ~ (all_4_20 = e1) % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | COMBINE_EQS: (1), (2) imply: % 75.19/11.22 | (4) all_4_20 = e1 % 75.19/11.22 | % 75.19/11.22 | SIMP: (4) implies: % 75.19/11.22 | (5) all_4_20 = e1 % 75.19/11.22 | % 75.19/11.22 | REDUCE: (3), (5) imply: % 75.19/11.22 | (6) $false % 75.19/11.22 | % 75.19/11.22 | CLOSE: (6) is inconsistent. % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #149 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) all_6_3 = all_4_15 % 75.19/11.22 (2) all_6_3 = e4 % 75.19/11.22 (3) ~ (all_4_15 = e4) % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | COMBINE_EQS: (1), (2) imply: % 75.19/11.22 | (4) all_4_15 = e4 % 75.19/11.22 | % 75.19/11.22 | SIMP: (4) implies: % 75.19/11.22 | (5) all_4_15 = e4 % 75.19/11.22 | % 75.19/11.22 | REDUCE: (3), (5) imply: % 75.19/11.22 | (6) $false % 75.19/11.22 | % 75.19/11.22 | CLOSE: (6) is inconsistent. % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #150 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) all_10_6 = e4 % 75.19/11.22 (2) all_10_6 = e0 % 75.19/11.22 (3) ~ (e4 = e0) % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | COMBINE_EQS: (1), (2) imply: % 75.19/11.22 | (4) e4 = e0 % 75.19/11.22 | % 75.19/11.22 | SIMP: (4) implies: % 75.19/11.22 | (5) e4 = e0 % 75.19/11.22 | % 75.19/11.22 | REDUCE: (3), (5) imply: % 75.19/11.22 | (6) $false % 75.19/11.22 | % 75.19/11.22 | CLOSE: (6) is inconsistent. % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #151 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) all_10_20 = e3 % 75.19/11.22 (2) all_10_20 = e1 % 75.19/11.22 (3) ~ (e3 = e1) % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | COMBINE_EQS: (1), (2) imply: % 75.19/11.22 | (4) e3 = e1 % 75.19/11.22 | % 75.19/11.22 | SIMP: (4) implies: % 75.19/11.22 | (5) e3 = e1 % 75.19/11.22 | % 75.19/11.22 | REDUCE: (3), (5) imply: % 75.19/11.22 | (6) $false % 75.19/11.22 | % 75.19/11.22 | CLOSE: (6) is inconsistent. % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #152 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) all_6_3 = all_4_15 % 75.19/11.22 (2) all_6_3 = e2 % 75.19/11.22 (3) ~ (all_4_15 = e2) % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | COMBINE_EQS: (1), (2) imply: % 75.19/11.22 | (4) all_4_15 = e2 % 75.19/11.22 | % 75.19/11.22 | SIMP: (4) implies: % 75.19/11.22 | (5) all_4_15 = e2 % 75.19/11.22 | % 75.19/11.22 | REDUCE: (3), (5) imply: % 75.19/11.22 | (6) $false % 75.19/11.22 | % 75.19/11.22 | CLOSE: (6) is inconsistent. % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #153 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) all_6_5 = all_4_1 % 75.19/11.22 (2) all_6_5 = e2 % 75.19/11.22 (3) ~ (all_4_1 = e2) % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | COMBINE_EQS: (1), (2) imply: % 75.19/11.22 | (4) all_4_1 = e2 % 75.19/11.22 | % 75.19/11.22 | SIMP: (4) implies: % 75.19/11.22 | (5) all_4_1 = e2 % 75.19/11.22 | % 75.19/11.22 | REDUCE: (3), (5) imply: % 75.19/11.22 | (6) $false % 75.19/11.22 | % 75.19/11.22 | CLOSE: (6) is inconsistent. % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #154 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) all_6_4 = all_4_20 % 75.19/11.22 (2) all_6_4 = e2 % 75.19/11.22 (3) ~ (all_4_20 = e2) % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | COMBINE_EQS: (1), (2) imply: % 75.19/11.22 | (4) all_4_20 = e2 % 75.19/11.22 | % 75.19/11.22 | SIMP: (4) implies: % 75.19/11.22 | (5) all_4_20 = e2 % 75.19/11.22 | % 75.19/11.22 | REDUCE: (3), (5) imply: % 75.19/11.22 | (6) $false % 75.19/11.22 | % 75.19/11.22 | CLOSE: (6) is inconsistent. % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #155 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) all_6_1 = all_4_5 % 75.19/11.22 (2) all_6_1 = e2 % 75.19/11.22 (3) ~ (all_4_5 = e2) % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | COMBINE_EQS: (1), (2) imply: % 75.19/11.22 | (4) all_4_5 = e2 % 75.19/11.22 | % 75.19/11.22 | SIMP: (4) implies: % 75.19/11.22 | (5) all_4_5 = e2 % 75.19/11.22 | % 75.19/11.22 | REDUCE: (3), (5) imply: % 75.19/11.22 | (6) $false % 75.19/11.22 | % 75.19/11.22 | CLOSE: (6) is inconsistent. % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #156 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) all_6_22 = all_4_14 % 75.19/11.22 (2) all_6_22 = e2 % 75.19/11.22 (3) ~ (all_4_14 = e2) % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | COMBINE_EQS: (1), (2) imply: % 75.19/11.22 | (4) all_4_14 = e2 % 75.19/11.22 | % 75.19/11.22 | SIMP: (4) implies: % 75.19/11.22 | (5) all_4_14 = e2 % 75.19/11.22 | % 75.19/11.22 | REDUCE: (3), (5) imply: % 75.19/11.22 | (6) $false % 75.19/11.22 | % 75.19/11.22 | CLOSE: (6) is inconsistent. % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #157 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) all_6_21 = all_4_9 % 75.19/11.22 (2) all_6_21 = e2 % 75.19/11.22 (3) ~ (all_4_9 = e2) % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | COMBINE_EQS: (1), (2) imply: % 75.19/11.22 | (4) all_4_9 = e2 % 75.19/11.22 | % 75.19/11.22 | SIMP: (4) implies: % 75.19/11.22 | (5) all_4_9 = e2 % 75.19/11.22 | % 75.19/11.22 | REDUCE: (3), (5) imply: % 75.19/11.22 | (6) $false % 75.19/11.22 | % 75.19/11.22 | CLOSE: (6) is inconsistent. % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #158 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) all_6_9 = all_4_21 % 75.19/11.22 (2) all_6_9 = e2 % 75.19/11.22 (3) ~ (all_4_21 = e2) % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | COMBINE_EQS: (1), (2) imply: % 75.19/11.22 | (4) all_4_21 = e2 % 75.19/11.22 | % 75.19/11.22 | SIMP: (4) implies: % 75.19/11.22 | (5) all_4_21 = e2 % 75.19/11.22 | % 75.19/11.22 | REDUCE: (3), (5) imply: % 75.19/11.22 | (6) $false % 75.19/11.22 | % 75.19/11.22 | CLOSE: (6) is inconsistent. % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #159 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) all_6_11 = all_4_7 % 75.19/11.22 (2) all_6_11 = e2 % 75.19/11.22 (3) ~ (all_4_7 = e2) % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | COMBINE_EQS: (1), (2) imply: % 75.19/11.22 | (4) all_4_7 = e2 % 75.19/11.22 | % 75.19/11.22 | SIMP: (4) implies: % 75.19/11.22 | (5) all_4_7 = e2 % 75.19/11.22 | % 75.19/11.22 | REDUCE: (3), (5) imply: % 75.19/11.22 | (6) $false % 75.19/11.22 | % 75.19/11.22 | CLOSE: (6) is inconsistent. % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #160 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) ~ (all_4_10 = e1) % 75.19/11.22 (2) ~ (all_4_10 = e3) % 75.19/11.22 (3) all_10_4 = all_4_10 % 75.19/11.22 (4) ~ (all_4_10 = e0) % 75.19/11.22 (5) op(e4, e4) = e2 % 75.19/11.22 (6) ~ (all_8_27 = e2) % 75.19/11.22 (7) op(e4, all_4_10) = all_8_27 % 75.19/11.22 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 75.19/11.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 75.19/11.22 (9) all_6_2 = all_4_10 % 75.19/11.22 (10) all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 | all_10_14 = e4 | % 75.19/11.22 all_10_22 = e4 % 75.19/11.22 (11) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | BETA: splitting (10) gives: % 75.19/11.22 | % 75.19/11.22 | Case 1: % 75.19/11.22 | | % 75.19/11.22 | | (12) all_10_4 = e4 % 75.19/11.22 | | % 75.19/11.22 | | REF_CLOSE: (3), (5), (6), (7), (8), (12) are inconsistent by sub-proof #165. % 75.19/11.22 | | % 75.19/11.22 | Case 2: % 75.19/11.22 | | % 75.19/11.22 | | (13) ~ (all_10_4 = e4) % 75.19/11.22 | | % 75.19/11.22 | | REDUCE: (3), (13) imply: % 75.19/11.22 | | (14) ~ (all_4_10 = e4) % 75.19/11.22 | | % 75.19/11.22 | | REF_CLOSE: (1), (2), (4), (9), (11), (14) are inconsistent by sub-proof % 75.19/11.22 | | #161. % 75.19/11.22 | | % 75.19/11.22 | End of split % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #161 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) ~ (all_4_10 = e1) % 75.19/11.22 (2) ~ (all_4_10 = e3) % 75.19/11.22 (3) ~ (all_4_10 = e0) % 75.19/11.22 (4) ~ (all_4_10 = e4) % 75.19/11.22 (5) all_6_2 = all_4_10 % 75.19/11.22 (6) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | BETA: splitting (6) gives: % 75.19/11.22 | % 75.19/11.22 | Case 1: % 75.19/11.22 | | % 75.19/11.22 | | (7) all_6_2 = e4 % 75.19/11.22 | | % 75.19/11.22 | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #164. % 75.19/11.22 | | % 75.19/11.22 | Case 2: % 75.19/11.22 | | % 75.19/11.22 | | (8) all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 75.19/11.22 | | % 75.19/11.22 | | REF_CLOSE: (1), (2), (3), (5), (8) are inconsistent by sub-proof #162. % 75.19/11.22 | | % 75.19/11.22 | End of split % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #162 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) ~ (all_4_10 = e1) % 75.19/11.22 (2) ~ (all_4_10 = e3) % 75.19/11.22 (3) ~ (all_4_10 = e0) % 75.19/11.22 (4) all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 75.19/11.22 (5) all_6_2 = all_4_10 % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | BETA: splitting (4) gives: % 75.19/11.22 | % 75.19/11.22 | Case 1: % 75.19/11.22 | | % 75.19/11.22 | | (6) all_6_2 = e1 % 75.19/11.22 | | % 75.19/11.22 | | COMBINE_EQS: (5), (6) imply: % 75.19/11.22 | | (7) all_4_10 = e1 % 75.19/11.22 | | % 75.19/11.22 | | SIMP: (7) implies: % 75.19/11.22 | | (8) all_4_10 = e1 % 75.19/11.22 | | % 75.19/11.22 | | REDUCE: (1), (8) imply: % 75.19/11.22 | | (9) $false % 75.19/11.22 | | % 75.19/11.22 | | CLOSE: (9) is inconsistent. % 75.19/11.22 | | % 75.19/11.22 | Case 2: % 75.19/11.22 | | % 75.19/11.22 | | (10) all_6_2 = e3 | all_6_2 = e0 % 75.19/11.22 | | % 75.19/11.22 | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #163. % 75.19/11.22 | | % 75.19/11.22 | End of split % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #163 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) all_6_2 = e3 | all_6_2 = e0 % 75.19/11.22 (2) all_6_2 = all_4_10 % 75.19/11.22 (3) ~ (all_4_10 = e3) % 75.19/11.22 (4) ~ (all_4_10 = e0) % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | BETA: splitting (1) gives: % 75.19/11.22 | % 75.19/11.22 | Case 1: % 75.19/11.22 | | % 75.19/11.22 | | (5) all_6_2 = e3 % 75.19/11.22 | | % 75.19/11.22 | | COMBINE_EQS: (2), (5) imply: % 75.19/11.22 | | (6) all_4_10 = e3 % 75.19/11.22 | | % 75.19/11.22 | | SIMP: (6) implies: % 75.19/11.22 | | (7) all_4_10 = e3 % 75.19/11.22 | | % 75.19/11.22 | | REDUCE: (3), (7) imply: % 75.19/11.22 | | (8) $false % 75.19/11.22 | | % 75.19/11.22 | | CLOSE: (8) is inconsistent. % 75.19/11.22 | | % 75.19/11.22 | Case 2: % 75.19/11.22 | | % 75.19/11.22 | | (9) all_6_2 = e0 % 75.19/11.22 | | % 75.19/11.22 | | COMBINE_EQS: (2), (9) imply: % 75.19/11.22 | | (10) all_4_10 = e0 % 75.19/11.22 | | % 75.19/11.22 | | SIMP: (10) implies: % 75.19/11.22 | | (11) all_4_10 = e0 % 75.19/11.22 | | % 75.19/11.22 | | REDUCE: (4), (11) imply: % 75.19/11.22 | | (12) $false % 75.19/11.22 | | % 75.19/11.22 | | CLOSE: (12) is inconsistent. % 75.19/11.22 | | % 75.19/11.22 | End of split % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #164 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) all_6_2 = all_4_10 % 75.19/11.22 (2) all_6_2 = e4 % 75.19/11.22 (3) ~ (all_4_10 = e4) % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | COMBINE_EQS: (1), (2) imply: % 75.19/11.22 | (4) all_4_10 = e4 % 75.19/11.22 | % 75.19/11.22 | SIMP: (4) implies: % 75.19/11.22 | (5) all_4_10 = e4 % 75.19/11.22 | % 75.19/11.22 | REDUCE: (3), (5) imply: % 75.19/11.22 | (6) $false % 75.19/11.22 | % 75.19/11.22 | CLOSE: (6) is inconsistent. % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #165 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) all_10_4 = all_4_10 % 75.19/11.22 (2) op(e4, e4) = e2 % 75.19/11.22 (3) ~ (all_8_27 = e2) % 75.19/11.22 (4) all_10_4 = e4 % 75.19/11.22 (5) op(e4, all_4_10) = all_8_27 % 75.19/11.22 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 75.19/11.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | COMBINE_EQS: (1), (4) imply: % 75.19/11.22 | (7) all_4_10 = e4 % 75.19/11.22 | % 75.19/11.22 | REDUCE: (5), (7) imply: % 75.19/11.22 | (8) op(e4, e4) = all_8_27 % 75.19/11.22 | % 75.19/11.22 | GROUND_INST: instantiating (6) with e2, all_8_27, e4, e4, simplifying with % 75.19/11.22 | (2), (8) gives: % 75.19/11.22 | (9) all_8_27 = e2 % 75.19/11.22 | % 75.19/11.22 | REDUCE: (3), (9) imply: % 75.19/11.22 | (10) $false % 75.19/11.22 | % 75.19/11.22 | CLOSE: (10) is inconsistent. % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #166 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) all_10_15 = e4 % 75.19/11.22 (2) ~ (e2 = e1) % 75.19/11.22 (3) all_10_23 = e2 % 75.19/11.22 (4) all_10_15 = e1 | all_10_23 = e1 % 75.19/11.22 (5) ~ (e4 = e1) % 75.19/11.22 % 75.19/11.22 Begin of proof % 75.19/11.22 | % 75.19/11.22 | BETA: splitting (4) gives: % 75.19/11.22 | % 75.19/11.22 | Case 1: % 75.19/11.22 | | % 75.19/11.22 | | (6) all_10_15 = e1 % 75.19/11.22 | | % 75.19/11.22 | | COMBINE_EQS: (1), (6) imply: % 75.19/11.22 | | (7) e4 = e1 % 75.19/11.22 | | % 75.19/11.22 | | REDUCE: (5), (7) imply: % 75.19/11.22 | | (8) $false % 75.19/11.22 | | % 75.19/11.22 | | CLOSE: (8) is inconsistent. % 75.19/11.22 | | % 75.19/11.22 | Case 2: % 75.19/11.22 | | % 75.19/11.22 | | (9) all_10_23 = e1 % 75.19/11.22 | | % 75.19/11.22 | | COMBINE_EQS: (3), (9) imply: % 75.19/11.22 | | (10) e2 = e1 % 75.19/11.22 | | % 75.19/11.22 | | SIMP: (10) implies: % 75.19/11.22 | | (11) e2 = e1 % 75.19/11.22 | | % 75.19/11.22 | | REDUCE: (2), (11) imply: % 75.19/11.22 | | (12) $false % 75.19/11.22 | | % 75.19/11.22 | | CLOSE: (12) is inconsistent. % 75.19/11.22 | | % 75.19/11.22 | End of split % 75.19/11.22 | % 75.19/11.22 End of proof % 75.19/11.22 % 75.19/11.22 Sub-proof #167 shows that the following formulas are inconsistent: % 75.19/11.22 ---------------------------------------------------------------- % 75.19/11.22 (1) op(e2, all_4_17) = all_8_46 % 75.19/11.22 (2) op(e2, e1) = e4 % 75.19/11.22 (3) op(e2, e1) = all_4_17 % 75.19/11.22 (4) ~ (all_4_17 = e4) % 75.19/11.23 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 75.19/11.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 75.19/11.23 (6) all_4_17 = e1 % 75.19/11.23 % 75.19/11.23 Begin of proof % 75.19/11.23 | % 75.19/11.23 | SIMP: (6) implies: % 75.19/11.23 | (7) all_4_17 = e1 % 75.19/11.23 | % 75.19/11.23 | REDUCE: (4), (7) imply: % 75.19/11.23 | (8) ~ (e4 = e1) % 75.19/11.23 | % 75.19/11.23 | SIMP: (8) implies: % 75.19/11.23 | (9) ~ (e4 = e1) % 75.19/11.23 | % 75.19/11.23 | REDUCE: (1), (7) imply: % 75.19/11.23 | (10) op(e2, e1) = all_8_46 % 75.19/11.23 | % 75.19/11.23 | REDUCE: (3), (7) imply: % 75.19/11.23 | (11) op(e2, e1) = e1 % 75.19/11.23 | % 75.19/11.23 | GROUND_INST: instantiating (5) with e4, all_8_46, e1, e2, simplifying with % 75.19/11.23 | (2), (10) gives: % 75.19/11.23 | (12) all_8_46 = e4 % 75.19/11.23 | % 75.19/11.23 | GROUND_INST: instantiating (5) with e1, all_8_46, e1, e2, simplifying with % 75.19/11.23 | (10), (11) gives: % 75.19/11.23 | (13) all_8_46 = e1 % 75.19/11.23 | % 75.19/11.23 | COMBINE_EQS: (12), (13) imply: % 75.19/11.23 | (14) e4 = e1 % 75.19/11.23 | % 75.19/11.23 | SIMP: (14) implies: % 75.19/11.23 | (15) e4 = e1 % 75.19/11.23 | % 75.19/11.23 | REDUCE: (9), (15) imply: % 75.19/11.23 | (16) $false % 75.19/11.23 | % 75.19/11.23 | CLOSE: (16) is inconsistent. % 75.19/11.23 | % 75.19/11.23 End of proof % 75.19/11.23 % 75.19/11.23 Sub-proof #168 shows that the following formulas are inconsistent: % 75.19/11.23 ---------------------------------------------------------------- % 75.19/11.23 (1) all_6_2 = all_4_10 % 75.19/11.23 (2) all_6_2 = e2 % 75.19/11.23 (3) ~ (all_4_10 = e2) % 75.19/11.23 % 75.19/11.23 Begin of proof % 75.19/11.23 | % 75.19/11.23 | COMBINE_EQS: (1), (2) imply: % 75.19/11.23 | (4) all_4_10 = e2 % 75.19/11.23 | % 75.19/11.23 | SIMP: (4) implies: % 75.19/11.23 | (5) all_4_10 = e2 % 75.19/11.23 | % 75.19/11.23 | REDUCE: (3), (5) imply: % 75.19/11.23 | (6) $false % 75.19/11.23 | % 75.19/11.23 | CLOSE: (6) is inconsistent. % 75.19/11.23 | % 75.19/11.23 End of proof % 75.19/11.23 % 75.19/11.23 Sub-proof #169 shows that the following formulas are inconsistent: % 75.19/11.23 ---------------------------------------------------------------- % 75.19/11.23 (1) all_6_15 = all_4_3 % 75.19/11.23 (2) all_6_15 = e2 % 75.19/11.23 (3) ~ (all_4_3 = e2) % 75.19/11.23 % 75.19/11.23 Begin of proof % 75.19/11.23 | % 75.19/11.23 | COMBINE_EQS: (1), (2) imply: % 75.19/11.23 | (4) all_4_3 = e2 % 75.19/11.23 | % 75.19/11.23 | SIMP: (4) implies: % 75.19/11.23 | (5) all_4_3 = e2 % 75.19/11.23 | % 75.19/11.23 | REDUCE: (3), (5) imply: % 75.19/11.23 | (6) $false % 75.19/11.23 | % 75.19/11.23 | CLOSE: (6) is inconsistent. % 75.19/11.23 | % 75.19/11.23 End of proof % 75.19/11.23 % 75.19/11.23 Sub-proof #170 shows that the following formulas are inconsistent: % 75.19/11.23 ---------------------------------------------------------------- % 75.19/11.23 (1) all_8_65 = e2 % 75.19/11.23 (2) all_8_65 = e1 % 75.19/11.23 (3) ~ (e2 = e1) % 75.19/11.23 % 75.19/11.23 Begin of proof % 75.19/11.23 | % 75.19/11.23 | COMBINE_EQS: (1), (2) imply: % 75.19/11.23 | (4) e2 = e1 % 75.19/11.23 | % 75.19/11.23 | SIMP: (4) implies: % 75.19/11.23 | (5) e2 = e1 % 75.19/11.23 | % 75.19/11.23 | REDUCE: (3), (5) imply: % 75.19/11.23 | (6) $false % 75.19/11.23 | % 75.19/11.23 | CLOSE: (6) is inconsistent. % 75.19/11.23 | % 75.19/11.23 End of proof % 75.19/11.23 % SZS output end Proof for theBenchmark % 75.19/11.23 % 75.19/11.23 10634ms %------------------------------------------------------------------------------