%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG014+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 : n010.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 16:35:36 EDT 2023 % Result : Theorem 8.77s 1.87s % Output : Proof 13.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : ALG014+1 : TPTP v8.1.2. Released v2.7.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n010.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 02:54:19 EDT 2023 % 0.14/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.23/1.27 Prover 1: Preprocessing ... % 4.23/1.27 Prover 4: Preprocessing ... % 4.43/1.31 Prover 2: Preprocessing ... % 4.43/1.31 Prover 5: Preprocessing ... % 4.43/1.31 Prover 3: Preprocessing ... % 4.43/1.31 Prover 6: Preprocessing ... % 4.43/1.31 Prover 0: Preprocessing ... % 7.80/1.75 Prover 2: Constructing countermodel ... % 7.80/1.75 Prover 1: Constructing countermodel ... % 7.80/1.75 Prover 0: Constructing countermodel ... % 7.80/1.75 Prover 6: Constructing countermodel ... % 7.80/1.75 Prover 3: Constructing countermodel ... % 7.80/1.76 Prover 4: Constructing countermodel ... % 8.33/1.87 Prover 3: proved (1230ms) % 8.33/1.87 Prover 2: proved (1231ms) % 8.77/1.87 % 8.77/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.77/1.87 % 8.77/1.87 % 8.77/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.77/1.87 % 8.77/1.87 Prover 0: proved (1232ms) % 8.77/1.87 % 8.77/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.77/1.87 % 8.77/1.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.77/1.89 Prover 6: proved (1233ms) % 8.77/1.89 % 8.77/1.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.77/1.89 % 8.77/1.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.77/1.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.77/1.90 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.46/2.03 Prover 7: Preprocessing ... % 9.46/2.05 Prover 5: Constructing countermodel ... % 9.46/2.05 Prover 5: stopped % 9.46/2.06 Prover 8: Preprocessing ... % 9.46/2.06 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.37/2.11 Prover 10: Preprocessing ... % 10.74/2.14 Prover 8: Constructing countermodel ... % 10.74/2.14 Prover 11: Preprocessing ... % 11.32/2.21 Prover 7: Constructing countermodel ... % 11.32/2.22 Prover 13: Preprocessing ... % 11.75/2.27 Prover 10: Constructing countermodel ... % 11.75/2.28 Prover 11: Constructing countermodel ... % 12.68/2.40 Prover 13: Constructing countermodel ... % 13.04/2.44 Prover 4: Found proof (size 103) % 13.04/2.44 Prover 4: proved (1807ms) % 13.14/2.44 Prover 8: stopped % 13.14/2.44 Prover 11: stopped % 13.14/2.44 Prover 1: stopped % 13.14/2.44 Prover 10: stopped % 13.14/2.44 Prover 7: stopped % 13.14/2.45 Prover 13: stopped % 13.14/2.45 % 13.14/2.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.14/2.45 % 13.14/2.46 % SZS output start Proof for theBenchmark % 13.14/2.46 Assumptions after simplification: % 13.14/2.46 --------------------------------- % 13.14/2.46 % 13.14/2.46 (ax1) % 13.14/2.50 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 13.14/2.51 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 13.14/2.51 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 13.14/2.51 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & % 13.14/2.51 op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & % 13.14/2.51 op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & % 13.14/2.51 op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 13.14/2.51 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 13.14/2.51 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 13.14/2.51 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 = % 13.14/2.51 e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 | % 13.14/2.51 v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 % 13.14/2.51 = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | % 13.14/2.51 v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | % 13.14/2.51 v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | % 13.14/2.51 v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & % 13.14/2.51 (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3 % 13.14/2.51 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1 % 13.14/2.51 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0)) % 13.14/2.51 % 13.14/2.51 (ax10) % 13.43/2.52 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 13.43/2.52 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 13.43/2.52 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 13.43/2.52 $i] : ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ % 13.43/2.52 (v15 = v12) & ~ (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = % 13.43/2.52 v13) & ~ (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & % 13.43/2.52 ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 = % 13.43/2.52 v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = v9) & ~ % 13.43/2.52 (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) & ~ (v10 = v8) & % 13.43/2.52 ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ (v9 = v5) & ~ (v9 = v1) & % 13.43/2.52 ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) & % 13.43/2.52 ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ % 13.43/2.52 (v5 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ % 13.43/2.52 (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = % 13.43/2.52 v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = % 13.43/2.52 v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = v9 % 13.43/2.52 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, e2) = v8 & % 13.43/2.52 op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 13.43/2.52 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 13.43/2.52 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 13.43/2.52 % 13.43/2.52 (ax2) % 13.43/2.53 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 13.43/2.53 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 13.43/2.53 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 13.43/2.53 $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: % 13.43/2.53 $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: % 13.43/2.53 $i] : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: % 13.43/2.53 $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? [v33: % 13.43/2.53 $i] : ? [v34: $i] : ? [v35: $i] : ? [v36: $i] : ? [v37: $i] : ? [v38: % 13.43/2.53 $i] : ? [v39: $i] : ? [v40: $i] : ? [v41: $i] : ? [v42: $i] : ? [v43: % 13.43/2.53 $i] : ? [v44: $i] : ? [v45: $i] : ? [v46: $i] : ? [v47: $i] : ? [v48: % 13.43/2.53 $i] : ? [v49: $i] : ? [v50: $i] : ? [v51: $i] : ? [v52: $i] : ? [v53: % 13.43/2.53 $i] : ? [v54: $i] : ? [v55: $i] : ? [v56: $i] : ? [v57: $i] : ? [v58: % 13.43/2.53 $i] : ? [v59: $i] : ? [v60: $i] : ? [v61: $i] : ? [v62: $i] : ? [v63: % 13.43/2.53 $i] : ? [v64: $i] : ? [v65: $i] : ? [v66: $i] : ? [v67: $i] : ? [v68: % 13.43/2.53 $i] : ? [v69: $i] : ? [v70: $i] : ? [v71: $i] : ? [v72: $i] : ? [v73: % 13.43/2.53 $i] : ? [v74: $i] : ? [v75: $i] : ? [v76: $i] : ? [v77: $i] : ? [v78: % 13.43/2.53 $i] : ? [v79: $i] : (op(v31, e3) = v79 & op(v31, e2) = v78 & op(v31, e1) = % 13.43/2.53 v77 & op(v31, e0) = v76 & op(v29, e3) = v75 & op(v29, e2) = v74 & op(v29, % 13.43/2.53 e1) = v73 & op(v29, e0) = v72 & op(v27, e3) = v71 & op(v27, e2) = v70 & % 13.43/2.53 op(v27, e1) = v69 & op(v27, e0) = v68 & op(v25, e3) = v67 & op(v25, e2) = % 13.43/2.53 v66 & op(v25, e1) = v65 & op(v25, e0) = v64 & op(v23, e3) = v63 & op(v23, % 13.43/2.53 e2) = v62 & op(v23, e1) = v61 & op(v23, e0) = v60 & op(v21, e3) = v59 & % 13.43/2.53 op(v21, e2) = v58 & op(v21, e1) = v57 & op(v21, e0) = v56 & op(v19, e3) = % 13.43/2.53 v55 & op(v19, e2) = v54 & op(v19, e1) = v53 & op(v19, e0) = v52 & op(v17, % 13.43/2.53 e3) = v51 & op(v17, e2) = v50 & op(v17, e1) = v49 & op(v17, e0) = v48 & % 13.43/2.53 op(v15, e3) = v47 & op(v15, e2) = v46 & op(v15, e1) = v45 & op(v15, e0) = % 13.43/2.53 v44 & op(v13, e3) = v43 & op(v13, e2) = v42 & op(v13, e1) = v41 & op(v13, % 13.43/2.53 e0) = v40 & op(v11, e3) = v39 & op(v11, e2) = v38 & op(v11, e1) = v37 & % 13.43/2.53 op(v11, e0) = v36 & op(v9, e3) = v35 & op(v9, e2) = v34 & op(v9, e1) = v33 & % 13.43/2.53 op(v9, e0) = v32 & op(v7, e3) = v30 & op(v7, e2) = v28 & op(v7, e1) = v26 & % 13.43/2.53 op(v7, e0) = v24 & op(v5, e3) = v22 & op(v5, e2) = v20 & op(v5, e1) = v18 & % 13.43/2.53 op(v5, e0) = v16 & op(v3, e3) = v14 & op(v3, e2) = v12 & op(v3, e1) = v10 & % 13.43/2.53 op(v3, e0) = v8 & op(v0, e3) = v6 & op(v0, e2) = v4 & op(v0, e1) = v2 & % 13.43/2.53 op(v0, e0) = v1 & op(e3, v31) = v79 & op(e3, v29) = v78 & op(e3, v27) = v77 % 13.43/2.53 & op(e3, v25) = v76 & op(e3, v23) = v75 & op(e3, v21) = v74 & op(e3, v19) = % 13.43/2.54 v73 & op(e3, v17) = v72 & op(e3, v15) = v71 & op(e3, v13) = v70 & op(e3, % 13.43/2.54 v11) = v69 & op(e3, v9) = v68 & op(e3, v7) = v67 & op(e3, v5) = v66 & % 13.43/2.54 op(e3, v3) = v65 & op(e3, v0) = v64 & op(e3, e3) = v31 & op(e3, e2) = v29 & % 13.43/2.54 op(e3, e1) = v27 & op(e3, e0) = v25 & op(e2, v31) = v63 & op(e2, v29) = v62 % 13.43/2.54 & op(e2, v27) = v61 & op(e2, v25) = v60 & op(e2, v23) = v59 & op(e2, v21) = % 13.43/2.54 v58 & op(e2, v19) = v57 & op(e2, v17) = v56 & op(e2, v15) = v55 & op(e2, % 13.43/2.54 v13) = v54 & op(e2, v11) = v53 & op(e2, v9) = v52 & op(e2, v7) = v51 & % 13.43/2.54 op(e2, v5) = v50 & op(e2, v3) = v49 & op(e2, v0) = v48 & op(e2, e3) = v23 & % 13.43/2.54 op(e2, e2) = v21 & op(e2, e1) = v19 & op(e2, e0) = v17 & op(e1, v31) = v47 & % 13.43/2.54 op(e1, v29) = v46 & op(e1, v27) = v45 & op(e1, v25) = v44 & op(e1, v23) = % 13.43/2.54 v43 & op(e1, v21) = v42 & op(e1, v19) = v41 & op(e1, v17) = v40 & op(e1, % 13.43/2.54 v15) = v39 & op(e1, v13) = v38 & op(e1, v11) = v37 & op(e1, v9) = v36 & % 13.43/2.54 op(e1, v7) = v35 & op(e1, v5) = v34 & op(e1, v3) = v33 & op(e1, v0) = v32 & % 13.43/2.54 op(e1, e3) = v15 & op(e1, e2) = v13 & op(e1, e1) = v11 & op(e1, e0) = v9 & % 13.43/2.54 op(e0, v31) = v30 & op(e0, v29) = v28 & op(e0, v27) = v26 & op(e0, v25) = % 13.43/2.54 v24 & op(e0, v23) = v22 & op(e0, v21) = v20 & op(e0, v19) = v18 & op(e0, % 13.43/2.54 v17) = v16 & op(e0, v15) = v14 & op(e0, v13) = v12 & op(e0, v11) = v10 & % 13.43/2.54 op(e0, v9) = v8 & op(e0, v7) = v6 & op(e0, v5) = v4 & op(e0, v3) = v2 & % 13.43/2.54 op(e0, v0) = v1 & op(e0, e3) = v7 & op(e0, e2) = v5 & op(e0, e1) = v3 & % 13.43/2.54 op(e0, e0) = v0 & $i(v79) & $i(v78) & $i(v77) & $i(v76) & $i(v75) & $i(v74) % 13.43/2.54 & $i(v73) & $i(v72) & $i(v71) & $i(v70) & $i(v69) & $i(v68) & $i(v67) & % 13.43/2.54 $i(v66) & $i(v65) & $i(v64) & $i(v63) & $i(v62) & $i(v61) & $i(v60) & % 13.43/2.54 $i(v59) & $i(v58) & $i(v57) & $i(v56) & $i(v55) & $i(v54) & $i(v53) & % 13.43/2.54 $i(v52) & $i(v51) & $i(v50) & $i(v49) & $i(v48) & $i(v47) & $i(v46) & % 13.43/2.54 $i(v45) & $i(v44) & $i(v43) & $i(v42) & $i(v41) & $i(v40) & $i(v39) & % 13.43/2.54 $i(v38) & $i(v37) & $i(v36) & $i(v35) & $i(v34) & $i(v33) & $i(v32) & % 13.43/2.54 $i(v31) & $i(v30) & $i(v29) & $i(v28) & $i(v27) & $i(v26) & $i(v25) & % 13.43/2.54 $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & % 13.43/2.54 $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & % 13.43/2.54 $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 13.43/2.54 $i(v2) & $i(v1) & $i(v0)) % 13.43/2.54 % 13.43/2.54 (ax3) % 13.43/2.54 op(unit, e3) = e3 & op(unit, e2) = e2 & op(unit, e1) = e1 & op(unit, e0) = e0 % 13.43/2.54 & op(e3, unit) = e3 & op(e2, unit) = e2 & op(e1, unit) = e1 & op(e0, unit) = % 13.43/2.54 e0 & $i(unit) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & (unit = e3 | unit = e2 | % 13.43/2.54 unit = e1 | unit = e0) % 13.43/2.54 % 13.43/2.54 (ax5) % 13.43/2.54 unit = e0 & $i(e0) % 13.43/2.54 % 13.43/2.54 (co1) % 13.43/2.54 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 13.43/2.54 ? [v3: $i] : (op(e3, e3) = v3 & op(e2, e2) = v2 & op(e1, e1) = v1 & op(e0, e0) % 13.43/2.54 = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = e3) | ~ (v2 = e3) | ~ % 13.43/2.54 (v1 = e3) | ~ (v0 = e3)) & ( ~ (v3 = e2) | ~ (v2 = e2) | ~ (v1 = e2) | % 13.43/2.54 ~ (v0 = e2)) & ( ~ (v3 = e1) | ~ (v2 = e1) | ~ (v1 = e1) | ~ (v0 = e1)) % 13.43/2.54 & ( ~ (v3 = e0) | ~ (v2 = e0) | ~ (v1 = e0) | ~ (v0 = e0)) & ((v3 = e3 & % 13.43/2.54 v2 = e3 & v1 = e3 & v0 = e3) | (v3 = e2 & v2 = e2 & v1 = e2 & v0 = e2) | % 13.43/2.54 (v3 = e1 & v2 = e1 & v1 = e1 & v0 = e1) | (v3 = e0 & v2 = e0 & v1 = e0 & % 13.43/2.54 v0 = e0))) % 13.43/2.54 % 13.43/2.54 (function-axioms) % 13.43/2.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3, % 13.43/2.54 v2) = v1) | ~ (op(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 13.43/2.54 $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) % 13.43/2.54 % 13.43/2.54 Further assumptions not needed in the proof: % 13.43/2.54 -------------------------------------------- % 13.43/2.54 ax11, ax4, ax6, ax7, ax8, ax9 % 13.43/2.54 % 13.43/2.54 Those formulas are unsatisfiable: % 13.43/2.54 --------------------------------- % 13.43/2.54 % 13.43/2.54 Begin of proof % 13.43/2.54 | % 13.43/2.54 | ALPHA: (ax1) implies: % 13.43/2.55 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 13.43/2.55 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 13.43/2.55 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 13.43/2.55 | ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13 % 13.43/2.55 | & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1) % 13.43/2.55 | = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1, % 13.43/2.55 | e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 13.43/2.55 | op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & % 13.43/2.55 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 13.43/2.55 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 % 13.43/2.55 | = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 % 13.43/2.55 | = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 | % 13.43/2.55 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 | % 13.43/2.55 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3 % 13.43/2.55 | | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8 % 13.43/2.55 | = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 = % 13.43/2.55 | e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & % 13.43/2.55 | (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = % 13.43/2.55 | e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 % 13.43/2.55 | | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 % 13.43/2.55 | = e0)) % 13.43/2.55 | % 13.43/2.55 | ALPHA: (ax2) implies: % 13.67/2.56 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 13.67/2.56 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 13.67/2.56 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 13.67/2.56 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 13.67/2.56 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 13.67/2.56 | [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : % 13.67/2.56 | ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? [v33: % 13.67/2.56 | $i] : ? [v34: $i] : ? [v35: $i] : ? [v36: $i] : ? [v37: $i] : ? % 13.67/2.56 | [v38: $i] : ? [v39: $i] : ? [v40: $i] : ? [v41: $i] : ? [v42: $i] : % 13.67/2.56 | ? [v43: $i] : ? [v44: $i] : ? [v45: $i] : ? [v46: $i] : ? [v47: % 13.67/2.56 | $i] : ? [v48: $i] : ? [v49: $i] : ? [v50: $i] : ? [v51: $i] : ? % 13.67/2.56 | [v52: $i] : ? [v53: $i] : ? [v54: $i] : ? [v55: $i] : ? [v56: $i] : % 13.67/2.56 | ? [v57: $i] : ? [v58: $i] : ? [v59: $i] : ? [v60: $i] : ? [v61: % 13.67/2.56 | $i] : ? [v62: $i] : ? [v63: $i] : ? [v64: $i] : ? [v65: $i] : ? % 13.67/2.56 | [v66: $i] : ? [v67: $i] : ? [v68: $i] : ? [v69: $i] : ? [v70: $i] : % 13.67/2.56 | ? [v71: $i] : ? [v72: $i] : ? [v73: $i] : ? [v74: $i] : ? [v75: % 13.67/2.56 | $i] : ? [v76: $i] : ? [v77: $i] : ? [v78: $i] : ? [v79: $i] : % 13.67/2.56 | (op(v31, e3) = v79 & op(v31, e2) = v78 & op(v31, e1) = v77 & op(v31, % 13.67/2.56 | e0) = v76 & op(v29, e3) = v75 & op(v29, e2) = v74 & op(v29, e1) = % 13.67/2.56 | v73 & op(v29, e0) = v72 & op(v27, e3) = v71 & op(v27, e2) = v70 & % 13.67/2.56 | op(v27, e1) = v69 & op(v27, e0) = v68 & op(v25, e3) = v67 & op(v25, % 13.67/2.56 | e2) = v66 & op(v25, e1) = v65 & op(v25, e0) = v64 & op(v23, e3) = % 13.67/2.56 | v63 & op(v23, e2) = v62 & op(v23, e1) = v61 & op(v23, e0) = v60 & % 13.67/2.56 | op(v21, e3) = v59 & op(v21, e2) = v58 & op(v21, e1) = v57 & op(v21, % 13.67/2.57 | e0) = v56 & op(v19, e3) = v55 & op(v19, e2) = v54 & op(v19, e1) = % 13.67/2.57 | v53 & op(v19, e0) = v52 & op(v17, e3) = v51 & op(v17, e2) = v50 & % 13.67/2.57 | op(v17, e1) = v49 & op(v17, e0) = v48 & op(v15, e3) = v47 & op(v15, % 13.67/2.57 | e2) = v46 & op(v15, e1) = v45 & op(v15, e0) = v44 & op(v13, e3) = % 13.67/2.57 | v43 & op(v13, e2) = v42 & op(v13, e1) = v41 & op(v13, e0) = v40 & % 13.67/2.57 | op(v11, e3) = v39 & op(v11, e2) = v38 & op(v11, e1) = v37 & op(v11, % 13.67/2.57 | e0) = v36 & op(v9, e3) = v35 & op(v9, e2) = v34 & op(v9, e1) = v33 % 13.67/2.57 | & op(v9, e0) = v32 & op(v7, e3) = v30 & op(v7, e2) = v28 & op(v7, e1) % 13.67/2.57 | = v26 & op(v7, e0) = v24 & op(v5, e3) = v22 & op(v5, e2) = v20 & % 13.67/2.57 | op(v5, e1) = v18 & op(v5, e0) = v16 & op(v3, e3) = v14 & op(v3, e2) = % 13.67/2.57 | v12 & op(v3, e1) = v10 & op(v3, e0) = v8 & op(v0, e3) = v6 & op(v0, % 13.67/2.57 | e2) = v4 & op(v0, e1) = v2 & op(v0, e0) = v1 & op(e3, v31) = v79 & % 13.67/2.57 | op(e3, v29) = v78 & op(e3, v27) = v77 & op(e3, v25) = v76 & op(e3, % 13.67/2.57 | v23) = v75 & op(e3, v21) = v74 & op(e3, v19) = v73 & op(e3, v17) = % 13.67/2.57 | v72 & op(e3, v15) = v71 & op(e3, v13) = v70 & op(e3, v11) = v69 & % 13.67/2.57 | op(e3, v9) = v68 & op(e3, v7) = v67 & op(e3, v5) = v66 & op(e3, v3) = % 13.67/2.57 | v65 & op(e3, v0) = v64 & op(e3, e3) = v31 & op(e3, e2) = v29 & op(e3, % 13.67/2.57 | e1) = v27 & op(e3, e0) = v25 & op(e2, v31) = v63 & op(e2, v29) = % 13.67/2.57 | v62 & op(e2, v27) = v61 & op(e2, v25) = v60 & op(e2, v23) = v59 & % 13.67/2.57 | op(e2, v21) = v58 & op(e2, v19) = v57 & op(e2, v17) = v56 & op(e2, % 13.67/2.57 | v15) = v55 & op(e2, v13) = v54 & op(e2, v11) = v53 & op(e2, v9) = % 13.67/2.57 | v52 & op(e2, v7) = v51 & op(e2, v5) = v50 & op(e2, v3) = v49 & op(e2, % 13.67/2.57 | v0) = v48 & op(e2, e3) = v23 & op(e2, e2) = v21 & op(e2, e1) = v19 % 13.67/2.57 | & op(e2, e0) = v17 & op(e1, v31) = v47 & op(e1, v29) = v46 & op(e1, % 13.67/2.57 | v27) = v45 & op(e1, v25) = v44 & op(e1, v23) = v43 & op(e1, v21) = % 13.67/2.57 | v42 & op(e1, v19) = v41 & op(e1, v17) = v40 & op(e1, v15) = v39 & % 13.67/2.57 | op(e1, v13) = v38 & op(e1, v11) = v37 & op(e1, v9) = v36 & op(e1, v7) % 13.67/2.57 | = v35 & op(e1, v5) = v34 & op(e1, v3) = v33 & op(e1, v0) = v32 & % 13.67/2.57 | op(e1, e3) = v15 & op(e1, e2) = v13 & op(e1, e1) = v11 & op(e1, e0) = % 13.67/2.57 | v9 & op(e0, v31) = v30 & op(e0, v29) = v28 & op(e0, v27) = v26 & % 13.67/2.57 | op(e0, v25) = v24 & op(e0, v23) = v22 & op(e0, v21) = v20 & op(e0, % 13.67/2.57 | v19) = v18 & op(e0, v17) = v16 & op(e0, v15) = v14 & op(e0, v13) = % 13.67/2.57 | v12 & op(e0, v11) = v10 & op(e0, v9) = v8 & op(e0, v7) = v6 & op(e0, % 13.67/2.57 | v5) = v4 & op(e0, v3) = v2 & op(e0, v0) = v1 & op(e0, e3) = v7 & % 13.67/2.57 | op(e0, e2) = v5 & op(e0, e1) = v3 & op(e0, e0) = v0 & $i(v79) & % 13.67/2.57 | $i(v78) & $i(v77) & $i(v76) & $i(v75) & $i(v74) & $i(v73) & $i(v72) & % 13.67/2.57 | $i(v71) & $i(v70) & $i(v69) & $i(v68) & $i(v67) & $i(v66) & $i(v65) & % 13.67/2.57 | $i(v64) & $i(v63) & $i(v62) & $i(v61) & $i(v60) & $i(v59) & $i(v58) & % 13.67/2.57 | $i(v57) & $i(v56) & $i(v55) & $i(v54) & $i(v53) & $i(v52) & $i(v51) & % 13.67/2.57 | $i(v50) & $i(v49) & $i(v48) & $i(v47) & $i(v46) & $i(v45) & $i(v44) & % 13.67/2.57 | $i(v43) & $i(v42) & $i(v41) & $i(v40) & $i(v39) & $i(v38) & $i(v37) & % 13.67/2.57 | $i(v36) & $i(v35) & $i(v34) & $i(v33) & $i(v32) & $i(v31) & $i(v30) & % 13.67/2.57 | $i(v29) & $i(v28) & $i(v27) & $i(v26) & $i(v25) & $i(v24) & $i(v23) & % 13.67/2.57 | $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & % 13.67/2.57 | $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & % 13.67/2.57 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) % 13.67/2.57 | & $i(v0)) % 13.67/2.57 | % 13.67/2.57 | ALPHA: (ax3) implies: % 13.67/2.57 | (3) op(e0, unit) = e0 % 13.67/2.57 | % 13.67/2.57 | ALPHA: (ax5) implies: % 13.67/2.57 | (4) unit = e0 % 13.67/2.57 | % 13.67/2.57 | ALPHA: (ax10) implies: % 13.67/2.57 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 13.67/2.57 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 13.67/2.57 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 13.67/2.57 | ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v12) & ~ % 13.67/2.57 | (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = v13) & ~ % 13.67/2.57 | (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & ~ % 13.67/2.57 | (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 % 13.67/2.57 | = v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = % 13.67/2.57 | v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) % 13.67/2.57 | & ~ (v10 = v8) & ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ % 13.67/2.57 | (v9 = v5) & ~ (v9 = v1) & ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) % 13.67/2.57 | & ~ (v7 = v5) & ~ (v7 = v4) & ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 % 13.67/2.57 | = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ (v5 = v1) & ~ (v4 = v0) & % 13.67/2.57 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = % 13.67/2.57 | v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = v11 & op(e3, % 13.67/2.57 | e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = v10 & % 13.67/2.57 | op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = % 13.67/2.57 | v9 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, % 13.67/2.57 | e2) = v8 & op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & % 13.67/2.57 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & % 13.67/2.57 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 13.67/2.57 | % 13.67/2.57 | ALPHA: (co1) implies: % 13.67/2.57 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (op(e3, e3) = % 13.67/2.57 | v3 & op(e2, e2) = v2 & op(e1, e1) = v1 & op(e0, e0) = v0 & $i(v3) & % 13.67/2.57 | $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = e3) | ~ (v2 = e3) | ~ (v1 = % 13.67/2.57 | e3) | ~ (v0 = e3)) & ( ~ (v3 = e2) | ~ (v2 = e2) | ~ (v1 = e2) % 13.67/2.57 | | ~ (v0 = e2)) & ( ~ (v3 = e1) | ~ (v2 = e1) | ~ (v1 = e1) | ~ % 13.67/2.57 | (v0 = e1)) & ( ~ (v3 = e0) | ~ (v2 = e0) | ~ (v1 = e0) | ~ (v0 = % 13.67/2.57 | e0)) & ((v3 = e3 & v2 = e3 & v1 = e3 & v0 = e3) | (v3 = e2 & v2 = % 13.67/2.57 | e2 & v1 = e2 & v0 = e2) | (v3 = e1 & v2 = e1 & v1 = e1 & v0 = e1) % 13.67/2.57 | | (v3 = e0 & v2 = e0 & v1 = e0 & v0 = e0))) % 13.67/2.57 | % 13.67/2.57 | ALPHA: (function-axioms) implies: % 13.67/2.58 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.67/2.58 | (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 13.67/2.58 | % 13.67/2.58 | DELTA: instantiating (6) with fresh symbols all_12_0, all_12_1, all_12_2, % 13.67/2.58 | all_12_3 gives: % 13.67/2.58 | (8) op(e3, e3) = all_12_0 & op(e2, e2) = all_12_1 & op(e1, e1) = all_12_2 & % 13.67/2.58 | op(e0, e0) = all_12_3 & $i(all_12_0) & $i(all_12_1) & $i(all_12_2) & % 13.67/2.58 | $i(all_12_3) & ( ~ (all_12_0 = e3) | ~ (all_12_1 = e3) | ~ (all_12_2 % 13.67/2.58 | = e3) | ~ (all_12_3 = e3)) & ( ~ (all_12_0 = e2) | ~ (all_12_1 = % 13.67/2.58 | e2) | ~ (all_12_2 = e2) | ~ (all_12_3 = e2)) & ( ~ (all_12_0 = % 13.67/2.58 | e1) | ~ (all_12_1 = e1) | ~ (all_12_2 = e1) | ~ (all_12_3 = e1)) % 13.67/2.58 | & ( ~ (all_12_0 = e0) | ~ (all_12_1 = e0) | ~ (all_12_2 = e0) | ~ % 13.67/2.58 | (all_12_3 = e0)) & ((all_12_0 = e3 & all_12_1 = e3 & all_12_2 = e3 & % 13.67/2.58 | all_12_3 = e3) | (all_12_0 = e2 & all_12_1 = e2 & all_12_2 = e2 & % 13.67/2.58 | all_12_3 = e2) | (all_12_0 = e1 & all_12_1 = e1 & all_12_2 = e1 & % 13.67/2.58 | all_12_3 = e1) | (all_12_0 = e0 & all_12_1 = e0 & all_12_2 = e0 & % 13.67/2.58 | all_12_3 = e0)) % 13.67/2.58 | % 13.67/2.58 | ALPHA: (8) implies: % 13.67/2.58 | (9) op(e0, e0) = all_12_3 % 13.67/2.58 | (10) (all_12_0 = e3 & all_12_1 = e3 & all_12_2 = e3 & all_12_3 = e3) | % 13.67/2.58 | (all_12_0 = e2 & all_12_1 = e2 & all_12_2 = e2 & all_12_3 = e2) | % 13.67/2.58 | (all_12_0 = e1 & all_12_1 = e1 & all_12_2 = e1 & all_12_3 = e1) | % 13.67/2.58 | (all_12_0 = e0 & all_12_1 = e0 & all_12_2 = e0 & all_12_3 = e0) % 13.67/2.58 | (11) ~ (all_12_0 = e0) | ~ (all_12_1 = e0) | ~ (all_12_2 = e0) | ~ % 13.67/2.58 | (all_12_3 = e0) % 13.67/2.58 | % 13.67/2.58 | DELTA: instantiating (5) with fresh symbols all_14_0, all_14_1, all_14_2, % 13.67/2.58 | all_14_3, all_14_4, all_14_5, all_14_6, all_14_7, all_14_8, all_14_9, % 13.67/2.58 | all_14_10, all_14_11, all_14_12, all_14_13, all_14_14, all_14_15 gives: % 13.67/2.58 | (12) ~ (all_14_0 = all_14_1) & ~ (all_14_0 = all_14_2) & ~ (all_14_0 = % 13.67/2.58 | all_14_3) & ~ (all_14_0 = all_14_4) & ~ (all_14_0 = all_14_8) & ~ % 13.67/2.58 | (all_14_0 = all_14_12) & ~ (all_14_1 = all_14_2) & ~ (all_14_1 = % 13.67/2.58 | all_14_3) & ~ (all_14_1 = all_14_5) & ~ (all_14_1 = all_14_9) & ~ % 13.67/2.58 | (all_14_1 = all_14_13) & ~ (all_14_2 = all_14_3) & ~ (all_14_2 = % 13.67/2.58 | all_14_6) & ~ (all_14_2 = all_14_10) & ~ (all_14_2 = all_14_14) & % 13.67/2.58 | ~ (all_14_3 = all_14_7) & ~ (all_14_3 = all_14_11) & ~ (all_14_3 = % 13.67/2.58 | all_14_15) & ~ (all_14_4 = all_14_5) & ~ (all_14_4 = all_14_6) & % 13.67/2.58 | ~ (all_14_4 = all_14_7) & ~ (all_14_4 = all_14_8) & ~ (all_14_4 = % 13.67/2.58 | all_14_12) & ~ (all_14_5 = all_14_6) & ~ (all_14_5 = all_14_7) & % 13.67/2.58 | ~ (all_14_5 = all_14_9) & ~ (all_14_5 = all_14_13) & ~ (all_14_6 = % 13.67/2.58 | all_14_7) & ~ (all_14_6 = all_14_10) & ~ (all_14_6 = all_14_14) & % 13.67/2.58 | ~ (all_14_7 = all_14_11) & ~ (all_14_7 = all_14_15) & ~ (all_14_8 = % 13.67/2.58 | all_14_9) & ~ (all_14_8 = all_14_10) & ~ (all_14_8 = all_14_11) & % 13.67/2.58 | ~ (all_14_8 = all_14_12) & ~ (all_14_9 = all_14_10) & ~ (all_14_9 = % 13.67/2.58 | all_14_11) & ~ (all_14_9 = all_14_13) & ~ (all_14_10 = all_14_11) % 13.67/2.58 | & ~ (all_14_10 = all_14_14) & ~ (all_14_11 = all_14_15) & ~ % 13.67/2.58 | (all_14_12 = all_14_13) & ~ (all_14_12 = all_14_14) & ~ (all_14_12 = % 13.67/2.58 | all_14_15) & ~ (all_14_13 = all_14_14) & ~ (all_14_13 = all_14_15) % 13.67/2.58 | & ~ (all_14_14 = all_14_15) & op(e3, e3) = all_14_0 & op(e3, e2) = % 13.67/2.58 | all_14_4 & op(e3, e1) = all_14_8 & op(e3, e0) = all_14_12 & op(e2, e3) % 13.67/2.58 | = all_14_1 & op(e2, e2) = all_14_5 & op(e2, e1) = all_14_9 & op(e2, % 13.67/2.58 | e0) = all_14_13 & op(e1, e3) = all_14_2 & op(e1, e2) = all_14_6 & % 13.67/2.58 | op(e1, e1) = all_14_10 & op(e1, e0) = all_14_14 & op(e0, e3) = % 13.67/2.58 | all_14_3 & op(e0, e2) = all_14_7 & op(e0, e1) = all_14_11 & op(e0, e0) % 13.67/2.58 | = all_14_15 & $i(all_14_0) & $i(all_14_1) & $i(all_14_2) & % 13.67/2.58 | $i(all_14_3) & $i(all_14_4) & $i(all_14_5) & $i(all_14_6) & % 13.67/2.58 | $i(all_14_7) & $i(all_14_8) & $i(all_14_9) & $i(all_14_10) & % 13.67/2.58 | $i(all_14_11) & $i(all_14_12) & $i(all_14_13) & $i(all_14_14) & % 13.67/2.58 | $i(all_14_15) % 13.67/2.59 | % 13.67/2.59 | ALPHA: (12) implies: % 13.67/2.59 | (13) op(e0, e0) = all_14_15 % 13.67/2.59 | % 13.67/2.59 | DELTA: instantiating (1) with fresh symbols all_16_0, all_16_1, all_16_2, % 13.67/2.59 | all_16_3, all_16_4, all_16_5, all_16_6, all_16_7, all_16_8, all_16_9, % 13.67/2.59 | all_16_10, all_16_11, all_16_12, all_16_13, all_16_14, all_16_15 gives: % 13.67/2.59 | (14) op(e3, e3) = all_16_0 & op(e3, e2) = all_16_1 & op(e3, e1) = all_16_2 % 13.67/2.59 | & op(e3, e0) = all_16_3 & op(e2, e3) = all_16_4 & op(e2, e2) = % 13.67/2.59 | all_16_5 & op(e2, e1) = all_16_6 & op(e2, e0) = all_16_7 & op(e1, e3) % 13.67/2.59 | = all_16_8 & op(e1, e2) = all_16_9 & op(e1, e1) = all_16_10 & op(e1, % 13.67/2.59 | e0) = all_16_11 & op(e0, e3) = all_16_12 & op(e0, e2) = all_16_13 & % 13.67/2.59 | op(e0, e1) = all_16_14 & op(e0, e0) = all_16_15 & $i(all_16_0) & % 13.67/2.59 | $i(all_16_1) & $i(all_16_2) & $i(all_16_3) & $i(all_16_4) & % 13.67/2.59 | $i(all_16_5) & $i(all_16_6) & $i(all_16_7) & $i(all_16_8) & % 13.67/2.59 | $i(all_16_9) & $i(all_16_10) & $i(all_16_11) & $i(all_16_12) & % 13.67/2.59 | $i(all_16_13) & $i(all_16_14) & $i(all_16_15) & (all_16_0 = e3 | % 13.67/2.59 | all_16_0 = e2 | all_16_0 = e1 | all_16_0 = e0) & (all_16_1 = e3 | % 13.67/2.59 | all_16_1 = e2 | all_16_1 = e1 | all_16_1 = e0) & (all_16_2 = e3 | % 13.67/2.59 | all_16_2 = e2 | all_16_2 = e1 | all_16_2 = e0) & (all_16_3 = e3 | % 13.67/2.59 | all_16_3 = e2 | all_16_3 = e1 | all_16_3 = e0) & (all_16_4 = e3 | % 13.67/2.59 | all_16_4 = e2 | all_16_4 = e1 | all_16_4 = e0) & (all_16_5 = e3 | % 13.67/2.59 | all_16_5 = e2 | all_16_5 = e1 | all_16_5 = e0) & (all_16_6 = e3 | % 13.67/2.59 | all_16_6 = e2 | all_16_6 = e1 | all_16_6 = e0) & (all_16_7 = e3 | % 13.67/2.59 | all_16_7 = e2 | all_16_7 = e1 | all_16_7 = e0) & (all_16_8 = e3 | % 13.67/2.59 | all_16_8 = e2 | all_16_8 = e1 | all_16_8 = e0) & (all_16_9 = e3 | % 13.67/2.59 | all_16_9 = e2 | all_16_9 = e1 | all_16_9 = e0) & (all_16_10 = e3 | % 13.67/2.59 | all_16_10 = e2 | all_16_10 = e1 | all_16_10 = e0) & (all_16_11 = e3 % 13.67/2.59 | | all_16_11 = e2 | all_16_11 = e1 | all_16_11 = e0) & (all_16_12 = % 13.67/2.59 | e3 | all_16_12 = e2 | all_16_12 = e1 | all_16_12 = e0) & (all_16_13 % 13.67/2.59 | = e3 | all_16_13 = e2 | all_16_13 = e1 | all_16_13 = e0) & % 13.67/2.59 | (all_16_14 = e3 | all_16_14 = e2 | all_16_14 = e1 | all_16_14 = e0) & % 13.67/2.59 | (all_16_15 = e3 | all_16_15 = e2 | all_16_15 = e1 | all_16_15 = e0) % 13.67/2.59 | % 13.67/2.59 | ALPHA: (14) implies: % 13.67/2.59 | (15) op(e0, e0) = all_16_15 % 13.67/2.59 | % 13.67/2.59 | DELTA: instantiating (2) with fresh symbols all_18_0, all_18_1, all_18_2, % 13.67/2.59 | all_18_3, all_18_4, all_18_5, all_18_6, all_18_7, all_18_8, all_18_9, % 13.67/2.59 | all_18_10, all_18_11, all_18_12, all_18_13, all_18_14, all_18_15, % 13.67/2.59 | all_18_16, all_18_17, all_18_18, all_18_19, all_18_20, all_18_21, % 13.67/2.59 | all_18_22, all_18_23, all_18_24, all_18_25, all_18_26, all_18_27, % 13.67/2.59 | all_18_28, all_18_29, all_18_30, all_18_31, all_18_32, all_18_33, % 13.67/2.59 | all_18_34, all_18_35, all_18_36, all_18_37, all_18_38, all_18_39, % 13.67/2.59 | all_18_40, all_18_41, all_18_42, all_18_43, all_18_44, all_18_45, % 13.67/2.59 | all_18_46, all_18_47, all_18_48, all_18_49, all_18_50, all_18_51, % 13.67/2.59 | all_18_52, all_18_53, all_18_54, all_18_55, all_18_56, all_18_57, % 13.67/2.59 | all_18_58, all_18_59, all_18_60, all_18_61, all_18_62, all_18_63, % 13.67/2.59 | all_18_64, all_18_65, all_18_66, all_18_67, all_18_68, all_18_69, % 13.67/2.59 | all_18_70, all_18_71, all_18_72, all_18_73, all_18_74, all_18_75, % 13.67/2.59 | all_18_76, all_18_77, all_18_78, all_18_79 gives: % 13.67/2.60 | (16) op(all_18_48, e3) = all_18_0 & op(all_18_48, e2) = all_18_1 & % 13.67/2.60 | op(all_18_48, e1) = all_18_2 & op(all_18_48, e0) = all_18_3 & % 13.67/2.60 | op(all_18_50, e3) = all_18_4 & op(all_18_50, e2) = all_18_5 & % 13.67/2.60 | op(all_18_50, e1) = all_18_6 & op(all_18_50, e0) = all_18_7 & % 13.67/2.60 | op(all_18_52, e3) = all_18_8 & op(all_18_52, e2) = all_18_9 & % 13.67/2.60 | op(all_18_52, e1) = all_18_10 & op(all_18_52, e0) = all_18_11 & % 13.67/2.60 | op(all_18_54, e3) = all_18_12 & op(all_18_54, e2) = all_18_13 & % 13.67/2.60 | op(all_18_54, e1) = all_18_14 & op(all_18_54, e0) = all_18_15 & % 13.67/2.60 | op(all_18_56, e3) = all_18_16 & op(all_18_56, e2) = all_18_17 & % 13.67/2.60 | op(all_18_56, e1) = all_18_18 & op(all_18_56, e0) = all_18_19 & % 13.67/2.60 | op(all_18_58, e3) = all_18_20 & op(all_18_58, e2) = all_18_21 & % 13.67/2.60 | op(all_18_58, e1) = all_18_22 & op(all_18_58, e0) = all_18_23 & % 13.67/2.60 | op(all_18_60, e3) = all_18_24 & op(all_18_60, e2) = all_18_25 & % 13.67/2.60 | op(all_18_60, e1) = all_18_26 & op(all_18_60, e0) = all_18_27 & % 13.67/2.60 | op(all_18_62, e3) = all_18_28 & op(all_18_62, e2) = all_18_29 & % 13.67/2.60 | op(all_18_62, e1) = all_18_30 & op(all_18_62, e0) = all_18_31 & % 13.67/2.60 | op(all_18_64, e3) = all_18_32 & op(all_18_64, e2) = all_18_33 & % 13.67/2.60 | op(all_18_64, e1) = all_18_34 & op(all_18_64, e0) = all_18_35 & % 13.67/2.60 | op(all_18_66, e3) = all_18_36 & op(all_18_66, e2) = all_18_37 & % 13.67/2.60 | op(all_18_66, e1) = all_18_38 & op(all_18_66, e0) = all_18_39 & % 13.67/2.60 | op(all_18_68, e3) = all_18_40 & op(all_18_68, e2) = all_18_41 & % 13.67/2.60 | op(all_18_68, e1) = all_18_42 & op(all_18_68, e0) = all_18_43 & % 13.67/2.60 | op(all_18_70, e3) = all_18_44 & op(all_18_70, e2) = all_18_45 & % 13.67/2.60 | op(all_18_70, e1) = all_18_46 & op(all_18_70, e0) = all_18_47 & % 13.67/2.60 | op(all_18_72, e3) = all_18_49 & op(all_18_72, e2) = all_18_51 & % 13.67/2.60 | op(all_18_72, e1) = all_18_53 & op(all_18_72, e0) = all_18_55 & % 13.67/2.60 | op(all_18_74, e3) = all_18_57 & op(all_18_74, e2) = all_18_59 & % 13.67/2.60 | op(all_18_74, e1) = all_18_61 & op(all_18_74, e0) = all_18_63 & % 13.67/2.60 | op(all_18_76, e3) = all_18_65 & op(all_18_76, e2) = all_18_67 & % 13.67/2.60 | op(all_18_76, e1) = all_18_69 & op(all_18_76, e0) = all_18_71 & % 13.67/2.60 | op(all_18_79, e3) = all_18_73 & op(all_18_79, e2) = all_18_75 & % 13.67/2.60 | op(all_18_79, e1) = all_18_77 & op(all_18_79, e0) = all_18_78 & op(e3, % 13.67/2.60 | all_18_48) = all_18_0 & op(e3, all_18_50) = all_18_1 & op(e3, % 13.67/2.60 | all_18_52) = all_18_2 & op(e3, all_18_54) = all_18_3 & op(e3, % 13.67/2.60 | all_18_56) = all_18_4 & op(e3, all_18_58) = all_18_5 & op(e3, % 13.67/2.60 | all_18_60) = all_18_6 & op(e3, all_18_62) = all_18_7 & op(e3, % 13.67/2.60 | all_18_64) = all_18_8 & op(e3, all_18_66) = all_18_9 & op(e3, % 13.67/2.60 | all_18_68) = all_18_10 & op(e3, all_18_70) = all_18_11 & op(e3, % 13.67/2.60 | all_18_72) = all_18_12 & op(e3, all_18_74) = all_18_13 & op(e3, % 13.67/2.60 | all_18_76) = all_18_14 & op(e3, all_18_79) = all_18_15 & op(e3, e3) % 13.67/2.60 | = all_18_48 & op(e3, e2) = all_18_50 & op(e3, e1) = all_18_52 & op(e3, % 13.67/2.60 | e0) = all_18_54 & op(e2, all_18_48) = all_18_16 & op(e2, all_18_50) % 13.67/2.60 | = all_18_17 & op(e2, all_18_52) = all_18_18 & op(e2, all_18_54) = % 13.67/2.60 | all_18_19 & op(e2, all_18_56) = all_18_20 & op(e2, all_18_58) = % 13.67/2.60 | all_18_21 & op(e2, all_18_60) = all_18_22 & op(e2, all_18_62) = % 13.67/2.60 | all_18_23 & op(e2, all_18_64) = all_18_24 & op(e2, all_18_66) = % 13.67/2.60 | all_18_25 & op(e2, all_18_68) = all_18_26 & op(e2, all_18_70) = % 13.67/2.60 | all_18_27 & op(e2, all_18_72) = all_18_28 & op(e2, all_18_74) = % 13.67/2.60 | all_18_29 & op(e2, all_18_76) = all_18_30 & op(e2, all_18_79) = % 13.67/2.60 | all_18_31 & op(e2, e3) = all_18_56 & op(e2, e2) = all_18_58 & op(e2, % 13.67/2.60 | e1) = all_18_60 & op(e2, e0) = all_18_62 & op(e1, all_18_48) = % 13.67/2.60 | all_18_32 & op(e1, all_18_50) = all_18_33 & op(e1, all_18_52) = % 13.67/2.60 | all_18_34 & op(e1, all_18_54) = all_18_35 & op(e1, all_18_56) = % 13.67/2.60 | all_18_36 & op(e1, all_18_58) = all_18_37 & op(e1, all_18_60) = % 13.67/2.60 | all_18_38 & op(e1, all_18_62) = all_18_39 & op(e1, all_18_64) = % 13.67/2.60 | all_18_40 & op(e1, all_18_66) = all_18_41 & op(e1, all_18_68) = % 13.67/2.60 | all_18_42 & op(e1, all_18_70) = all_18_43 & op(e1, all_18_72) = % 13.67/2.60 | all_18_44 & op(e1, all_18_74) = all_18_45 & op(e1, all_18_76) = % 13.67/2.60 | all_18_46 & op(e1, all_18_79) = all_18_47 & op(e1, e3) = all_18_64 & % 13.67/2.60 | op(e1, e2) = all_18_66 & op(e1, e1) = all_18_68 & op(e1, e0) = % 13.67/2.60 | all_18_70 & op(e0, all_18_48) = all_18_49 & op(e0, all_18_50) = % 13.67/2.60 | all_18_51 & op(e0, all_18_52) = all_18_53 & op(e0, all_18_54) = % 13.67/2.60 | all_18_55 & op(e0, all_18_56) = all_18_57 & op(e0, all_18_58) = % 13.67/2.60 | all_18_59 & op(e0, all_18_60) = all_18_61 & op(e0, all_18_62) = % 13.67/2.60 | all_18_63 & op(e0, all_18_64) = all_18_65 & op(e0, all_18_66) = % 13.67/2.60 | all_18_67 & op(e0, all_18_68) = all_18_69 & op(e0, all_18_70) = % 13.67/2.60 | all_18_71 & op(e0, all_18_72) = all_18_73 & op(e0, all_18_74) = % 13.67/2.60 | all_18_75 & op(e0, all_18_76) = all_18_77 & op(e0, all_18_79) = % 13.67/2.60 | all_18_78 & op(e0, e3) = all_18_72 & op(e0, e2) = all_18_74 & op(e0, % 13.67/2.60 | e1) = all_18_76 & op(e0, e0) = all_18_79 & $i(all_18_0) & % 13.67/2.60 | $i(all_18_1) & $i(all_18_2) & $i(all_18_3) & $i(all_18_4) & % 13.67/2.60 | $i(all_18_5) & $i(all_18_6) & $i(all_18_7) & $i(all_18_8) & % 13.67/2.60 | $i(all_18_9) & $i(all_18_10) & $i(all_18_11) & $i(all_18_12) & % 13.67/2.60 | $i(all_18_13) & $i(all_18_14) & $i(all_18_15) & $i(all_18_16) & % 13.67/2.60 | $i(all_18_17) & $i(all_18_18) & $i(all_18_19) & $i(all_18_20) & % 13.67/2.60 | $i(all_18_21) & $i(all_18_22) & $i(all_18_23) & $i(all_18_24) & % 13.67/2.60 | $i(all_18_25) & $i(all_18_26) & $i(all_18_27) & $i(all_18_28) & % 13.67/2.60 | $i(all_18_29) & $i(all_18_30) & $i(all_18_31) & $i(all_18_32) & % 13.67/2.60 | $i(all_18_33) & $i(all_18_34) & $i(all_18_35) & $i(all_18_36) & % 13.67/2.60 | $i(all_18_37) & $i(all_18_38) & $i(all_18_39) & $i(all_18_40) & % 13.67/2.60 | $i(all_18_41) & $i(all_18_42) & $i(all_18_43) & $i(all_18_44) & % 13.67/2.60 | $i(all_18_45) & $i(all_18_46) & $i(all_18_47) & $i(all_18_48) & % 13.67/2.60 | $i(all_18_49) & $i(all_18_50) & $i(all_18_51) & $i(all_18_52) & % 13.67/2.60 | $i(all_18_53) & $i(all_18_54) & $i(all_18_55) & $i(all_18_56) & % 13.67/2.60 | $i(all_18_57) & $i(all_18_58) & $i(all_18_59) & $i(all_18_60) & % 13.67/2.60 | $i(all_18_61) & $i(all_18_62) & $i(all_18_63) & $i(all_18_64) & % 13.67/2.60 | $i(all_18_65) & $i(all_18_66) & $i(all_18_67) & $i(all_18_68) & % 13.67/2.60 | $i(all_18_69) & $i(all_18_70) & $i(all_18_71) & $i(all_18_72) & % 13.67/2.60 | $i(all_18_73) & $i(all_18_74) & $i(all_18_75) & $i(all_18_76) & % 13.67/2.60 | $i(all_18_77) & $i(all_18_78) & $i(all_18_79) % 13.67/2.60 | % 13.67/2.60 | ALPHA: (16) implies: % 13.67/2.61 | (17) op(e0, e0) = all_18_79 % 13.67/2.61 | % 13.67/2.61 | REDUCE: (3), (4) imply: % 13.67/2.61 | (18) op(e0, e0) = e0 % 13.67/2.61 | % 13.67/2.61 | GROUND_INST: instantiating (7) with all_12_3, all_16_15, e0, e0, simplifying % 13.67/2.61 | with (9), (15) gives: % 13.67/2.61 | (19) all_16_15 = all_12_3 % 13.67/2.61 | % 13.67/2.61 | GROUND_INST: instantiating (7) with e0, all_16_15, e0, e0, simplifying with % 13.67/2.61 | (15), (18) gives: % 13.67/2.61 | (20) all_16_15 = e0 % 13.67/2.61 | % 13.67/2.61 | GROUND_INST: instantiating (7) with all_16_15, all_18_79, e0, e0, simplifying % 13.67/2.61 | with (15), (17) gives: % 13.67/2.61 | (21) all_18_79 = all_16_15 % 13.67/2.61 | % 13.67/2.61 | GROUND_INST: instantiating (7) with all_14_15, all_18_79, e0, e0, simplifying % 13.67/2.61 | with (13), (17) gives: % 13.67/2.61 | (22) all_18_79 = all_14_15 % 13.67/2.61 | % 13.67/2.61 | COMBINE_EQS: (21), (22) imply: % 13.67/2.61 | (23) all_16_15 = all_14_15 % 13.67/2.61 | % 13.67/2.61 | SIMP: (23) implies: % 13.67/2.61 | (24) all_16_15 = all_14_15 % 13.67/2.61 | % 13.67/2.61 | COMBINE_EQS: (20), (24) imply: % 13.67/2.61 | (25) all_14_15 = e0 % 13.67/2.61 | % 13.67/2.61 | COMBINE_EQS: (19), (24) imply: % 13.67/2.61 | (26) all_14_15 = all_12_3 % 13.67/2.61 | % 13.67/2.61 | COMBINE_EQS: (25), (26) imply: % 13.67/2.61 | (27) all_12_3 = e0 % 13.67/2.61 | % 13.67/2.61 | SIMP: (27) implies: % 13.67/2.61 | (28) all_12_3 = e0 % 13.67/2.61 | % 13.67/2.61 | BETA: splitting (10) gives: % 13.67/2.61 | % 13.67/2.61 | Case 1: % 13.67/2.61 | | % 13.67/2.61 | | (29) (all_12_0 = e3 & all_12_1 = e3 & all_12_2 = e3 & all_12_3 = e3) | % 13.67/2.61 | | (all_12_0 = e2 & all_12_1 = e2 & all_12_2 = e2 & all_12_3 = e2) % 13.67/2.61 | | % 13.67/2.61 | | BETA: splitting (29) gives: % 13.67/2.61 | | % 13.67/2.61 | | Case 1: % 13.67/2.61 | | | % 13.67/2.61 | | | (30) all_12_0 = e3 & all_12_1 = e3 & all_12_2 = e3 & all_12_3 = e3 % 13.67/2.61 | | | % 13.67/2.61 | | | ALPHA: (30) implies: % 13.67/2.61 | | | (31) all_12_3 = e3 % 13.67/2.61 | | | (32) all_12_2 = e3 % 13.67/2.61 | | | (33) all_12_1 = e3 % 13.67/2.61 | | | (34) all_12_0 = e3 % 13.67/2.61 | | | % 13.67/2.61 | | | COMBINE_EQS: (28), (31) imply: % 13.67/2.61 | | | (35) e3 = e0 % 13.67/2.61 | | | % 13.67/2.61 | | | COMBINE_EQS: (32), (35) imply: % 13.67/2.61 | | | (36) all_12_2 = e0 % 13.67/2.61 | | | % 13.67/2.61 | | | COMBINE_EQS: (33), (35) imply: % 13.67/2.61 | | | (37) all_12_1 = e0 % 13.67/2.61 | | | % 13.67/2.61 | | | COMBINE_EQS: (34), (35) imply: % 13.67/2.61 | | | (38) all_12_0 = e0 % 13.67/2.61 | | | % 13.67/2.61 | | | REF_CLOSE: (11), (28), (36), (37), (38) are inconsistent by sub-proof #1. % 13.67/2.61 | | | % 13.67/2.61 | | Case 2: % 13.67/2.61 | | | % 13.67/2.61 | | | (39) all_12_0 = e2 & all_12_1 = e2 & all_12_2 = e2 & all_12_3 = e2 % 13.67/2.61 | | | % 13.67/2.61 | | | ALPHA: (39) implies: % 13.67/2.61 | | | (40) all_12_3 = e2 % 13.67/2.61 | | | (41) all_12_2 = e2 % 13.67/2.61 | | | (42) all_12_1 = e2 % 13.67/2.61 | | | (43) all_12_0 = e2 % 13.67/2.61 | | | % 13.67/2.61 | | | COMBINE_EQS: (28), (40) imply: % 13.67/2.61 | | | (44) e2 = e0 % 13.67/2.61 | | | % 13.67/2.62 | | | COMBINE_EQS: (41), (44) imply: % 13.67/2.62 | | | (45) all_12_2 = e0 % 13.67/2.62 | | | % 13.67/2.62 | | | COMBINE_EQS: (42), (44) imply: % 13.67/2.62 | | | (46) all_12_1 = e0 % 13.67/2.62 | | | % 13.67/2.62 | | | COMBINE_EQS: (43), (44) imply: % 13.67/2.62 | | | (47) all_12_0 = e0 % 13.67/2.62 | | | % 13.67/2.62 | | | REF_CLOSE: (11), (28), (45), (46), (47) are inconsistent by sub-proof #1. % 13.67/2.62 | | | % 13.67/2.62 | | End of split % 13.67/2.62 | | % 13.67/2.62 | Case 2: % 13.67/2.62 | | % 13.67/2.62 | | (48) (all_12_0 = e1 & all_12_1 = e1 & all_12_2 = e1 & all_12_3 = e1) | % 13.67/2.62 | | (all_12_0 = e0 & all_12_1 = e0 & all_12_2 = e0 & all_12_3 = e0) % 13.67/2.62 | | % 13.67/2.62 | | BETA: splitting (48) gives: % 13.67/2.62 | | % 13.67/2.62 | | Case 1: % 13.67/2.62 | | | % 13.67/2.62 | | | (49) all_12_0 = e1 & all_12_1 = e1 & all_12_2 = e1 & all_12_3 = e1 % 13.67/2.62 | | | % 13.67/2.62 | | | ALPHA: (49) implies: % 13.67/2.62 | | | (50) all_12_3 = e1 % 13.67/2.62 | | | (51) all_12_2 = e1 % 13.67/2.62 | | | (52) all_12_1 = e1 % 13.67/2.62 | | | (53) all_12_0 = e1 % 13.67/2.62 | | | % 13.67/2.62 | | | COMBINE_EQS: (28), (50) imply: % 13.67/2.62 | | | (54) e1 = e0 % 13.67/2.62 | | | % 13.67/2.62 | | | COMBINE_EQS: (51), (54) imply: % 13.67/2.62 | | | (55) all_12_2 = e0 % 13.67/2.62 | | | % 13.67/2.62 | | | COMBINE_EQS: (52), (54) imply: % 13.67/2.62 | | | (56) all_12_1 = e0 % 13.67/2.62 | | | % 13.67/2.62 | | | COMBINE_EQS: (53), (54) imply: % 13.67/2.62 | | | (57) all_12_0 = e0 % 13.67/2.62 | | | % 13.67/2.62 | | | REF_CLOSE: (11), (28), (55), (56), (57) are inconsistent by sub-proof #1. % 13.67/2.62 | | | % 13.67/2.62 | | Case 2: % 13.67/2.62 | | | % 13.67/2.62 | | | (58) all_12_0 = e0 & all_12_1 = e0 & all_12_2 = e0 & all_12_3 = e0 % 13.67/2.62 | | | % 13.67/2.62 | | | ALPHA: (58) implies: % 13.67/2.62 | | | (59) all_12_2 = e0 % 13.67/2.62 | | | (60) all_12_1 = e0 % 13.67/2.62 | | | (61) all_12_0 = e0 % 13.67/2.62 | | | % 13.67/2.62 | | | REF_CLOSE: (11), (28), (59), (60), (61) are inconsistent by sub-proof #1. % 13.67/2.62 | | | % 13.67/2.62 | | End of split % 13.67/2.62 | | % 13.67/2.62 | End of split % 13.67/2.62 | % 13.67/2.62 End of proof % 13.67/2.62 % 13.67/2.62 Sub-proof #1 shows that the following formulas are inconsistent: % 13.67/2.62 ---------------------------------------------------------------- % 13.67/2.62 (1) all_12_1 = e0 % 13.67/2.62 (2) all_12_0 = e0 % 13.67/2.62 (3) ~ (all_12_0 = e0) | ~ (all_12_1 = e0) | ~ (all_12_2 = e0) | ~ % 13.67/2.62 (all_12_3 = e0) % 13.67/2.62 (4) all_12_3 = e0 % 13.67/2.62 (5) all_12_2 = e0 % 13.67/2.62 % 13.67/2.62 Begin of proof % 13.67/2.62 | % 13.67/2.62 | BETA: splitting (3) gives: % 13.67/2.62 | % 13.67/2.62 | Case 1: % 13.67/2.62 | | % 13.67/2.62 | | (6) ~ (all_12_0 = e0) % 13.67/2.62 | | % 13.67/2.62 | | REDUCE: (2), (6) imply: % 13.67/2.62 | | (7) $false % 13.67/2.62 | | % 13.67/2.62 | | CLOSE: (7) is inconsistent. % 13.67/2.62 | | % 13.67/2.62 | Case 2: % 13.67/2.62 | | % 13.67/2.62 | | (8) ~ (all_12_1 = e0) | ~ (all_12_2 = e0) | ~ (all_12_3 = e0) % 13.67/2.62 | | % 13.67/2.62 | | BETA: splitting (8) gives: % 13.67/2.62 | | % 13.67/2.62 | | Case 1: % 13.67/2.62 | | | % 13.67/2.62 | | | (9) ~ (all_12_1 = e0) % 13.67/2.62 | | | % 13.67/2.62 | | | REDUCE: (1), (9) imply: % 13.67/2.62 | | | (10) $false % 13.67/2.62 | | | % 13.67/2.62 | | | CLOSE: (10) is inconsistent. % 13.67/2.62 | | | % 13.67/2.62 | | Case 2: % 13.67/2.62 | | | % 13.67/2.62 | | | (11) ~ (all_12_2 = e0) | ~ (all_12_3 = e0) % 13.67/2.62 | | | % 13.67/2.62 | | | BETA: splitting (11) gives: % 13.67/2.62 | | | % 13.67/2.62 | | | Case 1: % 13.67/2.62 | | | | % 13.67/2.62 | | | | (12) ~ (all_12_2 = e0) % 13.67/2.62 | | | | % 13.67/2.62 | | | | REDUCE: (5), (12) imply: % 13.67/2.62 | | | | (13) $false % 13.67/2.62 | | | | % 13.67/2.62 | | | | CLOSE: (13) is inconsistent. % 13.67/2.62 | | | | % 13.67/2.62 | | | Case 2: % 13.67/2.62 | | | | % 13.67/2.62 | | | | (14) ~ (all_12_3 = e0) % 13.67/2.62 | | | | % 13.67/2.62 | | | | REDUCE: (4), (14) imply: % 13.67/2.62 | | | | (15) $false % 13.67/2.62 | | | | % 13.67/2.62 | | | | CLOSE: (15) is inconsistent. % 13.67/2.62 | | | | % 13.67/2.62 | | | End of split % 13.67/2.62 | | | % 13.67/2.62 | | End of split % 13.67/2.62 | | % 13.67/2.62 | End of split % 13.67/2.62 | % 13.67/2.62 End of proof % 13.67/2.62 % SZS output end Proof for theBenchmark % 13.67/2.62 % 13.67/2.62 2008ms %------------------------------------------------------------------------------