%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : COM145+1 : TPTP v8.1.0. Released v6.4.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n032.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 : Fri Jul 15 01:08:18 EDT 2022 % Result : Theorem 22.97s 6.59s % Output : Proof 38.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : COM145+1 : TPTP v8.1.0. Released v6.4.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.31 % Computer : n032.cluster.edu % 0.12/0.31 % Model : x86_64 x86_64 % 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.31 % Memory : 8042.1875MB % 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.31 % CPULimit : 300 % 0.16/0.31 % WCLimit : 600 % 0.16/0.31 % DateTime : Thu Jun 16 18:23:00 EDT 2022 % 0.16/0.31 % CPUTime : % 0.16/0.49 ____ _ % 0.16/0.49 ___ / __ \_____(_)___ ________ __________ % 0.16/0.49 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.16/0.49 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.16/0.49 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.16/0.49 % 0.16/0.49 A Theorem Prover for First-Order Logic % 0.16/0.49 (ePrincess v.1.0) % 0.16/0.49 % 0.16/0.49 (c) Philipp Rümmer, 2009-2015 % 0.16/0.49 (c) Peter Backeman, 2014-2015 % 0.16/0.49 (contributions by Angelo Brillout, Peter Baumgartner) % 0.16/0.49 Free software under GNU Lesser General Public License (LGPL). % 0.16/0.49 Bug reports to peter@backeman.se % 0.16/0.49 % 0.16/0.49 For more information, visit http://user.uu.se/~petba168/breu/ % 0.16/0.49 % 0.16/0.49 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.16/0.53 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.98/0.93 Prover 0: Preprocessing ... % 3.93/1.46 Prover 0: Warning: ignoring some quantifiers % 3.95/1.48 Prover 0: Constructing countermodel ... % 19.80/5.82 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 20.28/5.91 Prover 1: Preprocessing ... % 21.11/6.10 Prover 1: Constructing countermodel ... % 22.97/6.59 Prover 1: proved (771ms) % 22.97/6.59 Prover 0: stopped % 22.97/6.59 % 22.97/6.59 No countermodel exists, formula is valid % 22.97/6.59 % SZS status Theorem for theBenchmark % 22.97/6.59 % 22.97/6.59 Generating proof ... found it (size 976) % 36.97/11.08 % 36.97/11.08 % SZS output start Proof for theBenchmark % 36.97/11.08 Assumed formulas after preprocessing and simplification: % 36.97/11.08 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & vreduce(v2) = v3 & vreduce(ve2) = v1 & vreduce(ve1) = v0 & vsomeExp(v5) = v3 & vtcheck(v4, v5, v6) = v7 & vtcheck(v4, v2, v6) = 0 & vapp(ve1, ve2) = v2 & ~ (visSomeExp(vnoExp) = 0) & ~ (visSomeType(vnoType) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v11 | v13 = v8 | ~ (vsubst(v13, v16, v15) = v17) | ~ (vsubst(v8, v9, v18) = v19) | ~ (vsubst(v8, v9, v10) = v11) | ~ (vabs(v14, v12, v17) = v18) | ~ (vvar(v14) = v16) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (vgensym(v24) = v25 & visFreeVar(v13, v9) = v21 & vapp(v22, v23) = v24 & vapp(v9, v15) = v22 & vabs(v13, v12, v15) = v20 & vvar(v8) = v23 & ( ~ (v25 = v14) | ~ (v21 = 0) | ~ (v20 = v10)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | v10 = v8 | ~ (vtcheck(v16, v13, v14) = v17) | ~ (vbind(v10, v11, v12) = v15) | ~ (vbind(v8, v9, v15) = v16) | ? [v18] : ? [v19] : ? [v20] : ( ~ (v20 = 0) & vtcheck(v19, v13, v14) = v20 & vbind(v10, v11, v18) = v19 & vbind(v8, v9, v12) = v18)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (vreduce(v9) = v10) | ~ (vgetSomeExp(v14) = v16) | ~ (vapp(v15, v16) = v17) | ~ (vapp(v15, v8) = v9) | ~ (vabs(v11, v12, v13) = v15) | ? [v18] : ? [v19] : ? [v20] : (vreduce(v8) = v18 & visSomeExp(v14) = v19 & vsomeExp(v17) = v20 & ( ~ (v19 = 0) | ~ (v18 = v14) | v20 = v10))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v11 | v12 = v8 | ~ (vsubst(v8, v9, v14) = v15) | ~ (vsubst(v8, v9, v10) = v11) | ~ (vabs(v12, v13, v15) = v16) | ? [v17] : ? [v18] : (visFreeVar(v12, v9) = v18 & vabs(v12, v13, v14) = v17 & ( ~ (v17 = v10) | v18 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v11 | ~ (vsubst(v8, v9, v13) = v15) | ~ (vsubst(v8, v9, v12) = v14) | ~ (vsubst(v8, v9, v10) = v11) | ~ (vapp(v14, v15) = v16) | ? [v17] : ( ~ (v17 = v10) & vapp(v12, v13) = v17)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | v14 = vnoExp | ~ (vreduce(v13) = v14) | ~ (visSomeExp(v11) = v16) | ~ (vapp(v15, v12) = v13) | ~ (vabs(v8, v9, v10) = v15) | ? [v17] : ? [v18] : (vreduce(v12) = v17 & visValue(v12) = v18 & ( ~ (v17 = v11) | v18 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (vreduce(v10) = v11) | ~ (visSomeExp(v9) = v16) | ~ (vapp(v15, v13) = v10) | ~ (vabs(v12, v8, v14) = v15) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : (vreduce(v13) = v17 & vsomeExp(v19) = v20 & vsubst(v12, v13, v14) = v19 & visValue(v13) = v18 & ( ~ (v18 = 0) | ~ (v17 = v9) | v20 = v11))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (vsubst(v10, v11, v12) = v15) | ~ (vtcheck(v14, v12, v13) = 0) | ~ (vtcheck(v9, v15, v13) = v16) | ~ (vbind(v10, v8, v9) = v14) | ? [v17] : ( ~ (v17 = 0) & vtcheck(v9, v11, v8) = v17)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (varrow(v11, v12) = v14) | ~ (vtcheck(v8, v13, v14) = v15) | ~ (vabs(v9, v11, v10) = v13) | ? [v16] : ? [v17] : ( ~ (v17 = 0) & vtcheck(v16, v10, v12) = v17 & vbind(v9, v11, v8) = v16)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (varrow(v8, v12) = v13) | ~ (vtcheck(v9, v14, v12) = v15) | ~ (vtcheck(v9, v10, v13) = 0) | ~ (vapp(v10, v11) = v14) | ? [v16] : ( ~ (v16 = 0) & vtcheck(v9, v11, v8) = v16)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (vtcheck(v15, v12, v13) = 0) | ~ (vbind(v8, v10, v14) = v15) | ~ (vbind(v8, v9, v11) = v14) | ? [v16] : (vtcheck(v16, v12, v13) = 0 & vbind(v8, v10, v11) = v16)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | v10 = v9 | ~ (vlookup(v10, v13) = v14) | ~ (vlookup(v10, v11) = v12) | ~ (vbind(v9, v8, v13) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (vtcheck(v13, v11, v12) = v14) | ~ (vbind(v8, v9, v10) = v13) | ? [v15] : ? [v16] : (vtcheck(v10, v11, v12) = v16 & vlookup(v8, v10) = v15 & ( ~ (v16 = 0) | ~ (v15 = vnoType)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (vtcheck(v13, v11, v12) = v14) | ~ (vbind(v8, v9, v10) = v13) | ? [v15] : ? [v16] : (vtcheck(v10, v11, v12) = v16 & visFreeVar(v8, v11) = v15 & ( ~ (v16 = 0) | v15 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = v10 | ~ (vbind(v11, v12, v13) = v14) | ~ (vbind(v8, v9, v10) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = v10 | ~ (vabs(v11, v12, v13) = v14) | ~ (vabs(v8, v9, v10) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v9 | ~ (vbind(v11, v12, v13) = v14) | ~ (vbind(v8, v9, v10) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v9 | ~ (vabs(v11, v12, v13) = v14) | ~ (vabs(v8, v9, v10) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v8 | ~ (vbind(v11, v12, v13) = v14) | ~ (vbind(v8, v9, v10) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v8 | ~ (vabs(v11, v12, v13) = v14) | ~ (vabs(v8, v9, v10) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (vreduce(v9) = v10) | ~ (vreduce(v8) = v11) | ~ (vgetSomeExp(v11) = v13) | ~ (vapp(v13, v12) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = v8 & vabs(v15, v16, v17) = v8) | (visSomeExp(v11) = v16 & vsomeExp(v14) = v17 & vapp(v8, v12) = v15 & ( ~ (v16 = 0) | ~ (v15 = v9) | v17 = v10)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = vnoExp | ~ (vreduce(v11) = v12) | ~ (visSomeExp(v10) = v13) | ~ (vapp(v9, v8) = v11) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v9 & vabs(v14, v15, v16) = v9) | ( ~ (v14 = v10) & vreduce(v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = 0 | ~ (visFreeVar(v8, v11) = v13) | ~ (visFreeVar(v8, v10) = v12) | ~ (visFreeVar(v8, v9) = 0) | ? [v14] : ( ~ (v14 = v9) & vapp(v10, v11) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v11 = v9 | ~ (visFreeVar(v9, v12) = 0) | ~ (visFreeVar(v9, v10) = v13) | ~ (vabs(v11, v8, v12) = v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (visFreeVar(v9, v12) = v13) | ~ (visFreeVar(v9, v10) = 0) | ~ (vabs(v11, v8, v12) = v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (visFreeVar(v8, v11) = v12) | ~ (visFreeVar(v8, v10) = 0) | ~ (visFreeVar(v8, v9) = v13) | ? [v14] : ( ~ (v14 = v9) & vapp(v10, v11) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (visFreeVar(v8, v11) = 0) | ~ (visFreeVar(v8, v10) = v12) | ~ (visFreeVar(v8, v9) = v13) | ? [v14] : ( ~ (v14 = v9) & vapp(v10, v11) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (vsubst(v9, v8, v10) = v11) | ~ (vabs(v9, v12, v13) = v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (vtcheck(v13, v11, v12) = 0) | ~ (vbind(v8, v9, v10) = v13) | ? [v14] : ? [v15] : (vtcheck(v10, v11, v12) = v15 & visFreeVar(v8, v11) = v14 & (v15 = 0 | v14 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (vapp(v11, v12) = v13) | ~ (vabs(v8, v9, v10) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (vbind(v8, v9, v10) = v12) | ~ (vbind(v8, v9, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (vabs(v8, v9, v10) = v12) | ~ (vabs(v8, v9, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | v11 = v10 | ~ (vsubst(v9, v8, v10) = v11) | ~ (vvar(v12) = v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = vnoExp | ~ (vreduce(v11) = v12) | ~ (vabs(v8, v9, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (vtcheck(v8, v11, v10) = v12) | ~ (vvar(v9) = v11) | ? [v13] : ? [v14] : ( ~ (v14 = v13) & vlookup(v9, v8) = v13 & vsomeType(v10) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (visValue(v11) = v12) | ~ (vabs(v8, v9, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v9 | ~ (varrow(v10, v11) = v12) | ~ (varrow(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v9 | ~ (vapp(v10, v11) = v12) | ~ (vapp(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v8 | ~ (varrow(v10, v11) = v12) | ~ (varrow(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v8 | ~ (vapp(v10, v11) = v12) | ~ (vapp(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (vsubst(v12, v11, v10) = v9) | ~ (vsubst(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (vtcheck(v12, v11, v10) = v9) | ~ (vtcheck(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (vbind(v12, v11, v10) = v9) | ~ (vbind(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (vabs(v12, v11, v10) = v9) | ~ (vabs(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (vlookup(v9, v10) = v11) | ~ (vbind(v9, v12, v8) = v10) | vsomeType(v12) = v11) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (visFreeVar(v9, v11) = v12) | ~ (visFreeVar(v9, v10) = 0) | ~ (vabs(v9, v8, v11) = v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (vabs(v9, v10, v11) = v12) | ~ (vvar(v8) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (varrow(v8, v9) = v11) | ~ (varrow(v8, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (vapp(v8, v9) = v11) | ~ (vapp(v8, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (vsubst(v8, v9, v10) = v11) | ~ (vvar(v8) = v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (varrow(v11, v10) = v9) | ~ (varrow(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (vlookup(v11, v10) = v9) | ~ (vlookup(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (visFreeVar(v11, v10) = v9) | ~ (visFreeVar(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (vapp(v11, v10) = v9) | ~ (vapp(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (vsubst(v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ((v27 = v11 & v23 = v16 & v19 = 0 & v18 = v10 & v13 = v9 & v12 = v8 & ~ (v15 = v8) & vsubst(v15, v24, v17) = v25 & vsubst(v8, v9, v26) = v11 & vgensym(v22) = v16 & visFreeVar(v15, v9) = 0 & vapp(v20, v21) = v22 & vapp(v9, v17) = v20 & vabs(v16, v14, v25) = v26 & vabs(v15, v14, v17) = v10 & vvar(v16) = v24 & vvar(v8) = v21) | (v20 = v11 & v17 = v10 & v15 = v9 & v14 = v8 & ~ (v18 = 0) & ~ (v12 = v8) & vsubst(v8, v9, v16) = v19 & visFreeVar(v12, v9) = v18 & vabs(v12, v13, v19) = v11 & vabs(v12, v13, v16) = v10) | (v19 = v11 & v16 = v10 & v14 = v9 & v13 = v8 & vsubst(v8, v9, v15) = v18 & vsubst(v8, v9, v12) = v17 & vapp(v17, v18) = v11 & vapp(v12, v15) = v10) | (v17 = v10 & v14 = v8 & v13 = v8 & v12 = v9 & v11 = v10 & vabs(v8, v15, v16) = v10) | (v15 = v10 & v14 = v9 & v13 = v8 & v12 = v8 & v11 = v9 & vvar(v8) = v10) | (v15 = v10 & v13 = v8 & v12 = v9 & v11 = v10 & ~ (v14 = v8) & vvar(v14) = v10))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (vapp(v9, v10) = v11) | ~ (vvar(v8) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (vgetSomeExp(v8) = v9) | ~ (vsomeExp(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (vsomeExp(v8) = v10) | ~ (vsomeExp(v8) = v9)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (vgetSomeType(v8) = v9) | ~ (vsomeType(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (vsomeType(v8) = v10) | ~ (vsomeType(v8) = v9)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (vvar(v8) = v10) | ~ (vvar(v8) = v9)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (visFreeVar(v8, v9) = 0) | ~ (vvar(v10) = v9)) & ! [v8] : ! [v9] : ! [v10] : (v10 = vnoExp | ~ (vreduce(v9) = v10) | ~ (vvar(v8) = v9)) & ! [v8] : ! [v9] : ! [v10] : (v10 = vnoType | ~ (vlookup(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = v10 & v15 = v9 & v13 = v8 & v12 = v8 & vsomeType(v14) = v10 & vbind(v8, v14, v11) = v9) | (v16 = v10 & v15 = v9 & v13 = v8 & ~ (v12 = v8) & vlookup(v8, v14) = v10 & vbind(v12, v11, v14) = v9))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (visSomeExp(v9) = v10) | ~ (vsomeExp(v8) = v9)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (visSomeType(v9) = v10) | ~ (vsomeType(v8) = v9)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (visFreeVar(v8, v9) = v10) | ~ (vvar(v8) = v9)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (vreduce(v10) = v9) | ~ (vreduce(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (vgetSomeExp(v10) = v9) | ~ (vgetSomeExp(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (visSomeExp(v10) = v9) | ~ (visSomeExp(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (vsomeExp(v10) = v9) | ~ (vsomeExp(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (vsomeExp(v9) = v10) | ~ (vsomeExp(v8) = v10)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (vgensym(v10) = v9) | ~ (vgensym(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (vgetSomeType(v10) = v9) | ~ (vgetSomeType(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (visSomeType(v10) = v9) | ~ (visSomeType(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (vsomeType(v10) = v9) | ~ (vsomeType(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (vsomeType(v9) = v10) | ~ (vsomeType(v8) = v10)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (visValue(v10) = v9) | ~ (visValue(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (vvar(v10) = v9) | ~ (vvar(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (vvar(v9) = v10) | ~ (vvar(v8) = v10)) & ! [v8] : ! [v9] : ! [v10] : (v9 = vempty | ~ (vlookup(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = v10 & v15 = v9 & v13 = v8 & v12 = v8 & vsomeType(v14) = v10 & vbind(v8, v14, v11) = v9) | (v16 = v10 & v15 = v9 & v13 = v8 & ~ (v12 = v8) & vlookup(v8, v14) = v10 & vbind(v12, v11, v14) = v9))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (vsomeExp(v9) = v1) | ~ (vtcheck(v8, ve2, v10) = 0) | vtcheck(v8, v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (vsomeExp(v9) = v0) | ~ (vtcheck(v8, ve1, v10) = 0) | vtcheck(v8, v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (vtcheck(v10, v8, v9) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v16 = v9 & v15 = v8 & varrow(v13, v14) = v9 & vtcheck(v17, v12, v14) = 0 & vbind(v11, v13, v10) = v17 & vabs(v11, v13, v12) = v8) | (v17 = 0 & v16 = 0 & v14 = v8 & varrow(v13, v9) = v15 & vtcheck(v10, v12, v13) = 0 & vtcheck(v10, v11, v15) = 0 & vapp(v11, v12) = v8) | (v14 = v11 & v13 = v8 & vlookup(v12, v10) = v11 & vsomeType(v9) = v11 & vvar(v12) = v8))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (vlookup(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (v11 = v8 | (v16 = v10 & v15 = v9 & v13 = v8 & v12 = v8 & vsomeType(v14) = v10 & vbind(v8, v14, v11) = v9) | (v16 = v10 & v15 = v9 & v13 = v8 & ~ (v12 = v8) & vlookup(v8, v14) = v10 & vbind(v12, v11, v14) = v9))) & ! [v8] : ! [v9] : ! [v10] : ~ (vbind(v8, v9, v10) = vempty) & ! [v8] : ! [v9] : ! [v10] : ( ~ (visValue(v10) = 0) | ~ (vapp(v8, v9) = v10)) & ! [v8] : ! [v9] : (v9 = vnoType | ~ (vlookup(v8, vempty) = v9)) & ! [v8] : ! [v9] : ( ~ (vreduce(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ((v21 = v9 & v19 = 0 & v17 = v11 & v16 = v8 & ~ (v18 = 0) & vreduce(v13) = v11 & visSomeExp(v11) = v18 & vsomeExp(v20) = v9 & vsubst(v12, v13, v14) = v20 & visValue(v13) = 0 & vapp(v15, v13) = v8 & vabs(v12, v10, v14) = v15) | (v21 = v9 & v18 = 0 & v17 = v14 & v16 = v8 & vreduce(v10) = v14 & vgetSomeExp(v14) = v19 & visSomeExp(v14) = 0 & vsomeExp(v20) = v9 & vapp(v15, v19) = v20 & vapp(v15, v10) = v8 & vabs(v11, v12, v13) = v15) | (v18 = v9 & v15 = 0 & v14 = v11 & v13 = v8 & vreduce(v10) = v11 & vgetSomeExp(v11) = v16 & visSomeExp(v11) = 0 & vsomeExp(v17) = v9 & vapp(v16, v12) = v17 & vapp(v10, v12) = v8 & ! [v22] : ! [v23] : ! [v24] : ~ (vabs(v22, v23, v24) = v10)) | (v17 = v13 & v16 = v8 & v9 = vnoExp & ~ (v19 = 0) & ~ (v18 = 0) & vreduce(v14) = v13 & visSomeExp(v13) = v18 & visValue(v14) = v19 & vapp(v15, v14) = v8 & vabs(v10, v11, v12) = v15) | (v14 = v12 & v13 = v8 & v9 = vnoExp & ~ (v15 = 0) & vreduce(v11) = v12 & visSomeExp(v12) = v15 & vapp(v11, v10) = v8 & ! [v22] : ! [v23] : ! [v24] : ~ (vabs(v22, v23, v24) = v11)) | (v13 = v8 & v9 = vnoExp & vabs(v10, v11, v12) = v8) | (v11 = v8 & v9 = vnoExp & vvar(v10) = v8))) & ! [v8] : ! [v9] : ( ~ (visFreeVar(v8, v9) = 0) | ? [v10] : ( ~ (v10 = v8) & vgensym(v9) = v10)) & ! [v8] : ! [v9] : ( ~ (visValue(v9) = 0) | ~ (vvar(v8) = v9)) & ! [v8] : ~ (vsomeExp(v8) = vnoExp) & ! [v8] : ~ (vsomeType(v8) = vnoType)) % 37.21/11.15 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields: % 37.21/11.15 | (1) ~ (all_0_0_0 = 0) & vreduce(all_0_5_5) = all_0_4_4 & vreduce(ve2) = all_0_6_6 & vreduce(ve1) = all_0_7_7 & vsomeExp(all_0_2_2) = all_0_4_4 & vtcheck(all_0_3_3, all_0_2_2, all_0_1_1) = all_0_0_0 & vtcheck(all_0_3_3, all_0_5_5, all_0_1_1) = 0 & vapp(ve1, ve2) = all_0_5_5 & ~ (visSomeExp(vnoExp) = 0) & ~ (visSomeType(vnoType) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v3 | v5 = v0 | ~ (vsubst(v5, v8, v7) = v9) | ~ (vsubst(v0, v1, v10) = v11) | ~ (vsubst(v0, v1, v2) = v3) | ~ (vabs(v6, v4, v9) = v10) | ~ (vvar(v6) = v8) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (vgensym(v16) = v17 & visFreeVar(v5, v1) = v13 & vapp(v14, v15) = v16 & vapp(v1, v7) = v14 & vabs(v5, v4, v7) = v12 & vvar(v0) = v15 & ( ~ (v17 = v6) | ~ (v13 = 0) | ~ (v12 = v2)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v2 = v0 | ~ (vtcheck(v8, v5, v6) = v9) | ~ (vbind(v2, v3, v4) = v7) | ~ (vbind(v0, v1, v7) = v8) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = 0) & vtcheck(v11, v5, v6) = v12 & vbind(v2, v3, v10) = v11 & vbind(v0, v1, v4) = v10)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (vreduce(v1) = v2) | ~ (vgetSomeExp(v6) = v8) | ~ (vapp(v7, v8) = v9) | ~ (vapp(v7, v0) = v1) | ~ (vabs(v3, v4, v5) = v7) | ? [v10] : ? [v11] : ? [v12] : (vreduce(v0) = v10 & visSomeExp(v6) = v11 & vsomeExp(v9) = v12 & ( ~ (v11 = 0) | ~ (v10 = v6) | v12 = v2))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v3 | v4 = v0 | ~ (vsubst(v0, v1, v6) = v7) | ~ (vsubst(v0, v1, v2) = v3) | ~ (vabs(v4, v5, v7) = v8) | ? [v9] : ? [v10] : (visFreeVar(v4, v1) = v10 & vabs(v4, v5, v6) = v9 & ( ~ (v9 = v2) | v10 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v3 | ~ (vsubst(v0, v1, v5) = v7) | ~ (vsubst(v0, v1, v4) = v6) | ~ (vsubst(v0, v1, v2) = v3) | ~ (vapp(v6, v7) = v8) | ? [v9] : ( ~ (v9 = v2) & vapp(v4, v5) = v9)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v6 = vnoExp | ~ (vreduce(v5) = v6) | ~ (visSomeExp(v3) = v8) | ~ (vapp(v7, v4) = v5) | ~ (vabs(v0, v1, v2) = v7) | ? [v9] : ? [v10] : (vreduce(v4) = v9 & visValue(v4) = v10 & ( ~ (v9 = v3) | v10 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (vreduce(v2) = v3) | ~ (visSomeExp(v1) = v8) | ~ (vapp(v7, v5) = v2) | ~ (vabs(v4, v0, v6) = v7) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (vreduce(v5) = v9 & vsomeExp(v11) = v12 & vsubst(v4, v5, v6) = v11 & visValue(v5) = v10 & ( ~ (v10 = 0) | ~ (v9 = v1) | v12 = v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (vsubst(v2, v3, v4) = v7) | ~ (vtcheck(v6, v4, v5) = 0) | ~ (vtcheck(v1, v7, v5) = v8) | ~ (vbind(v2, v0, v1) = v6) | ? [v9] : ( ~ (v9 = 0) & vtcheck(v1, v3, v0) = v9)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (varrow(v3, v4) = v6) | ~ (vtcheck(v0, v5, v6) = v7) | ~ (vabs(v1, v3, v2) = v5) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & vtcheck(v8, v2, v4) = v9 & vbind(v1, v3, v0) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (varrow(v0, v4) = v5) | ~ (vtcheck(v1, v6, v4) = v7) | ~ (vtcheck(v1, v2, v5) = 0) | ~ (vapp(v2, v3) = v6) | ? [v8] : ( ~ (v8 = 0) & vtcheck(v1, v3, v0) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (vtcheck(v7, v4, v5) = 0) | ~ (vbind(v0, v2, v6) = v7) | ~ (vbind(v0, v1, v3) = v6) | ? [v8] : (vtcheck(v8, v4, v5) = 0 & vbind(v0, v2, v3) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v4 | v2 = v1 | ~ (vlookup(v2, v5) = v6) | ~ (vlookup(v2, v3) = v4) | ~ (vbind(v1, v0, v5) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vtcheck(v5, v3, v4) = v6) | ~ (vbind(v0, v1, v2) = v5) | ? [v7] : ? [v8] : (vtcheck(v2, v3, v4) = v8 & vlookup(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = vnoType)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vtcheck(v5, v3, v4) = v6) | ~ (vbind(v0, v1, v2) = v5) | ? [v7] : ? [v8] : (vtcheck(v2, v3, v4) = v8 & visFreeVar(v0, v3) = v7 & ( ~ (v8 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v2 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v2 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v1 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v1 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v0 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v0 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (vreduce(v1) = v2) | ~ (vreduce(v0) = v3) | ~ (vgetSomeExp(v3) = v5) | ~ (vapp(v5, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v10 = v0 & vabs(v7, v8, v9) = v0) | (visSomeExp(v3) = v8 & vsomeExp(v6) = v9 & vapp(v0, v4) = v7 & ( ~ (v8 = 0) | ~ (v7 = v1) | v9 = v2)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = vnoExp | ~ (vreduce(v3) = v4) | ~ (visSomeExp(v2) = v5) | ~ (vapp(v1, v0) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v9 = v1 & vabs(v6, v7, v8) = v1) | ( ~ (v6 = v2) & vreduce(v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (visFreeVar(v0, v3) = v5) | ~ (visFreeVar(v0, v2) = v4) | ~ (visFreeVar(v0, v1) = 0) | ? [v6] : ( ~ (v6 = v1) & vapp(v2, v3) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v3 = v1 | ~ (visFreeVar(v1, v4) = 0) | ~ (visFreeVar(v1, v2) = v5) | ~ (vabs(v3, v0, v4) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (visFreeVar(v1, v4) = v5) | ~ (visFreeVar(v1, v2) = 0) | ~ (vabs(v3, v0, v4) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (visFreeVar(v0, v3) = v4) | ~ (visFreeVar(v0, v2) = 0) | ~ (visFreeVar(v0, v1) = v5) | ? [v6] : ( ~ (v6 = v1) & vapp(v2, v3) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (visFreeVar(v0, v3) = 0) | ~ (visFreeVar(v0, v2) = v4) | ~ (visFreeVar(v0, v1) = v5) | ? [v6] : ( ~ (v6 = v1) & vapp(v2, v3) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (vsubst(v1, v0, v2) = v3) | ~ (vabs(v1, v4, v5) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vtcheck(v5, v3, v4) = 0) | ~ (vbind(v0, v1, v2) = v5) | ? [v6] : ? [v7] : (vtcheck(v2, v3, v4) = v7 & visFreeVar(v0, v3) = v6 & (v7 = 0 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vapp(v3, v4) = v5) | ~ (vabs(v0, v1, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (vbind(v0, v1, v2) = v4) | ~ (vbind(v0, v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (vabs(v0, v1, v2) = v4) | ~ (vabs(v0, v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v1 | v3 = v2 | ~ (vsubst(v1, v0, v2) = v3) | ~ (vvar(v4) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = vnoExp | ~ (vreduce(v3) = v4) | ~ (vabs(v0, v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (vtcheck(v0, v3, v2) = v4) | ~ (vvar(v1) = v3) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & vlookup(v1, v0) = v5 & vsomeType(v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (visValue(v3) = v4) | ~ (vabs(v0, v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (varrow(v2, v3) = v4) | ~ (varrow(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (varrow(v2, v3) = v4) | ~ (varrow(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vlookup(v1, v2) = v3) | ~ (vbind(v1, v4, v0) = v2) | vsomeType(v4) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (visFreeVar(v1, v3) = v4) | ~ (visFreeVar(v1, v2) = 0) | ~ (vabs(v1, v0, v3) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vabs(v1, v2, v3) = v4) | ~ (vvar(v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (varrow(v0, v1) = v3) | ~ (varrow(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (vapp(v0, v1) = v3) | ~ (vapp(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (vsubst(v0, v1, v2) = v3) | ~ (vvar(v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (varrow(v3, v2) = v1) | ~ (varrow(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~ (vlookup(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~ (vapp(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsubst(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = v3 & v15 = v8 & v11 = 0 & v10 = v2 & v5 = v1 & v4 = v0 & ~ (v7 = v0) & vsubst(v7, v16, v9) = v17 & vsubst(v0, v1, v18) = v3 & vgensym(v14) = v8 & visFreeVar(v7, v1) = 0 & vapp(v12, v13) = v14 & vapp(v1, v9) = v12 & vabs(v8, v6, v17) = v18 & vabs(v7, v6, v9) = v2 & vvar(v8) = v16 & vvar(v0) = v13) | (v12 = v3 & v9 = v2 & v7 = v1 & v6 = v0 & ~ (v10 = 0) & ~ (v4 = v0) & vsubst(v0, v1, v8) = v11 & visFreeVar(v4, v1) = v10 & vabs(v4, v5, v11) = v3 & vabs(v4, v5, v8) = v2) | (v11 = v3 & v8 = v2 & v6 = v1 & v5 = v0 & vsubst(v0, v1, v7) = v10 & vsubst(v0, v1, v4) = v9 & vapp(v9, v10) = v3 & vapp(v4, v7) = v2) | (v9 = v2 & v6 = v0 & v5 = v0 & v4 = v1 & v3 = v2 & vabs(v0, v7, v8) = v2) | (v7 = v2 & v6 = v1 & v5 = v0 & v4 = v0 & v3 = v1 & vvar(v0) = v2) | (v7 = v2 & v5 = v0 & v4 = v1 & v3 = v2 & ~ (v6 = v0) & vvar(v6) = v2))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vapp(v1, v2) = v3) | ~ (vvar(v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vgetSomeExp(v0) = v1) | ~ (vsomeExp(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vsomeExp(v0) = v2) | ~ (vsomeExp(v0) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vgetSomeType(v0) = v1) | ~ (vsomeType(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vsomeType(v0) = v2) | ~ (vsomeType(v0) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vvar(v0) = v2) | ~ (vvar(v0) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (visFreeVar(v0, v1) = 0) | ~ (vvar(v2) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = vnoExp | ~ (vreduce(v1) = v2) | ~ (vvar(v0) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = vnoType | ~ (vlookup(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = v2 & v7 = v1 & v5 = v0 & v4 = v0 & vsomeType(v6) = v2 & vbind(v0, v6, v3) = v1) | (v8 = v2 & v7 = v1 & v5 = v0 & ~ (v4 = v0) & vlookup(v0, v6) = v2 & vbind(v4, v3, v6) = v1))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (visSomeExp(v1) = v2) | ~ (vsomeExp(v0) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (visSomeType(v1) = v2) | ~ (vsomeType(v0) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (visFreeVar(v0, v1) = v2) | ~ (vvar(v0) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~ (vsomeExp(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeExp(v1) = v2) | ~ (vsomeExp(v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~ (vsomeType(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeType(v1) = v2) | ~ (vsomeType(v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (visValue(v2) = v1) | ~ (visValue(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vvar(v1) = v2) | ~ (vvar(v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = vempty | ~ (vlookup(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = v2 & v7 = v1 & v5 = v0 & v4 = v0 & vsomeType(v6) = v2 & vbind(v0, v6, v3) = v1) | (v8 = v2 & v7 = v1 & v5 = v0 & ~ (v4 = v0) & vlookup(v0, v6) = v2 & vbind(v4, v3, v6) = v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (vsomeExp(v1) = all_0_6_6) | ~ (vtcheck(v0, ve2, v2) = 0) | vtcheck(v0, v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (vsomeExp(v1) = all_0_7_7) | ~ (vtcheck(v0, ve1, v2) = 0) | vtcheck(v0, v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (vtcheck(v2, v0, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v8 = v1 & v7 = v0 & varrow(v5, v6) = v1 & vtcheck(v9, v4, v6) = 0 & vbind(v3, v5, v2) = v9 & vabs(v3, v5, v4) = v0) | (v9 = 0 & v8 = 0 & v6 = v0 & varrow(v5, v1) = v7 & vtcheck(v2, v4, v5) = 0 & vtcheck(v2, v3, v7) = 0 & vapp(v3, v4) = v0) | (v6 = v3 & v5 = v0 & vlookup(v4, v2) = v3 & vsomeType(v1) = v3 & vvar(v4) = v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (vlookup(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (v3 = v0 | (v8 = v2 & v7 = v1 & v5 = v0 & v4 = v0 & vsomeType(v6) = v2 & vbind(v0, v6, v3) = v1) | (v8 = v2 & v7 = v1 & v5 = v0 & ~ (v4 = v0) & vlookup(v0, v6) = v2 & vbind(v4, v3, v6) = v1))) & ! [v0] : ! [v1] : ! [v2] : ~ (vbind(v0, v1, v2) = vempty) & ! [v0] : ! [v1] : ! [v2] : ( ~ (visValue(v2) = 0) | ~ (vapp(v0, v1) = v2)) & ! [v0] : ! [v1] : (v1 = vnoType | ~ (vlookup(v0, vempty) = v1)) & ! [v0] : ! [v1] : ( ~ (vreduce(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v13 = v1 & v11 = 0 & v9 = v3 & v8 = v0 & ~ (v10 = 0) & vreduce(v5) = v3 & visSomeExp(v3) = v10 & vsomeExp(v12) = v1 & vsubst(v4, v5, v6) = v12 & visValue(v5) = 0 & vapp(v7, v5) = v0 & vabs(v4, v2, v6) = v7) | (v13 = v1 & v10 = 0 & v9 = v6 & v8 = v0 & vreduce(v2) = v6 & vgetSomeExp(v6) = v11 & visSomeExp(v6) = 0 & vsomeExp(v12) = v1 & vapp(v7, v11) = v12 & vapp(v7, v2) = v0 & vabs(v3, v4, v5) = v7) | (v10 = v1 & v7 = 0 & v6 = v3 & v5 = v0 & vreduce(v2) = v3 & vgetSomeExp(v3) = v8 & visSomeExp(v3) = 0 & vsomeExp(v9) = v1 & vapp(v8, v4) = v9 & vapp(v2, v4) = v0 & ! [v14] : ! [v15] : ! [v16] : ~ (vabs(v14, v15, v16) = v2)) | (v9 = v5 & v8 = v0 & v1 = vnoExp & ~ (v11 = 0) & ~ (v10 = 0) & vreduce(v6) = v5 & visSomeExp(v5) = v10 & visValue(v6) = v11 & vapp(v7, v6) = v0 & vabs(v2, v3, v4) = v7) | (v6 = v4 & v5 = v0 & v1 = vnoExp & ~ (v7 = 0) & vreduce(v3) = v4 & visSomeExp(v4) = v7 & vapp(v3, v2) = v0 & ! [v14] : ! [v15] : ! [v16] : ~ (vabs(v14, v15, v16) = v3)) | (v5 = v0 & v1 = vnoExp & vabs(v2, v3, v4) = v0) | (v3 = v0 & v1 = vnoExp & vvar(v2) = v0))) & ! [v0] : ! [v1] : ( ~ (visFreeVar(v0, v1) = 0) | ? [v2] : ( ~ (v2 = v0) & vgensym(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (visValue(v1) = 0) | ~ (vvar(v0) = v1)) & ! [v0] : ~ (vsomeExp(v0) = vnoExp) & ! [v0] : ~ (vsomeType(v0) = vnoType) % 37.21/11.18 | % 37.21/11.18 | Applying alpha-rule on (1) yields: % 37.21/11.18 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v1 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6)) % 37.21/11.18 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v2 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6)) % 37.21/11.18 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v1 | v3 = v2 | ~ (vsubst(v1, v0, v2) = v3) | ~ (vvar(v4) = v2)) % 37.21/11.18 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (varrow(v0, v4) = v5) | ~ (vtcheck(v1, v6, v4) = v7) | ~ (vtcheck(v1, v2, v5) = 0) | ~ (vapp(v2, v3) = v6) | ? [v8] : ( ~ (v8 = 0) & vtcheck(v1, v3, v0) = v8)) % 37.21/11.18 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vapp(v1, v2) = v3) | ~ (vvar(v0) = v3)) % 37.21/11.18 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (visValue(v3) = v4) | ~ (vabs(v0, v1, v2) = v3)) % 37.21/11.18 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (visFreeVar(v0, v3) = v5) | ~ (visFreeVar(v0, v2) = v4) | ~ (visFreeVar(v0, v1) = 0) | ? [v6] : ( ~ (v6 = v1) & vapp(v2, v3) = v6)) % 37.21/11.18 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0)) % 37.21/11.18 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (visFreeVar(v1, v4) = v5) | ~ (visFreeVar(v1, v2) = 0) | ~ (vabs(v3, v0, v4) = v2)) % 37.21/11.18 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeType(v1) = v2) | ~ (vsomeType(v0) = v2)) % 37.21/11.18 | (12) ! [v0] : ! [v1] : (v1 = vnoType | ~ (vlookup(v0, vempty) = v1)) % 37.21/11.18 | (13) ! [v0] : ! [v1] : ( ~ (vreduce(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v13 = v1 & v11 = 0 & v9 = v3 & v8 = v0 & ~ (v10 = 0) & vreduce(v5) = v3 & visSomeExp(v3) = v10 & vsomeExp(v12) = v1 & vsubst(v4, v5, v6) = v12 & visValue(v5) = 0 & vapp(v7, v5) = v0 & vabs(v4, v2, v6) = v7) | (v13 = v1 & v10 = 0 & v9 = v6 & v8 = v0 & vreduce(v2) = v6 & vgetSomeExp(v6) = v11 & visSomeExp(v6) = 0 & vsomeExp(v12) = v1 & vapp(v7, v11) = v12 & vapp(v7, v2) = v0 & vabs(v3, v4, v5) = v7) | (v10 = v1 & v7 = 0 & v6 = v3 & v5 = v0 & vreduce(v2) = v3 & vgetSomeExp(v3) = v8 & visSomeExp(v3) = 0 & vsomeExp(v9) = v1 & vapp(v8, v4) = v9 & vapp(v2, v4) = v0 & ! [v14] : ! [v15] : ! [v16] : ~ (vabs(v14, v15, v16) = v2)) | (v9 = v5 & v8 = v0 & v1 = vnoExp & ~ (v11 = 0) & ~ (v10 = 0) & vreduce(v6) = v5 & visSomeExp(v5) = v10 & visValue(v6) = v11 & vapp(v7, v6) = v0 & vabs(v2, v3, v4) = v7) | (v6 = v4 & v5 = v0 & v1 = vnoExp & ~ (v7 = 0) & vreduce(v3) = v4 & visSomeExp(v4) = v7 & vapp(v3, v2) = v0 & ! [v14] : ! [v15] : ! [v16] : ~ (vabs(v14, v15, v16) = v3)) | (v5 = v0 & v1 = vnoExp & vabs(v2, v3, v4) = v0) | (v3 = v0 & v1 = vnoExp & vvar(v2) = v0))) % 37.21/11.18 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (vbind(v0, v1, v2) = v4) | ~ (vbind(v0, v1, v2) = v3)) % 37.21/11.18 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v3 | ~ (vsubst(v0, v1, v5) = v7) | ~ (vsubst(v0, v1, v4) = v6) | ~ (vsubst(v0, v1, v2) = v3) | ~ (vapp(v6, v7) = v8) | ? [v9] : ( ~ (v9 = v2) & vapp(v4, v5) = v9)) % 37.21/11.18 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~ (vapp(v3, v2) = v0)) % 37.21/11.18 | (17) ~ (visSomeExp(vnoExp) = 0) % 37.21/11.18 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4)) % 37.21/11.18 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vvar(v1) = v2) | ~ (vvar(v0) = v2)) % 37.21/11.18 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4)) % 37.21/11.18 | (21) ! [v0] : ~ (vsomeType(v0) = vnoType) % 37.21/11.18 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (vlookup(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (v3 = v0 | (v8 = v2 & v7 = v1 & v5 = v0 & v4 = v0 & vsomeType(v6) = v2 & vbind(v0, v6, v3) = v1) | (v8 = v2 & v7 = v1 & v5 = v0 & ~ (v4 = v0) & vlookup(v0, v6) = v2 & vbind(v4, v3, v6) = v1))) % 37.21/11.18 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~ (vsomeType(v2) = v0)) % 37.21/11.18 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = vnoExp | ~ (vreduce(v3) = v4) | ~ (visSomeExp(v2) = v5) | ~ (vapp(v1, v0) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v9 = v1 & vabs(v6, v7, v8) = v1) | ( ~ (v6 = v2) & vreduce(v1) = v6))) % 37.21/11.18 | (25) vreduce(ve2) = all_0_6_6 % 37.21/11.18 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) = v0)) % 37.21/11.18 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v4 | v2 = v1 | ~ (vlookup(v2, v5) = v6) | ~ (vlookup(v2, v3) = v4) | ~ (vbind(v1, v0, v5) = v3)) % 37.21/11.18 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vsomeExp(v0) = v2) | ~ (vsomeExp(v0) = v1)) % 37.21/11.18 | (29) vreduce(ve1) = all_0_7_7 % 37.21/11.18 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = vempty | ~ (vlookup(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = v2 & v7 = v1 & v5 = v0 & v4 = v0 & vsomeType(v6) = v2 & vbind(v0, v6, v3) = v1) | (v8 = v2 & v7 = v1 & v5 = v0 & ~ (v4 = v0) & vlookup(v0, v6) = v2 & vbind(v4, v3, v6) = v1))) % 37.21/11.18 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (vsomeExp(v1) = all_0_7_7) | ~ (vtcheck(v0, ve1, v2) = 0) | vtcheck(v0, v1, v2) = 0) % 37.21/11.19 | (32) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vgetSomeExp(v0) = v1) | ~ (vsomeExp(v2) = v0)) % 37.21/11.19 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) % 37.21/11.19 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v6 = vnoExp | ~ (vreduce(v5) = v6) | ~ (visSomeExp(v3) = v8) | ~ (vapp(v7, v4) = v5) | ~ (vabs(v0, v1, v2) = v7) | ? [v9] : ? [v10] : (vreduce(v4) = v9 & visValue(v4) = v10 & ( ~ (v9 = v3) | v10 = 0))) % 37.21/11.19 | (35) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (visSomeType(v1) = v2) | ~ (vsomeType(v0) = v1)) % 37.70/11.19 | (36) ~ (all_0_0_0 = 0) % 37.70/11.19 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (varrow(v2, v3) = v4) | ~ (varrow(v0, v1) = v4)) % 37.70/11.19 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0)) % 37.70/11.19 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (vapp(v0, v1) = v3) | ~ (vapp(v0, v1) = v2)) % 37.70/11.19 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (vtcheck(v7, v4, v5) = 0) | ~ (vbind(v0, v2, v6) = v7) | ~ (vbind(v0, v1, v3) = v6) | ? [v8] : (vtcheck(v8, v4, v5) = 0 & vbind(v0, v2, v3) = v8)) % 37.70/11.19 | (41) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (visFreeVar(v0, v1) = 0) | ~ (vvar(v2) = v1)) % 37.70/11.19 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0)) % 37.70/11.19 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v3 | v5 = v0 | ~ (vsubst(v5, v8, v7) = v9) | ~ (vsubst(v0, v1, v10) = v11) | ~ (vsubst(v0, v1, v2) = v3) | ~ (vabs(v6, v4, v9) = v10) | ~ (vvar(v6) = v8) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (vgensym(v16) = v17 & visFreeVar(v5, v1) = v13 & vapp(v14, v15) = v16 & vapp(v1, v7) = v14 & vabs(v5, v4, v7) = v12 & vvar(v0) = v15 & ( ~ (v17 = v6) | ~ (v13 = 0) | ~ (v12 = v2)))) % 37.70/11.19 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v3 | v4 = v0 | ~ (vsubst(v0, v1, v6) = v7) | ~ (vsubst(v0, v1, v2) = v3) | ~ (vabs(v4, v5, v7) = v8) | ? [v9] : ? [v10] : (visFreeVar(v4, v1) = v10 & vabs(v4, v5, v6) = v9 & ( ~ (v9 = v2) | v10 = 0))) % 37.70/11.19 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (vreduce(v1) = v2) | ~ (vreduce(v0) = v3) | ~ (vgetSomeExp(v3) = v5) | ~ (vapp(v5, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v10 = v0 & vabs(v7, v8, v9) = v0) | (visSomeExp(v3) = v8 & vsomeExp(v6) = v9 & vapp(v0, v4) = v7 & ( ~ (v8 = 0) | ~ (v7 = v1) | v9 = v2)))) % 37.70/11.19 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v0 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6)) % 37.70/11.19 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0)) % 37.70/11.19 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (vsubst(v2, v3, v4) = v7) | ~ (vtcheck(v6, v4, v5) = 0) | ~ (vtcheck(v1, v7, v5) = v8) | ~ (vbind(v2, v0, v1) = v6) | ? [v9] : ( ~ (v9 = 0) & vtcheck(v1, v3, v0) = v9)) % 37.70/11.19 | (49) vsomeExp(all_0_2_2) = all_0_4_4 % 37.70/11.19 | (50) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeExp(v1) = v2) | ~ (vsomeExp(v0) = v2)) % 37.70/11.19 | (51) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vsomeType(v0) = v2) | ~ (vsomeType(v0) = v1)) % 37.70/11.19 | (52) vtcheck(all_0_3_3, all_0_5_5, all_0_1_1) = 0 % 37.70/11.19 | (53) ~ (visSomeType(vnoType) = 0) % 37.70/11.19 | (54) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vvar(v0) = v2) | ~ (vvar(v0) = v1)) % 37.70/11.19 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vapp(v3, v4) = v5) | ~ (vabs(v0, v1, v2) = v5)) % 37.70/11.19 | (56) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0)) % 37.70/11.19 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v1 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6)) % 37.70/11.19 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (vsubst(v0, v1, v2) = v3) | ~ (vvar(v0) = v2)) % 37.70/11.19 | (59) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) % 37.70/11.19 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (vtcheck(v0, v3, v2) = v4) | ~ (vvar(v1) = v3) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & vlookup(v1, v0) = v5 & vsomeType(v2) = v6)) % 37.70/11.19 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (visFreeVar(v0, v3) = v4) | ~ (visFreeVar(v0, v2) = 0) | ~ (visFreeVar(v0, v1) = v5) | ? [v6] : ( ~ (v6 = v1) & vapp(v2, v3) = v6)) % 37.70/11.19 | (62) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (visValue(v2) = v1) | ~ (visValue(v2) = v0)) % 37.70/11.19 | (63) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vgetSomeType(v0) = v1) | ~ (vsomeType(v2) = v0)) % 37.70/11.19 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (varrow(v2, v3) = v4) | ~ (varrow(v0, v1) = v4)) % 37.70/11.19 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) = v0)) % 37.70/11.19 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v2 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6)) % 37.70/11.19 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v3 = v1 | ~ (visFreeVar(v1, v4) = 0) | ~ (visFreeVar(v1, v2) = v5) | ~ (vabs(v3, v0, v4) = v2)) % 37.70/11.19 | (68) vtcheck(all_0_3_3, all_0_2_2, all_0_1_1) = all_0_0_0 % 37.70/11.19 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v2 = v0 | ~ (vtcheck(v8, v5, v6) = v9) | ~ (vbind(v2, v3, v4) = v7) | ~ (vbind(v0, v1, v7) = v8) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = 0) & vtcheck(v11, v5, v6) = v12 & vbind(v2, v3, v10) = v11 & vbind(v0, v1, v4) = v10)) % 37.75/11.19 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0)) % 37.75/11.19 | (71) ! [v0] : ! [v1] : ! [v2] : ~ (vbind(v0, v1, v2) = vempty) % 37.75/11.20 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (vsomeExp(v1) = all_0_6_6) | ~ (vtcheck(v0, ve2, v2) = 0) | vtcheck(v0, v1, v2) = 0) % 37.75/11.20 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vabs(v1, v2, v3) = v4) | ~ (vvar(v0) = v4)) % 37.75/11.20 | (74) vreduce(all_0_5_5) = all_0_4_4 % 37.75/11.20 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vlookup(v1, v2) = v3) | ~ (vbind(v1, v4, v0) = v2) | vsomeType(v4) = v3) % 37.75/11.20 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (varrow(v3, v4) = v6) | ~ (vtcheck(v0, v5, v6) = v7) | ~ (vabs(v1, v3, v2) = v5) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & vtcheck(v8, v2, v4) = v9 & vbind(v1, v3, v0) = v8)) % 37.75/11.20 | (77) ! [v0] : ~ (vsomeExp(v0) = vnoExp) % 37.75/11.20 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vtcheck(v5, v3, v4) = v6) | ~ (vbind(v0, v1, v2) = v5) | ? [v7] : ? [v8] : (vtcheck(v2, v3, v4) = v8 & vlookup(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = vnoType)))) % 37.75/11.20 | (79) ! [v0] : ! [v1] : ! [v2] : (v2 = vnoType | ~ (vlookup(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = v2 & v7 = v1 & v5 = v0 & v4 = v0 & vsomeType(v6) = v2 & vbind(v0, v6, v3) = v1) | (v8 = v2 & v7 = v1 & v5 = v0 & ~ (v4 = v0) & vlookup(v0, v6) = v2 & vbind(v4, v3, v6) = v1))) % 37.75/11.20 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (varrow(v3, v2) = v1) | ~ (varrow(v3, v2) = v0)) % 37.75/11.20 | (81) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (visFreeVar(v0, v1) = v2) | ~ (vvar(v0) = v1)) % 37.75/11.20 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsubst(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = v3 & v15 = v8 & v11 = 0 & v10 = v2 & v5 = v1 & v4 = v0 & ~ (v7 = v0) & vsubst(v7, v16, v9) = v17 & vsubst(v0, v1, v18) = v3 & vgensym(v14) = v8 & visFreeVar(v7, v1) = 0 & vapp(v12, v13) = v14 & vapp(v1, v9) = v12 & vabs(v8, v6, v17) = v18 & vabs(v7, v6, v9) = v2 & vvar(v8) = v16 & vvar(v0) = v13) | (v12 = v3 & v9 = v2 & v7 = v1 & v6 = v0 & ~ (v10 = 0) & ~ (v4 = v0) & vsubst(v0, v1, v8) = v11 & visFreeVar(v4, v1) = v10 & vabs(v4, v5, v11) = v3 & vabs(v4, v5, v8) = v2) | (v11 = v3 & v8 = v2 & v6 = v1 & v5 = v0 & vsubst(v0, v1, v7) = v10 & vsubst(v0, v1, v4) = v9 & vapp(v9, v10) = v3 & vapp(v4, v7) = v2) | (v9 = v2 & v6 = v0 & v5 = v0 & v4 = v1 & v3 = v2 & vabs(v0, v7, v8) = v2) | (v7 = v2 & v6 = v1 & v5 = v0 & v4 = v0 & v3 = v1 & vvar(v0) = v2) | (v7 = v2 & v5 = v0 & v4 = v1 & v3 = v2 & ~ (v6 = v0) & vvar(v6) = v2))) % 37.75/11.20 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (vsubst(v1, v0, v2) = v3) | ~ (vabs(v1, v4, v5) = v2)) % 37.75/11.20 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ (visValue(v2) = 0) | ~ (vapp(v0, v1) = v2)) % 37.75/11.20 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v0 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6)) % 37.75/11.20 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (visFreeVar(v1, v3) = v4) | ~ (visFreeVar(v1, v2) = 0) | ~ (vabs(v1, v0, v3) = v2)) % 37.75/11.20 | (87) ! [v0] : ! [v1] : ! [v2] : ( ~ (vtcheck(v2, v0, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v8 = v1 & v7 = v0 & varrow(v5, v6) = v1 & vtcheck(v9, v4, v6) = 0 & vbind(v3, v5, v2) = v9 & vabs(v3, v5, v4) = v0) | (v9 = 0 & v8 = 0 & v6 = v0 & varrow(v5, v1) = v7 & vtcheck(v2, v4, v5) = 0 & vtcheck(v2, v3, v7) = 0 & vapp(v3, v4) = v0) | (v6 = v3 & v5 = v0 & vlookup(v4, v2) = v3 & vsomeType(v1) = v3 & vvar(v4) = v0))) % 37.75/11.20 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~ (vlookup(v3, v2) = v0)) % 37.75/11.20 | (89) ! [v0] : ! [v1] : ( ~ (visFreeVar(v0, v1) = 0) | ? [v2] : ( ~ (v2 = v0) & vgensym(v1) = v2)) % 37.75/11.20 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (vreduce(v2) = v3) | ~ (visSomeExp(v1) = v8) | ~ (vapp(v7, v5) = v2) | ~ (vabs(v4, v0, v6) = v7) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (vreduce(v5) = v9 & vsomeExp(v11) = v12 & vsubst(v4, v5, v6) = v11 & visValue(v5) = v10 & ( ~ (v10 = 0) | ~ (v9 = v1) | v12 = v3))) % 37.75/11.20 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3, v2) = v0)) % 37.75/11.20 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (visFreeVar(v0, v3) = 0) | ~ (visFreeVar(v0, v2) = v4) | ~ (visFreeVar(v0, v1) = v5) | ? [v6] : ( ~ (v6 = v1) & vapp(v2, v3) = v6)) % 37.75/11.20 | (93) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~ (vsomeExp(v2) = v0)) % 37.75/11.20 | (94) ! [v0] : ! [v1] : ! [v2] : (v2 = vnoExp | ~ (vreduce(v1) = v2) | ~ (vvar(v0) = v1)) % 37.75/11.20 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (vreduce(v1) = v2) | ~ (vgetSomeExp(v6) = v8) | ~ (vapp(v7, v8) = v9) | ~ (vapp(v7, v0) = v1) | ~ (vabs(v3, v4, v5) = v7) | ? [v10] : ? [v11] : ? [v12] : (vreduce(v0) = v10 & visSomeExp(v6) = v11 & vsomeExp(v9) = v12 & ( ~ (v11 = 0) | ~ (v10 = v6) | v12 = v2))) % 37.75/11.20 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = vnoExp | ~ (vreduce(v3) = v4) | ~ (vabs(v0, v1, v2) = v3)) % 37.75/11.20 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (varrow(v0, v1) = v3) | ~ (varrow(v0, v1) = v2)) % 37.75/11.20 | (98) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0)) % 37.75/11.20 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vtcheck(v5, v3, v4) = 0) | ~ (vbind(v0, v1, v2) = v5) | ? [v6] : ? [v7] : (vtcheck(v2, v3, v4) = v7 & visFreeVar(v0, v3) = v6 & (v7 = 0 | v6 = 0))) % 37.75/11.20 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (vabs(v0, v1, v2) = v4) | ~ (vabs(v0, v1, v2) = v3)) % 37.75/11.20 | (101) ! [v0] : ! [v1] : ( ~ (visValue(v1) = 0) | ~ (vvar(v0) = v1)) % 37.75/11.21 | (102) vapp(ve1, ve2) = all_0_5_5 % 37.75/11.21 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vtcheck(v5, v3, v4) = v6) | ~ (vbind(v0, v1, v2) = v5) | ? [v7] : ? [v8] : (vtcheck(v2, v3, v4) = v8 & visFreeVar(v0, v3) = v7 & ( ~ (v8 = 0) | v7 = 0))) % 37.80/11.21 | (104) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (visSomeExp(v1) = v2) | ~ (vsomeExp(v0) = v1)) % 37.80/11.21 | % 37.81/11.21 | Instantiating formula (59) with ve2, all_0_6_6, all_0_4_4 and discharging atoms vreduce(ve2) = all_0_6_6, yields: % 37.81/11.21 | (105) all_0_4_4 = all_0_6_6 | ~ (vreduce(ve2) = all_0_4_4) % 37.81/11.21 | % 37.81/11.21 | Instantiating formula (59) with ve1, all_0_7_7, all_0_6_6 and discharging atoms vreduce(ve1) = all_0_7_7, yields: % 37.81/11.21 | (106) all_0_6_6 = all_0_7_7 | ~ (vreduce(ve1) = all_0_6_6) % 37.81/11.21 | % 37.81/11.21 | Instantiating formula (77) with all_0_2_2 yields: % 37.81/11.21 | (107) ~ (vsomeExp(all_0_2_2) = vnoExp) % 37.81/11.21 | % 37.81/11.21 | Using (49) and (107) yields: % 37.81/11.21 | (108) ~ (all_0_4_4 = vnoExp) % 37.81/11.21 | % 37.81/11.21 | Instantiating formula (13) with all_0_4_4, all_0_5_5 and discharging atoms vreduce(all_0_5_5) = all_0_4_4, yields: % 37.81/11.21 | (109) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = all_0_4_4 & v9 = 0 & v7 = v1 & v6 = all_0_5_5 & ~ (v8 = 0) & vreduce(v3) = v1 & visSomeExp(v1) = v8 & vsomeExp(v10) = all_0_4_4 & vsubst(v2, v3, v4) = v10 & visValue(v3) = 0 & vapp(v5, v3) = all_0_5_5 & vabs(v2, v0, v4) = v5) | (v11 = all_0_4_4 & v8 = 0 & v7 = v4 & v6 = all_0_5_5 & vreduce(v0) = v4 & vgetSomeExp(v4) = v9 & visSomeExp(v4) = 0 & vsomeExp(v10) = all_0_4_4 & vapp(v5, v9) = v10 & vapp(v5, v0) = all_0_5_5 & vabs(v1, v2, v3) = v5) | (v8 = all_0_4_4 & v5 = 0 & v4 = v1 & v3 = all_0_5_5 & vreduce(v0) = v1 & vgetSomeExp(v1) = v6 & visSomeExp(v1) = 0 & vsomeExp(v7) = all_0_4_4 & vapp(v6, v2) = v7 & vapp(v0, v2) = all_0_5_5 & ! [v12] : ! [v13] : ! [v14] : ~ (vabs(v12, v13, v14) = v0)) | (v7 = v3 & v6 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (v9 = 0) & ~ (v8 = 0) & vreduce(v4) = v3 & visSomeExp(v3) = v8 & visValue(v4) = v9 & vapp(v5, v4) = all_0_5_5 & vabs(v0, v1, v2) = v5) | (v4 = v2 & v3 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (v5 = 0) & vreduce(v1) = v2 & visSomeExp(v2) = v5 & vapp(v1, v0) = all_0_5_5 & ! [v12] : ! [v13] : ! [v14] : ~ (vabs(v12, v13, v14) = v1)) | (v3 = all_0_5_5 & all_0_4_4 = vnoExp & vabs(v0, v1, v2) = all_0_5_5) | (v1 = all_0_5_5 & all_0_4_4 = vnoExp & vvar(v0) = all_0_5_5)) % 37.81/11.21 | % 37.81/11.21 | Instantiating formula (13) with all_0_6_6, ve2 and discharging atoms vreduce(ve2) = all_0_6_6, yields: % 37.81/11.21 | (110) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = all_0_6_6 & v9 = 0 & v7 = v1 & v6 = ve2 & ~ (v8 = 0) & vreduce(v3) = v1 & visSomeExp(v1) = v8 & vsomeExp(v10) = all_0_6_6 & vsubst(v2, v3, v4) = v10 & visValue(v3) = 0 & vapp(v5, v3) = ve2 & vabs(v2, v0, v4) = v5) | (v11 = all_0_6_6 & v8 = 0 & v7 = v4 & v6 = ve2 & vreduce(v0) = v4 & vgetSomeExp(v4) = v9 & visSomeExp(v4) = 0 & vsomeExp(v10) = all_0_6_6 & vapp(v5, v9) = v10 & vapp(v5, v0) = ve2 & vabs(v1, v2, v3) = v5) | (v8 = all_0_6_6 & v5 = 0 & v4 = v1 & v3 = ve2 & vreduce(v0) = v1 & vgetSomeExp(v1) = v6 & visSomeExp(v1) = 0 & vsomeExp(v7) = all_0_6_6 & vapp(v6, v2) = v7 & vapp(v0, v2) = ve2 & ! [v12] : ! [v13] : ! [v14] : ~ (vabs(v12, v13, v14) = v0)) | (v7 = v3 & v6 = ve2 & all_0_6_6 = vnoExp & ~ (v9 = 0) & ~ (v8 = 0) & vreduce(v4) = v3 & visSomeExp(v3) = v8 & visValue(v4) = v9 & vapp(v5, v4) = ve2 & vabs(v0, v1, v2) = v5) | (v4 = v2 & v3 = ve2 & all_0_6_6 = vnoExp & ~ (v5 = 0) & vreduce(v1) = v2 & visSomeExp(v2) = v5 & vapp(v1, v0) = ve2 & ! [v12] : ! [v13] : ! [v14] : ~ (vabs(v12, v13, v14) = v1)) | (v3 = ve2 & all_0_6_6 = vnoExp & vabs(v0, v1, v2) = ve2) | (v1 = ve2 & all_0_6_6 = vnoExp & vvar(v0) = ve2)) % 37.81/11.21 | % 37.81/11.21 | Instantiating formula (13) with all_0_7_7, ve1 and discharging atoms vreduce(ve1) = all_0_7_7, yields: % 37.81/11.21 | (111) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = all_0_7_7 & v9 = 0 & v7 = v1 & v6 = ve1 & ~ (v8 = 0) & vreduce(v3) = v1 & visSomeExp(v1) = v8 & vsomeExp(v10) = all_0_7_7 & vsubst(v2, v3, v4) = v10 & visValue(v3) = 0 & vapp(v5, v3) = ve1 & vabs(v2, v0, v4) = v5) | (v11 = all_0_7_7 & v8 = 0 & v7 = v4 & v6 = ve1 & vreduce(v0) = v4 & vgetSomeExp(v4) = v9 & visSomeExp(v4) = 0 & vsomeExp(v10) = all_0_7_7 & vapp(v5, v9) = v10 & vapp(v5, v0) = ve1 & vabs(v1, v2, v3) = v5) | (v8 = all_0_7_7 & v5 = 0 & v4 = v1 & v3 = ve1 & vreduce(v0) = v1 & vgetSomeExp(v1) = v6 & visSomeExp(v1) = 0 & vsomeExp(v7) = all_0_7_7 & vapp(v6, v2) = v7 & vapp(v0, v2) = ve1 & ! [v12] : ! [v13] : ! [v14] : ~ (vabs(v12, v13, v14) = v0)) | (v7 = v3 & v6 = ve1 & all_0_7_7 = vnoExp & ~ (v9 = 0) & ~ (v8 = 0) & vreduce(v4) = v3 & visSomeExp(v3) = v8 & visValue(v4) = v9 & vapp(v5, v4) = ve1 & vabs(v0, v1, v2) = v5) | (v4 = v2 & v3 = ve1 & all_0_7_7 = vnoExp & ~ (v5 = 0) & vreduce(v1) = v2 & visSomeExp(v2) = v5 & vapp(v1, v0) = ve1 & ! [v12] : ! [v13] : ! [v14] : ~ (vabs(v12, v13, v14) = v1)) | (v3 = ve1 & all_0_7_7 = vnoExp & vabs(v0, v1, v2) = ve1) | (v1 = ve1 & all_0_7_7 = vnoExp & vvar(v0) = ve1)) % 37.81/11.21 | % 37.81/11.21 | Instantiating formula (87) with all_0_3_3, all_0_1_1, all_0_5_5 and discharging atoms vtcheck(all_0_3_3, all_0_5_5, all_0_1_1) = 0, yields: % 37.81/11.21 | (112) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v5 = all_0_1_1 & v4 = all_0_5_5 & varrow(v2, v3) = all_0_1_1 & vtcheck(v6, v1, v3) = 0 & vbind(v0, v2, all_0_3_3) = v6 & vabs(v0, v2, v1) = all_0_5_5) | (v6 = 0 & v5 = 0 & v3 = all_0_5_5 & varrow(v2, all_0_1_1) = v4 & vtcheck(all_0_3_3, v1, v2) = 0 & vtcheck(all_0_3_3, v0, v4) = 0 & vapp(v0, v1) = all_0_5_5) | (v3 = v0 & v2 = all_0_5_5 & vlookup(v1, all_0_3_3) = v0 & vsomeType(all_0_1_1) = v0 & vvar(v1) = all_0_5_5)) % 37.81/11.22 | % 37.81/11.22 | Instantiating (112) with all_16_0_8, all_16_1_9, all_16_2_10, all_16_3_11, all_16_4_12, all_16_5_13, all_16_6_14, all_16_7_15 yields: % 37.81/11.22 | (113) (all_16_0_8 = 0 & all_16_2_10 = all_0_1_1 & all_16_3_11 = all_0_5_5 & varrow(all_16_5_13, all_16_4_12) = all_0_1_1 & vtcheck(all_16_1_9, all_16_6_14, all_16_4_12) = 0 & vbind(all_16_7_15, all_16_5_13, all_0_3_3) = all_16_1_9 & vabs(all_16_7_15, all_16_5_13, all_16_6_14) = all_0_5_5) | (all_16_1_9 = 0 & all_16_2_10 = 0 & all_16_4_12 = all_0_5_5 & varrow(all_16_5_13, all_0_1_1) = all_16_3_11 & vtcheck(all_0_3_3, all_16_6_14, all_16_5_13) = 0 & vtcheck(all_0_3_3, all_16_7_15, all_16_3_11) = 0 & vapp(all_16_7_15, all_16_6_14) = all_0_5_5) | (all_16_4_12 = all_16_7_15 & all_16_5_13 = all_0_5_5 & vlookup(all_16_6_14, all_0_3_3) = all_16_7_15 & vsomeType(all_0_1_1) = all_16_7_15 & vvar(all_16_6_14) = all_0_5_5) % 37.81/11.22 | % 37.81/11.22 | Instantiating (111) with all_17_0_16, all_17_1_17, all_17_2_18, all_17_3_19, all_17_4_20, all_17_5_21, all_17_6_22, all_17_7_23, all_17_8_24, all_17_9_25, all_17_10_26, all_17_11_27 yields: % 37.81/11.22 | (114) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) | (all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22) | (all_17_7_23 = all_17_9_25 & all_17_8_24 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_6_22 = 0) & vreduce(all_17_10_26) = all_17_9_25 & visSomeExp(all_17_9_25) = all_17_6_22 & vapp(all_17_10_26, all_17_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26)) | (all_17_8_24 = ve1 & all_0_7_7 = vnoExp & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1) | (all_17_10_26 = ve1 & all_0_7_7 = vnoExp & vvar(all_17_11_27) = ve1) % 37.81/11.22 | % 37.81/11.22 | Instantiating (110) with all_18_0_28, all_18_1_29, all_18_2_30, all_18_3_31, all_18_4_32, all_18_5_33, all_18_6_34, all_18_7_35, all_18_8_36, all_18_9_37, all_18_10_38, all_18_11_39 yields: % 37.81/11.22 | (115) (all_18_0_28 = all_0_6_6 & all_18_2_30 = 0 & all_18_4_32 = all_18_10_38 & all_18_5_33 = ve2 & ~ (all_18_3_31 = 0) & vreduce(all_18_8_36) = all_18_10_38 & visSomeExp(all_18_10_38) = all_18_3_31 & vsomeExp(all_18_1_29) = all_0_6_6 & vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 & visValue(all_18_8_36) = 0 & vapp(all_18_6_34, all_18_8_36) = ve2 & vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34) | (all_18_0_28 = all_0_6_6 & all_18_3_31 = 0 & all_18_4_32 = all_18_7_35 & all_18_5_33 = ve2 & vreduce(all_18_11_39) = all_18_7_35 & vgetSomeExp(all_18_7_35) = all_18_2_30 & visSomeExp(all_18_7_35) = 0 & vsomeExp(all_18_1_29) = all_0_6_6 & vapp(all_18_6_34, all_18_2_30) = all_18_1_29 & vapp(all_18_6_34, all_18_11_39) = ve2 & vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34) | (all_18_3_31 = all_0_6_6 & all_18_6_34 = 0 & all_18_7_35 = all_18_10_38 & all_18_8_36 = ve2 & vreduce(all_18_11_39) = all_18_10_38 & vgetSomeExp(all_18_10_38) = all_18_5_33 & visSomeExp(all_18_10_38) = 0 & vsomeExp(all_18_4_32) = all_0_6_6 & vapp(all_18_5_33, all_18_9_37) = all_18_4_32 & vapp(all_18_11_39, all_18_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_11_39)) | (all_18_4_32 = all_18_8_36 & all_18_5_33 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_2_30 = 0) & ~ (all_18_3_31 = 0) & vreduce(all_18_7_35) = all_18_8_36 & visSomeExp(all_18_8_36) = all_18_3_31 & visValue(all_18_7_35) = all_18_2_30 & vapp(all_18_6_34, all_18_7_35) = ve2 & vabs(all_18_11_39, all_18_10_38, all_18_9_37) = all_18_6_34) | (all_18_7_35 = all_18_9_37 & all_18_8_36 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_6_34 = 0) & vreduce(all_18_10_38) = all_18_9_37 & visSomeExp(all_18_9_37) = all_18_6_34 & vapp(all_18_10_38, all_18_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_10_38)) | (all_18_8_36 = ve2 & all_0_6_6 = vnoExp & vabs(all_18_11_39, all_18_10_38, all_18_9_37) = ve2) | (all_18_10_38 = ve2 & all_0_6_6 = vnoExp & vvar(all_18_11_39) = ve2) % 37.81/11.22 | % 37.81/11.22 | Instantiating (109) with all_19_0_40, all_19_1_41, all_19_2_42, all_19_3_43, all_19_4_44, all_19_5_45, all_19_6_46, all_19_7_47, all_19_8_48, all_19_9_49, all_19_10_50, all_19_11_51 yields: % 37.81/11.22 | (116) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) | (all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46) | (all_19_7_47 = all_19_9_49 & all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_6_46 = 0) & vreduce(all_19_10_50) = all_19_9_49 & visSomeExp(all_19_9_49) = all_19_6_46 & vapp(all_19_10_50, all_19_11_51) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50)) | (all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_0_5_5) | (all_19_10_50 = all_0_5_5 & all_0_4_4 = vnoExp & vvar(all_19_11_51) = all_0_5_5) % 37.81/11.22 | % 37.81/11.22 +-Applying beta-rule and splitting (105), into two cases. % 37.81/11.22 |-Branch one: % 37.81/11.22 | (117) ~ (vreduce(ve2) = all_0_4_4) % 37.81/11.22 | % 37.81/11.22 | Using (25) and (117) yields: % 37.81/11.22 | (118) ~ (all_0_4_4 = all_0_6_6) % 37.81/11.22 | % 37.81/11.22 +-Applying beta-rule and splitting (106), into two cases. % 37.81/11.22 |-Branch one: % 37.81/11.22 | (119) ~ (vreduce(ve1) = all_0_6_6) % 37.81/11.22 | % 37.81/11.22 | Using (29) and (119) yields: % 37.81/11.22 | (120) ~ (all_0_6_6 = all_0_7_7) % 37.81/11.22 | % 37.81/11.22 +-Applying beta-rule and splitting (113), into two cases. % 37.81/11.22 |-Branch one: % 37.81/11.22 | (121) (all_16_0_8 = 0 & all_16_2_10 = all_0_1_1 & all_16_3_11 = all_0_5_5 & varrow(all_16_5_13, all_16_4_12) = all_0_1_1 & vtcheck(all_16_1_9, all_16_6_14, all_16_4_12) = 0 & vbind(all_16_7_15, all_16_5_13, all_0_3_3) = all_16_1_9 & vabs(all_16_7_15, all_16_5_13, all_16_6_14) = all_0_5_5) | (all_16_1_9 = 0 & all_16_2_10 = 0 & all_16_4_12 = all_0_5_5 & varrow(all_16_5_13, all_0_1_1) = all_16_3_11 & vtcheck(all_0_3_3, all_16_6_14, all_16_5_13) = 0 & vtcheck(all_0_3_3, all_16_7_15, all_16_3_11) = 0 & vapp(all_16_7_15, all_16_6_14) = all_0_5_5) % 37.81/11.22 | % 37.81/11.22 +-Applying beta-rule and splitting (121), into two cases. % 37.81/11.22 |-Branch one: % 37.81/11.22 | (122) all_16_0_8 = 0 & all_16_2_10 = all_0_1_1 & all_16_3_11 = all_0_5_5 & varrow(all_16_5_13, all_16_4_12) = all_0_1_1 & vtcheck(all_16_1_9, all_16_6_14, all_16_4_12) = 0 & vbind(all_16_7_15, all_16_5_13, all_0_3_3) = all_16_1_9 & vabs(all_16_7_15, all_16_5_13, all_16_6_14) = all_0_5_5 % 37.81/11.22 | % 37.81/11.22 | Applying alpha-rule on (122) yields: % 37.81/11.22 | (123) vbind(all_16_7_15, all_16_5_13, all_0_3_3) = all_16_1_9 % 37.81/11.22 | (124) vabs(all_16_7_15, all_16_5_13, all_16_6_14) = all_0_5_5 % 37.81/11.22 | (125) vtcheck(all_16_1_9, all_16_6_14, all_16_4_12) = 0 % 37.81/11.22 | (126) all_16_0_8 = 0 % 37.81/11.22 | (127) all_16_2_10 = all_0_1_1 % 37.81/11.22 | (128) varrow(all_16_5_13, all_16_4_12) = all_0_1_1 % 37.81/11.22 | (129) all_16_3_11 = all_0_5_5 % 37.81/11.22 | % 37.81/11.22 | Instantiating formula (55) with all_0_5_5, ve2, ve1, all_16_6_14, all_16_5_13, all_16_7_15 and discharging atoms vapp(ve1, ve2) = all_0_5_5, vabs(all_16_7_15, all_16_5_13, all_16_6_14) = all_0_5_5, yields: % 37.81/11.22 | (130) $false % 37.81/11.22 | % 37.81/11.22 |-The branch is then unsatisfiable % 37.81/11.22 |-Branch two: % 37.81/11.22 | (131) all_16_1_9 = 0 & all_16_2_10 = 0 & all_16_4_12 = all_0_5_5 & varrow(all_16_5_13, all_0_1_1) = all_16_3_11 & vtcheck(all_0_3_3, all_16_6_14, all_16_5_13) = 0 & vtcheck(all_0_3_3, all_16_7_15, all_16_3_11) = 0 & vapp(all_16_7_15, all_16_6_14) = all_0_5_5 % 37.81/11.22 | % 37.81/11.22 | Applying alpha-rule on (131) yields: % 37.81/11.22 | (132) vtcheck(all_0_3_3, all_16_7_15, all_16_3_11) = 0 % 37.81/11.22 | (133) varrow(all_16_5_13, all_0_1_1) = all_16_3_11 % 37.81/11.22 | (134) vtcheck(all_0_3_3, all_16_6_14, all_16_5_13) = 0 % 37.81/11.22 | (135) all_16_4_12 = all_0_5_5 % 37.81/11.22 | (136) all_16_1_9 = 0 % 37.81/11.22 | (137) all_16_2_10 = 0 % 37.81/11.22 | (138) vapp(all_16_7_15, all_16_6_14) = all_0_5_5 % 37.81/11.22 | % 37.81/11.22 | Instantiating formula (18) with all_0_5_5, all_16_6_14, all_16_7_15, ve2, ve1 and discharging atoms vapp(all_16_7_15, all_16_6_14) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 37.81/11.22 | (139) all_16_6_14 = ve2 % 37.81/11.22 | % 37.81/11.22 | Instantiating formula (20) with all_0_5_5, all_16_6_14, all_16_7_15, ve2, ve1 and discharging atoms vapp(all_16_7_15, all_16_6_14) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 37.81/11.22 | (140) all_16_7_15 = ve1 % 37.81/11.22 | % 37.81/11.22 | From (139) and (134) follows: % 37.81/11.22 | (141) vtcheck(all_0_3_3, ve2, all_16_5_13) = 0 % 37.81/11.22 | % 37.81/11.22 | From (140) and (132) follows: % 37.81/11.23 | (142) vtcheck(all_0_3_3, ve1, all_16_3_11) = 0 % 37.81/11.23 | % 37.81/11.23 | From (140)(139) and (138) follows: % 37.81/11.23 | (102) vapp(ve1, ve2) = all_0_5_5 % 37.81/11.23 | % 37.81/11.23 +-Applying beta-rule and splitting (116), into two cases. % 37.81/11.23 |-Branch one: % 37.81/11.23 | (144) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) | (all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46) | (all_19_7_47 = all_19_9_49 & all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_6_46 = 0) & vreduce(all_19_10_50) = all_19_9_49 & visSomeExp(all_19_9_49) = all_19_6_46 & vapp(all_19_10_50, all_19_11_51) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50)) | (all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_0_5_5) % 37.81/11.23 | % 37.81/11.23 +-Applying beta-rule and splitting (144), into two cases. % 37.81/11.23 |-Branch one: % 37.81/11.23 | (145) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) | (all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46) | (all_19_7_47 = all_19_9_49 & all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_6_46 = 0) & vreduce(all_19_10_50) = all_19_9_49 & visSomeExp(all_19_9_49) = all_19_6_46 & vapp(all_19_10_50, all_19_11_51) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50)) % 37.81/11.23 | % 37.81/11.23 +-Applying beta-rule and splitting (145), into two cases. % 37.81/11.23 |-Branch one: % 37.81/11.23 | (146) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) | (all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46) % 37.81/11.23 | % 37.81/11.23 +-Applying beta-rule and splitting (146), into two cases. % 37.81/11.23 |-Branch one: % 37.81/11.23 | (147) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) % 37.81/11.23 | % 37.81/11.23 +-Applying beta-rule and splitting (147), into two cases. % 37.81/11.23 |-Branch one: % 37.81/11.23 | (148) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) % 37.81/11.23 | % 37.81/11.23 +-Applying beta-rule and splitting (148), into two cases. % 37.81/11.23 |-Branch one: % 37.81/11.23 | (149) all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46 % 37.81/11.23 | % 37.81/11.23 | Applying alpha-rule on (149) yields: % 37.81/11.23 | (150) vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46 % 37.81/11.23 | (151) all_19_0_40 = all_0_4_4 % 37.81/11.23 | (152) vsomeExp(all_19_1_41) = all_0_4_4 % 37.81/11.23 | (153) vreduce(all_19_8_48) = all_19_10_50 % 37.81/11.23 | (154) vapp(all_19_6_46, all_19_8_48) = all_0_5_5 % 37.81/11.23 | (155) visValue(all_19_8_48) = 0 % 37.81/11.23 | (156) vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 % 37.81/11.23 | (157) visSomeExp(all_19_10_50) = all_19_3_43 % 37.81/11.23 | (158) all_19_4_44 = all_19_10_50 % 37.81/11.23 | (159) all_19_2_42 = 0 % 37.81/11.23 | (160) all_19_5_45 = all_0_5_5 % 37.81/11.23 | (161) ~ (all_19_3_43 = 0) % 37.81/11.23 | % 37.81/11.23 | Instantiating formula (18) with all_0_5_5, all_19_8_48, all_19_6_46, ve2, ve1 and discharging atoms vapp(all_19_6_46, all_19_8_48) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 37.81/11.23 | (162) all_19_8_48 = ve2 % 37.81/11.23 | % 37.81/11.23 | Instantiating formula (20) with all_0_5_5, all_19_8_48, all_19_6_46, ve2, ve1 and discharging atoms vapp(all_19_6_46, all_19_8_48) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 37.81/11.23 | (163) all_19_6_46 = ve1 % 37.81/11.23 | % 37.81/11.23 | Instantiating formula (96) with all_0_7_7, ve1, all_19_7_47, all_19_11_51, all_19_9_49 and discharging atoms vreduce(ve1) = all_0_7_7, yields: % 37.81/11.23 | (164) all_0_7_7 = vnoExp | ~ (vabs(all_19_9_49, all_19_11_51, all_19_7_47) = ve1) % 37.81/11.23 | % 37.81/11.23 | From (162) and (155) follows: % 37.81/11.23 | (165) visValue(ve2) = 0 % 37.81/11.23 | % 37.81/11.23 | From (163) and (150) follows: % 37.81/11.23 | (166) vabs(all_19_9_49, all_19_11_51, all_19_7_47) = ve1 % 37.81/11.23 | % 37.81/11.23 +-Applying beta-rule and splitting (164), into two cases. % 37.81/11.23 |-Branch one: % 37.81/11.23 | (167) ~ (vabs(all_19_9_49, all_19_11_51, all_19_7_47) = ve1) % 37.81/11.23 | % 37.81/11.23 | Using (166) and (167) yields: % 37.81/11.23 | (130) $false % 37.81/11.23 | % 37.81/11.23 |-The branch is then unsatisfiable % 37.81/11.23 |-Branch two: % 37.81/11.23 | (166) vabs(all_19_9_49, all_19_11_51, all_19_7_47) = ve1 % 37.81/11.23 | (170) all_0_7_7 = vnoExp % 37.81/11.23 | % 37.81/11.23 | Equations (170) can reduce 120 to: % 37.81/11.23 | (171) ~ (all_0_6_6 = vnoExp) % 37.81/11.23 | % 37.81/11.23 +-Applying beta-rule and splitting (115), into two cases. % 37.81/11.23 |-Branch one: % 37.81/11.23 | (172) (all_18_0_28 = all_0_6_6 & all_18_2_30 = 0 & all_18_4_32 = all_18_10_38 & all_18_5_33 = ve2 & ~ (all_18_3_31 = 0) & vreduce(all_18_8_36) = all_18_10_38 & visSomeExp(all_18_10_38) = all_18_3_31 & vsomeExp(all_18_1_29) = all_0_6_6 & vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 & visValue(all_18_8_36) = 0 & vapp(all_18_6_34, all_18_8_36) = ve2 & vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34) | (all_18_0_28 = all_0_6_6 & all_18_3_31 = 0 & all_18_4_32 = all_18_7_35 & all_18_5_33 = ve2 & vreduce(all_18_11_39) = all_18_7_35 & vgetSomeExp(all_18_7_35) = all_18_2_30 & visSomeExp(all_18_7_35) = 0 & vsomeExp(all_18_1_29) = all_0_6_6 & vapp(all_18_6_34, all_18_2_30) = all_18_1_29 & vapp(all_18_6_34, all_18_11_39) = ve2 & vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34) | (all_18_3_31 = all_0_6_6 & all_18_6_34 = 0 & all_18_7_35 = all_18_10_38 & all_18_8_36 = ve2 & vreduce(all_18_11_39) = all_18_10_38 & vgetSomeExp(all_18_10_38) = all_18_5_33 & visSomeExp(all_18_10_38) = 0 & vsomeExp(all_18_4_32) = all_0_6_6 & vapp(all_18_5_33, all_18_9_37) = all_18_4_32 & vapp(all_18_11_39, all_18_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_11_39)) | (all_18_4_32 = all_18_8_36 & all_18_5_33 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_2_30 = 0) & ~ (all_18_3_31 = 0) & vreduce(all_18_7_35) = all_18_8_36 & visSomeExp(all_18_8_36) = all_18_3_31 & visValue(all_18_7_35) = all_18_2_30 & vapp(all_18_6_34, all_18_7_35) = ve2 & vabs(all_18_11_39, all_18_10_38, all_18_9_37) = all_18_6_34) | (all_18_7_35 = all_18_9_37 & all_18_8_36 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_6_34 = 0) & vreduce(all_18_10_38) = all_18_9_37 & visSomeExp(all_18_9_37) = all_18_6_34 & vapp(all_18_10_38, all_18_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_10_38)) | (all_18_8_36 = ve2 & all_0_6_6 = vnoExp & vabs(all_18_11_39, all_18_10_38, all_18_9_37) = ve2) % 37.81/11.23 | % 37.81/11.23 +-Applying beta-rule and splitting (172), into two cases. % 37.81/11.23 |-Branch one: % 37.81/11.23 | (173) (all_18_0_28 = all_0_6_6 & all_18_2_30 = 0 & all_18_4_32 = all_18_10_38 & all_18_5_33 = ve2 & ~ (all_18_3_31 = 0) & vreduce(all_18_8_36) = all_18_10_38 & visSomeExp(all_18_10_38) = all_18_3_31 & vsomeExp(all_18_1_29) = all_0_6_6 & vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 & visValue(all_18_8_36) = 0 & vapp(all_18_6_34, all_18_8_36) = ve2 & vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34) | (all_18_0_28 = all_0_6_6 & all_18_3_31 = 0 & all_18_4_32 = all_18_7_35 & all_18_5_33 = ve2 & vreduce(all_18_11_39) = all_18_7_35 & vgetSomeExp(all_18_7_35) = all_18_2_30 & visSomeExp(all_18_7_35) = 0 & vsomeExp(all_18_1_29) = all_0_6_6 & vapp(all_18_6_34, all_18_2_30) = all_18_1_29 & vapp(all_18_6_34, all_18_11_39) = ve2 & vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34) | (all_18_3_31 = all_0_6_6 & all_18_6_34 = 0 & all_18_7_35 = all_18_10_38 & all_18_8_36 = ve2 & vreduce(all_18_11_39) = all_18_10_38 & vgetSomeExp(all_18_10_38) = all_18_5_33 & visSomeExp(all_18_10_38) = 0 & vsomeExp(all_18_4_32) = all_0_6_6 & vapp(all_18_5_33, all_18_9_37) = all_18_4_32 & vapp(all_18_11_39, all_18_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_11_39)) | (all_18_4_32 = all_18_8_36 & all_18_5_33 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_2_30 = 0) & ~ (all_18_3_31 = 0) & vreduce(all_18_7_35) = all_18_8_36 & visSomeExp(all_18_8_36) = all_18_3_31 & visValue(all_18_7_35) = all_18_2_30 & vapp(all_18_6_34, all_18_7_35) = ve2 & vabs(all_18_11_39, all_18_10_38, all_18_9_37) = all_18_6_34) | (all_18_7_35 = all_18_9_37 & all_18_8_36 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_6_34 = 0) & vreduce(all_18_10_38) = all_18_9_37 & visSomeExp(all_18_9_37) = all_18_6_34 & vapp(all_18_10_38, all_18_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_10_38)) % 37.81/11.23 | % 37.81/11.23 +-Applying beta-rule and splitting (173), into two cases. % 37.81/11.23 |-Branch one: % 37.81/11.23 | (174) (all_18_0_28 = all_0_6_6 & all_18_2_30 = 0 & all_18_4_32 = all_18_10_38 & all_18_5_33 = ve2 & ~ (all_18_3_31 = 0) & vreduce(all_18_8_36) = all_18_10_38 & visSomeExp(all_18_10_38) = all_18_3_31 & vsomeExp(all_18_1_29) = all_0_6_6 & vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 & visValue(all_18_8_36) = 0 & vapp(all_18_6_34, all_18_8_36) = ve2 & vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34) | (all_18_0_28 = all_0_6_6 & all_18_3_31 = 0 & all_18_4_32 = all_18_7_35 & all_18_5_33 = ve2 & vreduce(all_18_11_39) = all_18_7_35 & vgetSomeExp(all_18_7_35) = all_18_2_30 & visSomeExp(all_18_7_35) = 0 & vsomeExp(all_18_1_29) = all_0_6_6 & vapp(all_18_6_34, all_18_2_30) = all_18_1_29 & vapp(all_18_6_34, all_18_11_39) = ve2 & vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34) | (all_18_3_31 = all_0_6_6 & all_18_6_34 = 0 & all_18_7_35 = all_18_10_38 & all_18_8_36 = ve2 & vreduce(all_18_11_39) = all_18_10_38 & vgetSomeExp(all_18_10_38) = all_18_5_33 & visSomeExp(all_18_10_38) = 0 & vsomeExp(all_18_4_32) = all_0_6_6 & vapp(all_18_5_33, all_18_9_37) = all_18_4_32 & vapp(all_18_11_39, all_18_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_11_39)) | (all_18_4_32 = all_18_8_36 & all_18_5_33 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_2_30 = 0) & ~ (all_18_3_31 = 0) & vreduce(all_18_7_35) = all_18_8_36 & visSomeExp(all_18_8_36) = all_18_3_31 & visValue(all_18_7_35) = all_18_2_30 & vapp(all_18_6_34, all_18_7_35) = ve2 & vabs(all_18_11_39, all_18_10_38, all_18_9_37) = all_18_6_34) % 37.81/11.23 | % 37.81/11.23 +-Applying beta-rule and splitting (174), into two cases. % 37.81/11.23 |-Branch one: % 37.81/11.23 | (175) (all_18_0_28 = all_0_6_6 & all_18_2_30 = 0 & all_18_4_32 = all_18_10_38 & all_18_5_33 = ve2 & ~ (all_18_3_31 = 0) & vreduce(all_18_8_36) = all_18_10_38 & visSomeExp(all_18_10_38) = all_18_3_31 & vsomeExp(all_18_1_29) = all_0_6_6 & vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 & visValue(all_18_8_36) = 0 & vapp(all_18_6_34, all_18_8_36) = ve2 & vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34) | (all_18_0_28 = all_0_6_6 & all_18_3_31 = 0 & all_18_4_32 = all_18_7_35 & all_18_5_33 = ve2 & vreduce(all_18_11_39) = all_18_7_35 & vgetSomeExp(all_18_7_35) = all_18_2_30 & visSomeExp(all_18_7_35) = 0 & vsomeExp(all_18_1_29) = all_0_6_6 & vapp(all_18_6_34, all_18_2_30) = all_18_1_29 & vapp(all_18_6_34, all_18_11_39) = ve2 & vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34) | (all_18_3_31 = all_0_6_6 & all_18_6_34 = 0 & all_18_7_35 = all_18_10_38 & all_18_8_36 = ve2 & vreduce(all_18_11_39) = all_18_10_38 & vgetSomeExp(all_18_10_38) = all_18_5_33 & visSomeExp(all_18_10_38) = 0 & vsomeExp(all_18_4_32) = all_0_6_6 & vapp(all_18_5_33, all_18_9_37) = all_18_4_32 & vapp(all_18_11_39, all_18_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_11_39)) % 37.81/11.24 | % 37.81/11.24 +-Applying beta-rule and splitting (175), into two cases. % 37.81/11.24 |-Branch one: % 37.81/11.24 | (176) (all_18_0_28 = all_0_6_6 & all_18_2_30 = 0 & all_18_4_32 = all_18_10_38 & all_18_5_33 = ve2 & ~ (all_18_3_31 = 0) & vreduce(all_18_8_36) = all_18_10_38 & visSomeExp(all_18_10_38) = all_18_3_31 & vsomeExp(all_18_1_29) = all_0_6_6 & vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 & visValue(all_18_8_36) = 0 & vapp(all_18_6_34, all_18_8_36) = ve2 & vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34) | (all_18_0_28 = all_0_6_6 & all_18_3_31 = 0 & all_18_4_32 = all_18_7_35 & all_18_5_33 = ve2 & vreduce(all_18_11_39) = all_18_7_35 & vgetSomeExp(all_18_7_35) = all_18_2_30 & visSomeExp(all_18_7_35) = 0 & vsomeExp(all_18_1_29) = all_0_6_6 & vapp(all_18_6_34, all_18_2_30) = all_18_1_29 & vapp(all_18_6_34, all_18_11_39) = ve2 & vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34) % 37.81/11.24 | % 37.81/11.24 +-Applying beta-rule and splitting (176), into two cases. % 37.81/11.24 |-Branch one: % 37.81/11.24 | (177) all_18_0_28 = all_0_6_6 & all_18_2_30 = 0 & all_18_4_32 = all_18_10_38 & all_18_5_33 = ve2 & ~ (all_18_3_31 = 0) & vreduce(all_18_8_36) = all_18_10_38 & visSomeExp(all_18_10_38) = all_18_3_31 & vsomeExp(all_18_1_29) = all_0_6_6 & vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 & visValue(all_18_8_36) = 0 & vapp(all_18_6_34, all_18_8_36) = ve2 & vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34 % 37.81/11.24 | % 37.81/11.24 | Applying alpha-rule on (177) yields: % 37.81/11.24 | (178) all_18_2_30 = 0 % 37.81/11.24 | (179) ~ (all_18_3_31 = 0) % 37.81/11.24 | (180) vsomeExp(all_18_1_29) = all_0_6_6 % 37.81/11.24 | (181) vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34 % 37.81/11.24 | (182) all_18_4_32 = all_18_10_38 % 37.81/11.24 | (183) visValue(all_18_8_36) = 0 % 37.81/11.24 | (184) all_18_5_33 = ve2 % 37.81/11.24 | (185) all_18_0_28 = all_0_6_6 % 37.81/11.24 | (186) visSomeExp(all_18_10_38) = all_18_3_31 % 37.81/11.24 | (187) vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 % 37.81/11.24 | (188) vreduce(all_18_8_36) = all_18_10_38 % 37.81/11.24 | (189) vapp(all_18_6_34, all_18_8_36) = ve2 % 37.81/11.24 | % 37.81/11.24 | Instantiating formula (84) with ve2, all_18_8_36, all_18_6_34 and discharging atoms visValue(ve2) = 0, vapp(all_18_6_34, all_18_8_36) = ve2, yields: % 37.81/11.24 | (130) $false % 37.81/11.24 | % 37.81/11.24 |-The branch is then unsatisfiable % 37.81/11.24 |-Branch two: % 37.81/11.24 | (191) all_18_0_28 = all_0_6_6 & all_18_3_31 = 0 & all_18_4_32 = all_18_7_35 & all_18_5_33 = ve2 & vreduce(all_18_11_39) = all_18_7_35 & vgetSomeExp(all_18_7_35) = all_18_2_30 & visSomeExp(all_18_7_35) = 0 & vsomeExp(all_18_1_29) = all_0_6_6 & vapp(all_18_6_34, all_18_2_30) = all_18_1_29 & vapp(all_18_6_34, all_18_11_39) = ve2 & vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34 % 37.81/11.24 | % 37.81/11.24 | Applying alpha-rule on (191) yields: % 37.81/11.24 | (192) vapp(all_18_6_34, all_18_11_39) = ve2 % 37.81/11.24 | (193) vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34 % 37.81/11.24 | (194) all_18_3_31 = 0 % 37.81/11.24 | (180) vsomeExp(all_18_1_29) = all_0_6_6 % 37.81/11.24 | (196) visSomeExp(all_18_7_35) = 0 % 37.81/11.24 | (197) vapp(all_18_6_34, all_18_2_30) = all_18_1_29 % 37.81/11.24 | (184) all_18_5_33 = ve2 % 37.81/11.24 | (185) all_18_0_28 = all_0_6_6 % 37.81/11.24 | (200) all_18_4_32 = all_18_7_35 % 37.81/11.24 | (201) vreduce(all_18_11_39) = all_18_7_35 % 37.81/11.24 | (202) vgetSomeExp(all_18_7_35) = all_18_2_30 % 37.81/11.24 | % 37.81/11.24 | Instantiating formula (84) with ve2, all_18_11_39, all_18_6_34 and discharging atoms visValue(ve2) = 0, vapp(all_18_6_34, all_18_11_39) = ve2, yields: % 37.81/11.24 | (130) $false % 37.81/11.24 | % 37.81/11.24 |-The branch is then unsatisfiable % 37.81/11.24 |-Branch two: % 37.81/11.24 | (204) all_18_3_31 = all_0_6_6 & all_18_6_34 = 0 & all_18_7_35 = all_18_10_38 & all_18_8_36 = ve2 & vreduce(all_18_11_39) = all_18_10_38 & vgetSomeExp(all_18_10_38) = all_18_5_33 & visSomeExp(all_18_10_38) = 0 & vsomeExp(all_18_4_32) = all_0_6_6 & vapp(all_18_5_33, all_18_9_37) = all_18_4_32 & vapp(all_18_11_39, all_18_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_11_39) % 37.81/11.24 | % 37.81/11.24 | Applying alpha-rule on (204) yields: % 37.81/11.24 | (205) all_18_8_36 = ve2 % 37.81/11.24 | (206) vreduce(all_18_11_39) = all_18_10_38 % 37.81/11.24 | (207) vapp(all_18_5_33, all_18_9_37) = all_18_4_32 % 37.81/11.24 | (208) all_18_7_35 = all_18_10_38 % 37.81/11.24 | (209) vapp(all_18_11_39, all_18_9_37) = ve2 % 37.81/11.24 | (210) all_18_3_31 = all_0_6_6 % 37.81/11.24 | (211) vgetSomeExp(all_18_10_38) = all_18_5_33 % 37.81/11.24 | (212) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_11_39) % 37.81/11.24 | (213) visSomeExp(all_18_10_38) = 0 % 37.81/11.24 | (214) all_18_6_34 = 0 % 37.81/11.24 | (215) vsomeExp(all_18_4_32) = all_0_6_6 % 37.81/11.24 | % 37.81/11.24 | Instantiating formula (84) with ve2, all_18_9_37, all_18_11_39 and discharging atoms visValue(ve2) = 0, vapp(all_18_11_39, all_18_9_37) = ve2, yields: % 37.81/11.24 | (130) $false % 37.81/11.24 | % 37.81/11.24 |-The branch is then unsatisfiable % 37.81/11.24 |-Branch two: % 37.81/11.24 | (217) all_18_4_32 = all_18_8_36 & all_18_5_33 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_2_30 = 0) & ~ (all_18_3_31 = 0) & vreduce(all_18_7_35) = all_18_8_36 & visSomeExp(all_18_8_36) = all_18_3_31 & visValue(all_18_7_35) = all_18_2_30 & vapp(all_18_6_34, all_18_7_35) = ve2 & vabs(all_18_11_39, all_18_10_38, all_18_9_37) = all_18_6_34 % 37.81/11.24 | % 37.81/11.24 | Applying alpha-rule on (217) yields: % 37.81/11.24 | (218) visValue(all_18_7_35) = all_18_2_30 % 37.81/11.24 | (219) all_18_4_32 = all_18_8_36 % 37.81/11.24 | (220) ~ (all_18_2_30 = 0) % 37.81/11.24 | (179) ~ (all_18_3_31 = 0) % 37.81/11.24 | (222) vapp(all_18_6_34, all_18_7_35) = ve2 % 37.81/11.24 | (223) vreduce(all_18_7_35) = all_18_8_36 % 37.81/11.24 | (224) vabs(all_18_11_39, all_18_10_38, all_18_9_37) = all_18_6_34 % 37.81/11.24 | (184) all_18_5_33 = ve2 % 37.81/11.24 | (226) all_0_6_6 = vnoExp % 37.81/11.24 | (227) visSomeExp(all_18_8_36) = all_18_3_31 % 37.81/11.24 | % 37.81/11.24 | Equations (226) can reduce 171 to: % 37.81/11.24 | (228) $false % 37.81/11.24 | % 37.81/11.24 |-The branch is then unsatisfiable % 37.81/11.24 |-Branch two: % 37.81/11.24 | (229) all_18_7_35 = all_18_9_37 & all_18_8_36 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_6_34 = 0) & vreduce(all_18_10_38) = all_18_9_37 & visSomeExp(all_18_9_37) = all_18_6_34 & vapp(all_18_10_38, all_18_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_10_38) % 37.81/11.24 | % 37.81/11.24 | Applying alpha-rule on (229) yields: % 37.81/11.24 | (205) all_18_8_36 = ve2 % 37.81/11.24 | (231) vreduce(all_18_10_38) = all_18_9_37 % 37.81/11.24 | (232) vapp(all_18_10_38, all_18_11_39) = ve2 % 37.81/11.24 | (233) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_10_38) % 37.81/11.24 | (226) all_0_6_6 = vnoExp % 37.81/11.24 | (235) visSomeExp(all_18_9_37) = all_18_6_34 % 37.81/11.24 | (236) all_18_7_35 = all_18_9_37 % 37.81/11.24 | (237) ~ (all_18_6_34 = 0) % 37.81/11.24 | % 37.81/11.24 | Equations (226) can reduce 171 to: % 37.81/11.24 | (228) $false % 37.81/11.24 | % 37.81/11.24 |-The branch is then unsatisfiable % 37.81/11.24 |-Branch two: % 37.81/11.24 | (239) all_18_8_36 = ve2 & all_0_6_6 = vnoExp & vabs(all_18_11_39, all_18_10_38, all_18_9_37) = ve2 % 37.81/11.24 | % 37.81/11.24 | Applying alpha-rule on (239) yields: % 37.81/11.24 | (205) all_18_8_36 = ve2 % 37.81/11.24 | (226) all_0_6_6 = vnoExp % 37.81/11.24 | (242) vabs(all_18_11_39, all_18_10_38, all_18_9_37) = ve2 % 37.81/11.24 | % 37.81/11.24 | Equations (226) can reduce 171 to: % 37.81/11.24 | (228) $false % 37.81/11.24 | % 37.81/11.24 |-The branch is then unsatisfiable % 37.81/11.24 |-Branch two: % 37.81/11.24 | (244) all_18_10_38 = ve2 & all_0_6_6 = vnoExp & vvar(all_18_11_39) = ve2 % 37.81/11.24 | % 37.81/11.24 | Applying alpha-rule on (244) yields: % 37.81/11.24 | (245) all_18_10_38 = ve2 % 37.81/11.24 | (226) all_0_6_6 = vnoExp % 37.81/11.24 | (247) vvar(all_18_11_39) = ve2 % 37.81/11.24 | % 37.81/11.24 | Equations (226) can reduce 171 to: % 37.81/11.24 | (228) $false % 37.81/11.24 | % 37.81/11.24 |-The branch is then unsatisfiable % 37.81/11.24 |-Branch two: % 37.81/11.24 | (249) all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46 % 37.81/11.24 | % 37.81/11.24 | Applying alpha-rule on (249) yields: % 37.81/11.24 | (250) vreduce(all_19_11_51) = all_19_7_47 % 37.81/11.24 | (251) vapp(all_19_6_46, all_19_2_42) = all_19_1_41 % 37.81/11.24 | (151) all_19_0_40 = all_0_4_4 % 37.81/11.24 | (253) vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46 % 37.81/11.24 | (152) vsomeExp(all_19_1_41) = all_0_4_4 % 37.81/11.24 | (255) vgetSomeExp(all_19_7_47) = all_19_2_42 % 37.81/11.24 | (256) visSomeExp(all_19_7_47) = 0 % 37.81/11.24 | (257) all_19_4_44 = all_19_7_47 % 37.81/11.24 | (160) all_19_5_45 = all_0_5_5 % 37.81/11.24 | (259) all_19_3_43 = 0 % 37.81/11.24 | (260) vapp(all_19_6_46, all_19_11_51) = all_0_5_5 % 37.81/11.24 | % 37.81/11.24 | Instantiating formula (59) with ve2, all_19_7_47, all_0_6_6 and discharging atoms vreduce(ve2) = all_0_6_6, yields: % 37.81/11.24 | (261) all_19_7_47 = all_0_6_6 | ~ (vreduce(ve2) = all_19_7_47) % 37.81/11.24 | % 37.81/11.24 | Instantiating formula (50) with all_0_4_4, all_19_1_41, all_0_2_2 and discharging atoms vsomeExp(all_19_1_41) = all_0_4_4, vsomeExp(all_0_2_2) = all_0_4_4, yields: % 37.81/11.24 | (262) all_19_1_41 = all_0_2_2 % 37.81/11.24 | % 37.81/11.24 | Instantiating formula (18) with all_0_5_5, all_19_11_51, all_19_6_46, ve2, ve1 and discharging atoms vapp(all_19_6_46, all_19_11_51) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 37.81/11.24 | (263) all_19_11_51 = ve2 % 37.81/11.24 | % 37.81/11.24 | Instantiating formula (20) with all_0_5_5, all_19_11_51, all_19_6_46, ve2, ve1 and discharging atoms vapp(all_19_6_46, all_19_11_51) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 37.81/11.24 | (163) all_19_6_46 = ve1 % 37.81/11.24 | % 37.81/11.24 | Instantiating formula (96) with all_0_7_7, ve1, all_19_8_48, all_19_9_49, all_19_10_50 and discharging atoms vreduce(ve1) = all_0_7_7, yields: % 37.81/11.24 | (265) all_0_7_7 = vnoExp | ~ (vabs(all_19_10_50, all_19_9_49, all_19_8_48) = ve1) % 37.81/11.24 | % 37.81/11.24 | From (263) and (250) follows: % 37.81/11.24 | (266) vreduce(ve2) = all_19_7_47 % 37.81/11.24 | % 37.81/11.24 | From (163)(262) and (251) follows: % 37.81/11.24 | (267) vapp(ve1, all_19_2_42) = all_0_2_2 % 37.81/11.24 | % 37.81/11.24 | From (163) and (253) follows: % 37.81/11.24 | (268) vabs(all_19_10_50, all_19_9_49, all_19_8_48) = ve1 % 37.81/11.24 | % 37.81/11.24 +-Applying beta-rule and splitting (261), into two cases. % 37.81/11.24 |-Branch one: % 37.81/11.24 | (269) ~ (vreduce(ve2) = all_19_7_47) % 37.81/11.24 | % 37.81/11.24 | Using (266) and (269) yields: % 37.81/11.24 | (130) $false % 37.81/11.24 | % 37.81/11.24 |-The branch is then unsatisfiable % 37.81/11.24 |-Branch two: % 37.81/11.24 | (266) vreduce(ve2) = all_19_7_47 % 37.81/11.24 | (272) all_19_7_47 = all_0_6_6 % 37.81/11.24 | % 37.81/11.24 | From (272) and (255) follows: % 37.81/11.24 | (273) vgetSomeExp(all_0_6_6) = all_19_2_42 % 37.81/11.24 | % 37.81/11.24 +-Applying beta-rule and splitting (265), into two cases. % 37.81/11.24 |-Branch one: % 37.81/11.24 | (274) ~ (vabs(all_19_10_50, all_19_9_49, all_19_8_48) = ve1) % 37.81/11.24 | % 37.81/11.24 | Using (268) and (274) yields: % 37.81/11.24 | (130) $false % 37.81/11.24 | % 37.81/11.24 |-The branch is then unsatisfiable % 37.81/11.24 |-Branch two: % 37.81/11.24 | (268) vabs(all_19_10_50, all_19_9_49, all_19_8_48) = ve1 % 37.81/11.24 | (170) all_0_7_7 = vnoExp % 37.81/11.24 | % 37.81/11.24 | Equations (170) can reduce 120 to: % 37.81/11.24 | (171) ~ (all_0_6_6 = vnoExp) % 37.81/11.24 | % 37.81/11.24 | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_16_3_11, all_0_1_1, all_19_2_42, ve1, all_0_3_3, all_16_5_13 and discharging atoms varrow(all_16_5_13, all_0_1_1) = all_16_3_11, vtcheck(all_0_3_3, all_0_2_2, all_0_1_1) = all_0_0_0, vtcheck(all_0_3_3, ve1, all_16_3_11) = 0, vapp(ve1, all_19_2_42) = all_0_2_2, yields: % 37.81/11.24 | (279) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, all_19_2_42, all_16_5_13) = v0) % 37.81/11.24 | % 37.81/11.24 +-Applying beta-rule and splitting (115), into two cases. % 37.81/11.24 |-Branch one: % 37.81/11.24 | (172) (all_18_0_28 = all_0_6_6 & all_18_2_30 = 0 & all_18_4_32 = all_18_10_38 & all_18_5_33 = ve2 & ~ (all_18_3_31 = 0) & vreduce(all_18_8_36) = all_18_10_38 & visSomeExp(all_18_10_38) = all_18_3_31 & vsomeExp(all_18_1_29) = all_0_6_6 & vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 & visValue(all_18_8_36) = 0 & vapp(all_18_6_34, all_18_8_36) = ve2 & vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34) | (all_18_0_28 = all_0_6_6 & all_18_3_31 = 0 & all_18_4_32 = all_18_7_35 & all_18_5_33 = ve2 & vreduce(all_18_11_39) = all_18_7_35 & vgetSomeExp(all_18_7_35) = all_18_2_30 & visSomeExp(all_18_7_35) = 0 & vsomeExp(all_18_1_29) = all_0_6_6 & vapp(all_18_6_34, all_18_2_30) = all_18_1_29 & vapp(all_18_6_34, all_18_11_39) = ve2 & vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34) | (all_18_3_31 = all_0_6_6 & all_18_6_34 = 0 & all_18_7_35 = all_18_10_38 & all_18_8_36 = ve2 & vreduce(all_18_11_39) = all_18_10_38 & vgetSomeExp(all_18_10_38) = all_18_5_33 & visSomeExp(all_18_10_38) = 0 & vsomeExp(all_18_4_32) = all_0_6_6 & vapp(all_18_5_33, all_18_9_37) = all_18_4_32 & vapp(all_18_11_39, all_18_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_11_39)) | (all_18_4_32 = all_18_8_36 & all_18_5_33 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_2_30 = 0) & ~ (all_18_3_31 = 0) & vreduce(all_18_7_35) = all_18_8_36 & visSomeExp(all_18_8_36) = all_18_3_31 & visValue(all_18_7_35) = all_18_2_30 & vapp(all_18_6_34, all_18_7_35) = ve2 & vabs(all_18_11_39, all_18_10_38, all_18_9_37) = all_18_6_34) | (all_18_7_35 = all_18_9_37 & all_18_8_36 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_6_34 = 0) & vreduce(all_18_10_38) = all_18_9_37 & visSomeExp(all_18_9_37) = all_18_6_34 & vapp(all_18_10_38, all_18_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_10_38)) | (all_18_8_36 = ve2 & all_0_6_6 = vnoExp & vabs(all_18_11_39, all_18_10_38, all_18_9_37) = ve2) % 37.81/11.25 | % 37.81/11.25 +-Applying beta-rule and splitting (172), into two cases. % 37.81/11.25 |-Branch one: % 37.81/11.25 | (173) (all_18_0_28 = all_0_6_6 & all_18_2_30 = 0 & all_18_4_32 = all_18_10_38 & all_18_5_33 = ve2 & ~ (all_18_3_31 = 0) & vreduce(all_18_8_36) = all_18_10_38 & visSomeExp(all_18_10_38) = all_18_3_31 & vsomeExp(all_18_1_29) = all_0_6_6 & vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 & visValue(all_18_8_36) = 0 & vapp(all_18_6_34, all_18_8_36) = ve2 & vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34) | (all_18_0_28 = all_0_6_6 & all_18_3_31 = 0 & all_18_4_32 = all_18_7_35 & all_18_5_33 = ve2 & vreduce(all_18_11_39) = all_18_7_35 & vgetSomeExp(all_18_7_35) = all_18_2_30 & visSomeExp(all_18_7_35) = 0 & vsomeExp(all_18_1_29) = all_0_6_6 & vapp(all_18_6_34, all_18_2_30) = all_18_1_29 & vapp(all_18_6_34, all_18_11_39) = ve2 & vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34) | (all_18_3_31 = all_0_6_6 & all_18_6_34 = 0 & all_18_7_35 = all_18_10_38 & all_18_8_36 = ve2 & vreduce(all_18_11_39) = all_18_10_38 & vgetSomeExp(all_18_10_38) = all_18_5_33 & visSomeExp(all_18_10_38) = 0 & vsomeExp(all_18_4_32) = all_0_6_6 & vapp(all_18_5_33, all_18_9_37) = all_18_4_32 & vapp(all_18_11_39, all_18_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_11_39)) | (all_18_4_32 = all_18_8_36 & all_18_5_33 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_2_30 = 0) & ~ (all_18_3_31 = 0) & vreduce(all_18_7_35) = all_18_8_36 & visSomeExp(all_18_8_36) = all_18_3_31 & visValue(all_18_7_35) = all_18_2_30 & vapp(all_18_6_34, all_18_7_35) = ve2 & vabs(all_18_11_39, all_18_10_38, all_18_9_37) = all_18_6_34) | (all_18_7_35 = all_18_9_37 & all_18_8_36 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_6_34 = 0) & vreduce(all_18_10_38) = all_18_9_37 & visSomeExp(all_18_9_37) = all_18_6_34 & vapp(all_18_10_38, all_18_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_10_38)) % 37.81/11.25 | % 37.81/11.25 +-Applying beta-rule and splitting (173), into two cases. % 37.81/11.25 |-Branch one: % 37.81/11.25 | (174) (all_18_0_28 = all_0_6_6 & all_18_2_30 = 0 & all_18_4_32 = all_18_10_38 & all_18_5_33 = ve2 & ~ (all_18_3_31 = 0) & vreduce(all_18_8_36) = all_18_10_38 & visSomeExp(all_18_10_38) = all_18_3_31 & vsomeExp(all_18_1_29) = all_0_6_6 & vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 & visValue(all_18_8_36) = 0 & vapp(all_18_6_34, all_18_8_36) = ve2 & vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34) | (all_18_0_28 = all_0_6_6 & all_18_3_31 = 0 & all_18_4_32 = all_18_7_35 & all_18_5_33 = ve2 & vreduce(all_18_11_39) = all_18_7_35 & vgetSomeExp(all_18_7_35) = all_18_2_30 & visSomeExp(all_18_7_35) = 0 & vsomeExp(all_18_1_29) = all_0_6_6 & vapp(all_18_6_34, all_18_2_30) = all_18_1_29 & vapp(all_18_6_34, all_18_11_39) = ve2 & vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34) | (all_18_3_31 = all_0_6_6 & all_18_6_34 = 0 & all_18_7_35 = all_18_10_38 & all_18_8_36 = ve2 & vreduce(all_18_11_39) = all_18_10_38 & vgetSomeExp(all_18_10_38) = all_18_5_33 & visSomeExp(all_18_10_38) = 0 & vsomeExp(all_18_4_32) = all_0_6_6 & vapp(all_18_5_33, all_18_9_37) = all_18_4_32 & vapp(all_18_11_39, all_18_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_11_39)) | (all_18_4_32 = all_18_8_36 & all_18_5_33 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_2_30 = 0) & ~ (all_18_3_31 = 0) & vreduce(all_18_7_35) = all_18_8_36 & visSomeExp(all_18_8_36) = all_18_3_31 & visValue(all_18_7_35) = all_18_2_30 & vapp(all_18_6_34, all_18_7_35) = ve2 & vabs(all_18_11_39, all_18_10_38, all_18_9_37) = all_18_6_34) % 37.81/11.25 | % 37.81/11.25 +-Applying beta-rule and splitting (174), into two cases. % 37.81/11.25 |-Branch one: % 37.81/11.25 | (175) (all_18_0_28 = all_0_6_6 & all_18_2_30 = 0 & all_18_4_32 = all_18_10_38 & all_18_5_33 = ve2 & ~ (all_18_3_31 = 0) & vreduce(all_18_8_36) = all_18_10_38 & visSomeExp(all_18_10_38) = all_18_3_31 & vsomeExp(all_18_1_29) = all_0_6_6 & vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 & visValue(all_18_8_36) = 0 & vapp(all_18_6_34, all_18_8_36) = ve2 & vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34) | (all_18_0_28 = all_0_6_6 & all_18_3_31 = 0 & all_18_4_32 = all_18_7_35 & all_18_5_33 = ve2 & vreduce(all_18_11_39) = all_18_7_35 & vgetSomeExp(all_18_7_35) = all_18_2_30 & visSomeExp(all_18_7_35) = 0 & vsomeExp(all_18_1_29) = all_0_6_6 & vapp(all_18_6_34, all_18_2_30) = all_18_1_29 & vapp(all_18_6_34, all_18_11_39) = ve2 & vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34) | (all_18_3_31 = all_0_6_6 & all_18_6_34 = 0 & all_18_7_35 = all_18_10_38 & all_18_8_36 = ve2 & vreduce(all_18_11_39) = all_18_10_38 & vgetSomeExp(all_18_10_38) = all_18_5_33 & visSomeExp(all_18_10_38) = 0 & vsomeExp(all_18_4_32) = all_0_6_6 & vapp(all_18_5_33, all_18_9_37) = all_18_4_32 & vapp(all_18_11_39, all_18_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_11_39)) % 37.81/11.25 | % 37.81/11.25 +-Applying beta-rule and splitting (175), into two cases. % 37.81/11.25 |-Branch one: % 37.81/11.25 | (176) (all_18_0_28 = all_0_6_6 & all_18_2_30 = 0 & all_18_4_32 = all_18_10_38 & all_18_5_33 = ve2 & ~ (all_18_3_31 = 0) & vreduce(all_18_8_36) = all_18_10_38 & visSomeExp(all_18_10_38) = all_18_3_31 & vsomeExp(all_18_1_29) = all_0_6_6 & vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 & visValue(all_18_8_36) = 0 & vapp(all_18_6_34, all_18_8_36) = ve2 & vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34) | (all_18_0_28 = all_0_6_6 & all_18_3_31 = 0 & all_18_4_32 = all_18_7_35 & all_18_5_33 = ve2 & vreduce(all_18_11_39) = all_18_7_35 & vgetSomeExp(all_18_7_35) = all_18_2_30 & visSomeExp(all_18_7_35) = 0 & vsomeExp(all_18_1_29) = all_0_6_6 & vapp(all_18_6_34, all_18_2_30) = all_18_1_29 & vapp(all_18_6_34, all_18_11_39) = ve2 & vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34) % 37.81/11.25 | % 37.81/11.25 +-Applying beta-rule and splitting (176), into two cases. % 37.81/11.25 |-Branch one: % 37.81/11.25 | (177) all_18_0_28 = all_0_6_6 & all_18_2_30 = 0 & all_18_4_32 = all_18_10_38 & all_18_5_33 = ve2 & ~ (all_18_3_31 = 0) & vreduce(all_18_8_36) = all_18_10_38 & visSomeExp(all_18_10_38) = all_18_3_31 & vsomeExp(all_18_1_29) = all_0_6_6 & vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 & visValue(all_18_8_36) = 0 & vapp(all_18_6_34, all_18_8_36) = ve2 & vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34 % 37.81/11.25 | % 37.81/11.25 | Applying alpha-rule on (177) yields: % 37.81/11.25 | (178) all_18_2_30 = 0 % 37.81/11.25 | (179) ~ (all_18_3_31 = 0) % 37.81/11.25 | (180) vsomeExp(all_18_1_29) = all_0_6_6 % 37.81/11.25 | (181) vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34 % 37.81/11.25 | (182) all_18_4_32 = all_18_10_38 % 37.81/11.25 | (183) visValue(all_18_8_36) = 0 % 37.81/11.25 | (184) all_18_5_33 = ve2 % 37.81/11.25 | (185) all_18_0_28 = all_0_6_6 % 37.81/11.25 | (186) visSomeExp(all_18_10_38) = all_18_3_31 % 37.81/11.25 | (187) vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 % 37.81/11.25 | (188) vreduce(all_18_8_36) = all_18_10_38 % 37.81/11.25 | (189) vapp(all_18_6_34, all_18_8_36) = ve2 % 37.81/11.25 | % 37.81/11.25 +-Applying beta-rule and splitting (279), into two cases. % 37.81/11.25 |-Branch one: % 37.81/11.25 | (298) all_0_0_0 = 0 % 37.81/11.25 | % 37.81/11.25 | Equations (298) can reduce 36 to: % 37.81/11.25 | (228) $false % 37.81/11.25 | % 37.81/11.25 |-The branch is then unsatisfiable % 37.81/11.25 |-Branch two: % 37.81/11.25 | (36) ~ (all_0_0_0 = 0) % 37.81/11.25 | (301) ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, all_19_2_42, all_16_5_13) = v0) % 37.81/11.25 | % 37.81/11.25 | Instantiating (301) with all_106_0_96 yields: % 37.81/11.25 | (302) ~ (all_106_0_96 = 0) & vtcheck(all_0_3_3, all_19_2_42, all_16_5_13) = all_106_0_96 % 37.81/11.25 | % 37.81/11.25 | Applying alpha-rule on (302) yields: % 37.81/11.25 | (303) ~ (all_106_0_96 = 0) % 37.81/11.25 | (304) vtcheck(all_0_3_3, all_19_2_42, all_16_5_13) = all_106_0_96 % 37.81/11.25 | % 37.81/11.25 | Instantiating formula (32) with all_18_1_29, all_19_2_42, all_0_6_6 and discharging atoms vgetSomeExp(all_0_6_6) = all_19_2_42, vsomeExp(all_18_1_29) = all_0_6_6, yields: % 37.81/11.25 | (305) all_19_2_42 = all_18_1_29 % 37.81/11.25 | % 37.81/11.25 | From (305) and (304) follows: % 37.81/11.25 | (306) vtcheck(all_0_3_3, all_18_1_29, all_16_5_13) = all_106_0_96 % 37.81/11.25 | % 37.81/11.25 | Instantiating formula (72) with all_16_5_13, all_18_1_29, all_0_3_3 and discharging atoms vsomeExp(all_18_1_29) = all_0_6_6, vtcheck(all_0_3_3, ve2, all_16_5_13) = 0, yields: % 37.81/11.25 | (307) vtcheck(all_0_3_3, all_18_1_29, all_16_5_13) = 0 % 37.81/11.25 | % 37.81/11.25 | Instantiating formula (91) with all_0_3_3, all_18_1_29, all_16_5_13, 0, all_106_0_96 and discharging atoms vtcheck(all_0_3_3, all_18_1_29, all_16_5_13) = all_106_0_96, vtcheck(all_0_3_3, all_18_1_29, all_16_5_13) = 0, yields: % 37.81/11.25 | (308) all_106_0_96 = 0 % 37.81/11.25 | % 37.81/11.25 | Equations (308) can reduce 303 to: % 37.81/11.25 | (228) $false % 37.81/11.25 | % 37.81/11.25 |-The branch is then unsatisfiable % 37.81/11.25 |-Branch two: % 37.81/11.25 | (191) all_18_0_28 = all_0_6_6 & all_18_3_31 = 0 & all_18_4_32 = all_18_7_35 & all_18_5_33 = ve2 & vreduce(all_18_11_39) = all_18_7_35 & vgetSomeExp(all_18_7_35) = all_18_2_30 & visSomeExp(all_18_7_35) = 0 & vsomeExp(all_18_1_29) = all_0_6_6 & vapp(all_18_6_34, all_18_2_30) = all_18_1_29 & vapp(all_18_6_34, all_18_11_39) = ve2 & vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34 % 37.81/11.25 | % 37.81/11.25 | Applying alpha-rule on (191) yields: % 37.81/11.25 | (192) vapp(all_18_6_34, all_18_11_39) = ve2 % 37.81/11.25 | (193) vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34 % 37.81/11.25 | (194) all_18_3_31 = 0 % 37.81/11.25 | (180) vsomeExp(all_18_1_29) = all_0_6_6 % 37.81/11.25 | (196) visSomeExp(all_18_7_35) = 0 % 37.81/11.25 | (197) vapp(all_18_6_34, all_18_2_30) = all_18_1_29 % 37.81/11.25 | (184) all_18_5_33 = ve2 % 37.81/11.25 | (185) all_18_0_28 = all_0_6_6 % 37.81/11.25 | (200) all_18_4_32 = all_18_7_35 % 37.81/11.25 | (201) vreduce(all_18_11_39) = all_18_7_35 % 37.81/11.25 | (202) vgetSomeExp(all_18_7_35) = all_18_2_30 % 37.81/11.25 | % 37.81/11.25 +-Applying beta-rule and splitting (279), into two cases. % 37.81/11.25 |-Branch one: % 37.81/11.25 | (298) all_0_0_0 = 0 % 37.81/11.25 | % 37.81/11.25 | Equations (298) can reduce 36 to: % 37.81/11.25 | (228) $false % 37.81/11.25 | % 37.81/11.25 |-The branch is then unsatisfiable % 37.81/11.25 |-Branch two: % 37.81/11.25 | (36) ~ (all_0_0_0 = 0) % 37.81/11.25 | (301) ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, all_19_2_42, all_16_5_13) = v0) % 37.81/11.25 | % 37.81/11.25 | Instantiating (301) with all_106_0_137 yields: % 37.81/11.25 | (326) ~ (all_106_0_137 = 0) & vtcheck(all_0_3_3, all_19_2_42, all_16_5_13) = all_106_0_137 % 37.81/11.25 | % 37.81/11.25 | Applying alpha-rule on (326) yields: % 37.81/11.25 | (327) ~ (all_106_0_137 = 0) % 37.81/11.25 | (328) vtcheck(all_0_3_3, all_19_2_42, all_16_5_13) = all_106_0_137 % 37.81/11.25 | % 37.81/11.25 | Instantiating formula (32) with all_18_1_29, all_19_2_42, all_0_6_6 and discharging atoms vgetSomeExp(all_0_6_6) = all_19_2_42, vsomeExp(all_18_1_29) = all_0_6_6, yields: % 37.81/11.25 | (305) all_19_2_42 = all_18_1_29 % 37.81/11.25 | % 37.81/11.25 | From (305) and (328) follows: % 37.81/11.25 | (330) vtcheck(all_0_3_3, all_18_1_29, all_16_5_13) = all_106_0_137 % 37.81/11.25 | % 37.81/11.25 | Instantiating formula (72) with all_16_5_13, all_18_1_29, all_0_3_3 and discharging atoms vsomeExp(all_18_1_29) = all_0_6_6, vtcheck(all_0_3_3, ve2, all_16_5_13) = 0, yields: % 37.81/11.25 | (307) vtcheck(all_0_3_3, all_18_1_29, all_16_5_13) = 0 % 37.81/11.25 | % 37.81/11.25 | Instantiating formula (91) with all_0_3_3, all_18_1_29, all_16_5_13, 0, all_106_0_137 and discharging atoms vtcheck(all_0_3_3, all_18_1_29, all_16_5_13) = all_106_0_137, vtcheck(all_0_3_3, all_18_1_29, all_16_5_13) = 0, yields: % 37.81/11.25 | (332) all_106_0_137 = 0 % 37.81/11.25 | % 37.81/11.25 | Equations (332) can reduce 327 to: % 37.81/11.25 | (228) $false % 37.81/11.25 | % 37.81/11.25 |-The branch is then unsatisfiable % 37.81/11.25 |-Branch two: % 37.81/11.25 | (204) all_18_3_31 = all_0_6_6 & all_18_6_34 = 0 & all_18_7_35 = all_18_10_38 & all_18_8_36 = ve2 & vreduce(all_18_11_39) = all_18_10_38 & vgetSomeExp(all_18_10_38) = all_18_5_33 & visSomeExp(all_18_10_38) = 0 & vsomeExp(all_18_4_32) = all_0_6_6 & vapp(all_18_5_33, all_18_9_37) = all_18_4_32 & vapp(all_18_11_39, all_18_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_11_39) % 37.81/11.25 | % 37.81/11.25 | Applying alpha-rule on (204) yields: % 37.81/11.25 | (205) all_18_8_36 = ve2 % 37.81/11.25 | (206) vreduce(all_18_11_39) = all_18_10_38 % 37.81/11.25 | (207) vapp(all_18_5_33, all_18_9_37) = all_18_4_32 % 37.81/11.25 | (208) all_18_7_35 = all_18_10_38 % 37.81/11.25 | (209) vapp(all_18_11_39, all_18_9_37) = ve2 % 37.81/11.25 | (210) all_18_3_31 = all_0_6_6 % 37.81/11.25 | (211) vgetSomeExp(all_18_10_38) = all_18_5_33 % 37.81/11.25 | (212) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_11_39) % 37.81/11.25 | (213) visSomeExp(all_18_10_38) = 0 % 37.81/11.25 | (214) all_18_6_34 = 0 % 37.81/11.25 | (215) vsomeExp(all_18_4_32) = all_0_6_6 % 37.81/11.25 | % 37.81/11.25 +-Applying beta-rule and splitting (279), into two cases. % 37.81/11.25 |-Branch one: % 37.81/11.25 | (298) all_0_0_0 = 0 % 37.81/11.25 | % 37.81/11.25 | Equations (298) can reduce 36 to: % 37.81/11.25 | (228) $false % 37.81/11.25 | % 37.81/11.25 |-The branch is then unsatisfiable % 37.81/11.25 |-Branch two: % 37.81/11.25 | (36) ~ (all_0_0_0 = 0) % 37.81/11.25 | (301) ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, all_19_2_42, all_16_5_13) = v0) % 37.81/11.25 | % 37.81/11.25 | Instantiating (301) with all_108_0_150 yields: % 37.81/11.25 | (350) ~ (all_108_0_150 = 0) & vtcheck(all_0_3_3, all_19_2_42, all_16_5_13) = all_108_0_150 % 37.81/11.25 | % 37.81/11.25 | Applying alpha-rule on (350) yields: % 37.81/11.25 | (351) ~ (all_108_0_150 = 0) % 37.81/11.25 | (352) vtcheck(all_0_3_3, all_19_2_42, all_16_5_13) = all_108_0_150 % 37.81/11.25 | % 37.81/11.25 | Instantiating formula (32) with all_18_4_32, all_19_2_42, all_0_6_6 and discharging atoms vgetSomeExp(all_0_6_6) = all_19_2_42, vsomeExp(all_18_4_32) = all_0_6_6, yields: % 37.81/11.25 | (353) all_19_2_42 = all_18_4_32 % 37.81/11.25 | % 37.81/11.25 | From (353) and (352) follows: % 37.81/11.25 | (354) vtcheck(all_0_3_3, all_18_4_32, all_16_5_13) = all_108_0_150 % 37.81/11.25 | % 37.81/11.25 | Instantiating formula (72) with all_16_5_13, all_18_4_32, all_0_3_3 and discharging atoms vsomeExp(all_18_4_32) = all_0_6_6, vtcheck(all_0_3_3, ve2, all_16_5_13) = 0, yields: % 37.81/11.25 | (355) vtcheck(all_0_3_3, all_18_4_32, all_16_5_13) = 0 % 37.81/11.25 | % 37.81/11.25 | Instantiating formula (91) with all_0_3_3, all_18_4_32, all_16_5_13, 0, all_108_0_150 and discharging atoms vtcheck(all_0_3_3, all_18_4_32, all_16_5_13) = all_108_0_150, vtcheck(all_0_3_3, all_18_4_32, all_16_5_13) = 0, yields: % 37.81/11.25 | (356) all_108_0_150 = 0 % 37.81/11.25 | % 37.81/11.25 | Equations (356) can reduce 351 to: % 37.81/11.25 | (228) $false % 37.81/11.25 | % 37.81/11.25 |-The branch is then unsatisfiable % 37.81/11.25 |-Branch two: % 37.81/11.25 | (217) all_18_4_32 = all_18_8_36 & all_18_5_33 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_2_30 = 0) & ~ (all_18_3_31 = 0) & vreduce(all_18_7_35) = all_18_8_36 & visSomeExp(all_18_8_36) = all_18_3_31 & visValue(all_18_7_35) = all_18_2_30 & vapp(all_18_6_34, all_18_7_35) = ve2 & vabs(all_18_11_39, all_18_10_38, all_18_9_37) = all_18_6_34 % 37.81/11.26 | % 37.81/11.26 | Applying alpha-rule on (217) yields: % 37.81/11.26 | (218) visValue(all_18_7_35) = all_18_2_30 % 37.81/11.26 | (219) all_18_4_32 = all_18_8_36 % 37.81/11.26 | (220) ~ (all_18_2_30 = 0) % 37.81/11.26 | (179) ~ (all_18_3_31 = 0) % 37.81/11.26 | (222) vapp(all_18_6_34, all_18_7_35) = ve2 % 37.81/11.26 | (223) vreduce(all_18_7_35) = all_18_8_36 % 37.81/11.26 | (224) vabs(all_18_11_39, all_18_10_38, all_18_9_37) = all_18_6_34 % 37.81/11.26 | (184) all_18_5_33 = ve2 % 37.81/11.26 | (226) all_0_6_6 = vnoExp % 37.81/11.26 | (227) visSomeExp(all_18_8_36) = all_18_3_31 % 37.81/11.26 | % 37.81/11.26 | Equations (226) can reduce 171 to: % 37.81/11.26 | (228) $false % 37.81/11.26 | % 37.81/11.26 |-The branch is then unsatisfiable % 37.81/11.26 |-Branch two: % 37.81/11.26 | (229) all_18_7_35 = all_18_9_37 & all_18_8_36 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_6_34 = 0) & vreduce(all_18_10_38) = all_18_9_37 & visSomeExp(all_18_9_37) = all_18_6_34 & vapp(all_18_10_38, all_18_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_10_38) % 37.81/11.26 | % 37.81/11.26 | Applying alpha-rule on (229) yields: % 37.81/11.26 | (205) all_18_8_36 = ve2 % 37.81/11.26 | (231) vreduce(all_18_10_38) = all_18_9_37 % 37.81/11.26 | (232) vapp(all_18_10_38, all_18_11_39) = ve2 % 37.81/11.26 | (233) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_10_38) % 37.81/11.26 | (226) all_0_6_6 = vnoExp % 37.81/11.26 | (235) visSomeExp(all_18_9_37) = all_18_6_34 % 37.81/11.26 | (236) all_18_7_35 = all_18_9_37 % 37.81/11.26 | (237) ~ (all_18_6_34 = 0) % 37.81/11.26 | % 37.81/11.26 | Equations (226) can reduce 171 to: % 37.81/11.26 | (228) $false % 37.81/11.26 | % 37.81/11.26 |-The branch is then unsatisfiable % 37.81/11.26 |-Branch two: % 37.81/11.26 | (239) all_18_8_36 = ve2 & all_0_6_6 = vnoExp & vabs(all_18_11_39, all_18_10_38, all_18_9_37) = ve2 % 37.81/11.26 | % 37.81/11.26 | Applying alpha-rule on (239) yields: % 37.81/11.26 | (205) all_18_8_36 = ve2 % 37.81/11.26 | (226) all_0_6_6 = vnoExp % 37.81/11.26 | (242) vabs(all_18_11_39, all_18_10_38, all_18_9_37) = ve2 % 37.81/11.26 | % 37.81/11.26 | Equations (226) can reduce 171 to: % 37.81/11.26 | (228) $false % 37.81/11.26 | % 37.81/11.26 |-The branch is then unsatisfiable % 37.81/11.26 |-Branch two: % 37.81/11.26 | (244) all_18_10_38 = ve2 & all_0_6_6 = vnoExp & vvar(all_18_11_39) = ve2 % 37.81/11.26 | % 37.81/11.26 | Applying alpha-rule on (244) yields: % 37.81/11.26 | (245) all_18_10_38 = ve2 % 37.81/11.26 | (226) all_0_6_6 = vnoExp % 37.81/11.26 | (247) vvar(all_18_11_39) = ve2 % 37.81/11.26 | % 37.81/11.26 | Equations (226) can reduce 171 to: % 37.81/11.26 | (228) $false % 37.81/11.26 | % 37.81/11.26 |-The branch is then unsatisfiable % 37.81/11.26 |-Branch two: % 37.81/11.26 | (390) all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51) % 37.81/11.26 | % 37.81/11.26 | Applying alpha-rule on (390) yields: % 37.81/11.26 | (391) all_19_8_48 = all_0_5_5 % 37.81/11.26 | (392) vsomeExp(all_19_4_44) = all_0_4_4 % 37.81/11.26 | (393) vreduce(all_19_11_51) = all_19_10_50 % 37.81/11.26 | (394) all_19_7_47 = all_19_10_50 % 37.81/11.26 | (395) vapp(all_19_11_51, all_19_9_49) = all_0_5_5 % 37.81/11.26 | (396) all_19_6_46 = 0 % 37.81/11.26 | (397) visSomeExp(all_19_10_50) = 0 % 37.81/11.26 | (398) vapp(all_19_5_45, all_19_9_49) = all_19_4_44 % 37.81/11.26 | (399) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51) % 37.81/11.26 | (400) all_19_3_43 = all_0_4_4 % 37.81/11.26 | (401) vgetSomeExp(all_19_10_50) = all_19_5_45 % 37.81/11.26 | % 37.81/11.26 | Instantiating formula (59) with ve1, all_19_10_50, all_0_7_7 and discharging atoms vreduce(ve1) = all_0_7_7, yields: % 37.81/11.26 | (402) all_19_10_50 = all_0_7_7 | ~ (vreduce(ve1) = all_19_10_50) % 37.81/11.26 | % 37.81/11.26 | Using (397) and (17) yields: % 37.81/11.26 | (403) ~ (all_19_10_50 = vnoExp) % 37.81/11.26 | % 37.81/11.26 | Instantiating formula (50) with all_0_4_4, all_19_4_44, all_0_2_2 and discharging atoms vsomeExp(all_19_4_44) = all_0_4_4, vsomeExp(all_0_2_2) = all_0_4_4, yields: % 37.81/11.26 | (404) all_19_4_44 = all_0_2_2 % 37.81/11.26 | % 37.81/11.26 | Instantiating formula (18) with all_0_5_5, all_19_9_49, all_19_11_51, ve2, ve1 and discharging atoms vapp(all_19_11_51, all_19_9_49) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 37.81/11.26 | (405) all_19_9_49 = ve2 % 37.81/11.26 | % 37.81/11.26 | Instantiating formula (20) with all_0_5_5, all_19_9_49, all_19_11_51, ve2, ve1 and discharging atoms vapp(all_19_11_51, all_19_9_49) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 37.81/11.26 | (406) all_19_11_51 = ve1 % 37.81/11.26 | % 37.81/11.26 | From (406) and (393) follows: % 37.81/11.26 | (407) vreduce(ve1) = all_19_10_50 % 37.81/11.26 | % 37.81/11.26 | From (405)(404) and (398) follows: % 37.81/11.26 | (408) vapp(all_19_5_45, ve2) = all_0_2_2 % 37.81/11.26 | % 37.81/11.26 +-Applying beta-rule and splitting (402), into two cases. % 37.81/11.26 |-Branch one: % 37.81/11.26 | (409) ~ (vreduce(ve1) = all_19_10_50) % 37.81/11.26 | % 37.81/11.26 | Using (407) and (409) yields: % 37.81/11.26 | (130) $false % 37.81/11.26 | % 37.81/11.26 |-The branch is then unsatisfiable % 37.81/11.26 |-Branch two: % 37.81/11.26 | (407) vreduce(ve1) = all_19_10_50 % 37.81/11.26 | (412) all_19_10_50 = all_0_7_7 % 37.81/11.26 | % 37.81/11.26 | Equations (412) can reduce 403 to: % 37.81/11.26 | (413) ~ (all_0_7_7 = vnoExp) % 37.81/11.26 | % 37.81/11.26 | From (412) and (401) follows: % 37.81/11.26 | (414) vgetSomeExp(all_0_7_7) = all_19_5_45 % 37.81/11.26 | % 37.81/11.26 +-Applying beta-rule and splitting (114), into two cases. % 37.81/11.26 |-Branch one: % 37.81/11.26 | (415) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) | (all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22) | (all_17_7_23 = all_17_9_25 & all_17_8_24 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_6_22 = 0) & vreduce(all_17_10_26) = all_17_9_25 & visSomeExp(all_17_9_25) = all_17_6_22 & vapp(all_17_10_26, all_17_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26)) | (all_17_8_24 = ve1 & all_0_7_7 = vnoExp & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1) % 37.81/11.26 | % 37.81/11.26 +-Applying beta-rule and splitting (415), into two cases. % 37.81/11.26 |-Branch one: % 37.81/11.26 | (416) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) | (all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22) | (all_17_7_23 = all_17_9_25 & all_17_8_24 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_6_22 = 0) & vreduce(all_17_10_26) = all_17_9_25 & visSomeExp(all_17_9_25) = all_17_6_22 & vapp(all_17_10_26, all_17_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26)) % 37.81/11.26 | % 37.81/11.26 +-Applying beta-rule and splitting (416), into two cases. % 37.81/11.26 |-Branch one: % 37.81/11.26 | (417) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) | (all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22) % 37.81/11.26 | % 37.81/11.26 +-Applying beta-rule and splitting (417), into two cases. % 37.81/11.26 |-Branch one: % 37.81/11.26 | (418) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) % 37.81/11.26 | % 37.81/11.26 +-Applying beta-rule and splitting (418), into two cases. % 37.81/11.26 |-Branch one: % 37.81/11.26 | (419) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) % 37.81/11.26 | % 37.81/11.26 +-Applying beta-rule and splitting (419), into two cases. % 37.81/11.26 |-Branch one: % 37.81/11.26 | (420) all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22 % 37.81/11.26 | % 37.81/11.26 | Applying alpha-rule on (420) yields: % 37.81/11.26 | (421) vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 % 37.81/11.26 | (422) all_17_4_20 = all_17_10_26 % 37.81/11.26 | (423) ~ (all_17_3_19 = 0) % 37.81/11.26 | (424) vapp(all_17_6_22, all_17_8_24) = ve1 % 37.81/11.26 | (425) vreduce(all_17_8_24) = all_17_10_26 % 37.81/11.26 | (426) visSomeExp(all_17_10_26) = all_17_3_19 % 37.81/11.26 | (427) all_17_5_21 = ve1 % 37.81/11.26 | (428) vsomeExp(all_17_1_17) = all_0_7_7 % 37.81/11.26 | (429) all_17_2_18 = 0 % 37.81/11.26 | (430) vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22 % 37.81/11.26 | (431) all_17_0_16 = all_0_7_7 % 37.81/11.26 | (432) visValue(all_17_8_24) = 0 % 37.81/11.26 | % 37.81/11.26 | Instantiating formula (32) with all_17_1_17, all_19_5_45, all_0_7_7 and discharging atoms vgetSomeExp(all_0_7_7) = all_19_5_45, vsomeExp(all_17_1_17) = all_0_7_7, yields: % 37.81/11.26 | (433) all_19_5_45 = all_17_1_17 % 37.81/11.26 | % 37.81/11.26 | From (433) and (408) follows: % 37.81/11.26 | (434) vapp(all_17_1_17, ve2) = all_0_2_2 % 37.81/11.26 | % 37.81/11.26 | Instantiating formula (31) with all_16_3_11, all_17_1_17, all_0_3_3 and discharging atoms vsomeExp(all_17_1_17) = all_0_7_7, vtcheck(all_0_3_3, ve1, all_16_3_11) = 0, yields: % 37.81/11.26 | (435) vtcheck(all_0_3_3, all_17_1_17, all_16_3_11) = 0 % 37.81/11.26 | % 37.81/11.26 | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_16_3_11, all_0_1_1, ve2, all_17_1_17, all_0_3_3, all_16_5_13 and discharging atoms varrow(all_16_5_13, all_0_1_1) = all_16_3_11, vtcheck(all_0_3_3, all_17_1_17, all_16_3_11) = 0, vtcheck(all_0_3_3, all_0_2_2, all_0_1_1) = all_0_0_0, vapp(all_17_1_17, ve2) = all_0_2_2, yields: % 37.81/11.27 | (436) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 37.81/11.27 | % 37.81/11.27 +-Applying beta-rule and splitting (436), into two cases. % 37.81/11.27 |-Branch one: % 37.81/11.27 | (298) all_0_0_0 = 0 % 37.81/11.27 | % 37.81/11.27 | Equations (298) can reduce 36 to: % 37.81/11.27 | (228) $false % 37.81/11.27 | % 37.81/11.27 |-The branch is then unsatisfiable % 37.81/11.27 |-Branch two: % 37.81/11.27 | (36) ~ (all_0_0_0 = 0) % 37.81/11.27 | (440) ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 37.81/11.27 | % 37.81/11.27 | Instantiating (440) with all_147_0_239 yields: % 37.81/11.27 | (441) ~ (all_147_0_239 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = all_147_0_239 % 37.81/11.27 | % 37.81/11.27 | Applying alpha-rule on (441) yields: % 37.81/11.27 | (442) ~ (all_147_0_239 = 0) % 37.81/11.27 | (443) vtcheck(all_0_3_3, ve2, all_16_5_13) = all_147_0_239 % 37.81/11.27 | % 37.81/11.27 | Instantiating formula (91) with all_0_3_3, ve2, all_16_5_13, all_147_0_239, 0 and discharging atoms vtcheck(all_0_3_3, ve2, all_16_5_13) = all_147_0_239, vtcheck(all_0_3_3, ve2, all_16_5_13) = 0, yields: % 37.81/11.27 | (444) all_147_0_239 = 0 % 37.81/11.27 | % 37.81/11.27 | Equations (444) can reduce 442 to: % 37.81/11.27 | (228) $false % 37.81/11.27 | % 37.81/11.27 |-The branch is then unsatisfiable % 37.81/11.27 |-Branch two: % 37.81/11.27 | (446) all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22 % 37.81/11.27 | % 37.81/11.27 | Applying alpha-rule on (446) yields: % 37.81/11.27 | (447) vgetSomeExp(all_17_7_23) = all_17_2_18 % 37.81/11.27 | (448) vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22 % 37.81/11.27 | (449) vreduce(all_17_11_27) = all_17_7_23 % 37.81/11.27 | (450) all_17_3_19 = 0 % 37.81/11.27 | (451) vapp(all_17_6_22, all_17_11_27) = ve1 % 37.81/11.27 | (452) visSomeExp(all_17_7_23) = 0 % 37.81/11.27 | (453) all_17_4_20 = all_17_7_23 % 37.81/11.27 | (427) all_17_5_21 = ve1 % 37.81/11.27 | (428) vsomeExp(all_17_1_17) = all_0_7_7 % 37.81/11.27 | (431) all_17_0_16 = all_0_7_7 % 37.81/11.27 | (457) vapp(all_17_6_22, all_17_2_18) = all_17_1_17 % 37.81/11.27 | % 37.81/11.27 | Instantiating formula (32) with all_17_1_17, all_19_5_45, all_0_7_7 and discharging atoms vgetSomeExp(all_0_7_7) = all_19_5_45, vsomeExp(all_17_1_17) = all_0_7_7, yields: % 37.81/11.27 | (433) all_19_5_45 = all_17_1_17 % 37.81/11.27 | % 37.81/11.27 | From (433) and (408) follows: % 37.81/11.27 | (434) vapp(all_17_1_17, ve2) = all_0_2_2 % 37.81/11.27 | % 37.81/11.27 | Instantiating formula (31) with all_16_3_11, all_17_1_17, all_0_3_3 and discharging atoms vsomeExp(all_17_1_17) = all_0_7_7, vtcheck(all_0_3_3, ve1, all_16_3_11) = 0, yields: % 37.81/11.27 | (435) vtcheck(all_0_3_3, all_17_1_17, all_16_3_11) = 0 % 37.81/11.27 | % 37.81/11.27 | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_16_3_11, all_0_1_1, ve2, all_17_1_17, all_0_3_3, all_16_5_13 and discharging atoms varrow(all_16_5_13, all_0_1_1) = all_16_3_11, vtcheck(all_0_3_3, all_17_1_17, all_16_3_11) = 0, vtcheck(all_0_3_3, all_0_2_2, all_0_1_1) = all_0_0_0, vapp(all_17_1_17, ve2) = all_0_2_2, yields: % 37.81/11.27 | (436) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 37.81/11.27 | % 37.81/11.27 +-Applying beta-rule and splitting (436), into two cases. % 37.81/11.27 |-Branch one: % 37.81/11.27 | (298) all_0_0_0 = 0 % 37.81/11.27 | % 37.81/11.27 | Equations (298) can reduce 36 to: % 37.81/11.27 | (228) $false % 37.81/11.27 | % 37.81/11.27 |-The branch is then unsatisfiable % 37.81/11.27 |-Branch two: % 37.81/11.27 | (36) ~ (all_0_0_0 = 0) % 37.81/11.27 | (440) ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 37.81/11.27 | % 37.81/11.27 | Instantiating (440) with all_150_0_264 yields: % 37.81/11.27 | (466) ~ (all_150_0_264 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = all_150_0_264 % 37.81/11.27 | % 37.81/11.27 | Applying alpha-rule on (466) yields: % 37.81/11.27 | (467) ~ (all_150_0_264 = 0) % 37.81/11.27 | (468) vtcheck(all_0_3_3, ve2, all_16_5_13) = all_150_0_264 % 37.81/11.27 | % 37.81/11.27 | Instantiating formula (91) with all_0_3_3, ve2, all_16_5_13, all_150_0_264, 0 and discharging atoms vtcheck(all_0_3_3, ve2, all_16_5_13) = all_150_0_264, vtcheck(all_0_3_3, ve2, all_16_5_13) = 0, yields: % 37.81/11.27 | (469) all_150_0_264 = 0 % 37.81/11.27 | % 37.81/11.27 | Equations (469) can reduce 467 to: % 37.81/11.27 | (228) $false % 37.81/11.27 | % 37.81/11.27 |-The branch is then unsatisfiable % 37.81/11.27 |-Branch two: % 37.81/11.27 | (471) all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27) % 37.81/11.27 | % 37.81/11.27 | Applying alpha-rule on (471) yields: % 37.81/11.27 | (472) vapp(all_17_11_27, all_17_9_25) = ve1 % 37.81/11.27 | (473) vreduce(all_17_11_27) = all_17_10_26 % 37.81/11.27 | (474) vapp(all_17_5_21, all_17_9_25) = all_17_4_20 % 37.81/11.27 | (475) all_17_7_23 = all_17_10_26 % 37.81/11.27 | (476) vgetSomeExp(all_17_10_26) = all_17_5_21 % 37.81/11.27 | (477) all_17_6_22 = 0 % 37.81/11.27 | (478) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27) % 37.81/11.27 | (479) all_17_8_24 = ve1 % 37.81/11.27 | (480) all_17_3_19 = all_0_7_7 % 37.81/11.27 | (481) visSomeExp(all_17_10_26) = 0 % 37.81/11.27 | (482) vsomeExp(all_17_4_20) = all_0_7_7 % 37.81/11.27 | % 37.81/11.27 | Instantiating formula (32) with all_17_4_20, all_19_5_45, all_0_7_7 and discharging atoms vgetSomeExp(all_0_7_7) = all_19_5_45, vsomeExp(all_17_4_20) = all_0_7_7, yields: % 37.81/11.27 | (483) all_19_5_45 = all_17_4_20 % 37.81/11.27 | % 37.81/11.27 | From (483) and (408) follows: % 37.81/11.27 | (484) vapp(all_17_4_20, ve2) = all_0_2_2 % 37.81/11.27 | % 37.81/11.27 | Instantiating formula (31) with all_16_3_11, all_17_4_20, all_0_3_3 and discharging atoms vsomeExp(all_17_4_20) = all_0_7_7, vtcheck(all_0_3_3, ve1, all_16_3_11) = 0, yields: % 37.81/11.27 | (485) vtcheck(all_0_3_3, all_17_4_20, all_16_3_11) = 0 % 37.81/11.27 | % 37.81/11.27 | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_16_3_11, all_0_1_1, ve2, all_17_4_20, all_0_3_3, all_16_5_13 and discharging atoms varrow(all_16_5_13, all_0_1_1) = all_16_3_11, vtcheck(all_0_3_3, all_17_4_20, all_16_3_11) = 0, vtcheck(all_0_3_3, all_0_2_2, all_0_1_1) = all_0_0_0, vapp(all_17_4_20, ve2) = all_0_2_2, yields: % 37.81/11.27 | (436) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 37.81/11.27 | % 37.81/11.27 +-Applying beta-rule and splitting (436), into two cases. % 37.81/11.27 |-Branch one: % 37.81/11.27 | (298) all_0_0_0 = 0 % 37.81/11.27 | % 37.81/11.27 | Equations (298) can reduce 36 to: % 37.81/11.27 | (228) $false % 37.81/11.27 | % 37.81/11.27 |-The branch is then unsatisfiable % 37.81/11.27 |-Branch two: % 37.81/11.27 | (36) ~ (all_0_0_0 = 0) % 37.81/11.27 | (440) ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 37.81/11.27 | % 37.81/11.27 | Instantiating (440) with all_127_0_305 yields: % 37.81/11.27 | (491) ~ (all_127_0_305 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = all_127_0_305 % 37.81/11.27 | % 37.81/11.27 | Applying alpha-rule on (491) yields: % 37.81/11.27 | (492) ~ (all_127_0_305 = 0) % 37.81/11.27 | (493) vtcheck(all_0_3_3, ve2, all_16_5_13) = all_127_0_305 % 37.81/11.27 | % 37.81/11.27 | Instantiating formula (91) with all_0_3_3, ve2, all_16_5_13, all_127_0_305, 0 and discharging atoms vtcheck(all_0_3_3, ve2, all_16_5_13) = all_127_0_305, vtcheck(all_0_3_3, ve2, all_16_5_13) = 0, yields: % 37.81/11.27 | (494) all_127_0_305 = 0 % 37.81/11.27 | % 37.81/11.27 | Equations (494) can reduce 492 to: % 37.81/11.27 | (228) $false % 37.81/11.27 | % 37.81/11.27 |-The branch is then unsatisfiable % 37.81/11.27 |-Branch two: % 37.81/11.27 | (496) all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22 % 37.81/11.27 | % 37.81/11.27 | Applying alpha-rule on (496) yields: % 37.81/11.27 | (497) visValue(all_17_7_23) = all_17_2_18 % 37.81/11.27 | (498) visSomeExp(all_17_8_24) = all_17_3_19 % 37.81/11.27 | (423) ~ (all_17_3_19 = 0) % 37.81/11.27 | (500) all_17_4_20 = all_17_8_24 % 37.81/11.27 | (170) all_0_7_7 = vnoExp % 37.81/11.27 | (502) vapp(all_17_6_22, all_17_7_23) = ve1 % 37.81/11.27 | (427) all_17_5_21 = ve1 % 37.81/11.27 | (504) vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22 % 37.81/11.27 | (505) ~ (all_17_2_18 = 0) % 37.81/11.27 | (506) vreduce(all_17_7_23) = all_17_8_24 % 37.81/11.27 | % 37.81/11.27 | Equations (170) can reduce 413 to: % 37.81/11.27 | (228) $false % 37.81/11.27 | % 37.81/11.27 |-The branch is then unsatisfiable % 37.81/11.27 |-Branch two: % 37.81/11.27 | (508) all_17_7_23 = all_17_9_25 & all_17_8_24 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_6_22 = 0) & vreduce(all_17_10_26) = all_17_9_25 & visSomeExp(all_17_9_25) = all_17_6_22 & vapp(all_17_10_26, all_17_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26) % 37.81/11.27 | % 37.81/11.27 | Applying alpha-rule on (508) yields: % 37.81/11.27 | (509) all_17_7_23 = all_17_9_25 % 37.81/11.27 | (510) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26) % 37.81/11.27 | (511) visSomeExp(all_17_9_25) = all_17_6_22 % 37.81/11.27 | (512) ~ (all_17_6_22 = 0) % 37.81/11.27 | (170) all_0_7_7 = vnoExp % 37.81/11.27 | (514) vapp(all_17_10_26, all_17_11_27) = ve1 % 37.81/11.27 | (479) all_17_8_24 = ve1 % 37.81/11.27 | (516) vreduce(all_17_10_26) = all_17_9_25 % 37.81/11.27 | % 37.81/11.27 | Equations (170) can reduce 413 to: % 37.81/11.27 | (228) $false % 37.81/11.27 | % 37.81/11.27 |-The branch is then unsatisfiable % 37.81/11.27 |-Branch two: % 37.81/11.27 | (518) all_17_8_24 = ve1 & all_0_7_7 = vnoExp & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1 % 37.81/11.27 | % 37.81/11.27 | Applying alpha-rule on (518) yields: % 37.81/11.27 | (479) all_17_8_24 = ve1 % 37.81/11.27 | (170) all_0_7_7 = vnoExp % 37.81/11.27 | (521) vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1 % 37.81/11.27 | % 37.81/11.27 | Equations (170) can reduce 413 to: % 37.81/11.27 | (228) $false % 37.81/11.27 | % 37.81/11.27 |-The branch is then unsatisfiable % 37.81/11.27 |-Branch two: % 37.81/11.27 | (523) all_17_10_26 = ve1 & all_0_7_7 = vnoExp & vvar(all_17_11_27) = ve1 % 37.81/11.27 | % 37.81/11.27 | Applying alpha-rule on (523) yields: % 37.81/11.27 | (524) all_17_10_26 = ve1 % 37.81/11.27 | (170) all_0_7_7 = vnoExp % 37.81/11.27 | (526) vvar(all_17_11_27) = ve1 % 37.81/11.27 | % 37.81/11.27 | Equations (170) can reduce 413 to: % 37.81/11.27 | (228) $false % 37.81/11.27 | % 37.81/11.27 |-The branch is then unsatisfiable % 37.81/11.27 |-Branch two: % 37.81/11.27 | (528) all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46 % 37.81/11.27 | % 37.81/11.27 | Applying alpha-rule on (528) yields: % 37.81/11.27 | (529) visValue(all_19_7_47) = all_19_2_42 % 37.81/11.27 | (530) vapp(all_19_6_46, all_19_7_47) = all_0_5_5 % 37.81/11.27 | (531) all_19_4_44 = all_19_8_48 % 37.81/11.27 | (532) vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46 % 37.81/11.27 | (533) visSomeExp(all_19_8_48) = all_19_3_43 % 37.81/11.27 | (534) all_0_4_4 = vnoExp % 37.81/11.28 | (535) ~ (all_19_2_42 = 0) % 37.81/11.28 | (160) all_19_5_45 = all_0_5_5 % 37.81/11.28 | (537) vreduce(all_19_7_47) = all_19_8_48 % 37.81/11.28 | (161) ~ (all_19_3_43 = 0) % 37.81/11.28 | % 37.81/11.28 | Equations (534) can reduce 108 to: % 37.81/11.28 | (228) $false % 37.81/11.28 | % 37.81/11.28 |-The branch is then unsatisfiable % 37.81/11.28 |-Branch two: % 37.81/11.28 | (540) all_19_7_47 = all_19_9_49 & all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_6_46 = 0) & vreduce(all_19_10_50) = all_19_9_49 & visSomeExp(all_19_9_49) = all_19_6_46 & vapp(all_19_10_50, all_19_11_51) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50) % 37.81/11.28 | % 37.81/11.28 | Applying alpha-rule on (540) yields: % 37.81/11.28 | (391) all_19_8_48 = all_0_5_5 % 37.81/11.28 | (542) vreduce(all_19_10_50) = all_19_9_49 % 37.81/11.28 | (543) all_19_7_47 = all_19_9_49 % 37.81/11.28 | (544) ~ (all_19_6_46 = 0) % 37.81/11.28 | (534) all_0_4_4 = vnoExp % 37.81/11.28 | (546) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50) % 37.81/11.28 | (547) vapp(all_19_10_50, all_19_11_51) = all_0_5_5 % 37.81/11.28 | (548) visSomeExp(all_19_9_49) = all_19_6_46 % 37.81/11.28 | % 37.81/11.28 | Equations (534) can reduce 108 to: % 37.81/11.28 | (228) $false % 37.81/11.28 | % 37.81/11.28 |-The branch is then unsatisfiable % 37.81/11.28 |-Branch two: % 37.81/11.28 | (550) all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_0_5_5 % 37.81/11.28 | % 37.81/11.28 | Applying alpha-rule on (550) yields: % 37.81/11.28 | (391) all_19_8_48 = all_0_5_5 % 37.81/11.28 | (534) all_0_4_4 = vnoExp % 37.81/11.28 | (553) vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_0_5_5 % 37.81/11.28 | % 37.81/11.28 | Equations (534) can reduce 108 to: % 37.81/11.28 | (228) $false % 37.81/11.28 | % 37.81/11.28 |-The branch is then unsatisfiable % 37.81/11.28 |-Branch two: % 37.81/11.28 | (555) all_19_10_50 = all_0_5_5 & all_0_4_4 = vnoExp & vvar(all_19_11_51) = all_0_5_5 % 37.81/11.28 | % 37.81/11.28 | Applying alpha-rule on (555) yields: % 37.81/11.28 | (556) all_19_10_50 = all_0_5_5 % 37.81/11.28 | (534) all_0_4_4 = vnoExp % 37.81/11.28 | (558) vvar(all_19_11_51) = all_0_5_5 % 37.81/11.28 | % 37.81/11.28 | Equations (534) can reduce 108 to: % 37.81/11.28 | (228) $false % 37.81/11.28 | % 37.81/11.28 |-The branch is then unsatisfiable % 37.81/11.28 |-Branch two: % 37.81/11.28 | (560) all_16_4_12 = all_16_7_15 & all_16_5_13 = all_0_5_5 & vlookup(all_16_6_14, all_0_3_3) = all_16_7_15 & vsomeType(all_0_1_1) = all_16_7_15 & vvar(all_16_6_14) = all_0_5_5 % 37.81/11.28 | % 37.81/11.28 | Applying alpha-rule on (560) yields: % 37.81/11.28 | (561) vlookup(all_16_6_14, all_0_3_3) = all_16_7_15 % 37.81/11.28 | (562) vsomeType(all_0_1_1) = all_16_7_15 % 37.81/11.28 | (563) all_16_4_12 = all_16_7_15 % 37.81/11.28 | (564) all_16_5_13 = all_0_5_5 % 37.81/11.28 | (565) vvar(all_16_6_14) = all_0_5_5 % 37.81/11.28 | % 37.81/11.28 | Instantiating formula (6) with all_0_5_5, ve2, ve1, all_16_6_14 and discharging atoms vapp(ve1, ve2) = all_0_5_5, vvar(all_16_6_14) = all_0_5_5, yields: % 37.81/11.28 | (130) $false % 37.81/11.28 | % 37.81/11.28 |-The branch is then unsatisfiable % 37.81/11.28 |-Branch two: % 37.81/11.28 | (567) vreduce(ve1) = all_0_6_6 % 37.81/11.28 | (568) all_0_6_6 = all_0_7_7 % 37.81/11.28 | % 37.81/11.28 | Equations (568) can reduce 118 to: % 37.81/11.28 | (569) ~ (all_0_4_4 = all_0_7_7) % 37.81/11.28 | % 37.81/11.28 | From (568) and (25) follows: % 37.81/11.28 | (570) vreduce(ve2) = all_0_7_7 % 37.81/11.28 | % 37.81/11.28 | From (568) and (567) follows: % 37.81/11.28 | (29) vreduce(ve1) = all_0_7_7 % 37.81/11.28 | % 37.81/11.28 +-Applying beta-rule and splitting (113), into two cases. % 37.81/11.28 |-Branch one: % 37.81/11.28 | (121) (all_16_0_8 = 0 & all_16_2_10 = all_0_1_1 & all_16_3_11 = all_0_5_5 & varrow(all_16_5_13, all_16_4_12) = all_0_1_1 & vtcheck(all_16_1_9, all_16_6_14, all_16_4_12) = 0 & vbind(all_16_7_15, all_16_5_13, all_0_3_3) = all_16_1_9 & vabs(all_16_7_15, all_16_5_13, all_16_6_14) = all_0_5_5) | (all_16_1_9 = 0 & all_16_2_10 = 0 & all_16_4_12 = all_0_5_5 & varrow(all_16_5_13, all_0_1_1) = all_16_3_11 & vtcheck(all_0_3_3, all_16_6_14, all_16_5_13) = 0 & vtcheck(all_0_3_3, all_16_7_15, all_16_3_11) = 0 & vapp(all_16_7_15, all_16_6_14) = all_0_5_5) % 37.81/11.28 | % 37.81/11.28 +-Applying beta-rule and splitting (121), into two cases. % 37.81/11.28 |-Branch one: % 37.81/11.28 | (122) all_16_0_8 = 0 & all_16_2_10 = all_0_1_1 & all_16_3_11 = all_0_5_5 & varrow(all_16_5_13, all_16_4_12) = all_0_1_1 & vtcheck(all_16_1_9, all_16_6_14, all_16_4_12) = 0 & vbind(all_16_7_15, all_16_5_13, all_0_3_3) = all_16_1_9 & vabs(all_16_7_15, all_16_5_13, all_16_6_14) = all_0_5_5 % 37.81/11.28 | % 37.81/11.28 | Applying alpha-rule on (122) yields: % 37.81/11.28 | (123) vbind(all_16_7_15, all_16_5_13, all_0_3_3) = all_16_1_9 % 37.81/11.28 | (124) vabs(all_16_7_15, all_16_5_13, all_16_6_14) = all_0_5_5 % 37.81/11.28 | (125) vtcheck(all_16_1_9, all_16_6_14, all_16_4_12) = 0 % 37.81/11.28 | (126) all_16_0_8 = 0 % 37.81/11.28 | (127) all_16_2_10 = all_0_1_1 % 37.81/11.28 | (128) varrow(all_16_5_13, all_16_4_12) = all_0_1_1 % 37.81/11.28 | (129) all_16_3_11 = all_0_5_5 % 37.81/11.28 | % 37.81/11.28 | Instantiating formula (55) with all_0_5_5, ve2, ve1, all_16_6_14, all_16_5_13, all_16_7_15 and discharging atoms vapp(ve1, ve2) = all_0_5_5, vabs(all_16_7_15, all_16_5_13, all_16_6_14) = all_0_5_5, yields: % 37.81/11.28 | (130) $false % 37.81/11.28 | % 37.81/11.28 |-The branch is then unsatisfiable % 37.81/11.28 |-Branch two: % 37.81/11.28 | (131) all_16_1_9 = 0 & all_16_2_10 = 0 & all_16_4_12 = all_0_5_5 & varrow(all_16_5_13, all_0_1_1) = all_16_3_11 & vtcheck(all_0_3_3, all_16_6_14, all_16_5_13) = 0 & vtcheck(all_0_3_3, all_16_7_15, all_16_3_11) = 0 & vapp(all_16_7_15, all_16_6_14) = all_0_5_5 % 37.81/11.28 | % 37.81/11.28 | Applying alpha-rule on (131) yields: % 37.81/11.28 | (132) vtcheck(all_0_3_3, all_16_7_15, all_16_3_11) = 0 % 37.81/11.28 | (133) varrow(all_16_5_13, all_0_1_1) = all_16_3_11 % 37.81/11.28 | (134) vtcheck(all_0_3_3, all_16_6_14, all_16_5_13) = 0 % 37.81/11.28 | (135) all_16_4_12 = all_0_5_5 % 37.81/11.28 | (136) all_16_1_9 = 0 % 37.81/11.28 | (137) all_16_2_10 = 0 % 37.81/11.28 | (138) vapp(all_16_7_15, all_16_6_14) = all_0_5_5 % 37.81/11.28 | % 37.81/11.28 | Instantiating formula (18) with all_0_5_5, all_16_6_14, all_16_7_15, ve2, ve1 and discharging atoms vapp(all_16_7_15, all_16_6_14) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 37.81/11.28 | (139) all_16_6_14 = ve2 % 37.81/11.28 | % 37.81/11.28 | Instantiating formula (20) with all_0_5_5, all_16_6_14, all_16_7_15, ve2, ve1 and discharging atoms vapp(all_16_7_15, all_16_6_14) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 37.81/11.28 | (140) all_16_7_15 = ve1 % 37.81/11.28 | % 37.81/11.28 | From (139) and (134) follows: % 37.81/11.28 | (141) vtcheck(all_0_3_3, ve2, all_16_5_13) = 0 % 37.81/11.28 | % 37.81/11.28 | From (140) and (132) follows: % 37.81/11.28 | (142) vtcheck(all_0_3_3, ve1, all_16_3_11) = 0 % 37.81/11.28 | % 37.81/11.28 | From (140)(139) and (138) follows: % 37.81/11.28 | (102) vapp(ve1, ve2) = all_0_5_5 % 37.81/11.28 | % 37.81/11.28 | Instantiating formula (87) with all_0_3_3, all_16_3_11, ve1 and discharging atoms vtcheck(all_0_3_3, ve1, all_16_3_11) = 0, yields: % 37.81/11.28 | (595) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v5 = all_16_3_11 & v4 = ve1 & varrow(v2, v3) = all_16_3_11 & vtcheck(v6, v1, v3) = 0 & vbind(v0, v2, all_0_3_3) = v6 & vabs(v0, v2, v1) = ve1) | (v6 = 0 & v5 = 0 & v3 = ve1 & varrow(v2, all_16_3_11) = v4 & vtcheck(all_0_3_3, v1, v2) = 0 & vtcheck(all_0_3_3, v0, v4) = 0 & vapp(v0, v1) = ve1) | (v3 = v0 & v2 = ve1 & vlookup(v1, all_0_3_3) = v0 & vsomeType(all_16_3_11) = v0 & vvar(v1) = ve1)) % 37.81/11.28 | % 37.81/11.28 | Instantiating (595) with all_71_0_306, all_71_1_307, all_71_2_308, all_71_3_309, all_71_4_310, all_71_5_311, all_71_6_312, all_71_7_313 yields: % 37.81/11.28 | (596) (all_71_0_306 = 0 & all_71_2_308 = all_16_3_11 & all_71_3_309 = ve1 & varrow(all_71_5_311, all_71_4_310) = all_16_3_11 & vtcheck(all_71_1_307, all_71_6_312, all_71_4_310) = 0 & vbind(all_71_7_313, all_71_5_311, all_0_3_3) = all_71_1_307 & vabs(all_71_7_313, all_71_5_311, all_71_6_312) = ve1) | (all_71_1_307 = 0 & all_71_2_308 = 0 & all_71_4_310 = ve1 & varrow(all_71_5_311, all_16_3_11) = all_71_3_309 & vtcheck(all_0_3_3, all_71_6_312, all_71_5_311) = 0 & vtcheck(all_0_3_3, all_71_7_313, all_71_3_309) = 0 & vapp(all_71_7_313, all_71_6_312) = ve1) | (all_71_4_310 = all_71_7_313 & all_71_5_311 = ve1 & vlookup(all_71_6_312, all_0_3_3) = all_71_7_313 & vsomeType(all_16_3_11) = all_71_7_313 & vvar(all_71_6_312) = ve1) % 37.81/11.28 | % 37.81/11.28 +-Applying beta-rule and splitting (116), into two cases. % 37.81/11.28 |-Branch one: % 37.81/11.28 | (144) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) | (all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46) | (all_19_7_47 = all_19_9_49 & all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_6_46 = 0) & vreduce(all_19_10_50) = all_19_9_49 & visSomeExp(all_19_9_49) = all_19_6_46 & vapp(all_19_10_50, all_19_11_51) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50)) | (all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_0_5_5) % 37.81/11.28 | % 37.81/11.28 +-Applying beta-rule and splitting (144), into two cases. % 37.81/11.28 |-Branch one: % 37.81/11.28 | (145) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) | (all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46) | (all_19_7_47 = all_19_9_49 & all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_6_46 = 0) & vreduce(all_19_10_50) = all_19_9_49 & visSomeExp(all_19_9_49) = all_19_6_46 & vapp(all_19_10_50, all_19_11_51) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50)) % 37.81/11.28 | % 37.81/11.28 +-Applying beta-rule and splitting (145), into two cases. % 37.81/11.28 |-Branch one: % 37.81/11.28 | (146) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) | (all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46) % 37.81/11.28 | % 37.81/11.28 +-Applying beta-rule and splitting (146), into two cases. % 37.81/11.28 |-Branch one: % 37.81/11.28 | (147) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) % 37.81/11.28 | % 37.81/11.28 +-Applying beta-rule and splitting (147), into two cases. % 37.81/11.28 |-Branch one: % 37.81/11.28 | (148) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) % 37.81/11.28 | % 37.81/11.28 +-Applying beta-rule and splitting (148), into two cases. % 37.81/11.28 |-Branch one: % 37.81/11.28 | (149) all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46 % 37.81/11.28 | % 37.81/11.28 | Applying alpha-rule on (149) yields: % 37.81/11.28 | (150) vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46 % 37.81/11.29 | (151) all_19_0_40 = all_0_4_4 % 37.81/11.29 | (152) vsomeExp(all_19_1_41) = all_0_4_4 % 37.81/11.29 | (153) vreduce(all_19_8_48) = all_19_10_50 % 37.81/11.29 | (154) vapp(all_19_6_46, all_19_8_48) = all_0_5_5 % 37.81/11.29 | (155) visValue(all_19_8_48) = 0 % 37.81/11.29 | (156) vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 % 37.81/11.29 | (157) visSomeExp(all_19_10_50) = all_19_3_43 % 37.81/11.29 | (158) all_19_4_44 = all_19_10_50 % 37.81/11.29 | (159) all_19_2_42 = 0 % 37.81/11.29 | (160) all_19_5_45 = all_0_5_5 % 37.81/11.29 | (161) ~ (all_19_3_43 = 0) % 37.81/11.29 | % 37.81/11.29 | Instantiating formula (59) with ve2, all_19_10_50, all_0_7_7 and discharging atoms vreduce(ve2) = all_0_7_7, yields: % 37.81/11.29 | (615) all_19_10_50 = all_0_7_7 | ~ (vreduce(ve2) = all_19_10_50) % 37.81/11.29 | % 37.81/11.29 | Instantiating formula (50) with all_0_4_4, all_19_1_41, all_0_2_2 and discharging atoms vsomeExp(all_19_1_41) = all_0_4_4, vsomeExp(all_0_2_2) = all_0_4_4, yields: % 37.81/11.29 | (262) all_19_1_41 = all_0_2_2 % 37.81/11.29 | % 37.81/11.29 | Instantiating formula (18) with all_0_5_5, all_19_8_48, all_19_6_46, ve2, ve1 and discharging atoms vapp(all_19_6_46, all_19_8_48) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 37.81/11.29 | (162) all_19_8_48 = ve2 % 37.81/11.29 | % 37.81/11.29 | Instantiating formula (20) with all_0_5_5, all_19_8_48, all_19_6_46, ve2, ve1 and discharging atoms vapp(all_19_6_46, all_19_8_48) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 37.81/11.29 | (163) all_19_6_46 = ve1 % 37.81/11.29 | % 37.81/11.29 | Instantiating formula (96) with all_0_7_7, ve1, all_19_7_47, all_19_11_51, all_19_9_49 and discharging atoms vreduce(ve1) = all_0_7_7, yields: % 37.81/11.29 | (164) all_0_7_7 = vnoExp | ~ (vabs(all_19_9_49, all_19_11_51, all_19_7_47) = ve1) % 37.81/11.29 | % 37.81/11.29 | From (162) and (153) follows: % 37.81/11.29 | (620) vreduce(ve2) = all_19_10_50 % 37.81/11.29 | % 37.81/11.29 | From (162)(262) and (156) follows: % 37.81/11.29 | (621) vsubst(all_19_9_49, ve2, all_19_7_47) = all_0_2_2 % 37.81/11.29 | % 37.81/11.29 | From (163)(162) and (154) follows: % 37.81/11.29 | (102) vapp(ve1, ve2) = all_0_5_5 % 37.81/11.29 | % 37.81/11.29 | From (163) and (150) follows: % 37.81/11.29 | (166) vabs(all_19_9_49, all_19_11_51, all_19_7_47) = ve1 % 37.81/11.29 | % 37.81/11.29 +-Applying beta-rule and splitting (164), into two cases. % 37.81/11.29 |-Branch one: % 37.81/11.29 | (167) ~ (vabs(all_19_9_49, all_19_11_51, all_19_7_47) = ve1) % 37.81/11.29 | % 37.81/11.29 | Using (166) and (167) yields: % 37.81/11.29 | (130) $false % 37.81/11.29 | % 37.81/11.29 |-The branch is then unsatisfiable % 37.81/11.29 |-Branch two: % 37.81/11.29 | (166) vabs(all_19_9_49, all_19_11_51, all_19_7_47) = ve1 % 37.81/11.29 | (170) all_0_7_7 = vnoExp % 37.81/11.29 | % 37.81/11.29 | Equations (170) can reduce 569 to: % 37.81/11.29 | (108) ~ (all_0_4_4 = vnoExp) % 37.81/11.29 | % 37.81/11.29 +-Applying beta-rule and splitting (615), into two cases. % 37.81/11.29 |-Branch one: % 37.81/11.29 | (629) ~ (vreduce(ve2) = all_19_10_50) % 37.81/11.29 | % 37.81/11.29 | Using (620) and (629) yields: % 37.81/11.29 | (130) $false % 37.81/11.29 | % 37.81/11.29 |-The branch is then unsatisfiable % 37.81/11.29 |-Branch two: % 37.81/11.29 | (620) vreduce(ve2) = all_19_10_50 % 37.81/11.29 | (412) all_19_10_50 = all_0_7_7 % 37.81/11.29 | % 37.81/11.29 | Combining equations (170,412) yields a new equation: % 37.81/11.29 | (633) all_19_10_50 = vnoExp % 37.81/11.29 | % 37.81/11.29 | From (633) and (157) follows: % 37.81/11.29 | (634) visSomeExp(vnoExp) = all_19_3_43 % 37.81/11.29 | % 37.81/11.29 | Instantiating formula (24) with all_19_3_43, all_0_4_4, all_0_5_5, vnoExp, ve1, ve2 and discharging atoms vreduce(all_0_5_5) = all_0_4_4, visSomeExp(vnoExp) = all_19_3_43, vapp(ve1, ve2) = all_0_5_5, yields: % 37.81/11.29 | (635) all_19_3_43 = 0 | all_0_4_4 = vnoExp | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = ve1 & vabs(v0, v1, v2) = ve1) | ( ~ (v0 = vnoExp) & vreduce(ve1) = v0)) % 37.81/11.29 | % 37.81/11.29 +-Applying beta-rule and splitting (114), into two cases. % 37.81/11.29 |-Branch one: % 37.81/11.29 | (415) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) | (all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22) | (all_17_7_23 = all_17_9_25 & all_17_8_24 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_6_22 = 0) & vreduce(all_17_10_26) = all_17_9_25 & visSomeExp(all_17_9_25) = all_17_6_22 & vapp(all_17_10_26, all_17_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26)) | (all_17_8_24 = ve1 & all_0_7_7 = vnoExp & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1) % 37.81/11.29 | % 37.81/11.29 +-Applying beta-rule and splitting (415), into two cases. % 37.81/11.29 |-Branch one: % 37.81/11.29 | (416) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) | (all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22) | (all_17_7_23 = all_17_9_25 & all_17_8_24 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_6_22 = 0) & vreduce(all_17_10_26) = all_17_9_25 & visSomeExp(all_17_9_25) = all_17_6_22 & vapp(all_17_10_26, all_17_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26)) % 37.81/11.29 | % 37.81/11.29 +-Applying beta-rule and splitting (416), into two cases. % 37.81/11.29 |-Branch one: % 37.81/11.29 | (417) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) | (all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22) % 37.81/11.29 | % 37.81/11.29 +-Applying beta-rule and splitting (417), into two cases. % 37.81/11.29 |-Branch one: % 37.81/11.29 | (418) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) % 37.81/11.29 | % 37.81/11.29 +-Applying beta-rule and splitting (418), into two cases. % 37.81/11.29 |-Branch one: % 37.81/11.29 | (419) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) % 37.81/11.29 | % 37.81/11.29 +-Applying beta-rule and splitting (419), into two cases. % 37.81/11.29 |-Branch one: % 37.81/11.29 | (420) all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22 % 37.81/11.29 | % 37.81/11.29 | Applying alpha-rule on (420) yields: % 37.81/11.29 | (421) vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 % 37.81/11.29 | (422) all_17_4_20 = all_17_10_26 % 37.81/11.29 | (423) ~ (all_17_3_19 = 0) % 37.81/11.29 | (424) vapp(all_17_6_22, all_17_8_24) = ve1 % 37.81/11.29 | (425) vreduce(all_17_8_24) = all_17_10_26 % 37.81/11.29 | (426) visSomeExp(all_17_10_26) = all_17_3_19 % 37.81/11.29 | (427) all_17_5_21 = ve1 % 37.81/11.29 | (428) vsomeExp(all_17_1_17) = all_0_7_7 % 37.81/11.29 | (429) all_17_2_18 = 0 % 37.81/11.29 | (430) vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22 % 37.81/11.29 | (431) all_17_0_16 = all_0_7_7 % 37.81/11.29 | (432) visValue(all_17_8_24) = 0 % 37.81/11.29 | % 37.81/11.29 | Instantiating formula (55) with ve1, all_17_8_24, all_17_6_22, all_19_7_47, all_19_11_51, all_19_9_49 and discharging atoms vapp(all_17_6_22, all_17_8_24) = ve1, vabs(all_19_9_49, all_19_11_51, all_19_7_47) = ve1, yields: % 37.81/11.29 | (130) $false % 37.81/11.29 | % 37.81/11.29 |-The branch is then unsatisfiable % 37.81/11.29 |-Branch two: % 37.81/11.29 | (446) all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22 % 37.81/11.29 | % 37.81/11.29 | Applying alpha-rule on (446) yields: % 37.81/11.29 | (447) vgetSomeExp(all_17_7_23) = all_17_2_18 % 37.81/11.29 | (448) vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22 % 37.81/11.29 | (449) vreduce(all_17_11_27) = all_17_7_23 % 37.81/11.29 | (450) all_17_3_19 = 0 % 37.81/11.29 | (451) vapp(all_17_6_22, all_17_11_27) = ve1 % 37.81/11.29 | (452) visSomeExp(all_17_7_23) = 0 % 37.81/11.29 | (453) all_17_4_20 = all_17_7_23 % 37.81/11.29 | (427) all_17_5_21 = ve1 % 37.81/11.29 | (428) vsomeExp(all_17_1_17) = all_0_7_7 % 37.81/11.29 | (431) all_17_0_16 = all_0_7_7 % 37.81/11.29 | (457) vapp(all_17_6_22, all_17_2_18) = all_17_1_17 % 37.81/11.29 | % 37.81/11.29 | Instantiating formula (55) with ve1, all_17_11_27, all_17_6_22, all_19_7_47, all_19_11_51, all_19_9_49 and discharging atoms vapp(all_17_6_22, all_17_11_27) = ve1, vabs(all_19_9_49, all_19_11_51, all_19_7_47) = ve1, yields: % 37.81/11.29 | (130) $false % 37.81/11.29 | % 37.81/11.29 |-The branch is then unsatisfiable % 37.81/11.29 |-Branch two: % 37.81/11.29 | (471) all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27) % 37.81/11.29 | % 37.81/11.29 | Applying alpha-rule on (471) yields: % 37.81/11.29 | (472) vapp(all_17_11_27, all_17_9_25) = ve1 % 37.81/11.29 | (473) vreduce(all_17_11_27) = all_17_10_26 % 37.81/11.29 | (474) vapp(all_17_5_21, all_17_9_25) = all_17_4_20 % 37.81/11.29 | (475) all_17_7_23 = all_17_10_26 % 37.81/11.29 | (476) vgetSomeExp(all_17_10_26) = all_17_5_21 % 37.81/11.29 | (477) all_17_6_22 = 0 % 37.81/11.29 | (478) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27) % 37.81/11.29 | (479) all_17_8_24 = ve1 % 37.81/11.29 | (480) all_17_3_19 = all_0_7_7 % 37.81/11.29 | (481) visSomeExp(all_17_10_26) = 0 % 37.81/11.29 | (482) vsomeExp(all_17_4_20) = all_0_7_7 % 37.81/11.29 | % 37.81/11.29 | Instantiating formula (55) with ve1, all_17_9_25, all_17_11_27, all_19_7_47, all_19_11_51, all_19_9_49 and discharging atoms vapp(all_17_11_27, all_17_9_25) = ve1, vabs(all_19_9_49, all_19_11_51, all_19_7_47) = ve1, yields: % 37.81/11.30 | (130) $false % 37.81/11.30 | % 37.81/11.30 |-The branch is then unsatisfiable % 37.81/11.30 |-Branch two: % 37.81/11.30 | (496) all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22 % 37.81/11.30 | % 37.81/11.30 | Applying alpha-rule on (496) yields: % 37.81/11.30 | (497) visValue(all_17_7_23) = all_17_2_18 % 37.81/11.30 | (498) visSomeExp(all_17_8_24) = all_17_3_19 % 37.81/11.30 | (423) ~ (all_17_3_19 = 0) % 37.81/11.30 | (500) all_17_4_20 = all_17_8_24 % 37.81/11.30 | (170) all_0_7_7 = vnoExp % 37.81/11.30 | (502) vapp(all_17_6_22, all_17_7_23) = ve1 % 37.81/11.30 | (427) all_17_5_21 = ve1 % 37.81/11.30 | (504) vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22 % 37.81/11.30 | (505) ~ (all_17_2_18 = 0) % 37.81/11.30 | (506) vreduce(all_17_7_23) = all_17_8_24 % 37.81/11.30 | % 37.81/11.30 | Instantiating formula (55) with ve1, all_17_7_23, all_17_6_22, all_19_7_47, all_19_11_51, all_19_9_49 and discharging atoms vapp(all_17_6_22, all_17_7_23) = ve1, vabs(all_19_9_49, all_19_11_51, all_19_7_47) = ve1, yields: % 37.81/11.30 | (130) $false % 37.81/11.30 | % 37.81/11.30 |-The branch is then unsatisfiable % 37.81/11.30 |-Branch two: % 37.81/11.30 | (508) all_17_7_23 = all_17_9_25 & all_17_8_24 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_6_22 = 0) & vreduce(all_17_10_26) = all_17_9_25 & visSomeExp(all_17_9_25) = all_17_6_22 & vapp(all_17_10_26, all_17_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26) % 37.81/11.30 | % 37.81/11.30 | Applying alpha-rule on (508) yields: % 37.81/11.30 | (509) all_17_7_23 = all_17_9_25 % 37.81/11.30 | (510) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26) % 37.81/11.30 | (511) visSomeExp(all_17_9_25) = all_17_6_22 % 37.81/11.30 | (512) ~ (all_17_6_22 = 0) % 37.81/11.30 | (170) all_0_7_7 = vnoExp % 37.81/11.30 | (514) vapp(all_17_10_26, all_17_11_27) = ve1 % 37.81/11.30 | (479) all_17_8_24 = ve1 % 37.81/11.30 | (516) vreduce(all_17_10_26) = all_17_9_25 % 37.81/11.30 | % 37.81/11.30 | Instantiating formula (55) with ve1, all_17_11_27, all_17_10_26, all_19_7_47, all_19_11_51, all_19_9_49 and discharging atoms vapp(all_17_10_26, all_17_11_27) = ve1, vabs(all_19_9_49, all_19_11_51, all_19_7_47) = ve1, yields: % 37.81/11.30 | (130) $false % 37.81/11.30 | % 37.81/11.30 |-The branch is then unsatisfiable % 37.81/11.30 |-Branch two: % 37.81/11.30 | (518) all_17_8_24 = ve1 & all_0_7_7 = vnoExp & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1 % 37.81/11.30 | % 37.81/11.30 | Applying alpha-rule on (518) yields: % 37.81/11.30 | (479) all_17_8_24 = ve1 % 37.81/11.30 | (170) all_0_7_7 = vnoExp % 37.81/11.30 | (521) vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1 % 37.81/11.30 | % 37.81/11.30 +-Applying beta-rule and splitting (635), into two cases. % 37.81/11.30 |-Branch one: % 37.81/11.30 | (534) all_0_4_4 = vnoExp % 37.81/11.30 | % 37.81/11.30 | Equations (534) can reduce 108 to: % 37.81/11.30 | (228) $false % 37.81/11.30 | % 37.81/11.30 |-The branch is then unsatisfiable % 37.81/11.30 |-Branch two: % 37.81/11.30 | (108) ~ (all_0_4_4 = vnoExp) % 37.81/11.30 | (710) all_19_3_43 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = ve1 & vabs(v0, v1, v2) = ve1) | ( ~ (v0 = vnoExp) & vreduce(ve1) = v0)) % 37.81/11.30 | % 37.81/11.30 +-Applying beta-rule and splitting (710), into two cases. % 37.81/11.30 |-Branch one: % 37.81/11.30 | (259) all_19_3_43 = 0 % 37.81/11.30 | % 37.81/11.30 | Equations (259) can reduce 161 to: % 37.81/11.30 | (228) $false % 37.81/11.30 | % 37.81/11.30 |-The branch is then unsatisfiable % 37.81/11.30 |-Branch two: % 37.81/11.30 | (161) ~ (all_19_3_43 = 0) % 37.81/11.30 | (714) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = ve1 & vabs(v0, v1, v2) = ve1) | ( ~ (v0 = vnoExp) & vreduce(ve1) = v0)) % 37.81/11.30 | % 37.81/11.30 | Instantiating (714) with all_107_0_358, all_107_1_359, all_107_2_360, all_107_3_361 yields: % 37.81/11.30 | (715) (all_107_0_358 = ve1 & vabs(all_107_3_361, all_107_2_360, all_107_1_359) = ve1) | ( ~ (all_107_3_361 = vnoExp) & vreduce(ve1) = all_107_3_361) % 38.22/11.30 | % 38.22/11.30 +-Applying beta-rule and splitting (715), into two cases. % 38.22/11.30 |-Branch one: % 38.22/11.30 | (716) all_107_0_358 = ve1 & vabs(all_107_3_361, all_107_2_360, all_107_1_359) = ve1 % 38.22/11.30 | % 38.22/11.30 | Applying alpha-rule on (716) yields: % 38.22/11.30 | (717) all_107_0_358 = ve1 % 38.22/11.30 | (718) vabs(all_107_3_361, all_107_2_360, all_107_1_359) = ve1 % 38.22/11.30 | % 38.22/11.30 | Instantiating formula (3) with ve1, all_107_1_359, all_107_2_360, all_107_3_361, all_19_7_47, all_19_11_51, all_19_9_49 and discharging atoms vabs(all_107_3_361, all_107_2_360, all_107_1_359) = ve1, vabs(all_19_9_49, all_19_11_51, all_19_7_47) = ve1, yields: % 38.22/11.30 | (719) all_107_1_359 = all_19_7_47 % 38.22/11.30 | % 38.22/11.30 | Instantiating formula (2) with ve1, all_107_1_359, all_107_2_360, all_107_3_361, all_19_7_47, all_19_11_51, all_19_9_49 and discharging atoms vabs(all_107_3_361, all_107_2_360, all_107_1_359) = ve1, vabs(all_19_9_49, all_19_11_51, all_19_7_47) = ve1, yields: % 38.22/11.30 | (720) all_107_2_360 = all_19_11_51 % 38.22/11.30 | % 38.22/11.30 | Instantiating formula (85) with ve1, all_107_1_359, all_107_2_360, all_107_3_361, all_19_7_47, all_19_11_51, all_19_9_49 and discharging atoms vabs(all_107_3_361, all_107_2_360, all_107_1_359) = ve1, vabs(all_19_9_49, all_19_11_51, all_19_7_47) = ve1, yields: % 38.22/11.30 | (721) all_107_3_361 = all_19_9_49 % 38.22/11.30 | % 38.22/11.30 | Instantiating formula (3) with ve1, all_17_9_25, all_17_10_26, all_17_11_27, all_107_1_359, all_107_2_360, all_107_3_361 and discharging atoms vabs(all_107_3_361, all_107_2_360, all_107_1_359) = ve1, vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1, yields: % 38.22/11.30 | (722) all_107_1_359 = all_17_9_25 % 38.22/11.30 | % 38.22/11.30 | Instantiating formula (2) with ve1, all_17_9_25, all_17_10_26, all_17_11_27, all_107_1_359, all_107_2_360, all_107_3_361 and discharging atoms vabs(all_107_3_361, all_107_2_360, all_107_1_359) = ve1, vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1, yields: % 38.22/11.30 | (723) all_107_2_360 = all_17_10_26 % 38.22/11.30 | % 38.22/11.30 | Instantiating formula (85) with ve1, all_17_9_25, all_17_10_26, all_17_11_27, all_107_1_359, all_107_2_360, all_107_3_361 and discharging atoms vabs(all_107_3_361, all_107_2_360, all_107_1_359) = ve1, vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1, yields: % 38.22/11.30 | (724) all_107_3_361 = all_17_11_27 % 38.22/11.30 | % 38.22/11.30 | Combining equations (722,719) yields a new equation: % 38.22/11.30 | (725) all_19_7_47 = all_17_9_25 % 38.22/11.30 | % 38.22/11.30 | Combining equations (720,723) yields a new equation: % 38.22/11.30 | (726) all_19_11_51 = all_17_10_26 % 38.22/11.30 | % 38.22/11.30 | Simplifying 726 yields: % 38.22/11.30 | (727) all_19_11_51 = all_17_10_26 % 38.22/11.30 | % 38.22/11.30 | Combining equations (721,724) yields a new equation: % 38.22/11.30 | (728) all_19_9_49 = all_17_11_27 % 38.22/11.30 | % 38.22/11.30 | Simplifying 728 yields: % 38.22/11.30 | (729) all_19_9_49 = all_17_11_27 % 38.22/11.30 | % 38.22/11.30 | From (729)(725) and (621) follows: % 38.22/11.30 | (730) vsubst(all_17_11_27, ve2, all_17_9_25) = all_0_2_2 % 38.22/11.30 | % 38.22/11.30 | From (729)(727)(725) and (166) follows: % 38.22/11.30 | (521) vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1 % 38.22/11.30 | % 38.22/11.30 +-Applying beta-rule and splitting (596), into two cases. % 38.22/11.30 |-Branch one: % 38.22/11.30 | (732) (all_71_0_306 = 0 & all_71_2_308 = all_16_3_11 & all_71_3_309 = ve1 & varrow(all_71_5_311, all_71_4_310) = all_16_3_11 & vtcheck(all_71_1_307, all_71_6_312, all_71_4_310) = 0 & vbind(all_71_7_313, all_71_5_311, all_0_3_3) = all_71_1_307 & vabs(all_71_7_313, all_71_5_311, all_71_6_312) = ve1) | (all_71_1_307 = 0 & all_71_2_308 = 0 & all_71_4_310 = ve1 & varrow(all_71_5_311, all_16_3_11) = all_71_3_309 & vtcheck(all_0_3_3, all_71_6_312, all_71_5_311) = 0 & vtcheck(all_0_3_3, all_71_7_313, all_71_3_309) = 0 & vapp(all_71_7_313, all_71_6_312) = ve1) % 38.22/11.30 | % 38.22/11.30 +-Applying beta-rule and splitting (732), into two cases. % 38.22/11.30 |-Branch one: % 38.22/11.30 | (733) all_71_0_306 = 0 & all_71_2_308 = all_16_3_11 & all_71_3_309 = ve1 & varrow(all_71_5_311, all_71_4_310) = all_16_3_11 & vtcheck(all_71_1_307, all_71_6_312, all_71_4_310) = 0 & vbind(all_71_7_313, all_71_5_311, all_0_3_3) = all_71_1_307 & vabs(all_71_7_313, all_71_5_311, all_71_6_312) = ve1 % 38.22/11.30 | % 38.22/11.30 | Applying alpha-rule on (733) yields: % 38.22/11.30 | (734) all_71_2_308 = all_16_3_11 % 38.22/11.30 | (735) vbind(all_71_7_313, all_71_5_311, all_0_3_3) = all_71_1_307 % 38.22/11.30 | (736) all_71_3_309 = ve1 % 38.22/11.30 | (737) vtcheck(all_71_1_307, all_71_6_312, all_71_4_310) = 0 % 38.22/11.30 | (738) vabs(all_71_7_313, all_71_5_311, all_71_6_312) = ve1 % 38.22/11.30 | (739) all_71_0_306 = 0 % 38.22/11.30 | (740) varrow(all_71_5_311, all_71_4_310) = all_16_3_11 % 38.22/11.30 | % 38.22/11.30 | Instantiating formula (64) with all_16_3_11, all_71_4_310, all_71_5_311, all_0_1_1, all_16_5_13 and discharging atoms varrow(all_71_5_311, all_71_4_310) = all_16_3_11, varrow(all_16_5_13, all_0_1_1) = all_16_3_11, yields: % 38.22/11.30 | (741) all_71_4_310 = all_0_1_1 % 38.22/11.30 | % 38.22/11.30 | Instantiating formula (37) with all_16_3_11, all_71_4_310, all_71_5_311, all_0_1_1, all_16_5_13 and discharging atoms varrow(all_71_5_311, all_71_4_310) = all_16_3_11, varrow(all_16_5_13, all_0_1_1) = all_16_3_11, yields: % 38.22/11.30 | (742) all_71_5_311 = all_16_5_13 % 38.22/11.30 | % 38.22/11.30 | Instantiating formula (3) with ve1, all_71_6_312, all_71_5_311, all_71_7_313, all_17_9_25, all_17_10_26, all_17_11_27 and discharging atoms vabs(all_71_7_313, all_71_5_311, all_71_6_312) = ve1, vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1, yields: % 38.22/11.30 | (743) all_71_6_312 = all_17_9_25 % 38.22/11.30 | % 38.22/11.30 | Instantiating formula (2) with ve1, all_71_6_312, all_71_5_311, all_71_7_313, all_17_9_25, all_17_10_26, all_17_11_27 and discharging atoms vabs(all_71_7_313, all_71_5_311, all_71_6_312) = ve1, vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1, yields: % 38.22/11.30 | (744) all_71_5_311 = all_17_10_26 % 38.22/11.30 | % 38.22/11.30 | Instantiating formula (85) with ve1, all_71_6_312, all_71_5_311, all_71_7_313, all_17_9_25, all_17_10_26, all_17_11_27 and discharging atoms vabs(all_71_7_313, all_71_5_311, all_71_6_312) = ve1, vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1, yields: % 38.22/11.30 | (745) all_71_7_313 = all_17_11_27 % 38.22/11.30 | % 38.22/11.30 | Combining equations (742,744) yields a new equation: % 38.22/11.30 | (746) all_17_10_26 = all_16_5_13 % 38.22/11.30 | % 38.22/11.30 | Combining equations (746,744) yields a new equation: % 38.22/11.30 | (742) all_71_5_311 = all_16_5_13 % 38.22/11.30 | % 38.22/11.30 | From (743)(741) and (737) follows: % 38.22/11.30 | (748) vtcheck(all_71_1_307, all_17_9_25, all_0_1_1) = 0 % 38.22/11.30 | % 38.22/11.30 | From (745)(742) and (735) follows: % 38.22/11.30 | (749) vbind(all_17_11_27, all_16_5_13, all_0_3_3) = all_71_1_307 % 38.22/11.30 | % 38.22/11.30 | Instantiating formula (48) with all_0_0_0, all_0_2_2, all_71_1_307, all_0_1_1, all_17_9_25, ve2, all_17_11_27, all_0_3_3, all_16_5_13 and discharging atoms vsubst(all_17_11_27, ve2, all_17_9_25) = all_0_2_2, vtcheck(all_71_1_307, all_17_9_25, all_0_1_1) = 0, vtcheck(all_0_3_3, all_0_2_2, all_0_1_1) = all_0_0_0, vbind(all_17_11_27, all_16_5_13, all_0_3_3) = all_71_1_307, yields: % 38.22/11.30 | (436) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.22/11.30 | % 38.22/11.30 +-Applying beta-rule and splitting (436), into two cases. % 38.22/11.30 |-Branch one: % 38.22/11.30 | (298) all_0_0_0 = 0 % 38.22/11.30 | % 38.22/11.30 | Equations (298) can reduce 36 to: % 38.22/11.30 | (228) $false % 38.22/11.30 | % 38.22/11.30 |-The branch is then unsatisfiable % 38.22/11.30 |-Branch two: % 38.22/11.30 | (36) ~ (all_0_0_0 = 0) % 38.22/11.30 | (440) ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.22/11.31 | % 38.22/11.31 | Instantiating (440) with all_175_0_372 yields: % 38.22/11.31 | (755) ~ (all_175_0_372 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = all_175_0_372 % 38.22/11.31 | % 38.22/11.31 | Applying alpha-rule on (755) yields: % 38.22/11.31 | (756) ~ (all_175_0_372 = 0) % 38.22/11.31 | (757) vtcheck(all_0_3_3, ve2, all_16_5_13) = all_175_0_372 % 38.22/11.31 | % 38.22/11.31 | Instantiating formula (91) with all_0_3_3, ve2, all_16_5_13, all_175_0_372, 0 and discharging atoms vtcheck(all_0_3_3, ve2, all_16_5_13) = all_175_0_372, vtcheck(all_0_3_3, ve2, all_16_5_13) = 0, yields: % 38.22/11.31 | (758) all_175_0_372 = 0 % 38.22/11.31 | % 38.22/11.31 | Equations (758) can reduce 756 to: % 38.22/11.31 | (228) $false % 38.22/11.31 | % 38.22/11.31 |-The branch is then unsatisfiable % 38.22/11.31 |-Branch two: % 38.22/11.31 | (760) all_71_1_307 = 0 & all_71_2_308 = 0 & all_71_4_310 = ve1 & varrow(all_71_5_311, all_16_3_11) = all_71_3_309 & vtcheck(all_0_3_3, all_71_6_312, all_71_5_311) = 0 & vtcheck(all_0_3_3, all_71_7_313, all_71_3_309) = 0 & vapp(all_71_7_313, all_71_6_312) = ve1 % 38.22/11.31 | % 38.22/11.31 | Applying alpha-rule on (760) yields: % 38.22/11.31 | (761) all_71_1_307 = 0 % 38.22/11.31 | (762) vtcheck(all_0_3_3, all_71_6_312, all_71_5_311) = 0 % 38.22/11.31 | (763) varrow(all_71_5_311, all_16_3_11) = all_71_3_309 % 38.22/11.31 | (764) vapp(all_71_7_313, all_71_6_312) = ve1 % 38.22/11.31 | (765) vtcheck(all_0_3_3, all_71_7_313, all_71_3_309) = 0 % 38.22/11.31 | (766) all_71_2_308 = 0 % 38.22/11.31 | (767) all_71_4_310 = ve1 % 38.22/11.31 | % 38.22/11.31 | Instantiating formula (55) with ve1, all_71_6_312, all_71_7_313, all_17_9_25, all_17_10_26, all_17_11_27 and discharging atoms vapp(all_71_7_313, all_71_6_312) = ve1, vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1, yields: % 38.22/11.31 | (130) $false % 38.22/11.31 | % 38.22/11.31 |-The branch is then unsatisfiable % 38.22/11.31 |-Branch two: % 38.22/11.31 | (769) all_71_4_310 = all_71_7_313 & all_71_5_311 = ve1 & vlookup(all_71_6_312, all_0_3_3) = all_71_7_313 & vsomeType(all_16_3_11) = all_71_7_313 & vvar(all_71_6_312) = ve1 % 38.22/11.31 | % 38.22/11.31 | Applying alpha-rule on (769) yields: % 38.22/11.31 | (770) vsomeType(all_16_3_11) = all_71_7_313 % 38.22/11.31 | (771) vlookup(all_71_6_312, all_0_3_3) = all_71_7_313 % 38.22/11.31 | (772) vvar(all_71_6_312) = ve1 % 38.22/11.31 | (773) all_71_4_310 = all_71_7_313 % 38.22/11.31 | (774) all_71_5_311 = ve1 % 38.22/11.31 | % 38.22/11.31 | Instantiating formula (73) with ve1, all_17_9_25, all_17_10_26, all_17_11_27, all_71_6_312 and discharging atoms vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1, vvar(all_71_6_312) = ve1, yields: % 38.22/11.31 | (130) $false % 38.22/11.31 | % 38.22/11.31 |-The branch is then unsatisfiable % 38.22/11.31 |-Branch two: % 38.22/11.31 | (776) ~ (all_107_3_361 = vnoExp) & vreduce(ve1) = all_107_3_361 % 38.22/11.31 | % 38.22/11.31 | Applying alpha-rule on (776) yields: % 38.22/11.31 | (777) ~ (all_107_3_361 = vnoExp) % 38.22/11.31 | (778) vreduce(ve1) = all_107_3_361 % 38.22/11.31 | % 38.22/11.31 | Instantiating formula (96) with all_107_3_361, ve1, all_17_9_25, all_17_10_26, all_17_11_27 and discharging atoms vreduce(ve1) = all_107_3_361, vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1, yields: % 38.22/11.31 | (779) all_107_3_361 = vnoExp % 38.22/11.31 | % 38.22/11.31 | Equations (779) can reduce 777 to: % 38.22/11.31 | (228) $false % 38.22/11.31 | % 38.22/11.31 |-The branch is then unsatisfiable % 38.22/11.31 |-Branch two: % 38.22/11.31 | (523) all_17_10_26 = ve1 & all_0_7_7 = vnoExp & vvar(all_17_11_27) = ve1 % 38.22/11.31 | % 38.22/11.31 | Applying alpha-rule on (523) yields: % 38.22/11.31 | (524) all_17_10_26 = ve1 % 38.22/11.31 | (170) all_0_7_7 = vnoExp % 38.22/11.31 | (526) vvar(all_17_11_27) = ve1 % 38.22/11.31 | % 38.22/11.31 | Instantiating formula (73) with ve1, all_19_7_47, all_19_11_51, all_19_9_49, all_17_11_27 and discharging atoms vabs(all_19_9_49, all_19_11_51, all_19_7_47) = ve1, vvar(all_17_11_27) = ve1, yields: % 38.22/11.31 | (130) $false % 38.22/11.31 | % 38.22/11.31 |-The branch is then unsatisfiable % 38.22/11.31 |-Branch two: % 38.22/11.31 | (249) all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46 % 38.22/11.31 | % 38.22/11.31 | Applying alpha-rule on (249) yields: % 38.22/11.31 | (250) vreduce(all_19_11_51) = all_19_7_47 % 38.22/11.31 | (251) vapp(all_19_6_46, all_19_2_42) = all_19_1_41 % 38.22/11.31 | (151) all_19_0_40 = all_0_4_4 % 38.22/11.31 | (253) vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46 % 38.22/11.31 | (152) vsomeExp(all_19_1_41) = all_0_4_4 % 38.22/11.31 | (255) vgetSomeExp(all_19_7_47) = all_19_2_42 % 38.22/11.31 | (256) visSomeExp(all_19_7_47) = 0 % 38.22/11.31 | (257) all_19_4_44 = all_19_7_47 % 38.22/11.31 | (160) all_19_5_45 = all_0_5_5 % 38.22/11.31 | (259) all_19_3_43 = 0 % 38.22/11.31 | (260) vapp(all_19_6_46, all_19_11_51) = all_0_5_5 % 38.22/11.31 | % 38.22/11.31 | Instantiating formula (59) with ve2, all_19_7_47, all_0_7_7 and discharging atoms vreduce(ve2) = all_0_7_7, yields: % 38.22/11.31 | (798) all_19_7_47 = all_0_7_7 | ~ (vreduce(ve2) = all_19_7_47) % 38.22/11.31 | % 38.22/11.31 | Using (256) and (17) yields: % 38.22/11.31 | (799) ~ (all_19_7_47 = vnoExp) % 38.22/11.31 | % 38.22/11.31 | Instantiating formula (18) with all_0_5_5, all_19_11_51, all_19_6_46, ve2, ve1 and discharging atoms vapp(all_19_6_46, all_19_11_51) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.22/11.31 | (263) all_19_11_51 = ve2 % 38.22/11.31 | % 38.22/11.31 | Instantiating formula (20) with all_0_5_5, all_19_11_51, all_19_6_46, ve2, ve1 and discharging atoms vapp(all_19_6_46, all_19_11_51) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.22/11.31 | (163) all_19_6_46 = ve1 % 38.22/11.31 | % 38.22/11.31 | Instantiating formula (96) with all_0_7_7, ve1, all_19_8_48, all_19_9_49, all_19_10_50 and discharging atoms vreduce(ve1) = all_0_7_7, yields: % 38.22/11.31 | (265) all_0_7_7 = vnoExp | ~ (vabs(all_19_10_50, all_19_9_49, all_19_8_48) = ve1) % 38.22/11.31 | % 38.22/11.31 | From (263) and (250) follows: % 38.22/11.31 | (266) vreduce(ve2) = all_19_7_47 % 38.22/11.31 | % 38.22/11.31 | From (163) and (253) follows: % 38.22/11.31 | (268) vabs(all_19_10_50, all_19_9_49, all_19_8_48) = ve1 % 38.22/11.31 | % 38.22/11.31 +-Applying beta-rule and splitting (798), into two cases. % 38.22/11.31 |-Branch one: % 38.22/11.31 | (269) ~ (vreduce(ve2) = all_19_7_47) % 38.22/11.31 | % 38.22/11.31 | Using (266) and (269) yields: % 38.22/11.31 | (130) $false % 38.22/11.31 | % 38.22/11.31 |-The branch is then unsatisfiable % 38.22/11.31 |-Branch two: % 38.22/11.31 | (266) vreduce(ve2) = all_19_7_47 % 38.22/11.31 | (808) all_19_7_47 = all_0_7_7 % 38.22/11.31 | % 38.22/11.31 | Equations (808) can reduce 799 to: % 38.22/11.31 | (413) ~ (all_0_7_7 = vnoExp) % 38.22/11.31 | % 38.22/11.31 +-Applying beta-rule and splitting (265), into two cases. % 38.22/11.31 |-Branch one: % 38.22/11.31 | (274) ~ (vabs(all_19_10_50, all_19_9_49, all_19_8_48) = ve1) % 38.22/11.31 | % 38.22/11.31 | Using (268) and (274) yields: % 38.22/11.31 | (130) $false % 38.22/11.31 | % 38.22/11.31 |-The branch is then unsatisfiable % 38.22/11.31 |-Branch two: % 38.22/11.31 | (268) vabs(all_19_10_50, all_19_9_49, all_19_8_48) = ve1 % 38.22/11.31 | (170) all_0_7_7 = vnoExp % 38.22/11.31 | % 38.22/11.31 | Equations (170) can reduce 413 to: % 38.22/11.31 | (228) $false % 38.22/11.31 | % 38.22/11.31 |-The branch is then unsatisfiable % 38.22/11.31 |-Branch two: % 38.22/11.31 | (390) all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51) % 38.22/11.31 | % 38.22/11.31 | Applying alpha-rule on (390) yields: % 38.22/11.31 | (391) all_19_8_48 = all_0_5_5 % 38.22/11.31 | (392) vsomeExp(all_19_4_44) = all_0_4_4 % 38.22/11.31 | (393) vreduce(all_19_11_51) = all_19_10_50 % 38.22/11.31 | (394) all_19_7_47 = all_19_10_50 % 38.22/11.31 | (395) vapp(all_19_11_51, all_19_9_49) = all_0_5_5 % 38.22/11.31 | (396) all_19_6_46 = 0 % 38.22/11.31 | (397) visSomeExp(all_19_10_50) = 0 % 38.22/11.31 | (398) vapp(all_19_5_45, all_19_9_49) = all_19_4_44 % 38.22/11.31 | (399) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51) % 38.22/11.31 | (400) all_19_3_43 = all_0_4_4 % 38.22/11.31 | (401) vgetSomeExp(all_19_10_50) = all_19_5_45 % 38.22/11.31 | % 38.22/11.31 | Instantiating formula (59) with ve1, all_19_10_50, all_0_7_7 and discharging atoms vreduce(ve1) = all_0_7_7, yields: % 38.22/11.31 | (402) all_19_10_50 = all_0_7_7 | ~ (vreduce(ve1) = all_19_10_50) % 38.22/11.31 | % 38.22/11.31 | Using (397) and (17) yields: % 38.22/11.31 | (403) ~ (all_19_10_50 = vnoExp) % 38.22/11.31 | % 38.22/11.31 | Instantiating formula (50) with all_0_4_4, all_19_4_44, all_0_2_2 and discharging atoms vsomeExp(all_19_4_44) = all_0_4_4, vsomeExp(all_0_2_2) = all_0_4_4, yields: % 38.22/11.31 | (404) all_19_4_44 = all_0_2_2 % 38.22/11.31 | % 38.22/11.31 | Instantiating formula (18) with all_0_5_5, all_19_9_49, all_19_11_51, ve2, ve1 and discharging atoms vapp(all_19_11_51, all_19_9_49) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.22/11.31 | (405) all_19_9_49 = ve2 % 38.22/11.31 | % 38.22/11.31 | Instantiating formula (20) with all_0_5_5, all_19_9_49, all_19_11_51, ve2, ve1 and discharging atoms vapp(all_19_11_51, all_19_9_49) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.22/11.31 | (406) all_19_11_51 = ve1 % 38.22/11.31 | % 38.22/11.31 | From (406) and (393) follows: % 38.22/11.31 | (407) vreduce(ve1) = all_19_10_50 % 38.22/11.31 | % 38.22/11.31 | From (405)(404) and (398) follows: % 38.22/11.31 | (408) vapp(all_19_5_45, ve2) = all_0_2_2 % 38.22/11.31 | % 38.22/11.31 +-Applying beta-rule and splitting (402), into two cases. % 38.22/11.31 |-Branch one: % 38.22/11.31 | (409) ~ (vreduce(ve1) = all_19_10_50) % 38.22/11.31 | % 38.22/11.31 | Using (407) and (409) yields: % 38.22/11.31 | (130) $false % 38.22/11.31 | % 38.22/11.31 |-The branch is then unsatisfiable % 38.22/11.31 |-Branch two: % 38.22/11.31 | (407) vreduce(ve1) = all_19_10_50 % 38.22/11.31 | (412) all_19_10_50 = all_0_7_7 % 38.22/11.31 | % 38.22/11.31 | Equations (412) can reduce 403 to: % 38.22/11.31 | (413) ~ (all_0_7_7 = vnoExp) % 38.22/11.31 | % 38.22/11.31 | From (412) and (401) follows: % 38.22/11.31 | (414) vgetSomeExp(all_0_7_7) = all_19_5_45 % 38.22/11.31 | % 38.22/11.31 +-Applying beta-rule and splitting (114), into two cases. % 38.22/11.31 |-Branch one: % 38.22/11.31 | (415) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) | (all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22) | (all_17_7_23 = all_17_9_25 & all_17_8_24 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_6_22 = 0) & vreduce(all_17_10_26) = all_17_9_25 & visSomeExp(all_17_9_25) = all_17_6_22 & vapp(all_17_10_26, all_17_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26)) | (all_17_8_24 = ve1 & all_0_7_7 = vnoExp & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1) % 38.22/11.32 | % 38.22/11.32 +-Applying beta-rule and splitting (415), into two cases. % 38.22/11.32 |-Branch one: % 38.22/11.32 | (416) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) | (all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22) | (all_17_7_23 = all_17_9_25 & all_17_8_24 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_6_22 = 0) & vreduce(all_17_10_26) = all_17_9_25 & visSomeExp(all_17_9_25) = all_17_6_22 & vapp(all_17_10_26, all_17_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26)) % 38.22/11.32 | % 38.22/11.32 +-Applying beta-rule and splitting (416), into two cases. % 38.22/11.32 |-Branch one: % 38.22/11.32 | (417) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) | (all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22) % 38.22/11.32 | % 38.22/11.32 +-Applying beta-rule and splitting (417), into two cases. % 38.22/11.32 |-Branch one: % 38.22/11.32 | (418) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) % 38.22/11.32 | % 38.22/11.32 +-Applying beta-rule and splitting (418), into two cases. % 38.22/11.32 |-Branch one: % 38.22/11.32 | (419) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) % 38.22/11.32 | % 38.22/11.32 +-Applying beta-rule and splitting (419), into two cases. % 38.22/11.32 |-Branch one: % 38.22/11.32 | (420) all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22 % 38.22/11.32 | % 38.22/11.32 | Applying alpha-rule on (420) yields: % 38.22/11.32 | (421) vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 % 38.22/11.32 | (422) all_17_4_20 = all_17_10_26 % 38.22/11.32 | (423) ~ (all_17_3_19 = 0) % 38.22/11.32 | (424) vapp(all_17_6_22, all_17_8_24) = ve1 % 38.22/11.32 | (425) vreduce(all_17_8_24) = all_17_10_26 % 38.22/11.32 | (426) visSomeExp(all_17_10_26) = all_17_3_19 % 38.22/11.32 | (427) all_17_5_21 = ve1 % 38.22/11.32 | (428) vsomeExp(all_17_1_17) = all_0_7_7 % 38.22/11.32 | (429) all_17_2_18 = 0 % 38.22/11.32 | (430) vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22 % 38.22/11.32 | (431) all_17_0_16 = all_0_7_7 % 38.22/11.32 | (432) visValue(all_17_8_24) = 0 % 38.22/11.32 | % 38.22/11.32 | Instantiating formula (32) with all_17_1_17, all_19_5_45, all_0_7_7 and discharging atoms vgetSomeExp(all_0_7_7) = all_19_5_45, vsomeExp(all_17_1_17) = all_0_7_7, yields: % 38.22/11.32 | (433) all_19_5_45 = all_17_1_17 % 38.22/11.32 | % 38.22/11.32 | From (433) and (408) follows: % 38.22/11.32 | (434) vapp(all_17_1_17, ve2) = all_0_2_2 % 38.22/11.32 | % 38.22/11.32 | Instantiating formula (31) with all_16_3_11, all_17_1_17, all_0_3_3 and discharging atoms vsomeExp(all_17_1_17) = all_0_7_7, vtcheck(all_0_3_3, ve1, all_16_3_11) = 0, yields: % 38.22/11.32 | (435) vtcheck(all_0_3_3, all_17_1_17, all_16_3_11) = 0 % 38.22/11.32 | % 38.22/11.32 | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_16_3_11, all_0_1_1, ve2, all_17_1_17, all_0_3_3, all_16_5_13 and discharging atoms varrow(all_16_5_13, all_0_1_1) = all_16_3_11, vtcheck(all_0_3_3, all_17_1_17, all_16_3_11) = 0, vtcheck(all_0_3_3, all_0_2_2, all_0_1_1) = all_0_0_0, vapp(all_17_1_17, ve2) = all_0_2_2, yields: % 38.22/11.32 | (436) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.22/11.32 | % 38.22/11.32 +-Applying beta-rule and splitting (436), into two cases. % 38.22/11.32 |-Branch one: % 38.22/11.32 | (298) all_0_0_0 = 0 % 38.22/11.32 | % 38.22/11.32 | Equations (298) can reduce 36 to: % 38.22/11.32 | (228) $false % 38.22/11.32 | % 38.22/11.32 |-The branch is then unsatisfiable % 38.22/11.32 |-Branch two: % 38.22/11.32 | (36) ~ (all_0_0_0 = 0) % 38.22/11.32 | (440) ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.22/11.32 | % 38.22/11.32 | Instantiating (440) with all_160_0_461 yields: % 38.22/11.32 | (866) ~ (all_160_0_461 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = all_160_0_461 % 38.22/11.32 | % 38.22/11.32 | Applying alpha-rule on (866) yields: % 38.22/11.32 | (867) ~ (all_160_0_461 = 0) % 38.22/11.32 | (868) vtcheck(all_0_3_3, ve2, all_16_5_13) = all_160_0_461 % 38.22/11.32 | % 38.22/11.32 | Instantiating formula (91) with all_0_3_3, ve2, all_16_5_13, all_160_0_461, 0 and discharging atoms vtcheck(all_0_3_3, ve2, all_16_5_13) = all_160_0_461, vtcheck(all_0_3_3, ve2, all_16_5_13) = 0, yields: % 38.22/11.32 | (869) all_160_0_461 = 0 % 38.22/11.32 | % 38.22/11.32 | Equations (869) can reduce 867 to: % 38.22/11.32 | (228) $false % 38.22/11.32 | % 38.22/11.32 |-The branch is then unsatisfiable % 38.22/11.32 |-Branch two: % 38.22/11.32 | (446) all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22 % 38.22/11.32 | % 38.22/11.32 | Applying alpha-rule on (446) yields: % 38.22/11.32 | (447) vgetSomeExp(all_17_7_23) = all_17_2_18 % 38.22/11.32 | (448) vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22 % 38.22/11.32 | (449) vreduce(all_17_11_27) = all_17_7_23 % 38.22/11.32 | (450) all_17_3_19 = 0 % 38.22/11.32 | (451) vapp(all_17_6_22, all_17_11_27) = ve1 % 38.22/11.32 | (452) visSomeExp(all_17_7_23) = 0 % 38.22/11.32 | (453) all_17_4_20 = all_17_7_23 % 38.22/11.32 | (427) all_17_5_21 = ve1 % 38.22/11.32 | (428) vsomeExp(all_17_1_17) = all_0_7_7 % 38.22/11.32 | (431) all_17_0_16 = all_0_7_7 % 38.22/11.32 | (457) vapp(all_17_6_22, all_17_2_18) = all_17_1_17 % 38.22/11.32 | % 38.22/11.32 | Instantiating formula (32) with all_17_1_17, all_19_5_45, all_0_7_7 and discharging atoms vgetSomeExp(all_0_7_7) = all_19_5_45, vsomeExp(all_17_1_17) = all_0_7_7, yields: % 38.22/11.32 | (433) all_19_5_45 = all_17_1_17 % 38.22/11.32 | % 38.22/11.32 | From (433) and (408) follows: % 38.22/11.32 | (434) vapp(all_17_1_17, ve2) = all_0_2_2 % 38.22/11.32 | % 38.22/11.32 | Instantiating formula (31) with all_16_3_11, all_17_1_17, all_0_3_3 and discharging atoms vsomeExp(all_17_1_17) = all_0_7_7, vtcheck(all_0_3_3, ve1, all_16_3_11) = 0, yields: % 38.22/11.32 | (435) vtcheck(all_0_3_3, all_17_1_17, all_16_3_11) = 0 % 38.22/11.32 | % 38.22/11.32 | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_16_3_11, all_0_1_1, ve2, all_17_1_17, all_0_3_3, all_16_5_13 and discharging atoms varrow(all_16_5_13, all_0_1_1) = all_16_3_11, vtcheck(all_0_3_3, all_17_1_17, all_16_3_11) = 0, vtcheck(all_0_3_3, all_0_2_2, all_0_1_1) = all_0_0_0, vapp(all_17_1_17, ve2) = all_0_2_2, yields: % 38.22/11.32 | (436) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.22/11.32 | % 38.22/11.32 +-Applying beta-rule and splitting (436), into two cases. % 38.22/11.32 |-Branch one: % 38.22/11.32 | (298) all_0_0_0 = 0 % 38.22/11.32 | % 38.22/11.32 | Equations (298) can reduce 36 to: % 38.22/11.32 | (228) $false % 38.22/11.32 | % 38.22/11.32 |-The branch is then unsatisfiable % 38.22/11.32 |-Branch two: % 38.22/11.32 | (36) ~ (all_0_0_0 = 0) % 38.22/11.32 | (440) ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.22/11.32 | % 38.22/11.32 | Instantiating (440) with all_215_0_538 yields: % 38.22/11.32 | (891) ~ (all_215_0_538 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = all_215_0_538 % 38.22/11.32 | % 38.22/11.32 | Applying alpha-rule on (891) yields: % 38.22/11.32 | (892) ~ (all_215_0_538 = 0) % 38.22/11.32 | (893) vtcheck(all_0_3_3, ve2, all_16_5_13) = all_215_0_538 % 38.22/11.32 | % 38.22/11.32 | Instantiating formula (91) with all_0_3_3, ve2, all_16_5_13, all_215_0_538, 0 and discharging atoms vtcheck(all_0_3_3, ve2, all_16_5_13) = all_215_0_538, vtcheck(all_0_3_3, ve2, all_16_5_13) = 0, yields: % 38.22/11.32 | (894) all_215_0_538 = 0 % 38.22/11.32 | % 38.22/11.32 | Equations (894) can reduce 892 to: % 38.22/11.32 | (228) $false % 38.22/11.32 | % 38.22/11.32 |-The branch is then unsatisfiable % 38.22/11.32 |-Branch two: % 38.22/11.32 | (471) all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27) % 38.22/11.32 | % 38.22/11.32 | Applying alpha-rule on (471) yields: % 38.22/11.32 | (472) vapp(all_17_11_27, all_17_9_25) = ve1 % 38.22/11.32 | (473) vreduce(all_17_11_27) = all_17_10_26 % 38.22/11.32 | (474) vapp(all_17_5_21, all_17_9_25) = all_17_4_20 % 38.22/11.32 | (475) all_17_7_23 = all_17_10_26 % 38.22/11.32 | (476) vgetSomeExp(all_17_10_26) = all_17_5_21 % 38.22/11.32 | (477) all_17_6_22 = 0 % 38.22/11.32 | (478) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27) % 38.22/11.32 | (479) all_17_8_24 = ve1 % 38.22/11.32 | (480) all_17_3_19 = all_0_7_7 % 38.22/11.32 | (481) visSomeExp(all_17_10_26) = 0 % 38.22/11.32 | (482) vsomeExp(all_17_4_20) = all_0_7_7 % 38.22/11.32 | % 38.22/11.32 | Instantiating formula (32) with all_17_4_20, all_19_5_45, all_0_7_7 and discharging atoms vgetSomeExp(all_0_7_7) = all_19_5_45, vsomeExp(all_17_4_20) = all_0_7_7, yields: % 38.22/11.32 | (483) all_19_5_45 = all_17_4_20 % 38.22/11.32 | % 38.22/11.32 | From (483) and (408) follows: % 38.22/11.32 | (484) vapp(all_17_4_20, ve2) = all_0_2_2 % 38.22/11.32 | % 38.22/11.32 | Instantiating formula (31) with all_16_3_11, all_17_4_20, all_0_3_3 and discharging atoms vsomeExp(all_17_4_20) = all_0_7_7, vtcheck(all_0_3_3, ve1, all_16_3_11) = 0, yields: % 38.22/11.32 | (485) vtcheck(all_0_3_3, all_17_4_20, all_16_3_11) = 0 % 38.22/11.32 | % 38.22/11.32 | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_16_3_11, all_0_1_1, ve2, all_17_4_20, all_0_3_3, all_16_5_13 and discharging atoms varrow(all_16_5_13, all_0_1_1) = all_16_3_11, vtcheck(all_0_3_3, all_17_4_20, all_16_3_11) = 0, vtcheck(all_0_3_3, all_0_2_2, all_0_1_1) = all_0_0_0, vapp(all_17_4_20, ve2) = all_0_2_2, yields: % 38.22/11.32 | (436) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.22/11.32 | % 38.22/11.32 +-Applying beta-rule and splitting (436), into two cases. % 38.22/11.32 |-Branch one: % 38.22/11.32 | (298) all_0_0_0 = 0 % 38.22/11.32 | % 38.22/11.33 | Equations (298) can reduce 36 to: % 38.22/11.33 | (228) $false % 38.22/11.33 | % 38.22/11.33 |-The branch is then unsatisfiable % 38.22/11.33 |-Branch two: % 38.22/11.33 | (36) ~ (all_0_0_0 = 0) % 38.22/11.33 | (440) ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.22/11.33 | % 38.22/11.33 | Instantiating (440) with all_136_0_603 yields: % 38.22/11.33 | (916) ~ (all_136_0_603 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = all_136_0_603 % 38.22/11.33 | % 38.22/11.33 | Applying alpha-rule on (916) yields: % 38.22/11.33 | (917) ~ (all_136_0_603 = 0) % 38.22/11.33 | (918) vtcheck(all_0_3_3, ve2, all_16_5_13) = all_136_0_603 % 38.22/11.33 | % 38.22/11.33 | Instantiating formula (91) with all_0_3_3, ve2, all_16_5_13, all_136_0_603, 0 and discharging atoms vtcheck(all_0_3_3, ve2, all_16_5_13) = all_136_0_603, vtcheck(all_0_3_3, ve2, all_16_5_13) = 0, yields: % 38.22/11.33 | (919) all_136_0_603 = 0 % 38.22/11.33 | % 38.22/11.33 | Equations (919) can reduce 917 to: % 38.22/11.33 | (228) $false % 38.22/11.33 | % 38.22/11.33 |-The branch is then unsatisfiable % 38.22/11.33 |-Branch two: % 38.22/11.33 | (496) all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22 % 38.22/11.33 | % 38.22/11.33 | Applying alpha-rule on (496) yields: % 38.22/11.33 | (497) visValue(all_17_7_23) = all_17_2_18 % 38.22/11.33 | (498) visSomeExp(all_17_8_24) = all_17_3_19 % 38.22/11.33 | (423) ~ (all_17_3_19 = 0) % 38.22/11.33 | (500) all_17_4_20 = all_17_8_24 % 38.22/11.33 | (170) all_0_7_7 = vnoExp % 38.22/11.33 | (502) vapp(all_17_6_22, all_17_7_23) = ve1 % 38.22/11.33 | (427) all_17_5_21 = ve1 % 38.22/11.33 | (504) vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22 % 38.22/11.33 | (505) ~ (all_17_2_18 = 0) % 38.22/11.33 | (506) vreduce(all_17_7_23) = all_17_8_24 % 38.22/11.33 | % 38.22/11.33 | Equations (170) can reduce 413 to: % 38.22/11.33 | (228) $false % 38.22/11.33 | % 38.22/11.33 |-The branch is then unsatisfiable % 38.22/11.33 |-Branch two: % 38.22/11.33 | (508) all_17_7_23 = all_17_9_25 & all_17_8_24 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_6_22 = 0) & vreduce(all_17_10_26) = all_17_9_25 & visSomeExp(all_17_9_25) = all_17_6_22 & vapp(all_17_10_26, all_17_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26) % 38.22/11.33 | % 38.22/11.33 | Applying alpha-rule on (508) yields: % 38.22/11.33 | (509) all_17_7_23 = all_17_9_25 % 38.22/11.33 | (510) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26) % 38.22/11.33 | (511) visSomeExp(all_17_9_25) = all_17_6_22 % 38.22/11.33 | (512) ~ (all_17_6_22 = 0) % 38.22/11.33 | (170) all_0_7_7 = vnoExp % 38.22/11.33 | (514) vapp(all_17_10_26, all_17_11_27) = ve1 % 38.22/11.33 | (479) all_17_8_24 = ve1 % 38.22/11.33 | (516) vreduce(all_17_10_26) = all_17_9_25 % 38.22/11.33 | % 38.22/11.33 | Equations (170) can reduce 413 to: % 38.22/11.33 | (228) $false % 38.22/11.33 | % 38.22/11.33 |-The branch is then unsatisfiable % 38.22/11.33 |-Branch two: % 38.22/11.33 | (518) all_17_8_24 = ve1 & all_0_7_7 = vnoExp & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1 % 38.22/11.33 | % 38.22/11.33 | Applying alpha-rule on (518) yields: % 38.22/11.33 | (479) all_17_8_24 = ve1 % 38.22/11.33 | (170) all_0_7_7 = vnoExp % 38.22/11.33 | (521) vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1 % 38.22/11.33 | % 38.22/11.33 | Equations (170) can reduce 413 to: % 38.22/11.33 | (228) $false % 38.22/11.33 | % 38.22/11.33 |-The branch is then unsatisfiable % 38.22/11.33 |-Branch two: % 38.22/11.33 | (523) all_17_10_26 = ve1 & all_0_7_7 = vnoExp & vvar(all_17_11_27) = ve1 % 38.22/11.33 | % 38.22/11.33 | Applying alpha-rule on (523) yields: % 38.22/11.33 | (524) all_17_10_26 = ve1 % 38.22/11.33 | (170) all_0_7_7 = vnoExp % 38.22/11.33 | (526) vvar(all_17_11_27) = ve1 % 38.22/11.33 | % 38.22/11.33 | Equations (170) can reduce 413 to: % 38.22/11.33 | (228) $false % 38.22/11.33 | % 38.22/11.33 |-The branch is then unsatisfiable % 38.22/11.33 |-Branch two: % 38.22/11.33 | (528) all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46 % 38.22/11.33 | % 38.22/11.33 | Applying alpha-rule on (528) yields: % 38.22/11.33 | (529) visValue(all_19_7_47) = all_19_2_42 % 38.22/11.33 | (530) vapp(all_19_6_46, all_19_7_47) = all_0_5_5 % 38.22/11.33 | (531) all_19_4_44 = all_19_8_48 % 38.22/11.33 | (532) vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46 % 38.22/11.33 | (533) visSomeExp(all_19_8_48) = all_19_3_43 % 38.22/11.33 | (534) all_0_4_4 = vnoExp % 38.22/11.33 | (535) ~ (all_19_2_42 = 0) % 38.22/11.33 | (160) all_19_5_45 = all_0_5_5 % 38.22/11.33 | (537) vreduce(all_19_7_47) = all_19_8_48 % 38.22/11.33 | (161) ~ (all_19_3_43 = 0) % 38.22/11.33 | % 38.22/11.33 | Equations (534) can reduce 108 to: % 38.22/11.33 | (228) $false % 38.22/11.33 | % 38.22/11.33 |-The branch is then unsatisfiable % 38.22/11.33 |-Branch two: % 38.22/11.33 | (540) all_19_7_47 = all_19_9_49 & all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_6_46 = 0) & vreduce(all_19_10_50) = all_19_9_49 & visSomeExp(all_19_9_49) = all_19_6_46 & vapp(all_19_10_50, all_19_11_51) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50) % 38.22/11.33 | % 38.22/11.33 | Applying alpha-rule on (540) yields: % 38.22/11.33 | (391) all_19_8_48 = all_0_5_5 % 38.22/11.33 | (542) vreduce(all_19_10_50) = all_19_9_49 % 38.22/11.33 | (543) all_19_7_47 = all_19_9_49 % 38.22/11.33 | (544) ~ (all_19_6_46 = 0) % 38.22/11.33 | (534) all_0_4_4 = vnoExp % 38.22/11.33 | (546) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50) % 38.22/11.33 | (547) vapp(all_19_10_50, all_19_11_51) = all_0_5_5 % 38.22/11.33 | (548) visSomeExp(all_19_9_49) = all_19_6_46 % 38.22/11.33 | % 38.22/11.33 | Equations (534) can reduce 108 to: % 38.22/11.33 | (228) $false % 38.22/11.33 | % 38.22/11.33 |-The branch is then unsatisfiable % 38.22/11.33 |-Branch two: % 38.22/11.33 | (550) all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_0_5_5 % 38.22/11.33 | % 38.22/11.33 | Applying alpha-rule on (550) yields: % 38.22/11.33 | (391) all_19_8_48 = all_0_5_5 % 38.22/11.33 | (534) all_0_4_4 = vnoExp % 38.22/11.33 | (553) vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_0_5_5 % 38.22/11.33 | % 38.22/11.33 | Equations (534) can reduce 108 to: % 38.22/11.33 | (228) $false % 38.22/11.33 | % 38.22/11.33 |-The branch is then unsatisfiable % 38.22/11.33 |-Branch two: % 38.22/11.33 | (555) all_19_10_50 = all_0_5_5 & all_0_4_4 = vnoExp & vvar(all_19_11_51) = all_0_5_5 % 38.22/11.33 | % 38.22/11.33 | Applying alpha-rule on (555) yields: % 38.22/11.33 | (556) all_19_10_50 = all_0_5_5 % 38.22/11.33 | (534) all_0_4_4 = vnoExp % 38.22/11.33 | (558) vvar(all_19_11_51) = all_0_5_5 % 38.22/11.33 | % 38.22/11.33 | Equations (534) can reduce 108 to: % 38.22/11.33 | (228) $false % 38.22/11.33 | % 38.22/11.33 |-The branch is then unsatisfiable % 38.22/11.33 |-Branch two: % 38.22/11.33 | (560) all_16_4_12 = all_16_7_15 & all_16_5_13 = all_0_5_5 & vlookup(all_16_6_14, all_0_3_3) = all_16_7_15 & vsomeType(all_0_1_1) = all_16_7_15 & vvar(all_16_6_14) = all_0_5_5 % 38.22/11.33 | % 38.22/11.33 | Applying alpha-rule on (560) yields: % 38.22/11.33 | (561) vlookup(all_16_6_14, all_0_3_3) = all_16_7_15 % 38.22/11.33 | (562) vsomeType(all_0_1_1) = all_16_7_15 % 38.22/11.33 | (563) all_16_4_12 = all_16_7_15 % 38.22/11.33 | (564) all_16_5_13 = all_0_5_5 % 38.22/11.33 | (565) vvar(all_16_6_14) = all_0_5_5 % 38.22/11.33 | % 38.22/11.33 | Instantiating formula (6) with all_0_5_5, ve2, ve1, all_16_6_14 and discharging atoms vapp(ve1, ve2) = all_0_5_5, vvar(all_16_6_14) = all_0_5_5, yields: % 38.22/11.33 | (130) $false % 38.22/11.33 | % 38.22/11.33 |-The branch is then unsatisfiable % 38.22/11.33 |-Branch two: % 38.22/11.33 | (992) vreduce(ve2) = all_0_4_4 % 38.22/11.33 | (993) all_0_4_4 = all_0_6_6 % 38.22/11.33 | % 38.22/11.33 | Equations (993) can reduce 108 to: % 38.22/11.33 | (171) ~ (all_0_6_6 = vnoExp) % 38.22/11.33 | % 38.22/11.33 | From (993) and (74) follows: % 38.22/11.33 | (995) vreduce(all_0_5_5) = all_0_6_6 % 38.22/11.33 | % 38.22/11.33 | From (993) and (992) follows: % 38.22/11.33 | (25) vreduce(ve2) = all_0_6_6 % 38.22/11.33 | % 38.22/11.33 | From (993) and (49) follows: % 38.22/11.33 | (997) vsomeExp(all_0_2_2) = all_0_6_6 % 38.22/11.33 | % 38.22/11.33 +-Applying beta-rule and splitting (113), into two cases. % 38.22/11.33 |-Branch one: % 38.22/11.33 | (121) (all_16_0_8 = 0 & all_16_2_10 = all_0_1_1 & all_16_3_11 = all_0_5_5 & varrow(all_16_5_13, all_16_4_12) = all_0_1_1 & vtcheck(all_16_1_9, all_16_6_14, all_16_4_12) = 0 & vbind(all_16_7_15, all_16_5_13, all_0_3_3) = all_16_1_9 & vabs(all_16_7_15, all_16_5_13, all_16_6_14) = all_0_5_5) | (all_16_1_9 = 0 & all_16_2_10 = 0 & all_16_4_12 = all_0_5_5 & varrow(all_16_5_13, all_0_1_1) = all_16_3_11 & vtcheck(all_0_3_3, all_16_6_14, all_16_5_13) = 0 & vtcheck(all_0_3_3, all_16_7_15, all_16_3_11) = 0 & vapp(all_16_7_15, all_16_6_14) = all_0_5_5) % 38.22/11.33 | % 38.22/11.33 +-Applying beta-rule and splitting (121), into two cases. % 38.22/11.33 |-Branch one: % 38.22/11.33 | (122) all_16_0_8 = 0 & all_16_2_10 = all_0_1_1 & all_16_3_11 = all_0_5_5 & varrow(all_16_5_13, all_16_4_12) = all_0_1_1 & vtcheck(all_16_1_9, all_16_6_14, all_16_4_12) = 0 & vbind(all_16_7_15, all_16_5_13, all_0_3_3) = all_16_1_9 & vabs(all_16_7_15, all_16_5_13, all_16_6_14) = all_0_5_5 % 38.22/11.33 | % 38.22/11.33 | Applying alpha-rule on (122) yields: % 38.22/11.33 | (123) vbind(all_16_7_15, all_16_5_13, all_0_3_3) = all_16_1_9 % 38.22/11.33 | (124) vabs(all_16_7_15, all_16_5_13, all_16_6_14) = all_0_5_5 % 38.22/11.33 | (125) vtcheck(all_16_1_9, all_16_6_14, all_16_4_12) = 0 % 38.22/11.33 | (126) all_16_0_8 = 0 % 38.22/11.33 | (127) all_16_2_10 = all_0_1_1 % 38.22/11.33 | (128) varrow(all_16_5_13, all_16_4_12) = all_0_1_1 % 38.22/11.33 | (129) all_16_3_11 = all_0_5_5 % 38.22/11.33 | % 38.22/11.33 | Instantiating formula (55) with all_0_5_5, ve2, ve1, all_16_6_14, all_16_5_13, all_16_7_15 and discharging atoms vapp(ve1, ve2) = all_0_5_5, vabs(all_16_7_15, all_16_5_13, all_16_6_14) = all_0_5_5, yields: % 38.22/11.33 | (130) $false % 38.22/11.33 | % 38.22/11.33 |-The branch is then unsatisfiable % 38.22/11.33 |-Branch two: % 38.22/11.33 | (131) all_16_1_9 = 0 & all_16_2_10 = 0 & all_16_4_12 = all_0_5_5 & varrow(all_16_5_13, all_0_1_1) = all_16_3_11 & vtcheck(all_0_3_3, all_16_6_14, all_16_5_13) = 0 & vtcheck(all_0_3_3, all_16_7_15, all_16_3_11) = 0 & vapp(all_16_7_15, all_16_6_14) = all_0_5_5 % 38.22/11.33 | % 38.22/11.33 | Applying alpha-rule on (131) yields: % 38.22/11.33 | (132) vtcheck(all_0_3_3, all_16_7_15, all_16_3_11) = 0 % 38.22/11.33 | (133) varrow(all_16_5_13, all_0_1_1) = all_16_3_11 % 38.22/11.33 | (134) vtcheck(all_0_3_3, all_16_6_14, all_16_5_13) = 0 % 38.22/11.33 | (135) all_16_4_12 = all_0_5_5 % 38.22/11.33 | (136) all_16_1_9 = 0 % 38.22/11.33 | (137) all_16_2_10 = 0 % 38.22/11.33 | (138) vapp(all_16_7_15, all_16_6_14) = all_0_5_5 % 38.22/11.33 | % 38.22/11.33 | Instantiating formula (18) with all_0_5_5, all_16_6_14, all_16_7_15, ve2, ve1 and discharging atoms vapp(all_16_7_15, all_16_6_14) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.22/11.33 | (139) all_16_6_14 = ve2 % 38.22/11.33 | % 38.22/11.33 | Instantiating formula (20) with all_0_5_5, all_16_6_14, all_16_7_15, ve2, ve1 and discharging atoms vapp(all_16_7_15, all_16_6_14) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.22/11.33 | (140) all_16_7_15 = ve1 % 38.22/11.33 | % 38.22/11.33 | From (139) and (134) follows: % 38.22/11.33 | (141) vtcheck(all_0_3_3, ve2, all_16_5_13) = 0 % 38.22/11.34 | % 38.22/11.34 | From (140) and (132) follows: % 38.22/11.34 | (142) vtcheck(all_0_3_3, ve1, all_16_3_11) = 0 % 38.22/11.34 | % 38.22/11.34 | From (140)(139) and (138) follows: % 38.22/11.34 | (102) vapp(ve1, ve2) = all_0_5_5 % 38.22/11.34 | % 38.22/11.34 | Instantiating formula (72) with all_16_5_13, all_0_2_2, all_0_3_3 and discharging atoms vsomeExp(all_0_2_2) = all_0_6_6, vtcheck(all_0_3_3, ve2, all_16_5_13) = 0, yields: % 38.22/11.34 | (1021) vtcheck(all_0_3_3, all_0_2_2, all_16_5_13) = 0 % 38.22/11.34 | % 38.22/11.34 | Instantiating formula (87) with all_0_3_3, all_16_5_13, all_0_2_2 and discharging atoms vtcheck(all_0_3_3, all_0_2_2, all_16_5_13) = 0, yields: % 38.22/11.34 | (1022) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v5 = all_16_5_13 & v4 = all_0_2_2 & varrow(v2, v3) = all_16_5_13 & vtcheck(v6, v1, v3) = 0 & vbind(v0, v2, all_0_3_3) = v6 & vabs(v0, v2, v1) = all_0_2_2) | (v6 = 0 & v5 = 0 & v3 = all_0_2_2 & varrow(v2, all_16_5_13) = v4 & vtcheck(all_0_3_3, v1, v2) = 0 & vtcheck(all_0_3_3, v0, v4) = 0 & vapp(v0, v1) = all_0_2_2) | (v3 = v0 & v2 = all_0_2_2 & vlookup(v1, all_0_3_3) = v0 & vsomeType(all_16_5_13) = v0 & vvar(v1) = all_0_2_2)) % 38.22/11.34 | % 38.22/11.34 | Instantiating (1022) with all_91_0_620, all_91_1_621, all_91_2_622, all_91_3_623, all_91_4_624, all_91_5_625, all_91_6_626, all_91_7_627 yields: % 38.22/11.34 | (1023) (all_91_0_620 = 0 & all_91_2_622 = all_16_5_13 & all_91_3_623 = all_0_2_2 & varrow(all_91_5_625, all_91_4_624) = all_16_5_13 & vtcheck(all_91_1_621, all_91_6_626, all_91_4_624) = 0 & vbind(all_91_7_627, all_91_5_625, all_0_3_3) = all_91_1_621 & vabs(all_91_7_627, all_91_5_625, all_91_6_626) = all_0_2_2) | (all_91_1_621 = 0 & all_91_2_622 = 0 & all_91_4_624 = all_0_2_2 & varrow(all_91_5_625, all_16_5_13) = all_91_3_623 & vtcheck(all_0_3_3, all_91_6_626, all_91_5_625) = 0 & vtcheck(all_0_3_3, all_91_7_627, all_91_3_623) = 0 & vapp(all_91_7_627, all_91_6_626) = all_0_2_2) | (all_91_4_624 = all_91_7_627 & all_91_5_625 = all_0_2_2 & vlookup(all_91_6_626, all_0_3_3) = all_91_7_627 & vsomeType(all_16_5_13) = all_91_7_627 & vvar(all_91_6_626) = all_0_2_2) % 38.22/11.34 | % 38.22/11.34 +-Applying beta-rule and splitting (115), into two cases. % 38.22/11.34 |-Branch one: % 38.22/11.34 | (172) (all_18_0_28 = all_0_6_6 & all_18_2_30 = 0 & all_18_4_32 = all_18_10_38 & all_18_5_33 = ve2 & ~ (all_18_3_31 = 0) & vreduce(all_18_8_36) = all_18_10_38 & visSomeExp(all_18_10_38) = all_18_3_31 & vsomeExp(all_18_1_29) = all_0_6_6 & vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 & visValue(all_18_8_36) = 0 & vapp(all_18_6_34, all_18_8_36) = ve2 & vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34) | (all_18_0_28 = all_0_6_6 & all_18_3_31 = 0 & all_18_4_32 = all_18_7_35 & all_18_5_33 = ve2 & vreduce(all_18_11_39) = all_18_7_35 & vgetSomeExp(all_18_7_35) = all_18_2_30 & visSomeExp(all_18_7_35) = 0 & vsomeExp(all_18_1_29) = all_0_6_6 & vapp(all_18_6_34, all_18_2_30) = all_18_1_29 & vapp(all_18_6_34, all_18_11_39) = ve2 & vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34) | (all_18_3_31 = all_0_6_6 & all_18_6_34 = 0 & all_18_7_35 = all_18_10_38 & all_18_8_36 = ve2 & vreduce(all_18_11_39) = all_18_10_38 & vgetSomeExp(all_18_10_38) = all_18_5_33 & visSomeExp(all_18_10_38) = 0 & vsomeExp(all_18_4_32) = all_0_6_6 & vapp(all_18_5_33, all_18_9_37) = all_18_4_32 & vapp(all_18_11_39, all_18_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_11_39)) | (all_18_4_32 = all_18_8_36 & all_18_5_33 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_2_30 = 0) & ~ (all_18_3_31 = 0) & vreduce(all_18_7_35) = all_18_8_36 & visSomeExp(all_18_8_36) = all_18_3_31 & visValue(all_18_7_35) = all_18_2_30 & vapp(all_18_6_34, all_18_7_35) = ve2 & vabs(all_18_11_39, all_18_10_38, all_18_9_37) = all_18_6_34) | (all_18_7_35 = all_18_9_37 & all_18_8_36 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_6_34 = 0) & vreduce(all_18_10_38) = all_18_9_37 & visSomeExp(all_18_9_37) = all_18_6_34 & vapp(all_18_10_38, all_18_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_10_38)) | (all_18_8_36 = ve2 & all_0_6_6 = vnoExp & vabs(all_18_11_39, all_18_10_38, all_18_9_37) = ve2) % 38.22/11.34 | % 38.22/11.34 +-Applying beta-rule and splitting (172), into two cases. % 38.22/11.34 |-Branch one: % 38.22/11.34 | (173) (all_18_0_28 = all_0_6_6 & all_18_2_30 = 0 & all_18_4_32 = all_18_10_38 & all_18_5_33 = ve2 & ~ (all_18_3_31 = 0) & vreduce(all_18_8_36) = all_18_10_38 & visSomeExp(all_18_10_38) = all_18_3_31 & vsomeExp(all_18_1_29) = all_0_6_6 & vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 & visValue(all_18_8_36) = 0 & vapp(all_18_6_34, all_18_8_36) = ve2 & vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34) | (all_18_0_28 = all_0_6_6 & all_18_3_31 = 0 & all_18_4_32 = all_18_7_35 & all_18_5_33 = ve2 & vreduce(all_18_11_39) = all_18_7_35 & vgetSomeExp(all_18_7_35) = all_18_2_30 & visSomeExp(all_18_7_35) = 0 & vsomeExp(all_18_1_29) = all_0_6_6 & vapp(all_18_6_34, all_18_2_30) = all_18_1_29 & vapp(all_18_6_34, all_18_11_39) = ve2 & vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34) | (all_18_3_31 = all_0_6_6 & all_18_6_34 = 0 & all_18_7_35 = all_18_10_38 & all_18_8_36 = ve2 & vreduce(all_18_11_39) = all_18_10_38 & vgetSomeExp(all_18_10_38) = all_18_5_33 & visSomeExp(all_18_10_38) = 0 & vsomeExp(all_18_4_32) = all_0_6_6 & vapp(all_18_5_33, all_18_9_37) = all_18_4_32 & vapp(all_18_11_39, all_18_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_11_39)) | (all_18_4_32 = all_18_8_36 & all_18_5_33 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_2_30 = 0) & ~ (all_18_3_31 = 0) & vreduce(all_18_7_35) = all_18_8_36 & visSomeExp(all_18_8_36) = all_18_3_31 & visValue(all_18_7_35) = all_18_2_30 & vapp(all_18_6_34, all_18_7_35) = ve2 & vabs(all_18_11_39, all_18_10_38, all_18_9_37) = all_18_6_34) | (all_18_7_35 = all_18_9_37 & all_18_8_36 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_6_34 = 0) & vreduce(all_18_10_38) = all_18_9_37 & visSomeExp(all_18_9_37) = all_18_6_34 & vapp(all_18_10_38, all_18_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_10_38)) % 38.22/11.34 | % 38.22/11.34 +-Applying beta-rule and splitting (173), into two cases. % 38.22/11.34 |-Branch one: % 38.22/11.34 | (174) (all_18_0_28 = all_0_6_6 & all_18_2_30 = 0 & all_18_4_32 = all_18_10_38 & all_18_5_33 = ve2 & ~ (all_18_3_31 = 0) & vreduce(all_18_8_36) = all_18_10_38 & visSomeExp(all_18_10_38) = all_18_3_31 & vsomeExp(all_18_1_29) = all_0_6_6 & vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 & visValue(all_18_8_36) = 0 & vapp(all_18_6_34, all_18_8_36) = ve2 & vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34) | (all_18_0_28 = all_0_6_6 & all_18_3_31 = 0 & all_18_4_32 = all_18_7_35 & all_18_5_33 = ve2 & vreduce(all_18_11_39) = all_18_7_35 & vgetSomeExp(all_18_7_35) = all_18_2_30 & visSomeExp(all_18_7_35) = 0 & vsomeExp(all_18_1_29) = all_0_6_6 & vapp(all_18_6_34, all_18_2_30) = all_18_1_29 & vapp(all_18_6_34, all_18_11_39) = ve2 & vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34) | (all_18_3_31 = all_0_6_6 & all_18_6_34 = 0 & all_18_7_35 = all_18_10_38 & all_18_8_36 = ve2 & vreduce(all_18_11_39) = all_18_10_38 & vgetSomeExp(all_18_10_38) = all_18_5_33 & visSomeExp(all_18_10_38) = 0 & vsomeExp(all_18_4_32) = all_0_6_6 & vapp(all_18_5_33, all_18_9_37) = all_18_4_32 & vapp(all_18_11_39, all_18_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_11_39)) | (all_18_4_32 = all_18_8_36 & all_18_5_33 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_2_30 = 0) & ~ (all_18_3_31 = 0) & vreduce(all_18_7_35) = all_18_8_36 & visSomeExp(all_18_8_36) = all_18_3_31 & visValue(all_18_7_35) = all_18_2_30 & vapp(all_18_6_34, all_18_7_35) = ve2 & vabs(all_18_11_39, all_18_10_38, all_18_9_37) = all_18_6_34) % 38.22/11.34 | % 38.22/11.34 +-Applying beta-rule and splitting (174), into two cases. % 38.22/11.34 |-Branch one: % 38.22/11.34 | (175) (all_18_0_28 = all_0_6_6 & all_18_2_30 = 0 & all_18_4_32 = all_18_10_38 & all_18_5_33 = ve2 & ~ (all_18_3_31 = 0) & vreduce(all_18_8_36) = all_18_10_38 & visSomeExp(all_18_10_38) = all_18_3_31 & vsomeExp(all_18_1_29) = all_0_6_6 & vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 & visValue(all_18_8_36) = 0 & vapp(all_18_6_34, all_18_8_36) = ve2 & vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34) | (all_18_0_28 = all_0_6_6 & all_18_3_31 = 0 & all_18_4_32 = all_18_7_35 & all_18_5_33 = ve2 & vreduce(all_18_11_39) = all_18_7_35 & vgetSomeExp(all_18_7_35) = all_18_2_30 & visSomeExp(all_18_7_35) = 0 & vsomeExp(all_18_1_29) = all_0_6_6 & vapp(all_18_6_34, all_18_2_30) = all_18_1_29 & vapp(all_18_6_34, all_18_11_39) = ve2 & vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34) | (all_18_3_31 = all_0_6_6 & all_18_6_34 = 0 & all_18_7_35 = all_18_10_38 & all_18_8_36 = ve2 & vreduce(all_18_11_39) = all_18_10_38 & vgetSomeExp(all_18_10_38) = all_18_5_33 & visSomeExp(all_18_10_38) = 0 & vsomeExp(all_18_4_32) = all_0_6_6 & vapp(all_18_5_33, all_18_9_37) = all_18_4_32 & vapp(all_18_11_39, all_18_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_11_39)) % 38.22/11.34 | % 38.22/11.34 +-Applying beta-rule and splitting (175), into two cases. % 38.22/11.34 |-Branch one: % 38.22/11.34 | (176) (all_18_0_28 = all_0_6_6 & all_18_2_30 = 0 & all_18_4_32 = all_18_10_38 & all_18_5_33 = ve2 & ~ (all_18_3_31 = 0) & vreduce(all_18_8_36) = all_18_10_38 & visSomeExp(all_18_10_38) = all_18_3_31 & vsomeExp(all_18_1_29) = all_0_6_6 & vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 & visValue(all_18_8_36) = 0 & vapp(all_18_6_34, all_18_8_36) = ve2 & vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34) | (all_18_0_28 = all_0_6_6 & all_18_3_31 = 0 & all_18_4_32 = all_18_7_35 & all_18_5_33 = ve2 & vreduce(all_18_11_39) = all_18_7_35 & vgetSomeExp(all_18_7_35) = all_18_2_30 & visSomeExp(all_18_7_35) = 0 & vsomeExp(all_18_1_29) = all_0_6_6 & vapp(all_18_6_34, all_18_2_30) = all_18_1_29 & vapp(all_18_6_34, all_18_11_39) = ve2 & vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34) % 38.22/11.34 | % 38.22/11.34 +-Applying beta-rule and splitting (176), into two cases. % 38.22/11.34 |-Branch one: % 38.22/11.34 | (177) all_18_0_28 = all_0_6_6 & all_18_2_30 = 0 & all_18_4_32 = all_18_10_38 & all_18_5_33 = ve2 & ~ (all_18_3_31 = 0) & vreduce(all_18_8_36) = all_18_10_38 & visSomeExp(all_18_10_38) = all_18_3_31 & vsomeExp(all_18_1_29) = all_0_6_6 & vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 & visValue(all_18_8_36) = 0 & vapp(all_18_6_34, all_18_8_36) = ve2 & vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34 % 38.22/11.34 | % 38.22/11.34 | Applying alpha-rule on (177) yields: % 38.22/11.34 | (178) all_18_2_30 = 0 % 38.22/11.34 | (179) ~ (all_18_3_31 = 0) % 38.22/11.34 | (180) vsomeExp(all_18_1_29) = all_0_6_6 % 38.22/11.34 | (181) vabs(all_18_9_37, all_18_11_39, all_18_7_35) = all_18_6_34 % 38.22/11.34 | (182) all_18_4_32 = all_18_10_38 % 38.22/11.34 | (183) visValue(all_18_8_36) = 0 % 38.22/11.34 | (184) all_18_5_33 = ve2 % 38.22/11.34 | (185) all_18_0_28 = all_0_6_6 % 38.22/11.34 | (186) visSomeExp(all_18_10_38) = all_18_3_31 % 38.22/11.34 | (187) vsubst(all_18_9_37, all_18_8_36, all_18_7_35) = all_18_1_29 % 38.22/11.34 | (188) vreduce(all_18_8_36) = all_18_10_38 % 38.22/11.34 | (189) vapp(all_18_6_34, all_18_8_36) = ve2 % 38.22/11.34 | % 38.22/11.34 | Instantiating formula (50) with all_0_6_6, all_18_1_29, all_0_2_2 and discharging atoms vsomeExp(all_18_1_29) = all_0_6_6, vsomeExp(all_0_2_2) = all_0_6_6, yields: % 38.22/11.34 | (1042) all_18_1_29 = all_0_2_2 % 38.22/11.34 | % 38.22/11.34 | From (1042) and (180) follows: % 38.22/11.34 | (997) vsomeExp(all_0_2_2) = all_0_6_6 % 38.22/11.34 | % 38.22/11.34 +-Applying beta-rule and splitting (116), into two cases. % 38.22/11.34 |-Branch one: % 38.22/11.34 | (144) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) | (all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46) | (all_19_7_47 = all_19_9_49 & all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_6_46 = 0) & vreduce(all_19_10_50) = all_19_9_49 & visSomeExp(all_19_9_49) = all_19_6_46 & vapp(all_19_10_50, all_19_11_51) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50)) | (all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_0_5_5) % 38.22/11.34 | % 38.22/11.34 +-Applying beta-rule and splitting (144), into two cases. % 38.22/11.34 |-Branch one: % 38.22/11.34 | (145) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) | (all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46) | (all_19_7_47 = all_19_9_49 & all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_6_46 = 0) & vreduce(all_19_10_50) = all_19_9_49 & visSomeExp(all_19_9_49) = all_19_6_46 & vapp(all_19_10_50, all_19_11_51) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50)) % 38.22/11.34 | % 38.22/11.34 +-Applying beta-rule and splitting (145), into two cases. % 38.22/11.34 |-Branch one: % 38.22/11.34 | (146) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) | (all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46) % 38.22/11.35 | % 38.22/11.35 +-Applying beta-rule and splitting (146), into two cases. % 38.22/11.35 |-Branch one: % 38.22/11.35 | (147) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) % 38.22/11.35 | % 38.22/11.35 +-Applying beta-rule and splitting (147), into two cases. % 38.22/11.35 |-Branch one: % 38.22/11.35 | (148) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) % 38.22/11.35 | % 38.22/11.35 +-Applying beta-rule and splitting (148), into two cases. % 38.22/11.35 |-Branch one: % 38.22/11.35 | (149) all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46 % 38.22/11.35 | % 38.22/11.35 | Applying alpha-rule on (149) yields: % 38.22/11.35 | (150) vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46 % 38.22/11.35 | (151) all_19_0_40 = all_0_4_4 % 38.22/11.35 | (152) vsomeExp(all_19_1_41) = all_0_4_4 % 38.22/11.35 | (153) vreduce(all_19_8_48) = all_19_10_50 % 38.22/11.35 | (154) vapp(all_19_6_46, all_19_8_48) = all_0_5_5 % 38.22/11.35 | (155) visValue(all_19_8_48) = 0 % 38.22/11.35 | (156) vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 % 38.22/11.35 | (157) visSomeExp(all_19_10_50) = all_19_3_43 % 38.22/11.35 | (158) all_19_4_44 = all_19_10_50 % 38.22/11.35 | (159) all_19_2_42 = 0 % 38.22/11.35 | (160) all_19_5_45 = all_0_5_5 % 38.22/11.35 | (161) ~ (all_19_3_43 = 0) % 38.22/11.35 | % 38.22/11.35 | Instantiating formula (84) with ve2, all_18_8_36, all_18_6_34 and discharging atoms vapp(all_18_6_34, all_18_8_36) = ve2, yields: % 38.22/11.35 | (1062) ~ (visValue(ve2) = 0) % 38.22/11.35 | % 38.22/11.35 | Instantiating formula (18) with all_0_5_5, all_19_8_48, all_19_6_46, ve2, ve1 and discharging atoms vapp(all_19_6_46, all_19_8_48) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.22/11.35 | (162) all_19_8_48 = ve2 % 38.22/11.35 | % 38.22/11.35 | From (162) and (155) follows: % 38.22/11.35 | (165) visValue(ve2) = 0 % 38.22/11.35 | % 38.22/11.35 | Using (165) and (1062) yields: % 38.22/11.35 | (130) $false % 38.22/11.35 | % 38.22/11.35 |-The branch is then unsatisfiable % 38.22/11.35 |-Branch two: % 38.22/11.35 | (249) all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46 % 38.22/11.35 | % 38.22/11.35 | Applying alpha-rule on (249) yields: % 38.22/11.35 | (250) vreduce(all_19_11_51) = all_19_7_47 % 38.22/11.35 | (251) vapp(all_19_6_46, all_19_2_42) = all_19_1_41 % 38.22/11.35 | (151) all_19_0_40 = all_0_4_4 % 38.22/11.35 | (253) vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46 % 38.22/11.35 | (152) vsomeExp(all_19_1_41) = all_0_4_4 % 38.22/11.35 | (255) vgetSomeExp(all_19_7_47) = all_19_2_42 % 38.22/11.35 | (256) visSomeExp(all_19_7_47) = 0 % 38.22/11.35 | (257) all_19_4_44 = all_19_7_47 % 38.22/11.35 | (160) all_19_5_45 = all_0_5_5 % 38.22/11.35 | (259) all_19_3_43 = 0 % 38.22/11.35 | (260) vapp(all_19_6_46, all_19_11_51) = all_0_5_5 % 38.22/11.35 | % 38.22/11.35 | From (993) and (152) follows: % 38.22/11.35 | (1078) vsomeExp(all_19_1_41) = all_0_6_6 % 38.22/11.35 | % 38.22/11.35 | Instantiating formula (59) with ve2, all_19_7_47, all_0_6_6 and discharging atoms vreduce(ve2) = all_0_6_6, yields: % 38.22/11.35 | (261) all_19_7_47 = all_0_6_6 | ~ (vreduce(ve2) = all_19_7_47) % 38.22/11.35 | % 38.22/11.35 | Instantiating formula (32) with all_0_2_2, all_19_2_42, all_0_6_6 and discharging atoms vsomeExp(all_0_2_2) = all_0_6_6, yields: % 38.22/11.35 | (1080) all_19_2_42 = all_0_2_2 | ~ (vgetSomeExp(all_0_6_6) = all_19_2_42) % 38.22/11.35 | % 38.22/11.35 | Instantiating formula (50) with all_0_6_6, all_19_1_41, all_0_2_2 and discharging atoms vsomeExp(all_19_1_41) = all_0_6_6, vsomeExp(all_0_2_2) = all_0_6_6, yields: % 38.22/11.35 | (262) all_19_1_41 = all_0_2_2 % 38.22/11.35 | % 38.22/11.35 | Instantiating formula (18) with all_0_5_5, all_19_11_51, all_19_6_46, ve2, ve1 and discharging atoms vapp(all_19_6_46, all_19_11_51) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.22/11.35 | (263) all_19_11_51 = ve2 % 38.22/11.35 | % 38.22/11.35 | Instantiating formula (20) with all_0_5_5, all_19_11_51, all_19_6_46, ve2, ve1 and discharging atoms vapp(all_19_6_46, all_19_11_51) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.22/11.35 | (163) all_19_6_46 = ve1 % 38.22/11.35 | % 38.22/11.35 | From (263) and (250) follows: % 38.22/11.35 | (266) vreduce(ve2) = all_19_7_47 % 38.22/11.35 | % 38.22/11.35 | From (163)(262) and (251) follows: % 38.22/11.35 | (267) vapp(ve1, all_19_2_42) = all_0_2_2 % 38.22/11.35 | % 38.22/11.35 +-Applying beta-rule and splitting (261), into two cases. % 38.22/11.35 |-Branch one: % 38.22/11.35 | (269) ~ (vreduce(ve2) = all_19_7_47) % 38.22/11.35 | % 38.22/11.35 | Using (266) and (269) yields: % 38.22/11.35 | (130) $false % 38.22/11.35 | % 38.22/11.35 |-The branch is then unsatisfiable % 38.22/11.35 |-Branch two: % 38.22/11.35 | (266) vreduce(ve2) = all_19_7_47 % 38.22/11.35 | (272) all_19_7_47 = all_0_6_6 % 38.22/11.35 | % 38.22/11.35 | From (272) and (255) follows: % 38.22/11.35 | (273) vgetSomeExp(all_0_6_6) = all_19_2_42 % 38.22/11.35 | % 38.22/11.35 +-Applying beta-rule and splitting (1080), into two cases. % 38.22/11.35 |-Branch one: % 38.22/11.35 | (1091) ~ (vgetSomeExp(all_0_6_6) = all_19_2_42) % 38.22/11.35 | % 38.22/11.35 | Using (273) and (1091) yields: % 38.22/11.35 | (130) $false % 38.22/11.35 | % 38.22/11.35 |-The branch is then unsatisfiable % 38.22/11.35 |-Branch two: % 38.22/11.35 | (273) vgetSomeExp(all_0_6_6) = all_19_2_42 % 38.22/11.35 | (1094) all_19_2_42 = all_0_2_2 % 38.22/11.35 | % 38.22/11.35 | From (1094) and (267) follows: % 38.22/11.35 | (1095) vapp(ve1, all_0_2_2) = all_0_2_2 % 38.22/11.35 | % 38.22/11.35 | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_16_3_11, all_0_1_1, all_0_2_2, ve1, all_0_3_3, all_16_5_13 and discharging atoms varrow(all_16_5_13, all_0_1_1) = all_16_3_11, vtcheck(all_0_3_3, all_0_2_2, all_0_1_1) = all_0_0_0, vtcheck(all_0_3_3, ve1, all_16_3_11) = 0, vapp(ve1, all_0_2_2) = all_0_2_2, yields: % 38.22/11.35 | (1096) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, all_0_2_2, all_16_5_13) = v0) % 38.22/11.35 | % 38.22/11.35 +-Applying beta-rule and splitting (1096), into two cases. % 38.22/11.35 |-Branch one: % 38.22/11.35 | (298) all_0_0_0 = 0 % 38.22/11.35 | % 38.22/11.35 | Equations (298) can reduce 36 to: % 38.22/11.35 | (228) $false % 38.22/11.35 | % 38.22/11.35 |-The branch is then unsatisfiable % 38.22/11.35 |-Branch two: % 38.22/11.35 | (36) ~ (all_0_0_0 = 0) % 38.22/11.35 | (1100) ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, all_0_2_2, all_16_5_13) = v0) % 38.22/11.35 | % 38.22/11.35 | Instantiating (1100) with all_182_0_697 yields: % 38.22/11.35 | (1101) ~ (all_182_0_697 = 0) & vtcheck(all_0_3_3, all_0_2_2, all_16_5_13) = all_182_0_697 % 38.22/11.35 | % 38.22/11.35 | Applying alpha-rule on (1101) yields: % 38.22/11.35 | (1102) ~ (all_182_0_697 = 0) % 38.22/11.35 | (1103) vtcheck(all_0_3_3, all_0_2_2, all_16_5_13) = all_182_0_697 % 38.22/11.35 | % 38.22/11.35 | Instantiating formula (91) with all_0_3_3, all_0_2_2, all_16_5_13, all_182_0_697, 0 and discharging atoms vtcheck(all_0_3_3, all_0_2_2, all_16_5_13) = all_182_0_697, vtcheck(all_0_3_3, all_0_2_2, all_16_5_13) = 0, yields: % 38.22/11.35 | (1104) all_182_0_697 = 0 % 38.22/11.35 | % 38.22/11.35 | Equations (1104) can reduce 1102 to: % 38.22/11.35 | (228) $false % 38.22/11.35 | % 38.22/11.35 |-The branch is then unsatisfiable % 38.22/11.35 |-Branch two: % 38.22/11.35 | (390) all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51) % 38.22/11.35 | % 38.22/11.35 | Applying alpha-rule on (390) yields: % 38.22/11.35 | (391) all_19_8_48 = all_0_5_5 % 38.22/11.35 | (392) vsomeExp(all_19_4_44) = all_0_4_4 % 38.22/11.35 | (393) vreduce(all_19_11_51) = all_19_10_50 % 38.22/11.35 | (394) all_19_7_47 = all_19_10_50 % 38.22/11.35 | (395) vapp(all_19_11_51, all_19_9_49) = all_0_5_5 % 38.22/11.35 | (396) all_19_6_46 = 0 % 38.22/11.35 | (397) visSomeExp(all_19_10_50) = 0 % 38.22/11.35 | (398) vapp(all_19_5_45, all_19_9_49) = all_19_4_44 % 38.22/11.35 | (399) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51) % 38.22/11.35 | (400) all_19_3_43 = all_0_4_4 % 38.22/11.35 | (401) vgetSomeExp(all_19_10_50) = all_19_5_45 % 38.22/11.35 | % 38.22/11.35 | From (993) and (392) follows: % 38.22/11.35 | (1118) vsomeExp(all_19_4_44) = all_0_6_6 % 38.22/11.35 | % 38.22/11.35 | Instantiating formula (59) with ve1, all_19_10_50, all_0_7_7 and discharging atoms vreduce(ve1) = all_0_7_7, yields: % 38.22/11.35 | (402) all_19_10_50 = all_0_7_7 | ~ (vreduce(ve1) = all_19_10_50) % 38.22/11.35 | % 38.22/11.35 | Using (397) and (17) yields: % 38.22/11.35 | (403) ~ (all_19_10_50 = vnoExp) % 38.22/11.35 | % 38.22/11.35 | Instantiating formula (50) with all_0_6_6, all_19_4_44, all_0_2_2 and discharging atoms vsomeExp(all_19_4_44) = all_0_6_6, vsomeExp(all_0_2_2) = all_0_6_6, yields: % 38.22/11.35 | (404) all_19_4_44 = all_0_2_2 % 38.22/11.35 | % 38.22/11.35 | Instantiating formula (18) with all_0_5_5, all_19_9_49, all_19_11_51, ve2, ve1 and discharging atoms vapp(all_19_11_51, all_19_9_49) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.22/11.35 | (405) all_19_9_49 = ve2 % 38.22/11.35 | % 38.22/11.35 | Instantiating formula (20) with all_0_5_5, all_19_9_49, all_19_11_51, ve2, ve1 and discharging atoms vapp(all_19_11_51, all_19_9_49) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.22/11.35 | (406) all_19_11_51 = ve1 % 38.22/11.35 | % 38.22/11.35 | From (406) and (393) follows: % 38.22/11.35 | (407) vreduce(ve1) = all_19_10_50 % 38.22/11.35 | % 38.22/11.35 | From (405)(404) and (398) follows: % 38.22/11.35 | (408) vapp(all_19_5_45, ve2) = all_0_2_2 % 38.22/11.35 | % 38.22/11.35 +-Applying beta-rule and splitting (402), into two cases. % 38.22/11.35 |-Branch one: % 38.22/11.35 | (409) ~ (vreduce(ve1) = all_19_10_50) % 38.22/11.35 | % 38.22/11.35 | Using (407) and (409) yields: % 38.22/11.36 | (130) $false % 38.22/11.36 | % 38.22/11.36 |-The branch is then unsatisfiable % 38.22/11.36 |-Branch two: % 38.22/11.36 | (407) vreduce(ve1) = all_19_10_50 % 38.22/11.36 | (412) all_19_10_50 = all_0_7_7 % 38.22/11.36 | % 38.22/11.36 | Equations (412) can reduce 403 to: % 38.22/11.36 | (413) ~ (all_0_7_7 = vnoExp) % 38.22/11.36 | % 38.22/11.36 | From (412) and (401) follows: % 38.22/11.36 | (414) vgetSomeExp(all_0_7_7) = all_19_5_45 % 38.22/11.36 | % 38.22/11.36 +-Applying beta-rule and splitting (114), into two cases. % 38.22/11.36 |-Branch one: % 38.22/11.36 | (415) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) | (all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22) | (all_17_7_23 = all_17_9_25 & all_17_8_24 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_6_22 = 0) & vreduce(all_17_10_26) = all_17_9_25 & visSomeExp(all_17_9_25) = all_17_6_22 & vapp(all_17_10_26, all_17_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26)) | (all_17_8_24 = ve1 & all_0_7_7 = vnoExp & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1) % 38.22/11.36 | % 38.22/11.36 +-Applying beta-rule and splitting (415), into two cases. % 38.22/11.36 |-Branch one: % 38.22/11.36 | (416) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) | (all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22) | (all_17_7_23 = all_17_9_25 & all_17_8_24 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_6_22 = 0) & vreduce(all_17_10_26) = all_17_9_25 & visSomeExp(all_17_9_25) = all_17_6_22 & vapp(all_17_10_26, all_17_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26)) % 38.22/11.36 | % 38.22/11.36 +-Applying beta-rule and splitting (416), into two cases. % 38.22/11.36 |-Branch one: % 38.22/11.36 | (417) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) | (all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22) % 38.22/11.36 | % 38.22/11.36 +-Applying beta-rule and splitting (417), into two cases. % 38.22/11.36 |-Branch one: % 38.22/11.36 | (418) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) % 38.22/11.36 | % 38.22/11.36 +-Applying beta-rule and splitting (418), into two cases. % 38.22/11.36 |-Branch one: % 38.22/11.36 | (419) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) % 38.22/11.36 | % 38.22/11.36 +-Applying beta-rule and splitting (419), into two cases. % 38.22/11.36 |-Branch one: % 38.22/11.36 | (420) all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22 % 38.22/11.36 | % 38.22/11.36 | Applying alpha-rule on (420) yields: % 38.22/11.36 | (421) vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 % 38.22/11.36 | (422) all_17_4_20 = all_17_10_26 % 38.22/11.36 | (423) ~ (all_17_3_19 = 0) % 38.22/11.36 | (424) vapp(all_17_6_22, all_17_8_24) = ve1 % 38.22/11.36 | (425) vreduce(all_17_8_24) = all_17_10_26 % 38.22/11.36 | (426) visSomeExp(all_17_10_26) = all_17_3_19 % 38.22/11.36 | (427) all_17_5_21 = ve1 % 38.22/11.36 | (428) vsomeExp(all_17_1_17) = all_0_7_7 % 38.22/11.36 | (429) all_17_2_18 = 0 % 38.22/11.36 | (430) vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22 % 38.22/11.36 | (431) all_17_0_16 = all_0_7_7 % 38.22/11.36 | (432) visValue(all_17_8_24) = 0 % 38.22/11.36 | % 38.22/11.36 | Instantiating formula (32) with all_17_1_17, all_19_5_45, all_0_7_7 and discharging atoms vgetSomeExp(all_0_7_7) = all_19_5_45, vsomeExp(all_17_1_17) = all_0_7_7, yields: % 38.22/11.36 | (433) all_19_5_45 = all_17_1_17 % 38.22/11.36 | % 38.22/11.36 | From (433) and (408) follows: % 38.22/11.36 | (434) vapp(all_17_1_17, ve2) = all_0_2_2 % 38.22/11.36 | % 38.22/11.36 | Instantiating formula (31) with all_16_3_11, all_17_1_17, all_0_3_3 and discharging atoms vsomeExp(all_17_1_17) = all_0_7_7, vtcheck(all_0_3_3, ve1, all_16_3_11) = 0, yields: % 38.22/11.36 | (435) vtcheck(all_0_3_3, all_17_1_17, all_16_3_11) = 0 % 38.22/11.36 | % 38.22/11.36 | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_16_3_11, all_0_1_1, ve2, all_17_1_17, all_0_3_3, all_16_5_13 and discharging atoms varrow(all_16_5_13, all_0_1_1) = all_16_3_11, vtcheck(all_0_3_3, all_17_1_17, all_16_3_11) = 0, vtcheck(all_0_3_3, all_0_2_2, all_0_1_1) = all_0_0_0, vapp(all_17_1_17, ve2) = all_0_2_2, yields: % 38.22/11.36 | (436) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.22/11.36 | % 38.22/11.36 +-Applying beta-rule and splitting (436), into two cases. % 38.22/11.36 |-Branch one: % 38.22/11.36 | (298) all_0_0_0 = 0 % 38.22/11.36 | % 38.22/11.36 | Equations (298) can reduce 36 to: % 38.22/11.36 | (228) $false % 38.22/11.36 | % 38.22/11.36 |-The branch is then unsatisfiable % 38.22/11.36 |-Branch two: % 38.22/11.36 | (36) ~ (all_0_0_0 = 0) % 38.22/11.36 | (440) ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.22/11.36 | % 38.22/11.36 | Instantiating (440) with all_283_0_814 yields: % 38.22/11.36 | (1158) ~ (all_283_0_814 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = all_283_0_814 % 38.22/11.36 | % 38.22/11.36 | Applying alpha-rule on (1158) yields: % 38.22/11.36 | (1159) ~ (all_283_0_814 = 0) % 38.22/11.36 | (1160) vtcheck(all_0_3_3, ve2, all_16_5_13) = all_283_0_814 % 38.22/11.36 | % 38.22/11.36 | Instantiating formula (91) with all_0_3_3, ve2, all_16_5_13, all_283_0_814, 0 and discharging atoms vtcheck(all_0_3_3, ve2, all_16_5_13) = all_283_0_814, vtcheck(all_0_3_3, ve2, all_16_5_13) = 0, yields: % 38.22/11.36 | (1161) all_283_0_814 = 0 % 38.22/11.36 | % 38.22/11.36 | Equations (1161) can reduce 1159 to: % 38.22/11.36 | (228) $false % 38.22/11.36 | % 38.22/11.36 |-The branch is then unsatisfiable % 38.22/11.36 |-Branch two: % 38.22/11.36 | (446) all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22 % 38.22/11.36 | % 38.22/11.36 | Applying alpha-rule on (446) yields: % 38.22/11.36 | (447) vgetSomeExp(all_17_7_23) = all_17_2_18 % 38.22/11.36 | (448) vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22 % 38.22/11.36 | (449) vreduce(all_17_11_27) = all_17_7_23 % 38.22/11.36 | (450) all_17_3_19 = 0 % 38.22/11.36 | (451) vapp(all_17_6_22, all_17_11_27) = ve1 % 38.22/11.36 | (452) visSomeExp(all_17_7_23) = 0 % 38.22/11.36 | (453) all_17_4_20 = all_17_7_23 % 38.22/11.36 | (427) all_17_5_21 = ve1 % 38.22/11.36 | (428) vsomeExp(all_17_1_17) = all_0_7_7 % 38.22/11.36 | (431) all_17_0_16 = all_0_7_7 % 38.22/11.36 | (457) vapp(all_17_6_22, all_17_2_18) = all_17_1_17 % 38.22/11.36 | % 38.22/11.36 | Instantiating formula (32) with all_17_1_17, all_19_5_45, all_0_7_7 and discharging atoms vgetSomeExp(all_0_7_7) = all_19_5_45, vsomeExp(all_17_1_17) = all_0_7_7, yields: % 38.22/11.36 | (433) all_19_5_45 = all_17_1_17 % 38.22/11.36 | % 38.22/11.36 | From (433) and (408) follows: % 38.22/11.36 | (434) vapp(all_17_1_17, ve2) = all_0_2_2 % 38.22/11.36 | % 38.22/11.36 | Instantiating formula (31) with all_16_3_11, all_17_1_17, all_0_3_3 and discharging atoms vsomeExp(all_17_1_17) = all_0_7_7, vtcheck(all_0_3_3, ve1, all_16_3_11) = 0, yields: % 38.22/11.36 | (435) vtcheck(all_0_3_3, all_17_1_17, all_16_3_11) = 0 % 38.22/11.36 | % 38.22/11.36 +-Applying beta-rule and splitting (1023), into two cases. % 38.22/11.36 |-Branch one: % 38.22/11.36 | (1178) (all_91_0_620 = 0 & all_91_2_622 = all_16_5_13 & all_91_3_623 = all_0_2_2 & varrow(all_91_5_625, all_91_4_624) = all_16_5_13 & vtcheck(all_91_1_621, all_91_6_626, all_91_4_624) = 0 & vbind(all_91_7_627, all_91_5_625, all_0_3_3) = all_91_1_621 & vabs(all_91_7_627, all_91_5_625, all_91_6_626) = all_0_2_2) | (all_91_1_621 = 0 & all_91_2_622 = 0 & all_91_4_624 = all_0_2_2 & varrow(all_91_5_625, all_16_5_13) = all_91_3_623 & vtcheck(all_0_3_3, all_91_6_626, all_91_5_625) = 0 & vtcheck(all_0_3_3, all_91_7_627, all_91_3_623) = 0 & vapp(all_91_7_627, all_91_6_626) = all_0_2_2) % 38.22/11.36 | % 38.22/11.36 +-Applying beta-rule and splitting (1178), into two cases. % 38.22/11.36 |-Branch one: % 38.22/11.36 | (1179) all_91_0_620 = 0 & all_91_2_622 = all_16_5_13 & all_91_3_623 = all_0_2_2 & varrow(all_91_5_625, all_91_4_624) = all_16_5_13 & vtcheck(all_91_1_621, all_91_6_626, all_91_4_624) = 0 & vbind(all_91_7_627, all_91_5_625, all_0_3_3) = all_91_1_621 & vabs(all_91_7_627, all_91_5_625, all_91_6_626) = all_0_2_2 % 38.22/11.36 | % 38.22/11.36 | Applying alpha-rule on (1179) yields: % 38.22/11.36 | (1180) vabs(all_91_7_627, all_91_5_625, all_91_6_626) = all_0_2_2 % 38.22/11.36 | (1181) vbind(all_91_7_627, all_91_5_625, all_0_3_3) = all_91_1_621 % 38.22/11.36 | (1182) all_91_0_620 = 0 % 38.22/11.36 | (1183) varrow(all_91_5_625, all_91_4_624) = all_16_5_13 % 38.22/11.36 | (1184) all_91_2_622 = all_16_5_13 % 38.22/11.36 | (1185) vtcheck(all_91_1_621, all_91_6_626, all_91_4_624) = 0 % 38.22/11.36 | (1186) all_91_3_623 = all_0_2_2 % 38.22/11.36 | % 38.22/11.36 | Instantiating formula (55) with all_0_2_2, ve2, all_17_1_17, all_91_6_626, all_91_5_625, all_91_7_627 and discharging atoms vapp(all_17_1_17, ve2) = all_0_2_2, vabs(all_91_7_627, all_91_5_625, all_91_6_626) = all_0_2_2, yields: % 38.22/11.36 | (130) $false % 38.22/11.36 | % 38.22/11.36 |-The branch is then unsatisfiable % 38.22/11.36 |-Branch two: % 38.22/11.36 | (1188) all_91_1_621 = 0 & all_91_2_622 = 0 & all_91_4_624 = all_0_2_2 & varrow(all_91_5_625, all_16_5_13) = all_91_3_623 & vtcheck(all_0_3_3, all_91_6_626, all_91_5_625) = 0 & vtcheck(all_0_3_3, all_91_7_627, all_91_3_623) = 0 & vapp(all_91_7_627, all_91_6_626) = all_0_2_2 % 38.22/11.37 | % 38.22/11.37 | Applying alpha-rule on (1188) yields: % 38.22/11.37 | (1189) all_91_2_622 = 0 % 38.22/11.37 | (1190) all_91_1_621 = 0 % 38.22/11.37 | (1191) all_91_4_624 = all_0_2_2 % 38.22/11.37 | (1192) vapp(all_91_7_627, all_91_6_626) = all_0_2_2 % 38.22/11.37 | (1193) vtcheck(all_0_3_3, all_91_7_627, all_91_3_623) = 0 % 38.22/11.37 | (1194) varrow(all_91_5_625, all_16_5_13) = all_91_3_623 % 38.22/11.37 | (1195) vtcheck(all_0_3_3, all_91_6_626, all_91_5_625) = 0 % 38.22/11.37 | % 38.22/11.37 | Instantiating formula (18) with all_0_2_2, all_91_6_626, all_91_7_627, ve2, all_17_1_17 and discharging atoms vapp(all_91_7_627, all_91_6_626) = all_0_2_2, vapp(all_17_1_17, ve2) = all_0_2_2, yields: % 38.22/11.37 | (1196) all_91_6_626 = ve2 % 38.22/11.37 | % 38.22/11.37 | Instantiating formula (20) with all_0_2_2, all_91_6_626, all_91_7_627, ve2, all_17_1_17 and discharging atoms vapp(all_91_7_627, all_91_6_626) = all_0_2_2, vapp(all_17_1_17, ve2) = all_0_2_2, yields: % 38.22/11.37 | (1197) all_91_7_627 = all_17_1_17 % 38.22/11.37 | % 38.22/11.37 | From (1197)(1196) and (1192) follows: % 38.22/11.37 | (434) vapp(all_17_1_17, ve2) = all_0_2_2 % 38.22/11.37 | % 38.22/11.37 | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_16_3_11, all_0_1_1, ve2, all_17_1_17, all_0_3_3, all_16_5_13 and discharging atoms varrow(all_16_5_13, all_0_1_1) = all_16_3_11, vtcheck(all_0_3_3, all_17_1_17, all_16_3_11) = 0, vtcheck(all_0_3_3, all_0_2_2, all_0_1_1) = all_0_0_0, vapp(all_17_1_17, ve2) = all_0_2_2, yields: % 38.22/11.37 | (436) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.22/11.37 | % 38.22/11.37 +-Applying beta-rule and splitting (436), into two cases. % 38.22/11.37 |-Branch one: % 38.22/11.37 | (298) all_0_0_0 = 0 % 38.22/11.37 | % 38.22/11.37 | Equations (298) can reduce 36 to: % 38.22/11.37 | (228) $false % 38.22/11.37 | % 38.22/11.37 |-The branch is then unsatisfiable % 38.22/11.37 |-Branch two: % 38.22/11.37 | (36) ~ (all_0_0_0 = 0) % 38.22/11.37 | (440) ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.22/11.37 | % 38.22/11.37 | Instantiating (440) with all_359_0_911 yields: % 38.22/11.37 | (1204) ~ (all_359_0_911 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = all_359_0_911 % 38.22/11.37 | % 38.22/11.37 | Applying alpha-rule on (1204) yields: % 38.22/11.37 | (1205) ~ (all_359_0_911 = 0) % 38.22/11.37 | (1206) vtcheck(all_0_3_3, ve2, all_16_5_13) = all_359_0_911 % 38.22/11.37 | % 38.22/11.37 | Instantiating formula (91) with all_0_3_3, ve2, all_16_5_13, all_359_0_911, 0 and discharging atoms vtcheck(all_0_3_3, ve2, all_16_5_13) = all_359_0_911, vtcheck(all_0_3_3, ve2, all_16_5_13) = 0, yields: % 38.22/11.37 | (1207) all_359_0_911 = 0 % 38.22/11.37 | % 38.22/11.37 | Equations (1207) can reduce 1205 to: % 38.22/11.37 | (228) $false % 38.22/11.37 | % 38.22/11.37 |-The branch is then unsatisfiable % 38.22/11.37 |-Branch two: % 38.22/11.37 | (1209) all_91_4_624 = all_91_7_627 & all_91_5_625 = all_0_2_2 & vlookup(all_91_6_626, all_0_3_3) = all_91_7_627 & vsomeType(all_16_5_13) = all_91_7_627 & vvar(all_91_6_626) = all_0_2_2 % 38.22/11.37 | % 38.22/11.37 | Applying alpha-rule on (1209) yields: % 38.22/11.37 | (1210) all_91_4_624 = all_91_7_627 % 38.22/11.37 | (1211) all_91_5_625 = all_0_2_2 % 38.22/11.37 | (1212) vlookup(all_91_6_626, all_0_3_3) = all_91_7_627 % 38.22/11.37 | (1213) vsomeType(all_16_5_13) = all_91_7_627 % 38.22/11.37 | (1214) vvar(all_91_6_626) = all_0_2_2 % 38.22/11.37 | % 38.22/11.37 | Instantiating formula (6) with all_0_2_2, ve2, all_17_1_17, all_91_6_626 and discharging atoms vapp(all_17_1_17, ve2) = all_0_2_2, vvar(all_91_6_626) = all_0_2_2, yields: % 38.22/11.37 | (130) $false % 38.22/11.37 | % 38.22/11.37 |-The branch is then unsatisfiable % 38.22/11.37 |-Branch two: % 38.22/11.37 | (471) all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27) % 38.22/11.37 | % 38.22/11.37 | Applying alpha-rule on (471) yields: % 38.22/11.37 | (472) vapp(all_17_11_27, all_17_9_25) = ve1 % 38.22/11.37 | (473) vreduce(all_17_11_27) = all_17_10_26 % 38.22/11.37 | (474) vapp(all_17_5_21, all_17_9_25) = all_17_4_20 % 38.22/11.37 | (475) all_17_7_23 = all_17_10_26 % 38.22/11.37 | (476) vgetSomeExp(all_17_10_26) = all_17_5_21 % 38.22/11.37 | (477) all_17_6_22 = 0 % 38.22/11.37 | (478) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27) % 38.22/11.37 | (479) all_17_8_24 = ve1 % 38.22/11.37 | (480) all_17_3_19 = all_0_7_7 % 38.22/11.37 | (481) visSomeExp(all_17_10_26) = 0 % 38.22/11.37 | (482) vsomeExp(all_17_4_20) = all_0_7_7 % 38.22/11.37 | % 38.22/11.37 | Instantiating formula (32) with all_17_4_20, all_19_5_45, all_0_7_7 and discharging atoms vgetSomeExp(all_0_7_7) = all_19_5_45, vsomeExp(all_17_4_20) = all_0_7_7, yields: % 38.22/11.37 | (483) all_19_5_45 = all_17_4_20 % 38.22/11.37 | % 38.22/11.37 | From (483) and (408) follows: % 38.22/11.37 | (484) vapp(all_17_4_20, ve2) = all_0_2_2 % 38.22/11.37 | % 38.22/11.37 | Instantiating formula (31) with all_16_3_11, all_17_4_20, all_0_3_3 and discharging atoms vsomeExp(all_17_4_20) = all_0_7_7, vtcheck(all_0_3_3, ve1, all_16_3_11) = 0, yields: % 38.22/11.37 | (485) vtcheck(all_0_3_3, all_17_4_20, all_16_3_11) = 0 % 38.22/11.37 | % 38.22/11.37 | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_16_3_11, all_0_1_1, ve2, all_17_4_20, all_0_3_3, all_16_5_13 and discharging atoms varrow(all_16_5_13, all_0_1_1) = all_16_3_11, vtcheck(all_0_3_3, all_17_4_20, all_16_3_11) = 0, vtcheck(all_0_3_3, all_0_2_2, all_0_1_1) = all_0_0_0, vapp(all_17_4_20, ve2) = all_0_2_2, yields: % 38.22/11.37 | (436) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.22/11.37 | % 38.22/11.37 +-Applying beta-rule and splitting (436), into two cases. % 38.22/11.37 |-Branch one: % 38.22/11.37 | (298) all_0_0_0 = 0 % 38.22/11.37 | % 38.22/11.37 | Equations (298) can reduce 36 to: % 38.22/11.37 | (228) $false % 38.22/11.37 | % 38.22/11.37 |-The branch is then unsatisfiable % 38.22/11.37 |-Branch two: % 38.22/11.37 | (36) ~ (all_0_0_0 = 0) % 38.22/11.37 | (440) ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.22/11.37 | % 38.22/11.37 | Instantiating (440) with all_216_0_960 yields: % 38.22/11.37 | (1236) ~ (all_216_0_960 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = all_216_0_960 % 38.22/11.37 | % 38.22/11.37 | Applying alpha-rule on (1236) yields: % 38.22/11.37 | (1237) ~ (all_216_0_960 = 0) % 38.22/11.37 | (1238) vtcheck(all_0_3_3, ve2, all_16_5_13) = all_216_0_960 % 38.22/11.37 | % 38.22/11.37 | Instantiating formula (91) with all_0_3_3, ve2, all_16_5_13, all_216_0_960, 0 and discharging atoms vtcheck(all_0_3_3, ve2, all_16_5_13) = all_216_0_960, vtcheck(all_0_3_3, ve2, all_16_5_13) = 0, yields: % 38.22/11.37 | (1239) all_216_0_960 = 0 % 38.22/11.37 | % 38.22/11.37 | Equations (1239) can reduce 1237 to: % 38.22/11.37 | (228) $false % 38.22/11.37 | % 38.22/11.37 |-The branch is then unsatisfiable % 38.22/11.37 |-Branch two: % 38.22/11.37 | (496) all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22 % 38.22/11.37 | % 38.22/11.37 | Applying alpha-rule on (496) yields: % 38.22/11.37 | (497) visValue(all_17_7_23) = all_17_2_18 % 38.22/11.37 | (498) visSomeExp(all_17_8_24) = all_17_3_19 % 38.22/11.37 | (423) ~ (all_17_3_19 = 0) % 38.22/11.37 | (500) all_17_4_20 = all_17_8_24 % 38.22/11.37 | (170) all_0_7_7 = vnoExp % 38.22/11.37 | (502) vapp(all_17_6_22, all_17_7_23) = ve1 % 38.22/11.37 | (427) all_17_5_21 = ve1 % 38.22/11.37 | (504) vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22 % 38.22/11.37 | (505) ~ (all_17_2_18 = 0) % 38.22/11.37 | (506) vreduce(all_17_7_23) = all_17_8_24 % 38.22/11.37 | % 38.22/11.37 | Equations (170) can reduce 413 to: % 38.22/11.37 | (228) $false % 38.22/11.37 | % 38.22/11.37 |-The branch is then unsatisfiable % 38.22/11.37 |-Branch two: % 38.22/11.37 | (508) all_17_7_23 = all_17_9_25 & all_17_8_24 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_6_22 = 0) & vreduce(all_17_10_26) = all_17_9_25 & visSomeExp(all_17_9_25) = all_17_6_22 & vapp(all_17_10_26, all_17_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26) % 38.22/11.37 | % 38.22/11.37 | Applying alpha-rule on (508) yields: % 38.22/11.37 | (509) all_17_7_23 = all_17_9_25 % 38.22/11.37 | (510) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26) % 38.22/11.37 | (511) visSomeExp(all_17_9_25) = all_17_6_22 % 38.22/11.37 | (512) ~ (all_17_6_22 = 0) % 38.22/11.37 | (170) all_0_7_7 = vnoExp % 38.22/11.37 | (514) vapp(all_17_10_26, all_17_11_27) = ve1 % 38.22/11.37 | (479) all_17_8_24 = ve1 % 38.22/11.37 | (516) vreduce(all_17_10_26) = all_17_9_25 % 38.22/11.37 | % 38.22/11.37 | Equations (170) can reduce 413 to: % 38.22/11.37 | (228) $false % 38.22/11.37 | % 38.22/11.37 |-The branch is then unsatisfiable % 38.22/11.37 |-Branch two: % 38.22/11.37 | (518) all_17_8_24 = ve1 & all_0_7_7 = vnoExp & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1 % 38.22/11.37 | % 38.22/11.37 | Applying alpha-rule on (518) yields: % 38.22/11.37 | (479) all_17_8_24 = ve1 % 38.22/11.37 | (170) all_0_7_7 = vnoExp % 38.22/11.37 | (521) vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1 % 38.22/11.37 | % 38.22/11.37 | Equations (170) can reduce 413 to: % 38.22/11.37 | (228) $false % 38.22/11.37 | % 38.22/11.37 |-The branch is then unsatisfiable % 38.22/11.38 |-Branch two: % 38.22/11.38 | (523) all_17_10_26 = ve1 & all_0_7_7 = vnoExp & vvar(all_17_11_27) = ve1 % 38.22/11.38 | % 38.22/11.38 | Applying alpha-rule on (523) yields: % 38.22/11.38 | (524) all_17_10_26 = ve1 % 38.22/11.38 | (170) all_0_7_7 = vnoExp % 38.22/11.38 | (526) vvar(all_17_11_27) = ve1 % 38.22/11.38 | % 38.22/11.38 | Equations (170) can reduce 413 to: % 38.22/11.38 | (228) $false % 38.22/11.38 | % 38.22/11.38 |-The branch is then unsatisfiable % 38.22/11.38 |-Branch two: % 38.22/11.38 | (528) all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46 % 38.22/11.38 | % 38.22/11.38 | Applying alpha-rule on (528) yields: % 38.22/11.38 | (529) visValue(all_19_7_47) = all_19_2_42 % 38.22/11.38 | (530) vapp(all_19_6_46, all_19_7_47) = all_0_5_5 % 38.22/11.38 | (531) all_19_4_44 = all_19_8_48 % 38.22/11.38 | (532) vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46 % 38.22/11.38 | (533) visSomeExp(all_19_8_48) = all_19_3_43 % 38.22/11.38 | (534) all_0_4_4 = vnoExp % 38.22/11.38 | (535) ~ (all_19_2_42 = 0) % 38.22/11.38 | (160) all_19_5_45 = all_0_5_5 % 38.22/11.38 | (537) vreduce(all_19_7_47) = all_19_8_48 % 38.22/11.38 | (161) ~ (all_19_3_43 = 0) % 38.22/11.38 | % 38.22/11.38 | Combining equations (534,993) yields a new equation: % 38.22/11.38 | (226) all_0_6_6 = vnoExp % 38.22/11.38 | % 38.22/11.38 | Equations (226) can reduce 171 to: % 38.22/11.38 | (228) $false % 38.22/11.38 | % 38.22/11.38 |-The branch is then unsatisfiable % 38.22/11.38 |-Branch two: % 38.22/11.38 | (540) all_19_7_47 = all_19_9_49 & all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_6_46 = 0) & vreduce(all_19_10_50) = all_19_9_49 & visSomeExp(all_19_9_49) = all_19_6_46 & vapp(all_19_10_50, all_19_11_51) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50) % 38.22/11.38 | % 38.22/11.38 | Applying alpha-rule on (540) yields: % 38.22/11.38 | (391) all_19_8_48 = all_0_5_5 % 38.22/11.38 | (542) vreduce(all_19_10_50) = all_19_9_49 % 38.22/11.38 | (543) all_19_7_47 = all_19_9_49 % 38.22/11.38 | (544) ~ (all_19_6_46 = 0) % 38.22/11.38 | (534) all_0_4_4 = vnoExp % 38.22/11.38 | (546) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50) % 38.22/11.38 | (547) vapp(all_19_10_50, all_19_11_51) = all_0_5_5 % 38.22/11.38 | (548) visSomeExp(all_19_9_49) = all_19_6_46 % 38.22/11.38 | % 38.22/11.38 | Combining equations (534,993) yields a new equation: % 38.22/11.38 | (226) all_0_6_6 = vnoExp % 38.22/11.38 | % 38.22/11.38 | Equations (226) can reduce 171 to: % 38.22/11.38 | (228) $false % 38.22/11.38 | % 38.22/11.38 |-The branch is then unsatisfiable % 38.22/11.38 |-Branch two: % 38.22/11.38 | (550) all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_0_5_5 % 38.22/11.38 | % 38.22/11.38 | Applying alpha-rule on (550) yields: % 38.22/11.38 | (391) all_19_8_48 = all_0_5_5 % 38.22/11.38 | (534) all_0_4_4 = vnoExp % 38.22/11.38 | (553) vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_0_5_5 % 38.22/11.38 | % 38.22/11.38 | Combining equations (993,534) yields a new equation: % 38.22/11.38 | (1301) all_0_6_6 = vnoExp % 38.22/11.38 | % 38.22/11.38 | Simplifying 1301 yields: % 38.22/11.38 | (226) all_0_6_6 = vnoExp % 38.22/11.38 | % 38.22/11.38 | Equations (226) can reduce 171 to: % 38.22/11.38 | (228) $false % 38.22/11.38 | % 38.22/11.38 |-The branch is then unsatisfiable % 38.22/11.38 |-Branch two: % 38.22/11.38 | (555) all_19_10_50 = all_0_5_5 & all_0_4_4 = vnoExp & vvar(all_19_11_51) = all_0_5_5 % 38.22/11.38 | % 38.22/11.38 | Applying alpha-rule on (555) yields: % 38.22/11.38 | (556) all_19_10_50 = all_0_5_5 % 38.22/11.38 | (534) all_0_4_4 = vnoExp % 38.22/11.38 | (558) vvar(all_19_11_51) = all_0_5_5 % 38.22/11.38 | % 38.22/11.38 | Combining equations (993,534) yields a new equation: % 38.22/11.38 | (1301) all_0_6_6 = vnoExp % 38.22/11.38 | % 38.22/11.38 | Simplifying 1301 yields: % 38.22/11.38 | (226) all_0_6_6 = vnoExp % 38.22/11.38 | % 38.22/11.38 | Equations (226) can reduce 171 to: % 38.22/11.38 | (228) $false % 38.22/11.38 | % 38.22/11.38 |-The branch is then unsatisfiable % 38.22/11.38 |-Branch two: % 38.22/11.38 | (191) all_18_0_28 = all_0_6_6 & all_18_3_31 = 0 & all_18_4_32 = all_18_7_35 & all_18_5_33 = ve2 & vreduce(all_18_11_39) = all_18_7_35 & vgetSomeExp(all_18_7_35) = all_18_2_30 & visSomeExp(all_18_7_35) = 0 & vsomeExp(all_18_1_29) = all_0_6_6 & vapp(all_18_6_34, all_18_2_30) = all_18_1_29 & vapp(all_18_6_34, all_18_11_39) = ve2 & vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34 % 38.22/11.38 | % 38.22/11.38 | Applying alpha-rule on (191) yields: % 38.22/11.38 | (192) vapp(all_18_6_34, all_18_11_39) = ve2 % 38.22/11.38 | (193) vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_18_6_34 % 38.22/11.38 | (194) all_18_3_31 = 0 % 38.22/11.38 | (180) vsomeExp(all_18_1_29) = all_0_6_6 % 38.22/11.38 | (196) visSomeExp(all_18_7_35) = 0 % 38.22/11.38 | (197) vapp(all_18_6_34, all_18_2_30) = all_18_1_29 % 38.22/11.38 | (184) all_18_5_33 = ve2 % 38.22/11.38 | (185) all_18_0_28 = all_0_6_6 % 38.22/11.38 | (200) all_18_4_32 = all_18_7_35 % 38.22/11.38 | (201) vreduce(all_18_11_39) = all_18_7_35 % 38.22/11.38 | (202) vgetSomeExp(all_18_7_35) = all_18_2_30 % 38.22/11.38 | % 38.22/11.38 | Instantiating formula (50) with all_0_6_6, all_18_1_29, all_0_2_2 and discharging atoms vsomeExp(all_18_1_29) = all_0_6_6, vsomeExp(all_0_2_2) = all_0_6_6, yields: % 38.22/11.38 | (1042) all_18_1_29 = all_0_2_2 % 38.22/11.38 | % 38.22/11.38 | From (1042) and (180) follows: % 38.22/11.38 | (997) vsomeExp(all_0_2_2) = all_0_6_6 % 38.22/11.38 | % 38.22/11.38 | From (1042) and (197) follows: % 38.22/11.38 | (1325) vapp(all_18_6_34, all_18_2_30) = all_0_2_2 % 38.22/11.38 | % 38.22/11.38 | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_16_3_11, all_0_1_1, all_18_2_30, ve1, all_0_3_3, all_16_5_13 and discharging atoms varrow(all_16_5_13, all_0_1_1) = all_16_3_11, vtcheck(all_0_3_3, all_0_2_2, all_0_1_1) = all_0_0_0, vtcheck(all_0_3_3, ve1, all_16_3_11) = 0, yields: % 38.22/11.38 | (1326) all_0_0_0 = 0 | ~ (vapp(ve1, all_18_2_30) = all_0_2_2) | ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, all_18_2_30, all_16_5_13) = v0) % 38.22/11.38 | % 38.22/11.38 +-Applying beta-rule and splitting (116), into two cases. % 38.22/11.38 |-Branch one: % 38.22/11.38 | (144) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) | (all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46) | (all_19_7_47 = all_19_9_49 & all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_6_46 = 0) & vreduce(all_19_10_50) = all_19_9_49 & visSomeExp(all_19_9_49) = all_19_6_46 & vapp(all_19_10_50, all_19_11_51) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50)) | (all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_0_5_5) % 38.22/11.38 | % 38.22/11.38 +-Applying beta-rule and splitting (144), into two cases. % 38.22/11.38 |-Branch one: % 38.22/11.38 | (145) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) | (all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46) | (all_19_7_47 = all_19_9_49 & all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_6_46 = 0) & vreduce(all_19_10_50) = all_19_9_49 & visSomeExp(all_19_9_49) = all_19_6_46 & vapp(all_19_10_50, all_19_11_51) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50)) % 38.22/11.38 | % 38.22/11.38 +-Applying beta-rule and splitting (145), into two cases. % 38.22/11.38 |-Branch one: % 38.22/11.38 | (146) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) | (all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46) % 38.22/11.38 | % 38.22/11.38 +-Applying beta-rule and splitting (146), into two cases. % 38.22/11.38 |-Branch one: % 38.22/11.38 | (147) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) % 38.22/11.38 | % 38.22/11.38 +-Applying beta-rule and splitting (147), into two cases. % 38.22/11.38 |-Branch one: % 38.22/11.38 | (148) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) % 38.22/11.38 | % 38.22/11.38 +-Applying beta-rule and splitting (148), into two cases. % 38.22/11.38 |-Branch one: % 38.22/11.39 | (149) all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46 % 38.22/11.39 | % 38.22/11.39 | Applying alpha-rule on (149) yields: % 38.22/11.39 | (150) vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46 % 38.22/11.39 | (151) all_19_0_40 = all_0_4_4 % 38.22/11.39 | (152) vsomeExp(all_19_1_41) = all_0_4_4 % 38.22/11.39 | (153) vreduce(all_19_8_48) = all_19_10_50 % 38.22/11.39 | (154) vapp(all_19_6_46, all_19_8_48) = all_0_5_5 % 38.22/11.39 | (155) visValue(all_19_8_48) = 0 % 38.22/11.39 | (156) vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 % 38.22/11.39 | (157) visSomeExp(all_19_10_50) = all_19_3_43 % 38.22/11.39 | (158) all_19_4_44 = all_19_10_50 % 38.22/11.39 | (159) all_19_2_42 = 0 % 38.22/11.39 | (160) all_19_5_45 = all_0_5_5 % 38.22/11.39 | (161) ~ (all_19_3_43 = 0) % 38.22/11.39 | % 38.22/11.39 | Instantiating formula (84) with ve2, all_18_11_39, all_18_6_34 and discharging atoms vapp(all_18_6_34, all_18_11_39) = ve2, yields: % 38.22/11.39 | (1062) ~ (visValue(ve2) = 0) % 38.22/11.39 | % 38.22/11.39 | Instantiating formula (18) with all_0_5_5, all_19_8_48, all_19_6_46, ve2, ve1 and discharging atoms vapp(all_19_6_46, all_19_8_48) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.22/11.39 | (162) all_19_8_48 = ve2 % 38.22/11.39 | % 38.22/11.39 | From (162) and (155) follows: % 38.22/11.39 | (165) visValue(ve2) = 0 % 38.22/11.39 | % 38.22/11.39 | Using (165) and (1062) yields: % 38.22/11.39 | (130) $false % 38.22/11.39 | % 38.22/11.39 |-The branch is then unsatisfiable % 38.22/11.39 |-Branch two: % 38.22/11.39 | (249) all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46 % 38.22/11.39 | % 38.22/11.39 | Applying alpha-rule on (249) yields: % 38.22/11.39 | (250) vreduce(all_19_11_51) = all_19_7_47 % 38.22/11.39 | (251) vapp(all_19_6_46, all_19_2_42) = all_19_1_41 % 38.22/11.39 | (151) all_19_0_40 = all_0_4_4 % 38.22/11.39 | (253) vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46 % 38.22/11.39 | (152) vsomeExp(all_19_1_41) = all_0_4_4 % 38.22/11.39 | (255) vgetSomeExp(all_19_7_47) = all_19_2_42 % 38.22/11.39 | (256) visSomeExp(all_19_7_47) = 0 % 38.22/11.39 | (257) all_19_4_44 = all_19_7_47 % 38.22/11.39 | (160) all_19_5_45 = all_0_5_5 % 38.22/11.39 | (259) all_19_3_43 = 0 % 38.22/11.39 | (260) vapp(all_19_6_46, all_19_11_51) = all_0_5_5 % 38.22/11.39 | % 38.22/11.39 | From (993) and (152) follows: % 38.22/11.39 | (1078) vsomeExp(all_19_1_41) = all_0_6_6 % 38.22/11.39 | % 38.22/11.39 | Instantiating formula (59) with ve2, all_19_7_47, all_0_6_6 and discharging atoms vreduce(ve2) = all_0_6_6, yields: % 38.22/11.39 | (261) all_19_7_47 = all_0_6_6 | ~ (vreduce(ve2) = all_19_7_47) % 38.22/11.39 | % 38.22/11.39 | Instantiating formula (32) with all_19_1_41, all_18_2_30, all_0_6_6 and discharging atoms vsomeExp(all_19_1_41) = all_0_6_6, yields: % 38.22/11.39 | (1363) all_19_1_41 = all_18_2_30 | ~ (vgetSomeExp(all_0_6_6) = all_18_2_30) % 38.22/11.39 | % 38.22/11.39 | Instantiating formula (50) with all_0_6_6, all_19_1_41, all_0_2_2 and discharging atoms vsomeExp(all_19_1_41) = all_0_6_6, vsomeExp(all_0_2_2) = all_0_6_6, yields: % 38.61/11.39 | (262) all_19_1_41 = all_0_2_2 % 38.61/11.39 | % 38.61/11.39 | Instantiating formula (18) with all_0_2_2, all_19_2_42, all_19_6_46, all_18_2_30, all_18_6_34 and discharging atoms vapp(all_18_6_34, all_18_2_30) = all_0_2_2, yields: % 38.61/11.39 | (1365) all_19_2_42 = all_18_2_30 | ~ (vapp(all_19_6_46, all_19_2_42) = all_0_2_2) % 38.61/11.39 | % 38.61/11.39 | Instantiating formula (20) with all_0_2_2, all_19_2_42, all_19_6_46, all_18_2_30, all_18_6_34 and discharging atoms vapp(all_18_6_34, all_18_2_30) = all_0_2_2, yields: % 38.61/11.39 | (1366) all_19_6_46 = all_18_6_34 | ~ (vapp(all_19_6_46, all_19_2_42) = all_0_2_2) % 38.61/11.39 | % 38.61/11.39 | Instantiating formula (18) with all_0_5_5, all_19_11_51, all_19_6_46, ve2, ve1 and discharging atoms vapp(all_19_6_46, all_19_11_51) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.61/11.39 | (263) all_19_11_51 = ve2 % 38.61/11.39 | % 38.61/11.39 | Instantiating formula (20) with all_0_5_5, all_19_11_51, all_19_6_46, ve2, ve1 and discharging atoms vapp(all_19_6_46, all_19_11_51) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.61/11.39 | (163) all_19_6_46 = ve1 % 38.61/11.39 | % 38.61/11.39 | From (263) and (250) follows: % 38.61/11.39 | (266) vreduce(ve2) = all_19_7_47 % 38.61/11.39 | % 38.61/11.39 | From (163)(262) and (251) follows: % 38.61/11.39 | (267) vapp(ve1, all_19_2_42) = all_0_2_2 % 38.61/11.39 | % 38.61/11.39 +-Applying beta-rule and splitting (1366), into two cases. % 38.61/11.39 |-Branch one: % 38.61/11.39 | (1371) ~ (vapp(all_19_6_46, all_19_2_42) = all_0_2_2) % 38.61/11.39 | % 38.61/11.39 | From (163) and (1371) follows: % 38.61/11.39 | (1372) ~ (vapp(ve1, all_19_2_42) = all_0_2_2) % 38.61/11.39 | % 38.61/11.39 | Using (267) and (1372) yields: % 38.61/11.39 | (130) $false % 38.61/11.39 | % 38.61/11.39 |-The branch is then unsatisfiable % 38.61/11.39 |-Branch two: % 38.61/11.39 | (1374) vapp(all_19_6_46, all_19_2_42) = all_0_2_2 % 38.61/11.39 | (1375) all_19_6_46 = all_18_6_34 % 38.61/11.39 | % 38.61/11.39 | Combining equations (163,1375) yields a new equation: % 38.61/11.39 | (1376) all_18_6_34 = ve1 % 38.61/11.39 | % 38.61/11.39 | Combining equations (1376,1375) yields a new equation: % 38.61/11.39 | (163) all_19_6_46 = ve1 % 38.61/11.39 | % 38.61/11.39 | From (163) and (1374) follows: % 38.61/11.39 | (267) vapp(ve1, all_19_2_42) = all_0_2_2 % 38.61/11.39 | % 38.61/11.39 | From (1376) and (1325) follows: % 38.61/11.39 | (1379) vapp(ve1, all_18_2_30) = all_0_2_2 % 38.61/11.39 | % 38.61/11.39 +-Applying beta-rule and splitting (1326), into two cases. % 38.61/11.39 |-Branch one: % 38.61/11.39 | (1380) ~ (vapp(ve1, all_18_2_30) = all_0_2_2) % 38.61/11.39 | % 38.61/11.39 | Using (1379) and (1380) yields: % 38.61/11.39 | (130) $false % 38.61/11.39 | % 38.61/11.39 |-The branch is then unsatisfiable % 38.61/11.39 |-Branch two: % 38.61/11.39 | (1379) vapp(ve1, all_18_2_30) = all_0_2_2 % 38.61/11.39 | (1383) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, all_18_2_30, all_16_5_13) = v0) % 38.61/11.39 | % 38.61/11.39 +-Applying beta-rule and splitting (1383), into two cases. % 38.61/11.39 |-Branch one: % 38.61/11.39 | (298) all_0_0_0 = 0 % 38.61/11.39 | % 38.61/11.39 | Equations (298) can reduce 36 to: % 38.61/11.39 | (228) $false % 38.61/11.39 | % 38.61/11.39 |-The branch is then unsatisfiable % 38.61/11.39 |-Branch two: % 38.61/11.39 | (36) ~ (all_0_0_0 = 0) % 38.61/11.39 | (1387) ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, all_18_2_30, all_16_5_13) = v0) % 38.61/11.39 | % 38.61/11.39 | Instantiating (1387) with all_152_0_973 yields: % 38.61/11.39 | (1388) ~ (all_152_0_973 = 0) & vtcheck(all_0_3_3, all_18_2_30, all_16_5_13) = all_152_0_973 % 38.61/11.39 | % 38.61/11.39 | Applying alpha-rule on (1388) yields: % 38.61/11.39 | (1389) ~ (all_152_0_973 = 0) % 38.61/11.39 | (1390) vtcheck(all_0_3_3, all_18_2_30, all_16_5_13) = all_152_0_973 % 38.61/11.39 | % 38.61/11.39 +-Applying beta-rule and splitting (1365), into two cases. % 38.61/11.39 |-Branch one: % 38.61/11.39 | (1371) ~ (vapp(all_19_6_46, all_19_2_42) = all_0_2_2) % 38.61/11.39 | % 38.61/11.39 | From (163) and (1371) follows: % 38.61/11.39 | (1372) ~ (vapp(ve1, all_19_2_42) = all_0_2_2) % 38.61/11.39 | % 38.61/11.39 | Using (267) and (1372) yields: % 38.61/11.39 | (130) $false % 38.61/11.39 | % 38.61/11.39 |-The branch is then unsatisfiable % 38.61/11.39 |-Branch two: % 38.61/11.39 | (1374) vapp(all_19_6_46, all_19_2_42) = all_0_2_2 % 38.61/11.39 | (1395) all_19_2_42 = all_18_2_30 % 38.61/11.39 | % 38.61/11.39 | From (1395) and (255) follows: % 38.61/11.39 | (1396) vgetSomeExp(all_19_7_47) = all_18_2_30 % 38.61/11.39 | % 38.61/11.39 +-Applying beta-rule and splitting (261), into two cases. % 38.61/11.39 |-Branch one: % 38.61/11.39 | (269) ~ (vreduce(ve2) = all_19_7_47) % 38.61/11.39 | % 38.61/11.39 | Using (266) and (269) yields: % 38.61/11.39 | (130) $false % 38.61/11.39 | % 38.61/11.39 |-The branch is then unsatisfiable % 38.61/11.39 |-Branch two: % 38.61/11.39 | (266) vreduce(ve2) = all_19_7_47 % 38.61/11.39 | (272) all_19_7_47 = all_0_6_6 % 38.61/11.39 | % 38.61/11.39 | From (272) and (1396) follows: % 38.61/11.39 | (1401) vgetSomeExp(all_0_6_6) = all_18_2_30 % 38.61/11.39 | % 38.61/11.39 +-Applying beta-rule and splitting (1363), into two cases. % 38.61/11.39 |-Branch one: % 38.61/11.39 | (1402) ~ (vgetSomeExp(all_0_6_6) = all_18_2_30) % 38.61/11.39 | % 38.61/11.39 | Using (1401) and (1402) yields: % 38.61/11.39 | (130) $false % 38.61/11.39 | % 38.61/11.39 |-The branch is then unsatisfiable % 38.61/11.39 |-Branch two: % 38.61/11.39 | (1401) vgetSomeExp(all_0_6_6) = all_18_2_30 % 38.61/11.39 | (1405) all_19_1_41 = all_18_2_30 % 38.61/11.39 | % 38.61/11.39 | Combining equations (1405,262) yields a new equation: % 38.61/11.39 | (1406) all_18_2_30 = all_0_2_2 % 38.61/11.39 | % 38.61/11.39 | Simplifying 1406 yields: % 38.61/11.39 | (1407) all_18_2_30 = all_0_2_2 % 38.61/11.39 | % 38.61/11.39 | From (1407) and (1390) follows: % 38.61/11.39 | (1408) vtcheck(all_0_3_3, all_0_2_2, all_16_5_13) = all_152_0_973 % 38.61/11.39 | % 38.61/11.39 | Instantiating formula (91) with all_0_3_3, all_0_2_2, all_16_5_13, all_152_0_973, 0 and discharging atoms vtcheck(all_0_3_3, all_0_2_2, all_16_5_13) = all_152_0_973, vtcheck(all_0_3_3, all_0_2_2, all_16_5_13) = 0, yields: % 38.61/11.39 | (1409) all_152_0_973 = 0 % 38.61/11.39 | % 38.61/11.39 | Equations (1409) can reduce 1389 to: % 38.61/11.39 | (228) $false % 38.61/11.39 | % 38.61/11.39 |-The branch is then unsatisfiable % 38.61/11.40 |-Branch two: % 38.61/11.40 | (390) all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51) % 38.61/11.40 | % 38.61/11.40 | Applying alpha-rule on (390) yields: % 38.61/11.40 | (391) all_19_8_48 = all_0_5_5 % 38.61/11.40 | (392) vsomeExp(all_19_4_44) = all_0_4_4 % 38.61/11.40 | (393) vreduce(all_19_11_51) = all_19_10_50 % 38.61/11.40 | (394) all_19_7_47 = all_19_10_50 % 38.61/11.40 | (395) vapp(all_19_11_51, all_19_9_49) = all_0_5_5 % 38.61/11.40 | (396) all_19_6_46 = 0 % 38.61/11.40 | (397) visSomeExp(all_19_10_50) = 0 % 38.61/11.40 | (398) vapp(all_19_5_45, all_19_9_49) = all_19_4_44 % 38.61/11.40 | (399) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51) % 38.61/11.40 | (400) all_19_3_43 = all_0_4_4 % 38.61/11.40 | (401) vgetSomeExp(all_19_10_50) = all_19_5_45 % 38.61/11.40 | % 38.61/11.40 | From (993) and (392) follows: % 38.61/11.40 | (1118) vsomeExp(all_19_4_44) = all_0_6_6 % 38.61/11.40 | % 38.61/11.40 | Instantiating formula (59) with ve1, all_19_10_50, all_0_7_7 and discharging atoms vreduce(ve1) = all_0_7_7, yields: % 38.61/11.40 | (402) all_19_10_50 = all_0_7_7 | ~ (vreduce(ve1) = all_19_10_50) % 38.61/11.40 | % 38.61/11.40 | Using (397) and (17) yields: % 38.61/11.40 | (403) ~ (all_19_10_50 = vnoExp) % 38.61/11.40 | % 38.61/11.40 | Instantiating formula (50) with all_0_6_6, all_19_4_44, all_0_2_2 and discharging atoms vsomeExp(all_19_4_44) = all_0_6_6, vsomeExp(all_0_2_2) = all_0_6_6, yields: % 38.61/11.40 | (404) all_19_4_44 = all_0_2_2 % 38.61/11.40 | % 38.61/11.40 | Instantiating formula (18) with all_0_2_2, all_19_9_49, all_19_5_45, all_18_2_30, all_18_6_34 and discharging atoms vapp(all_18_6_34, all_18_2_30) = all_0_2_2, yields: % 38.61/11.40 | (1427) all_19_9_49 = all_18_2_30 | ~ (vapp(all_19_5_45, all_19_9_49) = all_0_2_2) % 38.61/11.40 | % 38.61/11.40 | Instantiating formula (20) with all_0_2_2, all_19_9_49, all_19_5_45, all_18_2_30, all_18_6_34 and discharging atoms vapp(all_18_6_34, all_18_2_30) = all_0_2_2, yields: % 38.61/11.40 | (1428) all_19_5_45 = all_18_6_34 | ~ (vapp(all_19_5_45, all_19_9_49) = all_0_2_2) % 38.61/11.40 | % 38.61/11.40 | Instantiating formula (18) with all_0_5_5, all_19_9_49, all_19_11_51, ve2, ve1 and discharging atoms vapp(all_19_11_51, all_19_9_49) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.61/11.40 | (405) all_19_9_49 = ve2 % 38.61/11.40 | % 38.61/11.40 | Instantiating formula (20) with all_0_5_5, all_19_9_49, all_19_11_51, ve2, ve1 and discharging atoms vapp(all_19_11_51, all_19_9_49) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.61/11.40 | (406) all_19_11_51 = ve1 % 38.61/11.40 | % 38.61/11.40 | From (406) and (393) follows: % 38.61/11.40 | (407) vreduce(ve1) = all_19_10_50 % 38.61/11.40 | % 38.61/11.40 | From (405)(404) and (398) follows: % 38.61/11.40 | (408) vapp(all_19_5_45, ve2) = all_0_2_2 % 38.61/11.40 | % 38.61/11.40 +-Applying beta-rule and splitting (1428), into two cases. % 38.61/11.40 |-Branch one: % 38.61/11.40 | (1433) ~ (vapp(all_19_5_45, all_19_9_49) = all_0_2_2) % 38.61/11.40 | % 38.61/11.40 | From (405) and (1433) follows: % 38.61/11.40 | (1434) ~ (vapp(all_19_5_45, ve2) = all_0_2_2) % 38.61/11.40 | % 38.61/11.40 | Using (408) and (1434) yields: % 38.61/11.40 | (130) $false % 38.61/11.40 | % 38.61/11.40 |-The branch is then unsatisfiable % 38.61/11.40 |-Branch two: % 38.61/11.40 | (1436) vapp(all_19_5_45, all_19_9_49) = all_0_2_2 % 38.61/11.40 | (1437) all_19_5_45 = all_18_6_34 % 38.61/11.40 | % 38.61/11.40 | From (1437) and (401) follows: % 38.61/11.40 | (1438) vgetSomeExp(all_19_10_50) = all_18_6_34 % 38.61/11.40 | % 38.61/11.40 | From (1437) and (408) follows: % 38.61/11.40 | (1439) vapp(all_18_6_34, ve2) = all_0_2_2 % 38.61/11.40 | % 38.61/11.40 +-Applying beta-rule and splitting (1427), into two cases. % 38.61/11.40 |-Branch one: % 38.61/11.40 | (1433) ~ (vapp(all_19_5_45, all_19_9_49) = all_0_2_2) % 38.61/11.40 | % 38.61/11.40 | From (1437)(405) and (1433) follows: % 38.61/11.40 | (1441) ~ (vapp(all_18_6_34, ve2) = all_0_2_2) % 38.61/11.40 | % 38.61/11.40 | Using (1439) and (1441) yields: % 38.61/11.40 | (130) $false % 38.61/11.40 | % 38.61/11.40 |-The branch is then unsatisfiable % 38.61/11.40 |-Branch two: % 38.61/11.40 | (1436) vapp(all_19_5_45, all_19_9_49) = all_0_2_2 % 38.61/11.40 | (1444) all_19_9_49 = all_18_2_30 % 38.61/11.40 | % 38.61/11.40 | Combining equations (405,1444) yields a new equation: % 38.61/11.40 | (1445) all_18_2_30 = ve2 % 38.61/11.40 | % 38.61/11.40 | From (1445) and (1325) follows: % 38.61/11.40 | (1439) vapp(all_18_6_34, ve2) = all_0_2_2 % 38.61/11.40 | % 38.61/11.40 +-Applying beta-rule and splitting (402), into two cases. % 38.61/11.40 |-Branch one: % 38.61/11.40 | (409) ~ (vreduce(ve1) = all_19_10_50) % 38.61/11.40 | % 38.61/11.40 | Using (407) and (409) yields: % 38.61/11.40 | (130) $false % 38.61/11.40 | % 38.61/11.40 |-The branch is then unsatisfiable % 38.61/11.40 |-Branch two: % 38.61/11.40 | (407) vreduce(ve1) = all_19_10_50 % 38.61/11.40 | (412) all_19_10_50 = all_0_7_7 % 38.61/11.40 | % 38.61/11.40 | Equations (412) can reduce 403 to: % 38.61/11.40 | (413) ~ (all_0_7_7 = vnoExp) % 38.61/11.40 | % 38.61/11.40 | From (412) and (1438) follows: % 38.61/11.40 | (1452) vgetSomeExp(all_0_7_7) = all_18_6_34 % 38.61/11.40 | % 38.61/11.40 +-Applying beta-rule and splitting (114), into two cases. % 38.61/11.40 |-Branch one: % 38.61/11.40 | (415) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) | (all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22) | (all_17_7_23 = all_17_9_25 & all_17_8_24 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_6_22 = 0) & vreduce(all_17_10_26) = all_17_9_25 & visSomeExp(all_17_9_25) = all_17_6_22 & vapp(all_17_10_26, all_17_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26)) | (all_17_8_24 = ve1 & all_0_7_7 = vnoExp & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1) % 38.61/11.40 | % 38.61/11.40 +-Applying beta-rule and splitting (415), into two cases. % 38.61/11.40 |-Branch one: % 38.61/11.40 | (416) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) | (all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22) | (all_17_7_23 = all_17_9_25 & all_17_8_24 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_6_22 = 0) & vreduce(all_17_10_26) = all_17_9_25 & visSomeExp(all_17_9_25) = all_17_6_22 & vapp(all_17_10_26, all_17_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26)) % 38.61/11.40 | % 38.61/11.40 +-Applying beta-rule and splitting (416), into two cases. % 38.61/11.40 |-Branch one: % 38.61/11.40 | (417) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) | (all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22) % 38.61/11.40 | % 38.61/11.40 +-Applying beta-rule and splitting (417), into two cases. % 38.61/11.40 |-Branch one: % 38.61/11.40 | (418) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) % 38.61/11.40 | % 38.61/11.40 +-Applying beta-rule and splitting (418), into two cases. % 38.61/11.40 |-Branch one: % 38.61/11.40 | (419) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) % 38.61/11.40 | % 38.61/11.40 +-Applying beta-rule and splitting (419), into two cases. % 38.61/11.40 |-Branch one: % 38.61/11.40 | (420) all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22 % 38.61/11.40 | % 38.61/11.40 | Applying alpha-rule on (420) yields: % 38.61/11.40 | (421) vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 % 38.61/11.40 | (422) all_17_4_20 = all_17_10_26 % 38.61/11.40 | (423) ~ (all_17_3_19 = 0) % 38.61/11.40 | (424) vapp(all_17_6_22, all_17_8_24) = ve1 % 38.61/11.40 | (425) vreduce(all_17_8_24) = all_17_10_26 % 38.61/11.40 | (426) visSomeExp(all_17_10_26) = all_17_3_19 % 38.61/11.40 | (427) all_17_5_21 = ve1 % 38.61/11.40 | (428) vsomeExp(all_17_1_17) = all_0_7_7 % 38.61/11.40 | (429) all_17_2_18 = 0 % 38.61/11.40 | (430) vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22 % 38.61/11.40 | (431) all_17_0_16 = all_0_7_7 % 38.61/11.40 | (432) visValue(all_17_8_24) = 0 % 38.61/11.40 | % 38.61/11.40 | Instantiating formula (32) with all_17_1_17, all_18_6_34, all_0_7_7 and discharging atoms vgetSomeExp(all_0_7_7) = all_18_6_34, vsomeExp(all_17_1_17) = all_0_7_7, yields: % 38.61/11.40 | (1471) all_18_6_34 = all_17_1_17 % 38.61/11.40 | % 38.61/11.40 | From (1471) and (1439) follows: % 38.61/11.40 | (434) vapp(all_17_1_17, ve2) = all_0_2_2 % 38.61/11.40 | % 38.61/11.40 | Instantiating formula (31) with all_16_3_11, all_17_1_17, all_0_3_3 and discharging atoms vsomeExp(all_17_1_17) = all_0_7_7, vtcheck(all_0_3_3, ve1, all_16_3_11) = 0, yields: % 38.61/11.40 | (435) vtcheck(all_0_3_3, all_17_1_17, all_16_3_11) = 0 % 38.61/11.40 | % 38.61/11.40 | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_16_3_11, all_0_1_1, ve2, all_17_1_17, all_0_3_3, all_16_5_13 and discharging atoms varrow(all_16_5_13, all_0_1_1) = all_16_3_11, vtcheck(all_0_3_3, all_17_1_17, all_16_3_11) = 0, vtcheck(all_0_3_3, all_0_2_2, all_0_1_1) = all_0_0_0, vapp(all_17_1_17, ve2) = all_0_2_2, yields: % 38.61/11.40 | (436) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.61/11.40 | % 38.61/11.40 +-Applying beta-rule and splitting (436), into two cases. % 38.61/11.40 |-Branch one: % 38.61/11.40 | (298) all_0_0_0 = 0 % 38.61/11.40 | % 38.61/11.40 | Equations (298) can reduce 36 to: % 38.61/11.40 | (228) $false % 38.61/11.40 | % 38.61/11.40 |-The branch is then unsatisfiable % 38.61/11.40 |-Branch two: % 38.61/11.40 | (36) ~ (all_0_0_0 = 0) % 38.61/11.40 | (440) ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.61/11.40 | % 38.61/11.40 | Instantiating (440) with all_249_0_1083 yields: % 38.61/11.40 | (1479) ~ (all_249_0_1083 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = all_249_0_1083 % 38.61/11.40 | % 38.61/11.40 | Applying alpha-rule on (1479) yields: % 38.61/11.40 | (1480) ~ (all_249_0_1083 = 0) % 38.61/11.40 | (1481) vtcheck(all_0_3_3, ve2, all_16_5_13) = all_249_0_1083 % 38.61/11.40 | % 38.61/11.40 | Instantiating formula (91) with all_0_3_3, ve2, all_16_5_13, all_249_0_1083, 0 and discharging atoms vtcheck(all_0_3_3, ve2, all_16_5_13) = all_249_0_1083, vtcheck(all_0_3_3, ve2, all_16_5_13) = 0, yields: % 38.61/11.40 | (1482) all_249_0_1083 = 0 % 38.61/11.40 | % 38.61/11.40 | Equations (1482) can reduce 1480 to: % 38.61/11.40 | (228) $false % 38.61/11.40 | % 38.61/11.40 |-The branch is then unsatisfiable % 38.61/11.40 |-Branch two: % 38.61/11.40 | (446) all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22 % 38.61/11.40 | % 38.61/11.40 | Applying alpha-rule on (446) yields: % 38.61/11.40 | (447) vgetSomeExp(all_17_7_23) = all_17_2_18 % 38.61/11.40 | (448) vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22 % 38.61/11.40 | (449) vreduce(all_17_11_27) = all_17_7_23 % 38.61/11.40 | (450) all_17_3_19 = 0 % 38.61/11.40 | (451) vapp(all_17_6_22, all_17_11_27) = ve1 % 38.61/11.40 | (452) visSomeExp(all_17_7_23) = 0 % 38.61/11.40 | (453) all_17_4_20 = all_17_7_23 % 38.61/11.40 | (427) all_17_5_21 = ve1 % 38.61/11.40 | (428) vsomeExp(all_17_1_17) = all_0_7_7 % 38.61/11.41 | (431) all_17_0_16 = all_0_7_7 % 38.61/11.41 | (457) vapp(all_17_6_22, all_17_2_18) = all_17_1_17 % 38.61/11.41 | % 38.61/11.41 | Instantiating formula (32) with all_17_1_17, all_18_6_34, all_0_7_7 and discharging atoms vgetSomeExp(all_0_7_7) = all_18_6_34, vsomeExp(all_17_1_17) = all_0_7_7, yields: % 38.61/11.41 | (1471) all_18_6_34 = all_17_1_17 % 38.61/11.41 | % 38.61/11.41 | Instantiating formula (55) with all_17_1_17, all_17_2_18, all_17_6_22, all_18_8_36, all_18_9_37, all_18_10_38 and discharging atoms vapp(all_17_6_22, all_17_2_18) = all_17_1_17, yields: % 38.61/11.41 | (1497) ~ (vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_17_1_17) % 38.61/11.41 | % 38.61/11.41 | From (1471) and (193) follows: % 38.61/11.41 | (1498) vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_17_1_17 % 38.61/11.41 | % 38.61/11.41 | Using (1498) and (1497) yields: % 38.61/11.41 | (130) $false % 38.61/11.41 | % 38.61/11.41 |-The branch is then unsatisfiable % 38.61/11.41 |-Branch two: % 38.61/11.41 | (471) all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27) % 38.61/11.41 | % 38.61/11.41 | Applying alpha-rule on (471) yields: % 38.61/11.41 | (472) vapp(all_17_11_27, all_17_9_25) = ve1 % 38.61/11.41 | (473) vreduce(all_17_11_27) = all_17_10_26 % 38.61/11.41 | (474) vapp(all_17_5_21, all_17_9_25) = all_17_4_20 % 38.61/11.41 | (475) all_17_7_23 = all_17_10_26 % 38.61/11.41 | (476) vgetSomeExp(all_17_10_26) = all_17_5_21 % 38.61/11.41 | (477) all_17_6_22 = 0 % 38.61/11.41 | (478) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27) % 38.61/11.41 | (479) all_17_8_24 = ve1 % 38.61/11.41 | (480) all_17_3_19 = all_0_7_7 % 38.61/11.41 | (481) visSomeExp(all_17_10_26) = 0 % 38.61/11.41 | (482) vsomeExp(all_17_4_20) = all_0_7_7 % 38.61/11.41 | % 38.61/11.41 | Instantiating formula (32) with all_17_4_20, all_18_6_34, all_0_7_7 and discharging atoms vgetSomeExp(all_0_7_7) = all_18_6_34, vsomeExp(all_17_4_20) = all_0_7_7, yields: % 38.61/11.41 | (1512) all_18_6_34 = all_17_4_20 % 38.61/11.41 | % 38.61/11.41 | Instantiating formula (55) with all_17_4_20, all_17_9_25, all_17_5_21, all_18_8_36, all_18_9_37, all_18_10_38 and discharging atoms vapp(all_17_5_21, all_17_9_25) = all_17_4_20, yields: % 38.61/11.41 | (1513) ~ (vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_17_4_20) % 38.61/11.41 | % 38.61/11.41 | From (1512) and (193) follows: % 38.61/11.41 | (1514) vabs(all_18_10_38, all_18_9_37, all_18_8_36) = all_17_4_20 % 38.61/11.41 | % 38.61/11.41 | Using (1514) and (1513) yields: % 38.61/11.41 | (130) $false % 38.61/11.41 | % 38.61/11.41 |-The branch is then unsatisfiable % 38.61/11.41 |-Branch two: % 38.61/11.41 | (496) all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22 % 38.61/11.41 | % 38.61/11.41 | Applying alpha-rule on (496) yields: % 38.61/11.41 | (497) visValue(all_17_7_23) = all_17_2_18 % 38.61/11.41 | (498) visSomeExp(all_17_8_24) = all_17_3_19 % 38.61/11.41 | (423) ~ (all_17_3_19 = 0) % 38.61/11.41 | (500) all_17_4_20 = all_17_8_24 % 38.61/11.41 | (170) all_0_7_7 = vnoExp % 38.61/11.41 | (502) vapp(all_17_6_22, all_17_7_23) = ve1 % 38.61/11.41 | (427) all_17_5_21 = ve1 % 38.61/11.41 | (504) vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22 % 38.61/11.41 | (505) ~ (all_17_2_18 = 0) % 38.61/11.41 | (506) vreduce(all_17_7_23) = all_17_8_24 % 38.61/11.41 | % 38.61/11.41 | Equations (170) can reduce 413 to: % 38.61/11.41 | (228) $false % 38.61/11.41 | % 38.61/11.41 |-The branch is then unsatisfiable % 38.61/11.41 |-Branch two: % 38.61/11.41 | (508) all_17_7_23 = all_17_9_25 & all_17_8_24 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_6_22 = 0) & vreduce(all_17_10_26) = all_17_9_25 & visSomeExp(all_17_9_25) = all_17_6_22 & vapp(all_17_10_26, all_17_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26) % 38.61/11.41 | % 38.61/11.41 | Applying alpha-rule on (508) yields: % 38.61/11.41 | (509) all_17_7_23 = all_17_9_25 % 38.61/11.41 | (510) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26) % 38.61/11.41 | (511) visSomeExp(all_17_9_25) = all_17_6_22 % 38.61/11.41 | (512) ~ (all_17_6_22 = 0) % 38.61/11.41 | (170) all_0_7_7 = vnoExp % 38.61/11.41 | (514) vapp(all_17_10_26, all_17_11_27) = ve1 % 38.61/11.41 | (479) all_17_8_24 = ve1 % 38.61/11.41 | (516) vreduce(all_17_10_26) = all_17_9_25 % 38.61/11.41 | % 38.61/11.41 | Equations (170) can reduce 413 to: % 38.61/11.41 | (228) $false % 38.61/11.41 | % 38.61/11.41 |-The branch is then unsatisfiable % 38.61/11.41 |-Branch two: % 38.61/11.41 | (518) all_17_8_24 = ve1 & all_0_7_7 = vnoExp & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1 % 38.61/11.41 | % 38.61/11.41 | Applying alpha-rule on (518) yields: % 38.61/11.41 | (479) all_17_8_24 = ve1 % 38.61/11.41 | (170) all_0_7_7 = vnoExp % 38.61/11.41 | (521) vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1 % 38.61/11.41 | % 38.61/11.41 | Equations (170) can reduce 413 to: % 38.61/11.41 | (228) $false % 38.61/11.41 | % 38.61/11.41 |-The branch is then unsatisfiable % 38.61/11.41 |-Branch two: % 38.61/11.41 | (523) all_17_10_26 = ve1 & all_0_7_7 = vnoExp & vvar(all_17_11_27) = ve1 % 38.61/11.41 | % 38.61/11.41 | Applying alpha-rule on (523) yields: % 38.61/11.41 | (524) all_17_10_26 = ve1 % 38.61/11.41 | (170) all_0_7_7 = vnoExp % 38.61/11.41 | (526) vvar(all_17_11_27) = ve1 % 38.61/11.41 | % 38.61/11.41 | Equations (170) can reduce 413 to: % 38.61/11.41 | (228) $false % 38.61/11.41 | % 38.61/11.41 |-The branch is then unsatisfiable % 38.61/11.41 |-Branch two: % 38.61/11.41 | (528) all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46 % 38.61/11.41 | % 38.61/11.41 | Applying alpha-rule on (528) yields: % 38.61/11.41 | (529) visValue(all_19_7_47) = all_19_2_42 % 38.61/11.41 | (530) vapp(all_19_6_46, all_19_7_47) = all_0_5_5 % 38.61/11.41 | (531) all_19_4_44 = all_19_8_48 % 38.61/11.41 | (532) vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46 % 38.61/11.41 | (533) visSomeExp(all_19_8_48) = all_19_3_43 % 38.61/11.41 | (534) all_0_4_4 = vnoExp % 38.61/11.41 | (535) ~ (all_19_2_42 = 0) % 38.61/11.41 | (160) all_19_5_45 = all_0_5_5 % 38.61/11.41 | (537) vreduce(all_19_7_47) = all_19_8_48 % 38.61/11.41 | (161) ~ (all_19_3_43 = 0) % 38.61/11.41 | % 38.61/11.41 | Combining equations (534,993) yields a new equation: % 38.61/11.41 | (226) all_0_6_6 = vnoExp % 38.61/11.41 | % 38.61/11.41 | Equations (226) can reduce 171 to: % 38.61/11.41 | (228) $false % 38.61/11.41 | % 38.61/11.41 |-The branch is then unsatisfiable % 38.61/11.41 |-Branch two: % 38.61/11.41 | (540) all_19_7_47 = all_19_9_49 & all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_6_46 = 0) & vreduce(all_19_10_50) = all_19_9_49 & visSomeExp(all_19_9_49) = all_19_6_46 & vapp(all_19_10_50, all_19_11_51) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50) % 38.61/11.41 | % 38.61/11.41 | Applying alpha-rule on (540) yields: % 38.61/11.41 | (391) all_19_8_48 = all_0_5_5 % 38.61/11.41 | (542) vreduce(all_19_10_50) = all_19_9_49 % 38.61/11.41 | (543) all_19_7_47 = all_19_9_49 % 38.61/11.41 | (544) ~ (all_19_6_46 = 0) % 38.61/11.41 | (534) all_0_4_4 = vnoExp % 38.61/11.41 | (546) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50) % 38.61/11.41 | (547) vapp(all_19_10_50, all_19_11_51) = all_0_5_5 % 38.61/11.41 | (548) visSomeExp(all_19_9_49) = all_19_6_46 % 38.61/11.41 | % 38.61/11.41 | Combining equations (534,993) yields a new equation: % 38.61/11.41 | (226) all_0_6_6 = vnoExp % 38.61/11.41 | % 38.61/11.41 | Equations (226) can reduce 171 to: % 38.61/11.41 | (228) $false % 38.61/11.41 | % 38.61/11.41 |-The branch is then unsatisfiable % 38.61/11.41 |-Branch two: % 38.61/11.41 | (550) all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_0_5_5 % 38.61/11.41 | % 38.61/11.41 | Applying alpha-rule on (550) yields: % 38.61/11.41 | (391) all_19_8_48 = all_0_5_5 % 38.61/11.41 | (534) all_0_4_4 = vnoExp % 38.61/11.41 | (553) vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_0_5_5 % 38.61/11.41 | % 38.61/11.41 | Combining equations (993,534) yields a new equation: % 38.61/11.41 | (1301) all_0_6_6 = vnoExp % 38.61/11.41 | % 38.61/11.41 | Simplifying 1301 yields: % 38.61/11.41 | (226) all_0_6_6 = vnoExp % 38.61/11.41 | % 38.61/11.41 | Equations (226) can reduce 171 to: % 38.61/11.41 | (228) $false % 38.61/11.41 | % 38.61/11.41 |-The branch is then unsatisfiable % 38.61/11.41 |-Branch two: % 38.61/11.41 | (555) all_19_10_50 = all_0_5_5 & all_0_4_4 = vnoExp & vvar(all_19_11_51) = all_0_5_5 % 38.61/11.41 | % 38.61/11.41 | Applying alpha-rule on (555) yields: % 38.61/11.41 | (556) all_19_10_50 = all_0_5_5 % 38.61/11.41 | (534) all_0_4_4 = vnoExp % 38.61/11.41 | (558) vvar(all_19_11_51) = all_0_5_5 % 38.61/11.41 | % 38.61/11.41 | Combining equations (993,534) yields a new equation: % 38.61/11.41 | (1301) all_0_6_6 = vnoExp % 38.61/11.41 | % 38.61/11.41 | Simplifying 1301 yields: % 38.61/11.41 | (226) all_0_6_6 = vnoExp % 38.61/11.41 | % 38.61/11.41 | Equations (226) can reduce 171 to: % 38.61/11.41 | (228) $false % 38.61/11.41 | % 38.61/11.41 |-The branch is then unsatisfiable % 38.61/11.41 |-Branch two: % 38.61/11.41 | (204) all_18_3_31 = all_0_6_6 & all_18_6_34 = 0 & all_18_7_35 = all_18_10_38 & all_18_8_36 = ve2 & vreduce(all_18_11_39) = all_18_10_38 & vgetSomeExp(all_18_10_38) = all_18_5_33 & visSomeExp(all_18_10_38) = 0 & vsomeExp(all_18_4_32) = all_0_6_6 & vapp(all_18_5_33, all_18_9_37) = all_18_4_32 & vapp(all_18_11_39, all_18_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_11_39) % 38.61/11.41 | % 38.61/11.41 | Applying alpha-rule on (204) yields: % 38.61/11.41 | (205) all_18_8_36 = ve2 % 38.61/11.41 | (206) vreduce(all_18_11_39) = all_18_10_38 % 38.61/11.41 | (207) vapp(all_18_5_33, all_18_9_37) = all_18_4_32 % 38.61/11.41 | (208) all_18_7_35 = all_18_10_38 % 38.61/11.41 | (209) vapp(all_18_11_39, all_18_9_37) = ve2 % 38.61/11.41 | (210) all_18_3_31 = all_0_6_6 % 38.61/11.41 | (211) vgetSomeExp(all_18_10_38) = all_18_5_33 % 38.61/11.41 | (212) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_11_39) % 38.61/11.41 | (213) visSomeExp(all_18_10_38) = 0 % 38.61/11.41 | (214) all_18_6_34 = 0 % 38.61/11.41 | (215) vsomeExp(all_18_4_32) = all_0_6_6 % 38.61/11.41 | % 38.61/11.41 | Instantiating formula (50) with all_0_6_6, all_18_4_32, all_0_2_2 and discharging atoms vsomeExp(all_18_4_32) = all_0_6_6, vsomeExp(all_0_2_2) = all_0_6_6, yields: % 38.61/11.41 | (1598) all_18_4_32 = all_0_2_2 % 38.61/11.41 | % 38.61/11.41 | From (1598) and (215) follows: % 38.61/11.41 | (997) vsomeExp(all_0_2_2) = all_0_6_6 % 38.61/11.41 | % 38.61/11.41 | From (1598) and (207) follows: % 38.61/11.41 | (1600) vapp(all_18_5_33, all_18_9_37) = all_0_2_2 % 38.61/11.41 | % 38.61/11.41 | Instantiating formula (45) with all_0_2_2, all_18_5_33, all_18_9_37, all_0_7_7, all_0_6_6, all_0_5_5, ve1 and discharging atoms vreduce(all_0_5_5) = all_0_6_6, vreduce(ve1) = all_0_7_7, vapp(all_18_5_33, all_18_9_37) = all_0_2_2, yields: % 38.61/11.41 | (1601) ~ (vgetSomeExp(all_0_7_7) = all_18_5_33) | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = ve1 & vabs(v0, v1, v2) = ve1) | (visSomeExp(all_0_7_7) = v1 & vsomeExp(all_0_2_2) = v2 & vapp(ve1, all_18_9_37) = v0 & ( ~ (v1 = 0) | ~ (v0 = all_0_5_5) | v2 = all_0_6_6))) % 38.61/11.41 | % 38.61/11.41 | Instantiating formula (45) with all_0_2_2, all_18_5_33, all_18_9_37, all_0_7_7, all_0_6_6, ve2, ve1 and discharging atoms vreduce(ve2) = all_0_6_6, vreduce(ve1) = all_0_7_7, vapp(all_18_5_33, all_18_9_37) = all_0_2_2, yields: % 38.61/11.41 | (1602) ~ (vgetSomeExp(all_0_7_7) = all_18_5_33) | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = ve1 & vabs(v0, v1, v2) = ve1) | (visSomeExp(all_0_7_7) = v1 & vsomeExp(all_0_2_2) = v2 & vapp(ve1, all_18_9_37) = v0 & ( ~ (v1 = 0) | ~ (v0 = ve2) | v2 = all_0_6_6))) % 38.61/11.41 | % 38.61/11.41 | Instantiating formula (45) with all_0_2_2, all_18_5_33, all_18_9_37, all_0_7_7, all_0_7_7, ve1, ve1 and discharging atoms vreduce(ve1) = all_0_7_7, vapp(all_18_5_33, all_18_9_37) = all_0_2_2, yields: % 38.61/11.41 | (1603) ~ (vgetSomeExp(all_0_7_7) = all_18_5_33) | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = ve1 & vabs(v0, v1, v2) = ve1) | (visSomeExp(all_0_7_7) = v1 & vsomeExp(all_0_2_2) = v2 & vapp(ve1, all_18_9_37) = v0 & ( ~ (v1 = 0) | ~ (v0 = ve1) | v2 = all_0_7_7))) % 38.61/11.41 | % 38.61/11.41 | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_16_3_11, all_0_1_1, all_18_9_37, ve1, all_0_3_3, all_16_5_13 and discharging atoms varrow(all_16_5_13, all_0_1_1) = all_16_3_11, vtcheck(all_0_3_3, all_0_2_2, all_0_1_1) = all_0_0_0, vtcheck(all_0_3_3, ve1, all_16_3_11) = 0, yields: % 38.61/11.41 | (1604) all_0_0_0 = 0 | ~ (vapp(ve1, all_18_9_37) = all_0_2_2) | ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, all_18_9_37, all_16_5_13) = v0) % 38.61/11.41 | % 38.61/11.41 +-Applying beta-rule and splitting (116), into two cases. % 38.61/11.41 |-Branch one: % 38.61/11.41 | (144) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) | (all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46) | (all_19_7_47 = all_19_9_49 & all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_6_46 = 0) & vreduce(all_19_10_50) = all_19_9_49 & visSomeExp(all_19_9_49) = all_19_6_46 & vapp(all_19_10_50, all_19_11_51) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50)) | (all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_0_5_5) % 38.61/11.41 | % 38.61/11.41 +-Applying beta-rule and splitting (144), into two cases. % 38.61/11.41 |-Branch one: % 38.61/11.41 | (145) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) | (all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46) | (all_19_7_47 = all_19_9_49 & all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_6_46 = 0) & vreduce(all_19_10_50) = all_19_9_49 & visSomeExp(all_19_9_49) = all_19_6_46 & vapp(all_19_10_50, all_19_11_51) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50)) % 38.61/11.41 | % 38.61/11.41 +-Applying beta-rule and splitting (145), into two cases. % 38.61/11.41 |-Branch one: % 38.61/11.41 | (146) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) | (all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46) % 38.61/11.42 | % 38.61/11.42 +-Applying beta-rule and splitting (146), into two cases. % 38.61/11.42 |-Branch one: % 38.61/11.42 | (147) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) | (all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51)) % 38.61/11.42 | % 38.61/11.42 +-Applying beta-rule and splitting (147), into two cases. % 38.61/11.42 |-Branch one: % 38.61/11.42 | (148) (all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46) | (all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46) % 38.61/11.42 | % 38.61/11.42 +-Applying beta-rule and splitting (148), into two cases. % 38.61/11.42 |-Branch one: % 38.61/11.42 | (149) all_19_0_40 = all_0_4_4 & all_19_2_42 = 0 & all_19_4_44 = all_19_10_50 & all_19_5_45 = all_0_5_5 & ~ (all_19_3_43 = 0) & vreduce(all_19_8_48) = all_19_10_50 & visSomeExp(all_19_10_50) = all_19_3_43 & vsomeExp(all_19_1_41) = all_0_4_4 & vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 & visValue(all_19_8_48) = 0 & vapp(all_19_6_46, all_19_8_48) = all_0_5_5 & vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46 % 38.61/11.42 | % 38.61/11.42 | Applying alpha-rule on (149) yields: % 38.61/11.42 | (150) vabs(all_19_9_49, all_19_11_51, all_19_7_47) = all_19_6_46 % 38.61/11.42 | (151) all_19_0_40 = all_0_4_4 % 38.61/11.42 | (152) vsomeExp(all_19_1_41) = all_0_4_4 % 38.61/11.42 | (153) vreduce(all_19_8_48) = all_19_10_50 % 38.61/11.42 | (154) vapp(all_19_6_46, all_19_8_48) = all_0_5_5 % 38.61/11.42 | (155) visValue(all_19_8_48) = 0 % 38.61/11.42 | (156) vsubst(all_19_9_49, all_19_8_48, all_19_7_47) = all_19_1_41 % 38.61/11.42 | (157) visSomeExp(all_19_10_50) = all_19_3_43 % 38.61/11.42 | (158) all_19_4_44 = all_19_10_50 % 38.61/11.42 | (159) all_19_2_42 = 0 % 38.61/11.42 | (160) all_19_5_45 = all_0_5_5 % 38.61/11.42 | (161) ~ (all_19_3_43 = 0) % 38.61/11.42 | % 38.61/11.42 | Instantiating formula (84) with ve2, all_18_9_37, all_18_11_39 and discharging atoms vapp(all_18_11_39, all_18_9_37) = ve2, yields: % 38.61/11.42 | (1062) ~ (visValue(ve2) = 0) % 38.61/11.42 | % 38.61/11.42 | Instantiating formula (18) with all_0_5_5, all_19_8_48, all_19_6_46, ve2, ve1 and discharging atoms vapp(all_19_6_46, all_19_8_48) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.61/11.42 | (162) all_19_8_48 = ve2 % 38.61/11.42 | % 38.61/11.42 | From (162) and (155) follows: % 38.61/11.42 | (165) visValue(ve2) = 0 % 38.61/11.42 | % 38.61/11.42 | Using (165) and (1062) yields: % 38.61/11.42 | (130) $false % 38.61/11.42 | % 38.61/11.42 |-The branch is then unsatisfiable % 38.61/11.42 |-Branch two: % 38.61/11.42 | (249) all_19_0_40 = all_0_4_4 & all_19_3_43 = 0 & all_19_4_44 = all_19_7_47 & all_19_5_45 = all_0_5_5 & vreduce(all_19_11_51) = all_19_7_47 & vgetSomeExp(all_19_7_47) = all_19_2_42 & visSomeExp(all_19_7_47) = 0 & vsomeExp(all_19_1_41) = all_0_4_4 & vapp(all_19_6_46, all_19_2_42) = all_19_1_41 & vapp(all_19_6_46, all_19_11_51) = all_0_5_5 & vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46 % 38.61/11.42 | % 38.61/11.42 | Applying alpha-rule on (249) yields: % 38.61/11.42 | (250) vreduce(all_19_11_51) = all_19_7_47 % 38.61/11.42 | (251) vapp(all_19_6_46, all_19_2_42) = all_19_1_41 % 38.61/11.42 | (151) all_19_0_40 = all_0_4_4 % 38.61/11.42 | (253) vabs(all_19_10_50, all_19_9_49, all_19_8_48) = all_19_6_46 % 38.61/11.42 | (152) vsomeExp(all_19_1_41) = all_0_4_4 % 38.61/11.42 | (255) vgetSomeExp(all_19_7_47) = all_19_2_42 % 38.61/11.42 | (256) visSomeExp(all_19_7_47) = 0 % 38.61/11.42 | (257) all_19_4_44 = all_19_7_47 % 38.61/11.42 | (160) all_19_5_45 = all_0_5_5 % 38.61/11.42 | (259) all_19_3_43 = 0 % 38.61/11.42 | (260) vapp(all_19_6_46, all_19_11_51) = all_0_5_5 % 38.61/11.42 | % 38.61/11.42 | From (993) and (152) follows: % 38.61/11.42 | (1078) vsomeExp(all_19_1_41) = all_0_6_6 % 38.61/11.42 | % 38.61/11.42 | Instantiating formula (59) with ve2, all_19_7_47, all_0_6_6 and discharging atoms vreduce(ve2) = all_0_6_6, yields: % 38.61/11.42 | (261) all_19_7_47 = all_0_6_6 | ~ (vreduce(ve2) = all_19_7_47) % 38.61/11.42 | % 38.61/11.42 | Instantiating formula (32) with all_19_1_41, all_19_2_42, all_0_6_6 and discharging atoms vsomeExp(all_19_1_41) = all_0_6_6, yields: % 38.61/11.42 | (1641) all_19_1_41 = all_19_2_42 | ~ (vgetSomeExp(all_0_6_6) = all_19_2_42) % 38.61/11.42 | % 38.61/11.42 | Instantiating formula (50) with all_0_6_6, all_19_1_41, all_0_2_2 and discharging atoms vsomeExp(all_19_1_41) = all_0_6_6, vsomeExp(all_0_2_2) = all_0_6_6, yields: % 38.61/11.42 | (262) all_19_1_41 = all_0_2_2 % 38.61/11.42 | % 38.61/11.42 | Instantiating formula (18) with all_0_2_2, all_19_2_42, all_19_6_46, all_18_9_37, all_18_5_33 and discharging atoms vapp(all_18_5_33, all_18_9_37) = all_0_2_2, yields: % 38.61/11.42 | (1643) all_19_2_42 = all_18_9_37 | ~ (vapp(all_19_6_46, all_19_2_42) = all_0_2_2) % 38.61/11.42 | % 38.61/11.42 | Instantiating formula (20) with all_0_2_2, all_19_2_42, all_19_6_46, all_18_9_37, all_18_5_33 and discharging atoms vapp(all_18_5_33, all_18_9_37) = all_0_2_2, yields: % 38.61/11.42 | (1644) all_19_6_46 = all_18_5_33 | ~ (vapp(all_19_6_46, all_19_2_42) = all_0_2_2) % 38.61/11.42 | % 38.61/11.42 | Instantiating formula (18) with all_0_5_5, all_19_11_51, all_19_6_46, ve2, ve1 and discharging atoms vapp(all_19_6_46, all_19_11_51) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.61/11.42 | (263) all_19_11_51 = ve2 % 38.61/11.42 | % 38.61/11.42 | Instantiating formula (20) with all_0_5_5, all_19_11_51, all_19_6_46, ve2, ve1 and discharging atoms vapp(all_19_6_46, all_19_11_51) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.61/11.42 | (163) all_19_6_46 = ve1 % 38.61/11.42 | % 38.61/11.42 | From (263) and (250) follows: % 38.61/11.42 | (266) vreduce(ve2) = all_19_7_47 % 38.61/11.42 | % 38.61/11.42 | From (163)(262) and (251) follows: % 38.61/11.42 | (267) vapp(ve1, all_19_2_42) = all_0_2_2 % 38.61/11.42 | % 38.61/11.42 +-Applying beta-rule and splitting (261), into two cases. % 38.61/11.42 |-Branch one: % 38.61/11.42 | (269) ~ (vreduce(ve2) = all_19_7_47) % 38.61/11.42 | % 38.61/11.42 | Using (266) and (269) yields: % 38.61/11.42 | (130) $false % 38.61/11.42 | % 38.61/11.42 |-The branch is then unsatisfiable % 38.61/11.42 |-Branch two: % 38.61/11.42 | (266) vreduce(ve2) = all_19_7_47 % 38.61/11.42 | (272) all_19_7_47 = all_0_6_6 % 38.61/11.42 | % 38.61/11.42 | From (272) and (255) follows: % 38.61/11.42 | (273) vgetSomeExp(all_0_6_6) = all_19_2_42 % 38.61/11.42 | % 38.61/11.42 +-Applying beta-rule and splitting (1641), into two cases. % 38.61/11.42 |-Branch one: % 38.61/11.42 | (1091) ~ (vgetSomeExp(all_0_6_6) = all_19_2_42) % 38.61/11.42 | % 38.61/11.42 | Using (273) and (1091) yields: % 38.61/11.42 | (130) $false % 38.61/11.42 | % 38.61/11.42 |-The branch is then unsatisfiable % 38.61/11.42 |-Branch two: % 38.61/11.42 | (273) vgetSomeExp(all_0_6_6) = all_19_2_42 % 38.61/11.42 | (1657) all_19_1_41 = all_19_2_42 % 38.61/11.42 | % 38.61/11.42 | Combining equations (1657,262) yields a new equation: % 38.61/11.42 | (1658) all_19_2_42 = all_0_2_2 % 38.61/11.42 | % 38.61/11.42 | Simplifying 1658 yields: % 38.61/11.42 | (1094) all_19_2_42 = all_0_2_2 % 38.61/11.42 | % 38.61/11.42 | From (1094) and (267) follows: % 38.61/11.42 | (1095) vapp(ve1, all_0_2_2) = all_0_2_2 % 38.61/11.42 | % 38.61/11.42 +-Applying beta-rule and splitting (1644), into two cases. % 38.61/11.42 |-Branch one: % 38.61/11.42 | (1371) ~ (vapp(all_19_6_46, all_19_2_42) = all_0_2_2) % 38.61/11.42 | % 38.61/11.42 | From (163)(1094) and (1371) follows: % 38.61/11.42 | (1662) ~ (vapp(ve1, all_0_2_2) = all_0_2_2) % 38.61/11.42 | % 38.61/11.42 | Using (1095) and (1662) yields: % 38.61/11.42 | (130) $false % 38.61/11.42 | % 38.61/11.42 |-The branch is then unsatisfiable % 38.61/11.42 |-Branch two: % 38.61/11.42 | (1374) vapp(all_19_6_46, all_19_2_42) = all_0_2_2 % 38.61/11.42 | (1665) all_19_6_46 = all_18_5_33 % 38.61/11.42 | % 38.61/11.42 | Combining equations (163,1665) yields a new equation: % 38.61/11.42 | (1666) all_18_5_33 = ve1 % 38.61/11.42 | % 38.61/11.42 | Combining equations (1666,1665) yields a new equation: % 38.61/11.42 | (163) all_19_6_46 = ve1 % 38.61/11.42 | % 38.61/11.42 | From (163)(1094) and (1374) follows: % 38.61/11.42 | (1095) vapp(ve1, all_0_2_2) = all_0_2_2 % 38.61/11.42 | % 38.61/11.42 | From (1666) and (1600) follows: % 38.61/11.42 | (1669) vapp(ve1, all_18_9_37) = all_0_2_2 % 38.61/11.42 | % 38.61/11.42 +-Applying beta-rule and splitting (1643), into two cases. % 38.61/11.42 |-Branch one: % 38.61/11.42 | (1371) ~ (vapp(all_19_6_46, all_19_2_42) = all_0_2_2) % 38.61/11.42 | % 38.61/11.42 | From (163)(1094) and (1371) follows: % 38.61/11.42 | (1662) ~ (vapp(ve1, all_0_2_2) = all_0_2_2) % 38.61/11.42 | % 38.61/11.42 | Using (1095) and (1662) yields: % 38.61/11.42 | (130) $false % 38.61/11.42 | % 38.61/11.42 |-The branch is then unsatisfiable % 38.61/11.42 |-Branch two: % 38.61/11.42 | (1374) vapp(all_19_6_46, all_19_2_42) = all_0_2_2 % 38.61/11.42 | (1674) all_19_2_42 = all_18_9_37 % 38.61/11.42 | % 38.61/11.42 | Combining equations (1674,1094) yields a new equation: % 38.61/11.42 | (1675) all_18_9_37 = all_0_2_2 % 38.61/11.42 | % 38.61/11.42 | Simplifying 1675 yields: % 38.61/11.42 | (1676) all_18_9_37 = all_0_2_2 % 38.61/11.42 | % 38.61/11.42 | From (1676) and (1669) follows: % 38.61/11.42 | (1095) vapp(ve1, all_0_2_2) = all_0_2_2 % 38.61/11.42 | % 38.61/11.42 +-Applying beta-rule and splitting (1604), into two cases. % 38.61/11.42 |-Branch one: % 38.61/11.42 | (1678) ~ (vapp(ve1, all_18_9_37) = all_0_2_2) % 38.61/11.42 | % 38.61/11.42 | From (1676) and (1678) follows: % 38.61/11.42 | (1662) ~ (vapp(ve1, all_0_2_2) = all_0_2_2) % 38.61/11.42 | % 38.61/11.42 | Using (1095) and (1662) yields: % 38.61/11.42 | (130) $false % 38.61/11.42 | % 38.61/11.42 |-The branch is then unsatisfiable % 38.61/11.42 |-Branch two: % 38.61/11.42 | (1669) vapp(ve1, all_18_9_37) = all_0_2_2 % 38.61/11.42 | (1682) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, all_18_9_37, all_16_5_13) = v0) % 38.61/11.42 | % 38.61/11.42 +-Applying beta-rule and splitting (1682), into two cases. % 38.61/11.42 |-Branch one: % 38.61/11.42 | (298) all_0_0_0 = 0 % 38.61/11.42 | % 38.61/11.42 | Equations (298) can reduce 36 to: % 38.61/11.42 | (228) $false % 38.61/11.42 | % 38.61/11.42 |-The branch is then unsatisfiable % 38.61/11.42 |-Branch two: % 38.61/11.42 | (36) ~ (all_0_0_0 = 0) % 38.61/11.42 | (1686) ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, all_18_9_37, all_16_5_13) = v0) % 38.61/11.42 | % 38.61/11.42 | Instantiating (1686) with all_158_0_1128 yields: % 38.61/11.42 | (1687) ~ (all_158_0_1128 = 0) & vtcheck(all_0_3_3, all_18_9_37, all_16_5_13) = all_158_0_1128 % 38.61/11.42 | % 38.61/11.42 | Applying alpha-rule on (1687) yields: % 38.61/11.42 | (1688) ~ (all_158_0_1128 = 0) % 38.61/11.42 | (1689) vtcheck(all_0_3_3, all_18_9_37, all_16_5_13) = all_158_0_1128 % 38.61/11.42 | % 38.61/11.42 | From (1676) and (1689) follows: % 38.61/11.42 | (1690) vtcheck(all_0_3_3, all_0_2_2, all_16_5_13) = all_158_0_1128 % 38.61/11.42 | % 38.61/11.42 | Instantiating formula (91) with all_0_3_3, all_0_2_2, all_16_5_13, all_158_0_1128, 0 and discharging atoms vtcheck(all_0_3_3, all_0_2_2, all_16_5_13) = all_158_0_1128, vtcheck(all_0_3_3, all_0_2_2, all_16_5_13) = 0, yields: % 38.61/11.42 | (1691) all_158_0_1128 = 0 % 38.61/11.42 | % 38.61/11.42 | Equations (1691) can reduce 1688 to: % 38.61/11.42 | (228) $false % 38.61/11.42 | % 38.61/11.42 |-The branch is then unsatisfiable % 38.61/11.42 |-Branch two: % 38.61/11.42 | (390) all_19_3_43 = all_0_4_4 & all_19_6_46 = 0 & all_19_7_47 = all_19_10_50 & all_19_8_48 = all_0_5_5 & vreduce(all_19_11_51) = all_19_10_50 & vgetSomeExp(all_19_10_50) = all_19_5_45 & visSomeExp(all_19_10_50) = 0 & vsomeExp(all_19_4_44) = all_0_4_4 & vapp(all_19_5_45, all_19_9_49) = all_19_4_44 & vapp(all_19_11_51, all_19_9_49) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51) % 38.61/11.42 | % 38.61/11.42 | Applying alpha-rule on (390) yields: % 38.61/11.42 | (391) all_19_8_48 = all_0_5_5 % 38.61/11.42 | (392) vsomeExp(all_19_4_44) = all_0_4_4 % 38.61/11.42 | (393) vreduce(all_19_11_51) = all_19_10_50 % 38.61/11.42 | (394) all_19_7_47 = all_19_10_50 % 38.61/11.42 | (395) vapp(all_19_11_51, all_19_9_49) = all_0_5_5 % 38.61/11.42 | (396) all_19_6_46 = 0 % 38.61/11.42 | (397) visSomeExp(all_19_10_50) = 0 % 38.61/11.42 | (398) vapp(all_19_5_45, all_19_9_49) = all_19_4_44 % 38.61/11.43 | (399) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_11_51) % 38.61/11.43 | (400) all_19_3_43 = all_0_4_4 % 38.61/11.43 | (401) vgetSomeExp(all_19_10_50) = all_19_5_45 % 38.61/11.43 | % 38.61/11.43 | From (993) and (392) follows: % 38.61/11.43 | (1118) vsomeExp(all_19_4_44) = all_0_6_6 % 38.61/11.43 | % 38.61/11.43 | Instantiating formula (59) with ve1, all_19_10_50, all_0_7_7 and discharging atoms vreduce(ve1) = all_0_7_7, yields: % 38.61/11.43 | (402) all_19_10_50 = all_0_7_7 | ~ (vreduce(ve1) = all_19_10_50) % 38.61/11.43 | % 38.61/11.43 | Using (397) and (17) yields: % 38.61/11.43 | (403) ~ (all_19_10_50 = vnoExp) % 38.61/11.43 | % 38.61/11.43 | Instantiating formula (50) with all_0_6_6, all_19_4_44, all_0_2_2 and discharging atoms vsomeExp(all_19_4_44) = all_0_6_6, vsomeExp(all_0_2_2) = all_0_6_6, yields: % 38.61/11.43 | (404) all_19_4_44 = all_0_2_2 % 38.61/11.43 | % 38.61/11.43 | Instantiating formula (18) with all_0_2_2, all_19_9_49, all_19_5_45, all_18_9_37, all_18_5_33 and discharging atoms vapp(all_18_5_33, all_18_9_37) = all_0_2_2, yields: % 38.61/11.43 | (1709) all_19_9_49 = all_18_9_37 | ~ (vapp(all_19_5_45, all_19_9_49) = all_0_2_2) % 38.61/11.43 | % 38.61/11.43 | Instantiating formula (20) with all_0_2_2, all_19_9_49, all_19_5_45, all_18_9_37, all_18_5_33 and discharging atoms vapp(all_18_5_33, all_18_9_37) = all_0_2_2, yields: % 38.61/11.43 | (1710) all_19_5_45 = all_18_5_33 | ~ (vapp(all_19_5_45, all_19_9_49) = all_0_2_2) % 38.61/11.43 | % 38.61/11.43 | Instantiating formula (18) with all_0_5_5, all_19_9_49, all_19_11_51, ve2, ve1 and discharging atoms vapp(all_19_11_51, all_19_9_49) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.61/11.43 | (405) all_19_9_49 = ve2 % 38.61/11.43 | % 38.61/11.43 | Instantiating formula (20) with all_0_5_5, all_19_9_49, all_19_11_51, ve2, ve1 and discharging atoms vapp(all_19_11_51, all_19_9_49) = all_0_5_5, vapp(ve1, ve2) = all_0_5_5, yields: % 38.61/11.43 | (406) all_19_11_51 = ve1 % 38.61/11.43 | % 38.61/11.43 | From (406) and (393) follows: % 38.61/11.43 | (407) vreduce(ve1) = all_19_10_50 % 38.61/11.43 | % 38.61/11.43 | From (405)(404) and (398) follows: % 38.61/11.43 | (408) vapp(all_19_5_45, ve2) = all_0_2_2 % 38.61/11.43 | % 38.61/11.43 +-Applying beta-rule and splitting (402), into two cases. % 38.61/11.43 |-Branch one: % 38.61/11.43 | (409) ~ (vreduce(ve1) = all_19_10_50) % 38.61/11.43 | % 38.61/11.43 | Using (407) and (409) yields: % 38.61/11.43 | (130) $false % 38.61/11.43 | % 38.61/11.43 |-The branch is then unsatisfiable % 38.61/11.43 |-Branch two: % 38.61/11.43 | (407) vreduce(ve1) = all_19_10_50 % 38.61/11.43 | (412) all_19_10_50 = all_0_7_7 % 38.61/11.43 | % 38.61/11.43 | Equations (412) can reduce 403 to: % 38.61/11.43 | (413) ~ (all_0_7_7 = vnoExp) % 38.61/11.43 | % 38.61/11.43 | From (412) and (401) follows: % 38.61/11.43 | (414) vgetSomeExp(all_0_7_7) = all_19_5_45 % 38.61/11.43 | % 38.61/11.43 +-Applying beta-rule and splitting (1710), into two cases. % 38.61/11.43 |-Branch one: % 38.61/11.43 | (1433) ~ (vapp(all_19_5_45, all_19_9_49) = all_0_2_2) % 38.61/11.43 | % 38.61/11.43 | From (405) and (1433) follows: % 38.61/11.43 | (1434) ~ (vapp(all_19_5_45, ve2) = all_0_2_2) % 38.61/11.43 | % 38.61/11.43 | Using (408) and (1434) yields: % 38.61/11.43 | (130) $false % 38.61/11.43 | % 38.61/11.43 |-The branch is then unsatisfiable % 38.61/11.43 |-Branch two: % 38.61/11.43 | (1436) vapp(all_19_5_45, all_19_9_49) = all_0_2_2 % 38.61/11.43 | (1725) all_19_5_45 = all_18_5_33 % 38.61/11.43 | % 38.61/11.43 | From (1725) and (414) follows: % 38.61/11.43 | (1726) vgetSomeExp(all_0_7_7) = all_18_5_33 % 38.61/11.43 | % 38.61/11.43 | From (1725) and (408) follows: % 38.61/11.43 | (1727) vapp(all_18_5_33, ve2) = all_0_2_2 % 38.61/11.43 | % 38.61/11.43 +-Applying beta-rule and splitting (1709), into two cases. % 38.61/11.43 |-Branch one: % 38.61/11.43 | (1433) ~ (vapp(all_19_5_45, all_19_9_49) = all_0_2_2) % 38.61/11.43 | % 38.61/11.43 | From (1725)(405) and (1433) follows: % 38.61/11.43 | (1729) ~ (vapp(all_18_5_33, ve2) = all_0_2_2) % 38.61/11.43 | % 38.61/11.43 | Using (1727) and (1729) yields: % 38.61/11.43 | (130) $false % 38.61/11.43 | % 38.61/11.43 |-The branch is then unsatisfiable % 38.61/11.43 |-Branch two: % 38.61/11.43 | (1436) vapp(all_19_5_45, all_19_9_49) = all_0_2_2 % 38.61/11.43 | (1732) all_19_9_49 = all_18_9_37 % 38.61/11.43 | % 38.61/11.43 | Combining equations (405,1732) yields a new equation: % 38.61/11.43 | (1733) all_18_9_37 = ve2 % 38.61/11.43 | % 38.61/11.43 | From (1733) and (1600) follows: % 38.61/11.43 | (1727) vapp(all_18_5_33, ve2) = all_0_2_2 % 38.61/11.43 | % 38.61/11.43 +-Applying beta-rule and splitting (1603), into two cases. % 38.61/11.43 |-Branch one: % 38.61/11.43 | (1735) ~ (vgetSomeExp(all_0_7_7) = all_18_5_33) % 38.61/11.43 | % 38.61/11.43 | Using (1726) and (1735) yields: % 38.61/11.43 | (130) $false % 38.61/11.43 | % 38.61/11.43 |-The branch is then unsatisfiable % 38.61/11.43 |-Branch two: % 38.61/11.43 | (1726) vgetSomeExp(all_0_7_7) = all_18_5_33 % 38.61/11.43 | (1738) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = ve1 & vabs(v0, v1, v2) = ve1) | (visSomeExp(all_0_7_7) = v1 & vsomeExp(all_0_2_2) = v2 & vapp(ve1, all_18_9_37) = v0 & ( ~ (v1 = 0) | ~ (v0 = ve1) | v2 = all_0_7_7))) % 38.61/11.43 | % 38.61/11.43 +-Applying beta-rule and splitting (1602), into two cases. % 38.61/11.43 |-Branch one: % 38.61/11.43 | (1735) ~ (vgetSomeExp(all_0_7_7) = all_18_5_33) % 38.61/11.43 | % 38.61/11.43 | Using (1726) and (1735) yields: % 38.61/11.43 | (130) $false % 38.61/11.43 | % 38.61/11.43 |-The branch is then unsatisfiable % 38.61/11.43 |-Branch two: % 38.61/11.43 | (1726) vgetSomeExp(all_0_7_7) = all_18_5_33 % 38.61/11.43 | (1742) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = ve1 & vabs(v0, v1, v2) = ve1) | (visSomeExp(all_0_7_7) = v1 & vsomeExp(all_0_2_2) = v2 & vapp(ve1, all_18_9_37) = v0 & ( ~ (v1 = 0) | ~ (v0 = ve2) | v2 = all_0_6_6))) % 38.61/11.43 | % 38.61/11.43 +-Applying beta-rule and splitting (1601), into two cases. % 38.61/11.43 |-Branch one: % 38.61/11.43 | (1735) ~ (vgetSomeExp(all_0_7_7) = all_18_5_33) % 38.61/11.43 | % 38.61/11.43 | Using (1726) and (1735) yields: % 38.61/11.43 | (130) $false % 38.61/11.43 | % 38.61/11.43 |-The branch is then unsatisfiable % 38.61/11.43 |-Branch two: % 38.61/11.43 | (1726) vgetSomeExp(all_0_7_7) = all_18_5_33 % 38.61/11.43 | (1746) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = ve1 & vabs(v0, v1, v2) = ve1) | (visSomeExp(all_0_7_7) = v1 & vsomeExp(all_0_2_2) = v2 & vapp(ve1, all_18_9_37) = v0 & ( ~ (v1 = 0) | ~ (v0 = all_0_5_5) | v2 = all_0_6_6))) % 38.61/11.43 | % 38.61/11.43 +-Applying beta-rule and splitting (114), into two cases. % 38.61/11.43 |-Branch one: % 38.61/11.43 | (415) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) | (all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22) | (all_17_7_23 = all_17_9_25 & all_17_8_24 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_6_22 = 0) & vreduce(all_17_10_26) = all_17_9_25 & visSomeExp(all_17_9_25) = all_17_6_22 & vapp(all_17_10_26, all_17_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26)) | (all_17_8_24 = ve1 & all_0_7_7 = vnoExp & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1) % 38.61/11.43 | % 38.61/11.43 +-Applying beta-rule and splitting (415), into two cases. % 38.61/11.43 |-Branch one: % 38.61/11.43 | (416) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) | (all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22) | (all_17_7_23 = all_17_9_25 & all_17_8_24 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_6_22 = 0) & vreduce(all_17_10_26) = all_17_9_25 & visSomeExp(all_17_9_25) = all_17_6_22 & vapp(all_17_10_26, all_17_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26)) % 38.61/11.43 | % 38.61/11.43 +-Applying beta-rule and splitting (416), into two cases. % 38.61/11.43 |-Branch one: % 38.61/11.43 | (417) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) | (all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22) % 38.61/11.43 | % 38.61/11.43 +-Applying beta-rule and splitting (417), into two cases. % 38.61/11.43 |-Branch one: % 38.61/11.43 | (418) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) | (all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27)) % 38.61/11.43 | % 38.61/11.43 +-Applying beta-rule and splitting (418), into two cases. % 38.61/11.43 |-Branch one: % 38.61/11.43 | (419) (all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22) | (all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22) % 38.61/11.43 | % 38.61/11.43 +-Applying beta-rule and splitting (419), into two cases. % 38.61/11.43 |-Branch one: % 38.61/11.43 | (420) all_17_0_16 = all_0_7_7 & all_17_2_18 = 0 & all_17_4_20 = all_17_10_26 & all_17_5_21 = ve1 & ~ (all_17_3_19 = 0) & vreduce(all_17_8_24) = all_17_10_26 & visSomeExp(all_17_10_26) = all_17_3_19 & vsomeExp(all_17_1_17) = all_0_7_7 & vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 & visValue(all_17_8_24) = 0 & vapp(all_17_6_22, all_17_8_24) = ve1 & vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22 % 38.61/11.43 | % 38.61/11.43 | Applying alpha-rule on (420) yields: % 38.61/11.43 | (421) vsubst(all_17_9_25, all_17_8_24, all_17_7_23) = all_17_1_17 % 38.61/11.43 | (422) all_17_4_20 = all_17_10_26 % 38.61/11.43 | (423) ~ (all_17_3_19 = 0) % 38.61/11.43 | (424) vapp(all_17_6_22, all_17_8_24) = ve1 % 38.61/11.43 | (425) vreduce(all_17_8_24) = all_17_10_26 % 38.61/11.43 | (426) visSomeExp(all_17_10_26) = all_17_3_19 % 38.61/11.43 | (427) all_17_5_21 = ve1 % 38.61/11.43 | (428) vsomeExp(all_17_1_17) = all_0_7_7 % 38.61/11.43 | (429) all_17_2_18 = 0 % 38.61/11.43 | (430) vabs(all_17_9_25, all_17_11_27, all_17_7_23) = all_17_6_22 % 38.61/11.43 | (431) all_17_0_16 = all_0_7_7 % 38.61/11.43 | (432) visValue(all_17_8_24) = 0 % 38.61/11.43 | % 38.61/11.43 | Instantiating formula (32) with all_17_1_17, all_18_5_33, all_0_7_7 and discharging atoms vgetSomeExp(all_0_7_7) = all_18_5_33, vsomeExp(all_17_1_17) = all_0_7_7, yields: % 38.61/11.43 | (1765) all_18_5_33 = all_17_1_17 % 38.61/11.43 | % 38.61/11.43 | From (1765) and (1727) follows: % 38.61/11.43 | (434) vapp(all_17_1_17, ve2) = all_0_2_2 % 38.61/11.43 | % 38.61/11.43 | Instantiating formula (31) with all_16_3_11, all_17_1_17, all_0_3_3 and discharging atoms vsomeExp(all_17_1_17) = all_0_7_7, vtcheck(all_0_3_3, ve1, all_16_3_11) = 0, yields: % 38.61/11.43 | (435) vtcheck(all_0_3_3, all_17_1_17, all_16_3_11) = 0 % 38.61/11.43 | % 38.61/11.43 | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_16_3_11, all_0_1_1, ve2, all_17_1_17, all_0_3_3, all_16_5_13 and discharging atoms varrow(all_16_5_13, all_0_1_1) = all_16_3_11, vtcheck(all_0_3_3, all_17_1_17, all_16_3_11) = 0, vtcheck(all_0_3_3, all_0_2_2, all_0_1_1) = all_0_0_0, vapp(all_17_1_17, ve2) = all_0_2_2, yields: % 38.61/11.44 | (436) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.61/11.44 | % 38.61/11.44 +-Applying beta-rule and splitting (436), into two cases. % 38.61/11.44 |-Branch one: % 38.61/11.44 | (298) all_0_0_0 = 0 % 38.61/11.44 | % 38.61/11.44 | Equations (298) can reduce 36 to: % 38.61/11.44 | (228) $false % 38.61/11.44 | % 38.61/11.44 |-The branch is then unsatisfiable % 38.61/11.44 |-Branch two: % 38.61/11.44 | (36) ~ (all_0_0_0 = 0) % 38.61/11.44 | (440) ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.61/11.44 | % 38.61/11.44 | Instantiating (440) with all_218_0_1202 yields: % 38.61/11.44 | (1773) ~ (all_218_0_1202 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = all_218_0_1202 % 38.61/11.44 | % 38.61/11.44 | Applying alpha-rule on (1773) yields: % 38.61/11.44 | (1774) ~ (all_218_0_1202 = 0) % 38.61/11.44 | (1775) vtcheck(all_0_3_3, ve2, all_16_5_13) = all_218_0_1202 % 38.61/11.44 | % 38.61/11.44 | Instantiating formula (91) with all_0_3_3, ve2, all_16_5_13, all_218_0_1202, 0 and discharging atoms vtcheck(all_0_3_3, ve2, all_16_5_13) = all_218_0_1202, vtcheck(all_0_3_3, ve2, all_16_5_13) = 0, yields: % 38.61/11.44 | (1776) all_218_0_1202 = 0 % 38.61/11.44 | % 38.61/11.44 | Equations (1776) can reduce 1774 to: % 38.61/11.44 | (228) $false % 38.61/11.44 | % 38.61/11.44 |-The branch is then unsatisfiable % 38.61/11.44 |-Branch two: % 38.61/11.44 | (446) all_17_0_16 = all_0_7_7 & all_17_3_19 = 0 & all_17_4_20 = all_17_7_23 & all_17_5_21 = ve1 & vreduce(all_17_11_27) = all_17_7_23 & vgetSomeExp(all_17_7_23) = all_17_2_18 & visSomeExp(all_17_7_23) = 0 & vsomeExp(all_17_1_17) = all_0_7_7 & vapp(all_17_6_22, all_17_2_18) = all_17_1_17 & vapp(all_17_6_22, all_17_11_27) = ve1 & vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22 % 38.61/11.44 | % 38.61/11.44 | Applying alpha-rule on (446) yields: % 38.61/11.44 | (447) vgetSomeExp(all_17_7_23) = all_17_2_18 % 38.61/11.44 | (448) vabs(all_17_10_26, all_17_9_25, all_17_8_24) = all_17_6_22 % 38.61/11.44 | (449) vreduce(all_17_11_27) = all_17_7_23 % 38.61/11.44 | (450) all_17_3_19 = 0 % 38.61/11.44 | (451) vapp(all_17_6_22, all_17_11_27) = ve1 % 38.61/11.44 | (452) visSomeExp(all_17_7_23) = 0 % 38.61/11.44 | (453) all_17_4_20 = all_17_7_23 % 38.61/11.44 | (427) all_17_5_21 = ve1 % 38.61/11.44 | (428) vsomeExp(all_17_1_17) = all_0_7_7 % 38.61/11.44 | (431) all_17_0_16 = all_0_7_7 % 38.61/11.44 | (457) vapp(all_17_6_22, all_17_2_18) = all_17_1_17 % 38.61/11.44 | % 38.61/11.44 | Instantiating formula (32) with all_17_1_17, all_18_5_33, all_0_7_7 and discharging atoms vgetSomeExp(all_0_7_7) = all_18_5_33, vsomeExp(all_17_1_17) = all_0_7_7, yields: % 38.61/11.44 | (1765) all_18_5_33 = all_17_1_17 % 38.61/11.44 | % 38.61/11.44 | From (1765) and (1727) follows: % 38.61/11.44 | (434) vapp(all_17_1_17, ve2) = all_0_2_2 % 38.61/11.44 | % 38.61/11.44 | Instantiating formula (31) with all_16_3_11, all_17_1_17, all_0_3_3 and discharging atoms vsomeExp(all_17_1_17) = all_0_7_7, vtcheck(all_0_3_3, ve1, all_16_3_11) = 0, yields: % 38.61/11.44 | (435) vtcheck(all_0_3_3, all_17_1_17, all_16_3_11) = 0 % 38.61/11.44 | % 38.61/11.44 +-Applying beta-rule and splitting (1023), into two cases. % 38.61/11.44 |-Branch one: % 38.61/11.44 | (1178) (all_91_0_620 = 0 & all_91_2_622 = all_16_5_13 & all_91_3_623 = all_0_2_2 & varrow(all_91_5_625, all_91_4_624) = all_16_5_13 & vtcheck(all_91_1_621, all_91_6_626, all_91_4_624) = 0 & vbind(all_91_7_627, all_91_5_625, all_0_3_3) = all_91_1_621 & vabs(all_91_7_627, all_91_5_625, all_91_6_626) = all_0_2_2) | (all_91_1_621 = 0 & all_91_2_622 = 0 & all_91_4_624 = all_0_2_2 & varrow(all_91_5_625, all_16_5_13) = all_91_3_623 & vtcheck(all_0_3_3, all_91_6_626, all_91_5_625) = 0 & vtcheck(all_0_3_3, all_91_7_627, all_91_3_623) = 0 & vapp(all_91_7_627, all_91_6_626) = all_0_2_2) % 38.61/11.44 | % 38.61/11.44 +-Applying beta-rule and splitting (1178), into two cases. % 38.61/11.44 |-Branch one: % 38.61/11.44 | (1179) all_91_0_620 = 0 & all_91_2_622 = all_16_5_13 & all_91_3_623 = all_0_2_2 & varrow(all_91_5_625, all_91_4_624) = all_16_5_13 & vtcheck(all_91_1_621, all_91_6_626, all_91_4_624) = 0 & vbind(all_91_7_627, all_91_5_625, all_0_3_3) = all_91_1_621 & vabs(all_91_7_627, all_91_5_625, all_91_6_626) = all_0_2_2 % 38.61/11.44 | % 38.61/11.44 | Applying alpha-rule on (1179) yields: % 38.61/11.44 | (1180) vabs(all_91_7_627, all_91_5_625, all_91_6_626) = all_0_2_2 % 38.61/11.44 | (1181) vbind(all_91_7_627, all_91_5_625, all_0_3_3) = all_91_1_621 % 38.61/11.44 | (1182) all_91_0_620 = 0 % 38.61/11.44 | (1183) varrow(all_91_5_625, all_91_4_624) = all_16_5_13 % 38.61/11.44 | (1184) all_91_2_622 = all_16_5_13 % 38.61/11.44 | (1185) vtcheck(all_91_1_621, all_91_6_626, all_91_4_624) = 0 % 38.61/11.44 | (1186) all_91_3_623 = all_0_2_2 % 38.61/11.44 | % 38.61/11.44 | Instantiating formula (55) with all_0_2_2, ve2, all_17_1_17, all_91_6_626, all_91_5_625, all_91_7_627 and discharging atoms vapp(all_17_1_17, ve2) = all_0_2_2, vabs(all_91_7_627, all_91_5_625, all_91_6_626) = all_0_2_2, yields: % 38.61/11.44 | (130) $false % 38.61/11.44 | % 38.61/11.44 |-The branch is then unsatisfiable % 38.61/11.44 |-Branch two: % 38.61/11.44 | (1188) all_91_1_621 = 0 & all_91_2_622 = 0 & all_91_4_624 = all_0_2_2 & varrow(all_91_5_625, all_16_5_13) = all_91_3_623 & vtcheck(all_0_3_3, all_91_6_626, all_91_5_625) = 0 & vtcheck(all_0_3_3, all_91_7_627, all_91_3_623) = 0 & vapp(all_91_7_627, all_91_6_626) = all_0_2_2 % 38.61/11.44 | % 38.61/11.44 | Applying alpha-rule on (1188) yields: % 38.61/11.44 | (1189) all_91_2_622 = 0 % 38.61/11.44 | (1190) all_91_1_621 = 0 % 38.61/11.44 | (1191) all_91_4_624 = all_0_2_2 % 38.61/11.44 | (1192) vapp(all_91_7_627, all_91_6_626) = all_0_2_2 % 38.61/11.44 | (1193) vtcheck(all_0_3_3, all_91_7_627, all_91_3_623) = 0 % 38.61/11.44 | (1194) varrow(all_91_5_625, all_16_5_13) = all_91_3_623 % 38.61/11.44 | (1195) vtcheck(all_0_3_3, all_91_6_626, all_91_5_625) = 0 % 38.61/11.44 | % 38.61/11.44 | Instantiating formula (18) with all_0_2_2, all_91_6_626, all_91_7_627, ve2, all_17_1_17 and discharging atoms vapp(all_91_7_627, all_91_6_626) = all_0_2_2, vapp(all_17_1_17, ve2) = all_0_2_2, yields: % 38.61/11.44 | (1196) all_91_6_626 = ve2 % 38.61/11.44 | % 38.61/11.44 | Instantiating formula (20) with all_0_2_2, all_91_6_626, all_91_7_627, ve2, all_17_1_17 and discharging atoms vapp(all_91_7_627, all_91_6_626) = all_0_2_2, vapp(all_17_1_17, ve2) = all_0_2_2, yields: % 38.61/11.44 | (1197) all_91_7_627 = all_17_1_17 % 38.61/11.44 | % 38.61/11.44 | From (1197)(1196) and (1192) follows: % 38.61/11.44 | (434) vapp(all_17_1_17, ve2) = all_0_2_2 % 38.61/11.44 | % 38.61/11.44 | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_16_3_11, all_0_1_1, ve2, all_17_1_17, all_0_3_3, all_16_5_13 and discharging atoms varrow(all_16_5_13, all_0_1_1) = all_16_3_11, vtcheck(all_0_3_3, all_17_1_17, all_16_3_11) = 0, vtcheck(all_0_3_3, all_0_2_2, all_0_1_1) = all_0_0_0, vapp(all_17_1_17, ve2) = all_0_2_2, yields: % 38.61/11.44 | (436) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.61/11.44 | % 38.61/11.44 +-Applying beta-rule and splitting (436), into two cases. % 38.61/11.44 |-Branch one: % 38.61/11.44 | (298) all_0_0_0 = 0 % 38.61/11.44 | % 38.61/11.44 | Equations (298) can reduce 36 to: % 38.61/11.44 | (228) $false % 38.61/11.44 | % 38.61/11.44 |-The branch is then unsatisfiable % 38.61/11.44 |-Branch two: % 38.61/11.44 | (36) ~ (all_0_0_0 = 0) % 38.61/11.44 | (440) ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.61/11.44 | % 38.61/11.44 | Instantiating (440) with all_313_0_1279 yields: % 38.61/11.44 | (1819) ~ (all_313_0_1279 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = all_313_0_1279 % 38.61/11.44 | % 38.61/11.44 | Applying alpha-rule on (1819) yields: % 38.61/11.44 | (1820) ~ (all_313_0_1279 = 0) % 38.61/11.44 | (1821) vtcheck(all_0_3_3, ve2, all_16_5_13) = all_313_0_1279 % 38.61/11.44 | % 38.61/11.44 | Instantiating formula (91) with all_0_3_3, ve2, all_16_5_13, all_313_0_1279, 0 and discharging atoms vtcheck(all_0_3_3, ve2, all_16_5_13) = all_313_0_1279, vtcheck(all_0_3_3, ve2, all_16_5_13) = 0, yields: % 38.61/11.44 | (1822) all_313_0_1279 = 0 % 38.61/11.44 | % 38.61/11.44 | Equations (1822) can reduce 1820 to: % 38.61/11.44 | (228) $false % 38.61/11.44 | % 38.61/11.44 |-The branch is then unsatisfiable % 38.61/11.44 |-Branch two: % 38.61/11.44 | (1209) all_91_4_624 = all_91_7_627 & all_91_5_625 = all_0_2_2 & vlookup(all_91_6_626, all_0_3_3) = all_91_7_627 & vsomeType(all_16_5_13) = all_91_7_627 & vvar(all_91_6_626) = all_0_2_2 % 38.61/11.44 | % 38.61/11.44 | Applying alpha-rule on (1209) yields: % 38.61/11.44 | (1210) all_91_4_624 = all_91_7_627 % 38.61/11.44 | (1211) all_91_5_625 = all_0_2_2 % 38.61/11.44 | (1212) vlookup(all_91_6_626, all_0_3_3) = all_91_7_627 % 38.61/11.44 | (1213) vsomeType(all_16_5_13) = all_91_7_627 % 38.61/11.44 | (1214) vvar(all_91_6_626) = all_0_2_2 % 38.61/11.44 | % 38.61/11.44 | Instantiating formula (6) with all_0_2_2, ve2, all_17_1_17, all_91_6_626 and discharging atoms vapp(all_17_1_17, ve2) = all_0_2_2, vvar(all_91_6_626) = all_0_2_2, yields: % 38.61/11.44 | (130) $false % 38.61/11.44 | % 38.61/11.44 |-The branch is then unsatisfiable % 38.61/11.44 |-Branch two: % 38.61/11.44 | (471) all_17_3_19 = all_0_7_7 & all_17_6_22 = 0 & all_17_7_23 = all_17_10_26 & all_17_8_24 = ve1 & vreduce(all_17_11_27) = all_17_10_26 & vgetSomeExp(all_17_10_26) = all_17_5_21 & visSomeExp(all_17_10_26) = 0 & vsomeExp(all_17_4_20) = all_0_7_7 & vapp(all_17_5_21, all_17_9_25) = all_17_4_20 & vapp(all_17_11_27, all_17_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27) % 38.61/11.44 | % 38.61/11.44 | Applying alpha-rule on (471) yields: % 38.61/11.44 | (472) vapp(all_17_11_27, all_17_9_25) = ve1 % 38.61/11.44 | (473) vreduce(all_17_11_27) = all_17_10_26 % 38.61/11.44 | (474) vapp(all_17_5_21, all_17_9_25) = all_17_4_20 % 38.61/11.44 | (475) all_17_7_23 = all_17_10_26 % 38.61/11.44 | (476) vgetSomeExp(all_17_10_26) = all_17_5_21 % 38.61/11.44 | (477) all_17_6_22 = 0 % 38.61/11.44 | (478) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_11_27) % 38.61/11.44 | (479) all_17_8_24 = ve1 % 38.61/11.44 | (480) all_17_3_19 = all_0_7_7 % 38.61/11.44 | (481) visSomeExp(all_17_10_26) = 0 % 38.61/11.44 | (482) vsomeExp(all_17_4_20) = all_0_7_7 % 38.61/11.44 | % 38.61/11.44 | Instantiating formula (32) with all_17_4_20, all_18_5_33, all_0_7_7 and discharging atoms vgetSomeExp(all_0_7_7) = all_18_5_33, vsomeExp(all_17_4_20) = all_0_7_7, yields: % 38.61/11.44 | (1843) all_18_5_33 = all_17_4_20 % 38.61/11.44 | % 38.61/11.44 | From (1843) and (1727) follows: % 38.61/11.44 | (484) vapp(all_17_4_20, ve2) = all_0_2_2 % 38.61/11.44 | % 38.61/11.44 | Instantiating formula (31) with all_16_3_11, all_17_4_20, all_0_3_3 and discharging atoms vsomeExp(all_17_4_20) = all_0_7_7, vtcheck(all_0_3_3, ve1, all_16_3_11) = 0, yields: % 38.61/11.44 | (485) vtcheck(all_0_3_3, all_17_4_20, all_16_3_11) = 0 % 38.61/11.44 | % 38.61/11.44 | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_16_3_11, all_0_1_1, ve2, all_17_4_20, all_0_3_3, all_16_5_13 and discharging atoms varrow(all_16_5_13, all_0_1_1) = all_16_3_11, vtcheck(all_0_3_3, all_17_4_20, all_16_3_11) = 0, vtcheck(all_0_3_3, all_0_2_2, all_0_1_1) = all_0_0_0, vapp(all_17_4_20, ve2) = all_0_2_2, yields: % 38.61/11.44 | (436) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.61/11.44 | % 38.61/11.44 +-Applying beta-rule and splitting (436), into two cases. % 38.61/11.44 |-Branch one: % 38.61/11.44 | (298) all_0_0_0 = 0 % 38.61/11.44 | % 38.61/11.44 | Equations (298) can reduce 36 to: % 38.61/11.44 | (228) $false % 38.61/11.44 | % 38.61/11.44 |-The branch is then unsatisfiable % 38.61/11.44 |-Branch two: % 38.61/11.44 | (36) ~ (all_0_0_0 = 0) % 38.61/11.44 | (440) ? [v0] : ( ~ (v0 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = v0) % 38.61/11.44 | % 38.61/11.44 | Instantiating (440) with all_180_0_1329 yields: % 38.61/11.44 | (1851) ~ (all_180_0_1329 = 0) & vtcheck(all_0_3_3, ve2, all_16_5_13) = all_180_0_1329 % 38.61/11.44 | % 38.61/11.44 | Applying alpha-rule on (1851) yields: % 38.61/11.44 | (1852) ~ (all_180_0_1329 = 0) % 38.61/11.44 | (1853) vtcheck(all_0_3_3, ve2, all_16_5_13) = all_180_0_1329 % 38.61/11.44 | % 38.61/11.44 | Instantiating formula (91) with all_0_3_3, ve2, all_16_5_13, all_180_0_1329, 0 and discharging atoms vtcheck(all_0_3_3, ve2, all_16_5_13) = all_180_0_1329, vtcheck(all_0_3_3, ve2, all_16_5_13) = 0, yields: % 38.61/11.44 | (1854) all_180_0_1329 = 0 % 38.61/11.44 | % 38.61/11.44 | Equations (1854) can reduce 1852 to: % 38.61/11.44 | (228) $false % 38.61/11.44 | % 38.61/11.44 |-The branch is then unsatisfiable % 38.61/11.44 |-Branch two: % 38.61/11.44 | (496) all_17_4_20 = all_17_8_24 & all_17_5_21 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_2_18 = 0) & ~ (all_17_3_19 = 0) & vreduce(all_17_7_23) = all_17_8_24 & visSomeExp(all_17_8_24) = all_17_3_19 & visValue(all_17_7_23) = all_17_2_18 & vapp(all_17_6_22, all_17_7_23) = ve1 & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22 % 38.61/11.44 | % 38.61/11.44 | Applying alpha-rule on (496) yields: % 38.61/11.44 | (497) visValue(all_17_7_23) = all_17_2_18 % 38.61/11.44 | (498) visSomeExp(all_17_8_24) = all_17_3_19 % 38.61/11.44 | (423) ~ (all_17_3_19 = 0) % 38.61/11.44 | (500) all_17_4_20 = all_17_8_24 % 38.61/11.44 | (170) all_0_7_7 = vnoExp % 38.61/11.44 | (502) vapp(all_17_6_22, all_17_7_23) = ve1 % 38.61/11.44 | (427) all_17_5_21 = ve1 % 38.61/11.44 | (504) vabs(all_17_11_27, all_17_10_26, all_17_9_25) = all_17_6_22 % 38.61/11.44 | (505) ~ (all_17_2_18 = 0) % 38.61/11.44 | (506) vreduce(all_17_7_23) = all_17_8_24 % 38.61/11.44 | % 38.61/11.44 | Equations (170) can reduce 413 to: % 38.61/11.44 | (228) $false % 38.61/11.44 | % 38.61/11.44 |-The branch is then unsatisfiable % 38.61/11.44 |-Branch two: % 38.61/11.44 | (508) all_17_7_23 = all_17_9_25 & all_17_8_24 = ve1 & all_0_7_7 = vnoExp & ~ (all_17_6_22 = 0) & vreduce(all_17_10_26) = all_17_9_25 & visSomeExp(all_17_9_25) = all_17_6_22 & vapp(all_17_10_26, all_17_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26) % 38.61/11.44 | % 38.61/11.44 | Applying alpha-rule on (508) yields: % 38.61/11.44 | (509) all_17_7_23 = all_17_9_25 % 38.61/11.44 | (510) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_17_10_26) % 38.61/11.44 | (511) visSomeExp(all_17_9_25) = all_17_6_22 % 38.61/11.44 | (512) ~ (all_17_6_22 = 0) % 38.61/11.44 | (170) all_0_7_7 = vnoExp % 38.61/11.44 | (514) vapp(all_17_10_26, all_17_11_27) = ve1 % 38.61/11.44 | (479) all_17_8_24 = ve1 % 38.61/11.44 | (516) vreduce(all_17_10_26) = all_17_9_25 % 38.61/11.44 | % 38.61/11.44 | Equations (170) can reduce 413 to: % 38.61/11.44 | (228) $false % 38.61/11.44 | % 38.61/11.44 |-The branch is then unsatisfiable % 38.61/11.44 |-Branch two: % 38.61/11.44 | (518) all_17_8_24 = ve1 & all_0_7_7 = vnoExp & vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1 % 38.61/11.44 | % 38.61/11.44 | Applying alpha-rule on (518) yields: % 38.61/11.44 | (479) all_17_8_24 = ve1 % 38.61/11.44 | (170) all_0_7_7 = vnoExp % 38.61/11.44 | (521) vabs(all_17_11_27, all_17_10_26, all_17_9_25) = ve1 % 38.61/11.44 | % 38.61/11.44 | Equations (170) can reduce 413 to: % 38.61/11.44 | (228) $false % 38.61/11.44 | % 38.61/11.44 |-The branch is then unsatisfiable % 38.61/11.44 |-Branch two: % 38.61/11.44 | (523) all_17_10_26 = ve1 & all_0_7_7 = vnoExp & vvar(all_17_11_27) = ve1 % 38.61/11.44 | % 38.61/11.44 | Applying alpha-rule on (523) yields: % 38.61/11.44 | (524) all_17_10_26 = ve1 % 38.61/11.44 | (170) all_0_7_7 = vnoExp % 38.61/11.44 | (526) vvar(all_17_11_27) = ve1 % 38.61/11.44 | % 38.61/11.44 | Equations (170) can reduce 413 to: % 38.61/11.44 | (228) $false % 38.61/11.44 | % 38.61/11.44 |-The branch is then unsatisfiable % 38.61/11.44 |-Branch two: % 38.61/11.44 | (528) all_19_4_44 = all_19_8_48 & all_19_5_45 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_2_42 = 0) & ~ (all_19_3_43 = 0) & vreduce(all_19_7_47) = all_19_8_48 & visSomeExp(all_19_8_48) = all_19_3_43 & visValue(all_19_7_47) = all_19_2_42 & vapp(all_19_6_46, all_19_7_47) = all_0_5_5 & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46 % 38.61/11.45 | % 38.61/11.45 | Applying alpha-rule on (528) yields: % 38.61/11.45 | (529) visValue(all_19_7_47) = all_19_2_42 % 38.61/11.45 | (530) vapp(all_19_6_46, all_19_7_47) = all_0_5_5 % 38.61/11.45 | (531) all_19_4_44 = all_19_8_48 % 38.61/11.45 | (532) vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_19_6_46 % 38.61/11.45 | (533) visSomeExp(all_19_8_48) = all_19_3_43 % 38.61/11.45 | (534) all_0_4_4 = vnoExp % 38.61/11.45 | (535) ~ (all_19_2_42 = 0) % 38.61/11.45 | (160) all_19_5_45 = all_0_5_5 % 38.61/11.45 | (537) vreduce(all_19_7_47) = all_19_8_48 % 38.61/11.45 | (161) ~ (all_19_3_43 = 0) % 38.61/11.45 | % 38.61/11.45 | Combining equations (534,993) yields a new equation: % 38.61/11.45 | (226) all_0_6_6 = vnoExp % 38.61/11.45 | % 38.61/11.45 | Equations (226) can reduce 171 to: % 38.61/11.45 | (228) $false % 38.61/11.45 | % 38.61/11.45 |-The branch is then unsatisfiable % 38.61/11.45 |-Branch two: % 38.61/11.45 | (540) all_19_7_47 = all_19_9_49 & all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & ~ (all_19_6_46 = 0) & vreduce(all_19_10_50) = all_19_9_49 & visSomeExp(all_19_9_49) = all_19_6_46 & vapp(all_19_10_50, all_19_11_51) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50) % 38.61/11.45 | % 38.61/11.45 | Applying alpha-rule on (540) yields: % 38.61/11.45 | (391) all_19_8_48 = all_0_5_5 % 38.61/11.45 | (542) vreduce(all_19_10_50) = all_19_9_49 % 38.61/11.45 | (543) all_19_7_47 = all_19_9_49 % 38.61/11.45 | (544) ~ (all_19_6_46 = 0) % 38.61/11.45 | (534) all_0_4_4 = vnoExp % 38.61/11.45 | (546) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_19_10_50) % 38.61/11.45 | (547) vapp(all_19_10_50, all_19_11_51) = all_0_5_5 % 38.61/11.45 | (548) visSomeExp(all_19_9_49) = all_19_6_46 % 38.61/11.45 | % 38.61/11.45 | Combining equations (534,993) yields a new equation: % 38.61/11.45 | (226) all_0_6_6 = vnoExp % 38.61/11.45 | % 38.61/11.45 | Equations (226) can reduce 171 to: % 38.61/11.45 | (228) $false % 38.61/11.45 | % 38.61/11.45 |-The branch is then unsatisfiable % 38.61/11.45 |-Branch two: % 38.61/11.45 | (550) all_19_8_48 = all_0_5_5 & all_0_4_4 = vnoExp & vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_0_5_5 % 38.61/11.45 | % 38.61/11.45 | Applying alpha-rule on (550) yields: % 38.61/11.45 | (391) all_19_8_48 = all_0_5_5 % 38.61/11.45 | (534) all_0_4_4 = vnoExp % 38.61/11.45 | (553) vabs(all_19_11_51, all_19_10_50, all_19_9_49) = all_0_5_5 % 38.61/11.45 | % 38.61/11.45 | Combining equations (993,534) yields a new equation: % 38.61/11.45 | (1301) all_0_6_6 = vnoExp % 38.61/11.45 | % 38.61/11.45 | Simplifying 1301 yields: % 38.61/11.45 | (226) all_0_6_6 = vnoExp % 38.61/11.45 | % 38.61/11.45 | Equations (226) can reduce 171 to: % 38.61/11.45 | (228) $false % 38.61/11.45 | % 38.61/11.45 |-The branch is then unsatisfiable % 38.61/11.45 |-Branch two: % 38.61/11.45 | (555) all_19_10_50 = all_0_5_5 & all_0_4_4 = vnoExp & vvar(all_19_11_51) = all_0_5_5 % 38.61/11.45 | % 38.61/11.45 | Applying alpha-rule on (555) yields: % 38.61/11.45 | (556) all_19_10_50 = all_0_5_5 % 38.61/11.45 | (534) all_0_4_4 = vnoExp % 38.61/11.45 | (558) vvar(all_19_11_51) = all_0_5_5 % 38.61/11.45 | % 38.61/11.45 | Combining equations (993,534) yields a new equation: % 38.61/11.45 | (1301) all_0_6_6 = vnoExp % 38.61/11.45 | % 38.61/11.45 | Simplifying 1301 yields: % 38.61/11.45 | (226) all_0_6_6 = vnoExp % 38.61/11.45 | % 38.61/11.45 | Equations (226) can reduce 171 to: % 38.61/11.45 | (228) $false % 38.61/11.45 | % 38.61/11.45 |-The branch is then unsatisfiable % 38.61/11.45 |-Branch two: % 38.61/11.45 | (217) all_18_4_32 = all_18_8_36 & all_18_5_33 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_2_30 = 0) & ~ (all_18_3_31 = 0) & vreduce(all_18_7_35) = all_18_8_36 & visSomeExp(all_18_8_36) = all_18_3_31 & visValue(all_18_7_35) = all_18_2_30 & vapp(all_18_6_34, all_18_7_35) = ve2 & vabs(all_18_11_39, all_18_10_38, all_18_9_37) = all_18_6_34 % 38.61/11.45 | % 38.61/11.45 | Applying alpha-rule on (217) yields: % 38.61/11.45 | (218) visValue(all_18_7_35) = all_18_2_30 % 38.61/11.45 | (219) all_18_4_32 = all_18_8_36 % 38.61/11.45 | (220) ~ (all_18_2_30 = 0) % 38.61/11.45 | (179) ~ (all_18_3_31 = 0) % 38.61/11.45 | (222) vapp(all_18_6_34, all_18_7_35) = ve2 % 38.61/11.45 | (223) vreduce(all_18_7_35) = all_18_8_36 % 38.61/11.45 | (224) vabs(all_18_11_39, all_18_10_38, all_18_9_37) = all_18_6_34 % 38.61/11.45 | (184) all_18_5_33 = ve2 % 38.61/11.45 | (226) all_0_6_6 = vnoExp % 38.61/11.45 | (227) visSomeExp(all_18_8_36) = all_18_3_31 % 38.61/11.45 | % 38.61/11.45 | Equations (226) can reduce 171 to: % 38.61/11.45 | (228) $false % 38.61/11.45 | % 38.61/11.45 |-The branch is then unsatisfiable % 38.61/11.45 |-Branch two: % 38.61/11.45 | (229) all_18_7_35 = all_18_9_37 & all_18_8_36 = ve2 & all_0_6_6 = vnoExp & ~ (all_18_6_34 = 0) & vreduce(all_18_10_38) = all_18_9_37 & visSomeExp(all_18_9_37) = all_18_6_34 & vapp(all_18_10_38, all_18_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_10_38) % 38.61/11.45 | % 38.61/11.45 | Applying alpha-rule on (229) yields: % 38.61/11.45 | (205) all_18_8_36 = ve2 % 38.61/11.45 | (231) vreduce(all_18_10_38) = all_18_9_37 % 38.61/11.45 | (232) vapp(all_18_10_38, all_18_11_39) = ve2 % 38.61/11.45 | (233) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_18_10_38) % 38.61/11.45 | (226) all_0_6_6 = vnoExp % 38.61/11.45 | (235) visSomeExp(all_18_9_37) = all_18_6_34 % 38.61/11.45 | (236) all_18_7_35 = all_18_9_37 % 38.61/11.45 | (237) ~ (all_18_6_34 = 0) % 38.61/11.45 | % 38.61/11.45 | Equations (226) can reduce 171 to: % 38.61/11.45 | (228) $false % 38.61/11.45 | % 38.61/11.45 |-The branch is then unsatisfiable % 38.61/11.45 |-Branch two: % 38.61/11.45 | (239) all_18_8_36 = ve2 & all_0_6_6 = vnoExp & vabs(all_18_11_39, all_18_10_38, all_18_9_37) = ve2 % 38.61/11.45 | % 38.61/11.45 | Applying alpha-rule on (239) yields: % 38.61/11.45 | (205) all_18_8_36 = ve2 % 38.61/11.45 | (226) all_0_6_6 = vnoExp % 38.61/11.45 | (242) vabs(all_18_11_39, all_18_10_38, all_18_9_37) = ve2 % 38.61/11.45 | % 38.61/11.45 | Equations (226) can reduce 171 to: % 38.61/11.45 | (228) $false % 38.61/11.45 | % 38.61/11.45 |-The branch is then unsatisfiable % 38.61/11.45 |-Branch two: % 38.61/11.45 | (244) all_18_10_38 = ve2 & all_0_6_6 = vnoExp & vvar(all_18_11_39) = ve2 % 38.61/11.45 | % 38.61/11.45 | Applying alpha-rule on (244) yields: % 38.61/11.45 | (245) all_18_10_38 = ve2 % 38.61/11.45 | (226) all_0_6_6 = vnoExp % 38.61/11.45 | (247) vvar(all_18_11_39) = ve2 % 38.61/11.45 | % 38.61/11.45 | Equations (226) can reduce 171 to: % 38.61/11.45 | (228) $false % 38.61/11.45 | % 38.61/11.45 |-The branch is then unsatisfiable % 38.61/11.45 |-Branch two: % 38.61/11.45 | (560) all_16_4_12 = all_16_7_15 & all_16_5_13 = all_0_5_5 & vlookup(all_16_6_14, all_0_3_3) = all_16_7_15 & vsomeType(all_0_1_1) = all_16_7_15 & vvar(all_16_6_14) = all_0_5_5 % 38.61/11.45 | % 38.61/11.45 | Applying alpha-rule on (560) yields: % 38.61/11.45 | (561) vlookup(all_16_6_14, all_0_3_3) = all_16_7_15 % 38.61/11.45 | (562) vsomeType(all_0_1_1) = all_16_7_15 % 38.61/11.45 | (563) all_16_4_12 = all_16_7_15 % 38.61/11.45 | (564) all_16_5_13 = all_0_5_5 % 38.61/11.45 | (565) vvar(all_16_6_14) = all_0_5_5 % 38.61/11.45 | % 38.61/11.45 | Instantiating formula (6) with all_0_5_5, ve2, ve1, all_16_6_14 and discharging atoms vapp(ve1, ve2) = all_0_5_5, vvar(all_16_6_14) = all_0_5_5, yields: % 38.61/11.45 | (130) $false % 38.61/11.45 | % 38.61/11.45 |-The branch is then unsatisfiable % 38.61/11.45 % SZS output end Proof for theBenchmark % 38.61/11.45 % 38.61/11.45 10954ms %------------------------------------------------------------------------------