%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG063+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 : n006.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 16:36:07 EDT 2023 % Result : Theorem 11.02s 2.20s % Output : Proof 17.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : ALG063+1 : TPTP v8.1.2. Released v2.7.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n006.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Mon Aug 28 02:54:36 EDT 2023 % 0.14/0.35 % CPUTime : % 0.22/0.61 ________ _____ % 0.22/0.61 ___ __ \_________(_)________________________________ % 0.22/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.61 % 0.22/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.61 (2023-06-19) % 0.22/0.61 % 0.22/0.61 (c) Philipp Rümmer, 2009-2023 % 0.22/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.61 Amanda Stjerna. % 0.22/0.61 Free software under BSD-3-Clause. % 0.22/0.61 % 0.22/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.61 % 0.22/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.22/0.62 Running up to 7 provers in parallel. % 0.22/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.24/1.42 Prover 4: Preprocessing ... % 5.24/1.43 Prover 1: Preprocessing ... % 5.24/1.49 Prover 0: Preprocessing ... % 5.24/1.49 Prover 2: Preprocessing ... % 5.24/1.49 Prover 3: Preprocessing ... % 5.24/1.49 Prover 5: Preprocessing ... % 5.24/1.49 Prover 6: Preprocessing ... % 9.15/1.97 Prover 2: Constructing countermodel ... % 9.15/1.97 Prover 1: Constructing countermodel ... % 9.15/1.97 Prover 3: Constructing countermodel ... % 9.15/1.97 Prover 4: Constructing countermodel ... % 9.15/1.98 Prover 0: Constructing countermodel ... % 9.75/2.01 Prover 6: Constructing countermodel ... % 11.02/2.20 Prover 3: proved (1556ms) % 11.02/2.20 % 11.02/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.02/2.20 % 11.02/2.20 Prover 2: stopped % 11.02/2.20 Prover 0: stopped % 11.02/2.20 Prover 6: stopped % 11.02/2.21 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.02/2.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.02/2.21 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.02/2.21 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.97/2.47 Prover 8: Preprocessing ... % 12.97/2.49 Prover 10: Preprocessing ... % 13.65/2.53 Prover 11: Preprocessing ... % 13.65/2.54 Prover 7: Preprocessing ... % 13.65/2.57 Prover 5: Constructing countermodel ... % 14.10/2.61 Prover 5: stopped % 14.10/2.61 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.10/2.65 Prover 8: Constructing countermodel ... % 14.95/2.72 Prover 13: Preprocessing ... % 15.22/2.80 Prover 10: Constructing countermodel ... % 15.22/2.81 Prover 11: Constructing countermodel ... % 15.22/2.82 Prover 7: Constructing countermodel ... % 15.22/2.96 Prover 13: Constructing countermodel ... % 15.22/2.96 Prover 4: Found proof (size 650) % 15.22/2.96 Prover 4: proved (2320ms) % 15.22/2.96 Prover 8: stopped % 15.22/2.96 Prover 11: stopped % 15.22/2.96 Prover 13: stopped % 15.22/2.96 Prover 10: stopped % 15.22/2.96 Prover 7: stopped % 15.22/2.97 Prover 1: Found proof (size 650) % 15.22/2.97 Prover 1: proved (2331ms) % 16.25/2.97 % 16.25/2.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.25/2.97 % 16.25/3.01 % SZS output start Proof for theBenchmark % 16.25/3.01 Assumptions after simplification: % 16.25/3.01 --------------------------------- % 16.25/3.01 % 16.25/3.01 (ax1) % 17.14/3.06 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 17.14/3.06 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 17.14/3.06 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 17.14/3.06 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 17.14/3.06 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 17.14/3.06 [v23: $i] : ? [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = % 17.14/3.06 v22 & op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, e4) = v19 & op(e3, e3) = % 17.14/3.06 v18 & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2, e4) = % 17.14/3.06 v14 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) = v11 & op(e2, e0) = % 17.14/3.06 v10 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = v7 & op(e1, e1) = v6 % 17.14/3.06 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 17.14/3.06 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & % 17.14/3.06 $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & % 17.14/3.06 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 17.14/3.06 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v24 = e3 | % 17.14/3.06 v24 = e2 | v24 = e1 | v24 = e0) & (v23 = e4 | v23 = e3 | v23 = e2 | v23 = % 17.14/3.06 e1 | v23 = e0) & (v22 = e4 | v22 = e3 | v22 = e2 | v22 = e1 | v22 = e0) & % 17.14/3.06 (v21 = e4 | v21 = e3 | v21 = e2 | v21 = e1 | v21 = e0) & (v20 = e4 | v20 = % 17.14/3.06 e3 | v20 = e2 | v20 = e1 | v20 = e0) & (v19 = e4 | v19 = e3 | v19 = e2 | % 17.14/3.06 v19 = e1 | v19 = e0) & (v18 = e4 | v18 = e3 | v18 = e2 | v18 = e1 | v18 = % 17.14/3.06 e0) & (v17 = e4 | v17 = e3 | v17 = e2 | v17 = e1 | v17 = e0) & (v16 = e4 | % 17.14/3.06 v16 = e3 | v16 = e2 | v16 = e1 | v16 = e0) & (v15 = e4 | v15 = e3 | v15 = % 17.14/3.06 e2 | v15 = e1 | v15 = e0) & (v14 = e4 | v14 = e3 | v14 = e2 | v14 = e1 | % 17.14/3.06 v14 = e0) & (v13 = e4 | v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 % 17.14/3.06 = e4 | v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e4 | v11 = e3 | % 17.14/3.06 v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e4 | v10 = e3 | v10 = e2 | v10 = % 17.14/3.06 e1 | v10 = e0) & (v9 = e4 | v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = % 17.14/3.06 e4 | v8 = e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e4 | v7 = e3 | v7 = e2 % 17.14/3.06 | v7 = e1 | v7 = e0) & (v6 = e4 | v6 = e3 | v6 = e2 | v6 = e1 | v6 = e0) & % 17.14/3.06 (v5 = e4 | v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e4 | v4 = e3 | v4 % 17.14/3.06 = e2 | v4 = e1 | v4 = e0) & (v3 = e4 | v3 = e3 | v3 = e2 | v3 = e1 | v3 = % 17.14/3.06 e0) & (v2 = e4 | v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e4 | v1 = % 17.14/3.06 e3 | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1 % 17.14/3.06 | v0 = e0)) % 17.14/3.06 % 17.14/3.06 (ax3) % 17.14/3.07 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 17.14/3.07 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 17.14/3.07 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 17.14/3.07 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 17.14/3.07 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 17.14/3.07 [v23: $i] : ? [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = % 17.14/3.07 v20 & op(e4, e1) = v15 & op(e4, e0) = v8 & op(e3, e4) = v22 & op(e3, e3) = % 17.14/3.07 v21 & op(e3, e2) = v19 & op(e3, e1) = v14 & op(e3, e0) = v7 & op(e2, e4) = % 17.14/3.07 v18 & op(e2, e3) = v17 & op(e2, e2) = v16 & op(e2, e1) = v13 & op(e2, e0) = % 17.14/3.07 v6 & op(e1, e4) = v12 & op(e1, e3) = v11 & op(e1, e2) = v10 & op(e1, e1) = % 17.14/3.07 v9 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 17.14/3.07 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & % 17.14/3.07 $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & % 17.14/3.07 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 17.14/3.07 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v23 = e4 | % 17.14/3.07 v20 = e4 | v15 = e4 | v8 = e4) & (v24 = e4 | v22 = e4 | v18 = e4 | v12 = % 17.14/3.07 e4 | v4 = e4) & (v24 = e3 | v23 = e3 | v20 = e3 | v15 = e3 | v8 = e3) & % 17.14/3.07 (v24 = e3 | v22 = e3 | v18 = e3 | v12 = e3 | v4 = e3) & (v24 = e2 | v23 = e2 % 17.14/3.07 | v20 = e2 | v15 = e2 | v8 = e2) & (v24 = e2 | v22 = e2 | v18 = e2 | v12 = % 17.14/3.07 e2 | v4 = e2) & (v24 = e1 | v23 = e1 | v20 = e1 | v15 = e1 | v8 = e1) & % 17.14/3.07 (v24 = e1 | v22 = e1 | v18 = e1 | v12 = e1 | v4 = e1) & (v24 = e0 | v23 = e0 % 17.14/3.07 | v20 = e0 | v15 = e0 | v8 = e0) & (v24 = e0 | v22 = e0 | v18 = e0 | v12 = % 17.14/3.07 e0 | v4 = e0) & (v23 = e4 | v21 = e4 | v17 = e4 | v11 = e4 | v3 = e4) & % 17.14/3.07 (v23 = e3 | v21 = e3 | v17 = e3 | v11 = e3 | v3 = e3) & (v23 = e2 | v21 = e2 % 17.14/3.07 | v17 = e2 | v11 = e2 | v3 = e2) & (v23 = e1 | v21 = e1 | v17 = e1 | v11 = % 17.14/3.07 e1 | v3 = e1) & (v23 = e0 | v21 = e0 | v17 = e0 | v11 = e0 | v3 = e0) & % 17.14/3.07 (v22 = e4 | v21 = e4 | v19 = e4 | v14 = e4 | v7 = e4) & (v22 = e3 | v21 = e3 % 17.14/3.07 | v19 = e3 | v14 = e3 | v7 = e3) & (v22 = e2 | v21 = e2 | v19 = e2 | v14 = % 17.14/3.07 e2 | v7 = e2) & (v22 = e1 | v21 = e1 | v19 = e1 | v14 = e1 | v7 = e1) & % 17.14/3.07 (v22 = e0 | v21 = e0 | v19 = e0 | v14 = e0 | v7 = e0) & (v20 = e4 | v19 = e4 % 17.14/3.07 | v16 = e4 | v10 = e4 | v2 = e4) & (v20 = e3 | v19 = e3 | v16 = e3 | v10 = % 17.14/3.07 e3 | v2 = e3) & (v20 = e2 | v19 = e2 | v16 = e2 | v10 = e2 | v2 = e2) & % 17.14/3.07 (v20 = e1 | v19 = e1 | v16 = e1 | v10 = e1 | v2 = e1) & (v20 = e0 | v19 = e0 % 17.14/3.07 | v16 = e0 | v10 = e0 | v2 = e0) & (v18 = e4 | v17 = e4 | v16 = e4 | v13 = % 17.14/3.07 e4 | v6 = e4) & (v18 = e3 | v17 = e3 | v16 = e3 | v13 = e3 | v6 = e3) & % 17.14/3.07 (v18 = e2 | v17 = e2 | v16 = e2 | v13 = e2 | v6 = e2) & (v18 = e1 | v17 = e1 % 17.14/3.07 | v16 = e1 | v13 = e1 | v6 = e1) & (v18 = e0 | v17 = e0 | v16 = e0 | v13 = % 17.14/3.07 e0 | v6 = e0) & (v15 = e4 | v14 = e4 | v13 = e4 | v9 = e4 | v1 = e4) & % 17.14/3.07 (v15 = e3 | v14 = e3 | v13 = e3 | v9 = e3 | v1 = e3) & (v15 = e2 | v14 = e2 % 17.14/3.07 | v13 = e2 | v9 = e2 | v1 = e2) & (v15 = e1 | v14 = e1 | v13 = e1 | v9 = % 17.14/3.07 e1 | v1 = e1) & (v15 = e0 | v14 = e0 | v13 = e0 | v9 = e0 | v1 = e0) & % 17.14/3.08 (v12 = e4 | v11 = e4 | v10 = e4 | v9 = e4 | v5 = e4) & (v12 = e3 | v11 = e3 % 17.14/3.08 | v10 = e3 | v9 = e3 | v5 = e3) & (v12 = e2 | v11 = e2 | v10 = e2 | v9 = % 17.14/3.08 e2 | v5 = e2) & (v12 = e1 | v11 = e1 | v10 = e1 | v9 = e1 | v5 = e1) & % 17.14/3.08 (v12 = e0 | v11 = e0 | v10 = e0 | v9 = e0 | v5 = e0) & (v8 = e4 | v7 = e4 | % 17.14/3.08 v6 = e4 | v5 = e4 | v0 = e4) & (v8 = e3 | v7 = e3 | v6 = e3 | v5 = e3 | v0 % 17.14/3.08 = e3) & (v8 = e2 | v7 = e2 | v6 = e2 | v5 = e2 | v0 = e2) & (v8 = e1 | v7 % 17.14/3.08 = e1 | v6 = e1 | v5 = e1 | v0 = e1) & (v4 = e4 | v3 = e4 | v2 = e4 | v1 = % 17.14/3.08 e4 | v0 = e4) & (v4 = e3 | v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (v4 = % 17.14/3.08 e2 | v3 = e2 | v2 = e2 | v1 = e2 | v0 = e2) & (v4 = e1 | v3 = e1 | v2 = e1 % 17.14/3.08 | v1 = e1 | v0 = e1) & (v0 = e0 | ((v8 = e0 | v7 = e0 | v6 = e0 | v5 = e0) % 17.14/3.08 & (v4 = e0 | v3 = e0 | v2 = e0 | v1 = e0)))) % 17.14/3.08 % 17.14/3.08 (ax4) % 17.14/3.08 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 17.14/3.08 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 17.14/3.08 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 17.14/3.08 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 17.14/3.08 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 17.14/3.08 [v23: $i] : ? [v24: $i] : ( ~ (v24 = v23) & ~ (v24 = v22) & ~ (v24 = v21) & % 17.14/3.08 ~ (v24 = v20) & ~ (v24 = v19) & ~ (v24 = v14) & ~ (v24 = v9) & ~ (v24 = % 17.14/3.08 v4) & ~ (v23 = v22) & ~ (v23 = v21) & ~ (v23 = v20) & ~ (v23 = v18) & % 17.14/3.08 ~ (v23 = v13) & ~ (v23 = v8) & ~ (v23 = v3) & ~ (v22 = v21) & ~ (v22 = % 17.14/3.08 v20) & ~ (v22 = v17) & ~ (v22 = v12) & ~ (v22 = v7) & ~ (v22 = v2) & % 17.14/3.08 ~ (v21 = v20) & ~ (v21 = v16) & ~ (v21 = v11) & ~ (v21 = v6) & ~ (v21 = % 17.14/3.08 v1) & ~ (v20 = v15) & ~ (v20 = v10) & ~ (v20 = v5) & ~ (v20 = v0) & ~ % 17.14/3.08 (v19 = v18) & ~ (v19 = v17) & ~ (v19 = v16) & ~ (v19 = v15) & ~ (v19 = % 17.14/3.08 v14) & ~ (v19 = v9) & ~ (v19 = v4) & ~ (v18 = v17) & ~ (v18 = v16) & % 17.14/3.08 ~ (v18 = v15) & ~ (v18 = v13) & ~ (v18 = v8) & ~ (v18 = v3) & ~ (v17 = % 17.14/3.08 v16) & ~ (v17 = v15) & ~ (v17 = v12) & ~ (v17 = v7) & ~ (v17 = v2) & % 17.14/3.08 ~ (v16 = v15) & ~ (v16 = v11) & ~ (v16 = v6) & ~ (v16 = v1) & ~ (v15 = % 17.14/3.08 v10) & ~ (v15 = v5) & ~ (v15 = v0) & ~ (v14 = v13) & ~ (v14 = v12) & % 17.14/3.08 ~ (v14 = v11) & ~ (v14 = v10) & ~ (v14 = v9) & ~ (v14 = v4) & ~ (v13 = % 17.14/3.08 v12) & ~ (v13 = v11) & ~ (v13 = v10) & ~ (v13 = v8) & ~ (v13 = v3) & % 17.14/3.08 ~ (v12 = v11) & ~ (v12 = v10) & ~ (v12 = v7) & ~ (v12 = v2) & ~ (v11 = % 17.14/3.08 v10) & ~ (v11 = v6) & ~ (v11 = v1) & ~ (v10 = v5) & ~ (v10 = v0) & ~ % 17.14/3.08 (v9 = v8) & ~ (v9 = v7) & ~ (v9 = v6) & ~ (v9 = v5) & ~ (v9 = v4) & ~ % 17.14/3.08 (v8 = v7) & ~ (v8 = v6) & ~ (v8 = v5) & ~ (v8 = v3) & ~ (v7 = v6) & ~ % 17.14/3.08 (v7 = v5) & ~ (v7 = v2) & ~ (v6 = v5) & ~ (v6 = v1) & ~ (v5 = v0) & ~ % 17.14/3.08 (v4 = v3) & ~ (v4 = v2) & ~ (v4 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ % 17.14/3.08 (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & % 17.14/3.08 op(e4, e4) = v24 & op(e4, e3) = v19 & op(e4, e2) = v14 & op(e4, e1) = v9 & % 17.14/3.08 op(e4, e0) = v4 & op(e3, e4) = v23 & op(e3, e3) = v18 & op(e3, e2) = v13 & % 17.14/3.08 op(e3, e1) = v8 & op(e3, e0) = v3 & op(e2, e4) = v22 & op(e2, e3) = v17 & % 17.14/3.08 op(e2, e2) = v12 & op(e2, e1) = v7 & op(e2, e0) = v2 & op(e1, e4) = v21 & % 17.14/3.08 op(e1, e3) = v16 & op(e1, e2) = v11 & op(e1, e1) = v6 & op(e1, e0) = v1 & % 17.14/3.08 op(e0, e4) = v20 & op(e0, e3) = v15 & op(e0, e2) = v10 & op(e0, e1) = v5 & % 17.14/3.08 op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) % 17.14/3.08 & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 17.14/3.08 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 17.14/3.08 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.14/3.08 % 17.14/3.08 (ax5) % 17.14/3.08 ~ (e4 = e3) & ~ (e4 = e2) & ~ (e4 = e1) & ~ (e4 = e0) & ~ (e3 = e2) & ~ % 17.14/3.08 (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ (e1 = e0) & $i(e4) % 17.14/3.08 & $i(e3) & $i(e2) & $i(e1) & $i(e0) % 17.14/3.08 % 17.14/3.08 (ax6) % 17.14/3.08 op(e4, e4) = e2 & op(e2, e2) = e3 & op(e1, e2) = e0 & op(e1, e1) = e4 & $i(e4) % 17.14/3.08 & $i(e3) & $i(e2) & $i(e1) & $i(e0) % 17.14/3.08 % 17.14/3.08 (co1) % 17.45/3.09 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 17.45/3.09 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 17.45/3.09 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 17.45/3.09 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 17.45/3.09 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 17.45/3.09 [v23: $i] : ? [v24: $i] : (op(e4, e4) = v4 & op(e4, e3) = v24 & op(e4, e2) = % 17.45/3.09 v23 & op(e4, e1) = v22 & op(e4, e0) = v21 & op(e3, e4) = v20 & op(e3, e3) = % 17.45/3.09 v3 & op(e3, e2) = v19 & op(e3, e1) = v18 & op(e3, e0) = v17 & op(e2, e4) = % 17.45/3.09 v16 & op(e2, e3) = v15 & op(e2, e2) = v2 & op(e2, e1) = v14 & op(e2, e0) = % 17.45/3.09 v13 & op(e1, e4) = v12 & op(e1, e3) = v11 & op(e1, e2) = v10 & op(e1, e1) = % 17.45/3.09 v1 & op(e1, e0) = v9 & op(e0, e4) = v8 & op(e0, e3) = v7 & op(e0, e2) = v6 & % 17.45/3.09 op(e0, e1) = v5 & op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & % 17.45/3.09 $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & % 17.45/3.09 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 17.45/3.09 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v4 = e4 | v3 = e4 | % 17.45/3.09 v2 = e4 | v1 = e4 | v0 = e4) & (v4 = e3 | v3 = e3 | v2 = e3 | v1 = e3 | v0 % 17.45/3.09 = e3) & (v4 = e2 | v3 = e2 | v2 = e2 | v1 = e2 | v0 = e2) & (v4 = e1 | v3 % 17.45/3.09 = e1 | v2 = e1 | v1 = e1 | v0 = e1) & (v4 = e0 | v3 = e0 | v2 = e0 | v1 = % 17.45/3.09 e0 | v0 = e0) & ((v4 = e3 & v3 = e4 & ~ (v24 = e4)) | (v4 = e3 & v3 = e4 % 17.45/3.09 & ~ (v20 = e3)) | (v4 = e2 & v2 = e4 & ~ (v23 = e4)) | (v4 = e2 & v2 = % 17.45/3.09 e4 & ~ (v16 = e2)) | (v4 = e1 & v1 = e4 & ~ (v22 = e4)) | (v4 = e1 & % 17.45/3.09 v1 = e4 & ~ (v12 = e1)) | (v4 = e0 & v0 = e4 & ~ (v21 = e4)) | (v4 = % 17.45/3.09 e0 & v0 = e4 & ~ (v8 = e0)) | (v3 = e2 & v2 = e3 & ~ (v19 = e3)) | (v3 % 17.45/3.09 = e2 & v2 = e3 & ~ (v15 = e2)) | (v3 = e1 & v1 = e3 & ~ (v18 = e3)) | % 17.45/3.09 (v3 = e1 & v1 = e3 & ~ (v11 = e1)) | (v3 = e0 & v0 = e3 & ~ (v17 = e3)) % 17.45/3.09 | (v3 = e0 & v0 = e3 & ~ (v7 = e0)) | (v2 = e1 & v1 = e2 & ~ (v14 = e2)) % 17.45/3.09 | (v2 = e1 & v1 = e2 & ~ (v10 = e1)) | (v2 = e0 & v0 = e2 & ~ (v13 = % 17.45/3.09 e2)) | (v2 = e0 & v0 = e2 & ~ (v6 = e0)) | (v1 = e0 & v0 = e1 & ~ % 17.45/3.09 (v9 = e1)) | (v1 = e0 & v0 = e1 & ~ (v5 = e0)))) % 17.45/3.09 % 17.45/3.09 (function-axioms) % 17.45/3.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3, % 17.45/3.09 v2) = v1) | ~ (op(v3, v2) = v0)) % 17.45/3.09 % 17.45/3.09 Further assumptions not needed in the proof: % 17.45/3.09 -------------------------------------------- % 17.45/3.09 ax2 % 17.45/3.09 % 17.45/3.09 Those formulas are unsatisfiable: % 17.45/3.09 --------------------------------- % 17.45/3.09 % 17.45/3.09 Begin of proof % 17.45/3.09 | % 17.45/3.09 | ALPHA: (ax1) implies: % 17.45/3.10 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 17.45/3.10 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 17.45/3.10 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 17.45/3.10 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 17.45/3.10 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 17.45/3.10 | [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = v22 & % 17.45/3.10 | op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, e4) = v19 & op(e3, e3) = % 17.45/3.10 | v18 & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2, % 17.45/3.10 | e4) = v14 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) = v11 % 17.45/3.10 | & op(e2, e0) = v10 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = % 17.45/3.10 | v7 & op(e1, e1) = v6 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) % 17.45/3.10 | = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) % 17.45/3.10 | & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) % 17.45/3.10 | & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) % 17.45/3.10 | & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 17.45/3.10 | $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v24 = e3 | v24 = e2 | v24 = e1 % 17.45/3.10 | | v24 = e0) & (v23 = e4 | v23 = e3 | v23 = e2 | v23 = e1 | v23 = % 17.45/3.10 | e0) & (v22 = e4 | v22 = e3 | v22 = e2 | v22 = e1 | v22 = e0) & (v21 % 17.45/3.10 | = e4 | v21 = e3 | v21 = e2 | v21 = e1 | v21 = e0) & (v20 = e4 | v20 % 17.45/3.10 | = e3 | v20 = e2 | v20 = e1 | v20 = e0) & (v19 = e4 | v19 = e3 | v19 % 17.45/3.10 | = e2 | v19 = e1 | v19 = e0) & (v18 = e4 | v18 = e3 | v18 = e2 | v18 % 17.45/3.10 | = e1 | v18 = e0) & (v17 = e4 | v17 = e3 | v17 = e2 | v17 = e1 | v17 % 17.45/3.10 | = e0) & (v16 = e4 | v16 = e3 | v16 = e2 | v16 = e1 | v16 = e0) & % 17.45/3.10 | (v15 = e4 | v15 = e3 | v15 = e2 | v15 = e1 | v15 = e0) & (v14 = e4 | % 17.45/3.10 | v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e4 | v13 = e3 | % 17.45/3.10 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e4 | v12 = e3 | v12 = e2 | % 17.45/3.10 | v12 = e1 | v12 = e0) & (v11 = e4 | v11 = e3 | v11 = e2 | v11 = e1 | % 17.45/3.10 | v11 = e0) & (v10 = e4 | v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) % 17.45/3.10 | & (v9 = e4 | v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e4 | v8 = % 17.45/3.10 | e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e4 | v7 = e3 | v7 = e2 | % 17.45/3.10 | v7 = e1 | v7 = e0) & (v6 = e4 | v6 = e3 | v6 = e2 | v6 = e1 | v6 = % 17.45/3.10 | e0) & (v5 = e4 | v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e4 % 17.45/3.10 | | v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e4 | v3 = e3 | v3 % 17.45/3.10 | = e2 | v3 = e1 | v3 = e0) & (v2 = e4 | v2 = e3 | v2 = e2 | v2 = e1 % 17.45/3.10 | | v2 = e0) & (v1 = e4 | v1 = e3 | v1 = e2 | v1 = e1 | v1 = e0) & % 17.45/3.10 | (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0)) % 17.45/3.10 | % 17.45/3.10 | ALPHA: (ax3) implies: % 17.45/3.11 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 17.45/3.11 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 17.45/3.11 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 17.45/3.11 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 17.45/3.11 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 17.45/3.11 | [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = v20 & % 17.45/3.11 | op(e4, e1) = v15 & op(e4, e0) = v8 & op(e3, e4) = v22 & op(e3, e3) = % 17.45/3.11 | v21 & op(e3, e2) = v19 & op(e3, e1) = v14 & op(e3, e0) = v7 & op(e2, % 17.45/3.11 | e4) = v18 & op(e2, e3) = v17 & op(e2, e2) = v16 & op(e2, e1) = v13 % 17.45/3.11 | & op(e2, e0) = v6 & op(e1, e4) = v12 & op(e1, e3) = v11 & op(e1, e2) % 17.45/3.11 | = v10 & op(e1, e1) = v9 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, % 17.45/3.11 | e3) = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & % 17.45/3.11 | $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & % 17.45/3.11 | $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & % 17.45/3.11 | $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 17.45/3.11 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v23 = e4 | v20 = e4 | % 17.45/3.11 | v15 = e4 | v8 = e4) & (v24 = e4 | v22 = e4 | v18 = e4 | v12 = e4 | % 17.45/3.11 | v4 = e4) & (v24 = e3 | v23 = e3 | v20 = e3 | v15 = e3 | v8 = e3) & % 17.45/3.11 | (v24 = e3 | v22 = e3 | v18 = e3 | v12 = e3 | v4 = e3) & (v24 = e2 | % 17.45/3.11 | v23 = e2 | v20 = e2 | v15 = e2 | v8 = e2) & (v24 = e2 | v22 = e2 | % 17.45/3.11 | v18 = e2 | v12 = e2 | v4 = e2) & (v24 = e1 | v23 = e1 | v20 = e1 | % 17.45/3.11 | v15 = e1 | v8 = e1) & (v24 = e1 | v22 = e1 | v18 = e1 | v12 = e1 | % 17.45/3.11 | v4 = e1) & (v24 = e0 | v23 = e0 | v20 = e0 | v15 = e0 | v8 = e0) & % 17.45/3.11 | (v24 = e0 | v22 = e0 | v18 = e0 | v12 = e0 | v4 = e0) & (v23 = e4 | % 17.45/3.11 | v21 = e4 | v17 = e4 | v11 = e4 | v3 = e4) & (v23 = e3 | v21 = e3 | % 17.45/3.11 | v17 = e3 | v11 = e3 | v3 = e3) & (v23 = e2 | v21 = e2 | v17 = e2 | % 17.45/3.11 | v11 = e2 | v3 = e2) & (v23 = e1 | v21 = e1 | v17 = e1 | v11 = e1 | % 17.45/3.11 | v3 = e1) & (v23 = e0 | v21 = e0 | v17 = e0 | v11 = e0 | v3 = e0) & % 17.45/3.11 | (v22 = e4 | v21 = e4 | v19 = e4 | v14 = e4 | v7 = e4) & (v22 = e3 | % 17.45/3.11 | v21 = e3 | v19 = e3 | v14 = e3 | v7 = e3) & (v22 = e2 | v21 = e2 | % 17.45/3.11 | v19 = e2 | v14 = e2 | v7 = e2) & (v22 = e1 | v21 = e1 | v19 = e1 | % 17.45/3.11 | v14 = e1 | v7 = e1) & (v22 = e0 | v21 = e0 | v19 = e0 | v14 = e0 | % 17.45/3.11 | v7 = e0) & (v20 = e4 | v19 = e4 | v16 = e4 | v10 = e4 | v2 = e4) & % 17.45/3.11 | (v20 = e3 | v19 = e3 | v16 = e3 | v10 = e3 | v2 = e3) & (v20 = e2 | % 17.45/3.11 | v19 = e2 | v16 = e2 | v10 = e2 | v2 = e2) & (v20 = e1 | v19 = e1 | % 17.45/3.11 | v16 = e1 | v10 = e1 | v2 = e1) & (v20 = e0 | v19 = e0 | v16 = e0 | % 17.45/3.11 | v10 = e0 | v2 = e0) & (v18 = e4 | v17 = e4 | v16 = e4 | v13 = e4 | % 17.45/3.11 | v6 = e4) & (v18 = e3 | v17 = e3 | v16 = e3 | v13 = e3 | v6 = e3) & % 17.45/3.11 | (v18 = e2 | v17 = e2 | v16 = e2 | v13 = e2 | v6 = e2) & (v18 = e1 | % 17.45/3.11 | v17 = e1 | v16 = e1 | v13 = e1 | v6 = e1) & (v18 = e0 | v17 = e0 | % 17.45/3.11 | v16 = e0 | v13 = e0 | v6 = e0) & (v15 = e4 | v14 = e4 | v13 = e4 | % 17.45/3.11 | v9 = e4 | v1 = e4) & (v15 = e3 | v14 = e3 | v13 = e3 | v9 = e3 | v1 % 17.45/3.11 | = e3) & (v15 = e2 | v14 = e2 | v13 = e2 | v9 = e2 | v1 = e2) & (v15 % 17.45/3.11 | = e1 | v14 = e1 | v13 = e1 | v9 = e1 | v1 = e1) & (v15 = e0 | v14 = % 17.45/3.11 | e0 | v13 = e0 | v9 = e0 | v1 = e0) & (v12 = e4 | v11 = e4 | v10 = % 17.45/3.11 | e4 | v9 = e4 | v5 = e4) & (v12 = e3 | v11 = e3 | v10 = e3 | v9 = e3 % 17.45/3.11 | | v5 = e3) & (v12 = e2 | v11 = e2 | v10 = e2 | v9 = e2 | v5 = e2) & % 17.45/3.11 | (v12 = e1 | v11 = e1 | v10 = e1 | v9 = e1 | v5 = e1) & (v12 = e0 | % 17.45/3.11 | v11 = e0 | v10 = e0 | v9 = e0 | v5 = e0) & (v8 = e4 | v7 = e4 | v6 % 17.45/3.11 | = e4 | v5 = e4 | v0 = e4) & (v8 = e3 | v7 = e3 | v6 = e3 | v5 = e3 % 17.45/3.11 | | v0 = e3) & (v8 = e2 | v7 = e2 | v6 = e2 | v5 = e2 | v0 = e2) & % 17.45/3.11 | (v8 = e1 | v7 = e1 | v6 = e1 | v5 = e1 | v0 = e1) & (v4 = e4 | v3 = % 17.45/3.11 | e4 | v2 = e4 | v1 = e4 | v0 = e4) & (v4 = e3 | v3 = e3 | v2 = e3 | % 17.45/3.11 | v1 = e3 | v0 = e3) & (v4 = e2 | v3 = e2 | v2 = e2 | v1 = e2 | v0 = % 17.45/3.11 | e2) & (v4 = e1 | v3 = e1 | v2 = e1 | v1 = e1 | v0 = e1) & (v0 = e0 % 17.45/3.11 | | ((v8 = e0 | v7 = e0 | v6 = e0 | v5 = e0) & (v4 = e0 | v3 = e0 | % 17.45/3.11 | v2 = e0 | v1 = e0)))) % 17.45/3.11 | % 17.45/3.11 | ALPHA: (ax4) implies: % 17.45/3.12 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 17.45/3.12 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 17.45/3.12 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 17.45/3.12 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 17.45/3.12 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 17.45/3.12 | [v24: $i] : ( ~ (v24 = v23) & ~ (v24 = v22) & ~ (v24 = v21) & ~ (v24 % 17.45/3.12 | = v20) & ~ (v24 = v19) & ~ (v24 = v14) & ~ (v24 = v9) & ~ (v24 % 17.45/3.12 | = v4) & ~ (v23 = v22) & ~ (v23 = v21) & ~ (v23 = v20) & ~ (v23 % 17.45/3.12 | = v18) & ~ (v23 = v13) & ~ (v23 = v8) & ~ (v23 = v3) & ~ (v22 = % 17.45/3.12 | v21) & ~ (v22 = v20) & ~ (v22 = v17) & ~ (v22 = v12) & ~ (v22 = % 17.45/3.12 | v7) & ~ (v22 = v2) & ~ (v21 = v20) & ~ (v21 = v16) & ~ (v21 = % 17.45/3.12 | v11) & ~ (v21 = v6) & ~ (v21 = v1) & ~ (v20 = v15) & ~ (v20 = % 17.45/3.12 | v10) & ~ (v20 = v5) & ~ (v20 = v0) & ~ (v19 = v18) & ~ (v19 = % 17.45/3.12 | v17) & ~ (v19 = v16) & ~ (v19 = v15) & ~ (v19 = v14) & ~ (v19 = % 17.45/3.12 | v9) & ~ (v19 = v4) & ~ (v18 = v17) & ~ (v18 = v16) & ~ (v18 = % 17.45/3.12 | v15) & ~ (v18 = v13) & ~ (v18 = v8) & ~ (v18 = v3) & ~ (v17 = % 17.45/3.12 | v16) & ~ (v17 = v15) & ~ (v17 = v12) & ~ (v17 = v7) & ~ (v17 = % 17.45/3.12 | v2) & ~ (v16 = v15) & ~ (v16 = v11) & ~ (v16 = v6) & ~ (v16 = % 17.45/3.12 | v1) & ~ (v15 = v10) & ~ (v15 = v5) & ~ (v15 = v0) & ~ (v14 = % 17.45/3.12 | v13) & ~ (v14 = v12) & ~ (v14 = v11) & ~ (v14 = v10) & ~ (v14 = % 17.45/3.12 | v9) & ~ (v14 = v4) & ~ (v13 = v12) & ~ (v13 = v11) & ~ (v13 = % 17.45/3.12 | v10) & ~ (v13 = v8) & ~ (v13 = v3) & ~ (v12 = v11) & ~ (v12 = % 17.45/3.12 | v10) & ~ (v12 = v7) & ~ (v12 = v2) & ~ (v11 = v10) & ~ (v11 = % 17.45/3.12 | v6) & ~ (v11 = v1) & ~ (v10 = v5) & ~ (v10 = v0) & ~ (v9 = v8) % 17.45/3.12 | & ~ (v9 = v7) & ~ (v9 = v6) & ~ (v9 = v5) & ~ (v9 = v4) & ~ (v8 % 17.45/3.12 | = v7) & ~ (v8 = v6) & ~ (v8 = v5) & ~ (v8 = v3) & ~ (v7 = v6) & % 17.45/3.12 | ~ (v7 = v5) & ~ (v7 = v2) & ~ (v6 = v5) & ~ (v6 = v1) & ~ (v5 = % 17.45/3.12 | v0) & ~ (v4 = v3) & ~ (v4 = v2) & ~ (v4 = v1) & ~ (v4 = v0) & % 17.45/3.12 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = % 17.45/3.12 | v0) & ~ (v1 = v0) & op(e4, e4) = v24 & op(e4, e3) = v19 & op(e4, % 17.45/3.12 | e2) = v14 & op(e4, e1) = v9 & op(e4, e0) = v4 & op(e3, e4) = v23 & % 17.45/3.12 | op(e3, e3) = v18 & op(e3, e2) = v13 & op(e3, e1) = v8 & op(e3, e0) = % 17.45/3.12 | v3 & op(e2, e4) = v22 & op(e2, e3) = v17 & op(e2, e2) = v12 & op(e2, % 17.45/3.12 | e1) = v7 & op(e2, e0) = v2 & op(e1, e4) = v21 & op(e1, e3) = v16 & % 17.45/3.12 | op(e1, e2) = v11 & op(e1, e1) = v6 & op(e1, e0) = v1 & op(e0, e4) = % 17.45/3.12 | v20 & op(e0, e3) = v15 & op(e0, e2) = v10 & op(e0, e1) = v5 & op(e0, % 17.45/3.12 | e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & % 17.45/3.12 | $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & % 17.45/3.12 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 17.45/3.12 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.45/3.12 | % 17.45/3.12 | ALPHA: (ax5) implies: % 17.45/3.12 | (4) ~ (e1 = e0) % 17.45/3.12 | (5) ~ (e2 = e0) % 17.45/3.12 | (6) ~ (e2 = e1) % 17.45/3.12 | (7) ~ (e3 = e1) % 17.45/3.12 | (8) ~ (e3 = e2) % 17.45/3.12 | (9) ~ (e4 = e1) % 17.45/3.12 | (10) ~ (e4 = e3) % 17.45/3.12 | % 17.45/3.12 | ALPHA: (ax6) implies: % 17.45/3.12 | (11) op(e1, e1) = e4 % 17.45/3.12 | (12) op(e1, e2) = e0 % 17.45/3.12 | (13) op(e2, e2) = e3 % 17.45/3.12 | (14) op(e4, e4) = e2 % 17.45/3.12 | % 17.45/3.12 | ALPHA: (co1) implies: % 17.45/3.12 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 17.45/3.12 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 17.45/3.12 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 17.45/3.12 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 17.45/3.12 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] % 17.45/3.12 | : ? [v24: $i] : (op(e4, e4) = v4 & op(e4, e3) = v24 & op(e4, e2) = % 17.45/3.12 | v23 & op(e4, e1) = v22 & op(e4, e0) = v21 & op(e3, e4) = v20 & % 17.45/3.12 | op(e3, e3) = v3 & op(e3, e2) = v19 & op(e3, e1) = v18 & op(e3, e0) = % 17.45/3.12 | v17 & op(e2, e4) = v16 & op(e2, e3) = v15 & op(e2, e2) = v2 & op(e2, % 17.45/3.12 | e1) = v14 & op(e2, e0) = v13 & op(e1, e4) = v12 & op(e1, e3) = v11 % 17.45/3.12 | & op(e1, e2) = v10 & op(e1, e1) = v1 & op(e1, e0) = v9 & op(e0, e4) % 17.45/3.12 | = v8 & op(e0, e3) = v7 & op(e0, e2) = v6 & op(e0, e1) = v5 & op(e0, % 17.45/3.12 | e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & % 17.45/3.12 | $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) % 17.45/3.12 | & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 17.45/3.12 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v4 = e4 | v3 % 17.45/3.12 | = e4 | v2 = e4 | v1 = e4 | v0 = e4) & (v4 = e3 | v3 = e3 | v2 = e3 % 17.45/3.12 | | v1 = e3 | v0 = e3) & (v4 = e2 | v3 = e2 | v2 = e2 | v1 = e2 | v0 % 17.45/3.12 | = e2) & (v4 = e1 | v3 = e1 | v2 = e1 | v1 = e1 | v0 = e1) & (v4 = % 17.45/3.12 | e0 | v3 = e0 | v2 = e0 | v1 = e0 | v0 = e0) & ((v4 = e3 & v3 = e4 % 17.45/3.12 | & ~ (v24 = e4)) | (v4 = e3 & v3 = e4 & ~ (v20 = e3)) | (v4 = % 17.45/3.12 | e2 & v2 = e4 & ~ (v23 = e4)) | (v4 = e2 & v2 = e4 & ~ (v16 = % 17.45/3.12 | e2)) | (v4 = e1 & v1 = e4 & ~ (v22 = e4)) | (v4 = e1 & v1 = % 17.45/3.12 | e4 & ~ (v12 = e1)) | (v4 = e0 & v0 = e4 & ~ (v21 = e4)) | (v4 % 17.45/3.12 | = e0 & v0 = e4 & ~ (v8 = e0)) | (v3 = e2 & v2 = e3 & ~ (v19 = % 17.45/3.12 | e3)) | (v3 = e2 & v2 = e3 & ~ (v15 = e2)) | (v3 = e1 & v1 = % 17.45/3.12 | e3 & ~ (v18 = e3)) | (v3 = e1 & v1 = e3 & ~ (v11 = e1)) | (v3 % 17.45/3.12 | = e0 & v0 = e3 & ~ (v17 = e3)) | (v3 = e0 & v0 = e3 & ~ (v7 = % 17.45/3.12 | e0)) | (v2 = e1 & v1 = e2 & ~ (v14 = e2)) | (v2 = e1 & v1 = % 17.45/3.12 | e2 & ~ (v10 = e1)) | (v2 = e0 & v0 = e2 & ~ (v13 = e2)) | (v2 % 17.45/3.12 | = e0 & v0 = e2 & ~ (v6 = e0)) | (v1 = e0 & v0 = e1 & ~ (v9 = % 17.45/3.12 | e1)) | (v1 = e0 & v0 = e1 & ~ (v5 = e0)))) % 17.45/3.13 | % 17.45/3.13 | DELTA: instantiating (15) with fresh symbols all_4_0, all_4_1, all_4_2, % 17.45/3.13 | all_4_3, all_4_4, all_4_5, all_4_6, all_4_7, all_4_8, all_4_9, % 17.45/3.13 | all_4_10, all_4_11, all_4_12, all_4_13, all_4_14, all_4_15, all_4_16, % 17.45/3.13 | all_4_17, all_4_18, all_4_19, all_4_20, all_4_21, all_4_22, all_4_23, % 17.45/3.13 | all_4_24 gives: % 17.45/3.13 | (16) op(e4, e4) = all_4_20 & op(e4, e3) = all_4_0 & op(e4, e2) = all_4_1 & % 17.45/3.13 | op(e4, e1) = all_4_2 & op(e4, e0) = all_4_3 & op(e3, e4) = all_4_4 & % 17.45/3.13 | op(e3, e3) = all_4_21 & op(e3, e2) = all_4_5 & op(e3, e1) = all_4_6 & % 17.45/3.13 | op(e3, e0) = all_4_7 & op(e2, e4) = all_4_8 & op(e2, e3) = all_4_9 & % 17.45/3.13 | op(e2, e2) = all_4_22 & op(e2, e1) = all_4_10 & op(e2, e0) = all_4_11 % 17.45/3.13 | & op(e1, e4) = all_4_12 & op(e1, e3) = all_4_13 & op(e1, e2) = % 17.45/3.13 | all_4_14 & op(e1, e1) = all_4_23 & op(e1, e0) = all_4_15 & op(e0, e4) % 17.45/3.13 | = all_4_16 & op(e0, e3) = all_4_17 & op(e0, e2) = all_4_18 & op(e0, % 17.45/3.13 | e1) = all_4_19 & op(e0, e0) = all_4_24 & $i(all_4_0) & $i(all_4_1) & % 17.45/3.13 | $i(all_4_2) & $i(all_4_3) & $i(all_4_4) & $i(all_4_5) & $i(all_4_6) & % 17.45/3.13 | $i(all_4_7) & $i(all_4_8) & $i(all_4_9) & $i(all_4_10) & $i(all_4_11) % 17.45/3.13 | & $i(all_4_12) & $i(all_4_13) & $i(all_4_14) & $i(all_4_15) & % 17.45/3.13 | $i(all_4_16) & $i(all_4_17) & $i(all_4_18) & $i(all_4_19) & % 17.45/3.13 | $i(all_4_20) & $i(all_4_21) & $i(all_4_22) & $i(all_4_23) & % 17.45/3.13 | $i(all_4_24) & (all_4_20 = e4 | all_4_21 = e4 | all_4_22 = e4 | % 17.45/3.13 | all_4_23 = e4 | all_4_24 = e4) & (all_4_20 = e3 | all_4_21 = e3 | % 17.45/3.13 | all_4_22 = e3 | all_4_23 = e3 | all_4_24 = e3) & (all_4_20 = e2 | % 17.45/3.13 | all_4_21 = e2 | all_4_22 = e2 | all_4_23 = e2 | all_4_24 = e2) & % 17.45/3.13 | (all_4_20 = e1 | all_4_21 = e1 | all_4_22 = e1 | all_4_23 = e1 | % 17.45/3.13 | all_4_24 = e1) & (all_4_20 = e0 | all_4_21 = e0 | all_4_22 = e0 | % 17.45/3.13 | all_4_23 = e0 | all_4_24 = e0) & ((all_4_20 = e3 & all_4_21 = e4 & % 17.45/3.13 | ~ (all_4_0 = e4)) | (all_4_20 = e3 & all_4_21 = e4 & ~ (all_4_4 = % 17.45/3.13 | e3)) | (all_4_20 = e2 & all_4_22 = e4 & ~ (all_4_1 = e4)) | % 17.45/3.13 | (all_4_20 = e2 & all_4_22 = e4 & ~ (all_4_8 = e2)) | (all_4_20 = e1 % 17.45/3.13 | & all_4_23 = e4 & ~ (all_4_2 = e4)) | (all_4_20 = e1 & all_4_23 = % 17.45/3.13 | e4 & ~ (all_4_12 = e1)) | (all_4_20 = e0 & all_4_24 = e4 & ~ % 17.45/3.13 | (all_4_3 = e4)) | (all_4_20 = e0 & all_4_24 = e4 & ~ (all_4_16 = % 17.45/3.13 | e0)) | (all_4_21 = e2 & all_4_22 = e3 & ~ (all_4_5 = e3)) | % 17.45/3.13 | (all_4_21 = e2 & all_4_22 = e3 & ~ (all_4_9 = e2)) | (all_4_21 = e1 % 17.45/3.13 | & all_4_23 = e3 & ~ (all_4_6 = e3)) | (all_4_21 = e1 & all_4_23 = % 17.45/3.13 | e3 & ~ (all_4_13 = e1)) | (all_4_21 = e0 & all_4_24 = e3 & ~ % 17.45/3.13 | (all_4_7 = e3)) | (all_4_21 = e0 & all_4_24 = e3 & ~ (all_4_17 = % 17.45/3.13 | e0)) | (all_4_22 = e1 & all_4_23 = e2 & ~ (all_4_10 = e2)) | % 17.45/3.13 | (all_4_22 = e1 & all_4_23 = e2 & ~ (all_4_14 = e1)) | (all_4_22 = % 17.45/3.13 | e0 & all_4_24 = e2 & ~ (all_4_11 = e2)) | (all_4_22 = e0 & % 17.45/3.13 | all_4_24 = e2 & ~ (all_4_18 = e0)) | (all_4_23 = e0 & all_4_24 = % 17.45/3.13 | e1 & ~ (all_4_15 = e1)) | (all_4_23 = e0 & all_4_24 = e1 & ~ % 17.45/3.13 | (all_4_19 = e0))) % 17.45/3.13 | % 17.45/3.13 | ALPHA: (16) implies: % 17.45/3.13 | (17) op(e0, e0) = all_4_24 % 17.45/3.13 | (18) op(e1, e1) = all_4_23 % 17.45/3.13 | (19) op(e1, e2) = all_4_14 % 17.45/3.13 | (20) op(e2, e2) = all_4_22 % 17.45/3.13 | (21) op(e4, e4) = all_4_20 % 17.45/3.13 | (22) (all_4_20 = e3 & all_4_21 = e4 & ~ (all_4_0 = e4)) | (all_4_20 = e3 & % 17.45/3.13 | all_4_21 = e4 & ~ (all_4_4 = e3)) | (all_4_20 = e2 & all_4_22 = e4 % 17.45/3.13 | & ~ (all_4_1 = e4)) | (all_4_20 = e2 & all_4_22 = e4 & ~ (all_4_8 % 17.45/3.13 | = e2)) | (all_4_20 = e1 & all_4_23 = e4 & ~ (all_4_2 = e4)) | % 17.45/3.13 | (all_4_20 = e1 & all_4_23 = e4 & ~ (all_4_12 = e1)) | (all_4_20 = e0 % 17.45/3.13 | & all_4_24 = e4 & ~ (all_4_3 = e4)) | (all_4_20 = e0 & all_4_24 = % 17.45/3.13 | e4 & ~ (all_4_16 = e0)) | (all_4_21 = e2 & all_4_22 = e3 & ~ % 17.45/3.13 | (all_4_5 = e3)) | (all_4_21 = e2 & all_4_22 = e3 & ~ (all_4_9 = % 17.45/3.13 | e2)) | (all_4_21 = e1 & all_4_23 = e3 & ~ (all_4_6 = e3)) | % 17.45/3.13 | (all_4_21 = e1 & all_4_23 = e3 & ~ (all_4_13 = e1)) | (all_4_21 = e0 % 17.45/3.13 | & all_4_24 = e3 & ~ (all_4_7 = e3)) | (all_4_21 = e0 & all_4_24 = % 17.45/3.13 | e3 & ~ (all_4_17 = e0)) | (all_4_22 = e1 & all_4_23 = e2 & ~ % 17.45/3.13 | (all_4_10 = e2)) | (all_4_22 = e1 & all_4_23 = e2 & ~ (all_4_14 = % 17.45/3.13 | e1)) | (all_4_22 = e0 & all_4_24 = e2 & ~ (all_4_11 = e2)) | % 17.45/3.13 | (all_4_22 = e0 & all_4_24 = e2 & ~ (all_4_18 = e0)) | (all_4_23 = e0 % 17.45/3.13 | & all_4_24 = e1 & ~ (all_4_15 = e1)) | (all_4_23 = e0 & all_4_24 = % 17.45/3.13 | e1 & ~ (all_4_19 = e0)) % 17.45/3.13 | (23) all_4_20 = e0 | all_4_21 = e0 | all_4_22 = e0 | all_4_23 = e0 | % 17.45/3.13 | all_4_24 = e0 % 17.45/3.13 | (24) all_4_20 = e1 | all_4_21 = e1 | all_4_22 = e1 | all_4_23 = e1 | % 17.45/3.13 | all_4_24 = e1 % 17.45/3.13 | % 17.45/3.13 | DELTA: instantiating (3) with fresh symbols all_6_0, all_6_1, all_6_2, % 17.45/3.13 | all_6_3, all_6_4, all_6_5, all_6_6, all_6_7, all_6_8, all_6_9, % 17.45/3.13 | all_6_10, all_6_11, all_6_12, all_6_13, all_6_14, all_6_15, all_6_16, % 17.45/3.13 | all_6_17, all_6_18, all_6_19, all_6_20, all_6_21, all_6_22, all_6_23, % 17.45/3.13 | all_6_24 gives: % 17.45/3.13 | (25) ~ (all_6_0 = all_6_1) & ~ (all_6_0 = all_6_2) & ~ (all_6_0 = % 17.45/3.13 | all_6_3) & ~ (all_6_0 = all_6_4) & ~ (all_6_0 = all_6_5) & ~ % 17.45/3.13 | (all_6_0 = all_6_10) & ~ (all_6_0 = all_6_15) & ~ (all_6_0 = % 17.45/3.13 | all_6_20) & ~ (all_6_1 = all_6_2) & ~ (all_6_1 = all_6_3) & ~ % 17.45/3.13 | (all_6_1 = all_6_4) & ~ (all_6_1 = all_6_6) & ~ (all_6_1 = all_6_11) % 17.45/3.13 | & ~ (all_6_1 = all_6_16) & ~ (all_6_1 = all_6_21) & ~ (all_6_2 = % 17.45/3.13 | all_6_3) & ~ (all_6_2 = all_6_4) & ~ (all_6_2 = all_6_7) & ~ % 17.45/3.13 | (all_6_2 = all_6_12) & ~ (all_6_2 = all_6_17) & ~ (all_6_2 = % 17.45/3.13 | all_6_22) & ~ (all_6_3 = all_6_4) & ~ (all_6_3 = all_6_8) & ~ % 17.45/3.13 | (all_6_3 = all_6_13) & ~ (all_6_3 = all_6_18) & ~ (all_6_3 = % 17.45/3.14 | all_6_23) & ~ (all_6_4 = all_6_9) & ~ (all_6_4 = all_6_14) & ~ % 17.45/3.14 | (all_6_4 = all_6_19) & ~ (all_6_4 = all_6_24) & ~ (all_6_5 = % 17.45/3.14 | all_6_6) & ~ (all_6_5 = all_6_7) & ~ (all_6_5 = all_6_8) & ~ % 17.45/3.14 | (all_6_5 = all_6_9) & ~ (all_6_5 = all_6_10) & ~ (all_6_5 = % 17.45/3.14 | all_6_15) & ~ (all_6_5 = all_6_20) & ~ (all_6_6 = all_6_7) & ~ % 17.45/3.14 | (all_6_6 = all_6_8) & ~ (all_6_6 = all_6_9) & ~ (all_6_6 = all_6_11) % 17.45/3.14 | & ~ (all_6_6 = all_6_16) & ~ (all_6_6 = all_6_21) & ~ (all_6_7 = % 17.45/3.14 | all_6_8) & ~ (all_6_7 = all_6_9) & ~ (all_6_7 = all_6_12) & ~ % 17.45/3.14 | (all_6_7 = all_6_17) & ~ (all_6_7 = all_6_22) & ~ (all_6_8 = % 17.45/3.14 | all_6_9) & ~ (all_6_8 = all_6_13) & ~ (all_6_8 = all_6_18) & ~ % 17.45/3.14 | (all_6_8 = all_6_23) & ~ (all_6_9 = all_6_14) & ~ (all_6_9 = % 17.45/3.14 | all_6_19) & ~ (all_6_9 = all_6_24) & ~ (all_6_10 = all_6_11) & ~ % 17.45/3.14 | (all_6_10 = all_6_12) & ~ (all_6_10 = all_6_13) & ~ (all_6_10 = % 17.45/3.14 | all_6_14) & ~ (all_6_10 = all_6_15) & ~ (all_6_10 = all_6_20) & ~ % 17.45/3.14 | (all_6_11 = all_6_12) & ~ (all_6_11 = all_6_13) & ~ (all_6_11 = % 17.45/3.14 | all_6_14) & ~ (all_6_11 = all_6_16) & ~ (all_6_11 = all_6_21) & ~ % 17.45/3.14 | (all_6_12 = all_6_13) & ~ (all_6_12 = all_6_14) & ~ (all_6_12 = % 17.45/3.14 | all_6_17) & ~ (all_6_12 = all_6_22) & ~ (all_6_13 = all_6_14) & ~ % 17.45/3.14 | (all_6_13 = all_6_18) & ~ (all_6_13 = all_6_23) & ~ (all_6_14 = % 17.45/3.14 | all_6_19) & ~ (all_6_14 = all_6_24) & ~ (all_6_15 = all_6_16) & ~ % 17.45/3.14 | (all_6_15 = all_6_17) & ~ (all_6_15 = all_6_18) & ~ (all_6_15 = % 17.45/3.14 | all_6_19) & ~ (all_6_15 = all_6_20) & ~ (all_6_16 = all_6_17) & ~ % 17.45/3.14 | (all_6_16 = all_6_18) & ~ (all_6_16 = all_6_19) & ~ (all_6_16 = % 17.45/3.14 | all_6_21) & ~ (all_6_17 = all_6_18) & ~ (all_6_17 = all_6_19) & ~ % 17.45/3.14 | (all_6_17 = all_6_22) & ~ (all_6_18 = all_6_19) & ~ (all_6_18 = % 17.45/3.14 | all_6_23) & ~ (all_6_19 = all_6_24) & ~ (all_6_20 = all_6_21) & ~ % 17.45/3.14 | (all_6_20 = all_6_22) & ~ (all_6_20 = all_6_23) & ~ (all_6_20 = % 17.45/3.14 | all_6_24) & ~ (all_6_21 = all_6_22) & ~ (all_6_21 = all_6_23) & ~ % 17.45/3.14 | (all_6_21 = all_6_24) & ~ (all_6_22 = all_6_23) & ~ (all_6_22 = % 17.45/3.14 | all_6_24) & ~ (all_6_23 = all_6_24) & op(e4, e4) = all_6_0 & op(e4, % 17.45/3.14 | e3) = all_6_5 & op(e4, e2) = all_6_10 & op(e4, e1) = all_6_15 & % 17.45/3.14 | op(e4, e0) = all_6_20 & op(e3, e4) = all_6_1 & op(e3, e3) = all_6_6 & % 17.45/3.14 | op(e3, e2) = all_6_11 & op(e3, e1) = all_6_16 & op(e3, e0) = all_6_21 % 17.45/3.14 | & op(e2, e4) = all_6_2 & op(e2, e3) = all_6_7 & op(e2, e2) = all_6_12 % 17.45/3.14 | & op(e2, e1) = all_6_17 & op(e2, e0) = all_6_22 & op(e1, e4) = all_6_3 % 17.45/3.14 | & op(e1, e3) = all_6_8 & op(e1, e2) = all_6_13 & op(e1, e1) = all_6_18 % 17.45/3.14 | & op(e1, e0) = all_6_23 & op(e0, e4) = all_6_4 & op(e0, e3) = all_6_9 % 17.45/3.14 | & op(e0, e2) = all_6_14 & op(e0, e1) = all_6_19 & op(e0, e0) = % 17.45/3.14 | all_6_24 & $i(all_6_0) & $i(all_6_1) & $i(all_6_2) & $i(all_6_3) & % 17.45/3.14 | $i(all_6_4) & $i(all_6_5) & $i(all_6_6) & $i(all_6_7) & $i(all_6_8) & % 17.45/3.14 | $i(all_6_9) & $i(all_6_10) & $i(all_6_11) & $i(all_6_12) & % 17.45/3.14 | $i(all_6_13) & $i(all_6_14) & $i(all_6_15) & $i(all_6_16) & % 17.45/3.14 | $i(all_6_17) & $i(all_6_18) & $i(all_6_19) & $i(all_6_20) & % 17.45/3.14 | $i(all_6_21) & $i(all_6_22) & $i(all_6_23) & $i(all_6_24) % 17.45/3.14 | % 17.45/3.14 | ALPHA: (25) implies: % 17.45/3.14 | (26) ~ (all_6_13 = all_6_18) % 17.45/3.14 | (27) ~ (all_6_12 = all_6_13) % 17.45/3.14 | (28) op(e1, e1) = all_6_18 % 17.45/3.14 | (29) op(e1, e2) = all_6_13 % 17.45/3.14 | (30) op(e2, e2) = all_6_12 % 17.45/3.14 | (31) op(e4, e4) = all_6_0 % 17.45/3.14 | % 17.45/3.14 | DELTA: instantiating (1) with fresh symbols all_8_0, all_8_1, all_8_2, % 17.45/3.14 | all_8_3, all_8_4, all_8_5, all_8_6, all_8_7, all_8_8, all_8_9, % 17.45/3.14 | all_8_10, all_8_11, all_8_12, all_8_13, all_8_14, all_8_15, all_8_16, % 17.45/3.14 | all_8_17, all_8_18, all_8_19, all_8_20, all_8_21, all_8_22, all_8_23, % 17.45/3.14 | all_8_24 gives: % 17.45/3.14 | (32) op(e4, e4) = all_8_0 & op(e4, e3) = all_8_1 & op(e4, e2) = all_8_2 & % 17.45/3.14 | op(e4, e1) = all_8_3 & op(e4, e0) = all_8_4 & op(e3, e4) = all_8_5 & % 17.45/3.14 | op(e3, e3) = all_8_6 & op(e3, e2) = all_8_7 & op(e3, e1) = all_8_8 & % 17.45/3.14 | op(e3, e0) = all_8_9 & op(e2, e4) = all_8_10 & op(e2, e3) = all_8_11 & % 17.45/3.14 | op(e2, e2) = all_8_12 & op(e2, e1) = all_8_13 & op(e2, e0) = all_8_14 % 17.45/3.14 | & op(e1, e4) = all_8_15 & op(e1, e3) = all_8_16 & op(e1, e2) = % 17.45/3.14 | all_8_17 & op(e1, e1) = all_8_18 & op(e1, e0) = all_8_19 & op(e0, e4) % 17.45/3.14 | = all_8_20 & op(e0, e3) = all_8_21 & op(e0, e2) = all_8_22 & op(e0, % 17.45/3.14 | e1) = all_8_23 & op(e0, e0) = all_8_24 & $i(all_8_0) & $i(all_8_1) & % 17.45/3.14 | $i(all_8_2) & $i(all_8_3) & $i(all_8_4) & $i(all_8_5) & $i(all_8_6) & % 17.45/3.14 | $i(all_8_7) & $i(all_8_8) & $i(all_8_9) & $i(all_8_10) & $i(all_8_11) % 17.45/3.14 | & $i(all_8_12) & $i(all_8_13) & $i(all_8_14) & $i(all_8_15) & % 17.45/3.14 | $i(all_8_16) & $i(all_8_17) & $i(all_8_18) & $i(all_8_19) & % 17.45/3.14 | $i(all_8_20) & $i(all_8_21) & $i(all_8_22) & $i(all_8_23) & % 17.45/3.14 | $i(all_8_24) & (all_8_0 = e4 | all_8_0 = e3 | all_8_0 = e2 | all_8_0 = % 17.45/3.14 | e1 | all_8_0 = e0) & (all_8_1 = e4 | all_8_1 = e3 | all_8_1 = e2 | % 17.45/3.14 | all_8_1 = e1 | all_8_1 = e0) & (all_8_2 = e4 | all_8_2 = e3 | % 17.45/3.14 | all_8_2 = e2 | all_8_2 = e1 | all_8_2 = e0) & (all_8_3 = e4 | % 17.45/3.14 | all_8_3 = e3 | all_8_3 = e2 | all_8_3 = e1 | all_8_3 = e0) & % 17.45/3.14 | (all_8_4 = e4 | all_8_4 = e3 | all_8_4 = e2 | all_8_4 = e1 | all_8_4 = % 17.45/3.14 | e0) & (all_8_5 = e4 | all_8_5 = e3 | all_8_5 = e2 | all_8_5 = e1 | % 17.45/3.14 | all_8_5 = e0) & (all_8_6 = e4 | all_8_6 = e3 | all_8_6 = e2 | % 17.45/3.14 | all_8_6 = e1 | all_8_6 = e0) & (all_8_7 = e4 | all_8_7 = e3 | % 17.45/3.14 | all_8_7 = e2 | all_8_7 = e1 | all_8_7 = e0) & (all_8_8 = e4 | % 17.45/3.14 | all_8_8 = e3 | all_8_8 = e2 | all_8_8 = e1 | all_8_8 = e0) & % 17.45/3.14 | (all_8_9 = e4 | all_8_9 = e3 | all_8_9 = e2 | all_8_9 = e1 | all_8_9 = % 17.45/3.14 | e0) & (all_8_10 = e4 | all_8_10 = e3 | all_8_10 = e2 | all_8_10 = e1 % 17.45/3.14 | | all_8_10 = e0) & (all_8_11 = e4 | all_8_11 = e3 | all_8_11 = e2 | % 17.45/3.14 | all_8_11 = e1 | all_8_11 = e0) & (all_8_12 = e4 | all_8_12 = e3 | % 17.45/3.14 | all_8_12 = e2 | all_8_12 = e1 | all_8_12 = e0) & (all_8_13 = e4 | % 17.45/3.14 | all_8_13 = e3 | all_8_13 = e2 | all_8_13 = e1 | all_8_13 = e0) & % 17.45/3.14 | (all_8_14 = e4 | all_8_14 = e3 | all_8_14 = e2 | all_8_14 = e1 | % 17.45/3.14 | all_8_14 = e0) & (all_8_15 = e4 | all_8_15 = e3 | all_8_15 = e2 | % 17.45/3.14 | all_8_15 = e1 | all_8_15 = e0) & (all_8_16 = e4 | all_8_16 = e3 | % 17.45/3.14 | all_8_16 = e2 | all_8_16 = e1 | all_8_16 = e0) & (all_8_17 = e4 | % 17.45/3.14 | all_8_17 = e3 | all_8_17 = e2 | all_8_17 = e1 | all_8_17 = e0) & % 17.45/3.14 | (all_8_18 = e4 | all_8_18 = e3 | all_8_18 = e2 | all_8_18 = e1 | % 17.45/3.14 | all_8_18 = e0) & (all_8_19 = e4 | all_8_19 = e3 | all_8_19 = e2 | % 17.45/3.14 | all_8_19 = e1 | all_8_19 = e0) & (all_8_20 = e4 | all_8_20 = e3 | % 17.45/3.14 | all_8_20 = e2 | all_8_20 = e1 | all_8_20 = e0) & (all_8_21 = e4 | % 17.45/3.14 | all_8_21 = e3 | all_8_21 = e2 | all_8_21 = e1 | all_8_21 = e0) & % 17.45/3.14 | (all_8_22 = e4 | all_8_22 = e3 | all_8_22 = e2 | all_8_22 = e1 | % 17.45/3.14 | all_8_22 = e0) & (all_8_23 = e4 | all_8_23 = e3 | all_8_23 = e2 | % 17.45/3.14 | all_8_23 = e1 | all_8_23 = e0) & (all_8_24 = e4 | all_8_24 = e3 | % 17.45/3.14 | all_8_24 = e2 | all_8_24 = e1 | all_8_24 = e0) % 17.45/3.14 | % 17.45/3.14 | ALPHA: (32) implies: % 17.45/3.14 | (33) op(e1, e1) = all_8_18 % 17.45/3.14 | (34) op(e1, e2) = all_8_17 % 17.45/3.14 | (35) op(e2, e2) = all_8_12 % 17.45/3.14 | (36) op(e4, e4) = all_8_0 % 17.45/3.14 | % 17.45/3.14 | DELTA: instantiating (2) with fresh symbols all_10_0, all_10_1, all_10_2, % 17.45/3.14 | all_10_3, all_10_4, all_10_5, all_10_6, all_10_7, all_10_8, all_10_9, % 17.45/3.14 | all_10_10, all_10_11, all_10_12, all_10_13, all_10_14, all_10_15, % 17.45/3.14 | all_10_16, all_10_17, all_10_18, all_10_19, all_10_20, all_10_21, % 17.45/3.14 | all_10_22, all_10_23, all_10_24 gives: % 17.45/3.15 | (37) op(e4, e4) = all_10_0 & op(e4, e3) = all_10_1 & op(e4, e2) = all_10_4 % 17.45/3.15 | & op(e4, e1) = all_10_9 & op(e4, e0) = all_10_16 & op(e3, e4) = % 17.45/3.15 | all_10_2 & op(e3, e3) = all_10_3 & op(e3, e2) = all_10_5 & op(e3, e1) % 17.45/3.15 | = all_10_10 & op(e3, e0) = all_10_17 & op(e2, e4) = all_10_6 & op(e2, % 17.45/3.15 | e3) = all_10_7 & op(e2, e2) = all_10_8 & op(e2, e1) = all_10_11 & % 17.45/3.15 | op(e2, e0) = all_10_18 & op(e1, e4) = all_10_12 & op(e1, e3) = % 17.45/3.15 | all_10_13 & op(e1, e2) = all_10_14 & op(e1, e1) = all_10_15 & op(e1, % 17.45/3.15 | e0) = all_10_19 & op(e0, e4) = all_10_20 & op(e0, e3) = all_10_21 & % 17.45/3.15 | op(e0, e2) = all_10_22 & op(e0, e1) = all_10_23 & op(e0, e0) = % 17.45/3.15 | all_10_24 & $i(all_10_0) & $i(all_10_1) & $i(all_10_2) & $i(all_10_3) % 17.45/3.15 | & $i(all_10_4) & $i(all_10_5) & $i(all_10_6) & $i(all_10_7) & % 17.45/3.15 | $i(all_10_8) & $i(all_10_9) & $i(all_10_10) & $i(all_10_11) & % 17.45/3.15 | $i(all_10_12) & $i(all_10_13) & $i(all_10_14) & $i(all_10_15) & % 17.45/3.15 | $i(all_10_16) & $i(all_10_17) & $i(all_10_18) & $i(all_10_19) & % 17.45/3.15 | $i(all_10_20) & $i(all_10_21) & $i(all_10_22) & $i(all_10_23) & % 17.45/3.15 | $i(all_10_24) & (all_10_0 = e4 | all_10_1 = e4 | all_10_4 = e4 | % 17.45/3.15 | all_10_9 = e4 | all_10_16 = e4) & (all_10_0 = e4 | all_10_2 = e4 | % 17.45/3.15 | all_10_6 = e4 | all_10_12 = e4 | all_10_20 = e4) & (all_10_0 = e3 | % 17.45/3.15 | all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | all_10_16 = e3) & % 17.45/3.15 | (all_10_0 = e3 | all_10_2 = e3 | all_10_6 = e3 | all_10_12 = e3 | % 17.45/3.15 | all_10_20 = e3) & (all_10_0 = e2 | all_10_1 = e2 | all_10_4 = e2 | % 17.45/3.15 | all_10_9 = e2 | all_10_16 = e2) & (all_10_0 = e2 | all_10_2 = e2 | % 17.45/3.15 | all_10_6 = e2 | all_10_12 = e2 | all_10_20 = e2) & (all_10_0 = e1 | % 17.45/3.15 | all_10_1 = e1 | all_10_4 = e1 | all_10_9 = e1 | all_10_16 = e1) & % 17.45/3.15 | (all_10_0 = e1 | all_10_2 = e1 | all_10_6 = e1 | all_10_12 = e1 | % 17.45/3.15 | all_10_20 = e1) & (all_10_0 = e0 | all_10_1 = e0 | all_10_4 = e0 | % 17.45/3.15 | all_10_9 = e0 | all_10_16 = e0) & (all_10_0 = e0 | all_10_2 = e0 | % 17.45/3.15 | all_10_6 = e0 | all_10_12 = e0 | all_10_20 = e0) & (all_10_1 = e4 | % 17.45/3.15 | all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | all_10_21 = e4) & % 17.45/3.15 | (all_10_1 = e3 | all_10_3 = e3 | all_10_7 = e3 | all_10_13 = e3 | % 17.45/3.15 | all_10_21 = e3) & (all_10_1 = e2 | all_10_3 = e2 | all_10_7 = e2 | % 17.45/3.15 | all_10_13 = e2 | all_10_21 = e2) & (all_10_1 = e1 | all_10_3 = e1 | % 17.45/3.15 | all_10_7 = e1 | all_10_13 = e1 | all_10_21 = e1) & (all_10_1 = e0 | % 17.45/3.15 | all_10_3 = e0 | all_10_7 = e0 | all_10_13 = e0 | all_10_21 = e0) & % 17.45/3.15 | (all_10_2 = e4 | all_10_3 = e4 | all_10_5 = e4 | all_10_10 = e4 | % 17.45/3.15 | all_10_17 = e4) & (all_10_2 = e3 | all_10_3 = e3 | all_10_5 = e3 | % 17.45/3.15 | all_10_10 = e3 | all_10_17 = e3) & (all_10_2 = e2 | all_10_3 = e2 | % 17.45/3.15 | all_10_5 = e2 | all_10_10 = e2 | all_10_17 = e2) & (all_10_2 = e1 | % 17.45/3.15 | all_10_3 = e1 | all_10_5 = e1 | all_10_10 = e1 | all_10_17 = e1) & % 17.45/3.15 | (all_10_2 = e0 | all_10_3 = e0 | all_10_5 = e0 | all_10_10 = e0 | % 17.45/3.15 | all_10_17 = e0) & (all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 | % 17.45/3.15 | all_10_14 = e4 | all_10_22 = e4) & (all_10_4 = e3 | all_10_5 = e3 | % 17.45/3.15 | all_10_8 = e3 | all_10_14 = e3 | all_10_22 = e3) & (all_10_4 = e2 | % 17.45/3.15 | all_10_5 = e2 | all_10_8 = e2 | all_10_14 = e2 | all_10_22 = e2) & % 17.45/3.15 | (all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 17.45/3.15 | all_10_22 = e1) & (all_10_4 = e0 | all_10_5 = e0 | all_10_8 = e0 | % 17.45/3.15 | all_10_14 = e0 | all_10_22 = e0) & (all_10_6 = e4 | all_10_7 = e4 | % 17.45/3.15 | all_10_8 = e4 | all_10_11 = e4 | all_10_18 = e4) & (all_10_6 = e3 | % 17.45/3.15 | all_10_7 = e3 | all_10_8 = e3 | all_10_11 = e3 | all_10_18 = e3) & % 17.45/3.15 | (all_10_6 = e2 | all_10_7 = e2 | all_10_8 = e2 | all_10_11 = e2 | % 17.45/3.15 | all_10_18 = e2) & (all_10_6 = e1 | all_10_7 = e1 | all_10_8 = e1 | % 17.45/3.15 | all_10_11 = e1 | all_10_18 = e1) & (all_10_6 = e0 | all_10_7 = e0 | % 17.45/3.15 | all_10_8 = e0 | all_10_11 = e0 | all_10_18 = e0) & (all_10_9 = e4 | % 17.45/3.15 | all_10_10 = e4 | all_10_11 = e4 | all_10_15 = e4 | all_10_23 = e4) & % 17.45/3.15 | (all_10_9 = e3 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 17.45/3.15 | all_10_23 = e3) & (all_10_9 = e2 | all_10_10 = e2 | all_10_11 = e2 | % 17.45/3.15 | all_10_15 = e2 | all_10_23 = e2) & (all_10_9 = e1 | all_10_10 = e1 | % 17.45/3.15 | all_10_11 = e1 | all_10_15 = e1 | all_10_23 = e1) & (all_10_9 = e0 | % 17.45/3.15 | all_10_10 = e0 | all_10_11 = e0 | all_10_15 = e0 | all_10_23 = e0) & % 17.45/3.15 | (all_10_12 = e4 | all_10_13 = e4 | all_10_14 = e4 | all_10_15 = e4 | % 17.45/3.15 | all_10_19 = e4) & (all_10_12 = e3 | all_10_13 = e3 | all_10_14 = e3 % 17.45/3.15 | | all_10_15 = e3 | all_10_19 = e3) & (all_10_12 = e2 | all_10_13 = % 17.45/3.15 | e2 | all_10_14 = e2 | all_10_15 = e2 | all_10_19 = e2) & (all_10_12 % 17.45/3.15 | = e1 | all_10_13 = e1 | all_10_14 = e1 | all_10_15 = e1 | all_10_19 % 17.45/3.15 | = e1) & (all_10_12 = e0 | all_10_13 = e0 | all_10_14 = e0 | % 17.45/3.15 | all_10_15 = e0 | all_10_19 = e0) & (all_10_16 = e4 | all_10_17 = e4 % 17.45/3.15 | | all_10_18 = e4 | all_10_19 = e4 | all_10_24 = e4) & (all_10_16 = % 17.45/3.15 | e3 | all_10_17 = e3 | all_10_18 = e3 | all_10_19 = e3 | all_10_24 = % 17.45/3.15 | e3) & (all_10_16 = e2 | all_10_17 = e2 | all_10_18 = e2 | all_10_19 % 17.45/3.15 | = e2 | all_10_24 = e2) & (all_10_16 = e1 | all_10_17 = e1 | % 17.45/3.15 | all_10_18 = e1 | all_10_19 = e1 | all_10_24 = e1) & (all_10_20 = e4 % 17.45/3.15 | | all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | all_10_24 = e4) % 17.45/3.15 | & (all_10_20 = e3 | all_10_21 = e3 | all_10_22 = e3 | all_10_23 = e3 | % 17.45/3.15 | all_10_24 = e3) & (all_10_20 = e2 | all_10_21 = e2 | all_10_22 = e2 % 17.45/3.15 | | all_10_23 = e2 | all_10_24 = e2) & (all_10_20 = e1 | all_10_21 = % 17.45/3.15 | e1 | all_10_22 = e1 | all_10_23 = e1 | all_10_24 = e1) & (all_10_24 % 17.45/3.15 | = e0 | ((all_10_16 = e0 | all_10_17 = e0 | all_10_18 = e0 | % 17.45/3.15 | all_10_19 = e0) & (all_10_20 = e0 | all_10_21 = e0 | all_10_22 = % 17.45/3.15 | e0 | all_10_23 = e0))) % 17.45/3.15 | % 17.45/3.15 | ALPHA: (37) implies: % 17.45/3.15 | (38) op(e0, e0) = all_10_24 % 17.45/3.15 | (39) op(e1, e1) = all_10_15 % 17.45/3.15 | (40) op(e1, e2) = all_10_14 % 17.45/3.15 | (41) op(e2, e2) = all_10_8 % 17.45/3.15 | (42) op(e4, e4) = all_10_0 % 17.45/3.15 | (43) all_10_24 = e0 | ((all_10_16 = e0 | all_10_17 = e0 | all_10_18 = e0 | % 17.45/3.15 | all_10_19 = e0) & (all_10_20 = e0 | all_10_21 = e0 | all_10_22 = % 17.45/3.15 | e0 | all_10_23 = e0)) % 17.45/3.15 | % 17.45/3.15 | GROUND_INST: instantiating (function-axioms) with all_4_24, all_10_24, e0, e0, % 17.45/3.15 | simplifying with (17), (38) gives: % 17.45/3.15 | (44) all_10_24 = all_4_24 % 17.45/3.15 | % 17.45/3.15 | GROUND_INST: instantiating (function-axioms) with all_4_23, all_8_18, e1, e1, % 17.45/3.15 | simplifying with (18), (33) gives: % 17.45/3.15 | (45) all_8_18 = all_4_23 % 17.45/3.15 | % 17.45/3.15 | GROUND_INST: instantiating (function-axioms) with e4, all_8_18, e1, e1, % 17.45/3.15 | simplifying with (11), (33) gives: % 17.45/3.15 | (46) all_8_18 = e4 % 17.45/3.15 | % 17.45/3.15 | GROUND_INST: instantiating (function-axioms) with all_8_18, all_10_15, e1, e1, % 17.45/3.15 | simplifying with (33), (39) gives: % 17.45/3.15 | (47) all_10_15 = all_8_18 % 17.45/3.15 | % 17.45/3.15 | GROUND_INST: instantiating (function-axioms) with all_6_18, all_10_15, e1, e1, % 17.45/3.15 | simplifying with (28), (39) gives: % 17.45/3.15 | (48) all_10_15 = all_6_18 % 17.45/3.15 | % 17.45/3.15 | GROUND_INST: instantiating (function-axioms) with all_6_13, all_8_17, e2, e1, % 17.45/3.15 | simplifying with (29), (34) gives: % 17.45/3.15 | (49) all_8_17 = all_6_13 % 17.45/3.15 | % 17.45/3.15 | GROUND_INST: instantiating (function-axioms) with all_4_14, all_8_17, e2, e1, % 17.45/3.15 | simplifying with (19), (34) gives: % 17.45/3.15 | (50) all_8_17 = all_4_14 % 17.45/3.15 | % 17.45/3.15 | GROUND_INST: instantiating (function-axioms) with all_6_13, all_10_14, e2, e1, % 17.45/3.15 | simplifying with (29), (40) gives: % 17.45/3.15 | (51) all_10_14 = all_6_13 % 17.45/3.15 | % 17.45/3.15 | GROUND_INST: instantiating (function-axioms) with e0, all_10_14, e2, e1, % 17.45/3.15 | simplifying with (12), (40) gives: % 17.45/3.15 | (52) all_10_14 = e0 % 17.45/3.15 | % 17.45/3.15 | GROUND_INST: instantiating (function-axioms) with all_4_22, all_6_12, e2, e2, % 17.45/3.15 | simplifying with (20), (30) gives: % 17.45/3.15 | (53) all_6_12 = all_4_22 % 17.45/3.15 | % 17.45/3.15 | GROUND_INST: instantiating (function-axioms) with all_6_12, all_8_12, e2, e2, % 17.45/3.15 | simplifying with (30), (35) gives: % 17.45/3.15 | (54) all_8_12 = all_6_12 % 17.45/3.15 | % 17.45/3.15 | GROUND_INST: instantiating (function-axioms) with all_8_12, all_10_8, e2, e2, % 17.45/3.15 | simplifying with (35), (41) gives: % 17.45/3.15 | (55) all_10_8 = all_8_12 % 17.45/3.15 | % 17.45/3.15 | GROUND_INST: instantiating (function-axioms) with e3, all_10_8, e2, e2, % 17.45/3.15 | simplifying with (13), (41) gives: % 17.45/3.15 | (56) all_10_8 = e3 % 17.45/3.15 | % 17.45/3.15 | GROUND_INST: instantiating (function-axioms) with all_4_20, all_6_0, e4, e4, % 17.45/3.15 | simplifying with (21), (31) gives: % 17.45/3.15 | (57) all_6_0 = all_4_20 % 17.45/3.15 | % 17.45/3.15 | GROUND_INST: instantiating (function-axioms) with all_6_0, all_8_0, e4, e4, % 17.45/3.15 | simplifying with (31), (36) gives: % 17.45/3.15 | (58) all_8_0 = all_6_0 % 17.45/3.15 | % 17.45/3.15 | GROUND_INST: instantiating (function-axioms) with all_8_0, all_10_0, e4, e4, % 17.45/3.15 | simplifying with (36), (42) gives: % 17.45/3.15 | (59) all_10_0 = all_8_0 % 17.45/3.15 | % 17.45/3.15 | GROUND_INST: instantiating (function-axioms) with e2, all_10_0, e4, e4, % 17.45/3.15 | simplifying with (14), (42) gives: % 17.45/3.15 | (60) all_10_0 = e2 % 17.45/3.15 | % 17.45/3.15 | COMBINE_EQS: (59), (60) imply: % 17.45/3.15 | (61) all_8_0 = e2 % 17.45/3.15 | % 17.45/3.15 | SIMP: (61) implies: % 17.45/3.15 | (62) all_8_0 = e2 % 17.45/3.15 | % 17.45/3.15 | COMBINE_EQS: (55), (56) imply: % 17.45/3.15 | (63) all_8_12 = e3 % 17.45/3.15 | % 17.45/3.15 | SIMP: (63) implies: % 17.45/3.15 | (64) all_8_12 = e3 % 17.45/3.15 | % 17.45/3.15 | COMBINE_EQS: (51), (52) imply: % 17.45/3.15 | (65) all_6_13 = e0 % 17.45/3.15 | % 17.45/3.15 | SIMP: (65) implies: % 17.45/3.15 | (66) all_6_13 = e0 % 17.45/3.15 | % 17.45/3.15 | COMBINE_EQS: (47), (48) imply: % 17.45/3.15 | (67) all_8_18 = all_6_18 % 17.45/3.15 | % 17.45/3.15 | SIMP: (67) implies: % 17.45/3.15 | (68) all_8_18 = all_6_18 % 17.45/3.15 | % 17.45/3.15 | COMBINE_EQS: (58), (62) imply: % 17.45/3.15 | (69) all_6_0 = e2 % 17.45/3.15 | % 17.45/3.15 | SIMP: (69) implies: % 17.45/3.15 | (70) all_6_0 = e2 % 17.45/3.15 | % 17.45/3.15 | COMBINE_EQS: (54), (64) imply: % 17.45/3.15 | (71) all_6_12 = e3 % 17.45/3.15 | % 17.45/3.15 | SIMP: (71) implies: % 17.45/3.15 | (72) all_6_12 = e3 % 17.45/3.15 | % 17.45/3.15 | COMBINE_EQS: (49), (50) imply: % 17.45/3.15 | (73) all_6_13 = all_4_14 % 17.45/3.15 | % 17.45/3.15 | SIMP: (73) implies: % 17.45/3.15 | (74) all_6_13 = all_4_14 % 17.45/3.15 | % 17.45/3.15 | COMBINE_EQS: (46), (68) imply: % 17.45/3.15 | (75) all_6_18 = e4 % 17.45/3.15 | % 17.45/3.15 | COMBINE_EQS: (45), (68) imply: % 17.45/3.15 | (76) all_6_18 = all_4_23 % 17.45/3.15 | % 17.45/3.15 | COMBINE_EQS: (57), (70) imply: % 17.45/3.16 | (77) all_4_20 = e2 % 17.45/3.16 | % 17.45/3.16 | SIMP: (77) implies: % 17.45/3.16 | (78) all_4_20 = e2 % 17.45/3.16 | % 17.45/3.16 | COMBINE_EQS: (53), (72) imply: % 17.45/3.16 | (79) all_4_22 = e3 % 17.45/3.16 | % 17.45/3.16 | COMBINE_EQS: (66), (74) imply: % 17.45/3.16 | (80) all_4_14 = e0 % 17.45/3.16 | % 17.45/3.16 | COMBINE_EQS: (75), (76) imply: % 17.45/3.16 | (81) all_4_23 = e4 % 17.45/3.16 | % 17.45/3.16 | SIMP: (81) implies: % 17.45/3.16 | (82) all_4_23 = e4 % 17.45/3.16 | % 17.45/3.16 | REDUCE: (27), (66), (72) imply: % 17.45/3.16 | (83) ~ (e3 = e0) % 17.45/3.16 | % 17.45/3.16 | REDUCE: (26), (66), (75) imply: % 17.45/3.16 | (84) ~ (e4 = e0) % 17.45/3.16 | % 17.45/3.16 | SIMP: (84) implies: % 17.45/3.16 | (85) ~ (e4 = e0) % 17.45/3.16 | % 17.45/3.16 | BETA: splitting (43) gives: % 17.45/3.16 | % 17.45/3.16 | Case 1: % 17.45/3.16 | | % 17.45/3.16 | | (86) all_10_24 = e0 % 17.45/3.16 | | % 17.45/3.16 | | COMBINE_EQS: (44), (86) imply: % 17.45/3.16 | | (87) all_4_24 = e0 % 17.45/3.16 | | % 17.45/3.16 | | SIMP: (87) implies: % 17.45/3.16 | | (88) all_4_24 = e0 % 17.45/3.16 | | % 17.45/3.16 | | BETA: splitting (22) gives: % 17.45/3.16 | | % 17.45/3.16 | | Case 1: % 17.45/3.16 | | | % 17.45/3.16 | | | (89) (all_4_20 = e3 & all_4_21 = e4 & ~ (all_4_0 = e4)) | (all_4_20 = % 17.45/3.16 | | | e3 & all_4_21 = e4 & ~ (all_4_4 = e3)) | (all_4_20 = e2 & % 17.45/3.16 | | | all_4_22 = e4 & ~ (all_4_1 = e4)) | (all_4_20 = e2 & all_4_22 = % 17.45/3.16 | | | e4 & ~ (all_4_8 = e2)) | (all_4_20 = e1 & all_4_23 = e4 & ~ % 17.45/3.16 | | | (all_4_2 = e4)) | (all_4_20 = e1 & all_4_23 = e4 & ~ (all_4_12 % 17.45/3.16 | | | = e1)) | (all_4_20 = e0 & all_4_24 = e4 & ~ (all_4_3 = e4)) | % 17.45/3.16 | | | (all_4_20 = e0 & all_4_24 = e4 & ~ (all_4_16 = e0)) | (all_4_21 = % 17.45/3.16 | | | e2 & all_4_22 = e3 & ~ (all_4_5 = e3)) | (all_4_21 = e2 & % 17.45/3.16 | | | all_4_22 = e3 & ~ (all_4_9 = e2)) % 17.45/3.16 | | | % 17.45/3.16 | | | BETA: splitting (89) gives: % 17.45/3.16 | | | % 17.45/3.16 | | | Case 1: % 17.45/3.16 | | | | % 17.45/3.16 | | | | (90) (all_4_20 = e3 & all_4_21 = e4 & ~ (all_4_0 = e4)) | (all_4_20 % 17.45/3.16 | | | | = e3 & all_4_21 = e4 & ~ (all_4_4 = e3)) | (all_4_20 = e2 & % 17.45/3.16 | | | | all_4_22 = e4 & ~ (all_4_1 = e4)) | (all_4_20 = e2 & all_4_22 % 17.45/3.16 | | | | = e4 & ~ (all_4_8 = e2)) | (all_4_20 = e1 & all_4_23 = e4 & % 17.45/3.16 | | | | ~ (all_4_2 = e4)) % 17.45/3.16 | | | | % 17.45/3.16 | | | | BETA: splitting (90) gives: % 17.45/3.16 | | | | % 17.45/3.16 | | | | Case 1: % 17.45/3.16 | | | | | % 17.45/3.16 | | | | | (91) (all_4_20 = e3 & all_4_21 = e4 & ~ (all_4_0 = e4)) | % 17.45/3.16 | | | | | (all_4_20 = e3 & all_4_21 = e4 & ~ (all_4_4 = e3)) % 17.45/3.16 | | | | | % 17.45/3.16 | | | | | REF_CLOSE: (8), (78), (91) are inconsistent by sub-proof #14. % 17.45/3.16 | | | | | % 17.77/3.16 | | | | Case 2: % 17.77/3.16 | | | | | % 17.77/3.16 | | | | | (92) (all_4_20 = e2 & all_4_22 = e4 & ~ (all_4_1 = e4)) | % 17.77/3.16 | | | | | (all_4_20 = e2 & all_4_22 = e4 & ~ (all_4_8 = e2)) | % 17.77/3.16 | | | | | (all_4_20 = e1 & all_4_23 = e4 & ~ (all_4_2 = e4)) % 17.77/3.16 | | | | | % 17.77/3.16 | | | | | BETA: splitting (92) gives: % 17.77/3.16 | | | | | % 17.77/3.16 | | | | | Case 1: % 17.77/3.16 | | | | | | % 17.77/3.16 | | | | | | (93) all_4_20 = e2 & all_4_22 = e4 & ~ (all_4_1 = e4) % 17.77/3.16 | | | | | | % 17.77/3.16 | | | | | | ALPHA: (93) implies: % 17.77/3.16 | | | | | | (94) all_4_22 = e4 % 17.77/3.16 | | | | | | % 17.77/3.16 | | | | | | REF_CLOSE: (10), (79), (94) are inconsistent by sub-proof #13. % 17.77/3.16 | | | | | | % 17.77/3.16 | | | | | Case 2: % 17.77/3.16 | | | | | | % 17.77/3.16 | | | | | | (95) (all_4_20 = e2 & all_4_22 = e4 & ~ (all_4_8 = e2)) | % 17.77/3.16 | | | | | | (all_4_20 = e1 & all_4_23 = e4 & ~ (all_4_2 = e4)) % 17.77/3.16 | | | | | | % 17.77/3.16 | | | | | | BETA: splitting (95) gives: % 17.77/3.16 | | | | | | % 17.77/3.16 | | | | | | Case 1: % 17.77/3.16 | | | | | | | % 17.77/3.16 | | | | | | | (96) all_4_20 = e2 & all_4_22 = e4 & ~ (all_4_8 = e2) % 17.77/3.16 | | | | | | | % 17.77/3.16 | | | | | | | ALPHA: (96) implies: % 17.77/3.16 | | | | | | | (97) all_4_22 = e4 % 17.77/3.16 | | | | | | | % 17.77/3.16 | | | | | | | REF_CLOSE: (10), (79), (97) are inconsistent by sub-proof #13. % 17.77/3.16 | | | | | | | % 17.77/3.16 | | | | | | Case 2: % 17.77/3.16 | | | | | | | % 17.77/3.16 | | | | | | | (98) all_4_20 = e1 & all_4_23 = e4 & ~ (all_4_2 = e4) % 17.77/3.16 | | | | | | | % 17.77/3.16 | | | | | | | REF_CLOSE: (6), (78), (98) are inconsistent by sub-proof #12. % 17.77/3.16 | | | | | | | % 17.77/3.16 | | | | | | End of split % 17.77/3.16 | | | | | | % 17.77/3.16 | | | | | End of split % 17.77/3.16 | | | | | % 17.77/3.16 | | | | End of split % 17.77/3.16 | | | | % 17.77/3.16 | | | Case 2: % 17.77/3.16 | | | | % 17.77/3.16 | | | | (99) (all_4_20 = e1 & all_4_23 = e4 & ~ (all_4_12 = e1)) | (all_4_20 % 17.77/3.16 | | | | = e0 & all_4_24 = e4 & ~ (all_4_3 = e4)) | (all_4_20 = e0 & % 17.77/3.16 | | | | all_4_24 = e4 & ~ (all_4_16 = e0)) | (all_4_21 = e2 & % 17.77/3.16 | | | | all_4_22 = e3 & ~ (all_4_5 = e3)) | (all_4_21 = e2 & all_4_22 % 17.77/3.16 | | | | = e3 & ~ (all_4_9 = e2)) % 17.77/3.16 | | | | % 17.77/3.16 | | | | BETA: splitting (99) gives: % 17.77/3.16 | | | | % 17.77/3.16 | | | | Case 1: % 17.77/3.16 | | | | | % 17.77/3.16 | | | | | (100) (all_4_20 = e1 & all_4_23 = e4 & ~ (all_4_12 = e1)) | % 17.77/3.16 | | | | | (all_4_20 = e0 & all_4_24 = e4 & ~ (all_4_3 = e4)) % 17.77/3.16 | | | | | % 17.77/3.16 | | | | | REF_CLOSE: (5), (6), (78), (100) are inconsistent by sub-proof #11. % 17.77/3.16 | | | | | % 17.77/3.16 | | | | Case 2: % 17.77/3.16 | | | | | % 17.77/3.16 | | | | | (101) (all_4_20 = e0 & all_4_24 = e4 & ~ (all_4_16 = e0)) | % 17.77/3.16 | | | | | (all_4_21 = e2 & all_4_22 = e3 & ~ (all_4_5 = e3)) | % 17.77/3.16 | | | | | (all_4_21 = e2 & all_4_22 = e3 & ~ (all_4_9 = e2)) % 17.77/3.16 | | | | | % 17.77/3.16 | | | | | BETA: splitting (101) gives: % 17.77/3.16 | | | | | % 17.77/3.16 | | | | | Case 1: % 17.77/3.16 | | | | | | % 17.77/3.16 | | | | | | (102) all_4_20 = e0 & all_4_24 = e4 & ~ (all_4_16 = e0) % 17.77/3.16 | | | | | | % 17.77/3.16 | | | | | | REF_CLOSE: (5), (78), (102) are inconsistent by sub-proof #10. % 17.77/3.16 | | | | | | % 17.77/3.16 | | | | | Case 2: % 17.77/3.16 | | | | | | % 17.77/3.16 | | | | | | (103) (all_4_21 = e2 & all_4_22 = e3 & ~ (all_4_5 = e3)) | % 17.77/3.16 | | | | | | (all_4_21 = e2 & all_4_22 = e3 & ~ (all_4_9 = e2)) % 17.77/3.16 | | | | | | % 17.77/3.16 | | | | | | BETA: splitting (103) gives: % 17.77/3.16 | | | | | | % 17.77/3.16 | | | | | | Case 1: % 17.77/3.16 | | | | | | | % 17.77/3.16 | | | | | | | (104) all_4_21 = e2 & all_4_22 = e3 & ~ (all_4_5 = e3) % 17.77/3.16 | | | | | | | % 17.77/3.16 | | | | | | | ALPHA: (104) implies: % 17.77/3.16 | | | | | | | (105) all_4_21 = e2 % 17.77/3.16 | | | | | | | % 17.77/3.16 | | | | | | | REF_CLOSE: (4), (6), (7), (9), (24), (78), (79), (82), (88), (105) % 17.77/3.16 | | | | | | | are inconsistent by sub-proof #7. % 17.77/3.16 | | | | | | | % 17.77/3.16 | | | | | | Case 2: % 17.77/3.16 | | | | | | | % 17.77/3.16 | | | | | | | (106) all_4_21 = e2 & all_4_22 = e3 & ~ (all_4_9 = e2) % 17.77/3.16 | | | | | | | % 17.77/3.16 | | | | | | | ALPHA: (106) implies: % 17.77/3.16 | | | | | | | (107) all_4_21 = e2 % 17.77/3.16 | | | | | | | % 17.77/3.16 | | | | | | | REF_CLOSE: (4), (6), (7), (9), (24), (78), (79), (82), (88), (107) % 17.77/3.16 | | | | | | | are inconsistent by sub-proof #7. % 17.77/3.16 | | | | | | | % 17.77/3.16 | | | | | | End of split % 17.77/3.16 | | | | | | % 17.77/3.16 | | | | | End of split % 17.77/3.16 | | | | | % 17.77/3.16 | | | | End of split % 17.77/3.16 | | | | % 17.77/3.16 | | | End of split % 17.77/3.16 | | | % 17.77/3.16 | | Case 2: % 17.77/3.16 | | | % 17.77/3.17 | | | (108) (all_4_21 = e1 & all_4_23 = e3 & ~ (all_4_6 = e3)) | (all_4_21 = % 17.77/3.17 | | | e1 & all_4_23 = e3 & ~ (all_4_13 = e1)) | (all_4_21 = e0 & % 17.77/3.17 | | | all_4_24 = e3 & ~ (all_4_7 = e3)) | (all_4_21 = e0 & all_4_24 % 17.77/3.17 | | | = e3 & ~ (all_4_17 = e0)) | (all_4_22 = e1 & all_4_23 = e2 & % 17.77/3.17 | | | ~ (all_4_10 = e2)) | (all_4_22 = e1 & all_4_23 = e2 & ~ % 17.77/3.17 | | | (all_4_14 = e1)) | (all_4_22 = e0 & all_4_24 = e2 & ~ % 17.77/3.17 | | | (all_4_11 = e2)) | (all_4_22 = e0 & all_4_24 = e2 & ~ % 17.77/3.17 | | | (all_4_18 = e0)) | (all_4_23 = e0 & all_4_24 = e1 & ~ % 17.77/3.17 | | | (all_4_15 = e1)) | (all_4_23 = e0 & all_4_24 = e1 & ~ % 17.77/3.17 | | | (all_4_19 = e0)) % 17.77/3.17 | | | % 17.77/3.17 | | | BETA: splitting (108) gives: % 17.77/3.17 | | | % 17.77/3.17 | | | Case 1: % 17.77/3.17 | | | | % 17.77/3.17 | | | | (109) (all_4_21 = e1 & all_4_23 = e3 & ~ (all_4_6 = e3)) | (all_4_21 % 17.77/3.17 | | | | = e1 & all_4_23 = e3 & ~ (all_4_13 = e1)) | (all_4_21 = e0 & % 17.77/3.17 | | | | all_4_24 = e3 & ~ (all_4_7 = e3)) | (all_4_21 = e0 & % 17.77/3.17 | | | | all_4_24 = e3 & ~ (all_4_17 = e0)) | (all_4_22 = e1 & % 17.77/3.17 | | | | all_4_23 = e2 & ~ (all_4_10 = e2)) % 17.77/3.17 | | | | % 17.77/3.17 | | | | BETA: splitting (109) gives: % 17.77/3.17 | | | | % 17.77/3.17 | | | | Case 1: % 17.77/3.17 | | | | | % 17.77/3.17 | | | | | (110) (all_4_21 = e1 & all_4_23 = e3 & ~ (all_4_6 = e3)) | % 17.77/3.17 | | | | | (all_4_21 = e1 & all_4_23 = e3 & ~ (all_4_13 = e1)) % 17.77/3.17 | | | | | % 17.77/3.17 | | | | | BETA: splitting (110) gives: % 17.77/3.17 | | | | | % 17.77/3.17 | | | | | Case 1: % 17.77/3.17 | | | | | | % 17.77/3.17 | | | | | | (111) all_4_21 = e1 & all_4_23 = e3 & ~ (all_4_6 = e3) % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | ALPHA: (111) implies: % 17.80/3.17 | | | | | | (112) all_4_23 = e3 % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | REF_CLOSE: (10), (82), (112) are inconsistent by sub-proof #6. % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | Case 2: % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | (113) all_4_21 = e1 & all_4_23 = e3 & ~ (all_4_13 = e1) % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | ALPHA: (113) implies: % 17.80/3.17 | | | | | | (114) all_4_23 = e3 % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | REF_CLOSE: (10), (82), (114) are inconsistent by sub-proof #6. % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | End of split % 17.80/3.17 | | | | | % 17.80/3.17 | | | | Case 2: % 17.80/3.17 | | | | | % 17.80/3.17 | | | | | (115) (all_4_21 = e0 & all_4_24 = e3 & ~ (all_4_7 = e3)) | % 17.80/3.17 | | | | | (all_4_21 = e0 & all_4_24 = e3 & ~ (all_4_17 = e0)) | % 17.80/3.17 | | | | | (all_4_22 = e1 & all_4_23 = e2 & ~ (all_4_10 = e2)) % 17.80/3.17 | | | | | % 17.80/3.17 | | | | | BETA: splitting (115) gives: % 17.80/3.17 | | | | | % 17.80/3.17 | | | | | Case 1: % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | (116) all_4_21 = e0 & all_4_24 = e3 & ~ (all_4_7 = e3) % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | ALPHA: (116) implies: % 17.80/3.17 | | | | | | (117) all_4_21 = e0 % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (22), (24), (78), % 17.80/3.17 | | | | | | (79), (82), (83), (85), (117) are inconsistent by % 17.80/3.17 | | | | | | sub-proof #3. % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | Case 2: % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | (118) (all_4_21 = e0 & all_4_24 = e3 & ~ (all_4_17 = e0)) | % 17.80/3.17 | | | | | | (all_4_22 = e1 & all_4_23 = e2 & ~ (all_4_10 = e2)) % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | BETA: splitting (118) gives: % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | Case 1: % 17.80/3.17 | | | | | | | % 17.80/3.17 | | | | | | | (119) all_4_21 = e0 & all_4_24 = e3 & ~ (all_4_17 = e0) % 17.80/3.17 | | | | | | | % 17.80/3.17 | | | | | | | ALPHA: (119) implies: % 17.80/3.17 | | | | | | | (120) all_4_21 = e0 % 17.80/3.17 | | | | | | | % 17.80/3.17 | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (22), (24), (78), % 17.80/3.17 | | | | | | | (79), (82), (83), (85), (120) are inconsistent by % 17.80/3.17 | | | | | | | sub-proof #3. % 17.80/3.17 | | | | | | | % 17.80/3.17 | | | | | | Case 2: % 17.80/3.17 | | | | | | | % 17.80/3.17 | | | | | | | (121) all_4_22 = e1 & all_4_23 = e2 & ~ (all_4_10 = e2) % 17.80/3.17 | | | | | | | % 17.80/3.17 | | | | | | | ALPHA: (121) implies: % 17.80/3.17 | | | | | | | (122) all_4_22 = e1 % 17.80/3.17 | | | | | | | % 17.80/3.17 | | | | | | | REF_CLOSE: (7), (79), (122) are inconsistent by sub-proof #2. % 17.80/3.17 | | | | | | | % 17.80/3.17 | | | | | | End of split % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | End of split % 17.80/3.17 | | | | | % 17.80/3.17 | | | | End of split % 17.80/3.17 | | | | % 17.80/3.17 | | | Case 2: % 17.80/3.17 | | | | % 17.80/3.17 | | | | (123) (all_4_22 = e1 & all_4_23 = e2 & ~ (all_4_14 = e1)) | % 17.80/3.17 | | | | (all_4_22 = e0 & all_4_24 = e2 & ~ (all_4_11 = e2)) | % 17.80/3.17 | | | | (all_4_22 = e0 & all_4_24 = e2 & ~ (all_4_18 = e0)) | % 17.80/3.17 | | | | (all_4_23 = e0 & all_4_24 = e1 & ~ (all_4_15 = e1)) | % 17.80/3.17 | | | | (all_4_23 = e0 & all_4_24 = e1 & ~ (all_4_19 = e0)) % 17.80/3.17 | | | | % 17.80/3.17 | | | | BETA: splitting (123) gives: % 17.80/3.17 | | | | % 17.80/3.17 | | | | Case 1: % 17.80/3.17 | | | | | % 17.80/3.17 | | | | | (124) (all_4_22 = e1 & all_4_23 = e2 & ~ (all_4_14 = e1)) | % 17.80/3.17 | | | | | (all_4_22 = e0 & all_4_24 = e2 & ~ (all_4_11 = e2)) % 17.80/3.17 | | | | | % 17.80/3.17 | | | | | BETA: splitting (124) gives: % 17.80/3.17 | | | | | % 17.80/3.17 | | | | | Case 1: % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | (125) all_4_22 = e1 & all_4_23 = e2 & ~ (all_4_14 = e1) % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | ALPHA: (125) implies: % 17.80/3.17 | | | | | | (126) all_4_22 = e1 % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | REF_CLOSE: (7), (79), (126) are inconsistent by sub-proof #2. % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | Case 2: % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | (127) all_4_22 = e0 & all_4_24 = e2 & ~ (all_4_11 = e2) % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | ALPHA: (127) implies: % 17.80/3.17 | | | | | | (128) all_4_24 = e2 % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | COMBINE_EQS: (88), (128) imply: % 17.80/3.17 | | | | | | (129) e2 = e0 % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | REDUCE: (5), (129) imply: % 17.80/3.17 | | | | | | (130) $false % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | CLOSE: (130) is inconsistent. % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | End of split % 17.80/3.17 | | | | | % 17.80/3.17 | | | | Case 2: % 17.80/3.17 | | | | | % 17.80/3.17 | | | | | (131) (all_4_22 = e0 & all_4_24 = e2 & ~ (all_4_18 = e0)) | % 17.80/3.17 | | | | | (all_4_23 = e0 & all_4_24 = e1 & ~ (all_4_15 = e1)) | % 17.80/3.17 | | | | | (all_4_23 = e0 & all_4_24 = e1 & ~ (all_4_19 = e0)) % 17.80/3.17 | | | | | % 17.80/3.17 | | | | | BETA: splitting (131) gives: % 17.80/3.17 | | | | | % 17.80/3.17 | | | | | Case 1: % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | (132) all_4_22 = e0 & all_4_24 = e2 & ~ (all_4_18 = e0) % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | ALPHA: (132) implies: % 17.80/3.17 | | | | | | (133) all_4_24 = e2 % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | COMBINE_EQS: (88), (133) imply: % 17.80/3.17 | | | | | | (134) e2 = e0 % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | REDUCE: (5), (134) imply: % 17.80/3.17 | | | | | | (135) $false % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | CLOSE: (135) is inconsistent. % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | Case 2: % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | (136) (all_4_23 = e0 & all_4_24 = e1 & ~ (all_4_15 = e1)) | % 17.80/3.17 | | | | | | (all_4_23 = e0 & all_4_24 = e1 & ~ (all_4_19 = e0)) % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | BETA: splitting (136) gives: % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | | Case 1: % 17.80/3.17 | | | | | | | % 17.80/3.17 | | | | | | | (137) all_4_23 = e0 & all_4_24 = e1 & ~ (all_4_15 = e1) % 17.80/3.17 | | | | | | | % 17.80/3.17 | | | | | | | ALPHA: (137) implies: % 17.80/3.17 | | | | | | | (138) all_4_24 = e1 % 17.80/3.17 | | | | | | | % 17.80/3.17 | | | | | | | REF_CLOSE: (4), (88), (138) are inconsistent by sub-proof #1. % 17.80/3.17 | | | | | | | % 17.80/3.17 | | | | | | Case 2: % 17.80/3.17 | | | | | | | % 17.80/3.17 | | | | | | | (139) all_4_23 = e0 & all_4_24 = e1 & ~ (all_4_19 = e0) % 17.80/3.17 | | | | | | | % 17.80/3.17 | | | | | | | ALPHA: (139) implies: % 17.80/3.17 | | | | | | | (140) all_4_24 = e1 % 17.80/3.17 | | | | | | | % 17.80/3.17 | | | | | | | REF_CLOSE: (4), (88), (140) are inconsistent by sub-proof #1. % 17.80/3.17 | | | | | | | % 17.80/3.17 | | | | | | End of split % 17.80/3.17 | | | | | | % 17.80/3.17 | | | | | End of split % 17.80/3.17 | | | | | % 17.80/3.17 | | | | End of split % 17.80/3.17 | | | | % 17.80/3.17 | | | End of split % 17.80/3.17 | | | % 17.80/3.17 | | End of split % 17.80/3.17 | | % 17.80/3.17 | Case 2: % 17.80/3.17 | | % 17.80/3.17 | | (141) ~ (all_10_24 = e0) % 17.80/3.17 | | % 17.80/3.17 | | REDUCE: (44), (141) imply: % 17.80/3.17 | | (142) ~ (all_4_24 = e0) % 17.80/3.17 | | % 17.80/3.17 | | BETA: splitting (23) gives: % 17.80/3.17 | | % 17.80/3.17 | | Case 1: % 17.80/3.17 | | | % 17.80/3.17 | | | (143) all_4_20 = e0 % 17.80/3.17 | | | % 17.80/3.17 | | | COMBINE_EQS: (78), (143) imply: % 17.80/3.17 | | | (144) e2 = e0 % 17.80/3.17 | | | % 17.80/3.17 | | | SIMP: (144) implies: % 17.80/3.17 | | | (145) e2 = e0 % 17.80/3.17 | | | % 17.80/3.17 | | | REDUCE: (5), (145) imply: % 17.80/3.17 | | | (146) $false % 17.80/3.17 | | | % 17.80/3.17 | | | CLOSE: (146) is inconsistent. % 17.80/3.17 | | | % 17.80/3.17 | | Case 2: % 17.80/3.17 | | | % 17.80/3.17 | | | (147) ~ (all_4_20 = e0) % 17.80/3.17 | | | (148) all_4_21 = e0 | all_4_22 = e0 | all_4_23 = e0 | all_4_24 = e0 % 17.80/3.17 | | | % 17.80/3.17 | | | BETA: splitting (148) gives: % 17.80/3.17 | | | % 17.80/3.17 | | | Case 1: % 17.80/3.17 | | | | % 17.80/3.17 | | | | (149) all_4_21 = e0 % 17.80/3.17 | | | | % 17.80/3.17 | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (22), (24), (78), (79), % 17.80/3.17 | | | | (82), (83), (85), (149) are inconsistent by sub-proof #3. % 17.80/3.17 | | | | % 17.80/3.17 | | | Case 2: % 17.80/3.17 | | | | % 17.80/3.18 | | | | (150) all_4_22 = e0 | all_4_23 = e0 | all_4_24 = e0 % 17.80/3.18 | | | | % 17.80/3.18 | | | | BETA: splitting (150) gives: % 17.80/3.18 | | | | % 17.80/3.18 | | | | Case 1: % 17.80/3.18 | | | | | % 17.80/3.18 | | | | | (151) all_4_22 = e0 % 17.80/3.18 | | | | | % 17.80/3.18 | | | | | COMBINE_EQS: (79), (151) imply: % 17.80/3.18 | | | | | (152) e3 = e0 % 17.80/3.18 | | | | | % 17.80/3.18 | | | | | SIMP: (152) implies: % 17.80/3.18 | | | | | (153) e3 = e0 % 17.80/3.18 | | | | | % 17.80/3.18 | | | | | REDUCE: (83), (153) imply: % 17.80/3.18 | | | | | (154) $false % 17.80/3.18 | | | | | % 17.80/3.18 | | | | | CLOSE: (154) is inconsistent. % 17.80/3.18 | | | | | % 17.80/3.18 | | | | Case 2: % 17.80/3.18 | | | | | % 17.80/3.18 | | | | | (155) all_4_23 = e0 | all_4_24 = e0 % 17.80/3.18 | | | | | % 17.80/3.18 | | | | | BETA: splitting (155) gives: % 17.80/3.18 | | | | | % 17.80/3.18 | | | | | Case 1: % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | (156) all_4_23 = e0 % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | COMBINE_EQS: (82), (156) imply: % 17.80/3.18 | | | | | | (157) e4 = e0 % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | SIMP: (157) implies: % 17.80/3.18 | | | | | | (158) e4 = e0 % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | REDUCE: (85), (158) imply: % 17.80/3.18 | | | | | | (159) $false % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | CLOSE: (159) is inconsistent. % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | Case 2: % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | (160) all_4_24 = e0 % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | REDUCE: (142), (160) imply: % 17.80/3.18 | | | | | | (161) $false % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | CLOSE: (161) is inconsistent. % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | End of split % 17.80/3.18 | | | | | % 17.80/3.18 | | | | End of split % 17.80/3.18 | | | | % 17.80/3.18 | | | End of split % 17.80/3.18 | | | % 17.80/3.18 | | End of split % 17.80/3.18 | | % 17.80/3.18 | End of split % 17.80/3.18 | % 17.80/3.18 End of proof % 17.80/3.18 % 17.80/3.18 Sub-proof #1 shows that the following formulas are inconsistent: % 17.80/3.18 ---------------------------------------------------------------- % 17.80/3.18 (1) all_4_24 = e1 % 17.80/3.18 (2) all_4_24 = e0 % 17.80/3.18 (3) ~ (e1 = e0) % 17.80/3.18 % 17.80/3.18 Begin of proof % 17.80/3.18 | % 17.80/3.18 | COMBINE_EQS: (1), (2) imply: % 17.80/3.18 | (4) e1 = e0 % 17.80/3.18 | % 17.80/3.18 | SIMP: (4) implies: % 17.80/3.18 | (5) e1 = e0 % 17.80/3.18 | % 17.80/3.18 | REDUCE: (3), (5) imply: % 17.80/3.18 | (6) $false % 17.80/3.18 | % 17.80/3.18 | CLOSE: (6) is inconsistent. % 17.80/3.18 | % 17.80/3.18 End of proof % 17.80/3.18 % 17.80/3.18 Sub-proof #2 shows that the following formulas are inconsistent: % 17.80/3.18 ---------------------------------------------------------------- % 17.80/3.18 (1) all_4_22 = e3 % 17.80/3.18 (2) all_4_22 = e1 % 17.80/3.18 (3) ~ (e3 = e1) % 17.80/3.18 % 17.80/3.18 Begin of proof % 17.80/3.18 | % 17.80/3.18 | COMBINE_EQS: (1), (2) imply: % 17.80/3.18 | (4) e3 = e1 % 17.80/3.18 | % 17.80/3.18 | SIMP: (4) implies: % 17.80/3.18 | (5) e3 = e1 % 17.80/3.18 | % 17.80/3.18 | REDUCE: (3), (5) imply: % 17.80/3.18 | (6) $false % 17.80/3.18 | % 17.80/3.18 | CLOSE: (6) is inconsistent. % 17.80/3.18 | % 17.80/3.18 End of proof % 17.80/3.18 % 17.80/3.18 Sub-proof #3 shows that the following formulas are inconsistent: % 17.80/3.18 ---------------------------------------------------------------- % 17.80/3.18 (1) ~ (e4 = e3) % 17.80/3.18 (2) ~ (e3 = e2) % 17.80/3.18 (3) ~ (e4 = e1) % 17.80/3.18 (4) all_4_20 = e2 % 17.80/3.18 (5) ~ (e4 = e0) % 17.80/3.18 (6) all_4_21 = e0 % 17.80/3.18 (7) ~ (e3 = e0) % 17.80/3.18 (8) all_4_20 = e1 | all_4_21 = e1 | all_4_22 = e1 | all_4_23 = e1 | all_4_24 % 17.80/3.18 = e1 % 17.80/3.18 (9) (all_4_20 = e3 & all_4_21 = e4 & ~ (all_4_0 = e4)) | (all_4_20 = e3 & % 17.80/3.18 all_4_21 = e4 & ~ (all_4_4 = e3)) | (all_4_20 = e2 & all_4_22 = e4 & % 17.80/3.18 ~ (all_4_1 = e4)) | (all_4_20 = e2 & all_4_22 = e4 & ~ (all_4_8 = e2)) % 17.80/3.18 | (all_4_20 = e1 & all_4_23 = e4 & ~ (all_4_2 = e4)) | (all_4_20 = e1 & % 17.80/3.18 all_4_23 = e4 & ~ (all_4_12 = e1)) | (all_4_20 = e0 & all_4_24 = e4 & % 17.80/3.18 ~ (all_4_3 = e4)) | (all_4_20 = e0 & all_4_24 = e4 & ~ (all_4_16 = % 17.80/3.18 e0)) | (all_4_21 = e2 & all_4_22 = e3 & ~ (all_4_5 = e3)) | % 17.80/3.18 (all_4_21 = e2 & all_4_22 = e3 & ~ (all_4_9 = e2)) | (all_4_21 = e1 & % 17.80/3.18 all_4_23 = e3 & ~ (all_4_6 = e3)) | (all_4_21 = e1 & all_4_23 = e3 & % 17.80/3.18 ~ (all_4_13 = e1)) | (all_4_21 = e0 & all_4_24 = e3 & ~ (all_4_7 = % 17.80/3.18 e3)) | (all_4_21 = e0 & all_4_24 = e3 & ~ (all_4_17 = e0)) | % 17.80/3.18 (all_4_22 = e1 & all_4_23 = e2 & ~ (all_4_10 = e2)) | (all_4_22 = e1 & % 17.80/3.18 all_4_23 = e2 & ~ (all_4_14 = e1)) | (all_4_22 = e0 & all_4_24 = e2 & % 17.80/3.18 ~ (all_4_11 = e2)) | (all_4_22 = e0 & all_4_24 = e2 & ~ (all_4_18 = % 17.80/3.18 e0)) | (all_4_23 = e0 & all_4_24 = e1 & ~ (all_4_15 = e1)) | % 17.80/3.18 (all_4_23 = e0 & all_4_24 = e1 & ~ (all_4_19 = e0)) % 17.80/3.18 (10) ~ (e2 = e0) % 17.80/3.18 (11) ~ (e2 = e1) % 17.80/3.18 (12) ~ (e3 = e1) % 17.80/3.18 (13) ~ (e1 = e0) % 17.80/3.18 (14) all_4_22 = e3 % 17.80/3.18 (15) all_4_23 = e4 % 17.80/3.18 % 17.80/3.18 Begin of proof % 17.80/3.18 | % 17.80/3.18 | BETA: splitting (8) gives: % 17.80/3.18 | % 17.80/3.18 | Case 1: % 17.80/3.18 | | % 17.80/3.18 | | (16) all_4_20 = e1 % 17.80/3.18 | | % 17.80/3.18 | | REF_CLOSE: (4), (11), (16) are inconsistent by sub-proof #9. % 17.80/3.18 | | % 17.80/3.18 | Case 2: % 17.80/3.18 | | % 17.80/3.18 | | (17) ~ (all_4_20 = e1) % 17.80/3.18 | | (18) all_4_21 = e1 | all_4_22 = e1 | all_4_23 = e1 | all_4_24 = e1 % 17.80/3.18 | | % 17.80/3.18 | | BETA: splitting (9) gives: % 17.80/3.18 | | % 17.80/3.18 | | Case 1: % 17.80/3.18 | | | % 17.80/3.18 | | | (19) (all_4_20 = e3 & all_4_21 = e4 & ~ (all_4_0 = e4)) | (all_4_20 = % 17.80/3.18 | | | e3 & all_4_21 = e4 & ~ (all_4_4 = e3)) | (all_4_20 = e2 & % 17.80/3.18 | | | all_4_22 = e4 & ~ (all_4_1 = e4)) | (all_4_20 = e2 & all_4_22 = % 17.80/3.18 | | | e4 & ~ (all_4_8 = e2)) | (all_4_20 = e1 & all_4_23 = e4 & ~ % 17.80/3.18 | | | (all_4_2 = e4)) | (all_4_20 = e1 & all_4_23 = e4 & ~ (all_4_12 % 17.80/3.18 | | | = e1)) | (all_4_20 = e0 & all_4_24 = e4 & ~ (all_4_3 = e4)) | % 17.80/3.18 | | | (all_4_20 = e0 & all_4_24 = e4 & ~ (all_4_16 = e0)) | (all_4_21 = % 17.80/3.18 | | | e2 & all_4_22 = e3 & ~ (all_4_5 = e3)) | (all_4_21 = e2 & % 17.80/3.18 | | | all_4_22 = e3 & ~ (all_4_9 = e2)) % 17.80/3.18 | | | % 17.80/3.18 | | | BETA: splitting (19) gives: % 17.80/3.18 | | | % 17.80/3.18 | | | Case 1: % 17.80/3.18 | | | | % 17.80/3.18 | | | | (20) (all_4_20 = e3 & all_4_21 = e4 & ~ (all_4_0 = e4)) | (all_4_20 % 17.80/3.18 | | | | = e3 & all_4_21 = e4 & ~ (all_4_4 = e3)) | (all_4_20 = e2 & % 17.80/3.18 | | | | all_4_22 = e4 & ~ (all_4_1 = e4)) | (all_4_20 = e2 & all_4_22 % 17.80/3.18 | | | | = e4 & ~ (all_4_8 = e2)) | (all_4_20 = e1 & all_4_23 = e4 & % 17.80/3.18 | | | | ~ (all_4_2 = e4)) % 17.80/3.18 | | | | % 17.80/3.18 | | | | BETA: splitting (20) gives: % 17.80/3.18 | | | | % 17.80/3.18 | | | | Case 1: % 17.80/3.18 | | | | | % 17.80/3.18 | | | | | (21) (all_4_20 = e3 & all_4_21 = e4 & ~ (all_4_0 = e4)) | % 17.80/3.18 | | | | | (all_4_20 = e3 & all_4_21 = e4 & ~ (all_4_4 = e3)) % 17.80/3.18 | | | | | % 17.80/3.18 | | | | | REF_CLOSE: (2), (4), (21) are inconsistent by sub-proof #14. % 17.80/3.18 | | | | | % 17.80/3.18 | | | | Case 2: % 17.80/3.18 | | | | | % 17.80/3.18 | | | | | (22) (all_4_20 = e2 & all_4_22 = e4 & ~ (all_4_1 = e4)) | % 17.80/3.18 | | | | | (all_4_20 = e2 & all_4_22 = e4 & ~ (all_4_8 = e2)) | % 17.80/3.18 | | | | | (all_4_20 = e1 & all_4_23 = e4 & ~ (all_4_2 = e4)) % 17.80/3.18 | | | | | % 17.80/3.18 | | | | | BETA: splitting (22) gives: % 17.80/3.18 | | | | | % 17.80/3.18 | | | | | Case 1: % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | (23) all_4_20 = e2 & all_4_22 = e4 & ~ (all_4_1 = e4) % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | ALPHA: (23) implies: % 17.80/3.18 | | | | | | (24) all_4_22 = e4 % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | COMBINE_EQS: (14), (24) imply: % 17.80/3.18 | | | | | | (25) e4 = e3 % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | REDUCE: (1), (25) imply: % 17.80/3.18 | | | | | | (26) $false % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | CLOSE: (26) is inconsistent. % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | Case 2: % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | (27) (all_4_20 = e2 & all_4_22 = e4 & ~ (all_4_8 = e2)) | % 17.80/3.18 | | | | | | (all_4_20 = e1 & all_4_23 = e4 & ~ (all_4_2 = e4)) % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | BETA: splitting (27) gives: % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | Case 1: % 17.80/3.18 | | | | | | | % 17.80/3.18 | | | | | | | (28) all_4_20 = e2 & all_4_22 = e4 & ~ (all_4_8 = e2) % 17.80/3.18 | | | | | | | % 17.80/3.18 | | | | | | | ALPHA: (28) implies: % 17.80/3.18 | | | | | | | (29) all_4_22 = e4 % 17.80/3.18 | | | | | | | % 17.80/3.18 | | | | | | | COMBINE_EQS: (14), (29) imply: % 17.80/3.18 | | | | | | | (30) e4 = e3 % 17.80/3.18 | | | | | | | % 17.80/3.18 | | | | | | | REDUCE: (1), (30) imply: % 17.80/3.18 | | | | | | | (31) $false % 17.80/3.18 | | | | | | | % 17.80/3.18 | | | | | | | CLOSE: (31) is inconsistent. % 17.80/3.18 | | | | | | | % 17.80/3.18 | | | | | | Case 2: % 17.80/3.18 | | | | | | | % 17.80/3.18 | | | | | | | (32) all_4_20 = e1 & all_4_23 = e4 & ~ (all_4_2 = e4) % 17.80/3.18 | | | | | | | % 17.80/3.18 | | | | | | | REF_CLOSE: (4), (11), (32) are inconsistent by sub-proof #12. % 17.80/3.18 | | | | | | | % 17.80/3.18 | | | | | | End of split % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | End of split % 17.80/3.18 | | | | | % 17.80/3.18 | | | | End of split % 17.80/3.18 | | | | % 17.80/3.18 | | | Case 2: % 17.80/3.18 | | | | % 17.80/3.18 | | | | (33) (all_4_20 = e1 & all_4_23 = e4 & ~ (all_4_12 = e1)) | (all_4_20 % 17.80/3.18 | | | | = e0 & all_4_24 = e4 & ~ (all_4_3 = e4)) | (all_4_20 = e0 & % 17.80/3.18 | | | | all_4_24 = e4 & ~ (all_4_16 = e0)) | (all_4_21 = e2 & % 17.80/3.18 | | | | all_4_22 = e3 & ~ (all_4_5 = e3)) | (all_4_21 = e2 & all_4_22 % 17.80/3.18 | | | | = e3 & ~ (all_4_9 = e2)) % 17.80/3.18 | | | | % 17.80/3.18 | | | | BETA: splitting (33) gives: % 17.80/3.18 | | | | % 17.80/3.18 | | | | Case 1: % 17.80/3.18 | | | | | % 17.80/3.18 | | | | | (34) (all_4_20 = e1 & all_4_23 = e4 & ~ (all_4_12 = e1)) | % 17.80/3.18 | | | | | (all_4_20 = e0 & all_4_24 = e4 & ~ (all_4_3 = e4)) % 17.80/3.18 | | | | | % 17.80/3.18 | | | | | REF_CLOSE: (4), (10), (11), (34) are inconsistent by sub-proof #11. % 17.80/3.18 | | | | | % 17.80/3.18 | | | | Case 2: % 17.80/3.18 | | | | | % 17.80/3.18 | | | | | (35) (all_4_20 = e0 & all_4_24 = e4 & ~ (all_4_16 = e0)) | % 17.80/3.18 | | | | | (all_4_21 = e2 & all_4_22 = e3 & ~ (all_4_5 = e3)) | % 17.80/3.18 | | | | | (all_4_21 = e2 & all_4_22 = e3 & ~ (all_4_9 = e2)) % 17.80/3.18 | | | | | % 17.80/3.18 | | | | | BETA: splitting (35) gives: % 17.80/3.18 | | | | | % 17.80/3.18 | | | | | Case 1: % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | (36) all_4_20 = e0 & all_4_24 = e4 & ~ (all_4_16 = e0) % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | REF_CLOSE: (4), (10), (36) are inconsistent by sub-proof #10. % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | Case 2: % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | (37) (all_4_21 = e2 & all_4_22 = e3 & ~ (all_4_5 = e3)) | % 17.80/3.18 | | | | | | (all_4_21 = e2 & all_4_22 = e3 & ~ (all_4_9 = e2)) % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | BETA: splitting (37) gives: % 17.80/3.18 | | | | | | % 17.80/3.18 | | | | | | Case 1: % 17.80/3.18 | | | | | | | % 17.80/3.18 | | | | | | | (38) all_4_21 = e2 & all_4_22 = e3 & ~ (all_4_5 = e3) % 17.80/3.18 | | | | | | | % 17.80/3.18 | | | | | | | ALPHA: (38) implies: % 17.80/3.18 | | | | | | | (39) all_4_21 = e2 % 17.80/3.18 | | | | | | | % 17.80/3.18 | | | | | | | COMBINE_EQS: (6), (39) imply: % 17.80/3.18 | | | | | | | (40) e2 = e0 % 17.80/3.18 | | | | | | | % 17.80/3.18 | | | | | | | REDUCE: (10), (40) imply: % 17.80/3.19 | | | | | | | (41) $false % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | | CLOSE: (41) is inconsistent. % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | Case 2: % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | | (42) all_4_21 = e2 & all_4_22 = e3 & ~ (all_4_9 = e2) % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | | ALPHA: (42) implies: % 17.80/3.19 | | | | | | | (43) all_4_21 = e2 % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | | COMBINE_EQS: (6), (43) imply: % 17.80/3.19 | | | | | | | (44) e2 = e0 % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | | REDUCE: (10), (44) imply: % 17.80/3.19 | | | | | | | (45) $false % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | | CLOSE: (45) is inconsistent. % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | End of split % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | End of split % 17.80/3.19 | | | | | % 17.80/3.19 | | | | End of split % 17.80/3.19 | | | | % 17.80/3.19 | | | End of split % 17.80/3.19 | | | % 17.80/3.19 | | Case 2: % 17.80/3.19 | | | % 17.80/3.19 | | | (46) (all_4_21 = e1 & all_4_23 = e3 & ~ (all_4_6 = e3)) | (all_4_21 = % 17.80/3.19 | | | e1 & all_4_23 = e3 & ~ (all_4_13 = e1)) | (all_4_21 = e0 & % 17.80/3.19 | | | all_4_24 = e3 & ~ (all_4_7 = e3)) | (all_4_21 = e0 & all_4_24 = % 17.80/3.19 | | | e3 & ~ (all_4_17 = e0)) | (all_4_22 = e1 & all_4_23 = e2 & ~ % 17.80/3.19 | | | (all_4_10 = e2)) | (all_4_22 = e1 & all_4_23 = e2 & ~ (all_4_14 % 17.80/3.19 | | | = e1)) | (all_4_22 = e0 & all_4_24 = e2 & ~ (all_4_11 = e2)) % 17.80/3.19 | | | | (all_4_22 = e0 & all_4_24 = e2 & ~ (all_4_18 = e0)) | (all_4_23 % 17.80/3.19 | | | = e0 & all_4_24 = e1 & ~ (all_4_15 = e1)) | (all_4_23 = e0 & % 17.80/3.19 | | | all_4_24 = e1 & ~ (all_4_19 = e0)) % 17.80/3.19 | | | % 17.80/3.19 | | | BETA: splitting (46) gives: % 17.80/3.19 | | | % 17.80/3.19 | | | Case 1: % 17.80/3.19 | | | | % 17.80/3.19 | | | | (47) (all_4_21 = e1 & all_4_23 = e3 & ~ (all_4_6 = e3)) | (all_4_21 % 17.80/3.19 | | | | = e1 & all_4_23 = e3 & ~ (all_4_13 = e1)) | (all_4_21 = e0 & % 17.80/3.19 | | | | all_4_24 = e3 & ~ (all_4_7 = e3)) | (all_4_21 = e0 & all_4_24 % 17.80/3.19 | | | | = e3 & ~ (all_4_17 = e0)) | (all_4_22 = e1 & all_4_23 = e2 & % 17.80/3.19 | | | | ~ (all_4_10 = e2)) % 17.80/3.19 | | | | % 17.80/3.19 | | | | BETA: splitting (47) gives: % 17.80/3.19 | | | | % 17.80/3.19 | | | | Case 1: % 17.80/3.19 | | | | | % 17.80/3.19 | | | | | (48) (all_4_21 = e1 & all_4_23 = e3 & ~ (all_4_6 = e3)) | % 17.80/3.19 | | | | | (all_4_21 = e1 & all_4_23 = e3 & ~ (all_4_13 = e1)) % 17.80/3.19 | | | | | % 17.80/3.19 | | | | | BETA: splitting (48) gives: % 17.80/3.19 | | | | | % 17.80/3.19 | | | | | Case 1: % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | (49) all_4_21 = e1 & all_4_23 = e3 & ~ (all_4_6 = e3) % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | ALPHA: (49) implies: % 17.80/3.19 | | | | | | (50) all_4_21 = e1 % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | COMBINE_EQS: (6), (50) imply: % 17.80/3.19 | | | | | | (51) e1 = e0 % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | REDUCE: (13), (51) imply: % 17.80/3.19 | | | | | | (52) $false % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | CLOSE: (52) is inconsistent. % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | Case 2: % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | (53) all_4_21 = e1 & all_4_23 = e3 & ~ (all_4_13 = e1) % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | ALPHA: (53) implies: % 17.80/3.19 | | | | | | (54) all_4_21 = e1 % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | COMBINE_EQS: (6), (54) imply: % 17.80/3.19 | | | | | | (55) e1 = e0 % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | REDUCE: (13), (55) imply: % 17.80/3.19 | | | | | | (56) $false % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | CLOSE: (56) is inconsistent. % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | End of split % 17.80/3.19 | | | | | % 17.80/3.19 | | | | Case 2: % 17.80/3.19 | | | | | % 17.80/3.19 | | | | | (57) (all_4_21 = e0 & all_4_24 = e3 & ~ (all_4_7 = e3)) | % 17.80/3.19 | | | | | (all_4_21 = e0 & all_4_24 = e3 & ~ (all_4_17 = e0)) | % 17.80/3.19 | | | | | (all_4_22 = e1 & all_4_23 = e2 & ~ (all_4_10 = e2)) % 17.80/3.19 | | | | | % 17.80/3.19 | | | | | BETA: splitting (57) gives: % 17.80/3.19 | | | | | % 17.80/3.19 | | | | | Case 1: % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | (58) all_4_21 = e0 & all_4_24 = e3 & ~ (all_4_7 = e3) % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | ALPHA: (58) implies: % 17.80/3.19 | | | | | | (59) all_4_24 = e3 % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | REF_CLOSE: (3), (6), (12), (13), (14), (15), (18), (59) are % 17.80/3.19 | | | | | | inconsistent by sub-proof #5. % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | Case 2: % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | (60) (all_4_21 = e0 & all_4_24 = e3 & ~ (all_4_17 = e0)) | % 17.80/3.19 | | | | | | (all_4_22 = e1 & all_4_23 = e2 & ~ (all_4_10 = e2)) % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | BETA: splitting (60) gives: % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | Case 1: % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | | (61) all_4_21 = e0 & all_4_24 = e3 & ~ (all_4_17 = e0) % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | | ALPHA: (61) implies: % 17.80/3.19 | | | | | | | (62) all_4_24 = e3 % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | | REF_CLOSE: (3), (6), (12), (13), (14), (15), (18), (62) are % 17.80/3.19 | | | | | | | inconsistent by sub-proof #5. % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | Case 2: % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | | (63) all_4_22 = e1 & all_4_23 = e2 & ~ (all_4_10 = e2) % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | | ALPHA: (63) implies: % 17.80/3.19 | | | | | | | (64) all_4_22 = e1 % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | | COMBINE_EQS: (14), (64) imply: % 17.80/3.19 | | | | | | | (65) e3 = e1 % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | | REDUCE: (12), (65) imply: % 17.80/3.19 | | | | | | | (66) $false % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | | CLOSE: (66) is inconsistent. % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | End of split % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | End of split % 17.80/3.19 | | | | | % 17.80/3.19 | | | | End of split % 17.80/3.19 | | | | % 17.80/3.19 | | | Case 2: % 17.80/3.19 | | | | % 17.80/3.19 | | | | (67) (all_4_22 = e1 & all_4_23 = e2 & ~ (all_4_14 = e1)) | (all_4_22 % 17.80/3.19 | | | | = e0 & all_4_24 = e2 & ~ (all_4_11 = e2)) | (all_4_22 = e0 & % 17.80/3.19 | | | | all_4_24 = e2 & ~ (all_4_18 = e0)) | (all_4_23 = e0 & % 17.80/3.19 | | | | all_4_24 = e1 & ~ (all_4_15 = e1)) | (all_4_23 = e0 & % 17.80/3.19 | | | | all_4_24 = e1 & ~ (all_4_19 = e0)) % 17.80/3.19 | | | | % 17.80/3.19 | | | | BETA: splitting (67) gives: % 17.80/3.19 | | | | % 17.80/3.19 | | | | Case 1: % 17.80/3.19 | | | | | % 17.80/3.19 | | | | | (68) (all_4_22 = e1 & all_4_23 = e2 & ~ (all_4_14 = e1)) | % 17.80/3.19 | | | | | (all_4_22 = e0 & all_4_24 = e2 & ~ (all_4_11 = e2)) % 17.80/3.19 | | | | | % 17.80/3.19 | | | | | BETA: splitting (68) gives: % 17.80/3.19 | | | | | % 17.80/3.19 | | | | | Case 1: % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | (69) all_4_22 = e1 & all_4_23 = e2 & ~ (all_4_14 = e1) % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | ALPHA: (69) implies: % 17.80/3.19 | | | | | | (70) all_4_22 = e1 % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | COMBINE_EQS: (14), (70) imply: % 17.80/3.19 | | | | | | (71) e3 = e1 % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | REDUCE: (12), (71) imply: % 17.80/3.19 | | | | | | (72) $false % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | CLOSE: (72) is inconsistent. % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | Case 2: % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | (73) all_4_22 = e0 & all_4_24 = e2 & ~ (all_4_11 = e2) % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | ALPHA: (73) implies: % 17.80/3.19 | | | | | | (74) all_4_22 = e0 % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | COMBINE_EQS: (14), (74) imply: % 17.80/3.19 | | | | | | (75) e3 = e0 % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | REDUCE: (7), (75) imply: % 17.80/3.19 | | | | | | (76) $false % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | CLOSE: (76) is inconsistent. % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | End of split % 17.80/3.19 | | | | | % 17.80/3.19 | | | | Case 2: % 17.80/3.19 | | | | | % 17.80/3.19 | | | | | (77) (all_4_22 = e0 & all_4_24 = e2 & ~ (all_4_18 = e0)) | % 17.80/3.19 | | | | | (all_4_23 = e0 & all_4_24 = e1 & ~ (all_4_15 = e1)) | % 17.80/3.19 | | | | | (all_4_23 = e0 & all_4_24 = e1 & ~ (all_4_19 = e0)) % 17.80/3.19 | | | | | % 17.80/3.19 | | | | | BETA: splitting (77) gives: % 17.80/3.19 | | | | | % 17.80/3.19 | | | | | Case 1: % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | (78) all_4_22 = e0 & all_4_24 = e2 & ~ (all_4_18 = e0) % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | ALPHA: (78) implies: % 17.80/3.19 | | | | | | (79) all_4_22 = e0 % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | COMBINE_EQS: (14), (79) imply: % 17.80/3.19 | | | | | | (80) e3 = e0 % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | REDUCE: (7), (80) imply: % 17.80/3.19 | | | | | | (81) $false % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | CLOSE: (81) is inconsistent. % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | Case 2: % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | (82) (all_4_23 = e0 & all_4_24 = e1 & ~ (all_4_15 = e1)) | % 17.80/3.19 | | | | | | (all_4_23 = e0 & all_4_24 = e1 & ~ (all_4_19 = e0)) % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | BETA: splitting (82) gives: % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | | Case 1: % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | | (83) all_4_23 = e0 & all_4_24 = e1 & ~ (all_4_15 = e1) % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | | ALPHA: (83) implies: % 17.80/3.19 | | | | | | | (84) all_4_23 = e0 % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | | REF_CLOSE: (5), (15), (84) are inconsistent by sub-proof #4. % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | Case 2: % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | | (85) all_4_23 = e0 & all_4_24 = e1 & ~ (all_4_19 = e0) % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | | ALPHA: (85) implies: % 17.80/3.19 | | | | | | | (86) all_4_23 = e0 % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | | REF_CLOSE: (5), (15), (86) are inconsistent by sub-proof #4. % 17.80/3.19 | | | | | | | % 17.80/3.19 | | | | | | End of split % 17.80/3.19 | | | | | | % 17.80/3.19 | | | | | End of split % 17.80/3.19 | | | | | % 17.80/3.19 | | | | End of split % 17.80/3.19 | | | | % 17.80/3.19 | | | End of split % 17.80/3.19 | | | % 17.80/3.19 | | End of split % 17.80/3.19 | | % 17.80/3.19 | End of split % 17.80/3.19 | % 17.80/3.19 End of proof % 17.80/3.19 % 17.80/3.19 Sub-proof #4 shows that the following formulas are inconsistent: % 17.80/3.19 ---------------------------------------------------------------- % 17.80/3.19 (1) all_4_23 = e4 % 17.80/3.19 (2) all_4_23 = e0 % 17.80/3.19 (3) ~ (e4 = e0) % 17.80/3.19 % 17.80/3.19 Begin of proof % 17.80/3.19 | % 17.80/3.19 | COMBINE_EQS: (1), (2) imply: % 17.80/3.19 | (4) e4 = e0 % 17.80/3.19 | % 17.80/3.19 | SIMP: (4) implies: % 17.80/3.19 | (5) e4 = e0 % 17.80/3.19 | % 17.80/3.19 | REDUCE: (3), (5) imply: % 17.80/3.19 | (6) $false % 17.80/3.19 | % 17.80/3.19 | CLOSE: (6) is inconsistent. % 17.80/3.19 | % 17.80/3.19 End of proof % 17.80/3.19 % 17.80/3.19 Sub-proof #5 shows that the following formulas are inconsistent: % 17.80/3.19 ---------------------------------------------------------------- % 17.80/3.19 (1) ~ (e4 = e1) % 17.80/3.19 (2) all_4_21 = e0 % 17.80/3.19 (3) all_4_21 = e1 | all_4_22 = e1 | all_4_23 = e1 | all_4_24 = e1 % 17.80/3.19 (4) all_4_24 = e3 % 17.80/3.19 (5) ~ (e3 = e1) % 17.80/3.19 (6) ~ (e1 = e0) % 17.80/3.19 (7) all_4_22 = e3 % 17.80/3.19 (8) all_4_23 = e4 % 17.80/3.19 % 17.80/3.19 Begin of proof % 17.80/3.19 | % 17.80/3.19 | BETA: splitting (3) gives: % 17.80/3.19 | % 17.80/3.19 | Case 1: % 17.80/3.19 | | % 17.80/3.19 | | (9) all_4_21 = e1 % 17.80/3.19 | | % 17.80/3.19 | | COMBINE_EQS: (2), (9) imply: % 17.80/3.19 | | (10) e1 = e0 % 17.80/3.19 | | % 17.80/3.19 | | REDUCE: (6), (10) imply: % 17.80/3.19 | | (11) $false % 17.80/3.19 | | % 17.80/3.19 | | CLOSE: (11) is inconsistent. % 17.80/3.19 | | % 17.80/3.19 | Case 2: % 17.80/3.19 | | % 17.80/3.19 | | (12) all_4_22 = e1 | all_4_23 = e1 | all_4_24 = e1 % 17.80/3.19 | | % 17.80/3.19 | | BETA: splitting (12) gives: % 17.80/3.19 | | % 17.80/3.19 | | Case 1: % 17.80/3.19 | | | % 17.80/3.19 | | | (13) all_4_22 = e1 % 17.80/3.19 | | | % 17.80/3.19 | | | COMBINE_EQS: (7), (13) imply: % 17.80/3.19 | | | (14) e3 = e1 % 17.80/3.19 | | | % 17.80/3.19 | | | REDUCE: (5), (14) imply: % 17.80/3.19 | | | (15) $false % 17.80/3.19 | | | % 17.80/3.19 | | | CLOSE: (15) is inconsistent. % 17.80/3.19 | | | % 17.80/3.19 | | Case 2: % 17.80/3.19 | | | % 17.80/3.19 | | | (16) ~ (all_4_22 = e1) % 17.80/3.19 | | | (17) all_4_23 = e1 | all_4_24 = e1 % 17.80/3.19 | | | % 17.80/3.19 | | | BETA: splitting (17) gives: % 17.80/3.19 | | | % 17.80/3.19 | | | Case 1: % 17.80/3.19 | | | | % 17.80/3.20 | | | | (18) all_4_23 = e1 % 17.80/3.20 | | | | % 17.80/3.20 | | | | REF_CLOSE: (1), (8), (18) are inconsistent by sub-proof #8. % 17.80/3.20 | | | | % 17.80/3.20 | | | Case 2: % 17.80/3.20 | | | | % 17.80/3.20 | | | | (19) all_4_24 = e1 % 17.80/3.20 | | | | % 17.80/3.20 | | | | COMBINE_EQS: (4), (19) imply: % 17.80/3.20 | | | | (20) e3 = e1 % 17.80/3.20 | | | | % 17.80/3.20 | | | | SIMP: (20) implies: % 17.80/3.20 | | | | (21) e3 = e1 % 17.80/3.20 | | | | % 17.80/3.20 | | | | REDUCE: (5), (21) imply: % 17.80/3.20 | | | | (22) $false % 17.80/3.20 | | | | % 17.80/3.20 | | | | CLOSE: (22) is inconsistent. % 17.80/3.20 | | | | % 17.80/3.20 | | | End of split % 17.80/3.20 | | | % 17.80/3.20 | | End of split % 17.80/3.20 | | % 17.80/3.20 | End of split % 17.80/3.20 | % 17.80/3.20 End of proof % 17.80/3.20 % 17.80/3.20 Sub-proof #6 shows that the following formulas are inconsistent: % 17.80/3.20 ---------------------------------------------------------------- % 17.80/3.20 (1) all_4_23 = e4 % 17.80/3.20 (2) all_4_23 = e3 % 17.80/3.20 (3) ~ (e4 = e3) % 17.80/3.20 % 17.80/3.20 Begin of proof % 17.80/3.20 | % 17.80/3.20 | COMBINE_EQS: (1), (2) imply: % 17.80/3.20 | (4) e4 = e3 % 17.80/3.20 | % 17.80/3.20 | SIMP: (4) implies: % 17.80/3.20 | (5) e4 = e3 % 17.80/3.20 | % 17.80/3.20 | REDUCE: (3), (5) imply: % 17.80/3.20 | (6) $false % 17.80/3.20 | % 17.80/3.20 | CLOSE: (6) is inconsistent. % 17.80/3.20 | % 17.80/3.20 End of proof % 17.80/3.20 % 17.80/3.20 Sub-proof #7 shows that the following formulas are inconsistent: % 17.80/3.20 ---------------------------------------------------------------- % 17.80/3.20 (1) ~ (e4 = e1) % 17.80/3.20 (2) all_4_21 = e2 % 17.80/3.20 (3) all_4_20 = e2 % 17.80/3.20 (4) all_4_24 = e0 % 17.80/3.20 (5) all_4_20 = e1 | all_4_21 = e1 | all_4_22 = e1 | all_4_23 = e1 | all_4_24 % 17.80/3.20 = e1 % 17.80/3.20 (6) ~ (e2 = e1) % 17.80/3.20 (7) ~ (e3 = e1) % 17.80/3.20 (8) ~ (e1 = e0) % 17.80/3.20 (9) all_4_22 = e3 % 17.80/3.20 (10) all_4_23 = e4 % 17.80/3.20 % 17.80/3.20 Begin of proof % 17.80/3.20 | % 17.80/3.20 | BETA: splitting (5) gives: % 17.80/3.20 | % 17.80/3.20 | Case 1: % 17.80/3.20 | | % 17.80/3.20 | | (11) all_4_20 = e1 % 17.80/3.20 | | % 17.80/3.20 | | REF_CLOSE: (3), (6), (11) are inconsistent by sub-proof #9. % 17.80/3.20 | | % 17.80/3.20 | Case 2: % 17.80/3.20 | | % 17.80/3.20 | | (12) ~ (all_4_20 = e1) % 17.80/3.20 | | (13) all_4_21 = e1 | all_4_22 = e1 | all_4_23 = e1 | all_4_24 = e1 % 17.80/3.20 | | % 17.80/3.20 | | BETA: splitting (13) gives: % 17.80/3.20 | | % 17.80/3.20 | | Case 1: % 17.80/3.20 | | | % 17.80/3.20 | | | (14) all_4_21 = e1 % 17.80/3.20 | | | % 17.80/3.20 | | | COMBINE_EQS: (2), (14) imply: % 17.80/3.20 | | | (15) e2 = e1 % 17.80/3.20 | | | % 17.80/3.20 | | | SIMP: (15) implies: % 17.80/3.20 | | | (16) e2 = e1 % 17.80/3.20 | | | % 17.80/3.20 | | | REDUCE: (6), (16) imply: % 17.80/3.20 | | | (17) $false % 17.80/3.20 | | | % 17.80/3.20 | | | CLOSE: (17) is inconsistent. % 17.80/3.20 | | | % 17.80/3.20 | | Case 2: % 17.80/3.20 | | | % 17.80/3.20 | | | (18) all_4_22 = e1 | all_4_23 = e1 | all_4_24 = e1 % 17.80/3.20 | | | % 17.80/3.20 | | | BETA: splitting (18) gives: % 17.80/3.20 | | | % 17.80/3.20 | | | Case 1: % 17.80/3.20 | | | | % 17.80/3.20 | | | | (19) all_4_22 = e1 % 17.80/3.20 | | | | % 17.80/3.20 | | | | COMBINE_EQS: (9), (19) imply: % 17.80/3.20 | | | | (20) e3 = e1 % 17.80/3.20 | | | | % 17.80/3.20 | | | | REDUCE: (7), (20) imply: % 17.80/3.20 | | | | (21) $false % 17.80/3.20 | | | | % 17.80/3.20 | | | | CLOSE: (21) is inconsistent. % 17.80/3.20 | | | | % 17.80/3.20 | | | Case 2: % 17.80/3.20 | | | | % 17.80/3.20 | | | | (22) all_4_23 = e1 | all_4_24 = e1 % 17.80/3.20 | | | | % 17.80/3.20 | | | | BETA: splitting (22) gives: % 17.80/3.20 | | | | % 17.80/3.20 | | | | Case 1: % 17.80/3.20 | | | | | % 17.80/3.20 | | | | | (23) all_4_23 = e1 % 17.80/3.20 | | | | | % 17.80/3.20 | | | | | REF_CLOSE: (1), (10), (23) are inconsistent by sub-proof #8. % 17.80/3.20 | | | | | % 17.80/3.20 | | | | Case 2: % 17.80/3.20 | | | | | % 17.80/3.20 | | | | | (24) all_4_24 = e1 % 17.80/3.20 | | | | | % 17.80/3.20 | | | | | COMBINE_EQS: (4), (24) imply: % 17.80/3.20 | | | | | (25) e1 = e0 % 17.80/3.20 | | | | | % 17.80/3.20 | | | | | REDUCE: (8), (25) imply: % 17.80/3.20 | | | | | (26) $false % 17.80/3.20 | | | | | % 17.80/3.20 | | | | | CLOSE: (26) is inconsistent. % 17.80/3.20 | | | | | % 17.80/3.20 | | | | End of split % 17.80/3.20 | | | | % 17.80/3.20 | | | End of split % 17.80/3.20 | | | % 17.80/3.20 | | End of split % 17.80/3.20 | | % 17.80/3.20 | End of split % 17.80/3.20 | % 17.80/3.20 End of proof % 17.80/3.20 % 17.80/3.20 Sub-proof #8 shows that the following formulas are inconsistent: % 17.80/3.20 ---------------------------------------------------------------- % 17.80/3.20 (1) all_4_23 = e4 % 17.80/3.20 (2) all_4_23 = e1 % 17.80/3.20 (3) ~ (e4 = e1) % 17.80/3.20 % 17.80/3.20 Begin of proof % 17.80/3.20 | % 17.80/3.20 | COMBINE_EQS: (1), (2) imply: % 17.80/3.20 | (4) e4 = e1 % 17.80/3.20 | % 17.80/3.20 | SIMP: (4) implies: % 17.80/3.20 | (5) e4 = e1 % 17.80/3.20 | % 17.80/3.20 | REDUCE: (3), (5) imply: % 17.80/3.20 | (6) $false % 17.80/3.20 | % 17.80/3.20 | CLOSE: (6) is inconsistent. % 17.80/3.20 | % 17.80/3.20 End of proof % 17.80/3.20 % 17.80/3.20 Sub-proof #9 shows that the following formulas are inconsistent: % 17.80/3.20 ---------------------------------------------------------------- % 17.80/3.20 (1) all_4_20 = e2 % 17.80/3.20 (2) all_4_20 = e1 % 17.80/3.20 (3) ~ (e2 = e1) % 17.80/3.20 % 17.80/3.20 Begin of proof % 17.80/3.20 | % 17.80/3.20 | COMBINE_EQS: (1), (2) imply: % 17.80/3.20 | (4) e2 = e1 % 17.80/3.20 | % 17.80/3.20 | SIMP: (4) implies: % 17.80/3.20 | (5) e2 = e1 % 17.80/3.20 | % 17.80/3.20 | REDUCE: (3), (5) imply: % 17.80/3.20 | (6) $false % 17.80/3.20 | % 17.80/3.20 | CLOSE: (6) is inconsistent. % 17.80/3.20 | % 17.80/3.20 End of proof % 17.80/3.20 % 17.80/3.20 Sub-proof #10 shows that the following formulas are inconsistent: % 17.80/3.20 ---------------------------------------------------------------- % 17.80/3.20 (1) all_4_20 = e0 & all_4_24 = e4 & ~ (all_4_16 = e0) % 17.80/3.20 (2) all_4_20 = e2 % 17.80/3.20 (3) ~ (e2 = e0) % 17.80/3.20 % 17.80/3.20 Begin of proof % 17.80/3.20 | % 17.80/3.20 | ALPHA: (1) implies: % 17.80/3.20 | (4) all_4_20 = e0 % 17.80/3.20 | % 17.80/3.20 | COMBINE_EQS: (2), (4) imply: % 17.80/3.20 | (5) e2 = e0 % 17.80/3.20 | % 17.80/3.20 | REDUCE: (3), (5) imply: % 17.80/3.20 | (6) $false % 17.80/3.20 | % 17.80/3.20 | CLOSE: (6) is inconsistent. % 17.80/3.20 | % 17.80/3.20 End of proof % 17.80/3.20 % 17.80/3.20 Sub-proof #11 shows that the following formulas are inconsistent: % 17.80/3.20 ---------------------------------------------------------------- % 17.80/3.20 (1) (all_4_20 = e1 & all_4_23 = e4 & ~ (all_4_12 = e1)) | (all_4_20 = e0 & % 17.80/3.20 all_4_24 = e4 & ~ (all_4_3 = e4)) % 17.80/3.20 (2) all_4_20 = e2 % 17.80/3.20 (3) ~ (e2 = e1) % 17.80/3.20 (4) ~ (e2 = e0) % 17.80/3.20 % 17.80/3.20 Begin of proof % 17.80/3.20 | % 17.80/3.20 | BETA: splitting (1) gives: % 17.80/3.20 | % 17.80/3.20 | Case 1: % 17.80/3.20 | | % 17.80/3.20 | | (5) all_4_20 = e1 & all_4_23 = e4 & ~ (all_4_12 = e1) % 17.80/3.20 | | % 17.80/3.20 | | ALPHA: (5) implies: % 17.80/3.20 | | (6) all_4_20 = e1 % 17.80/3.20 | | % 17.80/3.20 | | COMBINE_EQS: (2), (6) imply: % 17.80/3.20 | | (7) e2 = e1 % 17.80/3.20 | | % 17.80/3.20 | | REDUCE: (3), (7) imply: % 17.80/3.20 | | (8) $false % 17.80/3.20 | | % 17.80/3.20 | | CLOSE: (8) is inconsistent. % 17.80/3.20 | | % 17.80/3.20 | Case 2: % 17.80/3.20 | | % 17.80/3.20 | | (9) all_4_20 = e0 & all_4_24 = e4 & ~ (all_4_3 = e4) % 17.80/3.20 | | % 17.80/3.20 | | ALPHA: (9) implies: % 17.80/3.20 | | (10) all_4_20 = e0 % 17.80/3.20 | | % 17.80/3.20 | | COMBINE_EQS: (2), (10) imply: % 17.80/3.20 | | (11) e2 = e0 % 17.80/3.20 | | % 17.80/3.20 | | REDUCE: (4), (11) imply: % 17.80/3.20 | | (12) $false % 17.80/3.20 | | % 17.80/3.20 | | CLOSE: (12) is inconsistent. % 17.80/3.20 | | % 17.80/3.20 | End of split % 17.80/3.20 | % 17.80/3.20 End of proof % 17.80/3.20 % 17.80/3.20 Sub-proof #12 shows that the following formulas are inconsistent: % 17.80/3.20 ---------------------------------------------------------------- % 17.80/3.20 (1) all_4_20 = e1 & all_4_23 = e4 & ~ (all_4_2 = e4) % 17.80/3.20 (2) all_4_20 = e2 % 17.80/3.20 (3) ~ (e2 = e1) % 17.80/3.20 % 17.80/3.20 Begin of proof % 17.80/3.20 | % 17.80/3.20 | ALPHA: (1) implies: % 17.80/3.20 | (4) all_4_20 = e1 % 17.80/3.20 | % 17.80/3.20 | COMBINE_EQS: (2), (4) imply: % 17.80/3.20 | (5) e2 = e1 % 17.80/3.20 | % 17.80/3.20 | REDUCE: (3), (5) imply: % 17.80/3.20 | (6) $false % 17.80/3.20 | % 17.80/3.20 | CLOSE: (6) is inconsistent. % 17.80/3.20 | % 17.80/3.20 End of proof % 17.80/3.20 % 17.80/3.20 Sub-proof #13 shows that the following formulas are inconsistent: % 17.80/3.20 ---------------------------------------------------------------- % 17.80/3.20 (1) all_4_22 = e4 % 17.80/3.20 (2) all_4_22 = e3 % 17.80/3.20 (3) ~ (e4 = e3) % 17.80/3.20 % 17.80/3.20 Begin of proof % 17.80/3.20 | % 17.80/3.20 | COMBINE_EQS: (1), (2) imply: % 17.80/3.20 | (4) e4 = e3 % 17.80/3.20 | % 17.80/3.20 | SIMP: (4) implies: % 17.80/3.20 | (5) e4 = e3 % 17.80/3.20 | % 17.80/3.20 | REDUCE: (3), (5) imply: % 17.80/3.20 | (6) $false % 17.80/3.20 | % 17.80/3.20 | CLOSE: (6) is inconsistent. % 17.80/3.20 | % 17.80/3.20 End of proof % 17.80/3.20 % 17.80/3.20 Sub-proof #14 shows that the following formulas are inconsistent: % 17.80/3.20 ---------------------------------------------------------------- % 17.80/3.20 (1) (all_4_20 = e3 & all_4_21 = e4 & ~ (all_4_0 = e4)) | (all_4_20 = e3 & % 17.80/3.20 all_4_21 = e4 & ~ (all_4_4 = e3)) % 17.80/3.20 (2) all_4_20 = e2 % 17.80/3.20 (3) ~ (e3 = e2) % 17.80/3.20 % 17.80/3.20 Begin of proof % 17.80/3.20 | % 17.80/3.20 | BETA: splitting (1) gives: % 17.80/3.20 | % 17.80/3.20 | Case 1: % 17.80/3.20 | | % 17.80/3.20 | | (4) all_4_20 = e3 & all_4_21 = e4 & ~ (all_4_0 = e4) % 17.80/3.20 | | % 17.80/3.20 | | ALPHA: (4) implies: % 17.80/3.20 | | (5) all_4_20 = e3 % 17.80/3.20 | | % 17.80/3.20 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #15. % 17.80/3.20 | | % 17.80/3.20 | Case 2: % 17.80/3.20 | | % 17.98/3.20 | | (6) all_4_20 = e3 & all_4_21 = e4 & ~ (all_4_4 = e3) % 17.98/3.20 | | % 17.98/3.20 | | ALPHA: (6) implies: % 17.98/3.20 | | (7) all_4_20 = e3 % 17.98/3.20 | | % 17.98/3.20 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #15. % 17.98/3.20 | | % 17.98/3.20 | End of split % 17.98/3.20 | % 17.98/3.20 End of proof % 17.98/3.20 % 17.98/3.20 Sub-proof #15 shows that the following formulas are inconsistent: % 17.98/3.20 ---------------------------------------------------------------- % 17.98/3.20 (1) all_4_20 = e3 % 17.98/3.20 (2) all_4_20 = e2 % 17.98/3.20 (3) ~ (e3 = e2) % 17.98/3.20 % 17.98/3.20 Begin of proof % 17.98/3.20 | % 17.98/3.20 | COMBINE_EQS: (1), (2) imply: % 17.98/3.20 | (4) e3 = e2 % 17.98/3.20 | % 17.98/3.20 | SIMP: (4) implies: % 17.98/3.20 | (5) e3 = e2 % 17.98/3.20 | % 17.98/3.20 | REDUCE: (3), (5) imply: % 17.98/3.20 | (6) $false % 17.98/3.20 | % 17.98/3.20 | CLOSE: (6) is inconsistent. % 17.98/3.20 | % 17.98/3.20 End of proof % 17.98/3.20 % SZS output end Proof for theBenchmark % 17.98/3.20 % 17.98/3.20 2591ms %------------------------------------------------------------------------------