%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG175+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 : n014.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 16:39:39 EDT 2023 % Result : Theorem 8.95s 2.06s % Output : Proof 17.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG175+1 : TPTP v8.1.2. Released v2.7.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n014.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Mon Aug 28 04:52:31 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.66/1.48 Prover 1: Preprocessing ... % 4.66/1.49 Prover 4: Preprocessing ... % 4.66/1.49 Prover 0: Preprocessing ... % 4.66/1.49 Prover 3: Preprocessing ... % 4.66/1.49 Prover 6: Preprocessing ... % 4.66/1.49 Prover 5: Preprocessing ... % 4.66/1.49 Prover 2: Preprocessing ... % 8.95/1.96 Prover 0: Constructing countermodel ... % 8.95/1.96 Prover 2: Constructing countermodel ... % 8.95/1.96 Prover 6: Constructing countermodel ... % 8.95/1.97 Prover 1: Constructing countermodel ... % 8.95/1.97 Prover 4: Constructing countermodel ... % 8.95/1.98 Prover 3: Constructing countermodel ... % 8.95/2.06 Prover 6: proved (1411ms) % 8.95/2.06 % 8.95/2.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.95/2.06 % 8.95/2.07 Prover 2: stopped % 8.95/2.08 Prover 0: proved (1430ms) % 8.95/2.08 % 8.95/2.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.95/2.08 % 8.95/2.10 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.95/2.10 Prover 3: proved (1433ms) % 8.95/2.10 % 8.95/2.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.95/2.10 % 8.95/2.10 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.95/2.10 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.95/2.12 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.02/2.38 Prover 10: Preprocessing ... % 12.02/2.38 Prover 7: Preprocessing ... % 12.02/2.40 Prover 8: Preprocessing ... % 12.02/2.42 Prover 11: Preprocessing ... % 13.21/2.53 Prover 5: Constructing countermodel ... % 13.21/2.54 Prover 5: stopped % 13.21/2.54 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.21/2.55 Prover 8: Constructing countermodel ... % 13.94/2.63 Prover 7: Constructing countermodel ... % 13.94/2.67 Prover 10: Constructing countermodel ... % 13.94/2.67 Prover 13: Preprocessing ... % 13.94/2.68 Prover 11: Constructing countermodel ... % 15.87/2.87 Prover 13: Constructing countermodel ... % 15.87/3.02 Prover 4: Found proof (size 70) % 15.87/3.02 Prover 4: proved (2379ms) % 15.87/3.02 Prover 13: stopped % 15.87/3.02 Prover 7: stopped % 15.87/3.02 Prover 8: stopped % 15.87/3.02 Prover 11: stopped % 15.87/3.02 Prover 10: stopped % 15.87/3.03 Prover 1: Found proof (size 70) % 15.87/3.03 Prover 1: proved (2388ms) % 15.87/3.03 % 15.87/3.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.87/3.03 % 16.17/3.05 % SZS output start Proof for theBenchmark % 16.17/3.05 Assumptions after simplification: % 16.17/3.05 --------------------------------- % 16.17/3.05 % 16.17/3.05 (ax1) % 17.14/3.10 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 17.14/3.10 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 17.14/3.10 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 17.14/3.10 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 17.14/3.10 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 17.14/3.10 [v23: $i] : ? [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = % 17.14/3.10 v22 & op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, e4) = v19 & op(e3, e3) = % 17.14/3.10 v18 & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2, e4) = % 17.14/3.10 v14 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) = v11 & op(e2, e0) = % 17.14/3.10 v10 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = v7 & op(e1, e1) = v6 % 17.14/3.10 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 17.14/3.10 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & % 17.14/3.10 $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & % 17.14/3.10 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 17.14/3.10 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v24 = e3 | % 17.14/3.10 v24 = e2 | v24 = e1 | v24 = e0) & (v23 = e4 | v23 = e3 | v23 = e2 | v23 = % 17.14/3.10 e1 | v23 = e0) & (v22 = e4 | v22 = e3 | v22 = e2 | v22 = e1 | v22 = e0) & % 17.14/3.10 (v21 = e4 | v21 = e3 | v21 = e2 | v21 = e1 | v21 = e0) & (v20 = e4 | v20 = % 17.14/3.10 e3 | v20 = e2 | v20 = e1 | v20 = e0) & (v19 = e4 | v19 = e3 | v19 = e2 | % 17.14/3.10 v19 = e1 | v19 = e0) & (v18 = e4 | v18 = e3 | v18 = e2 | v18 = e1 | v18 = % 17.14/3.10 e0) & (v17 = e4 | v17 = e3 | v17 = e2 | v17 = e1 | v17 = e0) & (v16 = e4 | % 17.14/3.10 v16 = e3 | v16 = e2 | v16 = e1 | v16 = e0) & (v15 = e4 | v15 = e3 | v15 = % 17.14/3.10 e2 | v15 = e1 | v15 = e0) & (v14 = e4 | v14 = e3 | v14 = e2 | v14 = e1 | % 17.14/3.10 v14 = e0) & (v13 = e4 | v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 % 17.14/3.10 = e4 | v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e4 | v11 = e3 | % 17.14/3.10 v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e4 | v10 = e3 | v10 = e2 | v10 = % 17.14/3.10 e1 | v10 = e0) & (v9 = e4 | v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = % 17.14/3.10 e4 | v8 = e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e4 | v7 = e3 | v7 = e2 % 17.14/3.11 | v7 = e1 | v7 = e0) & (v6 = e4 | v6 = e3 | v6 = e2 | v6 = e1 | v6 = e0) & % 17.14/3.11 (v5 = e4 | v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e4 | v4 = e3 | v4 % 17.14/3.11 = e2 | v4 = e1 | v4 = e0) & (v3 = e4 | v3 = e3 | v3 = e2 | v3 = e1 | v3 = % 17.14/3.11 e0) & (v2 = e4 | v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e4 | v1 = % 17.14/3.11 e3 | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1 % 17.14/3.11 | v0 = e0)) % 17.14/3.11 % 17.14/3.11 (ax2) % 17.14/3.12 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 17.14/3.12 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 17.14/3.12 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 17.14/3.12 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 17.14/3.12 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 17.14/3.12 [v23: $i] : ? [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = % 17.14/3.12 v20 & op(e4, e1) = v15 & op(e4, e0) = v8 & op(e3, e4) = v22 & op(e3, e3) = % 17.14/3.12 v21 & op(e3, e2) = v19 & op(e3, e1) = v14 & op(e3, e0) = v7 & op(e2, e4) = % 17.14/3.12 v18 & op(e2, e3) = v17 & op(e2, e2) = v16 & op(e2, e1) = v13 & op(e2, e0) = % 17.14/3.12 v6 & op(e1, e4) = v12 & op(e1, e3) = v11 & op(e1, e2) = v10 & op(e1, e1) = % 17.14/3.12 v9 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 17.14/3.12 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & % 17.14/3.12 $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & % 17.14/3.12 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 17.14/3.12 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v23 = e4 | % 17.14/3.12 v20 = e4 | v15 = e4 | v8 = e4) & (v24 = e4 | v22 = e4 | v18 = e4 | v12 = % 17.14/3.12 e4 | v4 = e4) & (v24 = e3 | v23 = e3 | v20 = e3 | v15 = e3 | v8 = e3) & % 17.14/3.12 (v24 = e3 | v22 = e3 | v18 = e3 | v12 = e3 | v4 = e3) & (v24 = e2 | v23 = e2 % 17.14/3.12 | v20 = e2 | v15 = e2 | v8 = e2) & (v24 = e2 | v22 = e2 | v18 = e2 | v12 = % 17.14/3.12 e2 | v4 = e2) & (v24 = e1 | v23 = e1 | v20 = e1 | v15 = e1 | v8 = e1) & % 17.14/3.12 (v24 = e1 | v22 = e1 | v18 = e1 | v12 = e1 | v4 = e1) & (v24 = e0 | v23 = e0 % 17.14/3.12 | v20 = e0 | v15 = e0 | v8 = e0) & (v24 = e0 | v22 = e0 | v18 = e0 | v12 = % 17.14/3.12 e0 | v4 = e0) & (v23 = e4 | v21 = e4 | v17 = e4 | v11 = e4 | v3 = e4) & % 17.14/3.12 (v23 = e3 | v21 = e3 | v17 = e3 | v11 = e3 | v3 = e3) & (v23 = e2 | v21 = e2 % 17.14/3.12 | v17 = e2 | v11 = e2 | v3 = e2) & (v23 = e1 | v21 = e1 | v17 = e1 | v11 = % 17.14/3.12 e1 | v3 = e1) & (v23 = e0 | v21 = e0 | v17 = e0 | v11 = e0 | v3 = e0) & % 17.14/3.12 (v22 = e4 | v21 = e4 | v19 = e4 | v14 = e4 | v7 = e4) & (v22 = e3 | v21 = e3 % 17.14/3.12 | v19 = e3 | v14 = e3 | v7 = e3) & (v22 = e2 | v21 = e2 | v19 = e2 | v14 = % 17.14/3.12 e2 | v7 = e2) & (v22 = e1 | v21 = e1 | v19 = e1 | v14 = e1 | v7 = e1) & % 17.14/3.12 (v22 = e0 | v21 = e0 | v19 = e0 | v14 = e0 | v7 = e0) & (v20 = e4 | v19 = e4 % 17.14/3.12 | v16 = e4 | v10 = e4 | v2 = e4) & (v20 = e3 | v19 = e3 | v16 = e3 | v10 = % 17.14/3.12 e3 | v2 = e3) & (v20 = e2 | v19 = e2 | v16 = e2 | v10 = e2 | v2 = e2) & % 17.14/3.12 (v20 = e1 | v19 = e1 | v16 = e1 | v10 = e1 | v2 = e1) & (v20 = e0 | v19 = e0 % 17.14/3.12 | v16 = e0 | v10 = e0 | v2 = e0) & (v18 = e4 | v17 = e4 | v16 = e4 | v13 = % 17.14/3.12 e4 | v6 = e4) & (v18 = e3 | v17 = e3 | v16 = e3 | v13 = e3 | v6 = e3) & % 17.14/3.12 (v18 = e2 | v17 = e2 | v16 = e2 | v13 = e2 | v6 = e2) & (v18 = e1 | v17 = e1 % 17.14/3.12 | v16 = e1 | v13 = e1 | v6 = e1) & (v18 = e0 | v17 = e0 | v16 = e0 | v13 = % 17.14/3.12 e0 | v6 = e0) & (v15 = e4 | v14 = e4 | v13 = e4 | v9 = e4 | v1 = e4) & % 17.14/3.12 (v15 = e3 | v14 = e3 | v13 = e3 | v9 = e3 | v1 = e3) & (v15 = e2 | v14 = e2 % 17.14/3.12 | v13 = e2 | v9 = e2 | v1 = e2) & (v15 = e1 | v14 = e1 | v13 = e1 | v9 = % 17.14/3.12 e1 | v1 = e1) & (v15 = e0 | v14 = e0 | v13 = e0 | v9 = e0 | v1 = e0) & % 17.14/3.12 (v12 = e4 | v11 = e4 | v10 = e4 | v9 = e4 | v5 = e4) & (v12 = e3 | v11 = e3 % 17.14/3.12 | v10 = e3 | v9 = e3 | v5 = e3) & (v12 = e2 | v11 = e2 | v10 = e2 | v9 = % 17.14/3.12 e2 | v5 = e2) & (v12 = e1 | v11 = e1 | v10 = e1 | v9 = e1 | v5 = e1) & % 17.14/3.12 (v12 = e0 | v11 = e0 | v10 = e0 | v9 = e0 | v5 = e0) & (v8 = e4 | v7 = e4 | % 17.14/3.12 v6 = e4 | v5 = e4 | v0 = e4) & (v8 = e3 | v7 = e3 | v6 = e3 | v5 = e3 | v0 % 17.14/3.12 = e3) & (v8 = e2 | v7 = e2 | v6 = e2 | v5 = e2 | v0 = e2) & (v8 = e1 | v7 % 17.14/3.12 = e1 | v6 = e1 | v5 = e1 | v0 = e1) & (v4 = e4 | v3 = e4 | v2 = e4 | v1 = % 17.14/3.12 e4 | v0 = e4) & (v4 = e3 | v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (v4 = % 17.14/3.12 e2 | v3 = e2 | v2 = e2 | v1 = e2 | v0 = e2) & (v4 = e1 | v3 = e1 | v2 = e1 % 17.14/3.12 | v1 = e1 | v0 = e1) & (v0 = e0 | ((v8 = e0 | v7 = e0 | v6 = e0 | v5 = e0) % 17.14/3.12 & (v4 = e0 | v3 = e0 | v2 = e0 | v1 = e0)))) % 17.14/3.12 % 17.14/3.12 (ax3) % 17.14/3.12 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 17.14/3.12 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 17.14/3.12 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 17.14/3.12 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 17.14/3.12 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 17.14/3.12 [v23: $i] : ? [v24: $i] : (op(v24, v24) = e4 & op(v23, v22) = e4 & op(v22, % 17.14/3.12 v23) = e3 & op(v21, v21) = e3 & op(v20, v19) = e4 & op(v19, v20) = e2 & % 17.14/3.12 op(v18, v17) = e3 & op(v17, v18) = e2 & op(v16, v16) = e2 & op(v15, v14) = % 17.14/3.12 e4 & op(v14, v15) = e1 & op(v13, v12) = e3 & op(v12, v13) = e1 & op(v11, % 17.14/3.12 v10) = e2 & op(v10, v11) = e1 & op(v9, v9) = e1 & op(v8, v7) = e4 & op(v7, % 17.14/3.12 v8) = e0 & op(v6, v5) = e3 & op(v5, v6) = e0 & op(v4, v3) = e2 & op(v3, % 17.14/3.12 v4) = e0 & op(v2, v1) = e1 & op(v1, v2) = e0 & op(v0, v0) = e0 & op(e4, % 17.14/3.12 e4) = v24 & op(e4, e3) = v22 & op(e4, e2) = v19 & op(e4, e1) = v14 & % 17.14/3.12 op(e4, e0) = v7 & op(e3, e4) = v23 & op(e3, e3) = v21 & op(e3, e2) = v17 & % 17.14/3.12 op(e3, e1) = v12 & op(e3, e0) = v5 & op(e2, e4) = v20 & op(e2, e3) = v18 & % 17.14/3.12 op(e2, e2) = v16 & op(e2, e1) = v10 & op(e2, e0) = v3 & op(e1, e4) = v15 & % 17.14/3.12 op(e1, e3) = v13 & op(e1, e2) = v11 & op(e1, e1) = v9 & op(e1, e0) = v1 & % 17.14/3.12 op(e0, e4) = v8 & op(e0, e3) = v6 & op(e0, e2) = v4 & op(e0, e1) = v2 & % 17.14/3.12 op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) % 17.14/3.12 & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 17.14/3.12 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 17.14/3.12 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.14/3.12 % 17.14/3.12 (ax4) % 17.14/3.13 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 17.14/3.13 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 17.14/3.13 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 17.14/3.13 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 17.14/3.13 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 17.14/3.13 [v23: $i] : ? [v24: $i] : ( ~ (v24 = v23) & ~ (v24 = v22) & ~ (v24 = v21) & % 17.14/3.13 ~ (v24 = v20) & ~ (v24 = v19) & ~ (v24 = v14) & ~ (v24 = v9) & ~ (v24 = % 17.14/3.13 v4) & ~ (v23 = v22) & ~ (v23 = v21) & ~ (v23 = v20) & ~ (v23 = v18) & % 17.14/3.13 ~ (v23 = v13) & ~ (v23 = v8) & ~ (v23 = v3) & ~ (v22 = v21) & ~ (v22 = % 17.14/3.13 v20) & ~ (v22 = v17) & ~ (v22 = v12) & ~ (v22 = v7) & ~ (v22 = v2) & % 17.14/3.13 ~ (v21 = v20) & ~ (v21 = v16) & ~ (v21 = v11) & ~ (v21 = v6) & ~ (v21 = % 17.14/3.13 v1) & ~ (v20 = v15) & ~ (v20 = v10) & ~ (v20 = v5) & ~ (v20 = v0) & ~ % 17.14/3.13 (v19 = v18) & ~ (v19 = v17) & ~ (v19 = v16) & ~ (v19 = v15) & ~ (v19 = % 17.14/3.13 v14) & ~ (v19 = v9) & ~ (v19 = v4) & ~ (v18 = v17) & ~ (v18 = v16) & % 17.14/3.13 ~ (v18 = v15) & ~ (v18 = v13) & ~ (v18 = v8) & ~ (v18 = v3) & ~ (v17 = % 17.14/3.13 v16) & ~ (v17 = v15) & ~ (v17 = v12) & ~ (v17 = v7) & ~ (v17 = v2) & % 17.14/3.13 ~ (v16 = v15) & ~ (v16 = v11) & ~ (v16 = v6) & ~ (v16 = v1) & ~ (v15 = % 17.14/3.13 v10) & ~ (v15 = v5) & ~ (v15 = v0) & ~ (v14 = v13) & ~ (v14 = v12) & % 17.14/3.13 ~ (v14 = v11) & ~ (v14 = v10) & ~ (v14 = v9) & ~ (v14 = v4) & ~ (v13 = % 17.14/3.13 v12) & ~ (v13 = v11) & ~ (v13 = v10) & ~ (v13 = v8) & ~ (v13 = v3) & % 17.14/3.13 ~ (v12 = v11) & ~ (v12 = v10) & ~ (v12 = v7) & ~ (v12 = v2) & ~ (v11 = % 17.14/3.13 v10) & ~ (v11 = v6) & ~ (v11 = v1) & ~ (v10 = v5) & ~ (v10 = v0) & ~ % 17.14/3.13 (v9 = v8) & ~ (v9 = v7) & ~ (v9 = v6) & ~ (v9 = v5) & ~ (v9 = v4) & ~ % 17.14/3.13 (v8 = v7) & ~ (v8 = v6) & ~ (v8 = v5) & ~ (v8 = v3) & ~ (v7 = v6) & ~ % 17.14/3.13 (v7 = v5) & ~ (v7 = v2) & ~ (v6 = v5) & ~ (v6 = v1) & ~ (v5 = v0) & ~ % 17.14/3.13 (v4 = v3) & ~ (v4 = v2) & ~ (v4 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ % 17.14/3.13 (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & % 17.14/3.13 op(e4, e4) = v24 & op(e4, e3) = v19 & op(e4, e2) = v14 & op(e4, e1) = v9 & % 17.14/3.13 op(e4, e0) = v4 & op(e3, e4) = v23 & op(e3, e3) = v18 & op(e3, e2) = v13 & % 17.14/3.13 op(e3, e1) = v8 & op(e3, e0) = v3 & op(e2, e4) = v22 & op(e2, e3) = v17 & % 17.14/3.13 op(e2, e2) = v12 & op(e2, e1) = v7 & op(e2, e0) = v2 & op(e1, e4) = v21 & % 17.14/3.13 op(e1, e3) = v16 & op(e1, e2) = v11 & op(e1, e1) = v6 & op(e1, e0) = v1 & % 17.14/3.13 op(e0, e4) = v20 & op(e0, e3) = v15 & op(e0, e2) = v10 & op(e0, e1) = v5 & % 17.14/3.13 op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) % 17.14/3.13 & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 17.14/3.13 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 17.14/3.13 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.14/3.13 % 17.14/3.13 (ax6) % 17.14/3.13 op(e4, e3) = e0 & op(e3, e1) = e4 & op(e3, e0) = e2 & $i(e4) & $i(e3) & $i(e2) % 17.14/3.13 & $i(e1) & $i(e0) % 17.14/3.13 % 17.14/3.13 (co1) % 17.14/3.14 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 17.14/3.14 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 17.14/3.14 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 17.14/3.14 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 17.14/3.14 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 17.14/3.14 [v23: $i] : ? [v24: $i] : (op(v24, e4) = e4 & op(v23, e3) = e4 & op(v22, e2) % 17.14/3.14 = e4 & op(v21, e1) = e4 & op(v20, e0) = e4 & op(v19, e4) = e3 & op(v18, e3) % 17.14/3.14 = e3 & op(v17, e2) = e3 & op(v16, e1) = e3 & op(v15, e0) = e3 & op(v14, e4) % 17.14/3.14 = e2 & op(v13, e3) = e2 & op(v12, e2) = e2 & op(v11, e1) = e2 & op(v10, e0) % 17.14/3.14 = e2 & op(v9, e4) = e1 & op(v8, e3) = e1 & op(v7, e2) = e1 & op(v6, e1) = e1 % 17.14/3.14 & op(v5, e0) = e1 & op(v4, e4) = e0 & op(v3, e3) = e0 & op(v2, e2) = e0 & % 17.14/3.14 op(v1, e1) = e0 & op(v0, e0) = e0 & op(e4, v24) = e4 & op(e4, v23) = e3 & % 17.14/3.14 op(e4, v22) = e2 & op(e4, v21) = e1 & op(e4, v20) = e0 & op(e4, e4) = v24 & % 17.14/3.14 op(e4, e3) = v23 & op(e4, e2) = v22 & op(e4, e1) = v21 & op(e4, e0) = v20 & % 17.14/3.14 op(e3, v19) = e4 & op(e3, v18) = e3 & op(e3, v17) = e2 & op(e3, v16) = e1 & % 17.14/3.14 op(e3, v15) = e0 & op(e3, e4) = v19 & op(e3, e3) = v18 & op(e3, e2) = v17 & % 17.14/3.14 op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2, v14) = e4 & op(e2, v13) = e3 & % 17.14/3.14 op(e2, v12) = e2 & op(e2, v11) = e1 & op(e2, v10) = e0 & op(e2, e4) = v14 & % 17.14/3.14 op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) = v11 & op(e2, e0) = v10 & % 17.14/3.14 op(e1, v9) = e4 & op(e1, v8) = e3 & op(e1, v7) = e2 & op(e1, v6) = e1 & % 17.14/3.14 op(e1, v5) = e0 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = v7 & % 17.14/3.14 op(e1, e1) = v6 & op(e1, e0) = v5 & op(e0, v4) = e4 & op(e0, v3) = e3 & % 17.14/3.14 op(e0, v2) = e2 & op(e0, v1) = e1 & op(e0, v0) = e0 & op(e0, e4) = v4 & % 17.14/3.14 op(e0, e3) = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & % 17.14/3.14 $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & % 17.14/3.14 $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & % 17.14/3.14 $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 17.14/3.14 $i(v2) & $i(v1) & $i(v0)) % 17.14/3.14 % 17.14/3.14 (function-axioms) % 17.14/3.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3, % 17.14/3.14 v2) = v1) | ~ (op(v3, v2) = v0)) % 17.14/3.14 % 17.14/3.14 Further assumptions not needed in the proof: % 17.14/3.14 -------------------------------------------- % 17.14/3.14 ax5 % 17.14/3.14 % 17.14/3.14 Those formulas are unsatisfiable: % 17.14/3.14 --------------------------------- % 17.14/3.14 % 17.14/3.14 Begin of proof % 17.14/3.14 | % 17.14/3.14 | ALPHA: (ax1) implies: % 17.14/3.15 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 17.14/3.15 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 17.14/3.15 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 17.14/3.15 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 17.14/3.15 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 17.14/3.15 | [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = v22 & % 17.14/3.15 | op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, e4) = v19 & op(e3, e3) = % 17.14/3.15 | v18 & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2, % 17.14/3.15 | e4) = v14 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) = v11 % 17.14/3.15 | & op(e2, e0) = v10 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = % 17.14/3.15 | v7 & op(e1, e1) = v6 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) % 17.14/3.15 | = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) % 17.14/3.15 | & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) % 17.14/3.15 | & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) % 17.14/3.15 | & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 17.14/3.15 | $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v24 = e3 | v24 = e2 | v24 = e1 % 17.14/3.15 | | v24 = e0) & (v23 = e4 | v23 = e3 | v23 = e2 | v23 = e1 | v23 = % 17.14/3.15 | e0) & (v22 = e4 | v22 = e3 | v22 = e2 | v22 = e1 | v22 = e0) & (v21 % 17.14/3.15 | = e4 | v21 = e3 | v21 = e2 | v21 = e1 | v21 = e0) & (v20 = e4 | v20 % 17.14/3.15 | = e3 | v20 = e2 | v20 = e1 | v20 = e0) & (v19 = e4 | v19 = e3 | v19 % 17.14/3.15 | = e2 | v19 = e1 | v19 = e0) & (v18 = e4 | v18 = e3 | v18 = e2 | v18 % 17.14/3.15 | = e1 | v18 = e0) & (v17 = e4 | v17 = e3 | v17 = e2 | v17 = e1 | v17 % 17.14/3.15 | = e0) & (v16 = e4 | v16 = e3 | v16 = e2 | v16 = e1 | v16 = e0) & % 17.14/3.15 | (v15 = e4 | v15 = e3 | v15 = e2 | v15 = e1 | v15 = e0) & (v14 = e4 | % 17.14/3.15 | v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e4 | v13 = e3 | % 17.14/3.15 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e4 | v12 = e3 | v12 = e2 | % 17.14/3.15 | v12 = e1 | v12 = e0) & (v11 = e4 | v11 = e3 | v11 = e2 | v11 = e1 | % 17.14/3.15 | v11 = e0) & (v10 = e4 | v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) % 17.14/3.15 | & (v9 = e4 | v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e4 | v8 = % 17.14/3.15 | e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e4 | v7 = e3 | v7 = e2 | % 17.14/3.15 | v7 = e1 | v7 = e0) & (v6 = e4 | v6 = e3 | v6 = e2 | v6 = e1 | v6 = % 17.14/3.15 | e0) & (v5 = e4 | v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e4 % 17.14/3.15 | | v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e4 | v3 = e3 | v3 % 17.14/3.15 | = e2 | v3 = e1 | v3 = e0) & (v2 = e4 | v2 = e3 | v2 = e2 | v2 = e1 % 17.14/3.15 | | v2 = e0) & (v1 = e4 | v1 = e3 | v1 = e2 | v1 = e1 | v1 = e0) & % 17.14/3.15 | (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0)) % 17.14/3.15 | % 17.14/3.15 | ALPHA: (ax2) implies: % 17.62/3.17 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 17.62/3.17 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 17.62/3.17 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 17.62/3.17 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 17.62/3.17 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 17.62/3.17 | [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = v20 & % 17.62/3.17 | op(e4, e1) = v15 & op(e4, e0) = v8 & op(e3, e4) = v22 & op(e3, e3) = % 17.62/3.17 | v21 & op(e3, e2) = v19 & op(e3, e1) = v14 & op(e3, e0) = v7 & op(e2, % 17.62/3.17 | e4) = v18 & op(e2, e3) = v17 & op(e2, e2) = v16 & op(e2, e1) = v13 % 17.62/3.17 | & op(e2, e0) = v6 & op(e1, e4) = v12 & op(e1, e3) = v11 & op(e1, e2) % 17.62/3.17 | = v10 & op(e1, e1) = v9 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, % 17.62/3.17 | e3) = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & % 17.62/3.17 | $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & % 17.62/3.17 | $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & % 17.62/3.17 | $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 17.62/3.17 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v23 = e4 | v20 = e4 | % 17.62/3.17 | v15 = e4 | v8 = e4) & (v24 = e4 | v22 = e4 | v18 = e4 | v12 = e4 | % 17.62/3.17 | v4 = e4) & (v24 = e3 | v23 = e3 | v20 = e3 | v15 = e3 | v8 = e3) & % 17.62/3.17 | (v24 = e3 | v22 = e3 | v18 = e3 | v12 = e3 | v4 = e3) & (v24 = e2 | % 17.62/3.17 | v23 = e2 | v20 = e2 | v15 = e2 | v8 = e2) & (v24 = e2 | v22 = e2 | % 17.62/3.17 | v18 = e2 | v12 = e2 | v4 = e2) & (v24 = e1 | v23 = e1 | v20 = e1 | % 17.62/3.17 | v15 = e1 | v8 = e1) & (v24 = e1 | v22 = e1 | v18 = e1 | v12 = e1 | % 17.62/3.17 | v4 = e1) & (v24 = e0 | v23 = e0 | v20 = e0 | v15 = e0 | v8 = e0) & % 17.62/3.17 | (v24 = e0 | v22 = e0 | v18 = e0 | v12 = e0 | v4 = e0) & (v23 = e4 | % 17.62/3.17 | v21 = e4 | v17 = e4 | v11 = e4 | v3 = e4) & (v23 = e3 | v21 = e3 | % 17.62/3.17 | v17 = e3 | v11 = e3 | v3 = e3) & (v23 = e2 | v21 = e2 | v17 = e2 | % 17.62/3.17 | v11 = e2 | v3 = e2) & (v23 = e1 | v21 = e1 | v17 = e1 | v11 = e1 | % 17.62/3.17 | v3 = e1) & (v23 = e0 | v21 = e0 | v17 = e0 | v11 = e0 | v3 = e0) & % 17.62/3.17 | (v22 = e4 | v21 = e4 | v19 = e4 | v14 = e4 | v7 = e4) & (v22 = e3 | % 17.62/3.17 | v21 = e3 | v19 = e3 | v14 = e3 | v7 = e3) & (v22 = e2 | v21 = e2 | % 17.62/3.17 | v19 = e2 | v14 = e2 | v7 = e2) & (v22 = e1 | v21 = e1 | v19 = e1 | % 17.62/3.17 | v14 = e1 | v7 = e1) & (v22 = e0 | v21 = e0 | v19 = e0 | v14 = e0 | % 17.62/3.17 | v7 = e0) & (v20 = e4 | v19 = e4 | v16 = e4 | v10 = e4 | v2 = e4) & % 17.62/3.17 | (v20 = e3 | v19 = e3 | v16 = e3 | v10 = e3 | v2 = e3) & (v20 = e2 | % 17.62/3.17 | v19 = e2 | v16 = e2 | v10 = e2 | v2 = e2) & (v20 = e1 | v19 = e1 | % 17.62/3.17 | v16 = e1 | v10 = e1 | v2 = e1) & (v20 = e0 | v19 = e0 | v16 = e0 | % 17.62/3.17 | v10 = e0 | v2 = e0) & (v18 = e4 | v17 = e4 | v16 = e4 | v13 = e4 | % 17.62/3.17 | v6 = e4) & (v18 = e3 | v17 = e3 | v16 = e3 | v13 = e3 | v6 = e3) & % 17.62/3.17 | (v18 = e2 | v17 = e2 | v16 = e2 | v13 = e2 | v6 = e2) & (v18 = e1 | % 17.62/3.17 | v17 = e1 | v16 = e1 | v13 = e1 | v6 = e1) & (v18 = e0 | v17 = e0 | % 17.62/3.17 | v16 = e0 | v13 = e0 | v6 = e0) & (v15 = e4 | v14 = e4 | v13 = e4 | % 17.62/3.17 | v9 = e4 | v1 = e4) & (v15 = e3 | v14 = e3 | v13 = e3 | v9 = e3 | v1 % 17.62/3.17 | = e3) & (v15 = e2 | v14 = e2 | v13 = e2 | v9 = e2 | v1 = e2) & (v15 % 17.62/3.17 | = e1 | v14 = e1 | v13 = e1 | v9 = e1 | v1 = e1) & (v15 = e0 | v14 = % 17.62/3.17 | e0 | v13 = e0 | v9 = e0 | v1 = e0) & (v12 = e4 | v11 = e4 | v10 = % 17.62/3.17 | e4 | v9 = e4 | v5 = e4) & (v12 = e3 | v11 = e3 | v10 = e3 | v9 = e3 % 17.62/3.17 | | v5 = e3) & (v12 = e2 | v11 = e2 | v10 = e2 | v9 = e2 | v5 = e2) & % 17.62/3.17 | (v12 = e1 | v11 = e1 | v10 = e1 | v9 = e1 | v5 = e1) & (v12 = e0 | % 17.62/3.17 | v11 = e0 | v10 = e0 | v9 = e0 | v5 = e0) & (v8 = e4 | v7 = e4 | v6 % 17.62/3.17 | = e4 | v5 = e4 | v0 = e4) & (v8 = e3 | v7 = e3 | v6 = e3 | v5 = e3 % 17.62/3.17 | | v0 = e3) & (v8 = e2 | v7 = e2 | v6 = e2 | v5 = e2 | v0 = e2) & % 17.62/3.17 | (v8 = e1 | v7 = e1 | v6 = e1 | v5 = e1 | v0 = e1) & (v4 = e4 | v3 = % 17.62/3.17 | e4 | v2 = e4 | v1 = e4 | v0 = e4) & (v4 = e3 | v3 = e3 | v2 = e3 | % 17.62/3.17 | v1 = e3 | v0 = e3) & (v4 = e2 | v3 = e2 | v2 = e2 | v1 = e2 | v0 = % 17.62/3.17 | e2) & (v4 = e1 | v3 = e1 | v2 = e1 | v1 = e1 | v0 = e1) & (v0 = e0 % 17.62/3.17 | | ((v8 = e0 | v7 = e0 | v6 = e0 | v5 = e0) & (v4 = e0 | v3 = e0 | % 17.62/3.17 | v2 = e0 | v1 = e0)))) % 17.62/3.17 | % 17.62/3.17 | ALPHA: (ax3) implies: % 17.62/3.17 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 17.62/3.17 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 17.62/3.17 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 17.62/3.17 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 17.62/3.17 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 17.62/3.17 | [v24: $i] : (op(v24, v24) = e4 & op(v23, v22) = e4 & op(v22, v23) = e3 % 17.62/3.17 | & op(v21, v21) = e3 & op(v20, v19) = e4 & op(v19, v20) = e2 & op(v18, % 17.62/3.17 | v17) = e3 & op(v17, v18) = e2 & op(v16, v16) = e2 & op(v15, v14) = % 17.62/3.17 | e4 & op(v14, v15) = e1 & op(v13, v12) = e3 & op(v12, v13) = e1 & % 17.62/3.17 | op(v11, v10) = e2 & op(v10, v11) = e1 & op(v9, v9) = e1 & op(v8, v7) % 17.62/3.17 | = e4 & op(v7, v8) = e0 & op(v6, v5) = e3 & op(v5, v6) = e0 & op(v4, % 17.62/3.17 | v3) = e2 & op(v3, v4) = e0 & op(v2, v1) = e1 & op(v1, v2) = e0 & % 17.62/3.17 | op(v0, v0) = e0 & op(e4, e4) = v24 & op(e4, e3) = v22 & op(e4, e2) = % 17.62/3.17 | v19 & op(e4, e1) = v14 & op(e4, e0) = v7 & op(e3, e4) = v23 & op(e3, % 17.62/3.17 | e3) = v21 & op(e3, e2) = v17 & op(e3, e1) = v12 & op(e3, e0) = v5 & % 17.62/3.17 | op(e2, e4) = v20 & op(e2, e3) = v18 & op(e2, e2) = v16 & op(e2, e1) = % 17.62/3.17 | v10 & op(e2, e0) = v3 & op(e1, e4) = v15 & op(e1, e3) = v13 & op(e1, % 17.62/3.17 | e2) = v11 & op(e1, e1) = v9 & op(e1, e0) = v1 & op(e0, e4) = v8 & % 17.62/3.17 | op(e0, e3) = v6 & op(e0, e2) = v4 & op(e0, e1) = v2 & op(e0, e0) = v0 % 17.62/3.17 | & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) % 17.62/3.17 | & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) % 17.62/3.17 | & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 17.62/3.17 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.62/3.17 | % 17.62/3.17 | ALPHA: (ax4) implies: % 17.62/3.18 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 17.62/3.18 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 17.62/3.18 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 17.62/3.18 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 17.62/3.18 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 17.62/3.18 | [v24: $i] : ( ~ (v24 = v23) & ~ (v24 = v22) & ~ (v24 = v21) & ~ (v24 % 17.62/3.18 | = v20) & ~ (v24 = v19) & ~ (v24 = v14) & ~ (v24 = v9) & ~ (v24 % 17.62/3.18 | = v4) & ~ (v23 = v22) & ~ (v23 = v21) & ~ (v23 = v20) & ~ (v23 % 17.62/3.18 | = v18) & ~ (v23 = v13) & ~ (v23 = v8) & ~ (v23 = v3) & ~ (v22 = % 17.62/3.18 | v21) & ~ (v22 = v20) & ~ (v22 = v17) & ~ (v22 = v12) & ~ (v22 = % 17.62/3.18 | v7) & ~ (v22 = v2) & ~ (v21 = v20) & ~ (v21 = v16) & ~ (v21 = % 17.62/3.18 | v11) & ~ (v21 = v6) & ~ (v21 = v1) & ~ (v20 = v15) & ~ (v20 = % 17.62/3.18 | v10) & ~ (v20 = v5) & ~ (v20 = v0) & ~ (v19 = v18) & ~ (v19 = % 17.62/3.18 | v17) & ~ (v19 = v16) & ~ (v19 = v15) & ~ (v19 = v14) & ~ (v19 = % 17.62/3.18 | v9) & ~ (v19 = v4) & ~ (v18 = v17) & ~ (v18 = v16) & ~ (v18 = % 17.62/3.18 | v15) & ~ (v18 = v13) & ~ (v18 = v8) & ~ (v18 = v3) & ~ (v17 = % 17.62/3.18 | v16) & ~ (v17 = v15) & ~ (v17 = v12) & ~ (v17 = v7) & ~ (v17 = % 17.62/3.18 | v2) & ~ (v16 = v15) & ~ (v16 = v11) & ~ (v16 = v6) & ~ (v16 = % 17.62/3.18 | v1) & ~ (v15 = v10) & ~ (v15 = v5) & ~ (v15 = v0) & ~ (v14 = % 17.62/3.18 | v13) & ~ (v14 = v12) & ~ (v14 = v11) & ~ (v14 = v10) & ~ (v14 = % 17.62/3.18 | v9) & ~ (v14 = v4) & ~ (v13 = v12) & ~ (v13 = v11) & ~ (v13 = % 17.62/3.18 | v10) & ~ (v13 = v8) & ~ (v13 = v3) & ~ (v12 = v11) & ~ (v12 = % 17.62/3.18 | v10) & ~ (v12 = v7) & ~ (v12 = v2) & ~ (v11 = v10) & ~ (v11 = % 17.62/3.18 | v6) & ~ (v11 = v1) & ~ (v10 = v5) & ~ (v10 = v0) & ~ (v9 = v8) % 17.62/3.18 | & ~ (v9 = v7) & ~ (v9 = v6) & ~ (v9 = v5) & ~ (v9 = v4) & ~ (v8 % 17.62/3.18 | = v7) & ~ (v8 = v6) & ~ (v8 = v5) & ~ (v8 = v3) & ~ (v7 = v6) & % 17.62/3.18 | ~ (v7 = v5) & ~ (v7 = v2) & ~ (v6 = v5) & ~ (v6 = v1) & ~ (v5 = % 17.62/3.18 | v0) & ~ (v4 = v3) & ~ (v4 = v2) & ~ (v4 = v1) & ~ (v4 = v0) & % 17.62/3.18 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = % 17.62/3.18 | v0) & ~ (v1 = v0) & op(e4, e4) = v24 & op(e4, e3) = v19 & op(e4, % 17.62/3.18 | e2) = v14 & op(e4, e1) = v9 & op(e4, e0) = v4 & op(e3, e4) = v23 & % 17.62/3.18 | op(e3, e3) = v18 & op(e3, e2) = v13 & op(e3, e1) = v8 & op(e3, e0) = % 17.62/3.18 | v3 & op(e2, e4) = v22 & op(e2, e3) = v17 & op(e2, e2) = v12 & op(e2, % 17.62/3.18 | e1) = v7 & op(e2, e0) = v2 & op(e1, e4) = v21 & op(e1, e3) = v16 & % 17.62/3.18 | op(e1, e2) = v11 & op(e1, e1) = v6 & op(e1, e0) = v1 & op(e0, e4) = % 17.62/3.18 | v20 & op(e0, e3) = v15 & op(e0, e2) = v10 & op(e0, e1) = v5 & op(e0, % 17.62/3.18 | e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & % 17.62/3.18 | $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & % 17.62/3.18 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 17.62/3.18 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.62/3.18 | % 17.62/3.18 | ALPHA: (ax6) implies: % 17.62/3.18 | (5) op(e3, e0) = e2 % 17.62/3.18 | (6) op(e4, e3) = e0 % 17.62/3.18 | % 17.62/3.19 | ALPHA: (co1) implies: % 17.62/3.19 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 17.62/3.19 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 17.62/3.19 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 17.62/3.19 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 17.62/3.19 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 17.62/3.19 | [v24: $i] : (op(v24, e4) = e4 & op(v23, e3) = e4 & op(v22, e2) = e4 & % 17.62/3.19 | op(v21, e1) = e4 & op(v20, e0) = e4 & op(v19, e4) = e3 & op(v18, e3) % 17.62/3.19 | = e3 & op(v17, e2) = e3 & op(v16, e1) = e3 & op(v15, e0) = e3 & % 17.62/3.19 | op(v14, e4) = e2 & op(v13, e3) = e2 & op(v12, e2) = e2 & op(v11, e1) % 17.62/3.19 | = e2 & op(v10, e0) = e2 & op(v9, e4) = e1 & op(v8, e3) = e1 & op(v7, % 17.62/3.19 | e2) = e1 & op(v6, e1) = e1 & op(v5, e0) = e1 & op(v4, e4) = e0 & % 17.62/3.19 | op(v3, e3) = e0 & op(v2, e2) = e0 & op(v1, e1) = e0 & op(v0, e0) = e0 % 17.62/3.19 | & op(e4, v24) = e4 & op(e4, v23) = e3 & op(e4, v22) = e2 & op(e4, % 17.62/3.19 | v21) = e1 & op(e4, v20) = e0 & op(e4, e4) = v24 & op(e4, e3) = v23 % 17.62/3.19 | & op(e4, e2) = v22 & op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, % 17.62/3.19 | v19) = e4 & op(e3, v18) = e3 & op(e3, v17) = e2 & op(e3, v16) = e1 % 17.62/3.19 | & op(e3, v15) = e0 & op(e3, e4) = v19 & op(e3, e3) = v18 & op(e3, e2) % 17.62/3.19 | = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2, v14) = e4 & % 17.62/3.19 | op(e2, v13) = e3 & op(e2, v12) = e2 & op(e2, v11) = e1 & op(e2, v10) % 17.62/3.19 | = e0 & op(e2, e4) = v14 & op(e2, e3) = v13 & op(e2, e2) = v12 & % 17.62/3.19 | op(e2, e1) = v11 & op(e2, e0) = v10 & op(e1, v9) = e4 & op(e1, v8) = % 17.62/3.19 | e3 & op(e1, v7) = e2 & op(e1, v6) = e1 & op(e1, v5) = e0 & op(e1, e4) % 17.62/3.19 | = v9 & op(e1, e3) = v8 & op(e1, e2) = v7 & op(e1, e1) = v6 & op(e1, % 17.62/3.19 | e0) = v5 & op(e0, v4) = e4 & op(e0, v3) = e3 & op(e0, v2) = e2 & % 17.62/3.19 | op(e0, v1) = e1 & op(e0, v0) = e0 & op(e0, e4) = v4 & op(e0, e3) = v3 % 17.62/3.19 | & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) & % 17.62/3.19 | $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) & % 17.62/3.19 | $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & % 17.62/3.19 | $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) % 17.62/3.19 | & $i(v1) & $i(v0)) % 17.62/3.19 | % 17.62/3.19 | DELTA: instantiating (3) with fresh symbols all_4_0, all_4_1, all_4_2, % 17.62/3.19 | all_4_3, all_4_4, all_4_5, all_4_6, all_4_7, all_4_8, all_4_9, % 17.62/3.19 | all_4_10, all_4_11, all_4_12, all_4_13, all_4_14, all_4_15, all_4_16, % 17.62/3.19 | all_4_17, all_4_18, all_4_19, all_4_20, all_4_21, all_4_22, all_4_23, % 17.62/3.19 | all_4_24 gives: % 17.62/3.19 | (8) op(all_4_0, all_4_0) = e4 & op(all_4_1, all_4_2) = e4 & op(all_4_2, % 17.62/3.19 | all_4_1) = e3 & op(all_4_3, all_4_3) = e3 & op(all_4_4, all_4_5) = e4 % 17.62/3.19 | & op(all_4_5, all_4_4) = e2 & op(all_4_6, all_4_7) = e3 & op(all_4_7, % 17.62/3.19 | all_4_6) = e2 & op(all_4_8, all_4_8) = e2 & op(all_4_9, all_4_10) = % 17.62/3.19 | e4 & op(all_4_10, all_4_9) = e1 & op(all_4_11, all_4_12) = e3 & % 17.62/3.19 | op(all_4_12, all_4_11) = e1 & op(all_4_13, all_4_14) = e2 & % 17.62/3.19 | op(all_4_14, all_4_13) = e1 & op(all_4_15, all_4_15) = e1 & % 17.62/3.20 | op(all_4_16, all_4_17) = e4 & op(all_4_17, all_4_16) = e0 & % 17.62/3.20 | op(all_4_18, all_4_19) = e3 & op(all_4_19, all_4_18) = e0 & % 17.62/3.20 | op(all_4_20, all_4_21) = e2 & op(all_4_21, all_4_20) = e0 & % 17.62/3.20 | op(all_4_22, all_4_23) = e1 & op(all_4_23, all_4_22) = e0 & % 17.62/3.20 | op(all_4_24, all_4_24) = e0 & op(e4, e4) = all_4_0 & op(e4, e3) = % 17.62/3.20 | all_4_2 & op(e4, e2) = all_4_5 & op(e4, e1) = all_4_10 & op(e4, e0) = % 17.62/3.20 | all_4_17 & op(e3, e4) = all_4_1 & op(e3, e3) = all_4_3 & op(e3, e2) = % 17.62/3.20 | all_4_7 & op(e3, e1) = all_4_12 & op(e3, e0) = all_4_19 & op(e2, e4) = % 17.62/3.20 | all_4_4 & op(e2, e3) = all_4_6 & op(e2, e2) = all_4_8 & op(e2, e1) = % 17.62/3.20 | all_4_14 & op(e2, e0) = all_4_21 & op(e1, e4) = all_4_9 & op(e1, e3) = % 17.62/3.20 | all_4_11 & op(e1, e2) = all_4_13 & op(e1, e1) = all_4_15 & op(e1, e0) = % 17.62/3.20 | all_4_23 & op(e0, e4) = all_4_16 & op(e0, e3) = all_4_18 & op(e0, e2) = % 17.62/3.20 | all_4_20 & op(e0, e1) = all_4_22 & op(e0, e0) = all_4_24 & $i(all_4_0) % 17.62/3.20 | & $i(all_4_1) & $i(all_4_2) & $i(all_4_3) & $i(all_4_4) & $i(all_4_5) & % 17.62/3.20 | $i(all_4_6) & $i(all_4_7) & $i(all_4_8) & $i(all_4_9) & $i(all_4_10) & % 17.62/3.20 | $i(all_4_11) & $i(all_4_12) & $i(all_4_13) & $i(all_4_14) & % 17.62/3.20 | $i(all_4_15) & $i(all_4_16) & $i(all_4_17) & $i(all_4_18) & % 17.62/3.20 | $i(all_4_19) & $i(all_4_20) & $i(all_4_21) & $i(all_4_22) & % 17.62/3.20 | $i(all_4_23) & $i(all_4_24) % 17.62/3.20 | % 17.62/3.20 | ALPHA: (8) implies: % 17.81/3.20 | (9) op(e2, e0) = all_4_21 % 17.81/3.20 | (10) op(e3, e0) = all_4_19 % 17.81/3.20 | (11) op(e4, e0) = all_4_17 % 17.81/3.20 | % 17.81/3.20 | DELTA: instantiating (7) with fresh symbols all_6_0, all_6_1, all_6_2, % 17.81/3.20 | all_6_3, all_6_4, all_6_5, all_6_6, all_6_7, all_6_8, all_6_9, % 17.81/3.20 | all_6_10, all_6_11, all_6_12, all_6_13, all_6_14, all_6_15, all_6_16, % 17.81/3.20 | all_6_17, all_6_18, all_6_19, all_6_20, all_6_21, all_6_22, all_6_23, % 17.81/3.20 | all_6_24 gives: % 17.81/3.20 | (12) op(all_6_0, e4) = e4 & op(all_6_1, e3) = e4 & op(all_6_2, e2) = e4 & % 17.81/3.20 | op(all_6_3, e1) = e4 & op(all_6_4, e0) = e4 & op(all_6_5, e4) = e3 & % 17.81/3.20 | op(all_6_6, e3) = e3 & op(all_6_7, e2) = e3 & op(all_6_8, e1) = e3 & % 17.81/3.20 | op(all_6_9, e0) = e3 & op(all_6_10, e4) = e2 & op(all_6_11, e3) = e2 & % 17.81/3.20 | op(all_6_12, e2) = e2 & op(all_6_13, e1) = e2 & op(all_6_14, e0) = e2 % 17.81/3.20 | & op(all_6_15, e4) = e1 & op(all_6_16, e3) = e1 & op(all_6_17, e2) = % 17.81/3.20 | e1 & op(all_6_18, e1) = e1 & op(all_6_19, e0) = e1 & op(all_6_20, e4) % 17.81/3.20 | = e0 & op(all_6_21, e3) = e0 & op(all_6_22, e2) = e0 & op(all_6_23, % 17.81/3.20 | e1) = e0 & op(all_6_24, e0) = e0 & op(e4, all_6_0) = e4 & op(e4, % 17.81/3.20 | all_6_1) = e3 & op(e4, all_6_2) = e2 & op(e4, all_6_3) = e1 & op(e4, % 17.81/3.20 | all_6_4) = e0 & op(e4, e4) = all_6_0 & op(e4, e3) = all_6_1 & op(e4, % 17.81/3.20 | e2) = all_6_2 & op(e4, e1) = all_6_3 & op(e4, e0) = all_6_4 & op(e3, % 17.81/3.20 | all_6_5) = e4 & op(e3, all_6_6) = e3 & op(e3, all_6_7) = e2 & op(e3, % 17.81/3.20 | all_6_8) = e1 & op(e3, all_6_9) = e0 & op(e3, e4) = all_6_5 & op(e3, % 17.81/3.20 | e3) = all_6_6 & op(e3, e2) = all_6_7 & op(e3, e1) = all_6_8 & op(e3, % 17.81/3.20 | e0) = all_6_9 & op(e2, all_6_10) = e4 & op(e2, all_6_11) = e3 & % 17.81/3.20 | op(e2, all_6_12) = e2 & op(e2, all_6_13) = e1 & op(e2, all_6_14) = e0 % 17.81/3.20 | & op(e2, e4) = all_6_10 & op(e2, e3) = all_6_11 & op(e2, e2) = % 17.81/3.20 | all_6_12 & op(e2, e1) = all_6_13 & op(e2, e0) = all_6_14 & op(e1, % 17.81/3.20 | all_6_15) = e4 & op(e1, all_6_16) = e3 & op(e1, all_6_17) = e2 & % 17.81/3.20 | op(e1, all_6_18) = e1 & op(e1, all_6_19) = e0 & op(e1, e4) = all_6_15 % 17.81/3.20 | & op(e1, e3) = all_6_16 & op(e1, e2) = all_6_17 & op(e1, e1) = % 17.81/3.20 | all_6_18 & op(e1, e0) = all_6_19 & op(e0, all_6_20) = e4 & op(e0, % 17.81/3.20 | all_6_21) = e3 & op(e0, all_6_22) = e2 & op(e0, all_6_23) = e1 & % 17.81/3.20 | op(e0, all_6_24) = e0 & op(e0, e4) = all_6_20 & op(e0, e3) = all_6_21 % 17.81/3.20 | & op(e0, e2) = all_6_22 & op(e0, e1) = all_6_23 & op(e0, e0) = % 17.81/3.20 | all_6_24 & $i(all_6_0) & $i(all_6_1) & $i(all_6_2) & $i(all_6_3) & % 17.81/3.20 | $i(all_6_4) & $i(all_6_5) & $i(all_6_6) & $i(all_6_7) & $i(all_6_8) & % 17.81/3.20 | $i(all_6_9) & $i(all_6_10) & $i(all_6_11) & $i(all_6_12) & % 17.81/3.20 | $i(all_6_13) & $i(all_6_14) & $i(all_6_15) & $i(all_6_16) & % 17.81/3.20 | $i(all_6_17) & $i(all_6_18) & $i(all_6_19) & $i(all_6_20) & % 17.81/3.20 | $i(all_6_21) & $i(all_6_22) & $i(all_6_23) & $i(all_6_24) % 17.81/3.20 | % 17.81/3.20 | ALPHA: (12) implies: % 17.81/3.20 | (13) op(e2, e0) = all_6_14 % 17.81/3.20 | (14) op(e3, e0) = all_6_9 % 17.81/3.20 | (15) op(e4, e0) = all_6_4 % 17.81/3.20 | (16) op(e4, e3) = all_6_1 % 17.81/3.20 | (17) op(e4, all_6_1) = e3 % 17.81/3.20 | (18) op(all_6_9, e0) = e3 % 17.81/3.20 | % 17.81/3.20 | DELTA: instantiating (4) with fresh symbols all_8_0, all_8_1, all_8_2, % 17.81/3.20 | all_8_3, all_8_4, all_8_5, all_8_6, all_8_7, all_8_8, all_8_9, % 17.81/3.20 | all_8_10, all_8_11, all_8_12, all_8_13, all_8_14, all_8_15, all_8_16, % 17.81/3.20 | all_8_17, all_8_18, all_8_19, all_8_20, all_8_21, all_8_22, all_8_23, % 17.81/3.20 | all_8_24 gives: % 17.81/3.21 | (19) ~ (all_8_0 = all_8_1) & ~ (all_8_0 = all_8_2) & ~ (all_8_0 = % 17.81/3.21 | all_8_3) & ~ (all_8_0 = all_8_4) & ~ (all_8_0 = all_8_5) & ~ % 17.81/3.21 | (all_8_0 = all_8_10) & ~ (all_8_0 = all_8_15) & ~ (all_8_0 = % 17.81/3.21 | all_8_20) & ~ (all_8_1 = all_8_2) & ~ (all_8_1 = all_8_3) & ~ % 17.81/3.21 | (all_8_1 = all_8_4) & ~ (all_8_1 = all_8_6) & ~ (all_8_1 = all_8_11) % 17.81/3.21 | & ~ (all_8_1 = all_8_16) & ~ (all_8_1 = all_8_21) & ~ (all_8_2 = % 17.81/3.21 | all_8_3) & ~ (all_8_2 = all_8_4) & ~ (all_8_2 = all_8_7) & ~ % 17.81/3.21 | (all_8_2 = all_8_12) & ~ (all_8_2 = all_8_17) & ~ (all_8_2 = % 17.81/3.21 | all_8_22) & ~ (all_8_3 = all_8_4) & ~ (all_8_3 = all_8_8) & ~ % 17.81/3.21 | (all_8_3 = all_8_13) & ~ (all_8_3 = all_8_18) & ~ (all_8_3 = % 17.81/3.21 | all_8_23) & ~ (all_8_4 = all_8_9) & ~ (all_8_4 = all_8_14) & ~ % 17.81/3.21 | (all_8_4 = all_8_19) & ~ (all_8_4 = all_8_24) & ~ (all_8_5 = % 17.81/3.21 | all_8_6) & ~ (all_8_5 = all_8_7) & ~ (all_8_5 = all_8_8) & ~ % 17.81/3.21 | (all_8_5 = all_8_9) & ~ (all_8_5 = all_8_10) & ~ (all_8_5 = % 17.81/3.21 | all_8_15) & ~ (all_8_5 = all_8_20) & ~ (all_8_6 = all_8_7) & ~ % 17.81/3.21 | (all_8_6 = all_8_8) & ~ (all_8_6 = all_8_9) & ~ (all_8_6 = all_8_11) % 17.81/3.21 | & ~ (all_8_6 = all_8_16) & ~ (all_8_6 = all_8_21) & ~ (all_8_7 = % 17.81/3.21 | all_8_8) & ~ (all_8_7 = all_8_9) & ~ (all_8_7 = all_8_12) & ~ % 17.81/3.21 | (all_8_7 = all_8_17) & ~ (all_8_7 = all_8_22) & ~ (all_8_8 = % 17.81/3.21 | all_8_9) & ~ (all_8_8 = all_8_13) & ~ (all_8_8 = all_8_18) & ~ % 17.81/3.21 | (all_8_8 = all_8_23) & ~ (all_8_9 = all_8_14) & ~ (all_8_9 = % 17.81/3.21 | all_8_19) & ~ (all_8_9 = all_8_24) & ~ (all_8_10 = all_8_11) & ~ % 17.81/3.21 | (all_8_10 = all_8_12) & ~ (all_8_10 = all_8_13) & ~ (all_8_10 = % 17.81/3.21 | all_8_14) & ~ (all_8_10 = all_8_15) & ~ (all_8_10 = all_8_20) & ~ % 17.81/3.21 | (all_8_11 = all_8_12) & ~ (all_8_11 = all_8_13) & ~ (all_8_11 = % 17.81/3.21 | all_8_14) & ~ (all_8_11 = all_8_16) & ~ (all_8_11 = all_8_21) & ~ % 17.81/3.21 | (all_8_12 = all_8_13) & ~ (all_8_12 = all_8_14) & ~ (all_8_12 = % 17.81/3.21 | all_8_17) & ~ (all_8_12 = all_8_22) & ~ (all_8_13 = all_8_14) & ~ % 17.81/3.21 | (all_8_13 = all_8_18) & ~ (all_8_13 = all_8_23) & ~ (all_8_14 = % 17.81/3.21 | all_8_19) & ~ (all_8_14 = all_8_24) & ~ (all_8_15 = all_8_16) & ~ % 17.81/3.21 | (all_8_15 = all_8_17) & ~ (all_8_15 = all_8_18) & ~ (all_8_15 = % 17.81/3.21 | all_8_19) & ~ (all_8_15 = all_8_20) & ~ (all_8_16 = all_8_17) & ~ % 17.81/3.21 | (all_8_16 = all_8_18) & ~ (all_8_16 = all_8_19) & ~ (all_8_16 = % 17.81/3.21 | all_8_21) & ~ (all_8_17 = all_8_18) & ~ (all_8_17 = all_8_19) & ~ % 17.81/3.21 | (all_8_17 = all_8_22) & ~ (all_8_18 = all_8_19) & ~ (all_8_18 = % 17.81/3.21 | all_8_23) & ~ (all_8_19 = all_8_24) & ~ (all_8_20 = all_8_21) & ~ % 17.81/3.21 | (all_8_20 = all_8_22) & ~ (all_8_20 = all_8_23) & ~ (all_8_20 = % 17.81/3.21 | all_8_24) & ~ (all_8_21 = all_8_22) & ~ (all_8_21 = all_8_23) & ~ % 17.81/3.21 | (all_8_21 = all_8_24) & ~ (all_8_22 = all_8_23) & ~ (all_8_22 = % 17.81/3.21 | all_8_24) & ~ (all_8_23 = all_8_24) & op(e4, e4) = all_8_0 & op(e4, % 17.81/3.21 | e3) = all_8_5 & op(e4, e2) = all_8_10 & op(e4, e1) = all_8_15 & % 17.81/3.21 | op(e4, e0) = all_8_20 & op(e3, e4) = all_8_1 & op(e3, e3) = all_8_6 & % 17.81/3.21 | op(e3, e2) = all_8_11 & op(e3, e1) = all_8_16 & op(e3, e0) = all_8_21 % 17.81/3.21 | & op(e2, e4) = all_8_2 & op(e2, e3) = all_8_7 & op(e2, e2) = all_8_12 % 17.81/3.21 | & op(e2, e1) = all_8_17 & op(e2, e0) = all_8_22 & op(e1, e4) = all_8_3 % 17.81/3.21 | & op(e1, e3) = all_8_8 & op(e1, e2) = all_8_13 & op(e1, e1) = all_8_18 % 17.81/3.21 | & op(e1, e0) = all_8_23 & op(e0, e4) = all_8_4 & op(e0, e3) = all_8_9 % 17.81/3.21 | & op(e0, e2) = all_8_14 & op(e0, e1) = all_8_19 & op(e0, e0) = % 17.81/3.21 | all_8_24 & $i(all_8_0) & $i(all_8_1) & $i(all_8_2) & $i(all_8_3) & % 17.81/3.21 | $i(all_8_4) & $i(all_8_5) & $i(all_8_6) & $i(all_8_7) & $i(all_8_8) & % 17.81/3.21 | $i(all_8_9) & $i(all_8_10) & $i(all_8_11) & $i(all_8_12) & % 17.81/3.21 | $i(all_8_13) & $i(all_8_14) & $i(all_8_15) & $i(all_8_16) & % 17.81/3.21 | $i(all_8_17) & $i(all_8_18) & $i(all_8_19) & $i(all_8_20) & % 17.81/3.21 | $i(all_8_21) & $i(all_8_22) & $i(all_8_23) & $i(all_8_24) % 17.81/3.21 | % 17.81/3.21 | ALPHA: (19) implies: % 17.81/3.21 | (20) ~ (all_8_20 = all_8_22) % 17.81/3.21 | (21) op(e2, e0) = all_8_22 % 17.81/3.21 | (22) op(e3, e0) = all_8_21 % 17.81/3.21 | (23) op(e4, e0) = all_8_20 % 17.81/3.21 | (24) op(e4, e3) = all_8_5 % 17.81/3.21 | % 17.81/3.21 | DELTA: instantiating (1) with fresh symbols all_10_0, all_10_1, all_10_2, % 17.81/3.21 | all_10_3, all_10_4, all_10_5, all_10_6, all_10_7, all_10_8, all_10_9, % 17.81/3.21 | all_10_10, all_10_11, all_10_12, all_10_13, all_10_14, all_10_15, % 17.81/3.21 | all_10_16, all_10_17, all_10_18, all_10_19, all_10_20, all_10_21, % 17.81/3.21 | all_10_22, all_10_23, all_10_24 gives: % 17.81/3.22 | (25) op(e4, e4) = all_10_0 & op(e4, e3) = all_10_1 & op(e4, e2) = all_10_2 % 17.81/3.22 | & op(e4, e1) = all_10_3 & op(e4, e0) = all_10_4 & op(e3, e4) = % 17.81/3.22 | all_10_5 & op(e3, e3) = all_10_6 & op(e3, e2) = all_10_7 & op(e3, e1) % 17.81/3.22 | = all_10_8 & op(e3, e0) = all_10_9 & op(e2, e4) = all_10_10 & op(e2, % 17.81/3.22 | e3) = all_10_11 & op(e2, e2) = all_10_12 & op(e2, e1) = all_10_13 & % 17.81/3.22 | op(e2, e0) = all_10_14 & op(e1, e4) = all_10_15 & op(e1, e3) = % 17.81/3.22 | all_10_16 & op(e1, e2) = all_10_17 & op(e1, e1) = all_10_18 & op(e1, % 17.81/3.22 | e0) = all_10_19 & op(e0, e4) = all_10_20 & op(e0, e3) = all_10_21 & % 17.81/3.22 | op(e0, e2) = all_10_22 & op(e0, e1) = all_10_23 & op(e0, e0) = % 17.81/3.22 | all_10_24 & $i(all_10_0) & $i(all_10_1) & $i(all_10_2) & $i(all_10_3) % 17.81/3.22 | & $i(all_10_4) & $i(all_10_5) & $i(all_10_6) & $i(all_10_7) & % 17.81/3.22 | $i(all_10_8) & $i(all_10_9) & $i(all_10_10) & $i(all_10_11) & % 17.81/3.22 | $i(all_10_12) & $i(all_10_13) & $i(all_10_14) & $i(all_10_15) & % 17.81/3.22 | $i(all_10_16) & $i(all_10_17) & $i(all_10_18) & $i(all_10_19) & % 17.81/3.22 | $i(all_10_20) & $i(all_10_21) & $i(all_10_22) & $i(all_10_23) & % 17.81/3.22 | $i(all_10_24) & (all_10_0 = e4 | all_10_0 = e3 | all_10_0 = e2 | % 17.81/3.22 | all_10_0 = e1 | all_10_0 = e0) & (all_10_1 = e4 | all_10_1 = e3 | % 17.81/3.22 | all_10_1 = e2 | all_10_1 = e1 | all_10_1 = e0) & (all_10_2 = e4 | % 17.81/3.22 | all_10_2 = e3 | all_10_2 = e2 | all_10_2 = e1 | all_10_2 = e0) & % 17.81/3.22 | (all_10_3 = e4 | all_10_3 = e3 | all_10_3 = e2 | all_10_3 = e1 | % 17.81/3.22 | all_10_3 = e0) & (all_10_4 = e4 | all_10_4 = e3 | all_10_4 = e2 | % 17.81/3.22 | all_10_4 = e1 | all_10_4 = e0) & (all_10_5 = e4 | all_10_5 = e3 | % 17.81/3.22 | all_10_5 = e2 | all_10_5 = e1 | all_10_5 = e0) & (all_10_6 = e4 | % 17.81/3.22 | all_10_6 = e3 | all_10_6 = e2 | all_10_6 = e1 | all_10_6 = e0) & % 17.81/3.22 | (all_10_7 = e4 | all_10_7 = e3 | all_10_7 = e2 | all_10_7 = e1 | % 17.81/3.22 | all_10_7 = e0) & (all_10_8 = e4 | all_10_8 = e3 | all_10_8 = e2 | % 17.81/3.22 | all_10_8 = e1 | all_10_8 = e0) & (all_10_9 = e4 | all_10_9 = e3 | % 17.81/3.22 | all_10_9 = e2 | all_10_9 = e1 | all_10_9 = e0) & (all_10_10 = e4 | % 17.81/3.22 | all_10_10 = e3 | all_10_10 = e2 | all_10_10 = e1 | all_10_10 = e0) & % 17.81/3.22 | (all_10_11 = e4 | all_10_11 = e3 | all_10_11 = e2 | all_10_11 = e1 | % 17.81/3.22 | all_10_11 = e0) & (all_10_12 = e4 | all_10_12 = e3 | all_10_12 = e2 % 17.81/3.22 | | all_10_12 = e1 | all_10_12 = e0) & (all_10_13 = e4 | all_10_13 = % 17.81/3.22 | e3 | all_10_13 = e2 | all_10_13 = e1 | all_10_13 = e0) & (all_10_14 % 17.81/3.22 | = e4 | all_10_14 = e3 | all_10_14 = e2 | all_10_14 = e1 | all_10_14 % 17.81/3.22 | = e0) & (all_10_15 = e4 | all_10_15 = e3 | all_10_15 = e2 | % 17.81/3.22 | all_10_15 = e1 | all_10_15 = e0) & (all_10_16 = e4 | all_10_16 = e3 % 17.81/3.22 | | all_10_16 = e2 | all_10_16 = e1 | all_10_16 = e0) & (all_10_17 = % 17.81/3.22 | e4 | all_10_17 = e3 | all_10_17 = e2 | all_10_17 = e1 | all_10_17 = % 17.81/3.22 | e0) & (all_10_18 = e4 | all_10_18 = e3 | all_10_18 = e2 | all_10_18 % 17.81/3.22 | = e1 | all_10_18 = e0) & (all_10_19 = e4 | all_10_19 = e3 | % 17.81/3.22 | all_10_19 = e2 | all_10_19 = e1 | all_10_19 = e0) & (all_10_20 = e4 % 17.81/3.22 | | all_10_20 = e3 | all_10_20 = e2 | all_10_20 = e1 | all_10_20 = e0) % 17.81/3.22 | & (all_10_21 = e4 | all_10_21 = e3 | all_10_21 = e2 | all_10_21 = e1 | % 17.81/3.22 | all_10_21 = e0) & (all_10_22 = e4 | all_10_22 = e3 | all_10_22 = e2 % 17.81/3.22 | | all_10_22 = e1 | all_10_22 = e0) & (all_10_23 = e4 | all_10_23 = % 17.81/3.22 | e3 | all_10_23 = e2 | all_10_23 = e1 | all_10_23 = e0) & (all_10_24 % 17.81/3.22 | = e4 | all_10_24 = e3 | all_10_24 = e2 | all_10_24 = e1 | all_10_24 % 17.81/3.22 | = e0) % 17.81/3.22 | % 17.81/3.22 | ALPHA: (25) implies: % 17.81/3.22 | (26) op(e2, e0) = all_10_14 % 17.81/3.22 | (27) op(e3, e0) = all_10_9 % 17.81/3.22 | (28) op(e4, e0) = all_10_4 % 17.81/3.22 | (29) op(e4, e3) = all_10_1 % 17.81/3.22 | % 17.81/3.22 | DELTA: instantiating (2) with fresh symbols all_12_0, all_12_1, all_12_2, % 17.81/3.22 | all_12_3, all_12_4, all_12_5, all_12_6, all_12_7, all_12_8, all_12_9, % 17.81/3.22 | all_12_10, all_12_11, all_12_12, all_12_13, all_12_14, all_12_15, % 17.81/3.22 | all_12_16, all_12_17, all_12_18, all_12_19, all_12_20, all_12_21, % 17.81/3.22 | all_12_22, all_12_23, all_12_24 gives: % 17.81/3.23 | (30) op(e4, e4) = all_12_0 & op(e4, e3) = all_12_1 & op(e4, e2) = all_12_4 % 17.81/3.23 | & op(e4, e1) = all_12_9 & op(e4, e0) = all_12_16 & op(e3, e4) = % 17.81/3.23 | all_12_2 & op(e3, e3) = all_12_3 & op(e3, e2) = all_12_5 & op(e3, e1) % 17.81/3.23 | = all_12_10 & op(e3, e0) = all_12_17 & op(e2, e4) = all_12_6 & op(e2, % 17.81/3.23 | e3) = all_12_7 & op(e2, e2) = all_12_8 & op(e2, e1) = all_12_11 & % 17.81/3.23 | op(e2, e0) = all_12_18 & op(e1, e4) = all_12_12 & op(e1, e3) = % 17.81/3.23 | all_12_13 & op(e1, e2) = all_12_14 & op(e1, e1) = all_12_15 & op(e1, % 17.81/3.23 | e0) = all_12_19 & op(e0, e4) = all_12_20 & op(e0, e3) = all_12_21 & % 17.81/3.23 | op(e0, e2) = all_12_22 & op(e0, e1) = all_12_23 & op(e0, e0) = % 17.81/3.23 | all_12_24 & $i(all_12_0) & $i(all_12_1) & $i(all_12_2) & $i(all_12_3) % 17.81/3.23 | & $i(all_12_4) & $i(all_12_5) & $i(all_12_6) & $i(all_12_7) & % 17.81/3.23 | $i(all_12_8) & $i(all_12_9) & $i(all_12_10) & $i(all_12_11) & % 17.81/3.23 | $i(all_12_12) & $i(all_12_13) & $i(all_12_14) & $i(all_12_15) & % 17.81/3.23 | $i(all_12_16) & $i(all_12_17) & $i(all_12_18) & $i(all_12_19) & % 17.81/3.23 | $i(all_12_20) & $i(all_12_21) & $i(all_12_22) & $i(all_12_23) & % 17.81/3.23 | $i(all_12_24) & (all_12_0 = e4 | all_12_1 = e4 | all_12_4 = e4 | % 17.81/3.23 | all_12_9 = e4 | all_12_16 = e4) & (all_12_0 = e4 | all_12_2 = e4 | % 17.81/3.23 | all_12_6 = e4 | all_12_12 = e4 | all_12_20 = e4) & (all_12_0 = e3 | % 17.81/3.23 | all_12_1 = e3 | all_12_4 = e3 | all_12_9 = e3 | all_12_16 = e3) & % 17.81/3.23 | (all_12_0 = e3 | all_12_2 = e3 | all_12_6 = e3 | all_12_12 = e3 | % 17.81/3.23 | all_12_20 = e3) & (all_12_0 = e2 | all_12_1 = e2 | all_12_4 = e2 | % 17.81/3.23 | all_12_9 = e2 | all_12_16 = e2) & (all_12_0 = e2 | all_12_2 = e2 | % 17.81/3.23 | all_12_6 = e2 | all_12_12 = e2 | all_12_20 = e2) & (all_12_0 = e1 | % 17.81/3.23 | all_12_1 = e1 | all_12_4 = e1 | all_12_9 = e1 | all_12_16 = e1) & % 17.81/3.23 | (all_12_0 = e1 | all_12_2 = e1 | all_12_6 = e1 | all_12_12 = e1 | % 17.81/3.23 | all_12_20 = e1) & (all_12_0 = e0 | all_12_1 = e0 | all_12_4 = e0 | % 17.81/3.23 | all_12_9 = e0 | all_12_16 = e0) & (all_12_0 = e0 | all_12_2 = e0 | % 17.81/3.23 | all_12_6 = e0 | all_12_12 = e0 | all_12_20 = e0) & (all_12_1 = e4 | % 17.81/3.23 | all_12_3 = e4 | all_12_7 = e4 | all_12_13 = e4 | all_12_21 = e4) & % 17.81/3.23 | (all_12_1 = e3 | all_12_3 = e3 | all_12_7 = e3 | all_12_13 = e3 | % 17.81/3.23 | all_12_21 = e3) & (all_12_1 = e2 | all_12_3 = e2 | all_12_7 = e2 | % 17.81/3.23 | all_12_13 = e2 | all_12_21 = e2) & (all_12_1 = e1 | all_12_3 = e1 | % 17.81/3.23 | all_12_7 = e1 | all_12_13 = e1 | all_12_21 = e1) & (all_12_1 = e0 | % 17.81/3.23 | all_12_3 = e0 | all_12_7 = e0 | all_12_13 = e0 | all_12_21 = e0) & % 17.81/3.23 | (all_12_2 = e4 | all_12_3 = e4 | all_12_5 = e4 | all_12_10 = e4 | % 17.81/3.23 | all_12_17 = e4) & (all_12_2 = e3 | all_12_3 = e3 | all_12_5 = e3 | % 17.81/3.23 | all_12_10 = e3 | all_12_17 = e3) & (all_12_2 = e2 | all_12_3 = e2 | % 17.81/3.23 | all_12_5 = e2 | all_12_10 = e2 | all_12_17 = e2) & (all_12_2 = e1 | % 17.81/3.23 | all_12_3 = e1 | all_12_5 = e1 | all_12_10 = e1 | all_12_17 = e1) & % 17.81/3.23 | (all_12_2 = e0 | all_12_3 = e0 | all_12_5 = e0 | all_12_10 = e0 | % 17.81/3.23 | all_12_17 = e0) & (all_12_4 = e4 | all_12_5 = e4 | all_12_8 = e4 | % 17.81/3.23 | all_12_14 = e4 | all_12_22 = e4) & (all_12_4 = e3 | all_12_5 = e3 | % 17.81/3.23 | all_12_8 = e3 | all_12_14 = e3 | all_12_22 = e3) & (all_12_4 = e2 | % 17.81/3.23 | all_12_5 = e2 | all_12_8 = e2 | all_12_14 = e2 | all_12_22 = e2) & % 17.81/3.23 | (all_12_4 = e1 | all_12_5 = e1 | all_12_8 = e1 | all_12_14 = e1 | % 17.81/3.23 | all_12_22 = e1) & (all_12_4 = e0 | all_12_5 = e0 | all_12_8 = e0 | % 17.81/3.23 | all_12_14 = e0 | all_12_22 = e0) & (all_12_6 = e4 | all_12_7 = e4 | % 17.81/3.23 | all_12_8 = e4 | all_12_11 = e4 | all_12_18 = e4) & (all_12_6 = e3 | % 17.81/3.23 | all_12_7 = e3 | all_12_8 = e3 | all_12_11 = e3 | all_12_18 = e3) & % 17.81/3.23 | (all_12_6 = e2 | all_12_7 = e2 | all_12_8 = e2 | all_12_11 = e2 | % 17.81/3.23 | all_12_18 = e2) & (all_12_6 = e1 | all_12_7 = e1 | all_12_8 = e1 | % 17.81/3.23 | all_12_11 = e1 | all_12_18 = e1) & (all_12_6 = e0 | all_12_7 = e0 | % 17.81/3.23 | all_12_8 = e0 | all_12_11 = e0 | all_12_18 = e0) & (all_12_9 = e4 | % 17.81/3.23 | all_12_10 = e4 | all_12_11 = e4 | all_12_15 = e4 | all_12_23 = e4) & % 17.81/3.23 | (all_12_9 = e3 | all_12_10 = e3 | all_12_11 = e3 | all_12_15 = e3 | % 17.81/3.23 | all_12_23 = e3) & (all_12_9 = e2 | all_12_10 = e2 | all_12_11 = e2 | % 17.81/3.23 | all_12_15 = e2 | all_12_23 = e2) & (all_12_9 = e1 | all_12_10 = e1 | % 17.81/3.23 | all_12_11 = e1 | all_12_15 = e1 | all_12_23 = e1) & (all_12_9 = e0 | % 17.81/3.23 | all_12_10 = e0 | all_12_11 = e0 | all_12_15 = e0 | all_12_23 = e0) & % 17.81/3.23 | (all_12_12 = e4 | all_12_13 = e4 | all_12_14 = e4 | all_12_15 = e4 | % 17.81/3.23 | all_12_19 = e4) & (all_12_12 = e3 | all_12_13 = e3 | all_12_14 = e3 % 17.81/3.23 | | all_12_15 = e3 | all_12_19 = e3) & (all_12_12 = e2 | all_12_13 = % 17.81/3.23 | e2 | all_12_14 = e2 | all_12_15 = e2 | all_12_19 = e2) & (all_12_12 % 17.81/3.23 | = e1 | all_12_13 = e1 | all_12_14 = e1 | all_12_15 = e1 | all_12_19 % 17.81/3.23 | = e1) & (all_12_12 = e0 | all_12_13 = e0 | all_12_14 = e0 | % 17.81/3.23 | all_12_15 = e0 | all_12_19 = e0) & (all_12_16 = e4 | all_12_17 = e4 % 17.81/3.23 | | all_12_18 = e4 | all_12_19 = e4 | all_12_24 = e4) & (all_12_16 = % 17.81/3.23 | e3 | all_12_17 = e3 | all_12_18 = e3 | all_12_19 = e3 | all_12_24 = % 17.81/3.23 | e3) & (all_12_16 = e2 | all_12_17 = e2 | all_12_18 = e2 | all_12_19 % 17.81/3.23 | = e2 | all_12_24 = e2) & (all_12_16 = e1 | all_12_17 = e1 | % 17.81/3.23 | all_12_18 = e1 | all_12_19 = e1 | all_12_24 = e1) & (all_12_20 = e4 % 17.81/3.23 | | all_12_21 = e4 | all_12_22 = e4 | all_12_23 = e4 | all_12_24 = e4) % 17.81/3.23 | & (all_12_20 = e3 | all_12_21 = e3 | all_12_22 = e3 | all_12_23 = e3 | % 17.81/3.23 | all_12_24 = e3) & (all_12_20 = e2 | all_12_21 = e2 | all_12_22 = e2 % 17.81/3.23 | | all_12_23 = e2 | all_12_24 = e2) & (all_12_20 = e1 | all_12_21 = % 17.81/3.23 | e1 | all_12_22 = e1 | all_12_23 = e1 | all_12_24 = e1) & (all_12_24 % 17.81/3.23 | = e0 | ((all_12_16 = e0 | all_12_17 = e0 | all_12_18 = e0 | % 17.81/3.23 | all_12_19 = e0) & (all_12_20 = e0 | all_12_21 = e0 | all_12_22 = % 17.81/3.23 | e0 | all_12_23 = e0))) % 17.81/3.23 | % 17.81/3.23 | ALPHA: (30) implies: % 17.81/3.23 | (31) op(e2, e0) = all_12_18 % 17.81/3.23 | (32) op(e3, e0) = all_12_17 % 17.81/3.23 | (33) op(e4, e0) = all_12_16 % 17.81/3.23 | (34) op(e4, e3) = all_12_1 % 17.81/3.23 | % 17.81/3.23 | GROUND_INST: instantiating (function-axioms) with all_4_21, all_10_14, e0, e2, % 17.81/3.23 | simplifying with (9), (26) gives: % 17.81/3.23 | (35) all_10_14 = all_4_21 % 17.81/3.23 | % 17.81/3.23 | GROUND_INST: instantiating (function-axioms) with all_10_14, all_12_18, e0, % 17.81/3.23 | e2, simplifying with (26), (31) gives: % 17.81/3.23 | (36) all_12_18 = all_10_14 % 17.81/3.23 | % 17.81/3.23 | GROUND_INST: instantiating (function-axioms) with all_8_22, all_12_18, e0, e2, % 17.81/3.23 | simplifying with (21), (31) gives: % 17.81/3.23 | (37) all_12_18 = all_8_22 % 17.81/3.23 | % 17.81/3.23 | GROUND_INST: instantiating (function-axioms) with all_6_14, all_12_18, e0, e2, % 17.81/3.23 | simplifying with (13), (31) gives: % 17.81/3.23 | (38) all_12_18 = all_6_14 % 17.81/3.23 | % 17.81/3.23 | GROUND_INST: instantiating (function-axioms) with all_6_9, all_8_21, e0, e3, % 17.81/3.23 | simplifying with (14), (22) gives: % 17.81/3.23 | (39) all_8_21 = all_6_9 % 17.81/3.23 | % 17.81/3.23 | GROUND_INST: instantiating (function-axioms) with all_6_9, all_10_9, e0, e3, % 17.81/3.23 | simplifying with (14), (27) gives: % 17.81/3.23 | (40) all_10_9 = all_6_9 % 17.81/3.23 | % 17.81/3.23 | GROUND_INST: instantiating (function-axioms) with e2, all_10_9, e0, e3, % 17.81/3.23 | simplifying with (5), (27) gives: % 17.81/3.23 | (41) all_10_9 = e2 % 17.81/3.23 | % 17.81/3.23 | GROUND_INST: instantiating (function-axioms) with all_8_21, all_12_17, e0, e3, % 17.81/3.23 | simplifying with (22), (32) gives: % 17.81/3.23 | (42) all_12_17 = all_8_21 % 17.81/3.23 | % 17.81/3.23 | GROUND_INST: instantiating (function-axioms) with all_4_19, all_12_17, e0, e3, % 17.81/3.23 | simplifying with (10), (32) gives: % 17.81/3.23 | (43) all_12_17 = all_4_19 % 17.81/3.23 | % 17.81/3.23 | GROUND_INST: instantiating (function-axioms) with all_8_20, all_10_4, e0, e4, % 17.81/3.23 | simplifying with (23), (28) gives: % 17.81/3.23 | (44) all_10_4 = all_8_20 % 17.81/3.23 | % 17.81/3.23 | GROUND_INST: instantiating (function-axioms) with all_6_4, all_10_4, e0, e4, % 17.81/3.23 | simplifying with (15), (28) gives: % 17.81/3.23 | (45) all_10_4 = all_6_4 % 17.81/3.23 | % 17.81/3.23 | GROUND_INST: instantiating (function-axioms) with all_8_20, all_12_16, e0, e4, % 17.81/3.23 | simplifying with (23), (33) gives: % 17.81/3.23 | (46) all_12_16 = all_8_20 % 17.81/3.23 | % 17.81/3.23 | GROUND_INST: instantiating (function-axioms) with all_4_17, all_12_16, e0, e4, % 17.81/3.23 | simplifying with (11), (33) gives: % 17.81/3.23 | (47) all_12_16 = all_4_17 % 17.81/3.23 | % 17.81/3.24 | GROUND_INST: instantiating (function-axioms) with all_10_1, all_12_1, e3, e4, % 17.81/3.24 | simplifying with (29), (34) gives: % 17.81/3.24 | (48) all_12_1 = all_10_1 % 17.81/3.24 | % 17.81/3.24 | GROUND_INST: instantiating (function-axioms) with all_8_5, all_12_1, e3, e4, % 17.81/3.24 | simplifying with (24), (34) gives: % 17.81/3.24 | (49) all_12_1 = all_8_5 % 17.98/3.24 | % 17.98/3.24 | GROUND_INST: instantiating (function-axioms) with all_6_1, all_12_1, e3, e4, % 17.98/3.24 | simplifying with (16), (34) gives: % 17.98/3.24 | (50) all_12_1 = all_6_1 % 17.98/3.24 | % 17.98/3.24 | GROUND_INST: instantiating (function-axioms) with e0, all_12_1, e3, e4, % 17.98/3.24 | simplifying with (6), (34) gives: % 17.98/3.24 | (51) all_12_1 = e0 % 17.98/3.24 | % 17.98/3.24 | COMBINE_EQS: (48), (49) imply: % 17.98/3.24 | (52) all_10_1 = all_8_5 % 17.98/3.24 | % 17.98/3.24 | COMBINE_EQS: (48), (51) imply: % 17.98/3.24 | (53) all_10_1 = e0 % 17.98/3.24 | % 17.98/3.24 | COMBINE_EQS: (48), (50) imply: % 17.98/3.24 | (54) all_10_1 = all_6_1 % 17.98/3.24 | % 17.98/3.24 | COMBINE_EQS: (46), (47) imply: % 17.98/3.24 | (55) all_8_20 = all_4_17 % 17.98/3.24 | % 17.98/3.24 | SIMP: (55) implies: % 17.98/3.24 | (56) all_8_20 = all_4_17 % 17.98/3.24 | % 17.98/3.24 | COMBINE_EQS: (42), (43) imply: % 17.98/3.24 | (57) all_8_21 = all_4_19 % 17.98/3.24 | % 17.98/3.24 | SIMP: (57) implies: % 17.98/3.24 | (58) all_8_21 = all_4_19 % 17.98/3.24 | % 17.98/3.24 | COMBINE_EQS: (36), (37) imply: % 17.98/3.24 | (59) all_10_14 = all_8_22 % 17.98/3.24 | % 17.98/3.24 | SIMP: (59) implies: % 17.98/3.24 | (60) all_10_14 = all_8_22 % 17.98/3.24 | % 17.98/3.24 | COMBINE_EQS: (37), (38) imply: % 17.98/3.24 | (61) all_8_22 = all_6_14 % 17.98/3.24 | % 17.98/3.24 | COMBINE_EQS: (52), (53) imply: % 17.98/3.24 | (62) all_8_5 = e0 % 17.98/3.24 | % 17.98/3.24 | COMBINE_EQS: (52), (54) imply: % 17.98/3.24 | (63) all_8_5 = all_6_1 % 17.98/3.24 | % 17.98/3.24 | COMBINE_EQS: (44), (45) imply: % 17.98/3.24 | (64) all_8_20 = all_6_4 % 17.98/3.24 | % 17.98/3.24 | SIMP: (64) implies: % 17.98/3.24 | (65) all_8_20 = all_6_4 % 17.98/3.24 | % 17.98/3.24 | COMBINE_EQS: (40), (41) imply: % 17.98/3.24 | (66) all_6_9 = e2 % 17.98/3.24 | % 17.98/3.24 | SIMP: (66) implies: % 17.98/3.24 | (67) all_6_9 = e2 % 17.98/3.24 | % 17.98/3.24 | COMBINE_EQS: (35), (60) imply: % 17.98/3.24 | (68) all_8_22 = all_4_21 % 17.98/3.24 | % 17.98/3.24 | SIMP: (68) implies: % 17.98/3.24 | (69) all_8_22 = all_4_21 % 17.98/3.24 | % 17.98/3.24 | COMBINE_EQS: (62), (63) imply: % 17.98/3.24 | (70) all_6_1 = e0 % 17.98/3.24 | % 17.98/3.24 | SIMP: (70) implies: % 17.98/3.24 | (71) all_6_1 = e0 % 17.98/3.24 | % 17.98/3.24 | COMBINE_EQS: (56), (65) imply: % 17.98/3.24 | (72) all_6_4 = all_4_17 % 17.98/3.24 | % 17.98/3.24 | COMBINE_EQS: (39), (58) imply: % 17.98/3.24 | (73) all_6_9 = all_4_19 % 17.98/3.24 | % 17.98/3.24 | SIMP: (73) implies: % 17.98/3.24 | (74) all_6_9 = all_4_19 % 17.98/3.24 | % 17.98/3.24 | COMBINE_EQS: (61), (69) imply: % 17.98/3.24 | (75) all_6_14 = all_4_21 % 17.98/3.24 | % 17.98/3.24 | COMBINE_EQS: (67), (74) imply: % 17.98/3.24 | (76) all_4_19 = e2 % 17.98/3.24 | % 17.98/3.24 | REDUCE: (20), (56), (69) imply: % 17.98/3.24 | (77) ~ (all_4_17 = all_4_21) % 17.98/3.24 | % 17.98/3.24 | REDUCE: (18), (67) imply: % 17.98/3.24 | (78) op(e2, e0) = e3 % 17.98/3.24 | % 17.98/3.24 | REDUCE: (17), (71) imply: % 17.98/3.24 | (79) op(e4, e0) = e3 % 17.98/3.24 | % 17.98/3.24 | GROUND_INST: instantiating (function-axioms) with all_4_21, e3, e0, e2, % 17.98/3.24 | simplifying with (9), (78) gives: % 17.98/3.24 | (80) all_4_21 = e3 % 17.98/3.24 | % 17.98/3.24 | GROUND_INST: instantiating (function-axioms) with all_4_17, e3, e0, e4, % 17.98/3.24 | simplifying with (11), (79) gives: % 17.98/3.24 | (81) all_4_17 = e3 % 17.98/3.24 | % 17.98/3.24 | REDUCE: (77), (80), (81) imply: % 17.98/3.24 | (82) $false % 17.98/3.25 | % 17.98/3.25 | CLOSE: (82) is inconsistent. % 17.98/3.25 | % 17.98/3.25 End of proof % 17.98/3.25 % SZS output end Proof for theBenchmark % 17.98/3.25 % 17.98/3.25 2626ms %------------------------------------------------------------------------------