%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : RNG084+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n027.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 : 600s % DateTime : Mon Jul 18 20:25:18 EDT 2022 % Result : Theorem 5.40s 1.90s % Output : Proof 9.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : RNG084+1 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n027.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Mon May 30 18:40:46 EDT 2022 % 0.12/0.33 % CPUTime : % 0.20/0.58 ____ _ % 0.20/0.58 ___ / __ \_____(_)___ ________ __________ % 0.20/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.20/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.20/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.20/0.58 % 0.20/0.58 A Theorem Prover for First-Order Logic % 0.20/0.58 (ePrincess v.1.0) % 0.20/0.58 % 0.20/0.58 (c) Philipp Rümmer, 2009-2015 % 0.20/0.58 (c) Peter Backeman, 2014-2015 % 0.20/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.20/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.20/0.58 Bug reports to peter@backeman.se % 0.20/0.58 % 0.20/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.20/0.58 % 0.20/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.76/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.66/0.93 Prover 0: Preprocessing ... % 2.79/1.28 Prover 0: Constructing countermodel ... % 5.40/1.89 Prover 0: proved (1260ms) % 5.40/1.89 % 5.40/1.89 No countermodel exists, formula is valid % 5.40/1.90 % SZS status Theorem for theBenchmark % 5.40/1.90 % 5.40/1.90 Generating proof ... found it (size 145) % 8.60/2.62 % 8.60/2.62 % SZS output start Proof for theBenchmark % 8.60/2.62 Assumed formulas after preprocessing and simplification: % 8.60/2.62 | (0) ? [v0] : ? [v1] : ( ~ (sz10 = sz00) & sdtpldt1(xI, xJ) = v1 & smndt0(sz10) = v0 & aIdeal0(xJ) & aIdeal0(xI) & aElement0(sz10) & aElement0(sz00) & ~ aIdeal0(v1) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt1(v2, v3) = v4) | ~ (sdtpldt0(v6, v7) = v5) | ~ aElementOf0(v7, v3) | ~ aElementOf0(v6, v2) | ~ aSet0(v3) | ~ aSet0(v2) | aElementOf0(v5, v4)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v4, v2) = v6) | ~ (sdtasdt0(v3, v2) = v5) | ~ (sdtpldt0(v5, v6) = v7) | ~ aElement0(v4) | ~ aElement0(v3) | ~ aElement0(v2) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (sdtasdt0(v8, v2) = v7 & sdtasdt0(v2, v8) = v9 & sdtasdt0(v2, v4) = v11 & sdtasdt0(v2, v3) = v10 & sdtpldt0(v10, v11) = v9 & sdtpldt0(v3, v4) = v8)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v2, v4) = v6) | ~ (sdtasdt0(v2, v3) = v5) | ~ (sdtpldt0(v5, v6) = v7) | ~ aElement0(v4) | ~ aElement0(v3) | ~ aElement0(v2) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (sdtasdt0(v8, v2) = v9 & sdtasdt0(v4, v2) = v11 & sdtasdt0(v3, v2) = v10 & sdtasdt0(v2, v8) = v7 & sdtpldt0(v10, v11) = v9 & sdtpldt0(v3, v4) = v8)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v5, v4) = v6) | ~ (sdtasdt0(v2, v3) = v5) | ~ aElement0(v4) | ~ aElement0(v3) | ~ aElement0(v2) | ? [v7] : (sdtasdt0(v3, v4) = v7 & sdtasdt0(v2, v7) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v5, v2) = v6) | ~ (sdtpldt0(v3, v4) = v5) | ~ aElement0(v4) | ~ aElement0(v3) | ~ aElement0(v2) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (sdtasdt0(v4, v2) = v11 & sdtasdt0(v3, v2) = v10 & sdtasdt0(v2, v5) = v7 & sdtasdt0(v2, v4) = v9 & sdtasdt0(v2, v3) = v8 & sdtpldt0(v10, v11) = v6 & sdtpldt0(v8, v9) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v3, v4) = v5) | ~ (sdtasdt0(v2, v5) = v6) | ~ aElement0(v4) | ~ aElement0(v3) | ~ aElement0(v2) | ? [v7] : (sdtasdt0(v7, v4) = v6 & sdtasdt0(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v2, v5) = v6) | ~ (sdtpldt0(v3, v4) = v5) | ~ aElement0(v4) | ~ aElement0(v3) | ~ aElement0(v2) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (sdtasdt0(v5, v2) = v9 & sdtasdt0(v4, v2) = v11 & sdtasdt0(v3, v2) = v10 & sdtasdt0(v2, v4) = v8 & sdtasdt0(v2, v3) = v7 & sdtpldt0(v10, v11) = v9 & sdtpldt0(v7, v8) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ aElement0(v4) | ~ aElement0(v3) | ~ aElement0(v2) | ? [v7] : (sdtpldt0(v3, v4) = v7 & sdtpldt0(v2, v7) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v3, v4) = v5) | ~ (sdtpldt0(v2, v5) = v6) | ~ aElement0(v4) | ~ aElement0(v3) | ~ aElement0(v2) | ? [v7] : (sdtpldt0(v7, v4) = v6 & sdtpldt0(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtasasdt0(v2, v3) = v4) | ~ aSet0(v5) | ~ aSet0(v3) | ~ aSet0(v2) | ? [v6] : (( ~ aElementOf0(v6, v5) | ~ aElementOf0(v6, v3) | ~ aElementOf0(v6, v2)) & (aElementOf0(v6, v5) | (aElementOf0(v6, v3) & aElementOf0(v6, v2))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtpldt1(v2, v3) = v4) | ~ aSet0(v5) | ~ aSet0(v3) | ~ aSet0(v2) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (( ~ aElementOf0(v6, v5) | ! [v10] : ! [v11] : ( ~ (sdtpldt0(v10, v11) = v6) | ~ aElementOf0(v11, v3) | ~ aElementOf0(v10, v2))) & (aElementOf0(v6, v5) | (v9 = v6 & sdtpldt0(v7, v8) = v6 & aElementOf0(v8, v3) & aElementOf0(v7, v2))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sdtasasdt0(v5, v4) = v3) | ~ (sdtasasdt0(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sdtpldt1(v5, v4) = v3) | ~ (sdtpldt1(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sdtasdt0(v5, v4) = v3) | ~ (sdtasdt0(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sdtpldt0(v5, v4) = v3) | ~ (sdtpldt0(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasasdt0(v2, v3) = v4) | ~ aElementOf0(v5, v4) | ~ aSet0(v3) | ~ aSet0(v2) | aElementOf0(v5, v3)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasasdt0(v2, v3) = v4) | ~ aElementOf0(v5, v4) | ~ aSet0(v3) | ~ aSet0(v2) | aElementOf0(v5, v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasasdt0(v2, v3) = v4) | ~ aElementOf0(v5, v3) | ~ aElementOf0(v5, v2) | ~ aSet0(v3) | ~ aSet0(v2) | aElementOf0(v5, v4)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtpldt1(v2, v3) = v4) | ~ aElementOf0(v5, v4) | ~ aSet0(v3) | ~ aSet0(v2) | ? [v6] : ? [v7] : (sdtpldt0(v6, v7) = v5 & aElementOf0(v7, v3) & aElementOf0(v6, v2))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v4, v3) = v5) | ~ aIdeal0(v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v4) | aElementOf0(v5, v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtpldt0(v3, v4) = v5) | ~ aIdeal0(v2) | ~ aElementOf0(v4, v2) | ~ aElementOf0(v3, v2) | aElementOf0(v5, v2)) & ! [v2] : ! [v3] : ! [v4] : (v4 = sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (smndt0(v2) = v3) | ~ aElement0(v2)) & ! [v2] : ! [v3] : ! [v4] : (v4 = sz00 | ~ (sdtpldt0(v2, v3) = v4) | ~ (smndt0(v2) = v3) | ~ aElement0(v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (smndt0(v4) = v3) | ~ (smndt0(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasasdt0(v2, v3) = v4) | ~ aSet0(v3) | ~ aSet0(v2) | aSet0(v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt1(v2, v3) = v4) | ~ aSet0(v3) | ~ aSet0(v2) | aSet0(v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ aElement0(v3) | ~ aElement0(v2) | sdtasdt0(v2, v3) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v2, v3) = v4) | ~ aElement0(v3) | ~ aElement0(v2) | sdtasdt0(v3, v2) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v2, v3) = v4) | ~ aElement0(v3) | ~ aElement0(v2) | aElement0(v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (smndt0(v2) = v3) | ~ aElement0(v2) | sdtpldt0(v2, v3) = sz00) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ aElement0(v3) | ~ aElement0(v2) | sdtpldt0(v2, v3) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v2, v3) = v4) | ~ (smndt0(v2) = v3) | ~ aElement0(v2) | sdtpldt0(v3, v2) = sz00) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v2, v3) = v4) | ~ aElement0(v3) | ~ aElement0(v2) | sdtpldt0(v3, v2) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v2, v3) = v4) | ~ aElement0(v3) | ~ aElement0(v2) | aElement0(v4)) & ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtasdt0(v2, sz10) = v3) | ~ aElement0(v2)) & ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtasdt0(sz10, v2) = v3) | ~ aElement0(v2)) & ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtpldt0(v2, sz00) = v3) | ~ aElement0(v2)) & ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtpldt0(sz00, v2) = v3) | ~ aElement0(v2)) & ! [v2] : ! [v3] : (v3 = v2 | ~ aSet0(v3) | ~ aSet0(v2) | ? [v4] : ((aElementOf0(v4, v3) & ~ aElementOf0(v4, v2)) | (aElementOf0(v4, v2) & ~ aElementOf0(v4, v3)))) & ! [v2] : ! [v3] : (v3 = sz00 | v2 = sz00 | ~ (sdtasdt0(v2, v3) = sz00) | ~ aElement0(v3) | ~ aElement0(v2)) & ! [v2] : ! [v3] : (v3 = sz00 | ~ (sdtasdt0(v2, sz00) = v3) | ~ aElement0(v2)) & ! [v2] : ! [v3] : (v3 = sz00 | ~ (sdtasdt0(sz00, v2) = v3) | ~ aElement0(v2)) & ! [v2] : ! [v3] : ( ~ (sdtasdt0(v2, v0) = v3) | ~ aElement0(v2) | (sdtasdt0(v0, v2) = v3 & smndt0(v2) = v3)) & ! [v2] : ! [v3] : ( ~ (sdtasdt0(v2, sz10) = v3) | ~ aElement0(v2) | sdtasdt0(sz10, v2) = v2) & ! [v2] : ! [v3] : ( ~ (sdtasdt0(v2, sz00) = v3) | ~ aElement0(v2) | sdtasdt0(sz00, v2) = sz00) & ! [v2] : ! [v3] : ( ~ (sdtasdt0(v0, v2) = v3) | ~ aElement0(v2) | (sdtasdt0(v2, v0) = v3 & smndt0(v2) = v3)) & ! [v2] : ! [v3] : ( ~ (sdtasdt0(sz10, v2) = v3) | ~ aElement0(v2) | sdtasdt0(v2, sz10) = v2) & ! [v2] : ! [v3] : ( ~ (sdtasdt0(sz00, v2) = v3) | ~ aElement0(v2) | sdtasdt0(v2, sz00) = sz00) & ! [v2] : ! [v3] : ( ~ (sdtpldt0(v2, sz00) = v3) | ~ aElement0(v2) | sdtpldt0(sz00, v2) = v2) & ! [v2] : ! [v3] : ( ~ (sdtpldt0(sz00, v2) = v3) | ~ aElement0(v2) | sdtpldt0(v2, sz00) = v2) & ! [v2] : ! [v3] : ( ~ (smndt0(v2) = v3) | ~ aElement0(v2) | aElement0(v3)) & ! [v2] : ! [v3] : ( ~ (smndt0(v2) = v3) | ~ aElement0(v2) | (sdtasdt0(v2, v0) = v3 & sdtasdt0(v0, v2) = v3)) & ! [v2] : ! [v3] : ( ~ aElementOf0(v3, v2) | ~ aSet0(v2) | aElement0(v3)) & ! [v2] : ( ~ aIdeal0(v2) | aSet0(v2)) & ! [v2] : ( ~ aSet0(v2) | aIdeal0(v2) | ? [v3] : ? [v4] : ? [v5] : (aElementOf0(v3, v2) & ((sdtasdt0(v4, v3) = v5 & aElement0(v4) & ~ aElementOf0(v5, v2)) | (sdtpldt0(v3, v4) = v5 & aElementOf0(v4, v2) & ~ aElementOf0(v5, v2)))))) % 9.05/2.67 | Instantiating (0) with all_0_0_0, all_0_1_1 yields: % 9.05/2.67 | (1) ~ (sz10 = sz00) & sdtpldt1(xI, xJ) = all_0_0_0 & smndt0(sz10) = all_0_1_1 & aIdeal0(xJ) & aIdeal0(xI) & aElement0(sz10) & aElement0(sz00) & ~ aIdeal0(all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ (sdtpldt0(v4, v5) = v3) | ~ aElementOf0(v5, v1) | ~ aElementOf0(v4, v0) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & sdtpldt0(v6, v7) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtasasdt0(v0, v1) = v2) | ~ aSet0(v3) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4] : (( ~ aElementOf0(v4, v3) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v4, v0)) & (aElementOf0(v4, v3) | (aElementOf0(v4, v1) & aElementOf0(v4, v0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtpldt1(v0, v1) = v2) | ~ aSet0(v3) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ aElementOf0(v4, v3) | ! [v8] : ! [v9] : ( ~ (sdtpldt0(v8, v9) = v4) | ~ aElementOf0(v9, v1) | ~ aElementOf0(v8, v0))) & (aElementOf0(v4, v3) | (v7 = v4 & sdtpldt0(v5, v6) = v4 & aElementOf0(v6, v1) & aElementOf0(v5, v0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | ~ (sdtpldt1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ aElementOf0(v3, v1) | ~ aElementOf0(v3, v0) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4] : ? [v5] : (sdtpldt0(v4, v5) = v3 & aElementOf0(v5, v1) & aElementOf0(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasdt0(v2, v1) = v3) | ~ aIdeal0(v0) | ~ aElementOf0(v1, v0) | ~ aElement0(v2) | aElementOf0(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ aIdeal0(v0) | ~ aElementOf0(v2, v0) | ~ aElementOf0(v1, v0) | aElementOf0(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = sz00 | ~ (sdtpldt0(v1, v0) = v2) | ~ (smndt0(v0) = v1) | ~ aElement0(v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = sz00 | ~ (sdtpldt0(v0, v1) = v2) | ~ (smndt0(v0) = v1) | ~ aElement0(v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | sdtasdt0(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | sdtasdt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ (smndt0(v0) = v1) | ~ aElement0(v0) | sdtpldt0(v0, v1) = sz00) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | sdtpldt0(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ (smndt0(v0) = v1) | ~ aElement0(v0) | sdtpldt0(v1, v0) = sz00) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | sdtpldt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aElement0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aElement0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aElement0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aElement0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ aSet0(v1) | ~ aSet0(v0) | ? [v2] : ((aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)) | (aElementOf0(v2, v0) & ~ aElementOf0(v2, v1)))) & ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aElement0(v1) | ~ aElement0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aElement0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aElement0(v0)) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, all_0_1_1) = v1) | ~ aElement0(v0) | (sdtasdt0(all_0_1_1, v0) = v1 & smndt0(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aElement0(v0) | sdtasdt0(sz10, v0) = v0) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aElement0(v0) | sdtasdt0(sz00, v0) = sz00) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(all_0_1_1, v0) = v1) | ~ aElement0(v0) | (sdtasdt0(v0, all_0_1_1) = v1 & smndt0(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aElement0(v0) | sdtasdt0(v0, sz10) = v0) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aElement0(v0) | sdtasdt0(v0, sz00) = sz00) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aElement0(v0) | sdtpldt0(sz00, v0) = v0) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aElement0(v0) | sdtpldt0(v0, sz00) = v0) & ! [v0] : ! [v1] : ( ~ (smndt0(v0) = v1) | ~ aElement0(v0) | aElement0(v1)) & ! [v0] : ! [v1] : ( ~ (smndt0(v0) = v1) | ~ aElement0(v0) | (sdtasdt0(v0, all_0_1_1) = v1 & sdtasdt0(all_0_1_1, v0) = v1)) & ! [v0] : ! [v1] : ( ~ aElementOf0(v1, v0) | ~ aSet0(v0) | aElement0(v1)) & ! [v0] : ( ~ aIdeal0(v0) | aSet0(v0)) & ! [v0] : ( ~ aSet0(v0) | aIdeal0(v0) | ? [v1] : ? [v2] : ? [v3] : (aElementOf0(v1, v0) & ((sdtasdt0(v2, v1) = v3 & aElement0(v2) & ~ aElementOf0(v3, v0)) | (sdtpldt0(v1, v2) = v3 & aElementOf0(v2, v0) & ~ aElementOf0(v3, v0))))) % 9.05/2.69 | % 9.05/2.69 | Applying alpha-rule on (1) yields: % 9.05/2.69 | (2) ! [v0] : ! [v1] : ( ~ (smndt0(v0) = v1) | ~ aElement0(v0) | (sdtasdt0(v0, all_0_1_1) = v1 & sdtasdt0(all_0_1_1, v0) = v1)) % 9.05/2.69 | (3) aIdeal0(xI) % 9.05/2.69 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ aElementOf0(v3, v1) | ~ aElementOf0(v3, v0) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) % 9.05/2.69 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) % 9.05/2.69 | (6) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aElement0(v0) | sdtasdt0(sz10, v0) = v0) % 9.05/2.69 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4)) % 9.05/2.69 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 9.17/2.69 | (9) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aElement0(v0) | sdtasdt0(v0, sz10) = v0) % 9.17/2.69 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v1)) % 9.17/2.69 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 9.17/2.69 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) % 9.17/2.69 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2)) % 9.17/2.70 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5)) % 9.17/2.70 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2)) % 9.17/2.70 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | sdtpldt0(v1, v0) = v2) % 9.17/2.70 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2)) % 9.17/2.70 | (18) ! [v0] : ! [v1] : ( ~ aElementOf0(v1, v0) | ~ aSet0(v0) | aElement0(v1)) % 9.17/2.70 | (19) ! [v0] : ( ~ aIdeal0(v0) | aSet0(v0)) % 9.17/2.70 | (20) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aElement0(v0)) % 9.17/2.70 | (21) ! [v0] : ! [v1] : ( ~ (smndt0(v0) = v1) | ~ aElement0(v0) | aElement0(v1)) % 9.17/2.70 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aElement0(v0)) % 9.17/2.70 | (23) ! [v0] : ( ~ aSet0(v0) | aIdeal0(v0) | ? [v1] : ? [v2] : ? [v3] : (aElementOf0(v1, v0) & ((sdtasdt0(v2, v1) = v3 & aElement0(v2) & ~ aElementOf0(v3, v0)) | (sdtpldt0(v1, v2) = v3 & aElementOf0(v2, v0) & ~ aElementOf0(v3, v0))))) % 9.17/2.70 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = sz00 | ~ (sdtpldt0(v0, v1) = v2) | ~ (smndt0(v0) = v1) | ~ aElement0(v0)) % 9.17/2.70 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) % 9.17/2.70 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ (smndt0(v0) = v1) | ~ aElement0(v0) | sdtpldt0(v0, v1) = sz00) % 9.17/2.70 | (27) aIdeal0(xJ) % 9.17/2.70 | (28) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aElement0(v0)) % 9.17/2.70 | (29) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aElement0(v0) | sdtasdt0(v0, sz00) = sz00) % 9.17/2.70 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4)) % 9.17/2.70 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | sdtasdt0(v0, v1) = v2) % 9.17/2.70 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | sdtpldt0(v0, v1) = v2) % 9.17/2.70 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | ~ (sdtpldt1(v3, v2) = v0)) % 9.17/2.70 | (34) sdtpldt1(xI, xJ) = all_0_0_0 % 9.17/2.70 | (35) ~ (sz10 = sz00) % 9.17/2.70 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ (smndt0(v0) = v1) | ~ aElement0(v0) | sdtpldt0(v1, v0) = sz00) % 9.17/2.70 | (37) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aElement0(v0) | sdtpldt0(sz00, v0) = v0) % 9.17/2.70 | (38) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aElement0(v0)) % 9.17/2.70 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2)) % 9.17/2.70 | (40) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aElement0(v0)) % 9.17/2.70 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4] : ? [v5] : (sdtpldt0(v4, v5) = v3 & aElementOf0(v5, v1) & aElementOf0(v4, v0))) % 9.17/2.70 | (42) ! [v0] : ! [v1] : ( ~ (sdtasdt0(all_0_1_1, v0) = v1) | ~ aElement0(v0) | (sdtasdt0(v0, all_0_1_1) = v1 & smndt0(v0) = v1)) % 9.17/2.70 | (43) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, all_0_1_1) = v1) | ~ aElement0(v0) | (sdtasdt0(all_0_1_1, v0) = v1 & smndt0(v0) = v1)) % 9.17/2.70 | (44) ! [v0] : ! [v1] : ! [v2] : (v2 = sz00 | ~ (sdtpldt0(v1, v0) = v2) | ~ (smndt0(v0) = v1) | ~ aElement0(v0)) % 9.17/2.70 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ aIdeal0(v0) | ~ aElementOf0(v2, v0) | ~ aElementOf0(v1, v0) | aElementOf0(v3, v0)) % 9.17/2.70 | (46) ~ aIdeal0(all_0_0_0) % 9.17/2.70 | (47) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aElement0(v0)) % 9.17/2.70 | (48) ! [v0] : ! [v1] : (v1 = v0 | ~ aSet0(v1) | ~ aSet0(v0) | ? [v2] : ((aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)) | (aElementOf0(v2, v0) & ~ aElementOf0(v2, v1)))) % 9.17/2.70 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) % 9.17/2.71 | (50) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aElement0(v1) | ~ aElement0(v0)) % 9.17/2.71 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasdt0(v2, v1) = v3) | ~ aIdeal0(v0) | ~ aElementOf0(v1, v0) | ~ aElement0(v2) | aElementOf0(v3, v0)) % 9.17/2.71 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5)) % 9.17/2.71 | (53) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aElement0(v0) | sdtasdt0(sz00, v0) = sz00) % 9.17/2.71 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtpldt1(v0, v1) = v2) | ~ aSet0(v3) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ aElementOf0(v4, v3) | ! [v8] : ! [v9] : ( ~ (sdtpldt0(v8, v9) = v4) | ~ aElementOf0(v9, v1) | ~ aElementOf0(v8, v0))) & (aElementOf0(v4, v3) | (v7 = v4 & sdtpldt0(v5, v6) = v4 & aElementOf0(v6, v1) & aElementOf0(v5, v0))))) % 9.17/2.71 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4)) % 9.17/2.71 | (56) smndt0(sz10) = all_0_1_1 % 9.17/2.71 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & sdtpldt0(v6, v7) = v5)) % 9.17/2.71 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ (sdtpldt0(v4, v5) = v3) | ~ aElementOf0(v5, v1) | ~ aElementOf0(v4, v0) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) % 9.17/2.71 | (59) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aElement0(v0) | sdtpldt0(v0, sz00) = v0) % 9.17/2.71 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | sdtasdt0(v1, v0) = v2) % 9.17/2.71 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtasasdt0(v0, v1) = v2) | ~ aSet0(v3) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4] : (( ~ aElementOf0(v4, v3) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v4, v0)) & (aElementOf0(v4, v3) | (aElementOf0(v4, v1) & aElementOf0(v4, v0))))) % 9.17/2.71 | (62) aElement0(sz10) % 9.17/2.71 | (63) aElement0(sz00) % 9.17/2.71 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0)) % 9.17/2.71 | % 9.17/2.71 | Instantiating formula (19) with xJ and discharging atoms aIdeal0(xJ), yields: % 9.17/2.71 | (65) aSet0(xJ) % 9.17/2.71 | % 9.17/2.71 | Instantiating formula (19) with xI and discharging atoms aIdeal0(xI), yields: % 9.17/2.71 | (66) aSet0(xI) % 9.17/2.71 | % 9.17/2.71 | Instantiating formula (17) with all_0_0_0, xJ, xI and discharging atoms sdtpldt1(xI, xJ) = all_0_0_0, aSet0(xJ), aSet0(xI), yields: % 9.17/2.71 | (67) aSet0(all_0_0_0) % 9.17/2.71 | % 9.17/2.71 | Instantiating formula (23) with all_0_0_0 and discharging atoms aSet0(all_0_0_0), ~ aIdeal0(all_0_0_0), yields: % 9.17/2.71 | (68) ? [v0] : ? [v1] : ? [v2] : (aElementOf0(v0, all_0_0_0) & ((sdtasdt0(v1, v0) = v2 & aElement0(v1) & ~ aElementOf0(v2, all_0_0_0)) | (sdtpldt0(v0, v1) = v2 & aElementOf0(v1, all_0_0_0) & ~ aElementOf0(v2, all_0_0_0)))) % 9.17/2.71 | % 9.17/2.71 | Instantiating (68) with all_28_0_4, all_28_1_5, all_28_2_6 yields: % 9.17/2.71 | (69) aElementOf0(all_28_2_6, all_0_0_0) & ((sdtasdt0(all_28_1_5, all_28_2_6) = all_28_0_4 & aElement0(all_28_1_5) & ~ aElementOf0(all_28_0_4, all_0_0_0)) | (sdtpldt0(all_28_2_6, all_28_1_5) = all_28_0_4 & aElementOf0(all_28_1_5, all_0_0_0) & ~ aElementOf0(all_28_0_4, all_0_0_0))) % 9.17/2.71 | % 9.17/2.71 | Applying alpha-rule on (69) yields: % 9.17/2.71 | (70) aElementOf0(all_28_2_6, all_0_0_0) % 9.17/2.71 | (71) (sdtasdt0(all_28_1_5, all_28_2_6) = all_28_0_4 & aElement0(all_28_1_5) & ~ aElementOf0(all_28_0_4, all_0_0_0)) | (sdtpldt0(all_28_2_6, all_28_1_5) = all_28_0_4 & aElementOf0(all_28_1_5, all_0_0_0) & ~ aElementOf0(all_28_0_4, all_0_0_0)) % 9.17/2.71 | % 9.17/2.71 | Instantiating formula (41) with all_28_2_6, all_0_0_0, xJ, xI and discharging atoms sdtpldt1(xI, xJ) = all_0_0_0, aElementOf0(all_28_2_6, all_0_0_0), aSet0(xJ), aSet0(xI), yields: % 9.17/2.71 | (72) ? [v0] : ? [v1] : (sdtpldt0(v0, v1) = all_28_2_6 & aElementOf0(v1, xJ) & aElementOf0(v0, xI)) % 9.17/2.71 | % 9.17/2.71 | Instantiating formula (18) with all_28_2_6, all_0_0_0 and discharging atoms aElementOf0(all_28_2_6, all_0_0_0), aSet0(all_0_0_0), yields: % 9.17/2.72 | (73) aElement0(all_28_2_6) % 9.17/2.72 | % 9.17/2.72 | Instantiating (72) with all_36_0_7, all_36_1_8 yields: % 9.17/2.72 | (74) sdtpldt0(all_36_1_8, all_36_0_7) = all_28_2_6 & aElementOf0(all_36_0_7, xJ) & aElementOf0(all_36_1_8, xI) % 9.17/2.72 | % 9.17/2.72 | Applying alpha-rule on (74) yields: % 9.17/2.72 | (75) sdtpldt0(all_36_1_8, all_36_0_7) = all_28_2_6 % 9.17/2.72 | (76) aElementOf0(all_36_0_7, xJ) % 9.17/2.72 | (77) aElementOf0(all_36_1_8, xI) % 9.17/2.72 | % 9.17/2.72 | Instantiating formula (18) with all_36_0_7, xJ and discharging atoms aElementOf0(all_36_0_7, xJ), aSet0(xJ), yields: % 9.17/2.72 | (78) aElement0(all_36_0_7) % 9.17/2.72 | % 9.17/2.72 | Instantiating formula (18) with all_36_1_8, xI and discharging atoms aElementOf0(all_36_1_8, xI), aSet0(xI), yields: % 9.17/2.72 | (79) aElement0(all_36_1_8) % 9.17/2.72 | % 9.17/2.72 | Instantiating formula (32) with all_28_2_6, all_36_1_8, all_36_0_7 and discharging atoms sdtpldt0(all_36_1_8, all_36_0_7) = all_28_2_6, aElement0(all_36_0_7), aElement0(all_36_1_8), yields: % 9.17/2.72 | (80) sdtpldt0(all_36_0_7, all_36_1_8) = all_28_2_6 % 9.17/2.72 | % 9.17/2.72 +-Applying beta-rule and splitting (71), into two cases. % 9.17/2.72 |-Branch one: % 9.17/2.72 | (81) sdtasdt0(all_28_1_5, all_28_2_6) = all_28_0_4 & aElement0(all_28_1_5) & ~ aElementOf0(all_28_0_4, all_0_0_0) % 9.17/2.72 | % 9.17/2.72 | Applying alpha-rule on (81) yields: % 9.17/2.72 | (82) sdtasdt0(all_28_1_5, all_28_2_6) = all_28_0_4 % 9.17/2.72 | (83) aElement0(all_28_1_5) % 9.17/2.72 | (84) ~ aElementOf0(all_28_0_4, all_0_0_0) % 9.17/2.72 | % 9.17/2.72 | Instantiating formula (55) with all_28_0_4, all_28_2_6, all_36_1_8, all_36_0_7, all_28_1_5 and discharging atoms sdtasdt0(all_28_1_5, all_28_2_6) = all_28_0_4, sdtpldt0(all_36_0_7, all_36_1_8) = all_28_2_6, aElement0(all_36_0_7), aElement0(all_36_1_8), aElement0(all_28_1_5), yields: % 9.17/2.72 | (85) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_36_0_7, all_28_1_5) = v3 & sdtasdt0(all_36_1_8, all_28_1_5) = v4 & sdtasdt0(all_28_1_5, all_36_0_7) = v0 & sdtasdt0(all_28_1_5, all_36_1_8) = v1 & sdtasdt0(all_28_2_6, all_28_1_5) = v2 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_28_0_4) % 9.17/2.72 | % 9.17/2.72 | Instantiating formula (55) with all_28_0_4, all_28_2_6, all_36_0_7, all_36_1_8, all_28_1_5 and discharging atoms sdtasdt0(all_28_1_5, all_28_2_6) = all_28_0_4, sdtpldt0(all_36_1_8, all_36_0_7) = all_28_2_6, aElement0(all_36_0_7), aElement0(all_36_1_8), aElement0(all_28_1_5), yields: % 9.17/2.72 | (86) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_36_0_7, all_28_1_5) = v4 & sdtasdt0(all_36_1_8, all_28_1_5) = v3 & sdtasdt0(all_28_1_5, all_36_0_7) = v1 & sdtasdt0(all_28_1_5, all_36_1_8) = v0 & sdtasdt0(all_28_2_6, all_28_1_5) = v2 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_28_0_4) % 9.17/2.72 | % 9.17/2.72 | Instantiating formula (31) with all_28_0_4, all_28_1_5, all_28_2_6 and discharging atoms sdtasdt0(all_28_1_5, all_28_2_6) = all_28_0_4, aElement0(all_28_1_5), aElement0(all_28_2_6), yields: % 9.17/2.72 | (87) sdtasdt0(all_28_2_6, all_28_1_5) = all_28_0_4 % 9.17/2.72 | % 9.17/2.72 | Instantiating (86) with all_97_0_34, all_97_1_35, all_97_2_36, all_97_3_37, all_97_4_38 yields: % 9.17/2.72 | (88) sdtasdt0(all_36_0_7, all_28_1_5) = all_97_0_34 & sdtasdt0(all_36_1_8, all_28_1_5) = all_97_1_35 & sdtasdt0(all_28_1_5, all_36_0_7) = all_97_3_37 & sdtasdt0(all_28_1_5, all_36_1_8) = all_97_4_38 & sdtasdt0(all_28_2_6, all_28_1_5) = all_97_2_36 & sdtpldt0(all_97_1_35, all_97_0_34) = all_97_2_36 & sdtpldt0(all_97_4_38, all_97_3_37) = all_28_0_4 % 9.17/2.72 | % 9.17/2.72 | Applying alpha-rule on (88) yields: % 9.17/2.72 | (89) sdtasdt0(all_36_0_7, all_28_1_5) = all_97_0_34 % 9.17/2.72 | (90) sdtasdt0(all_28_1_5, all_36_0_7) = all_97_3_37 % 9.17/2.72 | (91) sdtasdt0(all_36_1_8, all_28_1_5) = all_97_1_35 % 9.17/2.72 | (92) sdtpldt0(all_97_1_35, all_97_0_34) = all_97_2_36 % 9.17/2.72 | (93) sdtasdt0(all_28_2_6, all_28_1_5) = all_97_2_36 % 9.17/2.72 | (94) sdtasdt0(all_28_1_5, all_36_1_8) = all_97_4_38 % 9.17/2.72 | (95) sdtpldt0(all_97_4_38, all_97_3_37) = all_28_0_4 % 9.17/2.72 | % 9.17/2.72 | Instantiating (85) with all_99_0_39, all_99_1_40, all_99_2_41, all_99_3_42, all_99_4_43 yields: % 9.17/2.72 | (96) sdtasdt0(all_36_0_7, all_28_1_5) = all_99_1_40 & sdtasdt0(all_36_1_8, all_28_1_5) = all_99_0_39 & sdtasdt0(all_28_1_5, all_36_0_7) = all_99_4_43 & sdtasdt0(all_28_1_5, all_36_1_8) = all_99_3_42 & sdtasdt0(all_28_2_6, all_28_1_5) = all_99_2_41 & sdtpldt0(all_99_1_40, all_99_0_39) = all_99_2_41 & sdtpldt0(all_99_4_43, all_99_3_42) = all_28_0_4 % 9.17/2.72 | % 9.17/2.72 | Applying alpha-rule on (96) yields: % 9.32/2.72 | (97) sdtpldt0(all_99_4_43, all_99_3_42) = all_28_0_4 % 9.32/2.72 | (98) sdtpldt0(all_99_1_40, all_99_0_39) = all_99_2_41 % 9.32/2.72 | (99) sdtasdt0(all_28_1_5, all_36_1_8) = all_99_3_42 % 9.32/2.72 | (100) sdtasdt0(all_36_1_8, all_28_1_5) = all_99_0_39 % 9.32/2.72 | (101) sdtasdt0(all_36_0_7, all_28_1_5) = all_99_1_40 % 9.32/2.72 | (102) sdtasdt0(all_28_1_5, all_36_0_7) = all_99_4_43 % 9.32/2.72 | (103) sdtasdt0(all_28_2_6, all_28_1_5) = all_99_2_41 % 9.32/2.72 | % 9.32/2.72 | Instantiating formula (8) with all_36_0_7, all_28_1_5, all_97_0_34, all_99_1_40 and discharging atoms sdtasdt0(all_36_0_7, all_28_1_5) = all_99_1_40, sdtasdt0(all_36_0_7, all_28_1_5) = all_97_0_34, yields: % 9.32/2.72 | (104) all_99_1_40 = all_97_0_34 % 9.32/2.72 | % 9.32/2.72 | Instantiating formula (8) with all_36_1_8, all_28_1_5, all_97_1_35, all_99_0_39 and discharging atoms sdtasdt0(all_36_1_8, all_28_1_5) = all_99_0_39, sdtasdt0(all_36_1_8, all_28_1_5) = all_97_1_35, yields: % 9.32/2.72 | (105) all_99_0_39 = all_97_1_35 % 9.32/2.72 | % 9.32/2.72 | Instantiating formula (8) with all_28_1_5, all_36_0_7, all_97_3_37, all_99_4_43 and discharging atoms sdtasdt0(all_28_1_5, all_36_0_7) = all_99_4_43, sdtasdt0(all_28_1_5, all_36_0_7) = all_97_3_37, yields: % 9.32/2.72 | (106) all_99_4_43 = all_97_3_37 % 9.32/2.72 | % 9.32/2.72 | Instantiating formula (8) with all_28_1_5, all_36_1_8, all_97_4_38, all_99_3_42 and discharging atoms sdtasdt0(all_28_1_5, all_36_1_8) = all_99_3_42, sdtasdt0(all_28_1_5, all_36_1_8) = all_97_4_38, yields: % 9.32/2.73 | (107) all_99_3_42 = all_97_4_38 % 9.32/2.73 | % 9.32/2.73 | Instantiating formula (8) with all_28_2_6, all_28_1_5, all_97_2_36, all_99_2_41 and discharging atoms sdtasdt0(all_28_2_6, all_28_1_5) = all_99_2_41, sdtasdt0(all_28_2_6, all_28_1_5) = all_97_2_36, yields: % 9.32/2.73 | (108) all_99_2_41 = all_97_2_36 % 9.32/2.73 | % 9.32/2.73 | Instantiating formula (8) with all_28_2_6, all_28_1_5, all_28_0_4, all_99_2_41 and discharging atoms sdtasdt0(all_28_2_6, all_28_1_5) = all_99_2_41, sdtasdt0(all_28_2_6, all_28_1_5) = all_28_0_4, yields: % 9.32/2.73 | (109) all_99_2_41 = all_28_0_4 % 9.32/2.73 | % 9.33/2.73 | Combining equations (109,108) yields a new equation: % 9.33/2.73 | (110) all_97_2_36 = all_28_0_4 % 9.33/2.73 | % 9.33/2.73 | From (104) and (101) follows: % 9.33/2.73 | (89) sdtasdt0(all_36_0_7, all_28_1_5) = all_97_0_34 % 9.33/2.73 | % 9.33/2.73 | From (105) and (100) follows: % 9.33/2.73 | (91) sdtasdt0(all_36_1_8, all_28_1_5) = all_97_1_35 % 9.33/2.73 | % 9.33/2.73 | From (106) and (102) follows: % 9.33/2.73 | (90) sdtasdt0(all_28_1_5, all_36_0_7) = all_97_3_37 % 9.33/2.73 | % 9.33/2.73 | From (107) and (99) follows: % 9.33/2.73 | (94) sdtasdt0(all_28_1_5, all_36_1_8) = all_97_4_38 % 9.33/2.73 | % 9.33/2.73 | From (110) and (92) follows: % 9.33/2.73 | (115) sdtpldt0(all_97_1_35, all_97_0_34) = all_28_0_4 % 9.33/2.73 | % 9.33/2.73 | Instantiating formula (31) with all_97_0_34, all_36_0_7, all_28_1_5 and discharging atoms sdtasdt0(all_36_0_7, all_28_1_5) = all_97_0_34, aElement0(all_36_0_7), aElement0(all_28_1_5), yields: % 9.33/2.73 | (116) sdtasdt0(all_28_1_5, all_36_0_7) = all_97_0_34 % 9.33/2.73 | % 9.33/2.73 | Instantiating formula (31) with all_97_1_35, all_36_1_8, all_28_1_5 and discharging atoms sdtasdt0(all_36_1_8, all_28_1_5) = all_97_1_35, aElement0(all_36_1_8), aElement0(all_28_1_5), yields: % 9.33/2.73 | (117) sdtasdt0(all_28_1_5, all_36_1_8) = all_97_1_35 % 9.33/2.73 | % 9.33/2.73 | Instantiating formula (51) with all_97_3_37, all_28_1_5, all_36_0_7, xJ and discharging atoms sdtasdt0(all_28_1_5, all_36_0_7) = all_97_3_37, aIdeal0(xJ), aElementOf0(all_36_0_7, xJ), aElement0(all_28_1_5), yields: % 9.33/2.73 | (118) aElementOf0(all_97_3_37, xJ) % 9.33/2.73 | % 9.33/2.73 | Instantiating formula (51) with all_97_4_38, all_28_1_5, all_36_1_8, xI and discharging atoms sdtasdt0(all_28_1_5, all_36_1_8) = all_97_4_38, aIdeal0(xI), aElementOf0(all_36_1_8, xI), aElement0(all_28_1_5), yields: % 9.33/2.73 | (119) aElementOf0(all_97_4_38, xI) % 9.33/2.73 | % 9.33/2.73 | Instantiating formula (8) with all_28_1_5, all_36_0_7, all_97_0_34, all_97_3_37 and discharging atoms sdtasdt0(all_28_1_5, all_36_0_7) = all_97_0_34, sdtasdt0(all_28_1_5, all_36_0_7) = all_97_3_37, yields: % 9.33/2.73 | (120) all_97_0_34 = all_97_3_37 % 9.33/2.73 | % 9.33/2.73 | Instantiating formula (8) with all_28_1_5, all_36_1_8, all_97_1_35, all_97_4_38 and discharging atoms sdtasdt0(all_28_1_5, all_36_1_8) = all_97_1_35, sdtasdt0(all_28_1_5, all_36_1_8) = all_97_4_38, yields: % 9.33/2.73 | (121) all_97_1_35 = all_97_4_38 % 9.33/2.73 | % 9.33/2.73 | From (121)(120) and (115) follows: % 9.33/2.73 | (95) sdtpldt0(all_97_4_38, all_97_3_37) = all_28_0_4 % 9.33/2.73 | % 9.33/2.73 | Instantiating formula (58) with all_97_3_37, all_97_4_38, all_28_0_4, all_0_0_0, xJ, xI and discharging atoms sdtpldt1(xI, xJ) = all_0_0_0, sdtpldt0(all_97_4_38, all_97_3_37) = all_28_0_4, aElementOf0(all_97_3_37, xJ), aElementOf0(all_97_4_38, xI), aSet0(xJ), aSet0(xI), ~ aElementOf0(all_28_0_4, all_0_0_0), yields: % 9.33/2.73 | (123) $false % 9.33/2.73 | % 9.33/2.73 |-The branch is then unsatisfiable % 9.33/2.73 |-Branch two: % 9.33/2.73 | (124) sdtpldt0(all_28_2_6, all_28_1_5) = all_28_0_4 & aElementOf0(all_28_1_5, all_0_0_0) & ~ aElementOf0(all_28_0_4, all_0_0_0) % 9.33/2.73 | % 9.33/2.73 | Applying alpha-rule on (124) yields: % 9.33/2.73 | (125) sdtpldt0(all_28_2_6, all_28_1_5) = all_28_0_4 % 9.33/2.73 | (126) aElementOf0(all_28_1_5, all_0_0_0) % 9.33/2.73 | (84) ~ aElementOf0(all_28_0_4, all_0_0_0) % 9.33/2.73 | % 9.33/2.73 | Instantiating formula (41) with all_28_1_5, all_0_0_0, xJ, xI and discharging atoms sdtpldt1(xI, xJ) = all_0_0_0, aElementOf0(all_28_1_5, all_0_0_0), aSet0(xJ), aSet0(xI), yields: % 9.33/2.73 | (128) ? [v0] : ? [v1] : (sdtpldt0(v0, v1) = all_28_1_5 & aElementOf0(v1, xJ) & aElementOf0(v0, xI)) % 9.33/2.73 | % 9.33/2.73 | Instantiating formula (18) with all_28_1_5, all_0_0_0 and discharging atoms aElementOf0(all_28_1_5, all_0_0_0), aSet0(all_0_0_0), yields: % 9.33/2.73 | (83) aElement0(all_28_1_5) % 9.33/2.73 | % 9.33/2.73 | Instantiating (128) with all_97_0_44, all_97_1_45 yields: % 9.33/2.73 | (130) sdtpldt0(all_97_1_45, all_97_0_44) = all_28_1_5 & aElementOf0(all_97_0_44, xJ) & aElementOf0(all_97_1_45, xI) % 9.33/2.73 | % 9.33/2.73 | Applying alpha-rule on (130) yields: % 9.33/2.73 | (131) sdtpldt0(all_97_1_45, all_97_0_44) = all_28_1_5 % 9.33/2.73 | (132) aElementOf0(all_97_0_44, xJ) % 9.33/2.73 | (133) aElementOf0(all_97_1_45, xI) % 9.33/2.73 | % 9.33/2.73 | Instantiating formula (18) with all_97_0_44, xJ and discharging atoms aElementOf0(all_97_0_44, xJ), aSet0(xJ), yields: % 9.33/2.73 | (134) aElement0(all_97_0_44) % 9.33/2.73 | % 9.33/2.73 | Instantiating formula (18) with all_97_1_45, xI and discharging atoms aElementOf0(all_97_1_45, xI), aSet0(xI), yields: % 9.33/2.73 | (135) aElement0(all_97_1_45) % 9.33/2.73 | % 9.33/2.73 | Instantiating formula (7) with all_28_0_4, all_28_2_6, all_28_1_5, all_36_1_8, all_36_0_7 and discharging atoms sdtpldt0(all_36_0_7, all_36_1_8) = all_28_2_6, sdtpldt0(all_28_2_6, all_28_1_5) = all_28_0_4, aElement0(all_36_0_7), aElement0(all_36_1_8), aElement0(all_28_1_5), yields: % 9.33/2.73 | (136) ? [v0] : (sdtpldt0(all_36_0_7, v0) = all_28_0_4 & sdtpldt0(all_36_1_8, all_28_1_5) = v0) % 9.33/2.73 | % 9.33/2.73 | Instantiating formula (7) with all_28_0_4, all_28_2_6, all_28_1_5, all_36_0_7, all_36_1_8 and discharging atoms sdtpldt0(all_36_1_8, all_36_0_7) = all_28_2_6, sdtpldt0(all_28_2_6, all_28_1_5) = all_28_0_4, aElement0(all_36_0_7), aElement0(all_36_1_8), aElement0(all_28_1_5), yields: % 9.33/2.73 | (137) ? [v0] : (sdtpldt0(all_36_0_7, all_28_1_5) = v0 & sdtpldt0(all_36_1_8, v0) = all_28_0_4) % 9.33/2.73 | % 9.33/2.73 | Instantiating formula (32) with all_28_0_4, all_28_2_6, all_28_1_5 and discharging atoms sdtpldt0(all_28_2_6, all_28_1_5) = all_28_0_4, aElement0(all_28_1_5), aElement0(all_28_2_6), yields: % 9.33/2.73 | (138) sdtpldt0(all_28_1_5, all_28_2_6) = all_28_0_4 % 9.33/2.73 | % 9.33/2.73 | Instantiating (137) with all_105_0_46 yields: % 9.33/2.73 | (139) sdtpldt0(all_36_0_7, all_28_1_5) = all_105_0_46 & sdtpldt0(all_36_1_8, all_105_0_46) = all_28_0_4 % 9.33/2.73 | % 9.33/2.73 | Applying alpha-rule on (139) yields: % 9.33/2.73 | (140) sdtpldt0(all_36_0_7, all_28_1_5) = all_105_0_46 % 9.33/2.73 | (141) sdtpldt0(all_36_1_8, all_105_0_46) = all_28_0_4 % 9.33/2.73 | % 9.33/2.73 | Instantiating (136) with all_107_0_47 yields: % 9.33/2.73 | (142) sdtpldt0(all_36_0_7, all_107_0_47) = all_28_0_4 & sdtpldt0(all_36_1_8, all_28_1_5) = all_107_0_47 % 9.33/2.73 | % 9.33/2.73 | Applying alpha-rule on (142) yields: % 9.33/2.73 | (143) sdtpldt0(all_36_0_7, all_107_0_47) = all_28_0_4 % 9.33/2.73 | (144) sdtpldt0(all_36_1_8, all_28_1_5) = all_107_0_47 % 9.33/2.73 | % 9.33/2.73 | Instantiating formula (32) with all_105_0_46, all_36_0_7, all_28_1_5 and discharging atoms sdtpldt0(all_36_0_7, all_28_1_5) = all_105_0_46, aElement0(all_36_0_7), aElement0(all_28_1_5), yields: % 9.33/2.74 | (145) sdtpldt0(all_28_1_5, all_36_0_7) = all_105_0_46 % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (32) with all_107_0_47, all_36_1_8, all_28_1_5 and discharging atoms sdtpldt0(all_36_1_8, all_28_1_5) = all_107_0_47, aElement0(all_36_1_8), aElement0(all_28_1_5), yields: % 9.33/2.74 | (146) sdtpldt0(all_28_1_5, all_36_1_8) = all_107_0_47 % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (52) with all_28_0_4, all_28_2_6, all_36_1_8, all_36_0_7, all_28_1_5 and discharging atoms sdtpldt0(all_36_0_7, all_36_1_8) = all_28_2_6, sdtpldt0(all_28_1_5, all_28_2_6) = all_28_0_4, aElement0(all_36_0_7), aElement0(all_36_1_8), aElement0(all_28_1_5), yields: % 9.33/2.74 | (147) ? [v0] : (sdtpldt0(v0, all_36_1_8) = all_28_0_4 & sdtpldt0(all_28_1_5, all_36_0_7) = v0) % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (52) with all_28_0_4, all_28_2_6, all_36_0_7, all_36_1_8, all_28_1_5 and discharging atoms sdtpldt0(all_36_1_8, all_36_0_7) = all_28_2_6, sdtpldt0(all_28_1_5, all_28_2_6) = all_28_0_4, aElement0(all_36_0_7), aElement0(all_36_1_8), aElement0(all_28_1_5), yields: % 9.33/2.74 | (148) ? [v0] : (sdtpldt0(v0, all_36_0_7) = all_28_0_4 & sdtpldt0(all_28_1_5, all_36_1_8) = v0) % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (52) with all_28_0_4, all_28_1_5, all_97_0_44, all_97_1_45, all_28_2_6 and discharging atoms sdtpldt0(all_97_1_45, all_97_0_44) = all_28_1_5, sdtpldt0(all_28_2_6, all_28_1_5) = all_28_0_4, aElement0(all_97_0_44), aElement0(all_97_1_45), aElement0(all_28_2_6), yields: % 9.33/2.74 | (149) ? [v0] : (sdtpldt0(v0, all_97_0_44) = all_28_0_4 & sdtpldt0(all_28_2_6, all_97_1_45) = v0) % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (52) with all_105_0_46, all_28_1_5, all_97_0_44, all_97_1_45, all_36_0_7 and discharging atoms sdtpldt0(all_97_1_45, all_97_0_44) = all_28_1_5, sdtpldt0(all_36_0_7, all_28_1_5) = all_105_0_46, aElement0(all_97_0_44), aElement0(all_97_1_45), aElement0(all_36_0_7), yields: % 9.33/2.74 | (150) ? [v0] : (sdtpldt0(v0, all_97_0_44) = all_105_0_46 & sdtpldt0(all_36_0_7, all_97_1_45) = v0) % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (52) with all_107_0_47, all_28_1_5, all_97_0_44, all_97_1_45, all_36_1_8 and discharging atoms sdtpldt0(all_97_1_45, all_97_0_44) = all_28_1_5, sdtpldt0(all_36_1_8, all_28_1_5) = all_107_0_47, aElement0(all_97_0_44), aElement0(all_97_1_45), aElement0(all_36_1_8), yields: % 9.33/2.74 | (151) ? [v0] : (sdtpldt0(v0, all_97_0_44) = all_107_0_47 & sdtpldt0(all_36_1_8, all_97_1_45) = v0) % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (32) with all_28_1_5, all_97_1_45, all_97_0_44 and discharging atoms sdtpldt0(all_97_1_45, all_97_0_44) = all_28_1_5, aElement0(all_97_0_44), aElement0(all_97_1_45), yields: % 9.33/2.74 | (152) sdtpldt0(all_97_0_44, all_97_1_45) = all_28_1_5 % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (7) with all_28_0_4, all_28_1_5, all_28_2_6, all_97_0_44, all_97_1_45 and discharging atoms sdtpldt0(all_97_1_45, all_97_0_44) = all_28_1_5, sdtpldt0(all_28_1_5, all_28_2_6) = all_28_0_4, aElement0(all_97_0_44), aElement0(all_97_1_45), aElement0(all_28_2_6), yields: % 9.33/2.74 | (153) ? [v0] : (sdtpldt0(all_97_0_44, all_28_2_6) = v0 & sdtpldt0(all_97_1_45, v0) = all_28_0_4) % 9.33/2.74 | % 9.33/2.74 | Instantiating (150) with all_115_0_48 yields: % 9.33/2.74 | (154) sdtpldt0(all_115_0_48, all_97_0_44) = all_105_0_46 & sdtpldt0(all_36_0_7, all_97_1_45) = all_115_0_48 % 9.33/2.74 | % 9.33/2.74 | Applying alpha-rule on (154) yields: % 9.33/2.74 | (155) sdtpldt0(all_115_0_48, all_97_0_44) = all_105_0_46 % 9.33/2.74 | (156) sdtpldt0(all_36_0_7, all_97_1_45) = all_115_0_48 % 9.33/2.74 | % 9.33/2.74 | Instantiating (148) with all_117_0_49 yields: % 9.33/2.74 | (157) sdtpldt0(all_117_0_49, all_36_0_7) = all_28_0_4 & sdtpldt0(all_28_1_5, all_36_1_8) = all_117_0_49 % 9.33/2.74 | % 9.33/2.74 | Applying alpha-rule on (157) yields: % 9.33/2.74 | (158) sdtpldt0(all_117_0_49, all_36_0_7) = all_28_0_4 % 9.33/2.74 | (159) sdtpldt0(all_28_1_5, all_36_1_8) = all_117_0_49 % 9.33/2.74 | % 9.33/2.74 | Instantiating (147) with all_119_0_50 yields: % 9.33/2.74 | (160) sdtpldt0(all_119_0_50, all_36_1_8) = all_28_0_4 & sdtpldt0(all_28_1_5, all_36_0_7) = all_119_0_50 % 9.33/2.74 | % 9.33/2.74 | Applying alpha-rule on (160) yields: % 9.33/2.74 | (161) sdtpldt0(all_119_0_50, all_36_1_8) = all_28_0_4 % 9.33/2.74 | (162) sdtpldt0(all_28_1_5, all_36_0_7) = all_119_0_50 % 9.33/2.74 | % 9.33/2.74 | Instantiating (149) with all_121_0_51 yields: % 9.33/2.74 | (163) sdtpldt0(all_121_0_51, all_97_0_44) = all_28_0_4 & sdtpldt0(all_28_2_6, all_97_1_45) = all_121_0_51 % 9.33/2.74 | % 9.33/2.74 | Applying alpha-rule on (163) yields: % 9.33/2.74 | (164) sdtpldt0(all_121_0_51, all_97_0_44) = all_28_0_4 % 9.33/2.74 | (165) sdtpldt0(all_28_2_6, all_97_1_45) = all_121_0_51 % 9.33/2.74 | % 9.33/2.74 | Instantiating (151) with all_123_0_52 yields: % 9.33/2.74 | (166) sdtpldt0(all_123_0_52, all_97_0_44) = all_107_0_47 & sdtpldt0(all_36_1_8, all_97_1_45) = all_123_0_52 % 9.33/2.74 | % 9.33/2.74 | Applying alpha-rule on (166) yields: % 9.33/2.74 | (167) sdtpldt0(all_123_0_52, all_97_0_44) = all_107_0_47 % 9.33/2.74 | (168) sdtpldt0(all_36_1_8, all_97_1_45) = all_123_0_52 % 9.33/2.74 | % 9.33/2.74 | Instantiating (153) with all_125_0_53 yields: % 9.33/2.74 | (169) sdtpldt0(all_97_0_44, all_28_2_6) = all_125_0_53 & sdtpldt0(all_97_1_45, all_125_0_53) = all_28_0_4 % 9.33/2.74 | % 9.33/2.74 | Applying alpha-rule on (169) yields: % 9.33/2.74 | (170) sdtpldt0(all_97_0_44, all_28_2_6) = all_125_0_53 % 9.33/2.74 | (171) sdtpldt0(all_97_1_45, all_125_0_53) = all_28_0_4 % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (11) with all_28_1_5, all_36_0_7, all_105_0_46, all_119_0_50 and discharging atoms sdtpldt0(all_28_1_5, all_36_0_7) = all_119_0_50, sdtpldt0(all_28_1_5, all_36_0_7) = all_105_0_46, yields: % 9.33/2.74 | (172) all_119_0_50 = all_105_0_46 % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (11) with all_28_1_5, all_36_1_8, all_107_0_47, all_117_0_49 and discharging atoms sdtpldt0(all_28_1_5, all_36_1_8) = all_117_0_49, sdtpldt0(all_28_1_5, all_36_1_8) = all_107_0_47, yields: % 9.33/2.74 | (173) all_117_0_49 = all_107_0_47 % 9.33/2.74 | % 9.33/2.74 | From (173) and (158) follows: % 9.33/2.74 | (174) sdtpldt0(all_107_0_47, all_36_0_7) = all_28_0_4 % 9.33/2.74 | % 9.33/2.74 | From (172) and (162) follows: % 9.33/2.74 | (145) sdtpldt0(all_28_1_5, all_36_0_7) = all_105_0_46 % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (52) with all_105_0_46, all_28_1_5, all_97_1_45, all_97_0_44, all_36_0_7 and discharging atoms sdtpldt0(all_97_0_44, all_97_1_45) = all_28_1_5, sdtpldt0(all_36_0_7, all_28_1_5) = all_105_0_46, aElement0(all_97_0_44), aElement0(all_97_1_45), aElement0(all_36_0_7), yields: % 9.33/2.74 | (176) ? [v0] : (sdtpldt0(v0, all_97_1_45) = all_105_0_46 & sdtpldt0(all_36_0_7, all_97_0_44) = v0) % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (7) with all_28_0_4, all_28_1_5, all_28_2_6, all_97_1_45, all_97_0_44 and discharging atoms sdtpldt0(all_97_0_44, all_97_1_45) = all_28_1_5, sdtpldt0(all_28_1_5, all_28_2_6) = all_28_0_4, aElement0(all_97_0_44), aElement0(all_97_1_45), aElement0(all_28_2_6), yields: % 9.33/2.74 | (177) ? [v0] : (sdtpldt0(all_97_0_44, v0) = all_28_0_4 & sdtpldt0(all_97_1_45, all_28_2_6) = v0) % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (52) with all_125_0_53, all_28_2_6, all_36_1_8, all_36_0_7, all_97_0_44 and discharging atoms sdtpldt0(all_97_0_44, all_28_2_6) = all_125_0_53, sdtpldt0(all_36_0_7, all_36_1_8) = all_28_2_6, aElement0(all_97_0_44), aElement0(all_36_0_7), aElement0(all_36_1_8), yields: % 9.33/2.74 | (178) ? [v0] : (sdtpldt0(v0, all_36_1_8) = all_125_0_53 & sdtpldt0(all_97_0_44, all_36_0_7) = v0) % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (16) with all_115_0_48, all_97_1_45, all_36_0_7 and discharging atoms sdtpldt0(all_36_0_7, all_97_1_45) = all_115_0_48, aElement0(all_97_1_45), aElement0(all_36_0_7), yields: % 9.33/2.74 | (179) sdtpldt0(all_97_1_45, all_36_0_7) = all_115_0_48 % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (45) with all_123_0_52, all_97_1_45, all_36_1_8, xI and discharging atoms sdtpldt0(all_36_1_8, all_97_1_45) = all_123_0_52, aIdeal0(xI), aElementOf0(all_97_1_45, xI), aElementOf0(all_36_1_8, xI), yields: % 9.33/2.74 | (180) aElementOf0(all_123_0_52, xI) % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (39) with all_123_0_52, all_97_1_45, all_36_1_8 and discharging atoms sdtpldt0(all_36_1_8, all_97_1_45) = all_123_0_52, aElement0(all_97_1_45), aElement0(all_36_1_8), yields: % 9.33/2.74 | (181) aElement0(all_123_0_52) % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (7) with all_105_0_46, all_28_1_5, all_36_0_7, all_97_0_44, all_97_1_45 and discharging atoms sdtpldt0(all_97_1_45, all_97_0_44) = all_28_1_5, sdtpldt0(all_28_1_5, all_36_0_7) = all_105_0_46, aElement0(all_97_0_44), aElement0(all_97_1_45), aElement0(all_36_0_7), yields: % 9.33/2.74 | (182) ? [v0] : (sdtpldt0(all_97_0_44, all_36_0_7) = v0 & sdtpldt0(all_97_1_45, v0) = all_105_0_46) % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (7) with all_105_0_46, all_28_1_5, all_36_0_7, all_97_1_45, all_97_0_44 and discharging atoms sdtpldt0(all_97_0_44, all_97_1_45) = all_28_1_5, sdtpldt0(all_28_1_5, all_36_0_7) = all_105_0_46, aElement0(all_97_0_44), aElement0(all_97_1_45), aElement0(all_36_0_7), yields: % 9.33/2.74 | (183) ? [v0] : (sdtpldt0(all_97_0_44, v0) = all_105_0_46 & sdtpldt0(all_97_1_45, all_36_0_7) = v0) % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (7) with all_121_0_51, all_28_2_6, all_97_1_45, all_36_1_8, all_36_0_7 and discharging atoms sdtpldt0(all_36_0_7, all_36_1_8) = all_28_2_6, sdtpldt0(all_28_2_6, all_97_1_45) = all_121_0_51, aElement0(all_97_1_45), aElement0(all_36_0_7), aElement0(all_36_1_8), yields: % 9.33/2.74 | (184) ? [v0] : (sdtpldt0(all_36_0_7, v0) = all_121_0_51 & sdtpldt0(all_36_1_8, all_97_1_45) = v0) % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (7) with all_121_0_51, all_28_2_6, all_97_1_45, all_36_0_7, all_36_1_8 and discharging atoms sdtpldt0(all_36_1_8, all_36_0_7) = all_28_2_6, sdtpldt0(all_28_2_6, all_97_1_45) = all_121_0_51, aElement0(all_97_1_45), aElement0(all_36_0_7), aElement0(all_36_1_8), yields: % 9.33/2.74 | (185) ? [v0] : (sdtpldt0(all_36_0_7, all_97_1_45) = v0 & sdtpldt0(all_36_1_8, v0) = all_121_0_51) % 9.33/2.74 | % 9.33/2.74 | Instantiating formula (16) with all_121_0_51, all_97_1_45, all_28_2_6 and discharging atoms sdtpldt0(all_28_2_6, all_97_1_45) = all_121_0_51, aElement0(all_97_1_45), aElement0(all_28_2_6), yields: % 9.33/2.74 | (186) sdtpldt0(all_97_1_45, all_28_2_6) = all_121_0_51 % 9.33/2.74 | % 9.33/2.74 | Instantiating (177) with all_139_0_55 yields: % 9.33/2.74 | (187) sdtpldt0(all_97_0_44, all_139_0_55) = all_28_0_4 & sdtpldt0(all_97_1_45, all_28_2_6) = all_139_0_55 % 9.33/2.74 | % 9.33/2.74 | Applying alpha-rule on (187) yields: % 9.33/2.74 | (188) sdtpldt0(all_97_0_44, all_139_0_55) = all_28_0_4 % 9.33/2.74 | (189) sdtpldt0(all_97_1_45, all_28_2_6) = all_139_0_55 % 9.33/2.74 | % 9.33/2.74 | Instantiating (176) with all_143_0_57 yields: % 9.33/2.74 | (190) sdtpldt0(all_143_0_57, all_97_1_45) = all_105_0_46 & sdtpldt0(all_36_0_7, all_97_0_44) = all_143_0_57 % 9.33/2.74 | % 9.33/2.74 | Applying alpha-rule on (190) yields: % 9.33/2.74 | (191) sdtpldt0(all_143_0_57, all_97_1_45) = all_105_0_46 % 9.33/2.74 | (192) sdtpldt0(all_36_0_7, all_97_0_44) = all_143_0_57 % 9.33/2.75 | % 9.33/2.75 | Instantiating (184) with all_145_0_58 yields: % 9.33/2.75 | (193) sdtpldt0(all_36_0_7, all_145_0_58) = all_121_0_51 & sdtpldt0(all_36_1_8, all_97_1_45) = all_145_0_58 % 9.33/2.75 | % 9.33/2.75 | Applying alpha-rule on (193) yields: % 9.33/2.75 | (194) sdtpldt0(all_36_0_7, all_145_0_58) = all_121_0_51 % 9.33/2.75 | (195) sdtpldt0(all_36_1_8, all_97_1_45) = all_145_0_58 % 9.33/2.75 | % 9.33/2.75 | Instantiating (178) with all_151_0_61 yields: % 9.33/2.75 | (196) sdtpldt0(all_151_0_61, all_36_1_8) = all_125_0_53 & sdtpldt0(all_97_0_44, all_36_0_7) = all_151_0_61 % 9.33/2.75 | % 9.33/2.75 | Applying alpha-rule on (196) yields: % 9.33/2.75 | (197) sdtpldt0(all_151_0_61, all_36_1_8) = all_125_0_53 % 9.33/2.75 | (198) sdtpldt0(all_97_0_44, all_36_0_7) = all_151_0_61 % 9.33/2.75 | % 9.33/2.75 | Instantiating (182) with all_153_0_62 yields: % 9.33/2.75 | (199) sdtpldt0(all_97_0_44, all_36_0_7) = all_153_0_62 & sdtpldt0(all_97_1_45, all_153_0_62) = all_105_0_46 % 9.33/2.75 | % 9.33/2.75 | Applying alpha-rule on (199) yields: % 9.33/2.75 | (200) sdtpldt0(all_97_0_44, all_36_0_7) = all_153_0_62 % 9.33/2.75 | (201) sdtpldt0(all_97_1_45, all_153_0_62) = all_105_0_46 % 9.33/2.75 | % 9.33/2.75 | Instantiating (185) with all_155_0_63 yields: % 9.33/2.75 | (202) sdtpldt0(all_36_0_7, all_97_1_45) = all_155_0_63 & sdtpldt0(all_36_1_8, all_155_0_63) = all_121_0_51 % 9.33/2.75 | % 9.33/2.75 | Applying alpha-rule on (202) yields: % 9.33/2.75 | (203) sdtpldt0(all_36_0_7, all_97_1_45) = all_155_0_63 % 9.33/2.75 | (204) sdtpldt0(all_36_1_8, all_155_0_63) = all_121_0_51 % 9.33/2.75 | % 9.33/2.75 | Instantiating (183) with all_159_0_65 yields: % 9.33/2.75 | (205) sdtpldt0(all_97_0_44, all_159_0_65) = all_105_0_46 & sdtpldt0(all_97_1_45, all_36_0_7) = all_159_0_65 % 9.33/2.75 | % 9.33/2.75 | Applying alpha-rule on (205) yields: % 9.33/2.75 | (206) sdtpldt0(all_97_0_44, all_159_0_65) = all_105_0_46 % 9.33/2.75 | (207) sdtpldt0(all_97_1_45, all_36_0_7) = all_159_0_65 % 9.33/2.75 | % 9.33/2.75 | Instantiating formula (11) with all_97_0_44, all_36_0_7, all_151_0_61, all_153_0_62 and discharging atoms sdtpldt0(all_97_0_44, all_36_0_7) = all_153_0_62, sdtpldt0(all_97_0_44, all_36_0_7) = all_151_0_61, yields: % 9.33/2.75 | (208) all_153_0_62 = all_151_0_61 % 9.33/2.75 | % 9.33/2.75 | Instantiating formula (11) with all_97_1_45, all_36_0_7, all_115_0_48, all_159_0_65 and discharging atoms sdtpldt0(all_97_1_45, all_36_0_7) = all_159_0_65, sdtpldt0(all_97_1_45, all_36_0_7) = all_115_0_48, yields: % 9.33/2.75 | (209) all_159_0_65 = all_115_0_48 % 9.33/2.75 | % 9.33/2.75 | Instantiating formula (11) with all_97_1_45, all_28_2_6, all_121_0_51, all_139_0_55 and discharging atoms sdtpldt0(all_97_1_45, all_28_2_6) = all_139_0_55, sdtpldt0(all_97_1_45, all_28_2_6) = all_121_0_51, yields: % 9.33/2.75 | (210) all_139_0_55 = all_121_0_51 % 9.33/2.75 | % 9.33/2.75 | Instantiating formula (11) with all_36_0_7, all_97_1_45, all_155_0_63, all_115_0_48 and discharging atoms sdtpldt0(all_36_0_7, all_97_1_45) = all_155_0_63, sdtpldt0(all_36_0_7, all_97_1_45) = all_115_0_48, yields: % 9.33/2.75 | (211) all_155_0_63 = all_115_0_48 % 9.33/2.75 | % 9.33/2.75 | Instantiating formula (11) with all_36_1_8, all_97_1_45, all_145_0_58, all_123_0_52 and discharging atoms sdtpldt0(all_36_1_8, all_97_1_45) = all_145_0_58, sdtpldt0(all_36_1_8, all_97_1_45) = all_123_0_52, yields: % 9.33/2.75 | (212) all_145_0_58 = all_123_0_52 % 9.33/2.75 | % 9.33/2.75 | From (209) and (206) follows: % 9.33/2.75 | (213) sdtpldt0(all_97_0_44, all_115_0_48) = all_105_0_46 % 9.33/2.75 | % 9.33/2.75 | From (210) and (188) follows: % 9.33/2.75 | (214) sdtpldt0(all_97_0_44, all_121_0_51) = all_28_0_4 % 9.33/2.75 | % 9.33/2.75 | From (208) and (200) follows: % 9.33/2.75 | (198) sdtpldt0(all_97_0_44, all_36_0_7) = all_151_0_61 % 9.33/2.75 | % 9.33/2.75 | From (212) and (194) follows: % 9.33/2.75 | (216) sdtpldt0(all_36_0_7, all_123_0_52) = all_121_0_51 % 9.33/2.75 | % 9.33/2.75 | From (211) and (203) follows: % 9.33/2.75 | (156) sdtpldt0(all_36_0_7, all_97_1_45) = all_115_0_48 % 9.33/2.75 | % 9.33/2.75 | Instantiating formula (52) with all_105_0_46, all_115_0_48, all_97_1_45, all_36_0_7, all_97_0_44 and discharging atoms sdtpldt0(all_97_0_44, all_115_0_48) = all_105_0_46, sdtpldt0(all_36_0_7, all_97_1_45) = all_115_0_48, aElement0(all_97_0_44), aElement0(all_97_1_45), aElement0(all_36_0_7), yields: % 9.33/2.75 | (218) ? [v0] : (sdtpldt0(v0, all_97_1_45) = all_105_0_46 & sdtpldt0(all_97_0_44, all_36_0_7) = v0) % 9.33/2.75 | % 9.33/2.75 | Instantiating formula (45) with all_151_0_61, all_36_0_7, all_97_0_44, xJ and discharging atoms sdtpldt0(all_97_0_44, all_36_0_7) = all_151_0_61, aIdeal0(xJ), aElementOf0(all_97_0_44, xJ), aElementOf0(all_36_0_7, xJ), yields: % 9.33/2.75 | (219) aElementOf0(all_151_0_61, xJ) % 9.33/2.75 | % 9.33/2.75 | Instantiating formula (16) with all_143_0_57, all_97_0_44, all_36_0_7 and discharging atoms sdtpldt0(all_36_0_7, all_97_0_44) = all_143_0_57, aElement0(all_97_0_44), aElement0(all_36_0_7), yields: % 9.33/2.75 | (220) sdtpldt0(all_97_0_44, all_36_0_7) = all_143_0_57 % 9.33/2.75 | % 9.33/2.75 | Instantiating formula (7) with all_28_0_4, all_107_0_47, all_36_0_7, all_97_0_44, all_123_0_52 and discharging atoms sdtpldt0(all_123_0_52, all_97_0_44) = all_107_0_47, sdtpldt0(all_107_0_47, all_36_0_7) = all_28_0_4, aElement0(all_123_0_52), aElement0(all_97_0_44), aElement0(all_36_0_7), yields: % 9.33/2.75 | (221) ? [v0] : (sdtpldt0(all_123_0_52, v0) = all_28_0_4 & sdtpldt0(all_97_0_44, all_36_0_7) = v0) % 9.33/2.75 | % 9.33/2.75 | Instantiating formula (52) with all_28_0_4, all_121_0_51, all_123_0_52, all_36_0_7, all_97_0_44 and discharging atoms sdtpldt0(all_97_0_44, all_121_0_51) = all_28_0_4, sdtpldt0(all_36_0_7, all_123_0_52) = all_121_0_51, aElement0(all_123_0_52), aElement0(all_97_0_44), aElement0(all_36_0_7), yields: % 9.33/2.75 | (222) ? [v0] : (sdtpldt0(v0, all_123_0_52) = all_28_0_4 & sdtpldt0(all_97_0_44, all_36_0_7) = v0) % 9.33/2.75 | % 9.33/2.75 | Instantiating (222) with all_175_0_68 yields: % 9.33/2.75 | (223) sdtpldt0(all_175_0_68, all_123_0_52) = all_28_0_4 & sdtpldt0(all_97_0_44, all_36_0_7) = all_175_0_68 % 9.33/2.75 | % 9.33/2.75 | Applying alpha-rule on (223) yields: % 9.33/2.75 | (224) sdtpldt0(all_175_0_68, all_123_0_52) = all_28_0_4 % 9.33/2.75 | (225) sdtpldt0(all_97_0_44, all_36_0_7) = all_175_0_68 % 9.33/2.75 | % 9.33/2.75 | Instantiating (221) with all_183_0_72 yields: % 9.33/2.75 | (226) sdtpldt0(all_123_0_52, all_183_0_72) = all_28_0_4 & sdtpldt0(all_97_0_44, all_36_0_7) = all_183_0_72 % 9.33/2.75 | % 9.33/2.75 | Applying alpha-rule on (226) yields: % 9.33/2.75 | (227) sdtpldt0(all_123_0_52, all_183_0_72) = all_28_0_4 % 9.33/2.75 | (228) sdtpldt0(all_97_0_44, all_36_0_7) = all_183_0_72 % 9.33/2.75 | % 9.33/2.75 | Instantiating (218) with all_201_0_81 yields: % 9.33/2.75 | (229) sdtpldt0(all_201_0_81, all_97_1_45) = all_105_0_46 & sdtpldt0(all_97_0_44, all_36_0_7) = all_201_0_81 % 9.33/2.75 | % 9.33/2.75 | Applying alpha-rule on (229) yields: % 9.33/2.75 | (230) sdtpldt0(all_201_0_81, all_97_1_45) = all_105_0_46 % 9.33/2.75 | (231) sdtpldt0(all_97_0_44, all_36_0_7) = all_201_0_81 % 9.33/2.75 | % 9.33/2.75 | Instantiating formula (11) with all_97_0_44, all_36_0_7, all_201_0_81, all_151_0_61 and discharging atoms sdtpldt0(all_97_0_44, all_36_0_7) = all_201_0_81, sdtpldt0(all_97_0_44, all_36_0_7) = all_151_0_61, yields: % 9.33/2.75 | (232) all_201_0_81 = all_151_0_61 % 9.33/2.75 | % 9.33/2.75 | Instantiating formula (11) with all_97_0_44, all_36_0_7, all_183_0_72, all_201_0_81 and discharging atoms sdtpldt0(all_97_0_44, all_36_0_7) = all_201_0_81, sdtpldt0(all_97_0_44, all_36_0_7) = all_183_0_72, yields: % 9.33/2.75 | (233) all_201_0_81 = all_183_0_72 % 9.33/2.75 | % 9.33/2.75 | Instantiating formula (11) with all_97_0_44, all_36_0_7, all_175_0_68, all_201_0_81 and discharging atoms sdtpldt0(all_97_0_44, all_36_0_7) = all_201_0_81, sdtpldt0(all_97_0_44, all_36_0_7) = all_175_0_68, yields: % 9.33/2.75 | (234) all_201_0_81 = all_175_0_68 % 9.33/2.75 | % 9.33/2.75 | Instantiating formula (11) with all_97_0_44, all_36_0_7, all_143_0_57, all_183_0_72 and discharging atoms sdtpldt0(all_97_0_44, all_36_0_7) = all_183_0_72, sdtpldt0(all_97_0_44, all_36_0_7) = all_143_0_57, yields: % 9.33/2.75 | (235) all_183_0_72 = all_143_0_57 % 9.33/2.75 | % 9.33/2.75 | Combining equations (233,234) yields a new equation: % 9.33/2.75 | (236) all_183_0_72 = all_175_0_68 % 9.33/2.75 | % 9.33/2.75 | Simplifying 236 yields: % 9.33/2.75 | (237) all_183_0_72 = all_175_0_68 % 9.33/2.75 | % 9.33/2.75 | Combining equations (232,234) yields a new equation: % 9.33/2.75 | (238) all_175_0_68 = all_151_0_61 % 9.33/2.75 | % 9.33/2.75 | Combining equations (237,235) yields a new equation: % 9.33/2.75 | (239) all_175_0_68 = all_143_0_57 % 9.33/2.75 | % 9.33/2.75 | Simplifying 239 yields: % 9.33/2.75 | (240) all_175_0_68 = all_143_0_57 % 9.33/2.75 | % 9.33/2.75 | Combining equations (238,240) yields a new equation: % 9.33/2.75 | (241) all_151_0_61 = all_143_0_57 % 9.33/2.75 | % 9.33/2.75 | Simplifying 241 yields: % 9.33/2.75 | (242) all_151_0_61 = all_143_0_57 % 9.33/2.75 | % 9.33/2.75 | From (235) and (227) follows: % 9.33/2.75 | (243) sdtpldt0(all_123_0_52, all_143_0_57) = all_28_0_4 % 9.33/2.75 | % 9.33/2.75 | From (242) and (219) follows: % 9.33/2.75 | (244) aElementOf0(all_143_0_57, xJ) % 9.33/2.75 | % 9.33/2.75 | Instantiating formula (58) with all_143_0_57, all_123_0_52, all_28_0_4, all_0_0_0, xJ, xI and discharging atoms sdtpldt1(xI, xJ) = all_0_0_0, sdtpldt0(all_123_0_52, all_143_0_57) = all_28_0_4, aElementOf0(all_143_0_57, xJ), aElementOf0(all_123_0_52, xI), aSet0(xJ), aSet0(xI), ~ aElementOf0(all_28_0_4, all_0_0_0), yields: % 9.33/2.75 | (123) $false % 9.33/2.75 | % 9.33/2.75 |-The branch is then unsatisfiable % 9.33/2.75 % SZS output end Proof for theBenchmark % 9.33/2.75 % 9.33/2.75 2160ms %------------------------------------------------------------------------------