TSTP Solution File: COM148+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : COM148+1 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.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 01:08:19 EDT 2022
% Result : Theorem 30.37s 8.33s
% Output : Proof 48.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : COM148+1 : TPTP v8.1.0. Released v6.4.0.
% 0.04/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 18:13:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.59/0.58 ____ _
% 0.59/0.58 ___ / __ \_____(_)___ ________ __________
% 0.59/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.58
% 0.59/0.58 A Theorem Prover for First-Order Logic
% 0.59/0.58 (ePrincess v.1.0)
% 0.59/0.58
% 0.59/0.58 (c) Philipp Rümmer, 2009-2015
% 0.59/0.58 (c) Peter Backeman, 2014-2015
% 0.59/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.58 Bug reports to peter@backeman.se
% 0.59/0.58
% 0.59/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.58
% 0.59/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.59/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.98/1.01 Prover 0: Preprocessing ...
% 4.11/1.52 Prover 0: Warning: ignoring some quantifiers
% 4.24/1.55 Prover 0: Constructing countermodel ...
% 20.38/5.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 20.98/6.04 Prover 1: Preprocessing ...
% 21.72/6.21 Prover 1: Constructing countermodel ...
% 30.37/8.33 Prover 1: proved (2407ms)
% 30.37/8.33 Prover 0: stopped
% 30.37/8.33
% 30.37/8.33 No countermodel exists, formula is valid
% 30.37/8.33 % SZS status Theorem for theBenchmark
% 30.37/8.33
% 30.37/8.33 Generating proof ... found it (size 1836)
% 45.19/12.88
% 45.19/12.88 % SZS output start Proof for theBenchmark
% 45.19/12.88 Assumed formulas after preprocessing and simplification:
% 45.19/12.88 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v5 = 0) & vreduce(v4) = v6 & vreduce(ve2) = v3 & vreduce(ve1) = v1 & vtcheck(vempty, v4, v7) = 0 & visValue(v4) = v5 & visValue(ve2) = v2 & visValue(ve1) = v0 & vapp(ve1, ve2) = v4 & ~ (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] : (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] : (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] : ( ~ (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] : (v2 = 0 | ~ (vtcheck(vempty, ve2, v8) = 0) | ? [v9] : vsomeExp(v9) = v3) & ! [v8] : (v0 = 0 | ~ (vtcheck(vempty, ve1, v8) = 0) | ? [v9] : vsomeExp(v9) = v1) & ! [v8] : ~ (vsomeExp(v8) = v6) & ! [v8] : ~ (vsomeExp(v8) = vnoExp) & ! [v8] : ~ (vsomeType(v8) = vnoType))
% 45.36/12.96 | 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:
% 45.36/12.96 | (1) ~ (all_0_2_2 = 0) & vreduce(all_0_3_3) = all_0_1_1 & vreduce(ve2) = all_0_4_4 & vreduce(ve1) = all_0_6_6 & vtcheck(vempty, all_0_3_3, all_0_0_0) = 0 & visValue(all_0_3_3) = all_0_2_2 & visValue(ve2) = all_0_5_5 & visValue(ve1) = all_0_7_7 & vapp(ve1, ve2) = all_0_3_3 & ~ (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] : (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] : (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] : ( ~ (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] : (all_0_5_5 = 0 | ~ (vtcheck(vempty, ve2, v0) = 0) | ? [v1] : vsomeExp(v1) = all_0_4_4) & ! [v0] : (all_0_7_7 = 0 | ~ (vtcheck(vempty, ve1, v0) = 0) | ? [v1] : vsomeExp(v1) = all_0_6_6) & ! [v0] : ~ (vsomeExp(v0) = all_0_1_1) & ! [v0] : ~ (vsomeExp(v0) = vnoExp) & ! [v0] : ~ (vsomeType(v0) = vnoType)
% 45.77/12.99 |
% 45.77/12.99 | Applying alpha-rule on (1) yields:
% 45.77/12.99 | (2) ! [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))
% 45.77/13.00 | (3) ! [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))
% 45.77/13.00 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v2 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6))
% 45.77/13.00 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~ (vsomeExp(v2) = v0))
% 45.77/13.00 | (6) ~ (visSomeType(vnoType) = 0)
% 45.77/13.00 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v1 | v3 = v2 | ~ (vsubst(v1, v0, v2) = v3) | ~ (vvar(v4) = v2))
% 45.77/13.00 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v4 | v2 = v1 | ~ (vlookup(v2, v5) = v6) | ~ (vlookup(v2, v3) = v4) | ~ (vbind(v1, v0, v5) = v3))
% 45.77/13.00 | (9) ! [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)))
% 45.77/13.00 | (10) ! [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)))
% 45.77/13.00 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vabs(v1, v2, v3) = v4) | ~ (vvar(v0) = v4))
% 45.77/13.00 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vsomeType(v0) = v2) | ~ (vsomeType(v0) = v1))
% 45.77/13.00 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) = v0))
% 45.77/13.00 | (14) vreduce(all_0_3_3) = all_0_1_1
% 45.77/13.00 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (vsubst(v1, v0, v2) = v3) | ~ (vabs(v1, v4, v5) = v2))
% 45.77/13.00 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (varrow(v0, v1) = v3) | ~ (varrow(v0, v1) = v2))
% 45.77/13.00 | (17) ! [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))
% 45.77/13.00 | (18) vtcheck(vempty, all_0_3_3, all_0_0_0) = 0
% 45.77/13.00 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vvar(v0) = v2) | ~ (vvar(v0) = v1))
% 45.77/13.00 | (20) ! [v0] : ~ (vsomeType(v0) = vnoType)
% 45.77/13.00 | (21) ! [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))
% 45.77/13.00 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (visValue(v3) = v4) | ~ (vabs(v0, v1, v2) = v3))
% 45.77/13.00 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0))
% 45.77/13.00 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (visFreeVar(v0, v1) = v2) | ~ (vvar(v0) = v1))
% 45.77/13.00 | (25) ~ (all_0_2_2 = 0)
% 45.77/13.00 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v0 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6))
% 45.77/13.00 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (visFreeVar(v1, v3) = v4) | ~ (visFreeVar(v1, v2) = 0) | ~ (vabs(v1, v0, v3) = v2))
% 45.92/13.00 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vvar(v1) = v2) | ~ (vvar(v0) = v2))
% 45.92/13.00 | (29) ! [v0] : (all_0_5_5 = 0 | ~ (vtcheck(vempty, ve2, v0) = 0) | ? [v1] : vsomeExp(v1) = all_0_4_4)
% 45.92/13.00 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v1 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6))
% 45.92/13.00 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4))
% 45.92/13.00 | (32) ! [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)))
% 45.92/13.01 | (33) ! [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))
% 45.92/13.01 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) = v0))
% 45.92/13.01 | (35) vapp(ve1, ve2) = all_0_3_3
% 45.92/13.01 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0))
% 45.92/13.01 | (37) ! [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)))
% 45.92/13.01 | (38) ! [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)))
% 45.92/13.01 | (39) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vgetSomeType(v0) = v1) | ~ (vsomeType(v2) = v0))
% 45.92/13.01 | (40) ! [v0] : ~ (vsomeExp(v0) = vnoExp)
% 45.92/13.01 | (41) ! [v0] : ! [v1] : ( ~ (visFreeVar(v0, v1) = 0) | ? [v2] : ( ~ (v2 = v0) & vgensym(v1) = v2))
% 45.92/13.01 | (42) vreduce(ve1) = all_0_6_6
% 45.92/13.01 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v1 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6))
% 45.92/13.01 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~ (vlookup(v3, v2) = v0))
% 45.92/13.01 | (45) ! [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))
% 45.92/13.01 | (46) ! [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)))
% 45.92/13.01 | (47) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (visSomeExp(v1) = v2) | ~ (vsomeExp(v0) = v1))
% 45.92/13.01 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v3 = v1 | ~ (visFreeVar(v1, v4) = 0) | ~ (visFreeVar(v1, v2) = v5) | ~ (vabs(v3, v0, v4) = v2))
% 45.92/13.01 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (vsubst(v0, v1, v2) = v3) | ~ (vvar(v0) = v2))
% 45.92/13.01 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (vbind(v0, v1, v2) = v4) | ~ (vbind(v0, v1, v2) = v3))
% 45.92/13.01 | (51) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (visSomeType(v1) = v2) | ~ (vsomeType(v0) = v1))
% 45.92/13.01 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vlookup(v1, v2) = v3) | ~ (vbind(v1, v4, v0) = v2) | vsomeType(v4) = v3)
% 45.92/13.01 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (vabs(v0, v1, v2) = v4) | ~ (vabs(v0, v1, v2) = v3))
% 45.92/13.01 | (54) ! [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)))
% 45.92/13.02 | (55) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0))
% 45.92/13.02 | (56) ! [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))))
% 45.92/13.02 | (57) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0))
% 45.92/13.02 | (58) ! [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)))
% 45.92/13.02 | (59) ! [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)))
% 45.92/13.02 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3, v2) = v0))
% 45.92/13.02 | (61) ! [v0] : ! [v1] : ! [v2] : ~ (vbind(v0, v1, v2) = vempty)
% 45.92/13.02 | (62) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vgetSomeExp(v0) = v1) | ~ (vsomeExp(v2) = v0))
% 45.92/13.02 | (63) ! [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))
% 45.92/13.02 | (64) ! [v0] : ! [v1] : ! [v2] : (v2 = vnoExp | ~ (vreduce(v1) = v2) | ~ (vvar(v0) = v1))
% 45.92/13.02 | (65) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vsomeExp(v0) = v2) | ~ (vsomeExp(v0) = v1))
% 45.92/13.02 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vapp(v3, v4) = v5) | ~ (vabs(v0, v1, v2) = v5))
% 45.92/13.02 | (67) ! [v0] : (all_0_7_7 = 0 | ~ (vtcheck(vempty, ve1, v0) = 0) | ? [v1] : vsomeExp(v1) = all_0_6_6)
% 45.92/13.02 | (68) visValue(ve1) = all_0_7_7
% 45.92/13.02 | (69) ~ (visSomeExp(vnoExp) = 0)
% 45.92/13.02 | (70) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeType(v1) = v2) | ~ (vsomeType(v0) = v2))
% 45.92/13.02 | (71) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0))
% 45.92/13.02 | (72) ! [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))))
% 45.92/13.02 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (varrow(v3, v2) = v1) | ~ (varrow(v3, v2) = v0))
% 45.92/13.02 | (74) ! [v0] : ~ (vsomeExp(v0) = all_0_1_1)
% 45.92/13.02 | (75) ! [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)))
% 45.92/13.02 | (76) ! [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)))
% 45.92/13.03 | (77) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~ (vsomeType(v2) = v0))
% 45.92/13.03 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v0 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6))
% 45.92/13.03 | (79) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0))
% 45.92/13.03 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~ (vapp(v3, v2) = v0))
% 45.92/13.03 | (81) vreduce(ve2) = all_0_4_4
% 45.92/13.03 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0))
% 46.03/13.03 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (varrow(v2, v3) = v4) | ~ (varrow(v0, v1) = v4))
% 46.03/13.03 | (84) ! [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))
% 46.03/13.03 | (85) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeExp(v1) = v2) | ~ (vsomeExp(v0) = v2))
% 46.03/13.03 | (86) ! [v0] : ! [v1] : (v1 = vnoType | ~ (vlookup(v0, vempty) = v1))
% 46.03/13.03 | (87) visValue(all_0_3_3) = all_0_2_2
% 46.03/13.03 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4))
% 46.03/13.03 | (89) visValue(ve2) = all_0_5_5
% 46.03/13.03 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = vnoExp | ~ (vreduce(v3) = v4) | ~ (vabs(v0, v1, v2) = v3))
% 46.03/13.03 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (vapp(v0, v1) = v3) | ~ (vapp(v0, v1) = v2))
% 46.03/13.03 | (92) ! [v0] : ! [v1] : ! [v2] : ( ~ (visValue(v2) = 0) | ~ (vapp(v0, v1) = v2))
% 46.03/13.03 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vapp(v1, v2) = v3) | ~ (vvar(v0) = v3))
% 46.03/13.03 | (94) ! [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))
% 46.03/13.03 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (varrow(v2, v3) = v4) | ~ (varrow(v0, v1) = v4))
% 46.03/13.03 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (visFreeVar(v1, v4) = v5) | ~ (visFreeVar(v1, v2) = 0) | ~ (vabs(v3, v0, v4) = v2))
% 46.03/13.03 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0))
% 46.03/13.03 | (98) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (visValue(v2) = v1) | ~ (visValue(v2) = v0))
% 46.03/13.03 | (99) ! [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)))
% 46.03/13.03 | (100) ! [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))))
% 46.03/13.03 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v2 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6))
% 46.03/13.03 | (102) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (visFreeVar(v0, v1) = 0) | ~ (vvar(v2) = v1))
% 46.03/13.03 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0))
% 46.03/13.03 | (104) ! [v0] : ! [v1] : ( ~ (visValue(v1) = 0) | ~ (vvar(v0) = v1))
% 46.03/13.03 |
% 46.03/13.04 | Instantiating formula (55) with ve2, all_0_4_4, all_0_1_1 and discharging atoms vreduce(ve2) = all_0_4_4, yields:
% 46.03/13.04 | (105) all_0_1_1 = all_0_4_4 | ~ (vreduce(ve2) = all_0_1_1)
% 46.03/13.04 |
% 46.03/13.04 | Instantiating formula (55) with ve1, all_0_6_6, all_0_1_1 and discharging atoms vreduce(ve1) = all_0_6_6, yields:
% 46.03/13.04 | (106) all_0_1_1 = all_0_6_6 | ~ (vreduce(ve1) = all_0_1_1)
% 46.03/13.04 |
% 46.03/13.04 | Instantiating formula (55) with ve1, all_0_6_6, all_0_4_4 and discharging atoms vreduce(ve1) = all_0_6_6, yields:
% 46.03/13.04 | (107) all_0_4_4 = all_0_6_6 | ~ (vreduce(ve1) = all_0_4_4)
% 46.03/13.04 |
% 46.03/13.04 | Instantiating formula (98) with ve1, all_0_7_7, all_0_5_5 and discharging atoms visValue(ve1) = all_0_7_7, yields:
% 46.03/13.04 | (108) all_0_5_5 = all_0_7_7 | ~ (visValue(ve1) = all_0_5_5)
% 46.03/13.04 |
% 46.03/13.04 | Instantiating formula (37) with all_0_1_1, all_0_3_3 and discharging atoms vreduce(all_0_3_3) = all_0_1_1, yields:
% 46.03/13.04 | (109) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = all_0_1_1 & v9 = 0 & v7 = v1 & v6 = all_0_3_3 & ~ (v8 = 0) & vreduce(v3) = v1 & visSomeExp(v1) = v8 & vsomeExp(v10) = all_0_1_1 & vsubst(v2, v3, v4) = v10 & visValue(v3) = 0 & vapp(v5, v3) = all_0_3_3 & vabs(v2, v0, v4) = v5) | (v11 = all_0_1_1 & v8 = 0 & v7 = v4 & v6 = all_0_3_3 & vreduce(v0) = v4 & vgetSomeExp(v4) = v9 & visSomeExp(v4) = 0 & vsomeExp(v10) = all_0_1_1 & vapp(v5, v9) = v10 & vapp(v5, v0) = all_0_3_3 & vabs(v1, v2, v3) = v5) | (v8 = all_0_1_1 & v5 = 0 & v4 = v1 & v3 = all_0_3_3 & vreduce(v0) = v1 & vgetSomeExp(v1) = v6 & visSomeExp(v1) = 0 & vsomeExp(v7) = all_0_1_1 & vapp(v6, v2) = v7 & vapp(v0, v2) = all_0_3_3 & ! [v12] : ! [v13] : ! [v14] : ~ (vabs(v12, v13, v14) = v0)) | (v7 = v3 & v6 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (v9 = 0) & ~ (v8 = 0) & vreduce(v4) = v3 & visSomeExp(v3) = v8 & visValue(v4) = v9 & vapp(v5, v4) = all_0_3_3 & vabs(v0, v1, v2) = v5) | (v4 = v2 & v3 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (v5 = 0) & vreduce(v1) = v2 & visSomeExp(v2) = v5 & vapp(v1, v0) = all_0_3_3 & ! [v12] : ! [v13] : ! [v14] : ~ (vabs(v12, v13, v14) = v1)) | (v3 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(v0, v1, v2) = all_0_3_3) | (v1 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(v0) = all_0_3_3))
% 46.03/13.04 |
% 46.03/13.04 | Instantiating formula (37) with all_0_4_4, ve2 and discharging atoms vreduce(ve2) = all_0_4_4, yields:
% 46.03/13.04 | (110) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = all_0_4_4 & v9 = 0 & v7 = v1 & v6 = ve2 & ~ (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) = ve2 & vabs(v2, v0, v4) = v5) | (v11 = all_0_4_4 & v8 = 0 & v7 = v4 & v6 = ve2 & vreduce(v0) = v4 & vgetSomeExp(v4) = v9 & visSomeExp(v4) = 0 & vsomeExp(v10) = all_0_4_4 & vapp(v5, v9) = v10 & vapp(v5, v0) = ve2 & vabs(v1, v2, v3) = v5) | (v8 = all_0_4_4 & v5 = 0 & v4 = v1 & v3 = ve2 & vreduce(v0) = v1 & vgetSomeExp(v1) = v6 & visSomeExp(v1) = 0 & vsomeExp(v7) = all_0_4_4 & vapp(v6, v2) = v7 & vapp(v0, v2) = ve2 & ! [v12] : ! [v13] : ! [v14] : ~ (vabs(v12, v13, v14) = v0)) | (v7 = v3 & v6 = ve2 & all_0_4_4 = 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_4_4 = 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_4_4 = vnoExp & vabs(v0, v1, v2) = ve2) | (v1 = ve2 & all_0_4_4 = vnoExp & vvar(v0) = ve2))
% 46.03/13.04 |
% 46.03/13.04 | Instantiating formula (37) with all_0_6_6, ve1 and discharging atoms vreduce(ve1) = all_0_6_6, yields:
% 46.03/13.04 | (111) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = all_0_6_6 & v9 = 0 & v7 = v1 & v6 = ve1 & ~ (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) = ve1 & vabs(v2, v0, v4) = v5) | (v11 = all_0_6_6 & v8 = 0 & v7 = v4 & v6 = ve1 & vreduce(v0) = v4 & vgetSomeExp(v4) = v9 & visSomeExp(v4) = 0 & vsomeExp(v10) = all_0_6_6 & vapp(v5, v9) = v10 & vapp(v5, v0) = ve1 & vabs(v1, v2, v3) = v5) | (v8 = all_0_6_6 & v5 = 0 & v4 = v1 & v3 = ve1 & vreduce(v0) = v1 & vgetSomeExp(v1) = v6 & visSomeExp(v1) = 0 & vsomeExp(v7) = all_0_6_6 & vapp(v6, v2) = v7 & vapp(v0, v2) = ve1 & ! [v12] : ! [v13] : ! [v14] : ~ (vabs(v12, v13, v14) = v0)) | (v7 = v3 & v6 = ve1 & all_0_6_6 = 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_6_6 = 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_6_6 = vnoExp & vabs(v0, v1, v2) = ve1) | (v1 = ve1 & all_0_6_6 = vnoExp & vvar(v0) = ve1))
% 46.03/13.04 |
% 46.03/13.04 | Instantiating formula (75) with vempty, all_0_0_0, all_0_3_3 and discharging atoms vtcheck(vempty, all_0_3_3, all_0_0_0) = 0, yields:
% 46.03/13.04 | (112) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v5 = all_0_0_0 & v4 = all_0_3_3 & varrow(v2, v3) = all_0_0_0 & vtcheck(v6, v1, v3) = 0 & vbind(v0, v2, vempty) = v6 & vabs(v0, v2, v1) = all_0_3_3) | (v6 = 0 & v5 = 0 & v3 = all_0_3_3 & varrow(v2, all_0_0_0) = v4 & vtcheck(vempty, v1, v2) = 0 & vtcheck(vempty, v0, v4) = 0 & vapp(v0, v1) = all_0_3_3) | (v3 = v0 & v2 = all_0_3_3 & vlookup(v1, vempty) = v0 & vsomeType(all_0_0_0) = v0 & vvar(v1) = all_0_3_3))
% 46.03/13.05 |
% 46.03/13.05 | Instantiating (112) with all_8_0_8, all_8_1_9, all_8_2_10, all_8_3_11, all_8_4_12, all_8_5_13, all_8_6_14, all_8_7_15 yields:
% 46.03/13.05 | (113) (all_8_0_8 = 0 & all_8_2_10 = all_0_0_0 & all_8_3_11 = all_0_3_3 & varrow(all_8_5_13, all_8_4_12) = all_0_0_0 & vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0 & vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9 & vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3) | (all_8_1_9 = 0 & all_8_2_10 = 0 & all_8_4_12 = all_0_3_3 & varrow(all_8_5_13, all_0_0_0) = all_8_3_11 & vtcheck(vempty, all_8_6_14, all_8_5_13) = 0 & vtcheck(vempty, all_8_7_15, all_8_3_11) = 0 & vapp(all_8_7_15, all_8_6_14) = all_0_3_3) | (all_8_4_12 = all_8_7_15 & all_8_5_13 = all_0_3_3 & vlookup(all_8_6_14, vempty) = all_8_7_15 & vsomeType(all_0_0_0) = all_8_7_15 & vvar(all_8_6_14) = all_0_3_3)
% 46.03/13.05 |
% 46.03/13.05 | Instantiating (111) with all_9_0_16, all_9_1_17, all_9_2_18, all_9_3_19, all_9_4_20, all_9_5_21, all_9_6_22, all_9_7_23, all_9_8_24, all_9_9_25, all_9_10_26, all_9_11_27 yields:
% 46.03/13.05 | (114) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22) | (all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)) | (all_9_8_24 = ve1 & all_0_6_6 = vnoExp & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1) | (all_9_10_26 = ve1 & all_0_6_6 = vnoExp & vvar(all_9_11_27) = ve1)
% 46.03/13.05 |
% 46.03/13.05 | Instantiating (110) with all_10_0_28, all_10_1_29, all_10_2_30, all_10_3_31, all_10_4_32, all_10_5_33, all_10_6_34, all_10_7_35, all_10_8_36, all_10_9_37, all_10_10_38, all_10_11_39 yields:
% 46.03/13.05 | (115) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34) | (all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)) | (all_10_8_36 = ve2 & all_0_4_4 = vnoExp & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2) | (all_10_10_38 = ve2 & all_0_4_4 = vnoExp & vvar(all_10_11_39) = ve2)
% 46.03/13.05 |
% 46.03/13.05 | Instantiating (109) with all_11_0_40, all_11_1_41, all_11_2_42, all_11_3_43, all_11_4_44, all_11_5_45, all_11_6_46, all_11_7_47, all_11_8_48, all_11_9_49, all_11_10_50, all_11_11_51 yields:
% 46.03/13.05 | (116) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3) | (all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3)
% 46.03/13.05 |
% 46.03/13.05 +-Applying beta-rule and splitting (108), into two cases.
% 46.03/13.05 |-Branch one:
% 46.03/13.05 | (117) ~ (visValue(ve1) = all_0_5_5)
% 46.03/13.05 |
% 46.03/13.05 | Using (68) and (117) yields:
% 46.03/13.05 | (118) ~ (all_0_5_5 = all_0_7_7)
% 46.03/13.05 |
% 46.03/13.05 +-Applying beta-rule and splitting (106), into two cases.
% 46.03/13.05 |-Branch one:
% 46.03/13.05 | (119) ~ (vreduce(ve1) = all_0_1_1)
% 46.03/13.05 |
% 46.03/13.05 | Using (42) and (119) yields:
% 46.03/13.05 | (120) ~ (all_0_1_1 = all_0_6_6)
% 46.03/13.05 |
% 46.03/13.05 +-Applying beta-rule and splitting (113), into two cases.
% 46.03/13.05 |-Branch one:
% 46.03/13.05 | (121) (all_8_0_8 = 0 & all_8_2_10 = all_0_0_0 & all_8_3_11 = all_0_3_3 & varrow(all_8_5_13, all_8_4_12) = all_0_0_0 & vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0 & vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9 & vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3) | (all_8_1_9 = 0 & all_8_2_10 = 0 & all_8_4_12 = all_0_3_3 & varrow(all_8_5_13, all_0_0_0) = all_8_3_11 & vtcheck(vempty, all_8_6_14, all_8_5_13) = 0 & vtcheck(vempty, all_8_7_15, all_8_3_11) = 0 & vapp(all_8_7_15, all_8_6_14) = all_0_3_3)
% 46.03/13.05 |
% 46.03/13.05 +-Applying beta-rule and splitting (121), into two cases.
% 46.03/13.05 |-Branch one:
% 46.03/13.05 | (122) all_8_0_8 = 0 & all_8_2_10 = all_0_0_0 & all_8_3_11 = all_0_3_3 & varrow(all_8_5_13, all_8_4_12) = all_0_0_0 & vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0 & vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9 & vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3
% 46.03/13.05 |
% 46.03/13.05 | Applying alpha-rule on (122) yields:
% 46.03/13.05 | (123) vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3
% 46.03/13.05 | (124) vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0
% 46.03/13.05 | (125) vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9
% 46.03/13.05 | (126) all_8_3_11 = all_0_3_3
% 46.03/13.05 | (127) all_8_0_8 = 0
% 46.03/13.05 | (128) all_8_2_10 = all_0_0_0
% 46.03/13.05 | (129) varrow(all_8_5_13, all_8_4_12) = all_0_0_0
% 46.03/13.05 |
% 46.03/13.05 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_8_6_14, all_8_5_13, all_8_7_15 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3, yields:
% 46.03/13.05 | (130) $false
% 46.03/13.06 |
% 46.03/13.06 |-The branch is then unsatisfiable
% 46.03/13.06 |-Branch two:
% 46.03/13.06 | (131) all_8_1_9 = 0 & all_8_2_10 = 0 & all_8_4_12 = all_0_3_3 & varrow(all_8_5_13, all_0_0_0) = all_8_3_11 & vtcheck(vempty, all_8_6_14, all_8_5_13) = 0 & vtcheck(vempty, all_8_7_15, all_8_3_11) = 0 & vapp(all_8_7_15, all_8_6_14) = all_0_3_3
% 46.03/13.06 |
% 46.03/13.06 | Applying alpha-rule on (131) yields:
% 46.03/13.06 | (132) varrow(all_8_5_13, all_0_0_0) = all_8_3_11
% 46.03/13.06 | (133) vtcheck(vempty, all_8_6_14, all_8_5_13) = 0
% 46.03/13.06 | (134) all_8_2_10 = 0
% 46.03/13.06 | (135) vtcheck(vempty, all_8_7_15, all_8_3_11) = 0
% 46.03/13.06 | (136) all_8_4_12 = all_0_3_3
% 46.03/13.06 | (137) all_8_1_9 = 0
% 46.03/13.06 | (138) vapp(all_8_7_15, all_8_6_14) = all_0_3_3
% 46.03/13.06 |
% 46.03/13.06 | Instantiating formula (31) with all_0_3_3, all_8_6_14, all_8_7_15, ve2, ve1 and discharging atoms vapp(all_8_7_15, all_8_6_14) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 46.03/13.06 | (139) all_8_6_14 = ve2
% 46.03/13.06 |
% 46.03/13.06 | Instantiating formula (88) with all_0_3_3, all_8_6_14, all_8_7_15, ve2, ve1 and discharging atoms vapp(all_8_7_15, all_8_6_14) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 46.03/13.06 | (140) all_8_7_15 = ve1
% 46.03/13.06 |
% 46.03/13.06 | From (140) and (135) follows:
% 46.03/13.06 | (141) vtcheck(vempty, ve1, all_8_3_11) = 0
% 46.03/13.06 |
% 46.03/13.06 | From (140)(139) and (138) follows:
% 46.03/13.06 | (35) vapp(ve1, ve2) = all_0_3_3
% 46.03/13.06 |
% 46.03/13.06 | Instantiating formula (67) with all_8_3_11 and discharging atoms vtcheck(vempty, ve1, all_8_3_11) = 0, yields:
% 46.03/13.06 | (143) all_0_7_7 = 0 | ? [v0] : vsomeExp(v0) = all_0_6_6
% 46.03/13.06 |
% 46.03/13.06 +-Applying beta-rule and splitting (114), into two cases.
% 46.03/13.06 |-Branch one:
% 46.03/13.06 | (144) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22) | (all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)) | (all_9_8_24 = ve1 & all_0_6_6 = vnoExp & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1)
% 46.03/13.06 |
% 46.03/13.06 +-Applying beta-rule and splitting (144), into two cases.
% 46.03/13.06 |-Branch one:
% 46.03/13.06 | (145) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22) | (all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26))
% 46.03/13.06 |
% 46.03/13.06 +-Applying beta-rule and splitting (145), into two cases.
% 46.03/13.06 |-Branch one:
% 46.03/13.06 | (146) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22)
% 46.03/13.06 |
% 46.03/13.06 +-Applying beta-rule and splitting (146), into two cases.
% 46.03/13.06 |-Branch one:
% 46.03/13.06 | (147) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27))
% 46.03/13.06 |
% 46.03/13.06 +-Applying beta-rule and splitting (147), into two cases.
% 46.03/13.06 |-Branch one:
% 46.03/13.06 | (148) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22)
% 46.03/13.06 |
% 46.03/13.06 +-Applying beta-rule and splitting (148), into two cases.
% 46.03/13.06 |-Branch one:
% 46.03/13.06 | (149) all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22
% 46.03/13.06 |
% 46.03/13.06 | Applying alpha-rule on (149) yields:
% 46.03/13.07 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 46.03/13.07 | (151) vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22
% 46.03/13.07 | (152) visSomeExp(all_9_10_26) = all_9_3_19
% 46.03/13.07 | (153) all_9_0_16 = all_0_6_6
% 46.03/13.07 | (154) vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17
% 46.03/13.07 | (155) vreduce(all_9_8_24) = all_9_10_26
% 46.03/13.07 | (156) ~ (all_9_3_19 = 0)
% 46.03/13.07 | (157) all_9_4_20 = all_9_10_26
% 46.03/13.07 | (158) vapp(all_9_6_22, all_9_8_24) = ve1
% 46.03/13.07 | (159) all_9_5_21 = ve1
% 46.03/13.07 | (160) all_9_2_18 = 0
% 46.03/13.07 | (161) visValue(all_9_8_24) = 0
% 46.03/13.07 |
% 46.03/13.07 | Instantiating formula (92) with ve1, all_9_8_24, all_9_6_22 and discharging atoms vapp(all_9_6_22, all_9_8_24) = ve1, yields:
% 46.03/13.07 | (162) ~ (visValue(ve1) = 0)
% 46.03/13.07 |
% 46.03/13.07 | Using (68) and (162) yields:
% 46.03/13.07 | (163) ~ (all_0_7_7 = 0)
% 46.03/13.07 |
% 46.03/13.07 +-Applying beta-rule and splitting (143), into two cases.
% 46.03/13.07 |-Branch one:
% 46.03/13.07 | (164) all_0_7_7 = 0
% 46.03/13.07 |
% 46.03/13.07 | Equations (164) can reduce 163 to:
% 46.03/13.07 | (165) $false
% 46.03/13.07 |
% 46.03/13.07 |-The branch is then unsatisfiable
% 46.03/13.07 |-Branch two:
% 46.03/13.07 | (163) ~ (all_0_7_7 = 0)
% 46.03/13.07 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 46.03/13.07 |
% 46.03/13.07 | Instantiating (167) with all_131_0_68 yields:
% 46.03/13.07 | (168) vsomeExp(all_131_0_68) = all_0_6_6
% 46.03/13.07 |
% 46.03/13.07 | Instantiating formula (85) with all_0_6_6, all_131_0_68, all_9_1_17 and discharging atoms vsomeExp(all_131_0_68) = all_0_6_6, vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 46.03/13.07 | (169) all_131_0_68 = all_9_1_17
% 46.03/13.07 |
% 46.03/13.07 | From (169) and (168) follows:
% 46.03/13.07 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 46.03/13.07 |
% 46.03/13.07 +-Applying beta-rule and splitting (116), into two cases.
% 46.03/13.07 |-Branch one:
% 46.03/13.07 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 46.03/13.07 |
% 46.03/13.07 +-Applying beta-rule and splitting (171), into two cases.
% 46.03/13.07 |-Branch one:
% 46.03/13.07 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 46.03/13.07 |
% 46.03/13.07 +-Applying beta-rule and splitting (172), into two cases.
% 46.03/13.07 |-Branch one:
% 46.03/13.07 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 46.03/13.07 |
% 46.03/13.07 +-Applying beta-rule and splitting (173), into two cases.
% 46.03/13.07 |-Branch one:
% 46.03/13.07 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 46.03/13.07 |
% 46.03/13.07 +-Applying beta-rule and splitting (174), into two cases.
% 46.03/13.07 |-Branch one:
% 46.03/13.07 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 46.03/13.07 |
% 46.03/13.07 +-Applying beta-rule and splitting (175), into two cases.
% 46.03/13.07 |-Branch one:
% 46.03/13.07 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 46.03/13.07 |
% 46.03/13.07 | Applying alpha-rule on (176) yields:
% 46.03/13.07 | (177) all_11_5_45 = all_0_3_3
% 46.03/13.07 | (178) all_11_4_44 = all_11_10_50
% 46.03/13.07 | (179) visValue(all_11_8_48) = 0
% 46.03/13.07 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 46.03/13.07 | (181) all_11_0_40 = all_0_1_1
% 46.03/13.07 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 46.03/13.07 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 46.03/13.07 | (184) vreduce(all_11_8_48) = all_11_10_50
% 46.03/13.07 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 46.03/13.07 | (186) ~ (all_11_3_43 = 0)
% 46.03/13.07 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 46.03/13.07 | (188) all_11_2_42 = 0
% 46.03/13.07 |
% 46.03/13.07 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 46.03/13.07 | (130) $false
% 46.03/13.07 |
% 46.03/13.07 |-The branch is then unsatisfiable
% 46.03/13.08 |-Branch two:
% 46.03/13.08 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 46.03/13.08 |
% 46.03/13.08 | Applying alpha-rule on (190) yields:
% 46.03/13.08 | (177) all_11_5_45 = all_0_3_3
% 46.03/13.08 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 46.03/13.08 | (193) visSomeExp(all_11_7_47) = 0
% 46.03/13.08 | (181) all_11_0_40 = all_0_1_1
% 46.03/13.08 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 46.03/13.08 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 46.03/13.08 | (197) vreduce(all_11_11_51) = all_11_7_47
% 46.03/13.08 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 46.03/13.08 | (199) all_11_3_43 = 0
% 46.03/13.08 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 46.03/13.08 | (201) all_11_4_44 = all_11_7_47
% 46.03/13.08 |
% 46.03/13.08 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 46.03/13.08 | (130) $false
% 46.03/13.08 |
% 46.03/13.08 |-The branch is then unsatisfiable
% 46.03/13.08 |-Branch two:
% 46.03/13.08 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 46.03/13.08 |
% 46.03/13.08 | Applying alpha-rule on (203) yields:
% 46.03/13.08 | (204) all_11_7_47 = all_11_10_50
% 46.03/13.08 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 46.03/13.08 | (206) all_11_6_46 = 0
% 46.03/13.08 | (207) all_11_3_43 = all_0_1_1
% 46.03/13.08 | (208) visSomeExp(all_11_10_50) = 0
% 46.03/13.08 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 46.03/13.08 | (210) vreduce(all_11_11_51) = all_11_10_50
% 46.03/13.08 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 46.03/13.08 | (212) all_11_8_48 = all_0_3_3
% 46.03/13.08 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 46.03/13.08 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 46.03/13.08 |
% 46.03/13.08 | Instantiating formula (74) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = all_0_1_1, yields:
% 46.03/13.08 | (130) $false
% 46.03/13.08 |
% 46.03/13.08 |-The branch is then unsatisfiable
% 46.03/13.08 |-Branch two:
% 46.03/13.08 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 46.03/13.08 |
% 46.03/13.08 | Applying alpha-rule on (216) yields:
% 46.03/13.08 | (177) all_11_5_45 = all_0_3_3
% 46.03/13.08 | (218) visValue(all_11_7_47) = all_11_2_42
% 46.03/13.08 | (219) all_0_1_1 = vnoExp
% 46.03/13.08 | (220) vreduce(all_11_7_47) = all_11_8_48
% 46.03/13.08 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 46.03/13.08 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 46.03/13.08 | (186) ~ (all_11_3_43 = 0)
% 46.03/13.08 | (224) all_11_4_44 = all_11_8_48
% 46.03/13.08 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 46.03/13.08 | (226) ~ (all_11_2_42 = 0)
% 46.03/13.08 |
% 46.03/13.08 | Instantiating formula (88) with all_0_3_3, all_11_7_47, all_11_6_46, ve2, ve1 and discharging atoms vapp(all_11_6_46, all_11_7_47) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 46.03/13.08 | (227) all_11_6_46 = ve1
% 46.03/13.08 |
% 46.03/13.08 | Instantiating formula (66) with ve1, all_9_8_24, all_9_6_22, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(all_9_6_22, all_9_8_24) = ve1, yields:
% 46.03/13.08 | (228) ~ (vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1)
% 46.03/13.08 |
% 46.03/13.08 | From (227) and (221) follows:
% 46.03/13.08 | (229) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1
% 46.03/13.08 |
% 46.03/13.08 | Using (229) and (228) yields:
% 46.03/13.08 | (130) $false
% 46.03/13.08 |
% 46.03/13.08 |-The branch is then unsatisfiable
% 46.03/13.08 |-Branch two:
% 46.03/13.08 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 46.03/13.08 |
% 46.03/13.08 | Applying alpha-rule on (231) yields:
% 46.03/13.08 | (232) all_11_7_47 = all_11_9_49
% 46.03/13.08 | (219) all_0_1_1 = vnoExp
% 46.03/13.08 | (234) ~ (all_11_6_46 = 0)
% 46.03/13.08 | (235) vreduce(all_11_10_50) = all_11_9_49
% 46.03/13.08 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 46.03/13.08 | (212) all_11_8_48 = all_0_3_3
% 46.03/13.08 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 46.03/13.08 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 46.03/13.08 |
% 46.03/13.08 | Instantiating formula (55) with ve1, all_11_9_49, all_0_6_6 and discharging atoms vreduce(ve1) = all_0_6_6, yields:
% 46.03/13.08 | (240) all_11_9_49 = all_0_6_6 | ~ (vreduce(ve1) = all_11_9_49)
% 46.03/13.08 |
% 46.03/13.08 | Instantiating formula (47) with all_11_6_46, all_0_6_6, all_9_1_17 and discharging atoms vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 46.03/13.08 | (241) all_11_6_46 = 0 | ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 46.03/13.08 |
% 46.03/13.08 | Instantiating formula (88) with all_0_3_3, all_11_11_51, all_11_10_50, ve2, ve1 and discharging atoms vapp(all_11_10_50, all_11_11_51) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 46.03/13.08 | (242) all_11_10_50 = ve1
% 46.03/13.08 |
% 46.03/13.08 | From (242) and (235) follows:
% 46.03/13.08 | (243) vreduce(ve1) = all_11_9_49
% 46.03/13.08 |
% 46.03/13.08 +-Applying beta-rule and splitting (241), into two cases.
% 46.03/13.08 |-Branch one:
% 46.03/13.08 | (244) ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 46.03/13.08 |
% 46.03/13.08 +-Applying beta-rule and splitting (240), into two cases.
% 46.03/13.08 |-Branch one:
% 46.03/13.08 | (245) ~ (vreduce(ve1) = all_11_9_49)
% 46.03/13.08 |
% 46.03/13.08 | Using (243) and (245) yields:
% 46.03/13.08 | (130) $false
% 46.03/13.08 |
% 46.03/13.08 |-The branch is then unsatisfiable
% 46.03/13.08 |-Branch two:
% 46.03/13.08 | (243) vreduce(ve1) = all_11_9_49
% 46.03/13.08 | (248) all_11_9_49 = all_0_6_6
% 46.03/13.08 |
% 46.03/13.08 | From (248) and (239) follows:
% 46.03/13.08 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 46.03/13.08 |
% 46.03/13.08 | Using (249) and (244) yields:
% 46.03/13.08 | (130) $false
% 46.03/13.08 |
% 46.03/13.08 |-The branch is then unsatisfiable
% 46.03/13.08 |-Branch two:
% 46.03/13.08 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 46.03/13.08 | (206) all_11_6_46 = 0
% 46.03/13.08 |
% 46.03/13.08 | Equations (206) can reduce 234 to:
% 46.03/13.08 | (165) $false
% 46.03/13.08 |
% 46.03/13.08 |-The branch is then unsatisfiable
% 46.03/13.08 |-Branch two:
% 46.03/13.08 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 46.03/13.08 |
% 46.03/13.08 | Applying alpha-rule on (254) yields:
% 46.03/13.08 | (212) all_11_8_48 = all_0_3_3
% 46.03/13.08 | (219) all_0_1_1 = vnoExp
% 46.03/13.08 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 46.03/13.08 |
% 46.03/13.08 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3, yields:
% 46.03/13.08 | (130) $false
% 46.03/13.08 |
% 46.03/13.08 |-The branch is then unsatisfiable
% 46.03/13.08 |-Branch two:
% 46.03/13.08 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 46.03/13.08 |
% 46.03/13.08 | Applying alpha-rule on (259) yields:
% 46.03/13.08 | (260) all_11_10_50 = all_0_3_3
% 46.03/13.08 | (219) all_0_1_1 = vnoExp
% 46.03/13.08 | (262) vvar(all_11_11_51) = all_0_3_3
% 46.03/13.08 |
% 46.03/13.08 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_11_11_51) = all_0_3_3, yields:
% 46.03/13.08 | (130) $false
% 46.03/13.08 |
% 46.03/13.08 |-The branch is then unsatisfiable
% 46.03/13.08 |-Branch two:
% 46.03/13.08 | (264) all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22
% 46.03/13.08 |
% 46.03/13.08 | Applying alpha-rule on (264) yields:
% 46.03/13.08 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 46.03/13.08 | (266) visSomeExp(all_9_7_23) = 0
% 46.03/13.08 | (267) vapp(all_9_6_22, all_9_2_18) = all_9_1_17
% 46.03/13.08 | (268) vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22
% 46.03/13.08 | (269) vreduce(all_9_11_27) = all_9_7_23
% 46.03/13.08 | (270) vapp(all_9_6_22, all_9_11_27) = ve1
% 46.03/13.08 | (153) all_9_0_16 = all_0_6_6
% 46.03/13.09 | (272) all_9_3_19 = 0
% 46.03/13.09 | (273) vgetSomeExp(all_9_7_23) = all_9_2_18
% 46.03/13.09 | (159) all_9_5_21 = ve1
% 46.03/13.09 | (275) all_9_4_20 = all_9_7_23
% 46.03/13.09 |
% 46.03/13.09 | Instantiating formula (92) with ve1, all_9_11_27, all_9_6_22 and discharging atoms vapp(all_9_6_22, all_9_11_27) = ve1, yields:
% 46.03/13.09 | (162) ~ (visValue(ve1) = 0)
% 46.03/13.09 |
% 46.03/13.09 | Using (68) and (162) yields:
% 46.03/13.09 | (163) ~ (all_0_7_7 = 0)
% 46.03/13.09 |
% 46.03/13.09 +-Applying beta-rule and splitting (143), into two cases.
% 46.03/13.09 |-Branch one:
% 46.03/13.09 | (164) all_0_7_7 = 0
% 46.03/13.09 |
% 46.03/13.09 | Equations (164) can reduce 163 to:
% 46.03/13.09 | (165) $false
% 46.03/13.09 |
% 46.03/13.09 |-The branch is then unsatisfiable
% 46.03/13.09 |-Branch two:
% 46.03/13.09 | (163) ~ (all_0_7_7 = 0)
% 46.03/13.09 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 46.03/13.09 |
% 46.03/13.09 | Instantiating (167) with all_131_0_102 yields:
% 46.03/13.09 | (282) vsomeExp(all_131_0_102) = all_0_6_6
% 46.03/13.09 |
% 46.03/13.09 | Instantiating formula (85) with all_0_6_6, all_131_0_102, all_9_1_17 and discharging atoms vsomeExp(all_131_0_102) = all_0_6_6, vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 46.03/13.09 | (283) all_131_0_102 = all_9_1_17
% 46.03/13.09 |
% 46.03/13.09 | From (283) and (282) follows:
% 46.03/13.09 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 46.03/13.09 |
% 46.03/13.09 +-Applying beta-rule and splitting (116), into two cases.
% 46.03/13.09 |-Branch one:
% 46.03/13.09 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 46.03/13.09 |
% 46.03/13.09 +-Applying beta-rule and splitting (171), into two cases.
% 46.03/13.09 |-Branch one:
% 46.03/13.09 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 46.03/13.09 |
% 46.03/13.09 +-Applying beta-rule and splitting (172), into two cases.
% 46.03/13.09 |-Branch one:
% 46.03/13.09 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 46.03/13.09 |
% 46.03/13.09 +-Applying beta-rule and splitting (173), into two cases.
% 46.03/13.09 |-Branch one:
% 46.03/13.09 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 46.03/13.09 |
% 46.03/13.09 +-Applying beta-rule and splitting (174), into two cases.
% 46.03/13.09 |-Branch one:
% 46.03/13.09 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 46.03/13.09 |
% 46.03/13.09 +-Applying beta-rule and splitting (175), into two cases.
% 46.03/13.09 |-Branch one:
% 46.03/13.09 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 46.03/13.09 |
% 46.03/13.09 | Applying alpha-rule on (176) yields:
% 46.03/13.09 | (177) all_11_5_45 = all_0_3_3
% 46.03/13.09 | (178) all_11_4_44 = all_11_10_50
% 46.03/13.09 | (179) visValue(all_11_8_48) = 0
% 46.03/13.09 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 46.03/13.09 | (181) all_11_0_40 = all_0_1_1
% 46.03/13.09 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 46.03/13.09 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 46.03/13.09 | (184) vreduce(all_11_8_48) = all_11_10_50
% 46.03/13.09 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 46.03/13.09 | (186) ~ (all_11_3_43 = 0)
% 46.03/13.09 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 46.03/13.09 | (188) all_11_2_42 = 0
% 46.03/13.09 |
% 46.03/13.09 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 46.03/13.09 | (130) $false
% 46.03/13.09 |
% 46.03/13.09 |-The branch is then unsatisfiable
% 46.03/13.09 |-Branch two:
% 46.03/13.09 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 46.03/13.09 |
% 46.03/13.09 | Applying alpha-rule on (190) yields:
% 46.03/13.09 | (177) all_11_5_45 = all_0_3_3
% 46.03/13.09 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 46.03/13.09 | (193) visSomeExp(all_11_7_47) = 0
% 46.03/13.09 | (181) all_11_0_40 = all_0_1_1
% 46.03/13.09 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 46.03/13.09 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 46.03/13.09 | (197) vreduce(all_11_11_51) = all_11_7_47
% 46.03/13.09 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 46.03/13.09 | (199) all_11_3_43 = 0
% 46.03/13.09 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 46.03/13.09 | (201) all_11_4_44 = all_11_7_47
% 46.03/13.09 |
% 46.03/13.10 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 46.03/13.10 | (130) $false
% 46.03/13.10 |
% 46.03/13.10 |-The branch is then unsatisfiable
% 46.03/13.10 |-Branch two:
% 46.03/13.10 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 46.03/13.10 |
% 46.03/13.10 | Applying alpha-rule on (203) yields:
% 46.03/13.10 | (204) all_11_7_47 = all_11_10_50
% 46.03/13.10 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 46.03/13.10 | (206) all_11_6_46 = 0
% 46.03/13.10 | (207) all_11_3_43 = all_0_1_1
% 46.03/13.10 | (208) visSomeExp(all_11_10_50) = 0
% 46.03/13.10 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 46.03/13.10 | (210) vreduce(all_11_11_51) = all_11_10_50
% 46.03/13.10 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 46.03/13.10 | (212) all_11_8_48 = all_0_3_3
% 46.03/13.10 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 46.03/13.10 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 46.03/13.10 |
% 46.03/13.10 | Instantiating formula (74) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = all_0_1_1, yields:
% 46.03/13.10 | (130) $false
% 46.03/13.10 |
% 46.03/13.10 |-The branch is then unsatisfiable
% 46.03/13.10 |-Branch two:
% 46.03/13.10 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 46.03/13.10 |
% 46.03/13.10 | Applying alpha-rule on (216) yields:
% 46.03/13.10 | (177) all_11_5_45 = all_0_3_3
% 46.03/13.10 | (218) visValue(all_11_7_47) = all_11_2_42
% 46.03/13.10 | (219) all_0_1_1 = vnoExp
% 46.03/13.10 | (220) vreduce(all_11_7_47) = all_11_8_48
% 46.03/13.10 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 46.03/13.10 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 46.03/13.10 | (186) ~ (all_11_3_43 = 0)
% 46.03/13.10 | (224) all_11_4_44 = all_11_8_48
% 46.03/13.10 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 46.03/13.10 | (226) ~ (all_11_2_42 = 0)
% 46.03/13.10 |
% 46.03/13.10 | Instantiating formula (88) with all_0_3_3, all_11_7_47, all_11_6_46, ve2, ve1 and discharging atoms vapp(all_11_6_46, all_11_7_47) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 46.03/13.10 | (227) all_11_6_46 = ve1
% 46.03/13.10 |
% 46.03/13.10 | Instantiating formula (66) with ve1, all_9_11_27, all_9_6_22, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(all_9_6_22, all_9_11_27) = ve1, yields:
% 46.03/13.10 | (228) ~ (vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1)
% 46.03/13.10 |
% 46.03/13.10 | From (227) and (221) follows:
% 46.03/13.10 | (229) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1
% 46.03/13.10 |
% 46.03/13.10 | Using (229) and (228) yields:
% 46.03/13.10 | (130) $false
% 46.03/13.10 |
% 46.03/13.10 |-The branch is then unsatisfiable
% 46.03/13.10 |-Branch two:
% 46.03/13.10 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 46.03/13.10 |
% 46.03/13.10 | Applying alpha-rule on (231) yields:
% 46.03/13.10 | (232) all_11_7_47 = all_11_9_49
% 46.03/13.10 | (219) all_0_1_1 = vnoExp
% 46.03/13.10 | (234) ~ (all_11_6_46 = 0)
% 46.03/13.10 | (235) vreduce(all_11_10_50) = all_11_9_49
% 46.03/13.10 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 46.03/13.10 | (212) all_11_8_48 = all_0_3_3
% 46.03/13.10 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 46.03/13.11 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 46.03/13.11 |
% 46.03/13.11 | Instantiating formula (55) with ve1, all_11_9_49, all_0_6_6 and discharging atoms vreduce(ve1) = all_0_6_6, yields:
% 46.03/13.11 | (240) all_11_9_49 = all_0_6_6 | ~ (vreduce(ve1) = all_11_9_49)
% 46.03/13.11 |
% 46.03/13.11 | Instantiating formula (47) with all_11_6_46, all_0_6_6, all_9_1_17 and discharging atoms vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 46.03/13.11 | (241) all_11_6_46 = 0 | ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 46.03/13.11 |
% 46.03/13.11 | Instantiating formula (88) with all_0_3_3, all_11_11_51, all_11_10_50, ve2, ve1 and discharging atoms vapp(all_11_10_50, all_11_11_51) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 46.03/13.11 | (242) all_11_10_50 = ve1
% 46.03/13.11 |
% 46.03/13.11 | From (242) and (235) follows:
% 46.03/13.11 | (243) vreduce(ve1) = all_11_9_49
% 46.03/13.11 |
% 46.03/13.11 +-Applying beta-rule and splitting (241), into two cases.
% 46.03/13.11 |-Branch one:
% 46.03/13.11 | (244) ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 46.03/13.11 |
% 46.03/13.11 +-Applying beta-rule and splitting (240), into two cases.
% 46.03/13.11 |-Branch one:
% 46.03/13.11 | (245) ~ (vreduce(ve1) = all_11_9_49)
% 46.03/13.11 |
% 46.03/13.11 | Using (243) and (245) yields:
% 46.03/13.11 | (130) $false
% 46.03/13.11 |
% 46.03/13.11 |-The branch is then unsatisfiable
% 46.03/13.11 |-Branch two:
% 46.03/13.11 | (243) vreduce(ve1) = all_11_9_49
% 46.03/13.11 | (248) all_11_9_49 = all_0_6_6
% 46.03/13.11 |
% 46.03/13.11 | From (248) and (239) follows:
% 46.03/13.11 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 46.03/13.11 |
% 46.03/13.11 | Using (249) and (244) yields:
% 46.03/13.11 | (130) $false
% 46.03/13.11 |
% 46.03/13.11 |-The branch is then unsatisfiable
% 46.03/13.11 |-Branch two:
% 46.03/13.11 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 46.03/13.11 | (206) all_11_6_46 = 0
% 46.03/13.11 |
% 46.03/13.11 | Equations (206) can reduce 234 to:
% 46.03/13.11 | (165) $false
% 46.03/13.11 |
% 46.03/13.11 |-The branch is then unsatisfiable
% 46.03/13.11 |-Branch two:
% 46.03/13.11 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 46.03/13.11 |
% 46.03/13.11 | Applying alpha-rule on (254) yields:
% 46.03/13.11 | (212) all_11_8_48 = all_0_3_3
% 46.03/13.11 | (219) all_0_1_1 = vnoExp
% 46.03/13.11 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 46.03/13.11 |
% 46.03/13.11 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3, yields:
% 46.03/13.11 | (130) $false
% 46.03/13.11 |
% 46.03/13.11 |-The branch is then unsatisfiable
% 46.03/13.11 |-Branch two:
% 46.03/13.11 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 46.03/13.11 |
% 46.03/13.11 | Applying alpha-rule on (259) yields:
% 46.03/13.11 | (260) all_11_10_50 = all_0_3_3
% 46.03/13.11 | (219) all_0_1_1 = vnoExp
% 46.03/13.11 | (262) vvar(all_11_11_51) = all_0_3_3
% 46.03/13.11 |
% 46.03/13.11 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_11_11_51) = all_0_3_3, yields:
% 46.03/13.11 | (130) $false
% 46.03/13.11 |
% 46.03/13.11 |-The branch is then unsatisfiable
% 46.03/13.11 |-Branch two:
% 46.03/13.11 | (378) all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)
% 46.03/13.11 |
% 46.03/13.11 | Applying alpha-rule on (378) yields:
% 46.03/13.11 | (379) vapp(all_9_5_21, all_9_9_25) = all_9_4_20
% 46.03/13.11 | (380) vsomeExp(all_9_4_20) = all_0_6_6
% 46.03/13.11 | (381) all_9_7_23 = all_9_10_26
% 46.03/13.11 | (382) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)
% 46.03/13.11 | (383) all_9_8_24 = ve1
% 46.03/13.11 | (384) all_9_6_22 = 0
% 46.03/13.11 | (385) visSomeExp(all_9_10_26) = 0
% 46.03/13.11 | (386) vapp(all_9_11_27, all_9_9_25) = ve1
% 46.03/13.11 | (387) all_9_3_19 = all_0_6_6
% 46.03/13.11 | (388) vreduce(all_9_11_27) = all_9_10_26
% 46.03/13.11 | (389) vgetSomeExp(all_9_10_26) = all_9_5_21
% 46.03/13.11 |
% 46.03/13.11 | Instantiating formula (92) with ve1, all_9_9_25, all_9_11_27 and discharging atoms vapp(all_9_11_27, all_9_9_25) = ve1, yields:
% 46.03/13.11 | (162) ~ (visValue(ve1) = 0)
% 46.03/13.11 |
% 46.03/13.11 | Using (68) and (162) yields:
% 46.03/13.11 | (163) ~ (all_0_7_7 = 0)
% 46.03/13.11 |
% 46.03/13.11 +-Applying beta-rule and splitting (143), into two cases.
% 46.03/13.11 |-Branch one:
% 46.03/13.11 | (164) all_0_7_7 = 0
% 46.03/13.11 |
% 46.03/13.11 | Equations (164) can reduce 163 to:
% 46.03/13.11 | (165) $false
% 46.03/13.11 |
% 46.03/13.11 |-The branch is then unsatisfiable
% 46.03/13.11 |-Branch two:
% 46.03/13.11 | (163) ~ (all_0_7_7 = 0)
% 46.03/13.11 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 46.03/13.11 |
% 46.03/13.11 | Instantiating (167) with all_124_0_116 yields:
% 46.03/13.11 | (396) vsomeExp(all_124_0_116) = all_0_6_6
% 46.03/13.11 |
% 46.03/13.11 | Instantiating formula (85) with all_0_6_6, all_124_0_116, all_9_4_20 and discharging atoms vsomeExp(all_124_0_116) = all_0_6_6, vsomeExp(all_9_4_20) = all_0_6_6, yields:
% 46.03/13.11 | (397) all_124_0_116 = all_9_4_20
% 46.03/13.11 |
% 46.03/13.11 | From (397) and (396) follows:
% 46.03/13.11 | (380) vsomeExp(all_9_4_20) = all_0_6_6
% 46.03/13.11 |
% 46.03/13.11 +-Applying beta-rule and splitting (116), into two cases.
% 46.03/13.11 |-Branch one:
% 46.03/13.11 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 46.03/13.12 |
% 46.03/13.12 +-Applying beta-rule and splitting (171), into two cases.
% 46.03/13.12 |-Branch one:
% 46.03/13.12 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 46.48/13.12 |
% 46.48/13.12 +-Applying beta-rule and splitting (172), into two cases.
% 46.48/13.12 |-Branch one:
% 46.48/13.12 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 46.48/13.12 |
% 46.48/13.12 +-Applying beta-rule and splitting (173), into two cases.
% 46.48/13.12 |-Branch one:
% 46.48/13.12 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 46.48/13.13 |
% 46.48/13.13 +-Applying beta-rule and splitting (174), into two cases.
% 46.48/13.13 |-Branch one:
% 46.48/13.13 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 46.48/13.13 |
% 46.48/13.13 +-Applying beta-rule and splitting (175), into two cases.
% 46.48/13.13 |-Branch one:
% 46.48/13.13 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 46.48/13.13 |
% 46.48/13.13 | Applying alpha-rule on (176) yields:
% 46.48/13.13 | (177) all_11_5_45 = all_0_3_3
% 46.48/13.13 | (178) all_11_4_44 = all_11_10_50
% 46.48/13.13 | (179) visValue(all_11_8_48) = 0
% 46.48/13.13 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 46.48/13.13 | (181) all_11_0_40 = all_0_1_1
% 46.48/13.13 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 46.48/13.13 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 46.48/13.13 | (184) vreduce(all_11_8_48) = all_11_10_50
% 46.48/13.13 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 46.48/13.13 | (186) ~ (all_11_3_43 = 0)
% 46.48/13.13 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 46.48/13.13 | (188) all_11_2_42 = 0
% 46.48/13.13 |
% 46.48/13.13 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 46.48/13.13 | (130) $false
% 46.48/13.13 |
% 46.48/13.13 |-The branch is then unsatisfiable
% 46.48/13.13 |-Branch two:
% 46.48/13.13 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 46.48/13.13 |
% 46.48/13.13 | Applying alpha-rule on (190) yields:
% 46.48/13.13 | (177) all_11_5_45 = all_0_3_3
% 46.48/13.13 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 46.48/13.13 | (193) visSomeExp(all_11_7_47) = 0
% 46.48/13.13 | (181) all_11_0_40 = all_0_1_1
% 46.48/13.13 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 46.48/13.13 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 46.48/13.13 | (197) vreduce(all_11_11_51) = all_11_7_47
% 46.48/13.13 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 46.48/13.13 | (199) all_11_3_43 = 0
% 46.48/13.13 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 46.48/13.13 | (201) all_11_4_44 = all_11_7_47
% 46.48/13.13 |
% 46.48/13.13 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 46.48/13.13 | (130) $false
% 46.48/13.13 |
% 46.48/13.13 |-The branch is then unsatisfiable
% 46.48/13.13 |-Branch two:
% 46.48/13.13 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 46.48/13.13 |
% 46.48/13.13 | Applying alpha-rule on (203) yields:
% 46.48/13.13 | (204) all_11_7_47 = all_11_10_50
% 46.48/13.13 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 46.48/13.13 | (206) all_11_6_46 = 0
% 46.48/13.13 | (207) all_11_3_43 = all_0_1_1
% 46.48/13.13 | (208) visSomeExp(all_11_10_50) = 0
% 46.48/13.13 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 46.48/13.13 | (210) vreduce(all_11_11_51) = all_11_10_50
% 46.48/13.13 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 46.48/13.13 | (212) all_11_8_48 = all_0_3_3
% 46.48/13.13 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 46.48/13.13 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 46.48/13.13 |
% 46.48/13.13 | Instantiating formula (74) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = all_0_1_1, yields:
% 46.48/13.13 | (130) $false
% 46.48/13.13 |
% 46.48/13.13 |-The branch is then unsatisfiable
% 46.48/13.13 |-Branch two:
% 46.48/13.13 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 46.48/13.13 |
% 46.48/13.13 | Applying alpha-rule on (216) yields:
% 46.48/13.13 | (177) all_11_5_45 = all_0_3_3
% 46.48/13.13 | (218) visValue(all_11_7_47) = all_11_2_42
% 46.48/13.13 | (219) all_0_1_1 = vnoExp
% 46.48/13.13 | (220) vreduce(all_11_7_47) = all_11_8_48
% 46.48/13.13 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 46.48/13.13 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 46.48/13.13 | (186) ~ (all_11_3_43 = 0)
% 46.48/13.13 | (224) all_11_4_44 = all_11_8_48
% 46.48/13.13 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 46.48/13.13 | (226) ~ (all_11_2_42 = 0)
% 46.48/13.13 |
% 46.48/13.13 | Instantiating formula (88) with all_0_3_3, all_11_7_47, all_11_6_46, ve2, ve1 and discharging atoms vapp(all_11_6_46, all_11_7_47) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 46.48/13.14 | (227) all_11_6_46 = ve1
% 46.48/13.14 |
% 46.48/13.14 | Instantiating formula (66) with ve1, all_9_9_25, all_9_11_27, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(all_9_11_27, all_9_9_25) = ve1, yields:
% 46.48/13.14 | (228) ~ (vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1)
% 46.48/13.14 |
% 46.48/13.14 | From (227) and (221) follows:
% 46.48/13.14 | (229) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1
% 46.48/13.14 |
% 46.48/13.14 | Using (229) and (228) yields:
% 46.48/13.14 | (130) $false
% 46.48/13.14 |
% 46.48/13.14 |-The branch is then unsatisfiable
% 46.48/13.14 |-Branch two:
% 46.48/13.14 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 46.48/13.14 |
% 46.48/13.14 | Applying alpha-rule on (231) yields:
% 46.48/13.14 | (232) all_11_7_47 = all_11_9_49
% 46.48/13.14 | (219) all_0_1_1 = vnoExp
% 46.48/13.14 | (234) ~ (all_11_6_46 = 0)
% 46.48/13.14 | (235) vreduce(all_11_10_50) = all_11_9_49
% 46.48/13.14 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 46.48/13.14 | (212) all_11_8_48 = all_0_3_3
% 46.48/13.14 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 46.48/13.14 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 46.48/13.14 |
% 46.48/13.14 | Instantiating formula (55) with ve1, all_11_9_49, all_0_6_6 and discharging atoms vreduce(ve1) = all_0_6_6, yields:
% 46.48/13.14 | (240) all_11_9_49 = all_0_6_6 | ~ (vreduce(ve1) = all_11_9_49)
% 46.48/13.14 |
% 46.48/13.14 | Instantiating formula (47) with all_11_6_46, all_0_6_6, all_9_4_20 and discharging atoms vsomeExp(all_9_4_20) = all_0_6_6, yields:
% 46.48/13.14 | (241) all_11_6_46 = 0 | ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 46.48/13.14 |
% 46.48/13.14 | Instantiating formula (88) with all_0_3_3, all_11_11_51, all_11_10_50, ve2, ve1 and discharging atoms vapp(all_11_10_50, all_11_11_51) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 46.48/13.14 | (242) all_11_10_50 = ve1
% 46.48/13.14 |
% 46.48/13.14 | From (242) and (235) follows:
% 46.48/13.14 | (243) vreduce(ve1) = all_11_9_49
% 46.48/13.14 |
% 46.48/13.14 +-Applying beta-rule and splitting (241), into two cases.
% 46.48/13.14 |-Branch one:
% 46.48/13.14 | (244) ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 46.48/13.14 |
% 46.48/13.14 +-Applying beta-rule and splitting (240), into two cases.
% 46.48/13.14 |-Branch one:
% 46.48/13.14 | (245) ~ (vreduce(ve1) = all_11_9_49)
% 46.48/13.14 |
% 46.48/13.14 | Using (243) and (245) yields:
% 46.48/13.14 | (130) $false
% 46.48/13.14 |
% 46.48/13.14 |-The branch is then unsatisfiable
% 46.48/13.14 |-Branch two:
% 46.48/13.14 | (243) vreduce(ve1) = all_11_9_49
% 46.48/13.14 | (248) all_11_9_49 = all_0_6_6
% 46.48/13.14 |
% 46.48/13.14 | From (248) and (239) follows:
% 46.48/13.14 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 46.48/13.14 |
% 46.48/13.14 | Using (249) and (244) yields:
% 46.48/13.14 | (130) $false
% 46.48/13.14 |
% 46.48/13.14 |-The branch is then unsatisfiable
% 46.48/13.14 |-Branch two:
% 46.48/13.14 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 46.48/13.14 | (206) all_11_6_46 = 0
% 46.48/13.14 |
% 46.48/13.14 | Equations (206) can reduce 234 to:
% 46.48/13.14 | (165) $false
% 46.48/13.14 |
% 46.48/13.14 |-The branch is then unsatisfiable
% 46.48/13.14 |-Branch two:
% 46.48/13.14 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 46.48/13.14 |
% 46.48/13.14 | Applying alpha-rule on (254) yields:
% 46.48/13.14 | (212) all_11_8_48 = all_0_3_3
% 46.48/13.14 | (219) all_0_1_1 = vnoExp
% 46.48/13.14 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 46.48/13.14 |
% 46.48/13.14 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3, yields:
% 46.48/13.14 | (130) $false
% 46.48/13.14 |
% 46.48/13.14 |-The branch is then unsatisfiable
% 46.48/13.14 |-Branch two:
% 46.48/13.14 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 46.48/13.14 |
% 46.48/13.14 | Applying alpha-rule on (259) yields:
% 46.48/13.14 | (260) all_11_10_50 = all_0_3_3
% 46.48/13.14 | (219) all_0_1_1 = vnoExp
% 46.48/13.14 | (262) vvar(all_11_11_51) = all_0_3_3
% 46.48/13.14 |
% 46.48/13.14 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_11_11_51) = all_0_3_3, yields:
% 46.48/13.14 | (130) $false
% 46.48/13.14 |
% 46.48/13.14 |-The branch is then unsatisfiable
% 46.48/13.14 |-Branch two:
% 46.48/13.14 | (492) all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22
% 46.48/13.14 |
% 46.48/13.14 | Applying alpha-rule on (492) yields:
% 46.48/13.14 | (493) vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22
% 46.48/13.14 | (494) vapp(all_9_6_22, all_9_7_23) = ve1
% 46.48/13.14 | (495) vreduce(all_9_7_23) = all_9_8_24
% 46.48/13.14 | (496) visSomeExp(all_9_8_24) = all_9_3_19
% 46.48/13.14 | (497) visValue(all_9_7_23) = all_9_2_18
% 46.48/13.14 | (498) all_9_4_20 = all_9_8_24
% 46.48/13.14 | (156) ~ (all_9_3_19 = 0)
% 46.48/13.14 | (159) all_9_5_21 = ve1
% 46.48/13.14 | (501) ~ (all_9_2_18 = 0)
% 46.48/13.15 | (502) all_0_6_6 = vnoExp
% 46.48/13.15 |
% 46.48/13.15 | Instantiating formula (92) with ve1, all_9_7_23, all_9_6_22 and discharging atoms vapp(all_9_6_22, all_9_7_23) = ve1, yields:
% 46.48/13.15 | (162) ~ (visValue(ve1) = 0)
% 46.48/13.15 |
% 46.48/13.15 | Using (68) and (162) yields:
% 46.48/13.15 | (163) ~ (all_0_7_7 = 0)
% 46.48/13.15 |
% 46.48/13.15 +-Applying beta-rule and splitting (143), into two cases.
% 46.48/13.15 |-Branch one:
% 46.48/13.15 | (164) all_0_7_7 = 0
% 46.48/13.15 |
% 46.48/13.15 | Equations (164) can reduce 163 to:
% 46.48/13.15 | (165) $false
% 46.48/13.15 |
% 46.48/13.15 |-The branch is then unsatisfiable
% 46.48/13.15 |-Branch two:
% 46.48/13.15 | (163) ~ (all_0_7_7 = 0)
% 46.48/13.15 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 46.48/13.15 |
% 46.48/13.15 | Instantiating (167) with all_135_0_146 yields:
% 46.48/13.15 | (509) vsomeExp(all_135_0_146) = all_0_6_6
% 46.48/13.15 |
% 46.48/13.15 | From (502) and (509) follows:
% 46.48/13.15 | (510) vsomeExp(all_135_0_146) = vnoExp
% 46.48/13.15 |
% 46.48/13.15 | Instantiating formula (40) with all_135_0_146 and discharging atoms vsomeExp(all_135_0_146) = vnoExp, yields:
% 46.48/13.15 | (130) $false
% 46.48/13.15 |
% 46.48/13.15 |-The branch is then unsatisfiable
% 46.48/13.15 |-Branch two:
% 46.48/13.15 | (512) all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)
% 46.48/13.15 |
% 46.48/13.15 | Applying alpha-rule on (512) yields:
% 46.48/13.15 | (383) all_9_8_24 = ve1
% 46.48/13.15 | (514) ~ (all_9_6_22 = 0)
% 46.48/13.15 | (515) all_9_7_23 = all_9_9_25
% 46.48/13.15 | (516) visSomeExp(all_9_9_25) = all_9_6_22
% 46.48/13.15 | (517) vapp(all_9_10_26, all_9_11_27) = ve1
% 46.48/13.15 | (518) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)
% 46.48/13.15 | (519) vreduce(all_9_10_26) = all_9_9_25
% 46.48/13.15 | (502) all_0_6_6 = vnoExp
% 46.48/13.15 |
% 46.48/13.15 | Instantiating formula (92) with ve1, all_9_11_27, all_9_10_26 and discharging atoms vapp(all_9_10_26, all_9_11_27) = ve1, yields:
% 46.48/13.15 | (162) ~ (visValue(ve1) = 0)
% 46.48/13.15 |
% 46.48/13.15 | Using (68) and (162) yields:
% 46.48/13.15 | (163) ~ (all_0_7_7 = 0)
% 46.48/13.15 |
% 46.48/13.15 +-Applying beta-rule and splitting (143), into two cases.
% 46.48/13.15 |-Branch one:
% 46.48/13.15 | (164) all_0_7_7 = 0
% 46.48/13.15 |
% 46.48/13.15 | Equations (164) can reduce 163 to:
% 46.48/13.15 | (165) $false
% 46.48/13.15 |
% 46.48/13.15 |-The branch is then unsatisfiable
% 46.48/13.15 |-Branch two:
% 46.48/13.15 | (163) ~ (all_0_7_7 = 0)
% 46.48/13.15 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 46.48/13.15 |
% 46.48/13.15 | Instantiating (167) with all_124_0_147 yields:
% 46.48/13.15 | (527) vsomeExp(all_124_0_147) = all_0_6_6
% 46.48/13.15 |
% 46.48/13.15 | From (502) and (527) follows:
% 46.48/13.15 | (528) vsomeExp(all_124_0_147) = vnoExp
% 46.48/13.15 |
% 46.48/13.15 | Instantiating formula (40) with all_124_0_147 and discharging atoms vsomeExp(all_124_0_147) = vnoExp, yields:
% 46.48/13.15 | (130) $false
% 46.48/13.15 |
% 46.48/13.15 |-The branch is then unsatisfiable
% 46.48/13.15 |-Branch two:
% 46.48/13.15 | (530) all_9_8_24 = ve1 & all_0_6_6 = vnoExp & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1
% 46.48/13.15 |
% 46.48/13.15 | Applying alpha-rule on (530) yields:
% 46.48/13.15 | (383) all_9_8_24 = ve1
% 46.48/13.15 | (502) all_0_6_6 = vnoExp
% 46.48/13.15 | (533) vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1
% 46.48/13.15 |
% 46.48/13.15 | Equations (502) can reduce 120 to:
% 46.48/13.15 | (534) ~ (all_0_1_1 = vnoExp)
% 46.48/13.15 |
% 46.48/13.15 +-Applying beta-rule and splitting (116), into two cases.
% 46.48/13.15 |-Branch one:
% 46.48/13.15 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 46.48/13.15 |
% 46.48/13.15 +-Applying beta-rule and splitting (171), into two cases.
% 46.48/13.15 |-Branch one:
% 46.48/13.15 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 46.48/13.16 |
% 46.48/13.16 +-Applying beta-rule and splitting (172), into two cases.
% 46.48/13.16 |-Branch one:
% 46.48/13.16 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 46.48/13.16 |
% 46.48/13.16 +-Applying beta-rule and splitting (173), into two cases.
% 46.48/13.16 |-Branch one:
% 46.48/13.16 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 46.48/13.16 |
% 46.48/13.16 +-Applying beta-rule and splitting (174), into two cases.
% 46.48/13.16 |-Branch one:
% 46.48/13.16 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 46.48/13.16 |
% 46.48/13.16 +-Applying beta-rule and splitting (175), into two cases.
% 46.48/13.16 |-Branch one:
% 46.48/13.16 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 46.48/13.16 |
% 46.48/13.16 | Applying alpha-rule on (176) yields:
% 46.48/13.16 | (177) all_11_5_45 = all_0_3_3
% 46.48/13.16 | (178) all_11_4_44 = all_11_10_50
% 46.48/13.16 | (179) visValue(all_11_8_48) = 0
% 46.48/13.16 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 46.48/13.16 | (181) all_11_0_40 = all_0_1_1
% 46.48/13.16 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 46.48/13.16 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 46.48/13.16 | (184) vreduce(all_11_8_48) = all_11_10_50
% 46.48/13.16 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 46.48/13.16 | (186) ~ (all_11_3_43 = 0)
% 46.48/13.16 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 46.48/13.16 | (188) all_11_2_42 = 0
% 46.48/13.16 |
% 46.48/13.16 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 46.48/13.16 | (130) $false
% 46.48/13.16 |
% 46.48/13.16 |-The branch is then unsatisfiable
% 46.48/13.16 |-Branch two:
% 46.48/13.16 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 46.48/13.16 |
% 46.48/13.16 | Applying alpha-rule on (190) yields:
% 46.48/13.16 | (177) all_11_5_45 = all_0_3_3
% 46.48/13.16 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 46.48/13.16 | (193) visSomeExp(all_11_7_47) = 0
% 46.48/13.16 | (181) all_11_0_40 = all_0_1_1
% 46.48/13.16 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 46.48/13.16 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 46.48/13.16 | (197) vreduce(all_11_11_51) = all_11_7_47
% 46.48/13.17 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 46.48/13.17 | (199) all_11_3_43 = 0
% 46.48/13.17 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 46.48/13.17 | (201) all_11_4_44 = all_11_7_47
% 46.48/13.17 |
% 46.48/13.17 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 46.48/13.17 | (130) $false
% 46.48/13.17 |
% 46.48/13.17 |-The branch is then unsatisfiable
% 46.48/13.17 |-Branch two:
% 46.48/13.17 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 46.48/13.17 |
% 46.48/13.17 | Applying alpha-rule on (203) yields:
% 46.48/13.17 | (204) all_11_7_47 = all_11_10_50
% 46.48/13.17 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 46.48/13.17 | (206) all_11_6_46 = 0
% 46.48/13.17 | (207) all_11_3_43 = all_0_1_1
% 46.48/13.17 | (208) visSomeExp(all_11_10_50) = 0
% 46.48/13.17 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 46.48/13.17 | (210) vreduce(all_11_11_51) = all_11_10_50
% 46.48/13.17 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 46.48/13.17 | (212) all_11_8_48 = all_0_3_3
% 46.48/13.17 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 46.48/13.17 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 46.48/13.17 |
% 46.48/13.17 | Instantiating formula (74) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = all_0_1_1, yields:
% 46.48/13.17 | (130) $false
% 46.48/13.17 |
% 46.48/13.17 |-The branch is then unsatisfiable
% 46.48/13.17 |-Branch two:
% 46.48/13.17 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 46.48/13.17 |
% 46.48/13.17 | Applying alpha-rule on (216) yields:
% 46.48/13.17 | (177) all_11_5_45 = all_0_3_3
% 46.48/13.17 | (218) visValue(all_11_7_47) = all_11_2_42
% 46.48/13.17 | (219) all_0_1_1 = vnoExp
% 46.48/13.17 | (220) vreduce(all_11_7_47) = all_11_8_48
% 46.48/13.17 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 46.48/13.17 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 46.48/13.17 | (186) ~ (all_11_3_43 = 0)
% 46.48/13.17 | (224) all_11_4_44 = all_11_8_48
% 46.48/13.17 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 46.48/13.17 | (226) ~ (all_11_2_42 = 0)
% 46.48/13.17 |
% 46.48/13.17 | Equations (219) can reduce 534 to:
% 46.48/13.17 | (165) $false
% 46.48/13.17 |
% 46.48/13.17 |-The branch is then unsatisfiable
% 46.48/13.17 |-Branch two:
% 46.48/13.17 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 46.48/13.17 |
% 46.48/13.17 | Applying alpha-rule on (231) yields:
% 46.48/13.17 | (232) all_11_7_47 = all_11_9_49
% 46.48/13.17 | (219) all_0_1_1 = vnoExp
% 46.48/13.17 | (234) ~ (all_11_6_46 = 0)
% 46.48/13.17 | (235) vreduce(all_11_10_50) = all_11_9_49
% 46.48/13.17 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 46.48/13.17 | (212) all_11_8_48 = all_0_3_3
% 46.48/13.17 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 46.48/13.17 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 46.48/13.17 |
% 46.48/13.17 | Equations (219) can reduce 534 to:
% 46.48/13.17 | (165) $false
% 46.48/13.17 |
% 46.48/13.17 |-The branch is then unsatisfiable
% 46.48/13.17 |-Branch two:
% 46.48/13.17 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 46.48/13.17 |
% 46.48/13.17 | Applying alpha-rule on (254) yields:
% 46.48/13.17 | (212) all_11_8_48 = all_0_3_3
% 46.48/13.17 | (219) all_0_1_1 = vnoExp
% 46.48/13.17 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 46.48/13.17 |
% 46.48/13.17 | Equations (219) can reduce 534 to:
% 46.48/13.17 | (165) $false
% 46.48/13.17 |
% 46.48/13.17 |-The branch is then unsatisfiable
% 46.48/13.17 |-Branch two:
% 46.48/13.17 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 46.48/13.17 |
% 46.48/13.17 | Applying alpha-rule on (259) yields:
% 46.48/13.17 | (260) all_11_10_50 = all_0_3_3
% 46.48/13.17 | (219) all_0_1_1 = vnoExp
% 46.48/13.17 | (262) vvar(all_11_11_51) = all_0_3_3
% 46.48/13.17 |
% 46.48/13.17 | Equations (219) can reduce 534 to:
% 46.48/13.17 | (165) $false
% 46.48/13.17 |
% 46.48/13.17 |-The branch is then unsatisfiable
% 46.48/13.17 |-Branch two:
% 46.48/13.17 | (612) all_9_10_26 = ve1 & all_0_6_6 = vnoExp & vvar(all_9_11_27) = ve1
% 46.48/13.17 |
% 46.48/13.17 | Applying alpha-rule on (612) yields:
% 46.48/13.17 | (613) all_9_10_26 = ve1
% 46.48/13.17 | (502) all_0_6_6 = vnoExp
% 46.48/13.17 | (615) vvar(all_9_11_27) = ve1
% 46.48/13.17 |
% 46.48/13.17 | Instantiating formula (104) with ve1, all_9_11_27 and discharging atoms vvar(all_9_11_27) = ve1, yields:
% 46.48/13.17 | (162) ~ (visValue(ve1) = 0)
% 46.48/13.17 |
% 46.48/13.17 | Using (68) and (162) yields:
% 46.48/13.17 | (163) ~ (all_0_7_7 = 0)
% 46.48/13.17 |
% 46.48/13.17 +-Applying beta-rule and splitting (143), into two cases.
% 46.48/13.17 |-Branch one:
% 46.48/13.17 | (164) all_0_7_7 = 0
% 46.48/13.17 |
% 46.48/13.17 | Equations (164) can reduce 163 to:
% 46.48/13.17 | (165) $false
% 46.48/13.17 |
% 46.48/13.17 |-The branch is then unsatisfiable
% 46.48/13.17 |-Branch two:
% 46.48/13.17 | (163) ~ (all_0_7_7 = 0)
% 46.48/13.17 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 46.48/13.17 |
% 46.48/13.17 | Instantiating (167) with all_123_0_149 yields:
% 46.48/13.17 | (622) vsomeExp(all_123_0_149) = all_0_6_6
% 46.48/13.17 |
% 46.48/13.17 | From (502) and (622) follows:
% 46.48/13.17 | (623) vsomeExp(all_123_0_149) = vnoExp
% 46.48/13.17 |
% 46.48/13.17 | Instantiating formula (40) with all_123_0_149 and discharging atoms vsomeExp(all_123_0_149) = vnoExp, yields:
% 46.48/13.17 | (130) $false
% 46.48/13.17 |
% 46.48/13.17 |-The branch is then unsatisfiable
% 46.48/13.17 |-Branch two:
% 46.48/13.17 | (625) all_8_4_12 = all_8_7_15 & all_8_5_13 = all_0_3_3 & vlookup(all_8_6_14, vempty) = all_8_7_15 & vsomeType(all_0_0_0) = all_8_7_15 & vvar(all_8_6_14) = all_0_3_3
% 46.48/13.17 |
% 46.48/13.17 | Applying alpha-rule on (625) yields:
% 46.48/13.17 | (626) all_8_4_12 = all_8_7_15
% 46.48/13.17 | (627) all_8_5_13 = all_0_3_3
% 46.48/13.17 | (628) vvar(all_8_6_14) = all_0_3_3
% 46.48/13.17 | (629) vsomeType(all_0_0_0) = all_8_7_15
% 46.48/13.17 | (630) vlookup(all_8_6_14, vempty) = all_8_7_15
% 46.48/13.17 |
% 46.48/13.17 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_8_6_14 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_8_6_14) = all_0_3_3, yields:
% 46.48/13.17 | (130) $false
% 46.48/13.17 |
% 46.48/13.17 |-The branch is then unsatisfiable
% 46.48/13.17 |-Branch two:
% 46.48/13.17 | (632) vreduce(ve1) = all_0_1_1
% 46.48/13.17 | (633) all_0_1_1 = all_0_6_6
% 46.48/13.18 |
% 46.48/13.18 | From (633) and (14) follows:
% 46.48/13.18 | (634) vreduce(all_0_3_3) = all_0_6_6
% 46.48/13.18 |
% 46.48/13.18 | From (633) and (632) follows:
% 46.48/13.18 | (42) vreduce(ve1) = all_0_6_6
% 46.48/13.18 |
% 46.48/13.18 +-Applying beta-rule and splitting (107), into two cases.
% 46.48/13.18 |-Branch one:
% 46.48/13.18 | (636) ~ (vreduce(ve1) = all_0_4_4)
% 46.48/13.18 |
% 46.48/13.18 | Using (42) and (636) yields:
% 46.48/13.18 | (637) ~ (all_0_4_4 = all_0_6_6)
% 46.48/13.18 |
% 46.48/13.18 +-Applying beta-rule and splitting (113), into two cases.
% 46.48/13.18 |-Branch one:
% 46.48/13.18 | (121) (all_8_0_8 = 0 & all_8_2_10 = all_0_0_0 & all_8_3_11 = all_0_3_3 & varrow(all_8_5_13, all_8_4_12) = all_0_0_0 & vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0 & vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9 & vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3) | (all_8_1_9 = 0 & all_8_2_10 = 0 & all_8_4_12 = all_0_3_3 & varrow(all_8_5_13, all_0_0_0) = all_8_3_11 & vtcheck(vempty, all_8_6_14, all_8_5_13) = 0 & vtcheck(vempty, all_8_7_15, all_8_3_11) = 0 & vapp(all_8_7_15, all_8_6_14) = all_0_3_3)
% 46.48/13.18 |
% 46.48/13.18 +-Applying beta-rule and splitting (121), into two cases.
% 46.48/13.18 |-Branch one:
% 46.48/13.18 | (122) all_8_0_8 = 0 & all_8_2_10 = all_0_0_0 & all_8_3_11 = all_0_3_3 & varrow(all_8_5_13, all_8_4_12) = all_0_0_0 & vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0 & vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9 & vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3
% 46.48/13.18 |
% 46.48/13.18 | Applying alpha-rule on (122) yields:
% 46.48/13.18 | (123) vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3
% 46.48/13.18 | (124) vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0
% 46.48/13.18 | (125) vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9
% 46.48/13.18 | (126) all_8_3_11 = all_0_3_3
% 46.48/13.18 | (127) all_8_0_8 = 0
% 46.48/13.18 | (128) all_8_2_10 = all_0_0_0
% 46.48/13.18 | (129) varrow(all_8_5_13, all_8_4_12) = all_0_0_0
% 46.48/13.18 |
% 46.48/13.18 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_8_6_14, all_8_5_13, all_8_7_15 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3, yields:
% 46.48/13.18 | (130) $false
% 46.48/13.18 |
% 46.48/13.18 |-The branch is then unsatisfiable
% 46.48/13.18 |-Branch two:
% 46.48/13.18 | (131) all_8_1_9 = 0 & all_8_2_10 = 0 & all_8_4_12 = all_0_3_3 & varrow(all_8_5_13, all_0_0_0) = all_8_3_11 & vtcheck(vempty, all_8_6_14, all_8_5_13) = 0 & vtcheck(vempty, all_8_7_15, all_8_3_11) = 0 & vapp(all_8_7_15, all_8_6_14) = all_0_3_3
% 46.48/13.18 |
% 46.48/13.18 | Applying alpha-rule on (131) yields:
% 46.48/13.18 | (132) varrow(all_8_5_13, all_0_0_0) = all_8_3_11
% 46.48/13.18 | (133) vtcheck(vempty, all_8_6_14, all_8_5_13) = 0
% 46.48/13.18 | (134) all_8_2_10 = 0
% 46.48/13.18 | (135) vtcheck(vempty, all_8_7_15, all_8_3_11) = 0
% 46.48/13.18 | (136) all_8_4_12 = all_0_3_3
% 46.48/13.18 | (137) all_8_1_9 = 0
% 46.48/13.18 | (138) vapp(all_8_7_15, all_8_6_14) = all_0_3_3
% 46.48/13.18 |
% 46.48/13.18 | Instantiating formula (31) with all_0_3_3, all_8_6_14, all_8_7_15, ve2, ve1 and discharging atoms vapp(all_8_7_15, all_8_6_14) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 46.48/13.18 | (139) all_8_6_14 = ve2
% 46.48/13.18 |
% 46.48/13.18 | Instantiating formula (88) with all_0_3_3, all_8_6_14, all_8_7_15, ve2, ve1 and discharging atoms vapp(all_8_7_15, all_8_6_14) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 46.48/13.18 | (140) all_8_7_15 = ve1
% 46.48/13.18 |
% 46.48/13.18 | From (139) and (133) follows:
% 46.48/13.18 | (658) vtcheck(vempty, ve2, all_8_5_13) = 0
% 46.48/13.18 |
% 46.48/13.18 | From (140) and (135) follows:
% 46.48/13.18 | (141) vtcheck(vempty, ve1, all_8_3_11) = 0
% 46.48/13.18 |
% 46.48/13.18 | From (140)(139) and (138) follows:
% 46.48/13.18 | (35) vapp(ve1, ve2) = all_0_3_3
% 46.48/13.18 |
% 46.48/13.18 | Instantiating formula (29) with all_8_5_13 and discharging atoms vtcheck(vempty, ve2, all_8_5_13) = 0, yields:
% 46.48/13.18 | (661) all_0_5_5 = 0 | ? [v0] : vsomeExp(v0) = all_0_4_4
% 46.48/13.18 |
% 46.48/13.18 | Instantiating formula (67) with all_8_3_11 and discharging atoms vtcheck(vempty, ve1, all_8_3_11) = 0, yields:
% 46.48/13.18 | (143) all_0_7_7 = 0 | ? [v0] : vsomeExp(v0) = all_0_6_6
% 46.48/13.18 |
% 46.48/13.18 +-Applying beta-rule and splitting (114), into two cases.
% 46.48/13.18 |-Branch one:
% 46.48/13.18 | (144) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22) | (all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)) | (all_9_8_24 = ve1 & all_0_6_6 = vnoExp & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1)
% 46.48/13.18 |
% 46.48/13.18 +-Applying beta-rule and splitting (144), into two cases.
% 46.48/13.18 |-Branch one:
% 46.48/13.18 | (145) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22) | (all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26))
% 46.48/13.19 |
% 46.48/13.19 +-Applying beta-rule and splitting (145), into two cases.
% 46.48/13.19 |-Branch one:
% 46.48/13.19 | (146) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22)
% 46.48/13.19 |
% 46.48/13.19 +-Applying beta-rule and splitting (146), into two cases.
% 46.48/13.19 |-Branch one:
% 46.48/13.19 | (147) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27))
% 46.77/13.19 |
% 46.77/13.19 +-Applying beta-rule and splitting (147), into two cases.
% 46.77/13.19 |-Branch one:
% 46.77/13.19 | (148) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22)
% 46.77/13.19 |
% 46.77/13.19 +-Applying beta-rule and splitting (148), into two cases.
% 46.77/13.19 |-Branch one:
% 46.77/13.19 | (149) all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22
% 46.77/13.19 |
% 46.77/13.19 | Applying alpha-rule on (149) yields:
% 46.77/13.19 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 46.77/13.19 | (151) vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22
% 46.77/13.19 | (152) visSomeExp(all_9_10_26) = all_9_3_19
% 46.77/13.19 | (153) all_9_0_16 = all_0_6_6
% 46.77/13.19 | (154) vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17
% 46.77/13.19 | (155) vreduce(all_9_8_24) = all_9_10_26
% 46.77/13.19 | (156) ~ (all_9_3_19 = 0)
% 46.77/13.19 | (157) all_9_4_20 = all_9_10_26
% 46.77/13.19 | (158) vapp(all_9_6_22, all_9_8_24) = ve1
% 46.77/13.19 | (159) all_9_5_21 = ve1
% 46.77/13.19 | (160) all_9_2_18 = 0
% 46.77/13.19 | (161) visValue(all_9_8_24) = 0
% 46.77/13.19 |
% 46.77/13.19 | Instantiating formula (74) with all_9_1_17 yields:
% 46.77/13.19 | (681) ~ (vsomeExp(all_9_1_17) = all_0_1_1)
% 46.77/13.19 |
% 46.77/13.19 | From (633) and (681) follows:
% 46.77/13.19 | (682) ~ (vsomeExp(all_9_1_17) = all_0_6_6)
% 46.77/13.19 |
% 46.77/13.19 | Using (150) and (682) yields:
% 46.77/13.19 | (130) $false
% 46.77/13.19 |
% 46.77/13.19 |-The branch is then unsatisfiable
% 46.77/13.19 |-Branch two:
% 46.77/13.19 | (264) all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22
% 46.77/13.19 |
% 46.77/13.19 | Applying alpha-rule on (264) yields:
% 46.77/13.19 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 46.77/13.19 | (266) visSomeExp(all_9_7_23) = 0
% 46.77/13.19 | (267) vapp(all_9_6_22, all_9_2_18) = all_9_1_17
% 46.77/13.19 | (268) vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22
% 46.77/13.19 | (269) vreduce(all_9_11_27) = all_9_7_23
% 46.77/13.19 | (270) vapp(all_9_6_22, all_9_11_27) = ve1
% 46.77/13.19 | (153) all_9_0_16 = all_0_6_6
% 46.77/13.19 | (272) all_9_3_19 = 0
% 46.77/13.19 | (273) vgetSomeExp(all_9_7_23) = all_9_2_18
% 46.77/13.19 | (159) all_9_5_21 = ve1
% 46.77/13.19 | (275) all_9_4_20 = all_9_7_23
% 46.77/13.19 |
% 46.77/13.19 | Instantiating formula (74) with all_9_1_17 yields:
% 46.77/13.19 | (681) ~ (vsomeExp(all_9_1_17) = all_0_1_1)
% 46.77/13.19 |
% 46.77/13.19 | From (633) and (681) follows:
% 46.77/13.19 | (682) ~ (vsomeExp(all_9_1_17) = all_0_6_6)
% 46.77/13.19 |
% 46.77/13.20 | Using (150) and (682) yields:
% 46.77/13.20 | (130) $false
% 46.77/13.20 |
% 46.77/13.20 |-The branch is then unsatisfiable
% 46.77/13.20 |-Branch two:
% 46.77/13.20 | (378) all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)
% 46.77/13.20 |
% 46.77/13.20 | Applying alpha-rule on (378) yields:
% 46.77/13.20 | (379) vapp(all_9_5_21, all_9_9_25) = all_9_4_20
% 46.77/13.20 | (380) vsomeExp(all_9_4_20) = all_0_6_6
% 46.77/13.20 | (381) all_9_7_23 = all_9_10_26
% 46.77/13.20 | (382) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)
% 46.77/13.20 | (383) all_9_8_24 = ve1
% 46.77/13.20 | (384) all_9_6_22 = 0
% 46.77/13.20 | (385) visSomeExp(all_9_10_26) = 0
% 46.77/13.20 | (386) vapp(all_9_11_27, all_9_9_25) = ve1
% 46.77/13.20 | (387) all_9_3_19 = all_0_6_6
% 46.77/13.20 | (388) vreduce(all_9_11_27) = all_9_10_26
% 46.77/13.20 | (389) vgetSomeExp(all_9_10_26) = all_9_5_21
% 46.77/13.20 |
% 46.77/13.20 | Instantiating formula (74) with all_9_4_20 yields:
% 46.77/13.20 | (711) ~ (vsomeExp(all_9_4_20) = all_0_1_1)
% 46.77/13.20 |
% 46.77/13.20 | From (633) and (711) follows:
% 46.77/13.20 | (712) ~ (vsomeExp(all_9_4_20) = all_0_6_6)
% 46.77/13.20 |
% 46.77/13.20 | Using (380) and (712) yields:
% 46.77/13.20 | (130) $false
% 46.77/13.20 |
% 46.77/13.20 |-The branch is then unsatisfiable
% 46.77/13.20 |-Branch two:
% 46.77/13.20 | (492) all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22
% 46.77/13.20 |
% 46.77/13.20 | Applying alpha-rule on (492) yields:
% 46.77/13.20 | (493) vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22
% 46.77/13.20 | (494) vapp(all_9_6_22, all_9_7_23) = ve1
% 46.77/13.20 | (495) vreduce(all_9_7_23) = all_9_8_24
% 46.77/13.20 | (496) visSomeExp(all_9_8_24) = all_9_3_19
% 46.77/13.20 | (497) visValue(all_9_7_23) = all_9_2_18
% 46.77/13.20 | (498) all_9_4_20 = all_9_8_24
% 46.77/13.20 | (156) ~ (all_9_3_19 = 0)
% 46.77/13.20 | (159) all_9_5_21 = ve1
% 46.77/13.20 | (501) ~ (all_9_2_18 = 0)
% 46.77/13.20 | (502) all_0_6_6 = vnoExp
% 46.77/13.20 |
% 46.77/13.20 | Instantiating formula (92) with ve1, all_9_7_23, all_9_6_22 and discharging atoms vapp(all_9_6_22, all_9_7_23) = ve1, yields:
% 46.77/13.20 | (162) ~ (visValue(ve1) = 0)
% 46.77/13.20 |
% 46.77/13.20 | Using (68) and (162) yields:
% 46.77/13.20 | (163) ~ (all_0_7_7 = 0)
% 46.77/13.20 |
% 46.77/13.20 +-Applying beta-rule and splitting (143), into two cases.
% 46.77/13.20 |-Branch one:
% 46.77/13.20 | (164) all_0_7_7 = 0
% 46.77/13.20 |
% 46.77/13.20 | Equations (164) can reduce 163 to:
% 46.77/13.20 | (165) $false
% 46.77/13.20 |
% 46.77/13.20 |-The branch is then unsatisfiable
% 46.77/13.20 |-Branch two:
% 46.77/13.20 | (163) ~ (all_0_7_7 = 0)
% 46.77/13.20 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 46.77/13.20 |
% 46.77/13.20 | Instantiating (167) with all_126_0_166 yields:
% 46.77/13.20 | (731) vsomeExp(all_126_0_166) = all_0_6_6
% 46.77/13.20 |
% 46.77/13.20 | From (502) and (731) follows:
% 46.77/13.20 | (732) vsomeExp(all_126_0_166) = vnoExp
% 46.77/13.20 |
% 46.77/13.20 | Instantiating formula (40) with all_126_0_166 and discharging atoms vsomeExp(all_126_0_166) = vnoExp, yields:
% 46.77/13.20 | (130) $false
% 46.77/13.20 |
% 46.77/13.20 |-The branch is then unsatisfiable
% 46.77/13.20 |-Branch two:
% 46.77/13.20 | (512) all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)
% 46.77/13.20 |
% 46.77/13.20 | Applying alpha-rule on (512) yields:
% 46.77/13.20 | (383) all_9_8_24 = ve1
% 46.77/13.20 | (514) ~ (all_9_6_22 = 0)
% 46.77/13.20 | (515) all_9_7_23 = all_9_9_25
% 46.77/13.20 | (516) visSomeExp(all_9_9_25) = all_9_6_22
% 46.77/13.20 | (517) vapp(all_9_10_26, all_9_11_27) = ve1
% 46.77/13.20 | (518) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)
% 46.77/13.20 | (519) vreduce(all_9_10_26) = all_9_9_25
% 46.77/13.20 | (502) all_0_6_6 = vnoExp
% 46.77/13.20 |
% 46.77/13.20 | Instantiating formula (92) with ve1, all_9_11_27, all_9_10_26 and discharging atoms vapp(all_9_10_26, all_9_11_27) = ve1, yields:
% 46.77/13.20 | (162) ~ (visValue(ve1) = 0)
% 46.77/13.20 |
% 46.77/13.20 | Using (68) and (162) yields:
% 46.77/13.20 | (163) ~ (all_0_7_7 = 0)
% 46.77/13.20 |
% 46.77/13.20 +-Applying beta-rule and splitting (143), into two cases.
% 46.77/13.20 |-Branch one:
% 46.77/13.20 | (164) all_0_7_7 = 0
% 46.77/13.20 |
% 46.77/13.20 | Equations (164) can reduce 163 to:
% 46.77/13.20 | (165) $false
% 46.77/13.20 |
% 46.77/13.20 |-The branch is then unsatisfiable
% 46.77/13.20 |-Branch two:
% 46.77/13.20 | (163) ~ (all_0_7_7 = 0)
% 46.77/13.20 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 46.77/13.20 |
% 46.77/13.20 | Instantiating (167) with all_116_0_167 yields:
% 46.77/13.20 | (749) vsomeExp(all_116_0_167) = all_0_6_6
% 46.77/13.20 |
% 46.77/13.20 | From (502) and (749) follows:
% 46.77/13.20 | (750) vsomeExp(all_116_0_167) = vnoExp
% 46.77/13.20 |
% 46.77/13.20 | Instantiating formula (40) with all_116_0_167 and discharging atoms vsomeExp(all_116_0_167) = vnoExp, yields:
% 46.77/13.20 | (130) $false
% 46.77/13.20 |
% 46.77/13.20 |-The branch is then unsatisfiable
% 46.77/13.20 |-Branch two:
% 46.77/13.20 | (530) all_9_8_24 = ve1 & all_0_6_6 = vnoExp & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1
% 46.77/13.20 |
% 46.77/13.20 | Applying alpha-rule on (530) yields:
% 46.77/13.20 | (383) all_9_8_24 = ve1
% 46.77/13.20 | (502) all_0_6_6 = vnoExp
% 46.77/13.20 | (533) vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1
% 46.77/13.20 |
% 46.77/13.20 | Combining equations (502,633) yields a new equation:
% 46.77/13.20 | (219) all_0_1_1 = vnoExp
% 46.77/13.20 |
% 46.77/13.20 | Equations (502) can reduce 637 to:
% 46.77/13.20 | (757) ~ (all_0_4_4 = vnoExp)
% 46.77/13.20 |
% 46.77/13.20 | From (502) and (634) follows:
% 46.77/13.20 | (758) vreduce(all_0_3_3) = vnoExp
% 46.77/13.20 |
% 46.77/13.20 | Instantiating formula (22) with all_0_7_7, ve1, all_9_9_25, all_9_10_26, all_9_11_27 and discharging atoms visValue(ve1) = all_0_7_7, vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1, yields:
% 46.77/13.20 | (164) all_0_7_7 = 0
% 46.77/13.20 |
% 46.77/13.20 | Equations (164) can reduce 118 to:
% 46.77/13.20 | (760) ~ (all_0_5_5 = 0)
% 46.77/13.20 |
% 46.77/13.20 +-Applying beta-rule and splitting (661), into two cases.
% 46.77/13.20 |-Branch one:
% 46.77/13.20 | (761) all_0_5_5 = 0
% 46.77/13.20 |
% 46.77/13.20 | Equations (761) can reduce 760 to:
% 46.77/13.20 | (165) $false
% 46.77/13.20 |
% 46.77/13.20 |-The branch is then unsatisfiable
% 46.77/13.20 |-Branch two:
% 46.77/13.20 | (760) ~ (all_0_5_5 = 0)
% 46.77/13.20 | (764) ? [v0] : vsomeExp(v0) = all_0_4_4
% 46.77/13.20 |
% 46.77/13.20 | Instantiating (764) with all_111_0_168 yields:
% 46.77/13.21 | (765) vsomeExp(all_111_0_168) = all_0_4_4
% 46.77/13.21 |
% 46.77/13.21 +-Applying beta-rule and splitting (115), into two cases.
% 46.77/13.21 |-Branch one:
% 46.77/13.21 | (766) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34) | (all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)) | (all_10_8_36 = ve2 & all_0_4_4 = vnoExp & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2)
% 46.77/13.21 |
% 46.77/13.21 +-Applying beta-rule and splitting (766), into two cases.
% 46.77/13.21 |-Branch one:
% 46.77/13.21 | (767) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34) | (all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38))
% 46.77/13.21 |
% 46.77/13.21 +-Applying beta-rule and splitting (767), into two cases.
% 46.77/13.21 |-Branch one:
% 46.77/13.21 | (768) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34)
% 46.77/13.21 |
% 46.77/13.21 +-Applying beta-rule and splitting (768), into two cases.
% 46.77/13.21 |-Branch one:
% 46.77/13.21 | (769) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39))
% 46.77/13.21 |
% 46.77/13.21 +-Applying beta-rule and splitting (769), into two cases.
% 46.77/13.21 |-Branch one:
% 46.77/13.21 | (770) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34)
% 46.77/13.21 |
% 46.77/13.21 +-Applying beta-rule and splitting (770), into two cases.
% 46.77/13.21 |-Branch one:
% 46.77/13.21 | (771) all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34
% 46.77/13.21 |
% 46.77/13.21 | Applying alpha-rule on (771) yields:
% 46.77/13.21 | (772) all_10_5_33 = ve2
% 46.77/13.21 | (773) visValue(all_10_8_36) = 0
% 46.77/13.21 | (774) all_10_4_32 = all_10_10_38
% 46.77/13.21 | (775) ~ (all_10_3_31 = 0)
% 46.77/13.21 | (776) all_10_2_30 = 0
% 46.77/13.21 | (777) vapp(all_10_6_34, all_10_8_36) = ve2
% 46.77/13.21 | (778) vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29
% 46.77/13.21 | (779) vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34
% 46.77/13.21 | (780) all_10_0_28 = all_0_4_4
% 46.77/13.21 | (781) visSomeExp(all_10_10_38) = all_10_3_31
% 46.77/13.21 | (782) vsomeExp(all_10_1_29) = all_0_4_4
% 46.77/13.21 | (783) vreduce(all_10_8_36) = all_10_10_38
% 46.77/13.21 |
% 46.77/13.21 | Instantiating formula (85) with all_0_4_4, all_10_1_29, all_111_0_168 and discharging atoms vsomeExp(all_111_0_168) = all_0_4_4, vsomeExp(all_10_1_29) = all_0_4_4, yields:
% 46.77/13.21 | (784) all_111_0_168 = all_10_1_29
% 46.77/13.21 |
% 46.77/13.21 | From (784) and (765) follows:
% 46.77/13.21 | (782) vsomeExp(all_10_1_29) = all_0_4_4
% 46.77/13.21 |
% 46.77/13.21 | Instantiating formula (32) with all_10_3_31, ve1, all_9_9_25, ve2, all_9_11_27, vnoExp, all_0_3_3, all_10_10_38, all_9_10_26 and discharging atoms vreduce(all_0_3_3) = vnoExp, visSomeExp(all_10_10_38) = all_10_3_31, vapp(ve1, ve2) = all_0_3_3, vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1, yields:
% 46.77/13.21 | (786) all_10_3_31 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (vreduce(ve2) = v0 & vsomeExp(v2) = v3 & vsubst(all_9_11_27, ve2, all_9_9_25) = v2 & visValue(ve2) = v1 & ( ~ (v1 = 0) | ~ (v0 = all_10_10_38) | v3 = vnoExp))
% 46.77/13.22 |
% 46.77/13.22 +-Applying beta-rule and splitting (116), into two cases.
% 46.77/13.22 |-Branch one:
% 46.77/13.22 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 46.77/13.22 |
% 46.77/13.22 +-Applying beta-rule and splitting (171), into two cases.
% 46.77/13.22 |-Branch one:
% 46.77/13.22 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 46.77/13.22 |
% 46.77/13.22 +-Applying beta-rule and splitting (172), into two cases.
% 46.77/13.22 |-Branch one:
% 46.77/13.22 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 46.77/13.22 |
% 46.77/13.22 +-Applying beta-rule and splitting (173), into two cases.
% 46.77/13.22 |-Branch one:
% 46.77/13.22 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 46.77/13.22 |
% 46.77/13.22 +-Applying beta-rule and splitting (174), into two cases.
% 46.77/13.22 |-Branch one:
% 46.77/13.22 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 46.77/13.22 |
% 46.77/13.22 +-Applying beta-rule and splitting (175), into two cases.
% 46.77/13.22 |-Branch one:
% 46.77/13.22 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 46.77/13.22 |
% 46.77/13.22 | Applying alpha-rule on (176) yields:
% 46.77/13.22 | (177) all_11_5_45 = all_0_3_3
% 46.77/13.22 | (178) all_11_4_44 = all_11_10_50
% 46.77/13.22 | (179) visValue(all_11_8_48) = 0
% 46.77/13.22 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 46.77/13.22 | (181) all_11_0_40 = all_0_1_1
% 46.77/13.22 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 46.77/13.22 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 46.77/13.22 | (184) vreduce(all_11_8_48) = all_11_10_50
% 46.77/13.22 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 46.77/13.22 | (186) ~ (all_11_3_43 = 0)
% 46.77/13.22 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 46.77/13.22 | (188) all_11_2_42 = 0
% 46.77/13.22 |
% 46.77/13.22 | From (219) and (182) follows:
% 46.77/13.22 | (805) vsomeExp(all_11_1_41) = vnoExp
% 46.77/13.22 |
% 46.77/13.22 | Instantiating formula (40) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = vnoExp, yields:
% 46.77/13.22 | (130) $false
% 46.77/13.22 |
% 46.77/13.22 |-The branch is then unsatisfiable
% 46.77/13.22 |-Branch two:
% 46.77/13.22 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 46.77/13.22 |
% 46.77/13.22 | Applying alpha-rule on (190) yields:
% 46.77/13.22 | (177) all_11_5_45 = all_0_3_3
% 46.77/13.22 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 46.77/13.22 | (193) visSomeExp(all_11_7_47) = 0
% 46.77/13.22 | (181) all_11_0_40 = all_0_1_1
% 46.77/13.22 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 46.77/13.22 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 46.77/13.22 | (197) vreduce(all_11_11_51) = all_11_7_47
% 46.77/13.22 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 46.77/13.22 | (199) all_11_3_43 = 0
% 46.77/13.22 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 46.77/13.22 | (201) all_11_4_44 = all_11_7_47
% 46.77/13.22 |
% 46.77/13.22 | From (219) and (182) follows:
% 46.77/13.22 | (805) vsomeExp(all_11_1_41) = vnoExp
% 46.77/13.22 |
% 46.77/13.22 | Instantiating formula (40) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = vnoExp, yields:
% 46.77/13.22 | (130) $false
% 46.77/13.22 |
% 46.77/13.22 |-The branch is then unsatisfiable
% 46.77/13.22 |-Branch two:
% 46.77/13.22 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 46.77/13.22 |
% 46.77/13.22 | Applying alpha-rule on (203) yields:
% 46.77/13.22 | (204) all_11_7_47 = all_11_10_50
% 46.77/13.22 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 46.77/13.22 | (206) all_11_6_46 = 0
% 46.77/13.22 | (207) all_11_3_43 = all_0_1_1
% 46.77/13.22 | (208) visSomeExp(all_11_10_50) = 0
% 46.77/13.22 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 46.77/13.22 | (210) vreduce(all_11_11_51) = all_11_10_50
% 46.77/13.22 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 46.77/13.22 | (212) all_11_8_48 = all_0_3_3
% 46.77/13.22 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 46.77/13.22 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 46.77/13.22 |
% 46.77/13.22 | From (219) and (209) follows:
% 46.77/13.22 | (833) vsomeExp(all_11_4_44) = vnoExp
% 46.77/13.22 |
% 46.77/13.22 | Instantiating formula (40) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = vnoExp, yields:
% 46.77/13.22 | (130) $false
% 46.77/13.22 |
% 46.77/13.22 |-The branch is then unsatisfiable
% 46.77/13.22 |-Branch two:
% 46.77/13.22 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 46.77/13.22 |
% 46.77/13.22 | Applying alpha-rule on (216) yields:
% 46.77/13.22 | (177) all_11_5_45 = all_0_3_3
% 46.77/13.22 | (218) visValue(all_11_7_47) = all_11_2_42
% 46.77/13.22 | (219) all_0_1_1 = vnoExp
% 46.77/13.22 | (220) vreduce(all_11_7_47) = all_11_8_48
% 46.77/13.22 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 46.77/13.22 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 46.77/13.23 | (186) ~ (all_11_3_43 = 0)
% 46.77/13.23 | (224) all_11_4_44 = all_11_8_48
% 46.77/13.23 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 46.77/13.23 | (226) ~ (all_11_2_42 = 0)
% 46.77/13.23 |
% 46.77/13.23 +-Applying beta-rule and splitting (786), into two cases.
% 46.77/13.23 |-Branch one:
% 46.77/13.23 | (846) all_10_3_31 = 0
% 46.77/13.23 |
% 46.77/13.23 | Equations (846) can reduce 775 to:
% 46.77/13.23 | (165) $false
% 46.77/13.23 |
% 46.77/13.23 |-The branch is then unsatisfiable
% 46.77/13.23 |-Branch two:
% 46.77/13.23 | (775) ~ (all_10_3_31 = 0)
% 46.77/13.23 | (849) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (vreduce(ve2) = v0 & vsomeExp(v2) = v3 & vsubst(all_9_11_27, ve2, all_9_9_25) = v2 & visValue(ve2) = v1 & ( ~ (v1 = 0) | ~ (v0 = all_10_10_38) | v3 = vnoExp))
% 46.77/13.23 |
% 46.77/13.23 | Instantiating (849) with all_149_0_221, all_149_1_222, all_149_2_223, all_149_3_224 yields:
% 46.77/13.23 | (850) vreduce(ve2) = all_149_3_224 & vsomeExp(all_149_1_222) = all_149_0_221 & vsubst(all_9_11_27, ve2, all_9_9_25) = all_149_1_222 & visValue(ve2) = all_149_2_223 & ( ~ (all_149_2_223 = 0) | ~ (all_149_3_224 = all_10_10_38) | all_149_0_221 = vnoExp)
% 46.77/13.23 |
% 46.77/13.23 | Applying alpha-rule on (850) yields:
% 46.77/13.23 | (851) vsomeExp(all_149_1_222) = all_149_0_221
% 46.77/13.23 | (852) visValue(ve2) = all_149_2_223
% 46.77/13.23 | (853) vsubst(all_9_11_27, ve2, all_9_9_25) = all_149_1_222
% 46.77/13.23 | (854) ~ (all_149_2_223 = 0) | ~ (all_149_3_224 = all_10_10_38) | all_149_0_221 = vnoExp
% 46.77/13.23 | (855) vreduce(ve2) = all_149_3_224
% 46.77/13.23 |
% 46.77/13.23 | Instantiating formula (55) with ve2, all_149_3_224, all_0_4_4 and discharging atoms vreduce(ve2) = all_149_3_224, vreduce(ve2) = all_0_4_4, yields:
% 46.77/13.23 | (856) all_149_3_224 = all_0_4_4
% 46.77/13.23 |
% 46.77/13.23 | Instantiating formula (55) with ve2, all_149_3_224, all_11_8_48 and discharging atoms vreduce(ve2) = all_149_3_224, yields:
% 46.77/13.23 | (857) all_149_3_224 = all_11_8_48 | ~ (vreduce(ve2) = all_11_8_48)
% 46.77/13.23 |
% 46.77/13.23 | Instantiating formula (47) with all_11_3_43, all_0_4_4, all_10_1_29 and discharging atoms vsomeExp(all_10_1_29) = all_0_4_4, yields:
% 46.77/13.23 | (858) all_11_3_43 = 0 | ~ (visSomeExp(all_0_4_4) = all_11_3_43)
% 46.77/13.23 |
% 46.77/13.23 | Instantiating formula (31) with all_0_3_3, all_11_7_47, all_11_6_46, ve2, ve1 and discharging atoms vapp(all_11_6_46, all_11_7_47) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 46.77/13.23 | (859) all_11_7_47 = ve2
% 46.77/13.23 |
% 46.77/13.23 | From (859) and (220) follows:
% 46.77/13.23 | (860) vreduce(ve2) = all_11_8_48
% 46.77/13.23 |
% 46.77/13.23 +-Applying beta-rule and splitting (857), into two cases.
% 46.77/13.23 |-Branch one:
% 46.77/13.23 | (861) ~ (vreduce(ve2) = all_11_8_48)
% 46.77/13.23 |
% 46.77/13.23 | Using (860) and (861) yields:
% 46.77/13.23 | (130) $false
% 46.77/13.23 |
% 46.77/13.23 |-The branch is then unsatisfiable
% 46.77/13.23 |-Branch two:
% 46.77/13.23 | (860) vreduce(ve2) = all_11_8_48
% 46.77/13.23 | (864) all_149_3_224 = all_11_8_48
% 46.77/13.23 |
% 46.77/13.23 | Combining equations (864,856) yields a new equation:
% 46.77/13.23 | (865) all_11_8_48 = all_0_4_4
% 46.77/13.23 |
% 46.77/13.23 | Simplifying 865 yields:
% 46.77/13.23 | (866) all_11_8_48 = all_0_4_4
% 46.77/13.23 |
% 46.77/13.23 | From (866) and (225) follows:
% 46.77/13.23 | (867) visSomeExp(all_0_4_4) = all_11_3_43
% 46.77/13.23 |
% 46.77/13.23 +-Applying beta-rule and splitting (858), into two cases.
% 46.77/13.23 |-Branch one:
% 46.77/13.23 | (868) ~ (visSomeExp(all_0_4_4) = all_11_3_43)
% 46.77/13.23 |
% 46.77/13.23 | Using (867) and (868) yields:
% 46.77/13.23 | (130) $false
% 46.77/13.23 |
% 46.77/13.23 |-The branch is then unsatisfiable
% 46.77/13.23 |-Branch two:
% 46.77/13.23 | (867) visSomeExp(all_0_4_4) = all_11_3_43
% 46.77/13.23 | (199) all_11_3_43 = 0
% 46.77/13.23 |
% 46.77/13.23 | Equations (199) can reduce 186 to:
% 46.77/13.23 | (165) $false
% 46.77/13.23 |
% 46.77/13.23 |-The branch is then unsatisfiable
% 46.77/13.23 |-Branch two:
% 46.77/13.23 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 46.77/13.23 |
% 46.77/13.23 | Applying alpha-rule on (231) yields:
% 46.77/13.23 | (232) all_11_7_47 = all_11_9_49
% 46.77/13.23 | (219) all_0_1_1 = vnoExp
% 46.77/13.23 | (234) ~ (all_11_6_46 = 0)
% 46.77/13.23 | (235) vreduce(all_11_10_50) = all_11_9_49
% 46.77/13.23 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 46.77/13.23 | (212) all_11_8_48 = all_0_3_3
% 46.77/13.23 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 46.77/13.23 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 46.77/13.23 |
% 46.77/13.23 | Instantiating formula (236) with all_9_9_25, all_9_10_26, all_9_11_27 yields:
% 46.77/13.23 | (882) ~ (vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_11_10_50)
% 46.77/13.23 |
% 46.77/13.23 | Instantiating formula (88) with all_0_3_3, all_11_11_51, all_11_10_50, ve2, ve1 and discharging atoms vapp(all_11_10_50, all_11_11_51) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 46.77/13.23 | (242) all_11_10_50 = ve1
% 46.77/13.23 |
% 46.77/13.23 | Using (533) and (882) yields:
% 46.77/13.23 | (884) ~ (all_11_10_50 = ve1)
% 46.77/13.23 |
% 46.77/13.23 | Equations (242) can reduce 884 to:
% 46.77/13.23 | (165) $false
% 46.77/13.23 |
% 46.77/13.23 |-The branch is then unsatisfiable
% 46.77/13.23 |-Branch two:
% 46.77/13.23 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 46.77/13.23 |
% 46.77/13.23 | Applying alpha-rule on (254) yields:
% 46.77/13.23 | (212) all_11_8_48 = all_0_3_3
% 46.77/13.23 | (219) all_0_1_1 = vnoExp
% 46.77/13.23 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 46.77/13.23 |
% 46.77/13.23 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3, yields:
% 46.77/13.23 | (130) $false
% 46.77/13.23 |
% 46.77/13.23 |-The branch is then unsatisfiable
% 46.77/13.23 |-Branch two:
% 46.77/13.23 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 46.77/13.23 |
% 46.77/13.23 | Applying alpha-rule on (259) yields:
% 46.77/13.23 | (260) all_11_10_50 = all_0_3_3
% 46.77/13.23 | (219) all_0_1_1 = vnoExp
% 46.77/13.23 | (262) vvar(all_11_11_51) = all_0_3_3
% 46.77/13.23 |
% 46.77/13.23 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_11_11_51) = all_0_3_3, yields:
% 46.77/13.23 | (130) $false
% 46.77/13.23 |
% 46.77/13.23 |-The branch is then unsatisfiable
% 46.77/13.23 |-Branch two:
% 46.77/13.23 | (896) all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34
% 46.77/13.23 |
% 46.77/13.23 | Applying alpha-rule on (896) yields:
% 46.77/13.23 | (772) all_10_5_33 = ve2
% 46.77/13.23 | (898) vreduce(all_10_11_39) = all_10_7_35
% 46.77/13.23 | (846) all_10_3_31 = 0
% 46.77/13.23 | (900) all_10_4_32 = all_10_7_35
% 46.77/13.23 | (901) visSomeExp(all_10_7_35) = 0
% 46.77/13.23 | (902) vapp(all_10_6_34, all_10_2_30) = all_10_1_29
% 46.77/13.23 | (780) all_10_0_28 = all_0_4_4
% 46.77/13.23 | (904) vgetSomeExp(all_10_7_35) = all_10_2_30
% 46.77/13.23 | (905) vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34
% 46.77/13.23 | (906) vapp(all_10_6_34, all_10_11_39) = ve2
% 46.77/13.23 | (782) vsomeExp(all_10_1_29) = all_0_4_4
% 46.77/13.23 |
% 46.77/13.23 | Instantiating formula (85) with all_0_4_4, all_10_1_29, all_111_0_168 and discharging atoms vsomeExp(all_111_0_168) = all_0_4_4, vsomeExp(all_10_1_29) = all_0_4_4, yields:
% 46.77/13.23 | (784) all_111_0_168 = all_10_1_29
% 46.77/13.23 |
% 46.77/13.23 | From (784) and (765) follows:
% 46.77/13.23 | (782) vsomeExp(all_10_1_29) = all_0_4_4
% 46.77/13.23 |
% 46.77/13.23 +-Applying beta-rule and splitting (116), into two cases.
% 46.77/13.23 |-Branch one:
% 46.77/13.23 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 46.77/13.23 |
% 46.77/13.23 +-Applying beta-rule and splitting (171), into two cases.
% 46.77/13.23 |-Branch one:
% 46.77/13.23 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 46.77/13.24 |
% 46.77/13.24 +-Applying beta-rule and splitting (172), into two cases.
% 46.77/13.24 |-Branch one:
% 46.77/13.24 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 46.77/13.24 |
% 46.77/13.24 +-Applying beta-rule and splitting (173), into two cases.
% 46.77/13.24 |-Branch one:
% 46.77/13.24 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 46.77/13.24 |
% 46.77/13.24 +-Applying beta-rule and splitting (174), into two cases.
% 46.77/13.24 |-Branch one:
% 46.77/13.24 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 46.77/13.24 |
% 46.77/13.24 +-Applying beta-rule and splitting (175), into two cases.
% 46.77/13.24 |-Branch one:
% 46.77/13.24 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 46.77/13.24 |
% 46.77/13.24 | Applying alpha-rule on (176) yields:
% 46.77/13.24 | (177) all_11_5_45 = all_0_3_3
% 46.77/13.24 | (178) all_11_4_44 = all_11_10_50
% 46.77/13.24 | (179) visValue(all_11_8_48) = 0
% 46.77/13.24 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 46.77/13.24 | (181) all_11_0_40 = all_0_1_1
% 46.77/13.24 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 46.77/13.24 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 46.77/13.24 | (184) vreduce(all_11_8_48) = all_11_10_50
% 46.77/13.24 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 46.77/13.24 | (186) ~ (all_11_3_43 = 0)
% 46.77/13.24 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 46.77/13.24 | (188) all_11_2_42 = 0
% 46.77/13.24 |
% 46.77/13.24 | From (219) and (182) follows:
% 46.77/13.24 | (805) vsomeExp(all_11_1_41) = vnoExp
% 46.77/13.24 |
% 46.77/13.24 | Instantiating formula (40) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = vnoExp, yields:
% 46.77/13.24 | (130) $false
% 46.77/13.24 |
% 46.77/13.24 |-The branch is then unsatisfiable
% 46.77/13.24 |-Branch two:
% 46.77/13.24 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 46.77/13.24 |
% 46.77/13.24 | Applying alpha-rule on (190) yields:
% 46.77/13.24 | (177) all_11_5_45 = all_0_3_3
% 46.77/13.24 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 46.77/13.24 | (193) visSomeExp(all_11_7_47) = 0
% 46.77/13.24 | (181) all_11_0_40 = all_0_1_1
% 46.77/13.24 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 46.77/13.24 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 46.77/13.24 | (197) vreduce(all_11_11_51) = all_11_7_47
% 46.77/13.24 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 46.77/13.24 | (199) all_11_3_43 = 0
% 46.77/13.24 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 46.77/13.24 | (201) all_11_4_44 = all_11_7_47
% 46.77/13.24 |
% 46.77/13.24 | From (219) and (182) follows:
% 46.77/13.24 | (805) vsomeExp(all_11_1_41) = vnoExp
% 46.77/13.24 |
% 46.77/13.24 | Instantiating formula (40) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = vnoExp, yields:
% 46.77/13.24 | (130) $false
% 46.77/13.24 |
% 46.77/13.24 |-The branch is then unsatisfiable
% 46.77/13.24 |-Branch two:
% 46.77/13.24 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 46.77/13.24 |
% 46.77/13.24 | Applying alpha-rule on (203) yields:
% 46.77/13.24 | (204) all_11_7_47 = all_11_10_50
% 46.77/13.24 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 46.77/13.24 | (206) all_11_6_46 = 0
% 46.77/13.24 | (207) all_11_3_43 = all_0_1_1
% 46.77/13.24 | (208) visSomeExp(all_11_10_50) = 0
% 46.77/13.24 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 46.77/13.24 | (210) vreduce(all_11_11_51) = all_11_10_50
% 46.77/13.24 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 46.77/13.24 | (212) all_11_8_48 = all_0_3_3
% 46.77/13.24 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 46.77/13.24 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 46.77/13.24 |
% 46.77/13.24 | From (219) and (209) follows:
% 46.77/13.24 | (833) vsomeExp(all_11_4_44) = vnoExp
% 46.77/13.24 |
% 46.77/13.24 | Instantiating formula (40) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = vnoExp, yields:
% 46.77/13.24 | (130) $false
% 46.77/13.24 |
% 46.77/13.24 |-The branch is then unsatisfiable
% 46.77/13.24 |-Branch two:
% 46.77/13.24 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 46.77/13.24 |
% 46.77/13.24 | Applying alpha-rule on (216) yields:
% 46.77/13.24 | (177) all_11_5_45 = all_0_3_3
% 46.77/13.24 | (218) visValue(all_11_7_47) = all_11_2_42
% 46.77/13.24 | (219) all_0_1_1 = vnoExp
% 46.77/13.24 | (220) vreduce(all_11_7_47) = all_11_8_48
% 46.77/13.24 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 46.77/13.24 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 46.77/13.24 | (186) ~ (all_11_3_43 = 0)
% 46.77/13.24 | (224) all_11_4_44 = all_11_8_48
% 46.77/13.24 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 46.77/13.24 | (226) ~ (all_11_2_42 = 0)
% 46.77/13.24 |
% 46.77/13.24 | Instantiating formula (55) with ve2, all_11_8_48, all_0_4_4 and discharging atoms vreduce(ve2) = all_0_4_4, yields:
% 46.77/13.24 | (969) all_11_8_48 = all_0_4_4 | ~ (vreduce(ve2) = all_11_8_48)
% 46.77/13.24 |
% 46.77/13.24 | Instantiating formula (47) with all_11_3_43, all_0_4_4, all_10_1_29 and discharging atoms vsomeExp(all_10_1_29) = all_0_4_4, yields:
% 46.77/13.24 | (858) all_11_3_43 = 0 | ~ (visSomeExp(all_0_4_4) = all_11_3_43)
% 46.77/13.24 |
% 46.77/13.24 | Instantiating formula (31) with all_0_3_3, all_11_7_47, all_11_6_46, ve2, ve1 and discharging atoms vapp(all_11_6_46, all_11_7_47) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 46.77/13.24 | (859) all_11_7_47 = ve2
% 46.77/13.24 |
% 46.77/13.24 | From (859) and (220) follows:
% 46.77/13.24 | (860) vreduce(ve2) = all_11_8_48
% 46.77/13.24 |
% 46.77/13.24 +-Applying beta-rule and splitting (858), into two cases.
% 46.77/13.24 |-Branch one:
% 46.77/13.24 | (868) ~ (visSomeExp(all_0_4_4) = all_11_3_43)
% 46.77/13.24 |
% 46.77/13.24 +-Applying beta-rule and splitting (969), into two cases.
% 46.77/13.24 |-Branch one:
% 46.77/13.24 | (861) ~ (vreduce(ve2) = all_11_8_48)
% 46.77/13.24 |
% 46.77/13.24 | Using (860) and (861) yields:
% 46.77/13.24 | (130) $false
% 46.77/13.24 |
% 46.77/13.24 |-The branch is then unsatisfiable
% 46.77/13.24 |-Branch two:
% 46.77/13.24 | (860) vreduce(ve2) = all_11_8_48
% 46.77/13.24 | (866) all_11_8_48 = all_0_4_4
% 46.77/13.24 |
% 46.77/13.24 | From (866) and (225) follows:
% 46.77/13.24 | (867) visSomeExp(all_0_4_4) = all_11_3_43
% 46.77/13.24 |
% 46.77/13.24 | Using (867) and (868) yields:
% 46.77/13.24 | (130) $false
% 46.77/13.24 |
% 46.77/13.24 |-The branch is then unsatisfiable
% 46.77/13.24 |-Branch two:
% 46.77/13.24 | (867) visSomeExp(all_0_4_4) = all_11_3_43
% 46.77/13.24 | (199) all_11_3_43 = 0
% 46.77/13.24 |
% 46.77/13.24 | Equations (199) can reduce 186 to:
% 46.77/13.24 | (165) $false
% 46.77/13.24 |
% 46.77/13.24 |-The branch is then unsatisfiable
% 46.77/13.24 |-Branch two:
% 46.77/13.24 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 46.77/13.25 |
% 46.77/13.25 | Applying alpha-rule on (231) yields:
% 46.77/13.25 | (232) all_11_7_47 = all_11_9_49
% 46.77/13.25 | (219) all_0_1_1 = vnoExp
% 46.77/13.25 | (234) ~ (all_11_6_46 = 0)
% 46.77/13.25 | (235) vreduce(all_11_10_50) = all_11_9_49
% 46.77/13.25 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 46.77/13.25 | (212) all_11_8_48 = all_0_3_3
% 46.77/13.25 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 46.77/13.25 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 46.77/13.25 |
% 46.77/13.25 | Instantiating formula (236) with all_9_9_25, all_9_10_26, all_9_11_27 yields:
% 46.77/13.25 | (882) ~ (vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_11_10_50)
% 46.77/13.25 |
% 46.77/13.25 | Instantiating formula (88) with all_0_3_3, all_11_11_51, all_11_10_50, ve2, ve1 and discharging atoms vapp(all_11_10_50, all_11_11_51) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 46.77/13.25 | (242) all_11_10_50 = ve1
% 46.77/13.25 |
% 46.77/13.25 | Using (533) and (882) yields:
% 46.77/13.25 | (884) ~ (all_11_10_50 = ve1)
% 46.77/13.25 |
% 46.77/13.25 | Equations (242) can reduce 884 to:
% 46.77/13.25 | (165) $false
% 46.77/13.25 |
% 46.77/13.25 |-The branch is then unsatisfiable
% 46.77/13.25 |-Branch two:
% 46.77/13.25 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 46.77/13.25 |
% 46.77/13.25 | Applying alpha-rule on (254) yields:
% 46.77/13.25 | (212) all_11_8_48 = all_0_3_3
% 46.77/13.25 | (219) all_0_1_1 = vnoExp
% 46.77/13.25 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 46.77/13.25 |
% 46.77/13.25 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3, yields:
% 46.77/13.25 | (130) $false
% 46.77/13.25 |
% 46.77/13.25 |-The branch is then unsatisfiable
% 46.77/13.25 |-Branch two:
% 46.77/13.25 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 46.77/13.25 |
% 46.77/13.25 | Applying alpha-rule on (259) yields:
% 46.77/13.25 | (260) all_11_10_50 = all_0_3_3
% 46.77/13.25 | (219) all_0_1_1 = vnoExp
% 46.77/13.25 | (262) vvar(all_11_11_51) = all_0_3_3
% 46.77/13.25 |
% 46.77/13.25 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_11_11_51) = all_0_3_3, yields:
% 46.77/13.25 | (130) $false
% 46.77/13.25 |
% 46.77/13.25 |-The branch is then unsatisfiable
% 46.77/13.25 |-Branch two:
% 46.77/13.25 | (1006) all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)
% 46.77/13.25 |
% 46.77/13.25 | Applying alpha-rule on (1006) yields:
% 46.77/13.25 | (1007) all_10_7_35 = all_10_10_38
% 46.77/13.25 | (1008) vgetSomeExp(all_10_10_38) = all_10_5_33
% 46.77/13.25 | (1009) vapp(all_10_5_33, all_10_9_37) = all_10_4_32
% 46.77/13.25 | (1010) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)
% 46.77/13.25 | (1011) visSomeExp(all_10_10_38) = 0
% 46.77/13.25 | (1012) all_10_8_36 = ve2
% 46.77/13.25 | (1013) vreduce(all_10_11_39) = all_10_10_38
% 46.77/13.25 | (1014) all_10_6_34 = 0
% 46.77/13.25 | (1015) vsomeExp(all_10_4_32) = all_0_4_4
% 46.77/13.25 | (1016) vapp(all_10_11_39, all_10_9_37) = ve2
% 46.77/13.25 | (1017) all_10_3_31 = all_0_4_4
% 46.77/13.25 |
% 46.77/13.25 | Instantiating formula (85) with all_0_4_4, all_10_4_32, all_111_0_168 and discharging atoms vsomeExp(all_111_0_168) = all_0_4_4, vsomeExp(all_10_4_32) = all_0_4_4, yields:
% 46.77/13.25 | (1018) all_111_0_168 = all_10_4_32
% 46.77/13.25 |
% 46.77/13.25 | From (1018) and (765) follows:
% 46.77/13.25 | (1015) vsomeExp(all_10_4_32) = all_0_4_4
% 46.77/13.25 |
% 46.77/13.25 +-Applying beta-rule and splitting (116), into two cases.
% 46.77/13.25 |-Branch one:
% 46.77/13.25 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 46.77/13.25 |
% 46.77/13.25 +-Applying beta-rule and splitting (171), into two cases.
% 46.77/13.25 |-Branch one:
% 46.77/13.25 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 46.77/13.25 |
% 46.77/13.25 +-Applying beta-rule and splitting (172), into two cases.
% 46.77/13.25 |-Branch one:
% 46.77/13.25 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 46.77/13.25 |
% 46.77/13.25 +-Applying beta-rule and splitting (173), into two cases.
% 46.77/13.25 |-Branch one:
% 46.77/13.25 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 46.77/13.25 |
% 46.77/13.25 +-Applying beta-rule and splitting (174), into two cases.
% 46.77/13.25 |-Branch one:
% 46.77/13.25 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 46.77/13.25 |
% 46.77/13.25 +-Applying beta-rule and splitting (175), into two cases.
% 46.77/13.25 |-Branch one:
% 46.77/13.25 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 46.77/13.25 |
% 46.77/13.25 | Applying alpha-rule on (176) yields:
% 46.77/13.25 | (177) all_11_5_45 = all_0_3_3
% 46.77/13.25 | (178) all_11_4_44 = all_11_10_50
% 46.77/13.25 | (179) visValue(all_11_8_48) = 0
% 46.77/13.25 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 46.77/13.25 | (181) all_11_0_40 = all_0_1_1
% 46.77/13.25 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 46.77/13.25 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 46.77/13.25 | (184) vreduce(all_11_8_48) = all_11_10_50
% 46.77/13.25 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 46.77/13.25 | (186) ~ (all_11_3_43 = 0)
% 46.77/13.25 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 46.77/13.25 | (188) all_11_2_42 = 0
% 46.77/13.25 |
% 46.77/13.25 | From (219) and (182) follows:
% 46.77/13.25 | (805) vsomeExp(all_11_1_41) = vnoExp
% 46.77/13.26 |
% 46.77/13.26 | Instantiating formula (40) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = vnoExp, yields:
% 46.77/13.26 | (130) $false
% 46.77/13.26 |
% 46.77/13.26 |-The branch is then unsatisfiable
% 46.77/13.26 |-Branch two:
% 46.77/13.26 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 46.77/13.26 |
% 46.77/13.26 | Applying alpha-rule on (190) yields:
% 46.77/13.26 | (177) all_11_5_45 = all_0_3_3
% 46.77/13.26 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 46.77/13.26 | (193) visSomeExp(all_11_7_47) = 0
% 46.77/13.26 | (181) all_11_0_40 = all_0_1_1
% 46.77/13.26 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 46.77/13.26 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 46.77/13.26 | (197) vreduce(all_11_11_51) = all_11_7_47
% 46.77/13.26 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 46.77/13.26 | (199) all_11_3_43 = 0
% 46.77/13.26 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 46.77/13.26 | (201) all_11_4_44 = all_11_7_47
% 46.77/13.26 |
% 46.77/13.26 | From (219) and (182) follows:
% 46.77/13.26 | (805) vsomeExp(all_11_1_41) = vnoExp
% 46.77/13.26 |
% 46.77/13.26 | Instantiating formula (40) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = vnoExp, yields:
% 46.77/13.26 | (130) $false
% 46.77/13.26 |
% 46.77/13.26 |-The branch is then unsatisfiable
% 46.77/13.26 |-Branch two:
% 46.77/13.26 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 46.77/13.26 |
% 46.77/13.26 | Applying alpha-rule on (203) yields:
% 46.77/13.26 | (204) all_11_7_47 = all_11_10_50
% 46.77/13.26 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 46.77/13.26 | (206) all_11_6_46 = 0
% 46.77/13.26 | (207) all_11_3_43 = all_0_1_1
% 46.77/13.26 | (208) visSomeExp(all_11_10_50) = 0
% 46.77/13.26 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 46.77/13.26 | (210) vreduce(all_11_11_51) = all_11_10_50
% 46.77/13.26 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 46.77/13.26 | (212) all_11_8_48 = all_0_3_3
% 46.77/13.26 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 46.77/13.26 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 46.77/13.26 |
% 46.77/13.26 | From (219) and (209) follows:
% 46.77/13.26 | (833) vsomeExp(all_11_4_44) = vnoExp
% 46.77/13.26 |
% 46.77/13.26 | Instantiating formula (40) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = vnoExp, yields:
% 46.77/13.26 | (130) $false
% 46.77/13.26 |
% 46.77/13.26 |-The branch is then unsatisfiable
% 46.77/13.26 |-Branch two:
% 46.77/13.26 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 46.77/13.26 |
% 46.77/13.26 | Applying alpha-rule on (216) yields:
% 46.77/13.26 | (177) all_11_5_45 = all_0_3_3
% 46.77/13.26 | (218) visValue(all_11_7_47) = all_11_2_42
% 46.77/13.26 | (219) all_0_1_1 = vnoExp
% 46.77/13.26 | (220) vreduce(all_11_7_47) = all_11_8_48
% 46.77/13.26 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 46.77/13.26 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 46.77/13.26 | (186) ~ (all_11_3_43 = 0)
% 46.77/13.26 | (224) all_11_4_44 = all_11_8_48
% 46.77/13.26 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 46.77/13.26 | (226) ~ (all_11_2_42 = 0)
% 46.77/13.26 |
% 46.77/13.26 | Instantiating formula (55) with ve2, all_11_8_48, all_0_4_4 and discharging atoms vreduce(ve2) = all_0_4_4, yields:
% 46.77/13.26 | (969) all_11_8_48 = all_0_4_4 | ~ (vreduce(ve2) = all_11_8_48)
% 46.77/13.26 |
% 46.77/13.26 | Instantiating formula (47) with all_11_3_43, all_0_4_4, all_10_4_32 and discharging atoms vsomeExp(all_10_4_32) = all_0_4_4, yields:
% 46.77/13.26 | (858) all_11_3_43 = 0 | ~ (visSomeExp(all_0_4_4) = all_11_3_43)
% 46.77/13.26 |
% 46.77/13.26 | Instantiating formula (31) with all_0_3_3, all_11_7_47, all_11_6_46, ve2, ve1 and discharging atoms vapp(all_11_6_46, all_11_7_47) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 46.77/13.26 | (859) all_11_7_47 = ve2
% 46.77/13.26 |
% 46.77/13.26 | From (859) and (220) follows:
% 46.77/13.26 | (860) vreduce(ve2) = all_11_8_48
% 46.77/13.26 |
% 46.77/13.26 +-Applying beta-rule and splitting (858), into two cases.
% 46.77/13.26 |-Branch one:
% 46.77/13.26 | (868) ~ (visSomeExp(all_0_4_4) = all_11_3_43)
% 46.77/13.26 |
% 46.77/13.26 +-Applying beta-rule and splitting (969), into two cases.
% 46.77/13.26 |-Branch one:
% 46.77/13.26 | (861) ~ (vreduce(ve2) = all_11_8_48)
% 46.77/13.26 |
% 46.77/13.26 | Using (860) and (861) yields:
% 46.77/13.26 | (130) $false
% 46.77/13.26 |
% 46.77/13.26 |-The branch is then unsatisfiable
% 46.77/13.26 |-Branch two:
% 46.77/13.26 | (860) vreduce(ve2) = all_11_8_48
% 46.77/13.26 | (866) all_11_8_48 = all_0_4_4
% 46.77/13.26 |
% 46.77/13.26 | From (866) and (225) follows:
% 46.77/13.26 | (867) visSomeExp(all_0_4_4) = all_11_3_43
% 46.77/13.26 |
% 46.77/13.26 | Using (867) and (868) yields:
% 46.77/13.26 | (130) $false
% 46.77/13.26 |
% 46.77/13.26 |-The branch is then unsatisfiable
% 46.77/13.26 |-Branch two:
% 46.77/13.26 | (867) visSomeExp(all_0_4_4) = all_11_3_43
% 46.77/13.26 | (199) all_11_3_43 = 0
% 46.77/13.26 |
% 46.77/13.26 | Equations (199) can reduce 186 to:
% 46.77/13.26 | (165) $false
% 46.77/13.26 |
% 46.77/13.26 |-The branch is then unsatisfiable
% 46.77/13.26 |-Branch two:
% 46.77/13.26 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 46.77/13.26 |
% 46.77/13.26 | Applying alpha-rule on (231) yields:
% 46.77/13.26 | (232) all_11_7_47 = all_11_9_49
% 46.77/13.26 | (219) all_0_1_1 = vnoExp
% 46.77/13.26 | (234) ~ (all_11_6_46 = 0)
% 46.77/13.26 | (235) vreduce(all_11_10_50) = all_11_9_49
% 46.77/13.26 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 46.77/13.26 | (212) all_11_8_48 = all_0_3_3
% 46.77/13.26 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 46.77/13.26 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 46.77/13.26 |
% 46.77/13.26 | Instantiating formula (236) with all_9_9_25, all_9_10_26, all_9_11_27 yields:
% 46.77/13.26 | (882) ~ (vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_11_10_50)
% 46.77/13.26 |
% 46.77/13.26 | Instantiating formula (88) with all_0_3_3, all_11_11_51, all_11_10_50, ve2, ve1 and discharging atoms vapp(all_11_10_50, all_11_11_51) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 46.77/13.26 | (242) all_11_10_50 = ve1
% 46.77/13.26 |
% 46.77/13.26 | Using (533) and (882) yields:
% 46.77/13.26 | (884) ~ (all_11_10_50 = ve1)
% 46.77/13.26 |
% 46.77/13.26 | Equations (242) can reduce 884 to:
% 46.77/13.26 | (165) $false
% 46.77/13.26 |
% 46.77/13.26 |-The branch is then unsatisfiable
% 46.77/13.26 |-Branch two:
% 46.77/13.26 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 46.77/13.26 |
% 46.77/13.26 | Applying alpha-rule on (254) yields:
% 46.77/13.26 | (212) all_11_8_48 = all_0_3_3
% 46.77/13.26 | (219) all_0_1_1 = vnoExp
% 46.77/13.26 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 46.77/13.26 |
% 46.77/13.26 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3, yields:
% 46.77/13.26 | (130) $false
% 46.77/13.26 |
% 46.77/13.26 |-The branch is then unsatisfiable
% 46.77/13.26 |-Branch two:
% 46.77/13.26 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 46.77/13.26 |
% 46.77/13.26 | Applying alpha-rule on (259) yields:
% 46.77/13.26 | (260) all_11_10_50 = all_0_3_3
% 46.77/13.26 | (219) all_0_1_1 = vnoExp
% 46.77/13.26 | (262) vvar(all_11_11_51) = all_0_3_3
% 46.77/13.26 |
% 46.77/13.26 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_11_11_51) = all_0_3_3, yields:
% 46.77/13.26 | (130) $false
% 46.77/13.26 |
% 46.77/13.26 |-The branch is then unsatisfiable
% 46.77/13.26 |-Branch two:
% 46.77/13.26 | (1116) all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34
% 46.77/13.26 |
% 46.77/13.26 | Applying alpha-rule on (1116) yields:
% 46.77/13.26 | (772) all_10_5_33 = ve2
% 46.77/13.26 | (1118) all_10_4_32 = all_10_8_36
% 46.77/13.26 | (775) ~ (all_10_3_31 = 0)
% 46.77/13.26 | (1120) ~ (all_10_2_30 = 0)
% 46.77/13.26 | (1121) visValue(all_10_7_35) = all_10_2_30
% 46.77/13.26 | (1122) vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34
% 46.77/13.26 | (1123) all_0_4_4 = vnoExp
% 46.77/13.26 | (1124) vreduce(all_10_7_35) = all_10_8_36
% 46.77/13.26 | (1125) visSomeExp(all_10_8_36) = all_10_3_31
% 46.77/13.26 | (1126) vapp(all_10_6_34, all_10_7_35) = ve2
% 46.77/13.26 |
% 46.77/13.26 | Equations (1123) can reduce 757 to:
% 46.77/13.26 | (165) $false
% 46.77/13.26 |
% 46.77/13.26 |-The branch is then unsatisfiable
% 46.77/13.26 |-Branch two:
% 46.77/13.26 | (1128) all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)
% 46.77/13.26 |
% 46.77/13.26 | Applying alpha-rule on (1128) yields:
% 46.77/13.26 | (1129) vreduce(all_10_10_38) = all_10_9_37
% 46.77/13.26 | (1130) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)
% 46.77/13.26 | (1123) all_0_4_4 = vnoExp
% 46.77/13.26 | (1012) all_10_8_36 = ve2
% 46.77/13.26 | (1133) ~ (all_10_6_34 = 0)
% 46.77/13.26 | (1134) vapp(all_10_10_38, all_10_11_39) = ve2
% 46.77/13.26 | (1135) visSomeExp(all_10_9_37) = all_10_6_34
% 46.77/13.26 | (1136) all_10_7_35 = all_10_9_37
% 46.77/13.26 |
% 46.77/13.26 | Equations (1123) can reduce 757 to:
% 46.77/13.26 | (165) $false
% 46.77/13.26 |
% 46.77/13.26 |-The branch is then unsatisfiable
% 46.77/13.26 |-Branch two:
% 46.77/13.26 | (1138) all_10_8_36 = ve2 & all_0_4_4 = vnoExp & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2
% 46.77/13.26 |
% 46.77/13.26 | Applying alpha-rule on (1138) yields:
% 46.77/13.26 | (1012) all_10_8_36 = ve2
% 46.77/13.26 | (1123) all_0_4_4 = vnoExp
% 46.77/13.26 | (1141) vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2
% 46.77/13.26 |
% 46.77/13.26 | Equations (1123) can reduce 757 to:
% 46.77/13.26 | (165) $false
% 46.77/13.26 |
% 46.77/13.26 |-The branch is then unsatisfiable
% 46.77/13.26 |-Branch two:
% 46.77/13.26 | (1143) all_10_10_38 = ve2 & all_0_4_4 = vnoExp & vvar(all_10_11_39) = ve2
% 46.77/13.26 |
% 46.77/13.26 | Applying alpha-rule on (1143) yields:
% 46.77/13.26 | (1144) all_10_10_38 = ve2
% 46.77/13.26 | (1123) all_0_4_4 = vnoExp
% 46.77/13.26 | (1146) vvar(all_10_11_39) = ve2
% 46.77/13.27 |
% 46.77/13.27 | Equations (1123) can reduce 757 to:
% 46.77/13.27 | (165) $false
% 46.77/13.27 |
% 46.77/13.27 |-The branch is then unsatisfiable
% 47.08/13.27 |-Branch two:
% 47.08/13.27 | (612) all_9_10_26 = ve1 & all_0_6_6 = vnoExp & vvar(all_9_11_27) = ve1
% 47.08/13.27 |
% 47.08/13.27 | Applying alpha-rule on (612) yields:
% 47.08/13.27 | (613) all_9_10_26 = ve1
% 47.08/13.27 | (502) all_0_6_6 = vnoExp
% 47.08/13.27 | (615) vvar(all_9_11_27) = ve1
% 47.08/13.27 |
% 47.08/13.27 | Instantiating formula (104) with ve1, all_9_11_27 and discharging atoms vvar(all_9_11_27) = ve1, yields:
% 47.08/13.27 | (162) ~ (visValue(ve1) = 0)
% 47.08/13.27 |
% 47.08/13.27 | Using (68) and (162) yields:
% 47.08/13.27 | (163) ~ (all_0_7_7 = 0)
% 47.08/13.27 |
% 47.08/13.27 +-Applying beta-rule and splitting (143), into two cases.
% 47.08/13.27 |-Branch one:
% 47.08/13.27 | (164) all_0_7_7 = 0
% 47.08/13.27 |
% 47.08/13.27 | Equations (164) can reduce 163 to:
% 47.08/13.27 | (165) $false
% 47.08/13.27 |
% 47.08/13.27 |-The branch is then unsatisfiable
% 47.08/13.27 |-Branch two:
% 47.08/13.27 | (163) ~ (all_0_7_7 = 0)
% 47.08/13.27 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.08/13.27 |
% 47.08/13.27 | Instantiating (167) with all_115_0_293 yields:
% 47.08/13.27 | (1158) vsomeExp(all_115_0_293) = all_0_6_6
% 47.08/13.27 |
% 47.08/13.27 | From (502) and (1158) follows:
% 47.08/13.27 | (1159) vsomeExp(all_115_0_293) = vnoExp
% 47.08/13.27 |
% 47.08/13.27 | Instantiating formula (40) with all_115_0_293 and discharging atoms vsomeExp(all_115_0_293) = vnoExp, yields:
% 47.08/13.27 | (130) $false
% 47.08/13.27 |
% 47.08/13.27 |-The branch is then unsatisfiable
% 47.08/13.27 |-Branch two:
% 47.08/13.27 | (625) all_8_4_12 = all_8_7_15 & all_8_5_13 = all_0_3_3 & vlookup(all_8_6_14, vempty) = all_8_7_15 & vsomeType(all_0_0_0) = all_8_7_15 & vvar(all_8_6_14) = all_0_3_3
% 47.08/13.27 |
% 47.08/13.27 | Applying alpha-rule on (625) yields:
% 47.08/13.27 | (626) all_8_4_12 = all_8_7_15
% 47.08/13.27 | (627) all_8_5_13 = all_0_3_3
% 47.08/13.27 | (628) vvar(all_8_6_14) = all_0_3_3
% 47.08/13.27 | (629) vsomeType(all_0_0_0) = all_8_7_15
% 47.08/13.27 | (630) vlookup(all_8_6_14, vempty) = all_8_7_15
% 47.08/13.27 |
% 47.08/13.27 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_8_6_14 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_8_6_14) = all_0_3_3, yields:
% 47.08/13.27 | (130) $false
% 47.08/13.27 |
% 47.08/13.27 |-The branch is then unsatisfiable
% 47.08/13.27 |-Branch two:
% 47.08/13.27 | (1168) vreduce(ve1) = all_0_4_4
% 47.08/13.27 | (1169) all_0_4_4 = all_0_6_6
% 47.08/13.27 |
% 47.08/13.27 | From (1169) and (81) follows:
% 47.08/13.27 | (1170) vreduce(ve2) = all_0_6_6
% 47.08/13.27 |
% 47.08/13.27 +-Applying beta-rule and splitting (105), into two cases.
% 47.08/13.27 |-Branch one:
% 47.08/13.27 | (1171) ~ (vreduce(ve2) = all_0_1_1)
% 47.08/13.27 |
% 47.08/13.27 | From (633) and (1171) follows:
% 47.08/13.27 | (1172) ~ (vreduce(ve2) = all_0_6_6)
% 47.08/13.27 |
% 47.08/13.27 | Using (1170) and (1172) yields:
% 47.08/13.27 | (130) $false
% 47.08/13.27 |
% 47.08/13.27 |-The branch is then unsatisfiable
% 47.08/13.27 |-Branch two:
% 47.08/13.27 | (1174) vreduce(ve2) = all_0_1_1
% 47.08/13.27 | (1175) all_0_1_1 = all_0_4_4
% 47.08/13.27 |
% 47.08/13.27 | Combining equations (1175,633) yields a new equation:
% 47.08/13.27 | (1176) all_0_4_4 = all_0_6_6
% 47.08/13.27 |
% 47.08/13.27 | Simplifying 1176 yields:
% 47.08/13.27 | (1169) all_0_4_4 = all_0_6_6
% 47.08/13.27 |
% 47.08/13.27 +-Applying beta-rule and splitting (113), into two cases.
% 47.08/13.27 |-Branch one:
% 47.08/13.27 | (121) (all_8_0_8 = 0 & all_8_2_10 = all_0_0_0 & all_8_3_11 = all_0_3_3 & varrow(all_8_5_13, all_8_4_12) = all_0_0_0 & vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0 & vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9 & vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3) | (all_8_1_9 = 0 & all_8_2_10 = 0 & all_8_4_12 = all_0_3_3 & varrow(all_8_5_13, all_0_0_0) = all_8_3_11 & vtcheck(vempty, all_8_6_14, all_8_5_13) = 0 & vtcheck(vempty, all_8_7_15, all_8_3_11) = 0 & vapp(all_8_7_15, all_8_6_14) = all_0_3_3)
% 47.08/13.27 |
% 47.08/13.27 +-Applying beta-rule and splitting (121), into two cases.
% 47.08/13.27 |-Branch one:
% 47.08/13.27 | (122) all_8_0_8 = 0 & all_8_2_10 = all_0_0_0 & all_8_3_11 = all_0_3_3 & varrow(all_8_5_13, all_8_4_12) = all_0_0_0 & vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0 & vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9 & vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3
% 47.08/13.27 |
% 47.08/13.27 | Applying alpha-rule on (122) yields:
% 47.08/13.27 | (123) vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3
% 47.08/13.27 | (124) vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0
% 47.08/13.27 | (125) vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9
% 47.08/13.27 | (126) all_8_3_11 = all_0_3_3
% 47.08/13.27 | (127) all_8_0_8 = 0
% 47.08/13.27 | (128) all_8_2_10 = all_0_0_0
% 47.08/13.27 | (129) varrow(all_8_5_13, all_8_4_12) = all_0_0_0
% 47.08/13.27 |
% 47.08/13.27 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_8_6_14, all_8_5_13, all_8_7_15 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3, yields:
% 47.08/13.27 | (130) $false
% 47.08/13.27 |
% 47.08/13.27 |-The branch is then unsatisfiable
% 47.08/13.27 |-Branch two:
% 47.08/13.27 | (131) all_8_1_9 = 0 & all_8_2_10 = 0 & all_8_4_12 = all_0_3_3 & varrow(all_8_5_13, all_0_0_0) = all_8_3_11 & vtcheck(vempty, all_8_6_14, all_8_5_13) = 0 & vtcheck(vempty, all_8_7_15, all_8_3_11) = 0 & vapp(all_8_7_15, all_8_6_14) = all_0_3_3
% 47.08/13.27 |
% 47.08/13.27 | Applying alpha-rule on (131) yields:
% 47.08/13.27 | (132) varrow(all_8_5_13, all_0_0_0) = all_8_3_11
% 47.08/13.27 | (133) vtcheck(vempty, all_8_6_14, all_8_5_13) = 0
% 47.08/13.27 | (134) all_8_2_10 = 0
% 47.08/13.27 | (135) vtcheck(vempty, all_8_7_15, all_8_3_11) = 0
% 47.08/13.27 | (136) all_8_4_12 = all_0_3_3
% 47.08/13.27 | (137) all_8_1_9 = 0
% 47.08/13.27 | (138) vapp(all_8_7_15, all_8_6_14) = all_0_3_3
% 47.08/13.27 |
% 47.08/13.27 | Instantiating formula (31) with all_0_3_3, all_8_6_14, all_8_7_15, ve2, ve1 and discharging atoms vapp(all_8_7_15, all_8_6_14) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.08/13.27 | (139) all_8_6_14 = ve2
% 47.08/13.27 |
% 47.08/13.27 | Instantiating formula (88) with all_0_3_3, all_8_6_14, all_8_7_15, ve2, ve1 and discharging atoms vapp(all_8_7_15, all_8_6_14) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.08/13.27 | (140) all_8_7_15 = ve1
% 47.08/13.27 |
% 47.08/13.27 | From (139) and (133) follows:
% 47.08/13.27 | (658) vtcheck(vempty, ve2, all_8_5_13) = 0
% 47.08/13.27 |
% 47.08/13.27 | From (140) and (135) follows:
% 47.08/13.27 | (141) vtcheck(vempty, ve1, all_8_3_11) = 0
% 47.08/13.27 |
% 47.08/13.27 | Instantiating formula (29) with all_8_5_13 and discharging atoms vtcheck(vempty, ve2, all_8_5_13) = 0, yields:
% 47.08/13.27 | (661) all_0_5_5 = 0 | ? [v0] : vsomeExp(v0) = all_0_4_4
% 47.08/13.27 |
% 47.08/13.27 | Instantiating formula (67) with all_8_3_11 and discharging atoms vtcheck(vempty, ve1, all_8_3_11) = 0, yields:
% 47.08/13.27 | (143) all_0_7_7 = 0 | ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.08/13.27 |
% 47.08/13.27 +-Applying beta-rule and splitting (114), into two cases.
% 47.08/13.27 |-Branch one:
% 47.08/13.27 | (144) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22) | (all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)) | (all_9_8_24 = ve1 & all_0_6_6 = vnoExp & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1)
% 47.08/13.27 |
% 47.08/13.27 +-Applying beta-rule and splitting (144), into two cases.
% 47.08/13.27 |-Branch one:
% 47.08/13.27 | (145) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22) | (all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26))
% 47.08/13.27 |
% 47.08/13.27 +-Applying beta-rule and splitting (145), into two cases.
% 47.08/13.27 |-Branch one:
% 47.08/13.27 | (146) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22)
% 47.08/13.27 |
% 47.08/13.27 +-Applying beta-rule and splitting (146), into two cases.
% 47.08/13.27 |-Branch one:
% 47.08/13.27 | (147) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27))
% 47.08/13.27 |
% 47.08/13.27 +-Applying beta-rule and splitting (147), into two cases.
% 47.08/13.27 |-Branch one:
% 47.08/13.27 | (148) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22)
% 47.08/13.28 |
% 47.08/13.28 +-Applying beta-rule and splitting (148), into two cases.
% 47.08/13.28 |-Branch one:
% 47.08/13.28 | (149) all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22
% 47.08/13.28 |
% 47.08/13.28 | Applying alpha-rule on (149) yields:
% 47.08/13.28 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 47.08/13.28 | (151) vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22
% 47.08/13.28 | (152) visSomeExp(all_9_10_26) = all_9_3_19
% 47.08/13.28 | (153) all_9_0_16 = all_0_6_6
% 47.08/13.28 | (154) vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17
% 47.08/13.28 | (155) vreduce(all_9_8_24) = all_9_10_26
% 47.08/13.28 | (156) ~ (all_9_3_19 = 0)
% 47.08/13.28 | (157) all_9_4_20 = all_9_10_26
% 47.08/13.28 | (158) vapp(all_9_6_22, all_9_8_24) = ve1
% 47.08/13.28 | (159) all_9_5_21 = ve1
% 47.08/13.28 | (160) all_9_2_18 = 0
% 47.08/13.28 | (161) visValue(all_9_8_24) = 0
% 47.08/13.28 |
% 47.08/13.28 | Instantiating formula (74) with all_9_1_17 yields:
% 47.08/13.28 | (681) ~ (vsomeExp(all_9_1_17) = all_0_1_1)
% 47.08/13.28 |
% 47.08/13.28 | From (633) and (681) follows:
% 47.08/13.28 | (682) ~ (vsomeExp(all_9_1_17) = all_0_6_6)
% 47.08/13.28 |
% 47.08/13.28 | Using (150) and (682) yields:
% 47.08/13.28 | (130) $false
% 47.08/13.28 |
% 47.08/13.28 |-The branch is then unsatisfiable
% 47.08/13.28 |-Branch two:
% 47.08/13.28 | (264) all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22
% 47.08/13.28 |
% 47.08/13.28 | Applying alpha-rule on (264) yields:
% 47.08/13.28 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 47.08/13.28 | (266) visSomeExp(all_9_7_23) = 0
% 47.08/13.28 | (267) vapp(all_9_6_22, all_9_2_18) = all_9_1_17
% 47.08/13.28 | (268) vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22
% 47.08/13.28 | (269) vreduce(all_9_11_27) = all_9_7_23
% 47.08/13.28 | (270) vapp(all_9_6_22, all_9_11_27) = ve1
% 47.08/13.28 | (153) all_9_0_16 = all_0_6_6
% 47.08/13.28 | (272) all_9_3_19 = 0
% 47.08/13.28 | (273) vgetSomeExp(all_9_7_23) = all_9_2_18
% 47.08/13.28 | (159) all_9_5_21 = ve1
% 47.08/13.28 | (275) all_9_4_20 = all_9_7_23
% 47.08/13.28 |
% 47.08/13.28 | Instantiating formula (74) with all_9_1_17 yields:
% 47.08/13.28 | (681) ~ (vsomeExp(all_9_1_17) = all_0_1_1)
% 47.08/13.28 |
% 47.08/13.28 | From (633) and (681) follows:
% 47.08/13.28 | (682) ~ (vsomeExp(all_9_1_17) = all_0_6_6)
% 47.08/13.28 |
% 47.08/13.28 | Using (150) and (682) yields:
% 47.08/13.28 | (130) $false
% 47.08/13.28 |
% 47.08/13.28 |-The branch is then unsatisfiable
% 47.08/13.28 |-Branch two:
% 47.08/13.28 | (378) all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)
% 47.08/13.28 |
% 47.08/13.28 | Applying alpha-rule on (378) yields:
% 47.08/13.28 | (379) vapp(all_9_5_21, all_9_9_25) = all_9_4_20
% 47.08/13.28 | (380) vsomeExp(all_9_4_20) = all_0_6_6
% 47.08/13.28 | (381) all_9_7_23 = all_9_10_26
% 47.08/13.28 | (382) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)
% 47.08/13.28 | (383) all_9_8_24 = ve1
% 47.08/13.28 | (384) all_9_6_22 = 0
% 47.08/13.28 | (385) visSomeExp(all_9_10_26) = 0
% 47.08/13.28 | (386) vapp(all_9_11_27, all_9_9_25) = ve1
% 47.08/13.28 | (387) all_9_3_19 = all_0_6_6
% 47.08/13.28 | (388) vreduce(all_9_11_27) = all_9_10_26
% 47.08/13.28 | (389) vgetSomeExp(all_9_10_26) = all_9_5_21
% 47.08/13.28 |
% 47.08/13.28 | Instantiating formula (74) with all_9_4_20 yields:
% 47.08/13.28 | (711) ~ (vsomeExp(all_9_4_20) = all_0_1_1)
% 47.08/13.28 |
% 47.08/13.28 | From (633) and (711) follows:
% 47.08/13.28 | (712) ~ (vsomeExp(all_9_4_20) = all_0_6_6)
% 47.08/13.28 |
% 47.08/13.28 | Using (380) and (712) yields:
% 47.08/13.28 | (130) $false
% 47.08/13.28 |
% 47.08/13.28 |-The branch is then unsatisfiable
% 47.08/13.28 |-Branch two:
% 47.08/13.28 | (492) all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22
% 47.08/13.28 |
% 47.08/13.28 | Applying alpha-rule on (492) yields:
% 47.08/13.28 | (493) vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22
% 47.08/13.28 | (494) vapp(all_9_6_22, all_9_7_23) = ve1
% 47.08/13.28 | (495) vreduce(all_9_7_23) = all_9_8_24
% 47.08/13.28 | (496) visSomeExp(all_9_8_24) = all_9_3_19
% 47.08/13.28 | (497) visValue(all_9_7_23) = all_9_2_18
% 47.08/13.28 | (498) all_9_4_20 = all_9_8_24
% 47.08/13.28 | (156) ~ (all_9_3_19 = 0)
% 47.08/13.28 | (159) all_9_5_21 = ve1
% 47.08/13.28 | (501) ~ (all_9_2_18 = 0)
% 47.08/13.28 | (502) all_0_6_6 = vnoExp
% 47.08/13.28 |
% 47.08/13.28 | Instantiating formula (92) with ve1, all_9_7_23, all_9_6_22 and discharging atoms vapp(all_9_6_22, all_9_7_23) = ve1, yields:
% 47.08/13.28 | (162) ~ (visValue(ve1) = 0)
% 47.08/13.28 |
% 47.08/13.28 | Using (68) and (162) yields:
% 47.08/13.28 | (163) ~ (all_0_7_7 = 0)
% 47.08/13.28 |
% 47.08/13.28 +-Applying beta-rule and splitting (143), into two cases.
% 47.08/13.28 |-Branch one:
% 47.08/13.28 | (164) all_0_7_7 = 0
% 47.08/13.28 |
% 47.08/13.28 | Equations (164) can reduce 163 to:
% 47.08/13.28 | (165) $false
% 47.08/13.28 |
% 47.08/13.28 |-The branch is then unsatisfiable
% 47.08/13.28 |-Branch two:
% 47.08/13.28 | (163) ~ (all_0_7_7 = 0)
% 47.08/13.28 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.08/13.28 |
% 47.08/13.28 | Instantiating (167) with all_118_0_310 yields:
% 47.08/13.28 | (1270) vsomeExp(all_118_0_310) = all_0_6_6
% 47.08/13.28 |
% 47.08/13.28 | From (502) and (1270) follows:
% 47.08/13.28 | (1271) vsomeExp(all_118_0_310) = vnoExp
% 47.08/13.28 |
% 47.08/13.28 | Instantiating formula (40) with all_118_0_310 and discharging atoms vsomeExp(all_118_0_310) = vnoExp, yields:
% 47.08/13.28 | (130) $false
% 47.08/13.28 |
% 47.08/13.28 |-The branch is then unsatisfiable
% 47.08/13.28 |-Branch two:
% 47.08/13.28 | (512) all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)
% 47.08/13.28 |
% 47.08/13.28 | Applying alpha-rule on (512) yields:
% 47.08/13.28 | (383) all_9_8_24 = ve1
% 47.08/13.28 | (514) ~ (all_9_6_22 = 0)
% 47.08/13.28 | (515) all_9_7_23 = all_9_9_25
% 47.08/13.28 | (516) visSomeExp(all_9_9_25) = all_9_6_22
% 47.08/13.28 | (517) vapp(all_9_10_26, all_9_11_27) = ve1
% 47.08/13.28 | (518) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)
% 47.08/13.28 | (519) vreduce(all_9_10_26) = all_9_9_25
% 47.08/13.28 | (502) all_0_6_6 = vnoExp
% 47.08/13.28 |
% 47.08/13.28 | Instantiating formula (92) with ve1, all_9_11_27, all_9_10_26 and discharging atoms vapp(all_9_10_26, all_9_11_27) = ve1, yields:
% 47.08/13.28 | (162) ~ (visValue(ve1) = 0)
% 47.08/13.28 |
% 47.08/13.28 | Using (68) and (162) yields:
% 47.08/13.28 | (163) ~ (all_0_7_7 = 0)
% 47.08/13.28 |
% 47.08/13.28 +-Applying beta-rule and splitting (143), into two cases.
% 47.08/13.28 |-Branch one:
% 47.08/13.28 | (164) all_0_7_7 = 0
% 47.08/13.28 |
% 47.08/13.28 | Equations (164) can reduce 163 to:
% 47.08/13.28 | (165) $false
% 47.08/13.28 |
% 47.08/13.28 |-The branch is then unsatisfiable
% 47.08/13.28 |-Branch two:
% 47.08/13.28 | (163) ~ (all_0_7_7 = 0)
% 47.08/13.28 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.08/13.28 |
% 47.08/13.28 | Instantiating (167) with all_112_0_311 yields:
% 47.08/13.28 | (1288) vsomeExp(all_112_0_311) = all_0_6_6
% 47.08/13.28 |
% 47.08/13.28 | From (502) and (1288) follows:
% 47.08/13.28 | (1289) vsomeExp(all_112_0_311) = vnoExp
% 47.08/13.28 |
% 47.08/13.28 | Instantiating formula (40) with all_112_0_311 and discharging atoms vsomeExp(all_112_0_311) = vnoExp, yields:
% 47.08/13.28 | (130) $false
% 47.08/13.28 |
% 47.08/13.28 |-The branch is then unsatisfiable
% 47.08/13.28 |-Branch two:
% 47.08/13.28 | (530) all_9_8_24 = ve1 & all_0_6_6 = vnoExp & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1
% 47.08/13.28 |
% 47.08/13.28 | Applying alpha-rule on (530) yields:
% 47.08/13.28 | (383) all_9_8_24 = ve1
% 47.08/13.28 | (502) all_0_6_6 = vnoExp
% 47.08/13.28 | (533) vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1
% 47.08/13.28 |
% 47.08/13.28 | Combining equations (502,1169) yields a new equation:
% 47.08/13.28 | (1123) all_0_4_4 = vnoExp
% 47.08/13.28 |
% 47.08/13.28 | Instantiating formula (22) with all_0_7_7, ve1, all_9_9_25, all_9_10_26, all_9_11_27 and discharging atoms visValue(ve1) = all_0_7_7, vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1, yields:
% 47.08/13.28 | (164) all_0_7_7 = 0
% 47.08/13.28 |
% 47.08/13.28 | Equations (164) can reduce 118 to:
% 47.08/13.28 | (760) ~ (all_0_5_5 = 0)
% 47.08/13.28 |
% 47.08/13.28 +-Applying beta-rule and splitting (661), into two cases.
% 47.08/13.28 |-Branch one:
% 47.08/13.28 | (761) all_0_5_5 = 0
% 47.08/13.28 |
% 47.08/13.28 | Equations (761) can reduce 760 to:
% 47.08/13.28 | (165) $false
% 47.08/13.28 |
% 47.08/13.28 |-The branch is then unsatisfiable
% 47.08/13.28 |-Branch two:
% 47.08/13.28 | (760) ~ (all_0_5_5 = 0)
% 47.08/13.28 | (764) ? [v0] : vsomeExp(v0) = all_0_4_4
% 47.08/13.28 |
% 47.08/13.28 | Instantiating (764) with all_107_0_312 yields:
% 47.08/13.28 | (1302) vsomeExp(all_107_0_312) = all_0_4_4
% 47.08/13.28 |
% 47.08/13.28 | From (1123) and (1302) follows:
% 47.08/13.28 | (1303) vsomeExp(all_107_0_312) = vnoExp
% 47.08/13.28 |
% 47.08/13.28 | Instantiating formula (40) with all_107_0_312 and discharging atoms vsomeExp(all_107_0_312) = vnoExp, yields:
% 47.08/13.28 | (130) $false
% 47.08/13.28 |
% 47.08/13.28 |-The branch is then unsatisfiable
% 47.08/13.28 |-Branch two:
% 47.08/13.28 | (612) all_9_10_26 = ve1 & all_0_6_6 = vnoExp & vvar(all_9_11_27) = ve1
% 47.08/13.28 |
% 47.08/13.28 | Applying alpha-rule on (612) yields:
% 47.08/13.28 | (613) all_9_10_26 = ve1
% 47.08/13.28 | (502) all_0_6_6 = vnoExp
% 47.08/13.28 | (615) vvar(all_9_11_27) = ve1
% 47.08/13.28 |
% 47.08/13.28 | Instantiating formula (104) with ve1, all_9_11_27 and discharging atoms vvar(all_9_11_27) = ve1, yields:
% 47.08/13.28 | (162) ~ (visValue(ve1) = 0)
% 47.08/13.28 |
% 47.08/13.28 | Using (68) and (162) yields:
% 47.08/13.28 | (163) ~ (all_0_7_7 = 0)
% 47.08/13.28 |
% 47.08/13.28 +-Applying beta-rule and splitting (143), into two cases.
% 47.08/13.28 |-Branch one:
% 47.08/13.28 | (164) all_0_7_7 = 0
% 47.08/13.28 |
% 47.08/13.28 | Equations (164) can reduce 163 to:
% 47.08/13.28 | (165) $false
% 47.08/13.28 |
% 47.08/13.28 |-The branch is then unsatisfiable
% 47.08/13.28 |-Branch two:
% 47.08/13.28 | (163) ~ (all_0_7_7 = 0)
% 47.08/13.28 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.08/13.29 |
% 47.08/13.29 | Instantiating (167) with all_111_0_313 yields:
% 47.08/13.29 | (1315) vsomeExp(all_111_0_313) = all_0_6_6
% 47.08/13.29 |
% 47.08/13.29 | From (502) and (1315) follows:
% 47.08/13.29 | (1316) vsomeExp(all_111_0_313) = vnoExp
% 47.08/13.29 |
% 47.08/13.29 | Instantiating formula (40) with all_111_0_313 and discharging atoms vsomeExp(all_111_0_313) = vnoExp, yields:
% 47.08/13.29 | (130) $false
% 47.08/13.29 |
% 47.08/13.29 |-The branch is then unsatisfiable
% 47.08/13.29 |-Branch two:
% 47.08/13.29 | (625) all_8_4_12 = all_8_7_15 & all_8_5_13 = all_0_3_3 & vlookup(all_8_6_14, vempty) = all_8_7_15 & vsomeType(all_0_0_0) = all_8_7_15 & vvar(all_8_6_14) = all_0_3_3
% 47.08/13.29 |
% 47.08/13.29 | Applying alpha-rule on (625) yields:
% 47.08/13.29 | (626) all_8_4_12 = all_8_7_15
% 47.08/13.29 | (627) all_8_5_13 = all_0_3_3
% 47.08/13.29 | (628) vvar(all_8_6_14) = all_0_3_3
% 47.08/13.29 | (629) vsomeType(all_0_0_0) = all_8_7_15
% 47.08/13.29 | (630) vlookup(all_8_6_14, vempty) = all_8_7_15
% 47.08/13.29 |
% 47.08/13.29 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_8_6_14 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_8_6_14) = all_0_3_3, yields:
% 47.08/13.29 | (130) $false
% 47.08/13.29 |
% 47.08/13.29 |-The branch is then unsatisfiable
% 47.08/13.29 |-Branch two:
% 47.08/13.29 | (1325) visValue(ve1) = all_0_5_5
% 47.08/13.29 | (1326) all_0_5_5 = all_0_7_7
% 47.08/13.29 |
% 47.08/13.29 | From (1326) and (89) follows:
% 47.08/13.29 | (1327) visValue(ve2) = all_0_7_7
% 47.08/13.29 |
% 47.08/13.29 | From (1326) and (1325) follows:
% 47.08/13.29 | (68) visValue(ve1) = all_0_7_7
% 47.08/13.29 |
% 47.08/13.29 +-Applying beta-rule and splitting (106), into two cases.
% 47.08/13.29 |-Branch one:
% 47.08/13.29 | (119) ~ (vreduce(ve1) = all_0_1_1)
% 47.08/13.29 |
% 47.08/13.29 | Using (42) and (119) yields:
% 47.08/13.29 | (120) ~ (all_0_1_1 = all_0_6_6)
% 47.08/13.29 |
% 47.08/13.29 +-Applying beta-rule and splitting (105), into two cases.
% 47.08/13.29 |-Branch one:
% 47.08/13.29 | (1171) ~ (vreduce(ve2) = all_0_1_1)
% 47.08/13.29 |
% 47.08/13.29 | Using (81) and (1171) yields:
% 47.08/13.29 | (1332) ~ (all_0_1_1 = all_0_4_4)
% 47.08/13.29 |
% 47.08/13.29 +-Applying beta-rule and splitting (107), into two cases.
% 47.08/13.29 |-Branch one:
% 47.08/13.29 | (636) ~ (vreduce(ve1) = all_0_4_4)
% 47.08/13.29 |
% 47.08/13.29 | Using (42) and (636) yields:
% 47.08/13.29 | (637) ~ (all_0_4_4 = all_0_6_6)
% 47.08/13.29 |
% 47.08/13.29 +-Applying beta-rule and splitting (113), into two cases.
% 47.08/13.29 |-Branch one:
% 47.08/13.29 | (121) (all_8_0_8 = 0 & all_8_2_10 = all_0_0_0 & all_8_3_11 = all_0_3_3 & varrow(all_8_5_13, all_8_4_12) = all_0_0_0 & vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0 & vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9 & vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3) | (all_8_1_9 = 0 & all_8_2_10 = 0 & all_8_4_12 = all_0_3_3 & varrow(all_8_5_13, all_0_0_0) = all_8_3_11 & vtcheck(vempty, all_8_6_14, all_8_5_13) = 0 & vtcheck(vempty, all_8_7_15, all_8_3_11) = 0 & vapp(all_8_7_15, all_8_6_14) = all_0_3_3)
% 47.08/13.29 |
% 47.08/13.29 +-Applying beta-rule and splitting (121), into two cases.
% 47.08/13.29 |-Branch one:
% 47.08/13.29 | (122) all_8_0_8 = 0 & all_8_2_10 = all_0_0_0 & all_8_3_11 = all_0_3_3 & varrow(all_8_5_13, all_8_4_12) = all_0_0_0 & vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0 & vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9 & vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3
% 47.08/13.29 |
% 47.08/13.29 | Applying alpha-rule on (122) yields:
% 47.08/13.29 | (123) vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3
% 47.08/13.29 | (124) vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0
% 47.08/13.29 | (125) vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9
% 47.08/13.29 | (126) all_8_3_11 = all_0_3_3
% 47.08/13.29 | (127) all_8_0_8 = 0
% 47.08/13.29 | (128) all_8_2_10 = all_0_0_0
% 47.08/13.29 | (129) varrow(all_8_5_13, all_8_4_12) = all_0_0_0
% 47.08/13.29 |
% 47.08/13.29 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_8_6_14, all_8_5_13, all_8_7_15 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3, yields:
% 47.08/13.29 | (130) $false
% 47.08/13.29 |
% 47.08/13.29 |-The branch is then unsatisfiable
% 47.08/13.29 |-Branch two:
% 47.08/13.29 | (131) all_8_1_9 = 0 & all_8_2_10 = 0 & all_8_4_12 = all_0_3_3 & varrow(all_8_5_13, all_0_0_0) = all_8_3_11 & vtcheck(vempty, all_8_6_14, all_8_5_13) = 0 & vtcheck(vempty, all_8_7_15, all_8_3_11) = 0 & vapp(all_8_7_15, all_8_6_14) = all_0_3_3
% 47.08/13.29 |
% 47.08/13.29 | Applying alpha-rule on (131) yields:
% 47.08/13.29 | (132) varrow(all_8_5_13, all_0_0_0) = all_8_3_11
% 47.08/13.29 | (133) vtcheck(vempty, all_8_6_14, all_8_5_13) = 0
% 47.08/13.29 | (134) all_8_2_10 = 0
% 47.08/13.29 | (135) vtcheck(vempty, all_8_7_15, all_8_3_11) = 0
% 47.08/13.29 | (136) all_8_4_12 = all_0_3_3
% 47.08/13.29 | (137) all_8_1_9 = 0
% 47.08/13.29 | (138) vapp(all_8_7_15, all_8_6_14) = all_0_3_3
% 47.08/13.29 |
% 47.08/13.29 | Instantiating formula (31) with all_0_3_3, all_8_6_14, all_8_7_15, ve2, ve1 and discharging atoms vapp(all_8_7_15, all_8_6_14) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.08/13.29 | (139) all_8_6_14 = ve2
% 47.08/13.29 |
% 47.08/13.29 | Instantiating formula (88) with all_0_3_3, all_8_6_14, all_8_7_15, ve2, ve1 and discharging atoms vapp(all_8_7_15, all_8_6_14) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.08/13.29 | (140) all_8_7_15 = ve1
% 47.08/13.29 |
% 47.08/13.29 | From (139) and (133) follows:
% 47.08/13.29 | (658) vtcheck(vempty, ve2, all_8_5_13) = 0
% 47.08/13.29 |
% 47.08/13.29 | From (140) and (135) follows:
% 47.08/13.29 | (141) vtcheck(vempty, ve1, all_8_3_11) = 0
% 47.08/13.29 |
% 47.08/13.29 | From (140)(139) and (138) follows:
% 47.08/13.29 | (35) vapp(ve1, ve2) = all_0_3_3
% 47.08/13.29 |
% 47.08/13.29 | Instantiating formula (29) with all_8_5_13 and discharging atoms vtcheck(vempty, ve2, all_8_5_13) = 0, yields:
% 47.08/13.29 | (661) all_0_5_5 = 0 | ? [v0] : vsomeExp(v0) = all_0_4_4
% 47.08/13.29 |
% 47.08/13.29 | Instantiating formula (67) with all_8_3_11 and discharging atoms vtcheck(vempty, ve1, all_8_3_11) = 0, yields:
% 47.08/13.29 | (143) all_0_7_7 = 0 | ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.16/13.29 |
% 47.16/13.29 +-Applying beta-rule and splitting (114), into two cases.
% 47.16/13.29 |-Branch one:
% 47.16/13.29 | (144) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22) | (all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)) | (all_9_8_24 = ve1 & all_0_6_6 = vnoExp & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1)
% 47.16/13.29 |
% 47.16/13.29 +-Applying beta-rule and splitting (144), into two cases.
% 47.16/13.29 |-Branch one:
% 47.16/13.29 | (145) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22) | (all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26))
% 47.16/13.29 |
% 47.16/13.29 +-Applying beta-rule and splitting (145), into two cases.
% 47.16/13.29 |-Branch one:
% 47.16/13.29 | (146) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22)
% 47.16/13.29 |
% 47.16/13.29 +-Applying beta-rule and splitting (146), into two cases.
% 47.16/13.29 |-Branch one:
% 47.16/13.29 | (147) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27))
% 47.16/13.29 |
% 47.16/13.29 +-Applying beta-rule and splitting (147), into two cases.
% 47.16/13.29 |-Branch one:
% 47.16/13.29 | (148) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22)
% 47.16/13.29 |
% 47.16/13.29 +-Applying beta-rule and splitting (148), into two cases.
% 47.16/13.29 |-Branch one:
% 47.16/13.29 | (149) all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22
% 47.16/13.29 |
% 47.16/13.30 | Applying alpha-rule on (149) yields:
% 47.16/13.30 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 47.16/13.30 | (151) vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22
% 47.16/13.30 | (152) visSomeExp(all_9_10_26) = all_9_3_19
% 47.16/13.30 | (153) all_9_0_16 = all_0_6_6
% 47.16/13.30 | (154) vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17
% 47.16/13.30 | (155) vreduce(all_9_8_24) = all_9_10_26
% 47.16/13.30 | (156) ~ (all_9_3_19 = 0)
% 47.16/13.30 | (157) all_9_4_20 = all_9_10_26
% 47.16/13.30 | (158) vapp(all_9_6_22, all_9_8_24) = ve1
% 47.16/13.30 | (159) all_9_5_21 = ve1
% 47.16/13.30 | (160) all_9_2_18 = 0
% 47.16/13.30 | (161) visValue(all_9_8_24) = 0
% 47.16/13.30 |
% 47.16/13.30 | Instantiating formula (92) with ve1, all_9_8_24, all_9_6_22 and discharging atoms vapp(all_9_6_22, all_9_8_24) = ve1, yields:
% 47.16/13.30 | (162) ~ (visValue(ve1) = 0)
% 47.16/13.30 |
% 47.16/13.30 | Using (68) and (162) yields:
% 47.16/13.30 | (163) ~ (all_0_7_7 = 0)
% 47.16/13.30 |
% 47.16/13.30 +-Applying beta-rule and splitting (143), into two cases.
% 47.16/13.30 |-Branch one:
% 47.16/13.30 | (164) all_0_7_7 = 0
% 47.16/13.30 |
% 47.16/13.30 | Equations (164) can reduce 163 to:
% 47.16/13.30 | (165) $false
% 47.16/13.30 |
% 47.16/13.30 |-The branch is then unsatisfiable
% 47.16/13.30 |-Branch two:
% 47.16/13.30 | (163) ~ (all_0_7_7 = 0)
% 47.16/13.30 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.16/13.30 |
% 47.16/13.30 | Instantiating (167) with all_127_0_330 yields:
% 47.16/13.30 | (1384) vsomeExp(all_127_0_330) = all_0_6_6
% 47.16/13.30 |
% 47.16/13.30 | Instantiating formula (85) with all_0_6_6, all_127_0_330, all_9_1_17 and discharging atoms vsomeExp(all_127_0_330) = all_0_6_6, vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 47.16/13.30 | (1385) all_127_0_330 = all_9_1_17
% 47.16/13.30 |
% 47.16/13.30 | From (1385) and (1384) follows:
% 47.16/13.30 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 47.16/13.30 |
% 47.16/13.30 +-Applying beta-rule and splitting (116), into two cases.
% 47.16/13.30 |-Branch one:
% 47.16/13.30 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 47.16/13.30 |
% 47.16/13.30 +-Applying beta-rule and splitting (171), into two cases.
% 47.16/13.30 |-Branch one:
% 47.16/13.30 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 47.16/13.30 |
% 47.16/13.30 +-Applying beta-rule and splitting (172), into two cases.
% 47.16/13.30 |-Branch one:
% 47.16/13.30 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 47.16/13.30 |
% 47.16/13.30 +-Applying beta-rule and splitting (173), into two cases.
% 47.16/13.30 |-Branch one:
% 47.16/13.30 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 47.16/13.30 |
% 47.16/13.30 +-Applying beta-rule and splitting (174), into two cases.
% 47.16/13.30 |-Branch one:
% 47.16/13.30 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 47.16/13.30 |
% 47.16/13.30 +-Applying beta-rule and splitting (175), into two cases.
% 47.16/13.30 |-Branch one:
% 47.16/13.30 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.16/13.30 |
% 47.16/13.30 | Applying alpha-rule on (176) yields:
% 47.16/13.30 | (177) all_11_5_45 = all_0_3_3
% 47.16/13.30 | (178) all_11_4_44 = all_11_10_50
% 47.16/13.30 | (179) visValue(all_11_8_48) = 0
% 47.16/13.30 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 47.16/13.30 | (181) all_11_0_40 = all_0_1_1
% 47.16/13.30 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.16/13.30 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.16/13.30 | (184) vreduce(all_11_8_48) = all_11_10_50
% 47.16/13.30 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 47.16/13.30 | (186) ~ (all_11_3_43 = 0)
% 47.16/13.30 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 47.16/13.30 | (188) all_11_2_42 = 0
% 47.16/13.30 |
% 47.16/13.30 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.16/13.30 | (130) $false
% 47.16/13.30 |
% 47.16/13.30 |-The branch is then unsatisfiable
% 47.16/13.30 |-Branch two:
% 47.16/13.30 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.16/13.30 |
% 47.16/13.30 | Applying alpha-rule on (190) yields:
% 47.16/13.30 | (177) all_11_5_45 = all_0_3_3
% 47.16/13.30 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 47.16/13.30 | (193) visSomeExp(all_11_7_47) = 0
% 47.16/13.30 | (181) all_11_0_40 = all_0_1_1
% 47.16/13.30 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.16/13.30 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 47.16/13.30 | (197) vreduce(all_11_11_51) = all_11_7_47
% 47.16/13.30 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 47.16/13.30 | (199) all_11_3_43 = 0
% 47.16/13.30 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.16/13.30 | (201) all_11_4_44 = all_11_7_47
% 47.16/13.30 |
% 47.16/13.30 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.16/13.30 | (130) $false
% 47.16/13.30 |
% 47.16/13.30 |-The branch is then unsatisfiable
% 47.16/13.30 |-Branch two:
% 47.16/13.30 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.16/13.30 |
% 47.16/13.30 | Applying alpha-rule on (203) yields:
% 47.16/13.30 | (204) all_11_7_47 = all_11_10_50
% 47.16/13.30 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.16/13.30 | (206) all_11_6_46 = 0
% 47.16/13.30 | (207) all_11_3_43 = all_0_1_1
% 47.16/13.30 | (208) visSomeExp(all_11_10_50) = 0
% 47.16/13.30 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 47.16/13.30 | (210) vreduce(all_11_11_51) = all_11_10_50
% 47.16/13.30 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 47.16/13.30 | (212) all_11_8_48 = all_0_3_3
% 47.16/13.30 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 47.16/13.30 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 47.16/13.30 |
% 47.16/13.30 | Instantiating formula (74) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = all_0_1_1, yields:
% 47.16/13.30 | (130) $false
% 47.16/13.30 |
% 47.16/13.30 |-The branch is then unsatisfiable
% 47.16/13.30 |-Branch two:
% 47.16/13.30 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.16/13.31 |
% 47.16/13.31 | Applying alpha-rule on (216) yields:
% 47.16/13.31 | (177) all_11_5_45 = all_0_3_3
% 47.16/13.31 | (218) visValue(all_11_7_47) = all_11_2_42
% 47.16/13.31 | (219) all_0_1_1 = vnoExp
% 47.16/13.31 | (220) vreduce(all_11_7_47) = all_11_8_48
% 47.16/13.31 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.16/13.31 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 47.16/13.31 | (186) ~ (all_11_3_43 = 0)
% 47.16/13.31 | (224) all_11_4_44 = all_11_8_48
% 47.16/13.31 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 47.16/13.31 | (226) ~ (all_11_2_42 = 0)
% 47.16/13.31 |
% 47.16/13.31 | Instantiating formula (88) with all_0_3_3, all_11_7_47, all_11_6_46, ve2, ve1 and discharging atoms vapp(all_11_6_46, all_11_7_47) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.16/13.31 | (227) all_11_6_46 = ve1
% 47.16/13.31 |
% 47.16/13.31 | Instantiating formula (66) with ve1, all_9_8_24, all_9_6_22, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(all_9_6_22, all_9_8_24) = ve1, yields:
% 47.16/13.31 | (228) ~ (vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1)
% 47.16/13.31 |
% 47.16/13.31 | From (227) and (221) follows:
% 47.16/13.31 | (229) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1
% 47.16/13.31 |
% 47.16/13.31 | Using (229) and (228) yields:
% 47.16/13.31 | (130) $false
% 47.16/13.31 |
% 47.16/13.31 |-The branch is then unsatisfiable
% 47.16/13.31 |-Branch two:
% 47.16/13.31 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.16/13.31 |
% 47.16/13.31 | Applying alpha-rule on (231) yields:
% 47.16/13.31 | (232) all_11_7_47 = all_11_9_49
% 47.16/13.31 | (219) all_0_1_1 = vnoExp
% 47.16/13.31 | (234) ~ (all_11_6_46 = 0)
% 47.16/13.31 | (235) vreduce(all_11_10_50) = all_11_9_49
% 47.16/13.31 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.16/13.31 | (212) all_11_8_48 = all_0_3_3
% 47.16/13.31 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 47.16/13.31 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 47.16/13.31 |
% 47.16/13.31 | Instantiating formula (55) with ve1, all_11_9_49, all_0_6_6 and discharging atoms vreduce(ve1) = all_0_6_6, yields:
% 47.16/13.31 | (240) all_11_9_49 = all_0_6_6 | ~ (vreduce(ve1) = all_11_9_49)
% 47.16/13.31 |
% 47.16/13.31 | Instantiating formula (47) with all_11_6_46, all_0_6_6, all_9_1_17 and discharging atoms vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 47.16/13.31 | (241) all_11_6_46 = 0 | ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.16/13.31 |
% 47.16/13.31 | Instantiating formula (88) with all_0_3_3, all_11_11_51, all_11_10_50, ve2, ve1 and discharging atoms vapp(all_11_10_50, all_11_11_51) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.16/13.31 | (242) all_11_10_50 = ve1
% 47.16/13.31 |
% 47.16/13.31 | From (242) and (235) follows:
% 47.16/13.31 | (243) vreduce(ve1) = all_11_9_49
% 47.16/13.31 |
% 47.16/13.31 +-Applying beta-rule and splitting (241), into two cases.
% 47.16/13.31 |-Branch one:
% 47.16/13.31 | (244) ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.16/13.31 |
% 47.16/13.31 +-Applying beta-rule and splitting (240), into two cases.
% 47.16/13.31 |-Branch one:
% 47.16/13.31 | (245) ~ (vreduce(ve1) = all_11_9_49)
% 47.16/13.31 |
% 47.16/13.31 | Using (243) and (245) yields:
% 47.16/13.31 | (130) $false
% 47.16/13.31 |
% 47.16/13.31 |-The branch is then unsatisfiable
% 47.16/13.31 |-Branch two:
% 47.16/13.31 | (243) vreduce(ve1) = all_11_9_49
% 47.16/13.31 | (248) all_11_9_49 = all_0_6_6
% 47.16/13.31 |
% 47.16/13.31 | From (248) and (239) follows:
% 47.16/13.31 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.16/13.31 |
% 47.16/13.31 | Using (249) and (244) yields:
% 47.16/13.31 | (130) $false
% 47.16/13.31 |
% 47.16/13.31 |-The branch is then unsatisfiable
% 47.16/13.31 |-Branch two:
% 47.16/13.31 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.16/13.31 | (206) all_11_6_46 = 0
% 47.16/13.31 |
% 47.16/13.31 | Equations (206) can reduce 234 to:
% 47.16/13.31 | (165) $false
% 47.16/13.31 |
% 47.16/13.31 |-The branch is then unsatisfiable
% 47.16/13.31 |-Branch two:
% 47.16/13.31 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.16/13.31 |
% 47.16/13.31 | Applying alpha-rule on (254) yields:
% 47.16/13.31 | (212) all_11_8_48 = all_0_3_3
% 47.16/13.31 | (219) all_0_1_1 = vnoExp
% 47.16/13.31 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.16/13.31 |
% 47.16/13.31 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3, yields:
% 47.16/13.31 | (130) $false
% 47.16/13.31 |
% 47.16/13.31 |-The branch is then unsatisfiable
% 47.16/13.31 |-Branch two:
% 47.16/13.31 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 47.16/13.31 |
% 47.16/13.31 | Applying alpha-rule on (259) yields:
% 47.16/13.31 | (260) all_11_10_50 = all_0_3_3
% 47.16/13.31 | (219) all_0_1_1 = vnoExp
% 47.16/13.31 | (262) vvar(all_11_11_51) = all_0_3_3
% 47.16/13.31 |
% 47.16/13.31 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_11_11_51) = all_0_3_3, yields:
% 47.16/13.31 | (130) $false
% 47.16/13.31 |
% 47.16/13.31 |-The branch is then unsatisfiable
% 47.16/13.31 |-Branch two:
% 47.16/13.31 | (264) all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22
% 47.16/13.31 |
% 47.16/13.31 | Applying alpha-rule on (264) yields:
% 47.16/13.31 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 47.16/13.31 | (266) visSomeExp(all_9_7_23) = 0
% 47.16/13.31 | (267) vapp(all_9_6_22, all_9_2_18) = all_9_1_17
% 47.16/13.31 | (268) vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22
% 47.16/13.31 | (269) vreduce(all_9_11_27) = all_9_7_23
% 47.16/13.31 | (270) vapp(all_9_6_22, all_9_11_27) = ve1
% 47.16/13.31 | (153) all_9_0_16 = all_0_6_6
% 47.16/13.31 | (272) all_9_3_19 = 0
% 47.16/13.31 | (273) vgetSomeExp(all_9_7_23) = all_9_2_18
% 47.16/13.31 | (159) all_9_5_21 = ve1
% 47.16/13.31 | (275) all_9_4_20 = all_9_7_23
% 47.16/13.31 |
% 47.16/13.31 | Instantiating formula (92) with ve1, all_9_11_27, all_9_6_22 and discharging atoms vapp(all_9_6_22, all_9_11_27) = ve1, yields:
% 47.16/13.31 | (162) ~ (visValue(ve1) = 0)
% 47.16/13.31 |
% 47.16/13.31 | Using (68) and (162) yields:
% 47.16/13.31 | (163) ~ (all_0_7_7 = 0)
% 47.16/13.31 |
% 47.16/13.31 +-Applying beta-rule and splitting (661), into two cases.
% 47.16/13.31 |-Branch one:
% 47.16/13.31 | (761) all_0_5_5 = 0
% 47.16/13.31 |
% 47.16/13.31 | Combining equations (761,1326) yields a new equation:
% 47.16/13.31 | (164) all_0_7_7 = 0
% 47.16/13.31 |
% 47.16/13.31 | Equations (164) can reduce 163 to:
% 47.16/13.31 | (165) $false
% 47.16/13.31 |
% 47.16/13.31 |-The branch is then unsatisfiable
% 47.16/13.31 |-Branch two:
% 47.16/13.31 | (760) ~ (all_0_5_5 = 0)
% 47.16/13.31 | (764) ? [v0] : vsomeExp(v0) = all_0_4_4
% 47.16/13.31 |
% 47.16/13.31 | Equations (1326) can reduce 760 to:
% 47.16/13.31 | (163) ~ (all_0_7_7 = 0)
% 47.16/13.31 |
% 47.16/13.31 +-Applying beta-rule and splitting (143), into two cases.
% 47.16/13.31 |-Branch one:
% 47.16/13.31 | (164) all_0_7_7 = 0
% 47.16/13.31 |
% 47.16/13.31 | Equations (164) can reduce 163 to:
% 47.16/13.31 | (165) $false
% 47.16/13.31 |
% 47.16/13.31 |-The branch is then unsatisfiable
% 47.16/13.31 |-Branch two:
% 47.16/13.31 | (163) ~ (all_0_7_7 = 0)
% 47.16/13.31 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.16/13.31 |
% 47.16/13.31 | Instantiating (167) with all_132_0_365 yields:
% 47.16/13.31 | (1504) vsomeExp(all_132_0_365) = all_0_6_6
% 47.16/13.31 |
% 47.16/13.31 | Instantiating formula (85) with all_0_6_6, all_132_0_365, all_9_1_17 and discharging atoms vsomeExp(all_132_0_365) = all_0_6_6, vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 47.16/13.31 | (1505) all_132_0_365 = all_9_1_17
% 47.16/13.31 |
% 47.16/13.31 | From (1505) and (1504) follows:
% 47.16/13.31 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 47.16/13.31 |
% 47.16/13.31 +-Applying beta-rule and splitting (116), into two cases.
% 47.16/13.31 |-Branch one:
% 47.16/13.31 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 47.16/13.31 |
% 47.16/13.31 +-Applying beta-rule and splitting (171), into two cases.
% 47.16/13.31 |-Branch one:
% 47.16/13.31 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 47.16/13.31 |
% 47.16/13.31 +-Applying beta-rule and splitting (172), into two cases.
% 47.16/13.31 |-Branch one:
% 47.16/13.31 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 47.16/13.31 |
% 47.16/13.31 +-Applying beta-rule and splitting (173), into two cases.
% 47.16/13.31 |-Branch one:
% 47.16/13.31 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 47.16/13.32 |
% 47.16/13.32 +-Applying beta-rule and splitting (174), into two cases.
% 47.16/13.32 |-Branch one:
% 47.16/13.32 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 47.16/13.32 |
% 47.16/13.32 +-Applying beta-rule and splitting (175), into two cases.
% 47.16/13.32 |-Branch one:
% 47.16/13.32 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.16/13.32 |
% 47.16/13.32 | Applying alpha-rule on (176) yields:
% 47.16/13.32 | (177) all_11_5_45 = all_0_3_3
% 47.16/13.32 | (178) all_11_4_44 = all_11_10_50
% 47.16/13.32 | (179) visValue(all_11_8_48) = 0
% 47.16/13.32 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 47.16/13.32 | (181) all_11_0_40 = all_0_1_1
% 47.16/13.32 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.16/13.32 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.16/13.32 | (184) vreduce(all_11_8_48) = all_11_10_50
% 47.16/13.32 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 47.16/13.32 | (186) ~ (all_11_3_43 = 0)
% 47.16/13.32 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 47.16/13.32 | (188) all_11_2_42 = 0
% 47.16/13.32 |
% 47.16/13.32 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.16/13.32 | (130) $false
% 47.16/13.32 |
% 47.16/13.32 |-The branch is then unsatisfiable
% 47.16/13.32 |-Branch two:
% 47.16/13.32 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.16/13.32 |
% 47.16/13.32 | Applying alpha-rule on (190) yields:
% 47.16/13.32 | (177) all_11_5_45 = all_0_3_3
% 47.16/13.32 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 47.16/13.32 | (193) visSomeExp(all_11_7_47) = 0
% 47.16/13.32 | (181) all_11_0_40 = all_0_1_1
% 47.16/13.32 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.16/13.32 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 47.16/13.32 | (197) vreduce(all_11_11_51) = all_11_7_47
% 47.16/13.32 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 47.16/13.32 | (199) all_11_3_43 = 0
% 47.16/13.32 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.16/13.32 | (201) all_11_4_44 = all_11_7_47
% 47.16/13.32 |
% 47.16/13.32 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.16/13.32 | (130) $false
% 47.16/13.32 |
% 47.16/13.32 |-The branch is then unsatisfiable
% 47.16/13.32 |-Branch two:
% 47.16/13.32 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.16/13.32 |
% 47.16/13.32 | Applying alpha-rule on (203) yields:
% 47.16/13.32 | (204) all_11_7_47 = all_11_10_50
% 47.16/13.32 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.16/13.32 | (206) all_11_6_46 = 0
% 47.16/13.32 | (207) all_11_3_43 = all_0_1_1
% 47.16/13.32 | (208) visSomeExp(all_11_10_50) = 0
% 47.16/13.32 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 47.16/13.32 | (210) vreduce(all_11_11_51) = all_11_10_50
% 47.16/13.32 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 47.16/13.32 | (212) all_11_8_48 = all_0_3_3
% 47.16/13.32 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 47.16/13.32 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 47.16/13.32 |
% 47.16/13.32 | Instantiating formula (74) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = all_0_1_1, yields:
% 47.16/13.32 | (130) $false
% 47.16/13.32 |
% 47.16/13.32 |-The branch is then unsatisfiable
% 47.16/13.32 |-Branch two:
% 47.16/13.32 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.16/13.32 |
% 47.16/13.32 | Applying alpha-rule on (216) yields:
% 47.16/13.32 | (177) all_11_5_45 = all_0_3_3
% 47.16/13.32 | (218) visValue(all_11_7_47) = all_11_2_42
% 47.16/13.32 | (219) all_0_1_1 = vnoExp
% 47.16/13.32 | (220) vreduce(all_11_7_47) = all_11_8_48
% 47.16/13.32 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.16/13.32 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 47.16/13.32 | (186) ~ (all_11_3_43 = 0)
% 47.16/13.32 | (224) all_11_4_44 = all_11_8_48
% 47.16/13.32 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 47.16/13.32 | (226) ~ (all_11_2_42 = 0)
% 47.16/13.32 |
% 47.16/13.32 | Instantiating formula (88) with all_0_3_3, all_11_7_47, all_11_6_46, ve2, ve1 and discharging atoms vapp(all_11_6_46, all_11_7_47) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.16/13.32 | (227) all_11_6_46 = ve1
% 47.16/13.32 |
% 47.16/13.32 | Instantiating formula (66) with ve1, all_9_11_27, all_9_6_22, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(all_9_6_22, all_9_11_27) = ve1, yields:
% 47.16/13.32 | (228) ~ (vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1)
% 47.16/13.32 |
% 47.16/13.32 | From (227) and (221) follows:
% 47.16/13.32 | (229) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1
% 47.16/13.32 |
% 47.32/13.32 | Using (229) and (228) yields:
% 47.32/13.32 | (130) $false
% 47.32/13.32 |
% 47.32/13.32 |-The branch is then unsatisfiable
% 47.32/13.32 |-Branch two:
% 47.32/13.32 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.32/13.32 |
% 47.32/13.32 | Applying alpha-rule on (231) yields:
% 47.32/13.32 | (232) all_11_7_47 = all_11_9_49
% 47.32/13.32 | (219) all_0_1_1 = vnoExp
% 47.32/13.32 | (234) ~ (all_11_6_46 = 0)
% 47.32/13.32 | (235) vreduce(all_11_10_50) = all_11_9_49
% 47.32/13.32 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.32/13.32 | (212) all_11_8_48 = all_0_3_3
% 47.32/13.32 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 47.32/13.32 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 47.32/13.32 |
% 47.32/13.32 | Instantiating formula (55) with ve1, all_11_9_49, all_0_6_6 and discharging atoms vreduce(ve1) = all_0_6_6, yields:
% 47.32/13.32 | (240) all_11_9_49 = all_0_6_6 | ~ (vreduce(ve1) = all_11_9_49)
% 47.32/13.32 |
% 47.32/13.32 | Instantiating formula (47) with all_11_6_46, all_0_6_6, all_9_1_17 and discharging atoms vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 47.32/13.32 | (241) all_11_6_46 = 0 | ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.32/13.32 |
% 47.32/13.32 | Instantiating formula (88) with all_0_3_3, all_11_11_51, all_11_10_50, ve2, ve1 and discharging atoms vapp(all_11_10_50, all_11_11_51) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.32/13.32 | (242) all_11_10_50 = ve1
% 47.32/13.32 |
% 47.32/13.32 | From (242) and (235) follows:
% 47.32/13.32 | (243) vreduce(ve1) = all_11_9_49
% 47.32/13.32 |
% 47.32/13.32 +-Applying beta-rule and splitting (241), into two cases.
% 47.32/13.32 |-Branch one:
% 47.32/13.32 | (244) ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.32/13.32 |
% 47.32/13.32 +-Applying beta-rule and splitting (240), into two cases.
% 47.32/13.32 |-Branch one:
% 47.32/13.32 | (245) ~ (vreduce(ve1) = all_11_9_49)
% 47.32/13.32 |
% 47.32/13.32 | Using (243) and (245) yields:
% 47.32/13.32 | (130) $false
% 47.32/13.32 |
% 47.32/13.32 |-The branch is then unsatisfiable
% 47.32/13.32 |-Branch two:
% 47.32/13.32 | (243) vreduce(ve1) = all_11_9_49
% 47.32/13.32 | (248) all_11_9_49 = all_0_6_6
% 47.32/13.32 |
% 47.32/13.32 | From (248) and (239) follows:
% 47.32/13.32 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.32/13.32 |
% 47.32/13.32 | Using (249) and (244) yields:
% 47.32/13.32 | (130) $false
% 47.32/13.32 |
% 47.32/13.32 |-The branch is then unsatisfiable
% 47.32/13.32 |-Branch two:
% 47.32/13.32 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.32/13.32 | (206) all_11_6_46 = 0
% 47.32/13.32 |
% 47.32/13.32 | Equations (206) can reduce 234 to:
% 47.32/13.32 | (165) $false
% 47.32/13.32 |
% 47.32/13.32 |-The branch is then unsatisfiable
% 47.32/13.32 |-Branch two:
% 47.32/13.32 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.32/13.32 |
% 47.32/13.32 | Applying alpha-rule on (254) yields:
% 47.32/13.32 | (212) all_11_8_48 = all_0_3_3
% 47.32/13.32 | (219) all_0_1_1 = vnoExp
% 47.32/13.32 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.32/13.32 |
% 47.32/13.32 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3, yields:
% 47.32/13.32 | (130) $false
% 47.32/13.32 |
% 47.32/13.32 |-The branch is then unsatisfiable
% 47.32/13.32 |-Branch two:
% 47.32/13.32 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 47.32/13.32 |
% 47.32/13.32 | Applying alpha-rule on (259) yields:
% 47.32/13.32 | (260) all_11_10_50 = all_0_3_3
% 47.32/13.32 | (219) all_0_1_1 = vnoExp
% 47.32/13.32 | (262) vvar(all_11_11_51) = all_0_3_3
% 47.32/13.32 |
% 47.32/13.32 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_11_11_51) = all_0_3_3, yields:
% 47.32/13.32 | (130) $false
% 47.32/13.32 |
% 47.32/13.32 |-The branch is then unsatisfiable
% 47.32/13.32 |-Branch two:
% 47.32/13.32 | (378) all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)
% 47.32/13.32 |
% 47.32/13.32 | Applying alpha-rule on (378) yields:
% 47.32/13.32 | (379) vapp(all_9_5_21, all_9_9_25) = all_9_4_20
% 47.32/13.32 | (380) vsomeExp(all_9_4_20) = all_0_6_6
% 47.32/13.32 | (381) all_9_7_23 = all_9_10_26
% 47.32/13.32 | (382) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)
% 47.32/13.32 | (383) all_9_8_24 = ve1
% 47.32/13.33 | (384) all_9_6_22 = 0
% 47.32/13.33 | (385) visSomeExp(all_9_10_26) = 0
% 47.32/13.33 | (386) vapp(all_9_11_27, all_9_9_25) = ve1
% 47.32/13.33 | (387) all_9_3_19 = all_0_6_6
% 47.32/13.33 | (388) vreduce(all_9_11_27) = all_9_10_26
% 47.32/13.33 | (389) vgetSomeExp(all_9_10_26) = all_9_5_21
% 47.32/13.33 |
% 47.32/13.33 | Instantiating formula (92) with ve1, all_9_9_25, all_9_11_27 and discharging atoms vapp(all_9_11_27, all_9_9_25) = ve1, yields:
% 47.32/13.33 | (162) ~ (visValue(ve1) = 0)
% 47.32/13.33 |
% 47.32/13.33 | Using (68) and (162) yields:
% 47.32/13.33 | (163) ~ (all_0_7_7 = 0)
% 47.32/13.33 |
% 47.32/13.33 +-Applying beta-rule and splitting (143), into two cases.
% 47.32/13.33 |-Branch one:
% 47.32/13.33 | (164) all_0_7_7 = 0
% 47.32/13.33 |
% 47.32/13.33 | Equations (164) can reduce 163 to:
% 47.32/13.33 | (165) $false
% 47.32/13.33 |
% 47.32/13.33 |-The branch is then unsatisfiable
% 47.32/13.33 |-Branch two:
% 47.32/13.33 | (163) ~ (all_0_7_7 = 0)
% 47.32/13.33 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.32/13.33 |
% 47.32/13.33 | Instantiating (167) with all_116_0_378 yields:
% 47.32/13.33 | (1618) vsomeExp(all_116_0_378) = all_0_6_6
% 47.32/13.33 |
% 47.32/13.33 | Instantiating formula (85) with all_0_6_6, all_116_0_378, all_9_4_20 and discharging atoms vsomeExp(all_116_0_378) = all_0_6_6, vsomeExp(all_9_4_20) = all_0_6_6, yields:
% 47.32/13.33 | (1619) all_116_0_378 = all_9_4_20
% 47.32/13.33 |
% 47.32/13.33 | From (1619) and (1618) follows:
% 47.32/13.33 | (380) vsomeExp(all_9_4_20) = all_0_6_6
% 47.32/13.33 |
% 47.32/13.33 +-Applying beta-rule and splitting (116), into two cases.
% 47.32/13.33 |-Branch one:
% 47.32/13.33 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 47.32/13.33 |
% 47.32/13.33 +-Applying beta-rule and splitting (171), into two cases.
% 47.32/13.33 |-Branch one:
% 47.32/13.33 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 47.32/13.33 |
% 47.32/13.33 +-Applying beta-rule and splitting (172), into two cases.
% 47.32/13.33 |-Branch one:
% 47.32/13.33 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 47.32/13.33 |
% 47.32/13.33 +-Applying beta-rule and splitting (173), into two cases.
% 47.32/13.33 |-Branch one:
% 47.32/13.33 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 47.32/13.33 |
% 47.32/13.33 +-Applying beta-rule and splitting (174), into two cases.
% 47.32/13.33 |-Branch one:
% 47.32/13.33 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 47.32/13.33 |
% 47.32/13.33 +-Applying beta-rule and splitting (175), into two cases.
% 47.32/13.33 |-Branch one:
% 47.32/13.33 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.32/13.33 |
% 47.32/13.33 | Applying alpha-rule on (176) yields:
% 47.32/13.33 | (177) all_11_5_45 = all_0_3_3
% 47.32/13.33 | (178) all_11_4_44 = all_11_10_50
% 47.32/13.33 | (179) visValue(all_11_8_48) = 0
% 47.32/13.33 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 47.32/13.33 | (181) all_11_0_40 = all_0_1_1
% 47.32/13.33 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.32/13.33 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.32/13.33 | (184) vreduce(all_11_8_48) = all_11_10_50
% 47.32/13.33 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 47.32/13.33 | (186) ~ (all_11_3_43 = 0)
% 47.32/13.33 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 47.32/13.33 | (188) all_11_2_42 = 0
% 47.32/13.33 |
% 47.32/13.33 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.32/13.33 | (130) $false
% 47.32/13.33 |
% 47.32/13.33 |-The branch is then unsatisfiable
% 47.32/13.33 |-Branch two:
% 47.32/13.33 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.32/13.33 |
% 47.32/13.33 | Applying alpha-rule on (190) yields:
% 47.32/13.33 | (177) all_11_5_45 = all_0_3_3
% 47.32/13.33 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 47.32/13.33 | (193) visSomeExp(all_11_7_47) = 0
% 47.32/13.33 | (181) all_11_0_40 = all_0_1_1
% 47.32/13.33 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.32/13.33 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 47.32/13.33 | (197) vreduce(all_11_11_51) = all_11_7_47
% 47.32/13.33 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 47.32/13.33 | (199) all_11_3_43 = 0
% 47.32/13.33 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.32/13.33 | (201) all_11_4_44 = all_11_7_47
% 47.32/13.33 |
% 47.32/13.33 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.32/13.33 | (130) $false
% 47.32/13.33 |
% 47.32/13.33 |-The branch is then unsatisfiable
% 47.32/13.33 |-Branch two:
% 47.32/13.33 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.32/13.33 |
% 47.32/13.33 | Applying alpha-rule on (203) yields:
% 47.32/13.33 | (204) all_11_7_47 = all_11_10_50
% 47.32/13.33 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.32/13.33 | (206) all_11_6_46 = 0
% 47.32/13.33 | (207) all_11_3_43 = all_0_1_1
% 47.32/13.33 | (208) visSomeExp(all_11_10_50) = 0
% 47.32/13.33 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 47.32/13.33 | (210) vreduce(all_11_11_51) = all_11_10_50
% 47.32/13.33 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 47.32/13.33 | (212) all_11_8_48 = all_0_3_3
% 47.32/13.33 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 47.32/13.33 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 47.32/13.33 |
% 47.32/13.33 | Instantiating formula (74) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = all_0_1_1, yields:
% 47.32/13.33 | (130) $false
% 47.32/13.33 |
% 47.32/13.33 |-The branch is then unsatisfiable
% 47.32/13.33 |-Branch two:
% 47.32/13.33 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.32/13.33 |
% 47.32/13.33 | Applying alpha-rule on (216) yields:
% 47.32/13.33 | (177) all_11_5_45 = all_0_3_3
% 47.32/13.33 | (218) visValue(all_11_7_47) = all_11_2_42
% 47.32/13.33 | (219) all_0_1_1 = vnoExp
% 47.32/13.33 | (220) vreduce(all_11_7_47) = all_11_8_48
% 47.32/13.33 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.32/13.33 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 47.32/13.33 | (186) ~ (all_11_3_43 = 0)
% 47.32/13.33 | (224) all_11_4_44 = all_11_8_48
% 47.32/13.33 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 47.32/13.33 | (226) ~ (all_11_2_42 = 0)
% 47.32/13.33 |
% 47.32/13.33 | Instantiating formula (88) with all_0_3_3, all_11_7_47, all_11_6_46, ve2, ve1 and discharging atoms vapp(all_11_6_46, all_11_7_47) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.32/13.33 | (227) all_11_6_46 = ve1
% 47.32/13.33 |
% 47.32/13.33 | Instantiating formula (66) with ve1, all_9_9_25, all_9_11_27, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(all_9_11_27, all_9_9_25) = ve1, yields:
% 47.32/13.33 | (228) ~ (vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1)
% 47.32/13.33 |
% 47.32/13.33 | From (227) and (221) follows:
% 47.32/13.34 | (229) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1
% 47.32/13.34 |
% 47.32/13.34 | Using (229) and (228) yields:
% 47.32/13.34 | (130) $false
% 47.32/13.34 |
% 47.32/13.34 |-The branch is then unsatisfiable
% 47.32/13.34 |-Branch two:
% 47.32/13.34 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.32/13.34 |
% 47.32/13.34 | Applying alpha-rule on (231) yields:
% 47.32/13.34 | (232) all_11_7_47 = all_11_9_49
% 47.32/13.34 | (219) all_0_1_1 = vnoExp
% 47.32/13.34 | (234) ~ (all_11_6_46 = 0)
% 47.32/13.34 | (235) vreduce(all_11_10_50) = all_11_9_49
% 47.32/13.34 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.32/13.34 | (212) all_11_8_48 = all_0_3_3
% 47.32/13.34 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 47.32/13.34 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 47.32/13.34 |
% 47.32/13.34 | Instantiating formula (55) with ve1, all_11_9_49, all_0_6_6 and discharging atoms vreduce(ve1) = all_0_6_6, yields:
% 47.32/13.34 | (240) all_11_9_49 = all_0_6_6 | ~ (vreduce(ve1) = all_11_9_49)
% 47.32/13.34 |
% 47.32/13.34 | Instantiating formula (47) with all_11_6_46, all_0_6_6, all_9_4_20 and discharging atoms vsomeExp(all_9_4_20) = all_0_6_6, yields:
% 47.32/13.34 | (241) all_11_6_46 = 0 | ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.32/13.34 |
% 47.32/13.34 | Instantiating formula (88) with all_0_3_3, all_11_11_51, all_11_10_50, ve2, ve1 and discharging atoms vapp(all_11_10_50, all_11_11_51) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.32/13.34 | (242) all_11_10_50 = ve1
% 47.32/13.34 |
% 47.32/13.34 | From (242) and (235) follows:
% 47.32/13.34 | (243) vreduce(ve1) = all_11_9_49
% 47.32/13.34 |
% 47.32/13.34 +-Applying beta-rule and splitting (241), into two cases.
% 47.32/13.34 |-Branch one:
% 47.32/13.34 | (244) ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.32/13.34 |
% 47.32/13.34 +-Applying beta-rule and splitting (240), into two cases.
% 47.32/13.34 |-Branch one:
% 47.32/13.34 | (245) ~ (vreduce(ve1) = all_11_9_49)
% 47.32/13.34 |
% 47.32/13.34 | Using (243) and (245) yields:
% 47.32/13.34 | (130) $false
% 47.32/13.34 |
% 47.32/13.34 |-The branch is then unsatisfiable
% 47.32/13.34 |-Branch two:
% 47.32/13.34 | (243) vreduce(ve1) = all_11_9_49
% 47.32/13.34 | (248) all_11_9_49 = all_0_6_6
% 47.32/13.34 |
% 47.32/13.34 | From (248) and (239) follows:
% 47.32/13.34 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.32/13.34 |
% 47.32/13.34 | Using (249) and (244) yields:
% 47.32/13.34 | (130) $false
% 47.32/13.34 |
% 47.32/13.34 |-The branch is then unsatisfiable
% 47.32/13.34 |-Branch two:
% 47.32/13.34 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.32/13.34 | (206) all_11_6_46 = 0
% 47.32/13.34 |
% 47.32/13.34 | Equations (206) can reduce 234 to:
% 47.32/13.34 | (165) $false
% 47.32/13.34 |
% 47.32/13.34 |-The branch is then unsatisfiable
% 47.32/13.34 |-Branch two:
% 47.32/13.34 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.32/13.34 |
% 47.32/13.34 | Applying alpha-rule on (254) yields:
% 47.32/13.34 | (212) all_11_8_48 = all_0_3_3
% 47.32/13.34 | (219) all_0_1_1 = vnoExp
% 47.32/13.34 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.32/13.34 |
% 47.32/13.34 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3, yields:
% 47.32/13.34 | (130) $false
% 47.32/13.34 |
% 47.32/13.34 |-The branch is then unsatisfiable
% 47.32/13.34 |-Branch two:
% 47.32/13.34 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 47.32/13.34 |
% 47.32/13.34 | Applying alpha-rule on (259) yields:
% 47.32/13.34 | (260) all_11_10_50 = all_0_3_3
% 47.32/13.34 | (219) all_0_1_1 = vnoExp
% 47.32/13.34 | (262) vvar(all_11_11_51) = all_0_3_3
% 47.32/13.34 |
% 47.32/13.34 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_11_11_51) = all_0_3_3, yields:
% 47.32/13.34 | (130) $false
% 47.32/13.34 |
% 47.32/13.34 |-The branch is then unsatisfiable
% 47.32/13.34 |-Branch two:
% 47.32/13.34 | (492) all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22
% 47.32/13.34 |
% 47.32/13.34 | Applying alpha-rule on (492) yields:
% 47.32/13.34 | (493) vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22
% 47.32/13.34 | (494) vapp(all_9_6_22, all_9_7_23) = ve1
% 47.32/13.34 | (495) vreduce(all_9_7_23) = all_9_8_24
% 47.32/13.34 | (496) visSomeExp(all_9_8_24) = all_9_3_19
% 47.32/13.34 | (497) visValue(all_9_7_23) = all_9_2_18
% 47.32/13.34 | (498) all_9_4_20 = all_9_8_24
% 47.32/13.34 | (156) ~ (all_9_3_19 = 0)
% 47.32/13.34 | (159) all_9_5_21 = ve1
% 47.32/13.34 | (501) ~ (all_9_2_18 = 0)
% 47.32/13.34 | (502) all_0_6_6 = vnoExp
% 47.32/13.34 |
% 47.32/13.34 | Instantiating formula (92) with ve1, all_9_7_23, all_9_6_22 and discharging atoms vapp(all_9_6_22, all_9_7_23) = ve1, yields:
% 47.32/13.34 | (162) ~ (visValue(ve1) = 0)
% 47.32/13.34 |
% 47.32/13.34 | Using (68) and (162) yields:
% 47.32/13.34 | (163) ~ (all_0_7_7 = 0)
% 47.32/13.34 |
% 47.32/13.34 +-Applying beta-rule and splitting (661), into two cases.
% 47.32/13.34 |-Branch one:
% 47.32/13.34 | (761) all_0_5_5 = 0
% 47.32/13.34 |
% 47.32/13.34 | Combining equations (1326,761) yields a new equation:
% 47.32/13.34 | (1728) all_0_7_7 = 0
% 47.32/13.34 |
% 47.32/13.34 | Simplifying 1728 yields:
% 47.32/13.34 | (164) all_0_7_7 = 0
% 47.32/13.34 |
% 47.32/13.34 | Equations (164) can reduce 163 to:
% 47.32/13.34 | (165) $false
% 47.32/13.34 |
% 47.32/13.34 |-The branch is then unsatisfiable
% 47.32/13.34 |-Branch two:
% 47.32/13.34 | (760) ~ (all_0_5_5 = 0)
% 47.32/13.34 | (764) ? [v0] : vsomeExp(v0) = all_0_4_4
% 47.32/13.34 |
% 47.32/13.34 | Equations (1326) can reduce 760 to:
% 47.32/13.34 | (163) ~ (all_0_7_7 = 0)
% 47.32/13.34 |
% 47.32/13.34 +-Applying beta-rule and splitting (143), into two cases.
% 47.32/13.34 |-Branch one:
% 47.32/13.34 | (164) all_0_7_7 = 0
% 47.32/13.34 |
% 47.32/13.34 | Equations (164) can reduce 163 to:
% 47.32/13.34 | (165) $false
% 47.32/13.34 |
% 47.32/13.34 |-The branch is then unsatisfiable
% 47.32/13.34 |-Branch two:
% 47.32/13.34 | (163) ~ (all_0_7_7 = 0)
% 47.32/13.34 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.32/13.34 |
% 47.32/13.34 | Instantiating (167) with all_132_0_409 yields:
% 47.32/13.34 | (1738) vsomeExp(all_132_0_409) = all_0_6_6
% 47.32/13.34 |
% 47.32/13.34 | From (502) and (1738) follows:
% 47.32/13.34 | (1739) vsomeExp(all_132_0_409) = vnoExp
% 47.32/13.34 |
% 47.32/13.34 | Instantiating formula (40) with all_132_0_409 and discharging atoms vsomeExp(all_132_0_409) = vnoExp, yields:
% 47.32/13.34 | (130) $false
% 47.32/13.34 |
% 47.32/13.34 |-The branch is then unsatisfiable
% 47.32/13.34 |-Branch two:
% 47.32/13.34 | (512) all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)
% 47.32/13.34 |
% 47.32/13.34 | Applying alpha-rule on (512) yields:
% 47.32/13.34 | (383) all_9_8_24 = ve1
% 47.32/13.34 | (514) ~ (all_9_6_22 = 0)
% 47.32/13.34 | (515) all_9_7_23 = all_9_9_25
% 47.32/13.34 | (516) visSomeExp(all_9_9_25) = all_9_6_22
% 47.32/13.34 | (517) vapp(all_9_10_26, all_9_11_27) = ve1
% 47.32/13.34 | (518) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)
% 47.32/13.34 | (519) vreduce(all_9_10_26) = all_9_9_25
% 47.32/13.34 | (502) all_0_6_6 = vnoExp
% 47.32/13.34 |
% 47.32/13.34 | Instantiating formula (92) with ve1, all_9_11_27, all_9_10_26 and discharging atoms vapp(all_9_10_26, all_9_11_27) = ve1, yields:
% 47.32/13.34 | (162) ~ (visValue(ve1) = 0)
% 47.32/13.34 |
% 47.32/13.34 | Using (68) and (162) yields:
% 47.32/13.34 | (163) ~ (all_0_7_7 = 0)
% 47.32/13.34 |
% 47.32/13.34 +-Applying beta-rule and splitting (661), into two cases.
% 47.32/13.34 |-Branch one:
% 47.32/13.34 | (761) all_0_5_5 = 0
% 47.32/13.34 |
% 47.32/13.34 | Combining equations (1326,761) yields a new equation:
% 47.32/13.34 | (1728) all_0_7_7 = 0
% 47.32/13.34 |
% 47.32/13.34 | Simplifying 1728 yields:
% 47.32/13.34 | (164) all_0_7_7 = 0
% 47.32/13.34 |
% 47.32/13.34 | Equations (164) can reduce 163 to:
% 47.32/13.34 | (165) $false
% 47.32/13.34 |
% 47.32/13.34 |-The branch is then unsatisfiable
% 47.32/13.34 |-Branch two:
% 47.32/13.34 | (760) ~ (all_0_5_5 = 0)
% 47.32/13.34 | (764) ? [v0] : vsomeExp(v0) = all_0_4_4
% 47.32/13.34 |
% 47.32/13.34 | Equations (1326) can reduce 760 to:
% 47.32/13.34 | (163) ~ (all_0_7_7 = 0)
% 47.32/13.34 |
% 47.32/13.34 +-Applying beta-rule and splitting (143), into two cases.
% 47.32/13.34 |-Branch one:
% 47.32/13.34 | (164) all_0_7_7 = 0
% 47.32/13.34 |
% 47.32/13.34 | Equations (164) can reduce 163 to:
% 47.32/13.34 | (165) $false
% 47.32/13.34 |
% 47.32/13.34 |-The branch is then unsatisfiable
% 47.32/13.34 |-Branch two:
% 47.32/13.34 | (163) ~ (all_0_7_7 = 0)
% 47.32/13.34 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.32/13.34 |
% 47.32/13.34 | Instantiating (167) with all_121_0_411 yields:
% 47.32/13.34 | (1763) vsomeExp(all_121_0_411) = all_0_6_6
% 47.32/13.34 |
% 47.32/13.34 | From (502) and (1763) follows:
% 47.32/13.34 | (1764) vsomeExp(all_121_0_411) = vnoExp
% 47.32/13.34 |
% 47.32/13.34 | Instantiating formula (40) with all_121_0_411 and discharging atoms vsomeExp(all_121_0_411) = vnoExp, yields:
% 47.32/13.34 | (130) $false
% 47.32/13.34 |
% 47.32/13.34 |-The branch is then unsatisfiable
% 47.32/13.34 |-Branch two:
% 47.32/13.34 | (530) all_9_8_24 = ve1 & all_0_6_6 = vnoExp & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1
% 47.32/13.34 |
% 47.32/13.34 | Applying alpha-rule on (530) yields:
% 47.32/13.34 | (383) all_9_8_24 = ve1
% 47.32/13.34 | (502) all_0_6_6 = vnoExp
% 47.32/13.34 | (533) vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1
% 47.32/13.34 |
% 47.32/13.34 | Equations (502) can reduce 637 to:
% 47.32/13.34 | (757) ~ (all_0_4_4 = vnoExp)
% 47.32/13.34 |
% 47.32/13.34 | Instantiating formula (22) with all_0_7_7, ve1, all_9_9_25, all_9_10_26, all_9_11_27 and discharging atoms visValue(ve1) = all_0_7_7, vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1, yields:
% 47.32/13.34 | (164) all_0_7_7 = 0
% 47.32/13.34 |
% 47.32/13.34 | From (164) and (1327) follows:
% 47.32/13.34 | (1772) visValue(ve2) = 0
% 47.32/13.34 |
% 47.32/13.34 +-Applying beta-rule and splitting (115), into two cases.
% 47.32/13.34 |-Branch one:
% 47.32/13.34 | (766) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34) | (all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)) | (all_10_8_36 = ve2 & all_0_4_4 = vnoExp & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2)
% 47.42/13.34 |
% 47.42/13.34 +-Applying beta-rule and splitting (766), into two cases.
% 47.42/13.34 |-Branch one:
% 47.42/13.34 | (767) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34) | (all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38))
% 47.42/13.35 |
% 47.42/13.35 +-Applying beta-rule and splitting (767), into two cases.
% 47.42/13.35 |-Branch one:
% 47.42/13.35 | (768) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34)
% 47.42/13.35 |
% 47.42/13.35 +-Applying beta-rule and splitting (768), into two cases.
% 47.42/13.35 |-Branch one:
% 47.42/13.35 | (769) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39))
% 47.42/13.35 |
% 47.42/13.35 +-Applying beta-rule and splitting (769), into two cases.
% 47.42/13.35 |-Branch one:
% 47.42/13.35 | (770) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34)
% 47.42/13.35 |
% 47.42/13.35 +-Applying beta-rule and splitting (770), into two cases.
% 47.42/13.35 |-Branch one:
% 47.42/13.35 | (771) all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34
% 47.42/13.35 |
% 47.42/13.35 | Applying alpha-rule on (771) yields:
% 47.42/13.35 | (772) all_10_5_33 = ve2
% 47.42/13.35 | (773) visValue(all_10_8_36) = 0
% 47.42/13.35 | (774) all_10_4_32 = all_10_10_38
% 47.42/13.35 | (775) ~ (all_10_3_31 = 0)
% 47.42/13.35 | (776) all_10_2_30 = 0
% 47.42/13.35 | (777) vapp(all_10_6_34, all_10_8_36) = ve2
% 47.42/13.35 | (778) vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29
% 47.42/13.35 | (779) vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34
% 47.42/13.35 | (780) all_10_0_28 = all_0_4_4
% 47.42/13.35 | (781) visSomeExp(all_10_10_38) = all_10_3_31
% 47.42/13.35 | (782) vsomeExp(all_10_1_29) = all_0_4_4
% 47.42/13.35 | (783) vreduce(all_10_8_36) = all_10_10_38
% 47.42/13.35 |
% 47.42/13.35 | Instantiating formula (92) with ve2, all_10_8_36, all_10_6_34 and discharging atoms visValue(ve2) = 0, vapp(all_10_6_34, all_10_8_36) = ve2, yields:
% 47.42/13.35 | (130) $false
% 47.42/13.35 |
% 47.42/13.35 |-The branch is then unsatisfiable
% 47.42/13.35 |-Branch two:
% 47.42/13.35 | (896) all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34
% 47.42/13.35 |
% 47.42/13.35 | Applying alpha-rule on (896) yields:
% 47.42/13.35 | (772) all_10_5_33 = ve2
% 47.42/13.35 | (898) vreduce(all_10_11_39) = all_10_7_35
% 47.42/13.35 | (846) all_10_3_31 = 0
% 47.42/13.35 | (900) all_10_4_32 = all_10_7_35
% 47.42/13.35 | (901) visSomeExp(all_10_7_35) = 0
% 47.42/13.35 | (902) vapp(all_10_6_34, all_10_2_30) = all_10_1_29
% 47.42/13.35 | (780) all_10_0_28 = all_0_4_4
% 47.42/13.35 | (904) vgetSomeExp(all_10_7_35) = all_10_2_30
% 47.42/13.35 | (905) vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34
% 47.42/13.35 | (906) vapp(all_10_6_34, all_10_11_39) = ve2
% 47.42/13.35 | (782) vsomeExp(all_10_1_29) = all_0_4_4
% 47.42/13.35 |
% 47.42/13.35 | Instantiating formula (92) with ve2, all_10_11_39, all_10_6_34 and discharging atoms visValue(ve2) = 0, vapp(all_10_6_34, all_10_11_39) = ve2, yields:
% 47.42/13.35 | (130) $false
% 47.42/13.35 |
% 47.42/13.35 |-The branch is then unsatisfiable
% 47.42/13.35 |-Branch two:
% 47.42/13.35 | (1006) all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)
% 47.42/13.35 |
% 47.42/13.35 | Applying alpha-rule on (1006) yields:
% 47.42/13.35 | (1007) all_10_7_35 = all_10_10_38
% 47.42/13.35 | (1008) vgetSomeExp(all_10_10_38) = all_10_5_33
% 47.42/13.35 | (1009) vapp(all_10_5_33, all_10_9_37) = all_10_4_32
% 47.42/13.35 | (1010) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)
% 47.42/13.35 | (1011) visSomeExp(all_10_10_38) = 0
% 47.42/13.35 | (1012) all_10_8_36 = ve2
% 47.42/13.35 | (1013) vreduce(all_10_11_39) = all_10_10_38
% 47.42/13.35 | (1014) all_10_6_34 = 0
% 47.42/13.35 | (1015) vsomeExp(all_10_4_32) = all_0_4_4
% 47.42/13.35 | (1016) vapp(all_10_11_39, all_10_9_37) = ve2
% 47.42/13.35 | (1017) all_10_3_31 = all_0_4_4
% 47.42/13.35 |
% 47.42/13.35 | Instantiating formula (92) with ve2, all_10_9_37, all_10_11_39 and discharging atoms visValue(ve2) = 0, vapp(all_10_11_39, all_10_9_37) = ve2, yields:
% 47.42/13.35 | (130) $false
% 47.42/13.35 |
% 47.42/13.35 |-The branch is then unsatisfiable
% 47.42/13.35 |-Branch two:
% 47.42/13.35 | (1116) all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34
% 47.42/13.35 |
% 47.42/13.35 | Applying alpha-rule on (1116) yields:
% 47.42/13.35 | (772) all_10_5_33 = ve2
% 47.42/13.35 | (1118) all_10_4_32 = all_10_8_36
% 47.42/13.35 | (775) ~ (all_10_3_31 = 0)
% 47.42/13.35 | (1120) ~ (all_10_2_30 = 0)
% 47.42/13.35 | (1121) visValue(all_10_7_35) = all_10_2_30
% 47.42/13.35 | (1122) vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34
% 47.42/13.35 | (1123) all_0_4_4 = vnoExp
% 47.42/13.35 | (1124) vreduce(all_10_7_35) = all_10_8_36
% 47.42/13.35 | (1125) visSomeExp(all_10_8_36) = all_10_3_31
% 47.42/13.35 | (1126) vapp(all_10_6_34, all_10_7_35) = ve2
% 47.42/13.35 |
% 47.42/13.35 | Equations (1123) can reduce 757 to:
% 47.42/13.35 | (165) $false
% 47.42/13.35 |
% 47.42/13.35 |-The branch is then unsatisfiable
% 47.42/13.35 |-Branch two:
% 47.42/13.35 | (1128) all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)
% 47.42/13.35 |
% 47.42/13.35 | Applying alpha-rule on (1128) yields:
% 47.42/13.35 | (1129) vreduce(all_10_10_38) = all_10_9_37
% 47.42/13.35 | (1130) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)
% 47.42/13.35 | (1123) all_0_4_4 = vnoExp
% 47.42/13.35 | (1012) all_10_8_36 = ve2
% 47.42/13.35 | (1133) ~ (all_10_6_34 = 0)
% 47.42/13.35 | (1134) vapp(all_10_10_38, all_10_11_39) = ve2
% 47.42/13.35 | (1135) visSomeExp(all_10_9_37) = all_10_6_34
% 47.42/13.35 | (1136) all_10_7_35 = all_10_9_37
% 47.42/13.35 |
% 47.42/13.35 | Equations (1123) can reduce 757 to:
% 47.42/13.35 | (165) $false
% 47.42/13.35 |
% 47.42/13.35 |-The branch is then unsatisfiable
% 47.42/13.35 |-Branch two:
% 47.42/13.35 | (1138) all_10_8_36 = ve2 & all_0_4_4 = vnoExp & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2
% 47.42/13.35 |
% 47.42/13.35 | Applying alpha-rule on (1138) yields:
% 47.42/13.35 | (1012) all_10_8_36 = ve2
% 47.42/13.35 | (1123) all_0_4_4 = vnoExp
% 47.42/13.35 | (1141) vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2
% 47.42/13.35 |
% 47.42/13.35 | Equations (1123) can reduce 757 to:
% 47.42/13.35 | (165) $false
% 47.42/13.35 |
% 47.42/13.35 |-The branch is then unsatisfiable
% 47.42/13.35 |-Branch two:
% 47.42/13.35 | (1143) all_10_10_38 = ve2 & all_0_4_4 = vnoExp & vvar(all_10_11_39) = ve2
% 47.42/13.35 |
% 47.42/13.36 | Applying alpha-rule on (1143) yields:
% 47.42/13.36 | (1144) all_10_10_38 = ve2
% 47.42/13.36 | (1123) all_0_4_4 = vnoExp
% 47.42/13.36 | (1146) vvar(all_10_11_39) = ve2
% 47.42/13.36 |
% 47.42/13.36 | Equations (1123) can reduce 757 to:
% 47.42/13.36 | (165) $false
% 47.42/13.36 |
% 47.42/13.36 |-The branch is then unsatisfiable
% 47.42/13.36 |-Branch two:
% 47.42/13.36 | (612) all_9_10_26 = ve1 & all_0_6_6 = vnoExp & vvar(all_9_11_27) = ve1
% 47.42/13.36 |
% 47.42/13.36 | Applying alpha-rule on (612) yields:
% 47.42/13.36 | (613) all_9_10_26 = ve1
% 47.42/13.36 | (502) all_0_6_6 = vnoExp
% 47.42/13.36 | (615) vvar(all_9_11_27) = ve1
% 47.42/13.36 |
% 47.42/13.36 | Instantiating formula (104) with ve1, all_9_11_27 and discharging atoms vvar(all_9_11_27) = ve1, yields:
% 47.42/13.36 | (162) ~ (visValue(ve1) = 0)
% 47.42/13.36 |
% 47.42/13.36 | Using (68) and (162) yields:
% 47.42/13.36 | (163) ~ (all_0_7_7 = 0)
% 47.42/13.36 |
% 47.42/13.36 +-Applying beta-rule and splitting (661), into two cases.
% 47.42/13.36 |-Branch one:
% 47.42/13.36 | (761) all_0_5_5 = 0
% 47.42/13.36 |
% 47.42/13.36 | Combining equations (1326,761) yields a new equation:
% 47.42/13.36 | (1728) all_0_7_7 = 0
% 47.42/13.36 |
% 47.42/13.36 | Simplifying 1728 yields:
% 47.42/13.36 | (164) all_0_7_7 = 0
% 47.42/13.36 |
% 47.42/13.36 | Equations (164) can reduce 163 to:
% 47.42/13.36 | (165) $false
% 47.42/13.36 |
% 47.42/13.36 |-The branch is then unsatisfiable
% 47.42/13.36 |-Branch two:
% 47.42/13.36 | (760) ~ (all_0_5_5 = 0)
% 47.42/13.36 | (764) ? [v0] : vsomeExp(v0) = all_0_4_4
% 47.42/13.36 |
% 47.42/13.36 | Equations (1326) can reduce 760 to:
% 47.42/13.36 | (163) ~ (all_0_7_7 = 0)
% 47.42/13.36 |
% 47.42/13.36 +-Applying beta-rule and splitting (143), into two cases.
% 47.42/13.36 |-Branch one:
% 47.42/13.36 | (164) all_0_7_7 = 0
% 47.42/13.36 |
% 47.42/13.36 | Equations (164) can reduce 163 to:
% 47.42/13.36 | (165) $false
% 47.42/13.36 |
% 47.42/13.36 |-The branch is then unsatisfiable
% 47.42/13.36 |-Branch two:
% 47.42/13.36 | (163) ~ (all_0_7_7 = 0)
% 47.42/13.36 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.42/13.36 |
% 47.42/13.36 | Instantiating (167) with all_120_0_413 yields:
% 47.42/13.36 | (1867) vsomeExp(all_120_0_413) = all_0_6_6
% 47.42/13.36 |
% 47.42/13.36 | From (502) and (1867) follows:
% 47.42/13.36 | (1868) vsomeExp(all_120_0_413) = vnoExp
% 47.42/13.36 |
% 47.42/13.36 | Instantiating formula (40) with all_120_0_413 and discharging atoms vsomeExp(all_120_0_413) = vnoExp, yields:
% 47.42/13.36 | (130) $false
% 47.42/13.36 |
% 47.42/13.36 |-The branch is then unsatisfiable
% 47.42/13.36 |-Branch two:
% 47.42/13.36 | (625) all_8_4_12 = all_8_7_15 & all_8_5_13 = all_0_3_3 & vlookup(all_8_6_14, vempty) = all_8_7_15 & vsomeType(all_0_0_0) = all_8_7_15 & vvar(all_8_6_14) = all_0_3_3
% 47.42/13.36 |
% 47.42/13.36 | Applying alpha-rule on (625) yields:
% 47.42/13.36 | (626) all_8_4_12 = all_8_7_15
% 47.42/13.36 | (627) all_8_5_13 = all_0_3_3
% 47.42/13.36 | (628) vvar(all_8_6_14) = all_0_3_3
% 47.42/13.36 | (629) vsomeType(all_0_0_0) = all_8_7_15
% 47.42/13.36 | (630) vlookup(all_8_6_14, vempty) = all_8_7_15
% 47.42/13.36 |
% 47.42/13.36 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_8_6_14 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_8_6_14) = all_0_3_3, yields:
% 47.42/13.36 | (130) $false
% 47.42/13.36 |
% 47.42/13.36 |-The branch is then unsatisfiable
% 47.42/13.36 |-Branch two:
% 47.42/13.36 | (1168) vreduce(ve1) = all_0_4_4
% 47.42/13.36 | (1169) all_0_4_4 = all_0_6_6
% 47.42/13.36 |
% 47.42/13.36 | Equations (1169) can reduce 1332 to:
% 47.42/13.36 | (120) ~ (all_0_1_1 = all_0_6_6)
% 47.42/13.36 |
% 47.42/13.36 | From (1169) and (1168) follows:
% 47.42/13.36 | (42) vreduce(ve1) = all_0_6_6
% 47.42/13.36 |
% 47.42/13.36 +-Applying beta-rule and splitting (113), into two cases.
% 47.42/13.36 |-Branch one:
% 47.42/13.36 | (121) (all_8_0_8 = 0 & all_8_2_10 = all_0_0_0 & all_8_3_11 = all_0_3_3 & varrow(all_8_5_13, all_8_4_12) = all_0_0_0 & vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0 & vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9 & vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3) | (all_8_1_9 = 0 & all_8_2_10 = 0 & all_8_4_12 = all_0_3_3 & varrow(all_8_5_13, all_0_0_0) = all_8_3_11 & vtcheck(vempty, all_8_6_14, all_8_5_13) = 0 & vtcheck(vempty, all_8_7_15, all_8_3_11) = 0 & vapp(all_8_7_15, all_8_6_14) = all_0_3_3)
% 47.42/13.36 |
% 47.42/13.36 +-Applying beta-rule and splitting (121), into two cases.
% 47.42/13.36 |-Branch one:
% 47.42/13.36 | (122) all_8_0_8 = 0 & all_8_2_10 = all_0_0_0 & all_8_3_11 = all_0_3_3 & varrow(all_8_5_13, all_8_4_12) = all_0_0_0 & vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0 & vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9 & vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3
% 47.42/13.36 |
% 47.42/13.36 | Applying alpha-rule on (122) yields:
% 47.42/13.36 | (123) vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3
% 47.42/13.36 | (124) vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0
% 47.42/13.36 | (125) vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9
% 47.42/13.36 | (126) all_8_3_11 = all_0_3_3
% 47.42/13.36 | (127) all_8_0_8 = 0
% 47.42/13.36 | (128) all_8_2_10 = all_0_0_0
% 47.42/13.36 | (129) varrow(all_8_5_13, all_8_4_12) = all_0_0_0
% 47.42/13.36 |
% 47.42/13.36 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_8_6_14, all_8_5_13, all_8_7_15 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3, yields:
% 47.42/13.36 | (130) $false
% 47.42/13.36 |
% 47.42/13.36 |-The branch is then unsatisfiable
% 47.42/13.36 |-Branch two:
% 47.42/13.36 | (131) all_8_1_9 = 0 & all_8_2_10 = 0 & all_8_4_12 = all_0_3_3 & varrow(all_8_5_13, all_0_0_0) = all_8_3_11 & vtcheck(vempty, all_8_6_14, all_8_5_13) = 0 & vtcheck(vempty, all_8_7_15, all_8_3_11) = 0 & vapp(all_8_7_15, all_8_6_14) = all_0_3_3
% 47.42/13.36 |
% 47.42/13.36 | Applying alpha-rule on (131) yields:
% 47.42/13.36 | (132) varrow(all_8_5_13, all_0_0_0) = all_8_3_11
% 47.42/13.36 | (133) vtcheck(vempty, all_8_6_14, all_8_5_13) = 0
% 47.42/13.36 | (134) all_8_2_10 = 0
% 47.42/13.36 | (135) vtcheck(vempty, all_8_7_15, all_8_3_11) = 0
% 47.42/13.36 | (136) all_8_4_12 = all_0_3_3
% 47.42/13.36 | (137) all_8_1_9 = 0
% 47.42/13.36 | (138) vapp(all_8_7_15, all_8_6_14) = all_0_3_3
% 47.42/13.36 |
% 47.42/13.36 | Instantiating formula (31) with all_0_3_3, all_8_6_14, all_8_7_15, ve2, ve1 and discharging atoms vapp(all_8_7_15, all_8_6_14) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.42/13.36 | (139) all_8_6_14 = ve2
% 47.42/13.36 |
% 47.42/13.36 | Instantiating formula (88) with all_0_3_3, all_8_6_14, all_8_7_15, ve2, ve1 and discharging atoms vapp(all_8_7_15, all_8_6_14) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.42/13.36 | (140) all_8_7_15 = ve1
% 47.42/13.36 |
% 47.42/13.36 | From (139) and (133) follows:
% 47.42/13.36 | (658) vtcheck(vempty, ve2, all_8_5_13) = 0
% 47.42/13.36 |
% 47.42/13.36 | From (140) and (135) follows:
% 47.42/13.36 | (141) vtcheck(vempty, ve1, all_8_3_11) = 0
% 47.42/13.36 |
% 47.42/13.36 | From (140)(139) and (138) follows:
% 47.42/13.36 | (35) vapp(ve1, ve2) = all_0_3_3
% 47.42/13.36 |
% 47.42/13.36 | Instantiating formula (29) with all_8_5_13 and discharging atoms vtcheck(vempty, ve2, all_8_5_13) = 0, yields:
% 47.42/13.36 | (661) all_0_5_5 = 0 | ? [v0] : vsomeExp(v0) = all_0_4_4
% 47.42/13.36 |
% 47.42/13.36 | Instantiating formula (67) with all_8_3_11 and discharging atoms vtcheck(vempty, ve1, all_8_3_11) = 0, yields:
% 47.42/13.36 | (143) all_0_7_7 = 0 | ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.42/13.36 |
% 47.42/13.36 +-Applying beta-rule and splitting (114), into two cases.
% 47.42/13.36 |-Branch one:
% 47.42/13.36 | (144) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22) | (all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)) | (all_9_8_24 = ve1 & all_0_6_6 = vnoExp & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1)
% 47.42/13.36 |
% 47.42/13.36 +-Applying beta-rule and splitting (144), into two cases.
% 47.42/13.36 |-Branch one:
% 47.42/13.36 | (145) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22) | (all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26))
% 47.42/13.36 |
% 47.42/13.36 +-Applying beta-rule and splitting (145), into two cases.
% 47.42/13.36 |-Branch one:
% 47.42/13.36 | (146) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22)
% 47.42/13.36 |
% 47.42/13.36 +-Applying beta-rule and splitting (146), into two cases.
% 47.42/13.36 |-Branch one:
% 47.42/13.36 | (147) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27))
% 47.42/13.36 |
% 47.42/13.36 +-Applying beta-rule and splitting (147), into two cases.
% 47.42/13.36 |-Branch one:
% 47.42/13.36 | (148) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22)
% 47.42/13.37 |
% 47.42/13.37 +-Applying beta-rule and splitting (148), into two cases.
% 47.42/13.37 |-Branch one:
% 47.42/13.37 | (149) all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22
% 47.42/13.37 |
% 47.42/13.37 | Applying alpha-rule on (149) yields:
% 47.42/13.37 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 47.42/13.37 | (151) vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22
% 47.42/13.37 | (152) visSomeExp(all_9_10_26) = all_9_3_19
% 47.42/13.37 | (153) all_9_0_16 = all_0_6_6
% 47.42/13.37 | (154) vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17
% 47.42/13.37 | (155) vreduce(all_9_8_24) = all_9_10_26
% 47.42/13.37 | (156) ~ (all_9_3_19 = 0)
% 47.42/13.37 | (157) all_9_4_20 = all_9_10_26
% 47.42/13.37 | (158) vapp(all_9_6_22, all_9_8_24) = ve1
% 47.42/13.37 | (159) all_9_5_21 = ve1
% 47.42/13.37 | (160) all_9_2_18 = 0
% 47.42/13.37 | (161) visValue(all_9_8_24) = 0
% 47.42/13.37 |
% 47.42/13.37 | Instantiating formula (40) with all_9_1_17 yields:
% 47.42/13.37 | (1924) ~ (vsomeExp(all_9_1_17) = vnoExp)
% 47.42/13.37 |
% 47.42/13.37 | Instantiating formula (92) with ve1, all_9_8_24, all_9_6_22 and discharging atoms vapp(all_9_6_22, all_9_8_24) = ve1, yields:
% 47.42/13.37 | (162) ~ (visValue(ve1) = 0)
% 47.42/13.37 |
% 47.42/13.37 | Using (150) and (1924) yields:
% 47.42/13.37 | (1926) ~ (all_0_6_6 = vnoExp)
% 47.42/13.37 |
% 47.42/13.37 | Using (68) and (162) yields:
% 47.42/13.37 | (163) ~ (all_0_7_7 = 0)
% 47.42/13.37 |
% 47.42/13.37 +-Applying beta-rule and splitting (143), into two cases.
% 47.42/13.37 |-Branch one:
% 47.42/13.37 | (164) all_0_7_7 = 0
% 47.42/13.37 |
% 47.42/13.37 | Equations (164) can reduce 163 to:
% 47.42/13.37 | (165) $false
% 47.42/13.37 |
% 47.42/13.37 |-The branch is then unsatisfiable
% 47.42/13.37 |-Branch two:
% 47.42/13.37 | (163) ~ (all_0_7_7 = 0)
% 47.42/13.37 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.42/13.37 |
% 47.42/13.37 | Instantiating (167) with all_123_0_430 yields:
% 47.42/13.37 | (1932) vsomeExp(all_123_0_430) = all_0_6_6
% 47.42/13.37 |
% 47.42/13.37 +-Applying beta-rule and splitting (661), into two cases.
% 47.42/13.37 |-Branch one:
% 47.42/13.37 | (761) all_0_5_5 = 0
% 47.42/13.37 |
% 47.42/13.37 | Combining equations (761,1326) yields a new equation:
% 47.42/13.37 | (164) all_0_7_7 = 0
% 47.42/13.37 |
% 47.42/13.37 | Equations (164) can reduce 163 to:
% 47.42/13.37 | (165) $false
% 47.42/13.37 |
% 47.42/13.37 |-The branch is then unsatisfiable
% 47.42/13.37 |-Branch two:
% 47.42/13.37 | (760) ~ (all_0_5_5 = 0)
% 47.42/13.37 | (764) ? [v0] : vsomeExp(v0) = all_0_4_4
% 47.42/13.37 |
% 47.42/13.37 | Instantiating (764) with all_128_0_431 yields:
% 47.42/13.37 | (1938) vsomeExp(all_128_0_431) = all_0_4_4
% 47.42/13.37 |
% 47.42/13.37 | From (1169) and (1938) follows:
% 47.42/13.37 | (1939) vsomeExp(all_128_0_431) = all_0_6_6
% 47.42/13.37 |
% 47.42/13.37 | Instantiating formula (85) with all_0_6_6, all_128_0_431, all_9_1_17 and discharging atoms vsomeExp(all_128_0_431) = all_0_6_6, vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 47.42/13.37 | (1940) all_128_0_431 = all_9_1_17
% 47.42/13.37 |
% 47.42/13.37 | Instantiating formula (85) with all_0_6_6, all_123_0_430, all_128_0_431 and discharging atoms vsomeExp(all_128_0_431) = all_0_6_6, vsomeExp(all_123_0_430) = all_0_6_6, yields:
% 47.42/13.37 | (1941) all_128_0_431 = all_123_0_430
% 47.42/13.37 |
% 47.42/13.37 | Combining equations (1940,1941) yields a new equation:
% 47.42/13.37 | (1942) all_123_0_430 = all_9_1_17
% 47.42/13.37 |
% 47.42/13.37 | From (1942) and (1932) follows:
% 47.42/13.37 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 47.42/13.37 |
% 47.42/13.37 +-Applying beta-rule and splitting (115), into two cases.
% 47.42/13.37 |-Branch one:
% 47.42/13.37 | (766) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34) | (all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)) | (all_10_8_36 = ve2 & all_0_4_4 = vnoExp & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2)
% 47.42/13.37 |
% 47.42/13.37 +-Applying beta-rule and splitting (766), into two cases.
% 47.42/13.37 |-Branch one:
% 47.42/13.37 | (767) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34) | (all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38))
% 47.42/13.37 |
% 47.42/13.37 +-Applying beta-rule and splitting (767), into two cases.
% 47.42/13.37 |-Branch one:
% 47.42/13.37 | (768) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34)
% 47.42/13.37 |
% 47.42/13.37 +-Applying beta-rule and splitting (768), into two cases.
% 47.42/13.37 |-Branch one:
% 47.42/13.37 | (769) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39))
% 47.42/13.37 |
% 47.42/13.37 +-Applying beta-rule and splitting (769), into two cases.
% 47.42/13.37 |-Branch one:
% 47.42/13.37 | (770) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34)
% 47.42/13.37 |
% 47.42/13.37 +-Applying beta-rule and splitting (770), into two cases.
% 47.42/13.37 |-Branch one:
% 47.42/13.37 | (771) all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34
% 47.42/13.37 |
% 47.42/13.37 | Applying alpha-rule on (771) yields:
% 47.42/13.37 | (772) all_10_5_33 = ve2
% 47.42/13.37 | (773) visValue(all_10_8_36) = 0
% 47.42/13.37 | (774) all_10_4_32 = all_10_10_38
% 47.42/13.37 | (775) ~ (all_10_3_31 = 0)
% 47.42/13.37 | (776) all_10_2_30 = 0
% 47.42/13.37 | (777) vapp(all_10_6_34, all_10_8_36) = ve2
% 47.42/13.37 | (778) vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29
% 47.42/13.37 | (779) vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34
% 47.42/13.37 | (780) all_10_0_28 = all_0_4_4
% 47.42/13.37 | (781) visSomeExp(all_10_10_38) = all_10_3_31
% 47.42/13.37 | (782) vsomeExp(all_10_1_29) = all_0_4_4
% 47.42/13.37 | (783) vreduce(all_10_8_36) = all_10_10_38
% 47.42/13.37 |
% 47.42/13.37 | From (1169) and (782) follows:
% 47.42/13.37 | (1962) vsomeExp(all_10_1_29) = all_0_6_6
% 47.42/13.37 |
% 47.42/13.37 | Instantiating formula (85) with all_0_6_6, all_10_1_29, all_9_1_17 and discharging atoms vsomeExp(all_10_1_29) = all_0_6_6, vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 47.42/13.37 | (1963) all_10_1_29 = all_9_1_17
% 47.42/13.37 |
% 47.42/13.37 | From (1963) and (1962) follows:
% 47.42/13.38 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 47.42/13.38 |
% 47.42/13.38 +-Applying beta-rule and splitting (116), into two cases.
% 47.42/13.38 |-Branch one:
% 47.42/13.38 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 47.42/13.38 |
% 47.42/13.38 +-Applying beta-rule and splitting (171), into two cases.
% 47.42/13.38 |-Branch one:
% 47.42/13.38 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 47.42/13.38 |
% 47.42/13.38 +-Applying beta-rule and splitting (172), into two cases.
% 47.42/13.38 |-Branch one:
% 47.42/13.38 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 47.42/13.38 |
% 47.42/13.38 +-Applying beta-rule and splitting (173), into two cases.
% 47.42/13.38 |-Branch one:
% 47.42/13.38 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 47.42/13.38 |
% 47.42/13.38 +-Applying beta-rule and splitting (174), into two cases.
% 47.42/13.38 |-Branch one:
% 47.42/13.38 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 47.42/13.38 |
% 47.42/13.38 +-Applying beta-rule and splitting (175), into two cases.
% 47.42/13.38 |-Branch one:
% 47.42/13.38 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.42/13.38 |
% 47.42/13.38 | Applying alpha-rule on (176) yields:
% 47.42/13.38 | (177) all_11_5_45 = all_0_3_3
% 47.42/13.38 | (178) all_11_4_44 = all_11_10_50
% 47.42/13.38 | (179) visValue(all_11_8_48) = 0
% 47.42/13.38 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 47.42/13.38 | (181) all_11_0_40 = all_0_1_1
% 47.42/13.38 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.42/13.38 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.42/13.38 | (184) vreduce(all_11_8_48) = all_11_10_50
% 47.42/13.38 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 47.42/13.38 | (186) ~ (all_11_3_43 = 0)
% 47.42/13.38 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 47.42/13.38 | (188) all_11_2_42 = 0
% 47.42/13.38 |
% 47.42/13.38 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.42/13.38 | (130) $false
% 47.42/13.38 |
% 47.42/13.38 |-The branch is then unsatisfiable
% 47.42/13.38 |-Branch two:
% 47.42/13.38 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.42/13.38 |
% 47.42/13.38 | Applying alpha-rule on (190) yields:
% 47.42/13.38 | (177) all_11_5_45 = all_0_3_3
% 47.42/13.38 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 47.42/13.38 | (193) visSomeExp(all_11_7_47) = 0
% 47.42/13.38 | (181) all_11_0_40 = all_0_1_1
% 47.42/13.38 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.42/13.38 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 47.42/13.38 | (197) vreduce(all_11_11_51) = all_11_7_47
% 47.42/13.38 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 47.42/13.38 | (199) all_11_3_43 = 0
% 47.42/13.38 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.42/13.38 | (201) all_11_4_44 = all_11_7_47
% 47.42/13.38 |
% 47.42/13.38 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.42/13.38 | (130) $false
% 47.42/13.38 |
% 47.42/13.38 |-The branch is then unsatisfiable
% 47.42/13.38 |-Branch two:
% 47.42/13.38 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.42/13.38 |
% 47.42/13.38 | Applying alpha-rule on (203) yields:
% 47.42/13.38 | (204) all_11_7_47 = all_11_10_50
% 47.42/13.38 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.42/13.38 | (206) all_11_6_46 = 0
% 47.42/13.38 | (207) all_11_3_43 = all_0_1_1
% 47.42/13.38 | (208) visSomeExp(all_11_10_50) = 0
% 47.42/13.38 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 47.42/13.38 | (210) vreduce(all_11_11_51) = all_11_10_50
% 47.42/13.38 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 47.42/13.38 | (212) all_11_8_48 = all_0_3_3
% 47.42/13.38 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 47.42/13.38 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 47.42/13.38 |
% 47.42/13.38 | Instantiating formula (74) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = all_0_1_1, yields:
% 47.42/13.38 | (130) $false
% 47.42/13.38 |
% 47.42/13.38 |-The branch is then unsatisfiable
% 47.42/13.38 |-Branch two:
% 47.42/13.38 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.42/13.38 |
% 47.42/13.38 | Applying alpha-rule on (216) yields:
% 47.42/13.38 | (177) all_11_5_45 = all_0_3_3
% 47.42/13.38 | (218) visValue(all_11_7_47) = all_11_2_42
% 47.42/13.38 | (219) all_0_1_1 = vnoExp
% 47.42/13.38 | (220) vreduce(all_11_7_47) = all_11_8_48
% 47.42/13.38 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.42/13.38 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 47.42/13.38 | (186) ~ (all_11_3_43 = 0)
% 47.42/13.38 | (224) all_11_4_44 = all_11_8_48
% 47.42/13.38 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 47.42/13.38 | (226) ~ (all_11_2_42 = 0)
% 47.42/13.38 |
% 47.42/13.38 | Instantiating formula (88) with all_0_3_3, all_11_7_47, all_11_6_46, ve2, ve1 and discharging atoms vapp(all_11_6_46, all_11_7_47) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.42/13.38 | (227) all_11_6_46 = ve1
% 47.42/13.38 |
% 47.42/13.38 | Instantiating formula (66) with ve1, all_9_8_24, all_9_6_22, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(all_9_6_22, all_9_8_24) = ve1, yields:
% 47.42/13.38 | (228) ~ (vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1)
% 47.42/13.38 |
% 47.42/13.38 | From (227) and (221) follows:
% 47.42/13.38 | (229) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1
% 47.42/13.38 |
% 47.42/13.38 | Using (229) and (228) yields:
% 47.42/13.38 | (130) $false
% 47.42/13.38 |
% 47.42/13.38 |-The branch is then unsatisfiable
% 47.42/13.38 |-Branch two:
% 47.42/13.38 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.42/13.38 |
% 47.42/13.38 | Applying alpha-rule on (231) yields:
% 47.42/13.38 | (232) all_11_7_47 = all_11_9_49
% 47.42/13.38 | (219) all_0_1_1 = vnoExp
% 47.42/13.38 | (234) ~ (all_11_6_46 = 0)
% 47.42/13.38 | (235) vreduce(all_11_10_50) = all_11_9_49
% 47.42/13.38 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.42/13.38 | (212) all_11_8_48 = all_0_3_3
% 47.42/13.38 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 47.42/13.38 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 47.42/13.38 |
% 47.42/13.38 | Instantiating formula (55) with ve1, all_11_9_49, all_0_6_6 and discharging atoms vreduce(ve1) = all_0_6_6, yields:
% 47.42/13.38 | (240) all_11_9_49 = all_0_6_6 | ~ (vreduce(ve1) = all_11_9_49)
% 47.42/13.38 |
% 47.42/13.38 | Instantiating formula (47) with all_11_6_46, all_0_6_6, all_9_1_17 and discharging atoms vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 47.42/13.38 | (241) all_11_6_46 = 0 | ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.42/13.38 |
% 47.42/13.38 | Instantiating formula (88) with all_0_3_3, all_11_11_51, all_11_10_50, ve2, ve1 and discharging atoms vapp(all_11_10_50, all_11_11_51) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.42/13.38 | (242) all_11_10_50 = ve1
% 47.42/13.38 |
% 47.42/13.38 | From (242) and (235) follows:
% 47.42/13.38 | (243) vreduce(ve1) = all_11_9_49
% 47.42/13.38 |
% 47.42/13.38 +-Applying beta-rule and splitting (240), into two cases.
% 47.42/13.38 |-Branch one:
% 47.42/13.38 | (245) ~ (vreduce(ve1) = all_11_9_49)
% 47.42/13.38 |
% 47.42/13.38 | Using (243) and (245) yields:
% 47.42/13.38 | (130) $false
% 47.42/13.38 |
% 47.42/13.38 |-The branch is then unsatisfiable
% 47.42/13.38 |-Branch two:
% 47.42/13.38 | (243) vreduce(ve1) = all_11_9_49
% 47.42/13.38 | (248) all_11_9_49 = all_0_6_6
% 47.42/13.38 |
% 47.42/13.38 | From (248) and (239) follows:
% 47.42/13.38 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.42/13.39 |
% 47.42/13.39 +-Applying beta-rule and splitting (241), into two cases.
% 47.42/13.39 |-Branch one:
% 47.42/13.39 | (244) ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.42/13.39 |
% 47.42/13.39 | Using (249) and (244) yields:
% 47.42/13.39 | (130) $false
% 47.42/13.39 |
% 47.42/13.39 |-The branch is then unsatisfiable
% 47.42/13.39 |-Branch two:
% 47.42/13.39 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.42/13.39 | (206) all_11_6_46 = 0
% 47.42/13.39 |
% 47.42/13.39 | Equations (206) can reduce 234 to:
% 47.42/13.39 | (165) $false
% 47.42/13.39 |
% 47.42/13.39 |-The branch is then unsatisfiable
% 47.42/13.39 |-Branch two:
% 47.42/13.39 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.42/13.39 |
% 47.42/13.39 | Applying alpha-rule on (254) yields:
% 47.42/13.39 | (212) all_11_8_48 = all_0_3_3
% 47.42/13.39 | (219) all_0_1_1 = vnoExp
% 47.42/13.39 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.42/13.39 |
% 47.42/13.39 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3, yields:
% 47.42/13.39 | (130) $false
% 47.42/13.39 |
% 47.42/13.39 |-The branch is then unsatisfiable
% 47.42/13.39 |-Branch two:
% 47.42/13.39 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 47.42/13.39 |
% 47.42/13.39 | Applying alpha-rule on (259) yields:
% 47.42/13.39 | (260) all_11_10_50 = all_0_3_3
% 47.42/13.39 | (219) all_0_1_1 = vnoExp
% 47.42/13.39 | (262) vvar(all_11_11_51) = all_0_3_3
% 47.42/13.39 |
% 47.42/13.39 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_11_11_51) = all_0_3_3, yields:
% 47.42/13.39 | (130) $false
% 47.42/13.39 |
% 47.42/13.39 |-The branch is then unsatisfiable
% 47.42/13.39 |-Branch two:
% 47.42/13.39 | (896) all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34
% 47.42/13.39 |
% 47.42/13.39 | Applying alpha-rule on (896) yields:
% 47.42/13.39 | (772) all_10_5_33 = ve2
% 47.42/13.39 | (898) vreduce(all_10_11_39) = all_10_7_35
% 47.42/13.39 | (846) all_10_3_31 = 0
% 47.42/13.39 | (900) all_10_4_32 = all_10_7_35
% 47.42/13.39 | (901) visSomeExp(all_10_7_35) = 0
% 47.42/13.39 | (902) vapp(all_10_6_34, all_10_2_30) = all_10_1_29
% 47.42/13.39 | (780) all_10_0_28 = all_0_4_4
% 47.42/13.39 | (904) vgetSomeExp(all_10_7_35) = all_10_2_30
% 47.42/13.39 | (905) vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34
% 47.42/13.39 | (906) vapp(all_10_6_34, all_10_11_39) = ve2
% 47.42/13.39 | (782) vsomeExp(all_10_1_29) = all_0_4_4
% 47.42/13.39 |
% 47.42/13.39 | From (1169) and (782) follows:
% 47.42/13.39 | (1962) vsomeExp(all_10_1_29) = all_0_6_6
% 47.42/13.39 |
% 47.42/13.39 | Instantiating formula (85) with all_0_6_6, all_10_1_29, all_9_1_17 and discharging atoms vsomeExp(all_10_1_29) = all_0_6_6, vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 47.42/13.39 | (1963) all_10_1_29 = all_9_1_17
% 47.42/13.39 |
% 47.42/13.39 | From (1963) and (1962) follows:
% 47.42/13.39 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 47.42/13.39 |
% 47.42/13.39 +-Applying beta-rule and splitting (116), into two cases.
% 47.42/13.39 |-Branch one:
% 47.42/13.39 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 47.42/13.39 |
% 47.42/13.39 +-Applying beta-rule and splitting (171), into two cases.
% 47.42/13.39 |-Branch one:
% 47.42/13.39 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 47.42/13.39 |
% 47.42/13.39 +-Applying beta-rule and splitting (172), into two cases.
% 47.42/13.39 |-Branch one:
% 47.42/13.39 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 47.42/13.39 |
% 47.42/13.39 +-Applying beta-rule and splitting (173), into two cases.
% 47.42/13.39 |-Branch one:
% 47.42/13.39 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 47.42/13.39 |
% 47.42/13.39 +-Applying beta-rule and splitting (174), into two cases.
% 47.42/13.39 |-Branch one:
% 47.42/13.39 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 47.42/13.39 |
% 47.42/13.39 +-Applying beta-rule and splitting (175), into two cases.
% 47.42/13.39 |-Branch one:
% 47.42/13.39 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.42/13.39 |
% 47.42/13.39 | Applying alpha-rule on (176) yields:
% 47.42/13.39 | (177) all_11_5_45 = all_0_3_3
% 47.42/13.39 | (178) all_11_4_44 = all_11_10_50
% 47.42/13.39 | (179) visValue(all_11_8_48) = 0
% 47.42/13.39 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 47.42/13.39 | (181) all_11_0_40 = all_0_1_1
% 47.42/13.39 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.42/13.39 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.42/13.39 | (184) vreduce(all_11_8_48) = all_11_10_50
% 47.42/13.39 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 47.42/13.39 | (186) ~ (all_11_3_43 = 0)
% 47.42/13.39 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 47.42/13.39 | (188) all_11_2_42 = 0
% 47.42/13.39 |
% 47.42/13.39 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.42/13.39 | (130) $false
% 47.42/13.39 |
% 47.42/13.39 |-The branch is then unsatisfiable
% 47.42/13.39 |-Branch two:
% 47.42/13.39 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.42/13.39 |
% 47.42/13.39 | Applying alpha-rule on (190) yields:
% 47.42/13.39 | (177) all_11_5_45 = all_0_3_3
% 47.42/13.39 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 47.42/13.39 | (193) visSomeExp(all_11_7_47) = 0
% 47.42/13.39 | (181) all_11_0_40 = all_0_1_1
% 47.42/13.39 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.42/13.39 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 47.42/13.39 | (197) vreduce(all_11_11_51) = all_11_7_47
% 47.42/13.39 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 47.42/13.39 | (199) all_11_3_43 = 0
% 47.42/13.39 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.42/13.39 | (201) all_11_4_44 = all_11_7_47
% 47.42/13.39 |
% 47.42/13.39 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.42/13.39 | (130) $false
% 47.42/13.39 |
% 47.42/13.39 |-The branch is then unsatisfiable
% 47.42/13.39 |-Branch two:
% 47.42/13.39 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.42/13.39 |
% 47.42/13.39 | Applying alpha-rule on (203) yields:
% 47.42/13.39 | (204) all_11_7_47 = all_11_10_50
% 47.42/13.39 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.42/13.39 | (206) all_11_6_46 = 0
% 47.42/13.39 | (207) all_11_3_43 = all_0_1_1
% 47.42/13.39 | (208) visSomeExp(all_11_10_50) = 0
% 47.42/13.39 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 47.42/13.39 | (210) vreduce(all_11_11_51) = all_11_10_50
% 47.42/13.39 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 47.42/13.39 | (212) all_11_8_48 = all_0_3_3
% 47.42/13.39 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 47.42/13.39 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 47.42/13.39 |
% 47.42/13.39 | Instantiating formula (74) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = all_0_1_1, yields:
% 47.42/13.39 | (130) $false
% 47.42/13.39 |
% 47.42/13.39 |-The branch is then unsatisfiable
% 47.42/13.39 |-Branch two:
% 47.42/13.39 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.42/13.39 |
% 47.42/13.39 | Applying alpha-rule on (216) yields:
% 47.42/13.39 | (177) all_11_5_45 = all_0_3_3
% 47.42/13.39 | (218) visValue(all_11_7_47) = all_11_2_42
% 47.42/13.39 | (219) all_0_1_1 = vnoExp
% 47.42/13.40 | (220) vreduce(all_11_7_47) = all_11_8_48
% 47.42/13.40 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.42/13.40 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 47.42/13.40 | (186) ~ (all_11_3_43 = 0)
% 47.42/13.40 | (224) all_11_4_44 = all_11_8_48
% 47.42/13.40 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 47.42/13.40 | (226) ~ (all_11_2_42 = 0)
% 47.42/13.40 |
% 47.42/13.40 | Instantiating formula (88) with all_0_3_3, all_11_7_47, all_11_6_46, ve2, ve1 and discharging atoms vapp(all_11_6_46, all_11_7_47) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.42/13.40 | (227) all_11_6_46 = ve1
% 47.42/13.40 |
% 47.42/13.40 | Instantiating formula (66) with ve1, all_9_8_24, all_9_6_22, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(all_9_6_22, all_9_8_24) = ve1, yields:
% 47.42/13.40 | (228) ~ (vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1)
% 47.42/13.40 |
% 47.42/13.40 | From (227) and (221) follows:
% 47.42/13.40 | (229) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1
% 47.42/13.40 |
% 47.42/13.40 | Using (229) and (228) yields:
% 47.42/13.40 | (130) $false
% 47.42/13.40 |
% 47.42/13.40 |-The branch is then unsatisfiable
% 47.42/13.40 |-Branch two:
% 47.42/13.40 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.42/13.40 |
% 47.42/13.40 | Applying alpha-rule on (231) yields:
% 47.42/13.40 | (232) all_11_7_47 = all_11_9_49
% 47.42/13.40 | (219) all_0_1_1 = vnoExp
% 47.42/13.40 | (234) ~ (all_11_6_46 = 0)
% 47.42/13.40 | (235) vreduce(all_11_10_50) = all_11_9_49
% 47.42/13.40 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.42/13.40 | (212) all_11_8_48 = all_0_3_3
% 47.42/13.40 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 47.42/13.40 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 47.42/13.40 |
% 47.42/13.40 | Instantiating formula (55) with ve1, all_11_9_49, all_0_6_6 and discharging atoms vreduce(ve1) = all_0_6_6, yields:
% 47.42/13.40 | (240) all_11_9_49 = all_0_6_6 | ~ (vreduce(ve1) = all_11_9_49)
% 47.42/13.40 |
% 47.42/13.40 | Instantiating formula (47) with all_11_6_46, all_0_6_6, all_9_1_17 and discharging atoms vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 47.42/13.40 | (241) all_11_6_46 = 0 | ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.42/13.40 |
% 47.42/13.40 | Instantiating formula (88) with all_0_3_3, all_11_11_51, all_11_10_50, ve2, ve1 and discharging atoms vapp(all_11_10_50, all_11_11_51) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.42/13.40 | (242) all_11_10_50 = ve1
% 47.42/13.40 |
% 47.42/13.40 | From (242) and (235) follows:
% 47.42/13.40 | (243) vreduce(ve1) = all_11_9_49
% 47.42/13.40 |
% 47.42/13.40 +-Applying beta-rule and splitting (240), into two cases.
% 47.42/13.40 |-Branch one:
% 47.42/13.40 | (245) ~ (vreduce(ve1) = all_11_9_49)
% 47.42/13.40 |
% 47.42/13.40 | Using (243) and (245) yields:
% 47.42/13.40 | (130) $false
% 47.42/13.40 |
% 47.42/13.40 |-The branch is then unsatisfiable
% 47.42/13.40 |-Branch two:
% 47.42/13.40 | (243) vreduce(ve1) = all_11_9_49
% 47.42/13.40 | (248) all_11_9_49 = all_0_6_6
% 47.42/13.40 |
% 47.42/13.40 | From (248) and (239) follows:
% 47.42/13.40 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.42/13.40 |
% 47.42/13.40 +-Applying beta-rule and splitting (241), into two cases.
% 47.42/13.40 |-Branch one:
% 47.42/13.40 | (244) ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.42/13.40 |
% 47.42/13.40 | Using (249) and (244) yields:
% 47.42/13.40 | (130) $false
% 47.42/13.40 |
% 47.42/13.40 |-The branch is then unsatisfiable
% 47.42/13.40 |-Branch two:
% 47.42/13.40 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.42/13.40 | (206) all_11_6_46 = 0
% 47.42/13.40 |
% 47.42/13.40 | Equations (206) can reduce 234 to:
% 47.42/13.40 | (165) $false
% 47.42/13.40 |
% 47.42/13.40 |-The branch is then unsatisfiable
% 47.42/13.40 |-Branch two:
% 47.42/13.40 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.42/13.40 |
% 47.42/13.40 | Applying alpha-rule on (254) yields:
% 47.42/13.40 | (212) all_11_8_48 = all_0_3_3
% 47.42/13.40 | (219) all_0_1_1 = vnoExp
% 47.42/13.40 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.42/13.40 |
% 47.42/13.40 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3, yields:
% 47.42/13.40 | (130) $false
% 47.42/13.40 |
% 47.42/13.40 |-The branch is then unsatisfiable
% 47.42/13.40 |-Branch two:
% 47.42/13.40 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 47.42/13.40 |
% 47.42/13.40 | Applying alpha-rule on (259) yields:
% 47.42/13.40 | (260) all_11_10_50 = all_0_3_3
% 47.42/13.40 | (219) all_0_1_1 = vnoExp
% 47.42/13.40 | (262) vvar(all_11_11_51) = all_0_3_3
% 47.42/13.40 |
% 47.42/13.40 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_11_11_51) = all_0_3_3, yields:
% 47.42/13.40 | (130) $false
% 47.42/13.40 |
% 47.42/13.40 |-The branch is then unsatisfiable
% 47.42/13.40 |-Branch two:
% 47.42/13.40 | (1006) all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)
% 47.42/13.40 |
% 47.42/13.40 | Applying alpha-rule on (1006) yields:
% 47.42/13.40 | (1007) all_10_7_35 = all_10_10_38
% 47.42/13.40 | (1008) vgetSomeExp(all_10_10_38) = all_10_5_33
% 47.42/13.40 | (1009) vapp(all_10_5_33, all_10_9_37) = all_10_4_32
% 47.42/13.40 | (1010) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)
% 47.42/13.40 | (1011) visSomeExp(all_10_10_38) = 0
% 47.42/13.40 | (1012) all_10_8_36 = ve2
% 47.42/13.40 | (1013) vreduce(all_10_11_39) = all_10_10_38
% 47.42/13.40 | (1014) all_10_6_34 = 0
% 47.42/13.40 | (1015) vsomeExp(all_10_4_32) = all_0_4_4
% 47.42/13.40 | (1016) vapp(all_10_11_39, all_10_9_37) = ve2
% 47.42/13.40 | (1017) all_10_3_31 = all_0_4_4
% 47.42/13.40 |
% 47.42/13.40 | From (1169) and (1015) follows:
% 47.42/13.40 | (2178) vsomeExp(all_10_4_32) = all_0_6_6
% 47.42/13.40 |
% 47.42/13.40 | Instantiating formula (85) with all_0_6_6, all_10_4_32, all_9_1_17 and discharging atoms vsomeExp(all_10_4_32) = all_0_6_6, vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 47.42/13.40 | (2179) all_10_4_32 = all_9_1_17
% 47.42/13.40 |
% 47.42/13.40 | From (2179) and (2178) follows:
% 47.42/13.40 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 47.42/13.40 |
% 47.42/13.40 +-Applying beta-rule and splitting (116), into two cases.
% 47.42/13.40 |-Branch one:
% 47.42/13.40 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 47.42/13.40 |
% 47.42/13.40 +-Applying beta-rule and splitting (171), into two cases.
% 47.42/13.40 |-Branch one:
% 47.42/13.40 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 47.42/13.40 |
% 47.42/13.40 +-Applying beta-rule and splitting (172), into two cases.
% 47.42/13.40 |-Branch one:
% 47.42/13.40 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 47.42/13.40 |
% 47.42/13.40 +-Applying beta-rule and splitting (173), into two cases.
% 47.42/13.40 |-Branch one:
% 47.42/13.40 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 47.42/13.40 |
% 47.42/13.40 +-Applying beta-rule and splitting (174), into two cases.
% 47.42/13.40 |-Branch one:
% 47.42/13.40 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 47.42/13.40 |
% 47.42/13.40 +-Applying beta-rule and splitting (175), into two cases.
% 47.42/13.40 |-Branch one:
% 47.42/13.40 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.42/13.40 |
% 47.42/13.40 | Applying alpha-rule on (176) yields:
% 47.42/13.40 | (177) all_11_5_45 = all_0_3_3
% 47.42/13.40 | (178) all_11_4_44 = all_11_10_50
% 47.42/13.40 | (179) visValue(all_11_8_48) = 0
% 47.42/13.40 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 47.42/13.40 | (181) all_11_0_40 = all_0_1_1
% 47.42/13.40 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.42/13.40 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.42/13.40 | (184) vreduce(all_11_8_48) = all_11_10_50
% 47.42/13.40 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 47.42/13.40 | (186) ~ (all_11_3_43 = 0)
% 47.42/13.40 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 47.42/13.40 | (188) all_11_2_42 = 0
% 47.42/13.40 |
% 47.42/13.40 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.42/13.40 | (130) $false
% 47.42/13.40 |
% 47.42/13.41 |-The branch is then unsatisfiable
% 47.42/13.41 |-Branch two:
% 47.42/13.41 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.42/13.41 |
% 47.42/13.41 | Applying alpha-rule on (190) yields:
% 47.42/13.41 | (177) all_11_5_45 = all_0_3_3
% 47.42/13.41 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 47.42/13.41 | (193) visSomeExp(all_11_7_47) = 0
% 47.42/13.41 | (181) all_11_0_40 = all_0_1_1
% 47.42/13.41 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.42/13.41 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 47.42/13.41 | (197) vreduce(all_11_11_51) = all_11_7_47
% 47.42/13.41 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 47.42/13.41 | (199) all_11_3_43 = 0
% 47.42/13.41 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.42/13.41 | (201) all_11_4_44 = all_11_7_47
% 47.42/13.41 |
% 47.42/13.41 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.42/13.41 | (130) $false
% 47.42/13.41 |
% 47.42/13.41 |-The branch is then unsatisfiable
% 47.42/13.41 |-Branch two:
% 47.42/13.41 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.42/13.41 |
% 47.42/13.41 | Applying alpha-rule on (203) yields:
% 47.42/13.41 | (204) all_11_7_47 = all_11_10_50
% 47.42/13.41 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.42/13.41 | (206) all_11_6_46 = 0
% 47.42/13.41 | (207) all_11_3_43 = all_0_1_1
% 47.42/13.41 | (208) visSomeExp(all_11_10_50) = 0
% 47.42/13.41 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 47.42/13.41 | (210) vreduce(all_11_11_51) = all_11_10_50
% 47.42/13.41 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 47.42/13.41 | (212) all_11_8_48 = all_0_3_3
% 47.42/13.41 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 47.42/13.41 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 47.42/13.41 |
% 47.42/13.41 | Instantiating formula (74) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = all_0_1_1, yields:
% 47.42/13.41 | (130) $false
% 47.42/13.41 |
% 47.42/13.41 |-The branch is then unsatisfiable
% 47.42/13.41 |-Branch two:
% 47.42/13.41 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.42/13.41 |
% 47.42/13.41 | Applying alpha-rule on (216) yields:
% 47.42/13.41 | (177) all_11_5_45 = all_0_3_3
% 47.42/13.41 | (218) visValue(all_11_7_47) = all_11_2_42
% 47.42/13.41 | (219) all_0_1_1 = vnoExp
% 47.42/13.41 | (220) vreduce(all_11_7_47) = all_11_8_48
% 47.42/13.41 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.42/13.41 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 47.42/13.41 | (186) ~ (all_11_3_43 = 0)
% 47.42/13.41 | (224) all_11_4_44 = all_11_8_48
% 47.42/13.41 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 47.42/13.41 | (226) ~ (all_11_2_42 = 0)
% 47.42/13.41 |
% 47.42/13.41 | Instantiating formula (88) with all_0_3_3, all_11_7_47, all_11_6_46, ve2, ve1 and discharging atoms vapp(all_11_6_46, all_11_7_47) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.42/13.41 | (227) all_11_6_46 = ve1
% 47.42/13.41 |
% 47.42/13.41 | Instantiating formula (66) with ve1, all_9_8_24, all_9_6_22, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(all_9_6_22, all_9_8_24) = ve1, yields:
% 47.42/13.41 | (228) ~ (vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1)
% 47.42/13.41 |
% 47.42/13.41 | From (227) and (221) follows:
% 47.42/13.41 | (229) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1
% 47.42/13.41 |
% 47.42/13.41 | Using (229) and (228) yields:
% 47.42/13.41 | (130) $false
% 47.42/13.41 |
% 47.42/13.41 |-The branch is then unsatisfiable
% 47.42/13.41 |-Branch two:
% 47.42/13.41 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.42/13.41 |
% 47.42/13.41 | Applying alpha-rule on (231) yields:
% 47.42/13.41 | (232) all_11_7_47 = all_11_9_49
% 47.42/13.41 | (219) all_0_1_1 = vnoExp
% 47.42/13.41 | (234) ~ (all_11_6_46 = 0)
% 47.42/13.41 | (235) vreduce(all_11_10_50) = all_11_9_49
% 47.42/13.41 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.42/13.41 | (212) all_11_8_48 = all_0_3_3
% 47.42/13.41 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 47.42/13.41 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 47.42/13.41 |
% 47.42/13.41 | Instantiating formula (55) with ve1, all_11_9_49, all_0_6_6 and discharging atoms vreduce(ve1) = all_0_6_6, yields:
% 47.42/13.41 | (240) all_11_9_49 = all_0_6_6 | ~ (vreduce(ve1) = all_11_9_49)
% 47.42/13.41 |
% 47.42/13.41 | Instantiating formula (47) with all_11_6_46, all_0_6_6, all_9_1_17 and discharging atoms vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 47.42/13.41 | (241) all_11_6_46 = 0 | ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.42/13.41 |
% 47.42/13.41 | Instantiating formula (88) with all_0_3_3, all_11_11_51, all_11_10_50, ve2, ve1 and discharging atoms vapp(all_11_10_50, all_11_11_51) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.42/13.41 | (242) all_11_10_50 = ve1
% 47.42/13.41 |
% 47.42/13.41 | From (242) and (235) follows:
% 47.42/13.41 | (243) vreduce(ve1) = all_11_9_49
% 47.42/13.41 |
% 47.42/13.41 +-Applying beta-rule and splitting (241), into two cases.
% 47.42/13.41 |-Branch one:
% 47.42/13.41 | (244) ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.42/13.41 |
% 47.42/13.41 +-Applying beta-rule and splitting (240), into two cases.
% 47.42/13.41 |-Branch one:
% 47.42/13.41 | (245) ~ (vreduce(ve1) = all_11_9_49)
% 47.42/13.41 |
% 47.42/13.41 | Using (243) and (245) yields:
% 47.42/13.41 | (130) $false
% 47.42/13.41 |
% 47.42/13.41 |-The branch is then unsatisfiable
% 47.42/13.41 |-Branch two:
% 47.42/13.41 | (243) vreduce(ve1) = all_11_9_49
% 47.42/13.41 | (248) all_11_9_49 = all_0_6_6
% 47.42/13.41 |
% 47.42/13.41 | From (248) and (239) follows:
% 47.42/13.41 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.42/13.41 |
% 47.42/13.41 | Using (249) and (244) yields:
% 47.42/13.41 | (130) $false
% 47.42/13.41 |
% 47.42/13.41 |-The branch is then unsatisfiable
% 47.42/13.41 |-Branch two:
% 47.42/13.41 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.42/13.41 | (206) all_11_6_46 = 0
% 47.42/13.41 |
% 47.42/13.41 | Equations (206) can reduce 234 to:
% 47.42/13.41 | (165) $false
% 47.42/13.41 |
% 47.42/13.41 |-The branch is then unsatisfiable
% 47.42/13.41 |-Branch two:
% 47.42/13.41 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.42/13.41 |
% 47.42/13.41 | Applying alpha-rule on (254) yields:
% 47.42/13.41 | (212) all_11_8_48 = all_0_3_3
% 47.42/13.41 | (219) all_0_1_1 = vnoExp
% 47.42/13.41 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.42/13.41 |
% 47.42/13.41 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3, yields:
% 47.42/13.41 | (130) $false
% 47.42/13.41 |
% 47.42/13.41 |-The branch is then unsatisfiable
% 47.42/13.41 |-Branch two:
% 47.42/13.41 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 47.42/13.41 |
% 47.42/13.41 | Applying alpha-rule on (259) yields:
% 47.42/13.41 | (260) all_11_10_50 = all_0_3_3
% 47.42/13.41 | (219) all_0_1_1 = vnoExp
% 47.42/13.41 | (262) vvar(all_11_11_51) = all_0_3_3
% 47.42/13.41 |
% 47.42/13.41 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_11_11_51) = all_0_3_3, yields:
% 47.42/13.41 | (130) $false
% 47.42/13.41 |
% 47.42/13.41 |-The branch is then unsatisfiable
% 47.42/13.41 |-Branch two:
% 47.42/13.41 | (1116) all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34
% 47.42/13.41 |
% 47.42/13.41 | Applying alpha-rule on (1116) yields:
% 47.42/13.41 | (772) all_10_5_33 = ve2
% 47.42/13.41 | (1118) all_10_4_32 = all_10_8_36
% 47.42/13.41 | (775) ~ (all_10_3_31 = 0)
% 47.42/13.41 | (1120) ~ (all_10_2_30 = 0)
% 47.42/13.41 | (1121) visValue(all_10_7_35) = all_10_2_30
% 47.42/13.41 | (1122) vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34
% 47.42/13.41 | (1123) all_0_4_4 = vnoExp
% 47.42/13.41 | (1124) vreduce(all_10_7_35) = all_10_8_36
% 47.42/13.41 | (1125) visSomeExp(all_10_8_36) = all_10_3_31
% 47.42/13.41 | (1126) vapp(all_10_6_34, all_10_7_35) = ve2
% 47.42/13.41 |
% 47.42/13.41 | Combining equations (1169,1123) yields a new equation:
% 47.42/13.41 | (2285) all_0_6_6 = vnoExp
% 47.42/13.41 |
% 47.42/13.41 | Simplifying 2285 yields:
% 47.42/13.41 | (502) all_0_6_6 = vnoExp
% 47.42/13.41 |
% 47.42/13.41 | Equations (502) can reduce 1926 to:
% 47.42/13.41 | (165) $false
% 47.42/13.41 |
% 47.42/13.41 |-The branch is then unsatisfiable
% 47.42/13.41 |-Branch two:
% 47.42/13.41 | (1128) all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)
% 47.42/13.41 |
% 47.42/13.41 | Applying alpha-rule on (1128) yields:
% 47.42/13.41 | (1129) vreduce(all_10_10_38) = all_10_9_37
% 47.42/13.41 | (1130) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)
% 47.42/13.41 | (1123) all_0_4_4 = vnoExp
% 47.42/13.41 | (1012) all_10_8_36 = ve2
% 47.42/13.41 | (1133) ~ (all_10_6_34 = 0)
% 47.42/13.41 | (1134) vapp(all_10_10_38, all_10_11_39) = ve2
% 47.42/13.41 | (1135) visSomeExp(all_10_9_37) = all_10_6_34
% 47.42/13.41 | (1136) all_10_7_35 = all_10_9_37
% 47.42/13.41 |
% 47.42/13.41 | Combining equations (1169,1123) yields a new equation:
% 47.42/13.41 | (2285) all_0_6_6 = vnoExp
% 47.42/13.41 |
% 47.42/13.41 | Simplifying 2285 yields:
% 47.42/13.41 | (502) all_0_6_6 = vnoExp
% 47.42/13.41 |
% 47.42/13.41 | Equations (502) can reduce 1926 to:
% 47.42/13.41 | (165) $false
% 47.42/13.41 |
% 47.42/13.41 |-The branch is then unsatisfiable
% 47.42/13.41 |-Branch two:
% 47.42/13.41 | (1138) all_10_8_36 = ve2 & all_0_4_4 = vnoExp & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2
% 47.42/13.41 |
% 47.42/13.41 | Applying alpha-rule on (1138) yields:
% 47.42/13.41 | (1012) all_10_8_36 = ve2
% 47.42/13.41 | (1123) all_0_4_4 = vnoExp
% 47.42/13.41 | (1141) vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2
% 47.42/13.41 |
% 47.42/13.41 | Combining equations (1169,1123) yields a new equation:
% 47.42/13.41 | (2285) all_0_6_6 = vnoExp
% 47.42/13.41 |
% 47.42/13.41 | Simplifying 2285 yields:
% 47.42/13.41 | (502) all_0_6_6 = vnoExp
% 47.42/13.41 |
% 47.42/13.41 | Equations (502) can reduce 1926 to:
% 47.42/13.41 | (165) $false
% 47.42/13.41 |
% 47.42/13.41 |-The branch is then unsatisfiable
% 47.42/13.41 |-Branch two:
% 47.42/13.41 | (1143) all_10_10_38 = ve2 & all_0_4_4 = vnoExp & vvar(all_10_11_39) = ve2
% 47.42/13.41 |
% 47.42/13.41 | Applying alpha-rule on (1143) yields:
% 47.42/13.41 | (1144) all_10_10_38 = ve2
% 47.42/13.41 | (1123) all_0_4_4 = vnoExp
% 47.42/13.41 | (1146) vvar(all_10_11_39) = ve2
% 47.42/13.41 |
% 47.42/13.41 | Combining equations (1169,1123) yields a new equation:
% 47.42/13.41 | (2285) all_0_6_6 = vnoExp
% 47.42/13.41 |
% 47.42/13.41 | Simplifying 2285 yields:
% 47.42/13.41 | (502) all_0_6_6 = vnoExp
% 47.42/13.41 |
% 47.42/13.41 | Equations (502) can reduce 1926 to:
% 47.42/13.41 | (165) $false
% 47.42/13.41 |
% 47.42/13.41 |-The branch is then unsatisfiable
% 47.42/13.41 |-Branch two:
% 47.42/13.41 | (264) all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22
% 47.42/13.41 |
% 47.42/13.41 | Applying alpha-rule on (264) yields:
% 47.42/13.41 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 47.42/13.41 | (266) visSomeExp(all_9_7_23) = 0
% 47.42/13.41 | (267) vapp(all_9_6_22, all_9_2_18) = all_9_1_17
% 47.42/13.41 | (268) vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22
% 47.42/13.41 | (269) vreduce(all_9_11_27) = all_9_7_23
% 47.42/13.41 | (270) vapp(all_9_6_22, all_9_11_27) = ve1
% 47.42/13.41 | (153) all_9_0_16 = all_0_6_6
% 47.42/13.41 | (272) all_9_3_19 = 0
% 47.42/13.41 | (273) vgetSomeExp(all_9_7_23) = all_9_2_18
% 47.42/13.41 | (159) all_9_5_21 = ve1
% 47.42/13.41 | (275) all_9_4_20 = all_9_7_23
% 47.42/13.41 |
% 47.42/13.41 | Instantiating formula (40) with all_9_1_17 yields:
% 47.42/13.42 | (1924) ~ (vsomeExp(all_9_1_17) = vnoExp)
% 47.42/13.42 |
% 47.42/13.42 | Instantiating formula (92) with ve1, all_9_11_27, all_9_6_22 and discharging atoms vapp(all_9_6_22, all_9_11_27) = ve1, yields:
% 47.42/13.42 | (162) ~ (visValue(ve1) = 0)
% 47.42/13.42 |
% 47.42/13.42 | Using (150) and (1924) yields:
% 47.42/13.42 | (1926) ~ (all_0_6_6 = vnoExp)
% 47.42/13.42 |
% 47.42/13.42 | Using (68) and (162) yields:
% 47.42/13.42 | (163) ~ (all_0_7_7 = 0)
% 47.42/13.42 |
% 47.42/13.42 +-Applying beta-rule and splitting (143), into two cases.
% 47.42/13.42 |-Branch one:
% 47.42/13.42 | (164) all_0_7_7 = 0
% 47.42/13.42 |
% 47.42/13.42 | Equations (164) can reduce 163 to:
% 47.42/13.42 | (165) $false
% 47.42/13.42 |
% 47.42/13.42 |-The branch is then unsatisfiable
% 47.42/13.42 |-Branch two:
% 47.42/13.42 | (163) ~ (all_0_7_7 = 0)
% 47.42/13.42 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.42/13.42 |
% 47.42/13.42 | Instantiating (167) with all_122_0_472 yields:
% 47.42/13.42 | (2334) vsomeExp(all_122_0_472) = all_0_6_6
% 47.42/13.42 |
% 47.42/13.42 +-Applying beta-rule and splitting (661), into two cases.
% 47.42/13.42 |-Branch one:
% 47.42/13.42 | (761) all_0_5_5 = 0
% 47.42/13.42 |
% 47.42/13.42 | Combining equations (761,1326) yields a new equation:
% 47.42/13.42 | (164) all_0_7_7 = 0
% 47.42/13.42 |
% 47.42/13.42 | Equations (164) can reduce 163 to:
% 47.42/13.42 | (165) $false
% 47.42/13.42 |
% 47.42/13.42 |-The branch is then unsatisfiable
% 47.42/13.42 |-Branch two:
% 47.42/13.42 | (760) ~ (all_0_5_5 = 0)
% 47.42/13.42 | (764) ? [v0] : vsomeExp(v0) = all_0_4_4
% 47.42/13.42 |
% 47.42/13.42 | Instantiating (764) with all_128_0_473 yields:
% 47.42/13.42 | (2340) vsomeExp(all_128_0_473) = all_0_4_4
% 47.42/13.42 |
% 47.42/13.42 | From (1169) and (2340) follows:
% 47.42/13.42 | (2341) vsomeExp(all_128_0_473) = all_0_6_6
% 47.42/13.42 |
% 47.42/13.42 | Instantiating formula (85) with all_0_6_6, all_128_0_473, all_9_1_17 and discharging atoms vsomeExp(all_128_0_473) = all_0_6_6, vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 47.42/13.42 | (2342) all_128_0_473 = all_9_1_17
% 47.42/13.42 |
% 47.42/13.42 | Instantiating formula (85) with all_0_6_6, all_122_0_472, all_128_0_473 and discharging atoms vsomeExp(all_128_0_473) = all_0_6_6, vsomeExp(all_122_0_472) = all_0_6_6, yields:
% 47.42/13.42 | (2343) all_128_0_473 = all_122_0_472
% 47.42/13.42 |
% 47.42/13.42 | Combining equations (2342,2343) yields a new equation:
% 47.42/13.42 | (2344) all_122_0_472 = all_9_1_17
% 47.42/13.42 |
% 47.42/13.42 | From (2344) and (2334) follows:
% 47.42/13.42 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 47.42/13.42 |
% 47.42/13.42 +-Applying beta-rule and splitting (115), into two cases.
% 47.42/13.42 |-Branch one:
% 47.42/13.42 | (766) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34) | (all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)) | (all_10_8_36 = ve2 & all_0_4_4 = vnoExp & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2)
% 47.42/13.42 |
% 47.42/13.42 +-Applying beta-rule and splitting (766), into two cases.
% 47.42/13.42 |-Branch one:
% 47.42/13.42 | (767) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34) | (all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38))
% 47.42/13.42 |
% 47.42/13.42 +-Applying beta-rule and splitting (767), into two cases.
% 47.42/13.42 |-Branch one:
% 47.42/13.42 | (768) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34)
% 47.70/13.42 |
% 47.70/13.42 +-Applying beta-rule and splitting (768), into two cases.
% 47.70/13.42 |-Branch one:
% 47.70/13.42 | (769) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39))
% 47.70/13.42 |
% 47.70/13.42 +-Applying beta-rule and splitting (769), into two cases.
% 47.70/13.42 |-Branch one:
% 47.70/13.42 | (770) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34)
% 47.70/13.42 |
% 47.70/13.42 +-Applying beta-rule and splitting (770), into two cases.
% 47.70/13.42 |-Branch one:
% 47.70/13.42 | (771) all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34
% 47.70/13.42 |
% 47.70/13.42 | Applying alpha-rule on (771) yields:
% 47.70/13.42 | (772) all_10_5_33 = ve2
% 47.70/13.42 | (773) visValue(all_10_8_36) = 0
% 47.70/13.42 | (774) all_10_4_32 = all_10_10_38
% 47.70/13.42 | (775) ~ (all_10_3_31 = 0)
% 47.70/13.42 | (776) all_10_2_30 = 0
% 47.70/13.42 | (777) vapp(all_10_6_34, all_10_8_36) = ve2
% 47.70/13.42 | (778) vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29
% 47.70/13.42 | (779) vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34
% 47.70/13.42 | (780) all_10_0_28 = all_0_4_4
% 47.70/13.42 | (781) visSomeExp(all_10_10_38) = all_10_3_31
% 47.70/13.42 | (782) vsomeExp(all_10_1_29) = all_0_4_4
% 47.70/13.42 | (783) vreduce(all_10_8_36) = all_10_10_38
% 47.70/13.42 |
% 47.70/13.42 | From (1169) and (782) follows:
% 47.70/13.42 | (1962) vsomeExp(all_10_1_29) = all_0_6_6
% 47.70/13.42 |
% 47.70/13.42 | Instantiating formula (85) with all_0_6_6, all_10_1_29, all_9_1_17 and discharging atoms vsomeExp(all_10_1_29) = all_0_6_6, vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 47.70/13.42 | (1963) all_10_1_29 = all_9_1_17
% 47.70/13.42 |
% 47.70/13.42 | From (1963) and (1962) follows:
% 47.70/13.42 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 47.70/13.42 |
% 47.70/13.42 +-Applying beta-rule and splitting (116), into two cases.
% 47.70/13.42 |-Branch one:
% 47.70/13.42 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 47.70/13.42 |
% 47.70/13.42 +-Applying beta-rule and splitting (171), into two cases.
% 47.70/13.42 |-Branch one:
% 47.70/13.42 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 47.70/13.43 |
% 47.70/13.43 +-Applying beta-rule and splitting (172), into two cases.
% 47.70/13.43 |-Branch one:
% 47.70/13.43 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 47.70/13.43 |
% 47.70/13.43 +-Applying beta-rule and splitting (173), into two cases.
% 47.70/13.43 |-Branch one:
% 47.70/13.43 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 47.70/13.43 |
% 47.70/13.43 +-Applying beta-rule and splitting (174), into two cases.
% 47.70/13.43 |-Branch one:
% 47.70/13.43 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 47.70/13.43 |
% 47.70/13.43 +-Applying beta-rule and splitting (175), into two cases.
% 47.70/13.43 |-Branch one:
% 47.70/13.43 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.70/13.43 |
% 47.70/13.43 | Applying alpha-rule on (176) yields:
% 47.70/13.43 | (177) all_11_5_45 = all_0_3_3
% 47.70/13.43 | (178) all_11_4_44 = all_11_10_50
% 47.70/13.43 | (179) visValue(all_11_8_48) = 0
% 47.70/13.43 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 47.70/13.43 | (181) all_11_0_40 = all_0_1_1
% 47.70/13.43 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.70/13.43 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.70/13.43 | (184) vreduce(all_11_8_48) = all_11_10_50
% 47.70/13.43 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 47.70/13.43 | (186) ~ (all_11_3_43 = 0)
% 47.70/13.43 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 47.70/13.43 | (188) all_11_2_42 = 0
% 47.70/13.43 |
% 47.70/13.43 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.70/13.43 | (130) $false
% 47.70/13.43 |
% 47.70/13.43 |-The branch is then unsatisfiable
% 47.70/13.43 |-Branch two:
% 47.70/13.43 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.70/13.43 |
% 47.70/13.43 | Applying alpha-rule on (190) yields:
% 47.70/13.43 | (177) all_11_5_45 = all_0_3_3
% 47.70/13.43 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 47.70/13.43 | (193) visSomeExp(all_11_7_47) = 0
% 47.70/13.43 | (181) all_11_0_40 = all_0_1_1
% 47.70/13.43 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.70/13.43 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 47.70/13.43 | (197) vreduce(all_11_11_51) = all_11_7_47
% 47.70/13.43 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 47.70/13.43 | (199) all_11_3_43 = 0
% 47.70/13.43 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.70/13.43 | (201) all_11_4_44 = all_11_7_47
% 47.70/13.43 |
% 47.70/13.43 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.70/13.43 | (130) $false
% 47.70/13.43 |
% 47.70/13.43 |-The branch is then unsatisfiable
% 47.70/13.43 |-Branch two:
% 47.70/13.43 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.70/13.43 |
% 47.70/13.43 | Applying alpha-rule on (203) yields:
% 47.70/13.43 | (204) all_11_7_47 = all_11_10_50
% 47.70/13.43 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.70/13.43 | (206) all_11_6_46 = 0
% 47.70/13.43 | (207) all_11_3_43 = all_0_1_1
% 47.70/13.43 | (208) visSomeExp(all_11_10_50) = 0
% 47.70/13.43 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 47.70/13.43 | (210) vreduce(all_11_11_51) = all_11_10_50
% 47.70/13.43 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 47.70/13.43 | (212) all_11_8_48 = all_0_3_3
% 47.70/13.43 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 47.70/13.43 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 47.70/13.43 |
% 47.70/13.43 | Instantiating formula (74) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = all_0_1_1, yields:
% 47.70/13.43 | (130) $false
% 47.70/13.43 |
% 47.70/13.43 |-The branch is then unsatisfiable
% 47.70/13.43 |-Branch two:
% 47.70/13.43 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.70/13.43 |
% 47.70/13.43 | Applying alpha-rule on (216) yields:
% 47.70/13.43 | (177) all_11_5_45 = all_0_3_3
% 47.70/13.43 | (218) visValue(all_11_7_47) = all_11_2_42
% 47.70/13.43 | (219) all_0_1_1 = vnoExp
% 47.70/13.43 | (220) vreduce(all_11_7_47) = all_11_8_48
% 47.70/13.43 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.70/13.43 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 47.70/13.43 | (186) ~ (all_11_3_43 = 0)
% 47.70/13.43 | (224) all_11_4_44 = all_11_8_48
% 47.70/13.43 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 47.70/13.43 | (226) ~ (all_11_2_42 = 0)
% 47.70/13.43 |
% 47.70/13.43 | Instantiating formula (88) with all_0_3_3, all_11_7_47, all_11_6_46, ve2, ve1 and discharging atoms vapp(all_11_6_46, all_11_7_47) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.70/13.43 | (227) all_11_6_46 = ve1
% 47.70/13.43 |
% 47.70/13.43 | Instantiating formula (66) with ve1, all_9_11_27, all_9_6_22, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(all_9_6_22, all_9_11_27) = ve1, yields:
% 47.70/13.43 | (228) ~ (vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1)
% 47.70/13.43 |
% 47.70/13.43 | From (227) and (221) follows:
% 47.70/13.43 | (229) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1
% 47.70/13.43 |
% 47.70/13.43 | Using (229) and (228) yields:
% 47.70/13.43 | (130) $false
% 47.70/13.43 |
% 47.70/13.43 |-The branch is then unsatisfiable
% 47.70/13.43 |-Branch two:
% 47.70/13.43 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.70/13.43 |
% 47.70/13.43 | Applying alpha-rule on (231) yields:
% 47.70/13.43 | (232) all_11_7_47 = all_11_9_49
% 47.70/13.43 | (219) all_0_1_1 = vnoExp
% 47.70/13.43 | (234) ~ (all_11_6_46 = 0)
% 47.70/13.43 | (235) vreduce(all_11_10_50) = all_11_9_49
% 47.70/13.43 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.70/13.43 | (212) all_11_8_48 = all_0_3_3
% 47.70/13.43 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 47.70/13.43 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 47.70/13.43 |
% 47.70/13.43 | Instantiating formula (55) with ve1, all_11_9_49, all_0_6_6 and discharging atoms vreduce(ve1) = all_0_6_6, yields:
% 47.70/13.43 | (240) all_11_9_49 = all_0_6_6 | ~ (vreduce(ve1) = all_11_9_49)
% 47.70/13.43 |
% 47.70/13.43 | Instantiating formula (47) with all_11_6_46, all_0_6_6, all_9_1_17 and discharging atoms vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 47.70/13.43 | (241) all_11_6_46 = 0 | ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.70/13.43 |
% 47.70/13.43 | Instantiating formula (88) with all_0_3_3, all_11_11_51, all_11_10_50, ve2, ve1 and discharging atoms vapp(all_11_10_50, all_11_11_51) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.70/13.43 | (242) all_11_10_50 = ve1
% 47.70/13.43 |
% 47.70/13.43 | From (242) and (235) follows:
% 47.70/13.43 | (243) vreduce(ve1) = all_11_9_49
% 47.70/13.43 |
% 47.70/13.43 +-Applying beta-rule and splitting (240), into two cases.
% 47.70/13.43 |-Branch one:
% 47.70/13.43 | (245) ~ (vreduce(ve1) = all_11_9_49)
% 47.70/13.43 |
% 47.70/13.43 | Using (243) and (245) yields:
% 47.70/13.43 | (130) $false
% 47.70/13.43 |
% 47.70/13.43 |-The branch is then unsatisfiable
% 47.70/13.43 |-Branch two:
% 47.70/13.43 | (243) vreduce(ve1) = all_11_9_49
% 47.70/13.43 | (248) all_11_9_49 = all_0_6_6
% 47.70/13.43 |
% 47.70/13.43 | From (248) and (239) follows:
% 47.70/13.43 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.70/13.43 |
% 47.70/13.43 +-Applying beta-rule and splitting (241), into two cases.
% 47.70/13.43 |-Branch one:
% 47.70/13.43 | (244) ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.70/13.43 |
% 47.70/13.43 | Using (249) and (244) yields:
% 47.70/13.43 | (130) $false
% 47.70/13.43 |
% 47.70/13.43 |-The branch is then unsatisfiable
% 47.70/13.43 |-Branch two:
% 47.70/13.43 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.70/13.43 | (206) all_11_6_46 = 0
% 47.70/13.43 |
% 47.70/13.43 | Equations (206) can reduce 234 to:
% 47.70/13.43 | (165) $false
% 47.70/13.43 |
% 47.70/13.43 |-The branch is then unsatisfiable
% 47.70/13.43 |-Branch two:
% 47.70/13.43 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.70/13.43 |
% 47.70/13.43 | Applying alpha-rule on (254) yields:
% 47.70/13.43 | (212) all_11_8_48 = all_0_3_3
% 47.70/13.43 | (219) all_0_1_1 = vnoExp
% 47.70/13.43 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.70/13.43 |
% 47.70/13.43 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3, yields:
% 47.70/13.43 | (130) $false
% 47.70/13.43 |
% 47.70/13.43 |-The branch is then unsatisfiable
% 47.70/13.43 |-Branch two:
% 47.70/13.43 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 47.70/13.43 |
% 47.70/13.43 | Applying alpha-rule on (259) yields:
% 47.70/13.43 | (260) all_11_10_50 = all_0_3_3
% 47.70/13.43 | (219) all_0_1_1 = vnoExp
% 47.70/13.43 | (262) vvar(all_11_11_51) = all_0_3_3
% 47.70/13.43 |
% 47.70/13.43 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_11_11_51) = all_0_3_3, yields:
% 47.70/13.43 | (130) $false
% 47.70/13.43 |
% 47.70/13.43 |-The branch is then unsatisfiable
% 47.70/13.43 |-Branch two:
% 47.70/13.43 | (896) all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34
% 47.70/13.43 |
% 47.70/13.43 | Applying alpha-rule on (896) yields:
% 47.70/13.43 | (772) all_10_5_33 = ve2
% 47.70/13.43 | (898) vreduce(all_10_11_39) = all_10_7_35
% 47.70/13.43 | (846) all_10_3_31 = 0
% 47.70/13.43 | (900) all_10_4_32 = all_10_7_35
% 47.70/13.43 | (901) visSomeExp(all_10_7_35) = 0
% 47.70/13.43 | (902) vapp(all_10_6_34, all_10_2_30) = all_10_1_29
% 47.70/13.43 | (780) all_10_0_28 = all_0_4_4
% 47.70/13.44 | (904) vgetSomeExp(all_10_7_35) = all_10_2_30
% 47.70/13.44 | (905) vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34
% 47.70/13.44 | (906) vapp(all_10_6_34, all_10_11_39) = ve2
% 47.70/13.44 | (782) vsomeExp(all_10_1_29) = all_0_4_4
% 47.70/13.44 |
% 47.70/13.44 | From (1169) and (782) follows:
% 47.70/13.44 | (1962) vsomeExp(all_10_1_29) = all_0_6_6
% 47.70/13.44 |
% 47.70/13.44 | Instantiating formula (85) with all_0_6_6, all_10_1_29, all_9_1_17 and discharging atoms vsomeExp(all_10_1_29) = all_0_6_6, vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 47.70/13.44 | (1963) all_10_1_29 = all_9_1_17
% 47.70/13.44 |
% 47.70/13.44 | From (1963) and (1962) follows:
% 47.70/13.44 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 47.70/13.44 |
% 47.70/13.44 +-Applying beta-rule and splitting (116), into two cases.
% 47.70/13.44 |-Branch one:
% 47.70/13.44 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 47.70/13.44 |
% 47.70/13.44 +-Applying beta-rule and splitting (171), into two cases.
% 47.70/13.44 |-Branch one:
% 47.70/13.44 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 47.70/13.44 |
% 47.70/13.44 +-Applying beta-rule and splitting (172), into two cases.
% 47.70/13.44 |-Branch one:
% 47.70/13.44 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 47.70/13.44 |
% 47.70/13.44 +-Applying beta-rule and splitting (173), into two cases.
% 47.70/13.44 |-Branch one:
% 47.70/13.44 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 47.70/13.44 |
% 47.70/13.44 +-Applying beta-rule and splitting (174), into two cases.
% 47.70/13.44 |-Branch one:
% 47.70/13.44 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 47.70/13.44 |
% 47.70/13.44 +-Applying beta-rule and splitting (175), into two cases.
% 47.70/13.44 |-Branch one:
% 47.70/13.44 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.70/13.44 |
% 47.70/13.44 | Applying alpha-rule on (176) yields:
% 47.70/13.44 | (177) all_11_5_45 = all_0_3_3
% 47.70/13.44 | (178) all_11_4_44 = all_11_10_50
% 47.70/13.44 | (179) visValue(all_11_8_48) = 0
% 47.70/13.44 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 47.70/13.44 | (181) all_11_0_40 = all_0_1_1
% 47.70/13.44 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.70/13.44 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.70/13.44 | (184) vreduce(all_11_8_48) = all_11_10_50
% 47.70/13.44 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 47.70/13.44 | (186) ~ (all_11_3_43 = 0)
% 47.70/13.44 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 47.70/13.44 | (188) all_11_2_42 = 0
% 47.70/13.44 |
% 47.70/13.44 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.70/13.44 | (130) $false
% 47.70/13.44 |
% 47.70/13.44 |-The branch is then unsatisfiable
% 47.70/13.44 |-Branch two:
% 47.70/13.44 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.70/13.44 |
% 47.70/13.44 | Applying alpha-rule on (190) yields:
% 47.70/13.44 | (177) all_11_5_45 = all_0_3_3
% 47.70/13.44 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 47.70/13.44 | (193) visSomeExp(all_11_7_47) = 0
% 47.70/13.44 | (181) all_11_0_40 = all_0_1_1
% 47.70/13.44 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.70/13.44 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 47.70/13.44 | (197) vreduce(all_11_11_51) = all_11_7_47
% 47.70/13.44 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 47.70/13.44 | (199) all_11_3_43 = 0
% 47.70/13.44 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.70/13.44 | (201) all_11_4_44 = all_11_7_47
% 47.70/13.44 |
% 47.70/13.44 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.70/13.44 | (130) $false
% 47.70/13.44 |
% 47.70/13.44 |-The branch is then unsatisfiable
% 47.70/13.44 |-Branch two:
% 47.70/13.44 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.70/13.44 |
% 47.70/13.44 | Applying alpha-rule on (203) yields:
% 47.70/13.44 | (204) all_11_7_47 = all_11_10_50
% 47.70/13.44 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.70/13.44 | (206) all_11_6_46 = 0
% 47.70/13.44 | (207) all_11_3_43 = all_0_1_1
% 47.70/13.44 | (208) visSomeExp(all_11_10_50) = 0
% 47.70/13.44 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 47.70/13.44 | (210) vreduce(all_11_11_51) = all_11_10_50
% 47.70/13.44 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 47.70/13.44 | (212) all_11_8_48 = all_0_3_3
% 47.70/13.44 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 47.70/13.44 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 47.70/13.44 |
% 47.70/13.44 | Instantiating formula (74) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = all_0_1_1, yields:
% 47.70/13.44 | (130) $false
% 47.70/13.44 |
% 47.70/13.44 |-The branch is then unsatisfiable
% 47.70/13.44 |-Branch two:
% 47.70/13.44 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.70/13.44 |
% 47.70/13.44 | Applying alpha-rule on (216) yields:
% 47.70/13.44 | (177) all_11_5_45 = all_0_3_3
% 47.70/13.44 | (218) visValue(all_11_7_47) = all_11_2_42
% 47.70/13.44 | (219) all_0_1_1 = vnoExp
% 47.70/13.44 | (220) vreduce(all_11_7_47) = all_11_8_48
% 47.70/13.44 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.70/13.44 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 47.70/13.44 | (186) ~ (all_11_3_43 = 0)
% 47.70/13.44 | (224) all_11_4_44 = all_11_8_48
% 47.70/13.44 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 47.70/13.44 | (226) ~ (all_11_2_42 = 0)
% 47.70/13.44 |
% 47.70/13.44 | Instantiating formula (88) with all_0_3_3, all_11_7_47, all_11_6_46, ve2, ve1 and discharging atoms vapp(all_11_6_46, all_11_7_47) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.70/13.44 | (227) all_11_6_46 = ve1
% 47.70/13.44 |
% 47.70/13.44 | Instantiating formula (66) with ve1, all_9_11_27, all_9_6_22, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(all_9_6_22, all_9_11_27) = ve1, yields:
% 47.70/13.44 | (228) ~ (vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1)
% 47.70/13.44 |
% 47.70/13.44 | From (227) and (221) follows:
% 47.70/13.44 | (229) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1
% 47.70/13.44 |
% 47.70/13.44 | Using (229) and (228) yields:
% 47.70/13.44 | (130) $false
% 47.70/13.44 |
% 47.70/13.44 |-The branch is then unsatisfiable
% 47.70/13.44 |-Branch two:
% 47.70/13.44 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.70/13.44 |
% 47.70/13.44 | Applying alpha-rule on (231) yields:
% 47.70/13.44 | (232) all_11_7_47 = all_11_9_49
% 47.70/13.44 | (219) all_0_1_1 = vnoExp
% 47.70/13.44 | (234) ~ (all_11_6_46 = 0)
% 47.70/13.44 | (235) vreduce(all_11_10_50) = all_11_9_49
% 47.70/13.44 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.70/13.44 | (212) all_11_8_48 = all_0_3_3
% 47.70/13.44 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 47.70/13.44 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 47.70/13.44 |
% 47.70/13.44 | Instantiating formula (55) with ve1, all_11_9_49, all_0_6_6 and discharging atoms vreduce(ve1) = all_0_6_6, yields:
% 47.70/13.44 | (240) all_11_9_49 = all_0_6_6 | ~ (vreduce(ve1) = all_11_9_49)
% 47.70/13.44 |
% 47.70/13.44 | Instantiating formula (47) with all_11_6_46, all_0_6_6, all_9_1_17 and discharging atoms vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 47.70/13.44 | (241) all_11_6_46 = 0 | ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.70/13.44 |
% 47.70/13.44 | Instantiating formula (88) with all_0_3_3, all_11_11_51, all_11_10_50, ve2, ve1 and discharging atoms vapp(all_11_10_50, all_11_11_51) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.70/13.44 | (242) all_11_10_50 = ve1
% 47.70/13.44 |
% 47.70/13.44 | From (242) and (235) follows:
% 47.70/13.44 | (243) vreduce(ve1) = all_11_9_49
% 47.70/13.44 |
% 47.70/13.44 +-Applying beta-rule and splitting (241), into two cases.
% 47.70/13.44 |-Branch one:
% 47.70/13.44 | (244) ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.70/13.44 |
% 47.70/13.44 +-Applying beta-rule and splitting (240), into two cases.
% 47.70/13.44 |-Branch one:
% 47.70/13.44 | (245) ~ (vreduce(ve1) = all_11_9_49)
% 47.70/13.45 |
% 47.70/13.45 | Using (243) and (245) yields:
% 47.70/13.45 | (130) $false
% 47.70/13.45 |
% 47.70/13.45 |-The branch is then unsatisfiable
% 47.70/13.45 |-Branch two:
% 47.70/13.45 | (243) vreduce(ve1) = all_11_9_49
% 47.70/13.45 | (248) all_11_9_49 = all_0_6_6
% 47.70/13.45 |
% 47.70/13.45 | From (248) and (239) follows:
% 47.70/13.45 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.70/13.45 |
% 47.70/13.45 | Using (249) and (244) yields:
% 47.70/13.45 | (130) $false
% 47.70/13.45 |
% 47.70/13.45 |-The branch is then unsatisfiable
% 47.70/13.45 |-Branch two:
% 47.70/13.45 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.70/13.45 | (206) all_11_6_46 = 0
% 47.70/13.45 |
% 47.70/13.45 | Equations (206) can reduce 234 to:
% 47.70/13.45 | (165) $false
% 47.70/13.45 |
% 47.70/13.45 |-The branch is then unsatisfiable
% 47.70/13.45 |-Branch two:
% 47.70/13.45 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.70/13.45 |
% 47.70/13.45 | Applying alpha-rule on (254) yields:
% 47.70/13.45 | (212) all_11_8_48 = all_0_3_3
% 47.70/13.45 | (219) all_0_1_1 = vnoExp
% 47.70/13.45 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.70/13.45 |
% 47.70/13.45 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3, yields:
% 47.70/13.45 | (130) $false
% 47.70/13.45 |
% 47.70/13.45 |-The branch is then unsatisfiable
% 47.70/13.45 |-Branch two:
% 47.70/13.45 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 47.70/13.45 |
% 47.70/13.45 | Applying alpha-rule on (259) yields:
% 47.70/13.45 | (260) all_11_10_50 = all_0_3_3
% 47.70/13.45 | (219) all_0_1_1 = vnoExp
% 47.70/13.45 | (262) vvar(all_11_11_51) = all_0_3_3
% 47.70/13.45 |
% 47.70/13.45 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_11_11_51) = all_0_3_3, yields:
% 47.70/13.45 | (130) $false
% 47.70/13.45 |
% 47.70/13.45 |-The branch is then unsatisfiable
% 47.70/13.45 |-Branch two:
% 47.70/13.45 | (1006) all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)
% 47.70/13.45 |
% 47.70/13.45 | Applying alpha-rule on (1006) yields:
% 47.70/13.45 | (1007) all_10_7_35 = all_10_10_38
% 47.70/13.45 | (1008) vgetSomeExp(all_10_10_38) = all_10_5_33
% 47.70/13.45 | (1009) vapp(all_10_5_33, all_10_9_37) = all_10_4_32
% 47.70/13.45 | (1010) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)
% 47.70/13.45 | (1011) visSomeExp(all_10_10_38) = 0
% 47.70/13.45 | (1012) all_10_8_36 = ve2
% 47.70/13.45 | (1013) vreduce(all_10_11_39) = all_10_10_38
% 47.70/13.45 | (1014) all_10_6_34 = 0
% 47.70/13.45 | (1015) vsomeExp(all_10_4_32) = all_0_4_4
% 47.70/13.45 | (1016) vapp(all_10_11_39, all_10_9_37) = ve2
% 47.70/13.45 | (1017) all_10_3_31 = all_0_4_4
% 47.70/13.45 |
% 47.70/13.45 | From (1169) and (1015) follows:
% 47.70/13.45 | (2178) vsomeExp(all_10_4_32) = all_0_6_6
% 47.70/13.45 |
% 47.70/13.45 | Instantiating formula (85) with all_0_6_6, all_10_4_32, all_9_1_17 and discharging atoms vsomeExp(all_10_4_32) = all_0_6_6, vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 47.70/13.45 | (2179) all_10_4_32 = all_9_1_17
% 47.70/13.45 |
% 47.70/13.45 | From (2179) and (2178) follows:
% 47.70/13.45 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 47.70/13.45 |
% 47.70/13.45 +-Applying beta-rule and splitting (116), into two cases.
% 47.70/13.45 |-Branch one:
% 47.70/13.45 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 47.70/13.45 |
% 47.70/13.45 +-Applying beta-rule and splitting (171), into two cases.
% 47.70/13.45 |-Branch one:
% 47.70/13.45 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 47.70/13.45 |
% 47.70/13.45 +-Applying beta-rule and splitting (172), into two cases.
% 47.70/13.45 |-Branch one:
% 47.70/13.45 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 47.70/13.45 |
% 47.70/13.45 +-Applying beta-rule and splitting (173), into two cases.
% 47.70/13.45 |-Branch one:
% 47.70/13.45 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 47.70/13.45 |
% 47.70/13.45 +-Applying beta-rule and splitting (174), into two cases.
% 47.70/13.45 |-Branch one:
% 47.70/13.45 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 47.70/13.45 |
% 47.70/13.45 +-Applying beta-rule and splitting (175), into two cases.
% 47.70/13.45 |-Branch one:
% 47.70/13.45 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.70/13.45 |
% 47.70/13.45 | Applying alpha-rule on (176) yields:
% 47.70/13.45 | (177) all_11_5_45 = all_0_3_3
% 47.70/13.45 | (178) all_11_4_44 = all_11_10_50
% 47.70/13.45 | (179) visValue(all_11_8_48) = 0
% 47.70/13.45 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 47.70/13.45 | (181) all_11_0_40 = all_0_1_1
% 47.70/13.45 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.70/13.45 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.70/13.45 | (184) vreduce(all_11_8_48) = all_11_10_50
% 47.70/13.45 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 47.70/13.45 | (186) ~ (all_11_3_43 = 0)
% 47.70/13.45 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 47.70/13.45 | (188) all_11_2_42 = 0
% 47.70/13.45 |
% 47.70/13.45 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.70/13.45 | (130) $false
% 47.70/13.45 |
% 47.70/13.45 |-The branch is then unsatisfiable
% 47.70/13.45 |-Branch two:
% 47.70/13.45 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.70/13.45 |
% 47.70/13.45 | Applying alpha-rule on (190) yields:
% 47.70/13.45 | (177) all_11_5_45 = all_0_3_3
% 47.70/13.45 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 47.70/13.45 | (193) visSomeExp(all_11_7_47) = 0
% 47.70/13.45 | (181) all_11_0_40 = all_0_1_1
% 47.70/13.45 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.70/13.45 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 47.70/13.45 | (197) vreduce(all_11_11_51) = all_11_7_47
% 47.70/13.45 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 47.70/13.45 | (199) all_11_3_43 = 0
% 47.70/13.45 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.70/13.45 | (201) all_11_4_44 = all_11_7_47
% 47.70/13.45 |
% 47.70/13.45 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.70/13.45 | (130) $false
% 47.70/13.45 |
% 47.70/13.45 |-The branch is then unsatisfiable
% 47.70/13.45 |-Branch two:
% 47.70/13.45 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.70/13.45 |
% 47.70/13.45 | Applying alpha-rule on (203) yields:
% 47.70/13.45 | (204) all_11_7_47 = all_11_10_50
% 47.70/13.45 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.70/13.45 | (206) all_11_6_46 = 0
% 47.70/13.45 | (207) all_11_3_43 = all_0_1_1
% 47.70/13.45 | (208) visSomeExp(all_11_10_50) = 0
% 47.70/13.45 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 47.70/13.45 | (210) vreduce(all_11_11_51) = all_11_10_50
% 47.70/13.45 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 47.70/13.45 | (212) all_11_8_48 = all_0_3_3
% 47.70/13.45 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 47.70/13.45 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 47.70/13.45 |
% 47.70/13.45 | Instantiating formula (74) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = all_0_1_1, yields:
% 47.70/13.45 | (130) $false
% 47.70/13.45 |
% 47.70/13.45 |-The branch is then unsatisfiable
% 47.70/13.45 |-Branch two:
% 47.70/13.45 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.70/13.45 |
% 47.70/13.45 | Applying alpha-rule on (216) yields:
% 47.70/13.45 | (177) all_11_5_45 = all_0_3_3
% 47.70/13.45 | (218) visValue(all_11_7_47) = all_11_2_42
% 47.70/13.45 | (219) all_0_1_1 = vnoExp
% 47.70/13.45 | (220) vreduce(all_11_7_47) = all_11_8_48
% 47.70/13.45 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.70/13.45 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 47.70/13.45 | (186) ~ (all_11_3_43 = 0)
% 47.70/13.45 | (224) all_11_4_44 = all_11_8_48
% 47.70/13.45 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 47.70/13.45 | (226) ~ (all_11_2_42 = 0)
% 47.70/13.45 |
% 47.70/13.45 | Instantiating formula (88) with all_0_3_3, all_11_7_47, all_11_6_46, ve2, ve1 and discharging atoms vapp(all_11_6_46, all_11_7_47) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.70/13.45 | (227) all_11_6_46 = ve1
% 47.70/13.45 |
% 47.70/13.45 | Instantiating formula (66) with ve1, all_9_11_27, all_9_6_22, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(all_9_6_22, all_9_11_27) = ve1, yields:
% 47.70/13.46 | (228) ~ (vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1)
% 47.70/13.46 |
% 47.70/13.46 | From (227) and (221) follows:
% 47.70/13.46 | (229) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1
% 47.70/13.46 |
% 47.70/13.46 | Using (229) and (228) yields:
% 47.70/13.46 | (130) $false
% 47.70/13.46 |
% 47.70/13.46 |-The branch is then unsatisfiable
% 47.70/13.46 |-Branch two:
% 47.70/13.46 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.70/13.46 |
% 47.70/13.46 | Applying alpha-rule on (231) yields:
% 47.70/13.46 | (232) all_11_7_47 = all_11_9_49
% 47.70/13.46 | (219) all_0_1_1 = vnoExp
% 47.70/13.46 | (234) ~ (all_11_6_46 = 0)
% 47.70/13.46 | (235) vreduce(all_11_10_50) = all_11_9_49
% 47.70/13.46 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.70/13.46 | (212) all_11_8_48 = all_0_3_3
% 47.70/13.46 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 47.70/13.46 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 47.70/13.46 |
% 47.70/13.46 | Instantiating formula (55) with ve1, all_11_9_49, all_0_6_6 and discharging atoms vreduce(ve1) = all_0_6_6, yields:
% 47.70/13.46 | (240) all_11_9_49 = all_0_6_6 | ~ (vreduce(ve1) = all_11_9_49)
% 47.70/13.46 |
% 47.70/13.46 | Instantiating formula (47) with all_11_6_46, all_0_6_6, all_9_1_17 and discharging atoms vsomeExp(all_9_1_17) = all_0_6_6, yields:
% 47.70/13.46 | (241) all_11_6_46 = 0 | ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.70/13.46 |
% 47.70/13.46 | Instantiating formula (88) with all_0_3_3, all_11_11_51, all_11_10_50, ve2, ve1 and discharging atoms vapp(all_11_10_50, all_11_11_51) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.70/13.46 | (242) all_11_10_50 = ve1
% 47.70/13.46 |
% 47.70/13.46 | From (242) and (235) follows:
% 47.70/13.46 | (243) vreduce(ve1) = all_11_9_49
% 47.70/13.46 |
% 47.70/13.46 +-Applying beta-rule and splitting (241), into two cases.
% 47.70/13.46 |-Branch one:
% 47.70/13.46 | (244) ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.70/13.46 |
% 47.70/13.46 +-Applying beta-rule and splitting (240), into two cases.
% 47.70/13.46 |-Branch one:
% 47.70/13.46 | (245) ~ (vreduce(ve1) = all_11_9_49)
% 47.70/13.46 |
% 47.70/13.46 | Using (243) and (245) yields:
% 47.70/13.46 | (130) $false
% 47.70/13.46 |
% 47.70/13.46 |-The branch is then unsatisfiable
% 47.70/13.46 |-Branch two:
% 47.70/13.46 | (243) vreduce(ve1) = all_11_9_49
% 47.70/13.46 | (248) all_11_9_49 = all_0_6_6
% 47.70/13.46 |
% 47.70/13.46 | From (248) and (239) follows:
% 47.70/13.46 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.70/13.46 |
% 47.70/13.46 | Using (249) and (244) yields:
% 47.70/13.46 | (130) $false
% 47.70/13.46 |
% 47.70/13.46 |-The branch is then unsatisfiable
% 47.70/13.46 |-Branch two:
% 47.70/13.46 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.70/13.46 | (206) all_11_6_46 = 0
% 47.70/13.46 |
% 47.70/13.46 | Equations (206) can reduce 234 to:
% 47.70/13.46 | (165) $false
% 47.70/13.46 |
% 47.70/13.46 |-The branch is then unsatisfiable
% 47.70/13.46 |-Branch two:
% 47.70/13.46 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.70/13.46 |
% 47.70/13.46 | Applying alpha-rule on (254) yields:
% 47.70/13.46 | (212) all_11_8_48 = all_0_3_3
% 47.70/13.46 | (219) all_0_1_1 = vnoExp
% 47.70/13.46 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.70/13.46 |
% 47.70/13.46 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3, yields:
% 47.70/13.46 | (130) $false
% 47.70/13.46 |
% 47.70/13.46 |-The branch is then unsatisfiable
% 47.70/13.46 |-Branch two:
% 47.70/13.46 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 47.70/13.46 |
% 47.70/13.46 | Applying alpha-rule on (259) yields:
% 47.70/13.46 | (260) all_11_10_50 = all_0_3_3
% 47.70/13.46 | (219) all_0_1_1 = vnoExp
% 47.70/13.46 | (262) vvar(all_11_11_51) = all_0_3_3
% 47.70/13.46 |
% 47.70/13.46 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_11_11_51) = all_0_3_3, yields:
% 47.70/13.46 | (130) $false
% 47.70/13.46 |
% 47.70/13.46 |-The branch is then unsatisfiable
% 47.70/13.46 |-Branch two:
% 47.70/13.46 | (1116) all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34
% 47.70/13.46 |
% 47.70/13.46 | Applying alpha-rule on (1116) yields:
% 47.70/13.46 | (772) all_10_5_33 = ve2
% 47.70/13.46 | (1118) all_10_4_32 = all_10_8_36
% 47.70/13.46 | (775) ~ (all_10_3_31 = 0)
% 47.70/13.46 | (1120) ~ (all_10_2_30 = 0)
% 47.70/13.46 | (1121) visValue(all_10_7_35) = all_10_2_30
% 47.70/13.46 | (1122) vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34
% 47.70/13.46 | (1123) all_0_4_4 = vnoExp
% 47.70/13.46 | (1124) vreduce(all_10_7_35) = all_10_8_36
% 47.70/13.46 | (1125) visSomeExp(all_10_8_36) = all_10_3_31
% 47.70/13.46 | (1126) vapp(all_10_6_34, all_10_7_35) = ve2
% 47.70/13.46 |
% 47.70/13.46 | Combining equations (1123,1169) yields a new equation:
% 47.70/13.46 | (502) all_0_6_6 = vnoExp
% 47.70/13.46 |
% 47.70/13.46 | Equations (502) can reduce 1926 to:
% 47.70/13.46 | (165) $false
% 47.70/13.46 |
% 47.70/13.46 |-The branch is then unsatisfiable
% 47.70/13.46 |-Branch two:
% 47.70/13.46 | (1128) all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)
% 47.70/13.46 |
% 47.70/13.46 | Applying alpha-rule on (1128) yields:
% 47.70/13.46 | (1129) vreduce(all_10_10_38) = all_10_9_37
% 47.70/13.46 | (1130) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)
% 47.70/13.46 | (1123) all_0_4_4 = vnoExp
% 47.70/13.46 | (1012) all_10_8_36 = ve2
% 47.70/13.46 | (1133) ~ (all_10_6_34 = 0)
% 47.70/13.46 | (1134) vapp(all_10_10_38, all_10_11_39) = ve2
% 47.70/13.46 | (1135) visSomeExp(all_10_9_37) = all_10_6_34
% 47.70/13.46 | (1136) all_10_7_35 = all_10_9_37
% 47.70/13.46 |
% 47.70/13.46 | Combining equations (1123,1169) yields a new equation:
% 47.70/13.46 | (502) all_0_6_6 = vnoExp
% 47.70/13.46 |
% 47.70/13.46 | Equations (502) can reduce 1926 to:
% 47.70/13.46 | (165) $false
% 47.70/13.46 |
% 47.70/13.46 |-The branch is then unsatisfiable
% 47.70/13.46 |-Branch two:
% 47.70/13.46 | (1138) all_10_8_36 = ve2 & all_0_4_4 = vnoExp & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2
% 47.70/13.46 |
% 47.70/13.46 | Applying alpha-rule on (1138) yields:
% 47.70/13.46 | (1012) all_10_8_36 = ve2
% 47.70/13.46 | (1123) all_0_4_4 = vnoExp
% 47.70/13.46 | (1141) vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2
% 47.70/13.46 |
% 47.70/13.46 | Combining equations (1169,1123) yields a new equation:
% 47.70/13.46 | (2285) all_0_6_6 = vnoExp
% 47.70/13.46 |
% 47.70/13.46 | Simplifying 2285 yields:
% 47.70/13.46 | (502) all_0_6_6 = vnoExp
% 47.70/13.46 |
% 47.70/13.46 | Equations (502) can reduce 1926 to:
% 47.70/13.46 | (165) $false
% 47.70/13.46 |
% 47.70/13.46 |-The branch is then unsatisfiable
% 47.70/13.46 |-Branch two:
% 47.70/13.46 | (1143) all_10_10_38 = ve2 & all_0_4_4 = vnoExp & vvar(all_10_11_39) = ve2
% 47.70/13.46 |
% 47.70/13.46 | Applying alpha-rule on (1143) yields:
% 47.70/13.46 | (1144) all_10_10_38 = ve2
% 47.70/13.46 | (1123) all_0_4_4 = vnoExp
% 47.70/13.46 | (1146) vvar(all_10_11_39) = ve2
% 47.70/13.46 |
% 47.70/13.46 | Combining equations (1169,1123) yields a new equation:
% 47.70/13.46 | (2285) all_0_6_6 = vnoExp
% 47.70/13.46 |
% 47.70/13.46 | Simplifying 2285 yields:
% 47.70/13.46 | (502) all_0_6_6 = vnoExp
% 47.70/13.46 |
% 47.70/13.46 | Equations (502) can reduce 1926 to:
% 47.70/13.46 | (165) $false
% 47.70/13.46 |
% 47.70/13.46 |-The branch is then unsatisfiable
% 47.70/13.46 |-Branch two:
% 47.70/13.46 | (378) all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)
% 47.70/13.46 |
% 47.70/13.46 | Applying alpha-rule on (378) yields:
% 47.70/13.46 | (379) vapp(all_9_5_21, all_9_9_25) = all_9_4_20
% 47.70/13.46 | (380) vsomeExp(all_9_4_20) = all_0_6_6
% 47.70/13.46 | (381) all_9_7_23 = all_9_10_26
% 47.70/13.46 | (382) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)
% 47.70/13.46 | (383) all_9_8_24 = ve1
% 47.70/13.46 | (384) all_9_6_22 = 0
% 47.70/13.46 | (385) visSomeExp(all_9_10_26) = 0
% 47.70/13.46 | (386) vapp(all_9_11_27, all_9_9_25) = ve1
% 47.70/13.46 | (387) all_9_3_19 = all_0_6_6
% 47.70/13.46 | (388) vreduce(all_9_11_27) = all_9_10_26
% 47.70/13.46 | (389) vgetSomeExp(all_9_10_26) = all_9_5_21
% 47.70/13.46 |
% 47.70/13.46 | Instantiating formula (40) with all_9_4_20 yields:
% 47.70/13.46 | (2726) ~ (vsomeExp(all_9_4_20) = vnoExp)
% 47.70/13.46 |
% 47.70/13.46 | Instantiating formula (92) with ve1, all_9_9_25, all_9_11_27 and discharging atoms vapp(all_9_11_27, all_9_9_25) = ve1, yields:
% 47.70/13.46 | (162) ~ (visValue(ve1) = 0)
% 47.70/13.46 |
% 47.70/13.46 | Using (380) and (2726) yields:
% 47.70/13.46 | (1926) ~ (all_0_6_6 = vnoExp)
% 47.70/13.46 |
% 47.70/13.46 | Using (68) and (162) yields:
% 47.70/13.46 | (163) ~ (all_0_7_7 = 0)
% 47.70/13.46 |
% 47.70/13.46 +-Applying beta-rule and splitting (661), into two cases.
% 47.70/13.46 |-Branch one:
% 47.70/13.46 | (761) all_0_5_5 = 0
% 47.70/13.46 |
% 47.70/13.46 | Combining equations (761,1326) yields a new equation:
% 47.70/13.46 | (164) all_0_7_7 = 0
% 47.70/13.46 |
% 47.70/13.46 | Equations (164) can reduce 163 to:
% 47.70/13.46 | (165) $false
% 47.70/13.46 |
% 47.70/13.46 |-The branch is then unsatisfiable
% 47.70/13.46 |-Branch two:
% 47.70/13.46 | (760) ~ (all_0_5_5 = 0)
% 47.70/13.46 | (764) ? [v0] : vsomeExp(v0) = all_0_4_4
% 47.70/13.46 |
% 47.70/13.46 | Instantiating (764) with all_112_0_486 yields:
% 47.70/13.46 | (2735) vsomeExp(all_112_0_486) = all_0_4_4
% 47.70/13.46 |
% 47.70/13.46 | Equations (1326) can reduce 760 to:
% 47.70/13.46 | (163) ~ (all_0_7_7 = 0)
% 47.70/13.46 |
% 47.70/13.46 | From (1169) and (2735) follows:
% 47.70/13.46 | (2737) vsomeExp(all_112_0_486) = all_0_6_6
% 47.70/13.46 |
% 47.70/13.46 +-Applying beta-rule and splitting (143), into two cases.
% 47.70/13.46 |-Branch one:
% 47.70/13.46 | (164) all_0_7_7 = 0
% 47.70/13.46 |
% 47.70/13.46 | Equations (164) can reduce 163 to:
% 47.70/13.46 | (165) $false
% 47.70/13.46 |
% 47.70/13.46 |-The branch is then unsatisfiable
% 47.70/13.46 |-Branch two:
% 47.70/13.46 | (163) ~ (all_0_7_7 = 0)
% 47.70/13.46 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.70/13.46 |
% 47.70/13.46 | Instantiating (167) with all_117_0_487 yields:
% 47.70/13.46 | (2742) vsomeExp(all_117_0_487) = all_0_6_6
% 47.70/13.46 |
% 47.70/13.46 | Instantiating formula (85) with all_0_6_6, all_117_0_487, all_9_4_20 and discharging atoms vsomeExp(all_117_0_487) = all_0_6_6, vsomeExp(all_9_4_20) = all_0_6_6, yields:
% 47.70/13.46 | (2743) all_117_0_487 = all_9_4_20
% 47.70/13.46 |
% 47.70/13.46 | Instantiating formula (85) with all_0_6_6, all_112_0_486, all_117_0_487 and discharging atoms vsomeExp(all_117_0_487) = all_0_6_6, vsomeExp(all_112_0_486) = all_0_6_6, yields:
% 47.70/13.46 | (2744) all_117_0_487 = all_112_0_486
% 47.70/13.46 |
% 47.70/13.46 | Combining equations (2743,2744) yields a new equation:
% 47.70/13.46 | (2745) all_112_0_486 = all_9_4_20
% 47.70/13.46 |
% 47.70/13.46 | From (2745) and (2737) follows:
% 47.70/13.47 | (380) vsomeExp(all_9_4_20) = all_0_6_6
% 47.70/13.47 |
% 47.70/13.47 +-Applying beta-rule and splitting (115), into two cases.
% 47.70/13.47 |-Branch one:
% 47.70/13.47 | (766) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34) | (all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)) | (all_10_8_36 = ve2 & all_0_4_4 = vnoExp & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2)
% 47.70/13.47 |
% 47.70/13.47 +-Applying beta-rule and splitting (766), into two cases.
% 47.70/13.47 |-Branch one:
% 47.70/13.47 | (767) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34) | (all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38))
% 47.70/13.47 |
% 47.70/13.47 +-Applying beta-rule and splitting (767), into two cases.
% 47.70/13.47 |-Branch one:
% 47.70/13.47 | (768) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34)
% 47.70/13.47 |
% 47.70/13.47 +-Applying beta-rule and splitting (768), into two cases.
% 47.70/13.47 |-Branch one:
% 47.70/13.47 | (769) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39))
% 47.70/13.47 |
% 47.70/13.47 +-Applying beta-rule and splitting (769), into two cases.
% 47.70/13.47 |-Branch one:
% 47.70/13.47 | (770) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34)
% 47.70/13.47 |
% 47.70/13.47 +-Applying beta-rule and splitting (770), into two cases.
% 47.70/13.47 |-Branch one:
% 47.70/13.47 | (771) all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34
% 47.70/13.47 |
% 47.70/13.47 | Applying alpha-rule on (771) yields:
% 47.70/13.47 | (772) all_10_5_33 = ve2
% 47.70/13.47 | (773) visValue(all_10_8_36) = 0
% 47.70/13.47 | (774) all_10_4_32 = all_10_10_38
% 47.70/13.47 | (775) ~ (all_10_3_31 = 0)
% 47.70/13.47 | (776) all_10_2_30 = 0
% 47.70/13.47 | (777) vapp(all_10_6_34, all_10_8_36) = ve2
% 47.70/13.47 | (778) vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29
% 47.70/13.47 | (779) vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34
% 47.70/13.47 | (780) all_10_0_28 = all_0_4_4
% 47.70/13.47 | (781) visSomeExp(all_10_10_38) = all_10_3_31
% 47.70/13.47 | (782) vsomeExp(all_10_1_29) = all_0_4_4
% 47.70/13.47 | (783) vreduce(all_10_8_36) = all_10_10_38
% 47.70/13.47 |
% 47.70/13.47 | From (1169) and (782) follows:
% 47.70/13.47 | (1962) vsomeExp(all_10_1_29) = all_0_6_6
% 47.70/13.47 |
% 47.70/13.47 | Instantiating formula (85) with all_0_6_6, all_10_1_29, all_9_4_20 and discharging atoms vsomeExp(all_10_1_29) = all_0_6_6, vsomeExp(all_9_4_20) = all_0_6_6, yields:
% 47.70/13.47 | (2766) all_10_1_29 = all_9_4_20
% 47.70/13.47 |
% 47.70/13.47 | From (2766) and (1962) follows:
% 47.70/13.47 | (380) vsomeExp(all_9_4_20) = all_0_6_6
% 47.70/13.47 |
% 47.70/13.47 +-Applying beta-rule and splitting (116), into two cases.
% 47.70/13.47 |-Branch one:
% 47.70/13.47 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 47.70/13.47 |
% 47.70/13.47 +-Applying beta-rule and splitting (171), into two cases.
% 47.70/13.47 |-Branch one:
% 47.70/13.47 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 47.86/13.47 |
% 47.86/13.47 +-Applying beta-rule and splitting (172), into two cases.
% 47.86/13.47 |-Branch one:
% 47.86/13.47 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 47.86/13.47 |
% 47.86/13.47 +-Applying beta-rule and splitting (173), into two cases.
% 47.86/13.47 |-Branch one:
% 47.86/13.47 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 47.86/13.48 |
% 47.86/13.48 +-Applying beta-rule and splitting (174), into two cases.
% 47.86/13.48 |-Branch one:
% 47.86/13.48 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 47.86/13.48 |
% 47.86/13.48 +-Applying beta-rule and splitting (175), into two cases.
% 47.86/13.48 |-Branch one:
% 47.86/13.48 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.86/13.48 |
% 47.86/13.48 | Applying alpha-rule on (176) yields:
% 47.86/13.48 | (177) all_11_5_45 = all_0_3_3
% 47.86/13.48 | (178) all_11_4_44 = all_11_10_50
% 47.86/13.48 | (179) visValue(all_11_8_48) = 0
% 47.86/13.48 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 47.86/13.48 | (181) all_11_0_40 = all_0_1_1
% 47.86/13.48 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.86/13.48 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.86/13.48 | (184) vreduce(all_11_8_48) = all_11_10_50
% 47.86/13.48 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 47.86/13.48 | (186) ~ (all_11_3_43 = 0)
% 47.86/13.48 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 47.86/13.48 | (188) all_11_2_42 = 0
% 47.86/13.48 |
% 47.86/13.48 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.86/13.48 | (130) $false
% 47.86/13.48 |
% 47.86/13.48 |-The branch is then unsatisfiable
% 47.86/13.48 |-Branch two:
% 47.86/13.48 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.86/13.48 |
% 47.86/13.48 | Applying alpha-rule on (190) yields:
% 47.86/13.48 | (177) all_11_5_45 = all_0_3_3
% 47.86/13.48 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 47.86/13.48 | (193) visSomeExp(all_11_7_47) = 0
% 47.86/13.48 | (181) all_11_0_40 = all_0_1_1
% 47.86/13.48 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.86/13.48 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 47.86/13.48 | (197) vreduce(all_11_11_51) = all_11_7_47
% 47.86/13.48 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 47.86/13.48 | (199) all_11_3_43 = 0
% 47.86/13.48 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.86/13.48 | (201) all_11_4_44 = all_11_7_47
% 47.86/13.48 |
% 47.86/13.48 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.86/13.48 | (130) $false
% 47.86/13.48 |
% 47.86/13.48 |-The branch is then unsatisfiable
% 47.86/13.48 |-Branch two:
% 47.86/13.48 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.86/13.48 |
% 47.86/13.48 | Applying alpha-rule on (203) yields:
% 47.86/13.48 | (204) all_11_7_47 = all_11_10_50
% 47.86/13.48 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.86/13.48 | (206) all_11_6_46 = 0
% 47.86/13.48 | (207) all_11_3_43 = all_0_1_1
% 47.86/13.48 | (208) visSomeExp(all_11_10_50) = 0
% 47.86/13.48 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 47.86/13.48 | (210) vreduce(all_11_11_51) = all_11_10_50
% 47.86/13.48 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 47.86/13.48 | (212) all_11_8_48 = all_0_3_3
% 47.86/13.48 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 47.86/13.48 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 47.86/13.48 |
% 47.86/13.48 | Instantiating formula (74) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = all_0_1_1, yields:
% 47.86/13.48 | (130) $false
% 47.86/13.48 |
% 47.86/13.48 |-The branch is then unsatisfiable
% 47.86/13.48 |-Branch two:
% 47.86/13.48 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.86/13.48 |
% 47.86/13.48 | Applying alpha-rule on (216) yields:
% 47.86/13.48 | (177) all_11_5_45 = all_0_3_3
% 47.86/13.48 | (218) visValue(all_11_7_47) = all_11_2_42
% 47.86/13.48 | (219) all_0_1_1 = vnoExp
% 47.86/13.48 | (220) vreduce(all_11_7_47) = all_11_8_48
% 47.86/13.48 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.86/13.48 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 47.86/13.48 | (186) ~ (all_11_3_43 = 0)
% 47.86/13.48 | (224) all_11_4_44 = all_11_8_48
% 47.86/13.48 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 47.86/13.48 | (226) ~ (all_11_2_42 = 0)
% 47.86/13.48 |
% 47.86/13.48 | Instantiating formula (88) with all_0_3_3, all_11_7_47, all_11_6_46, ve2, ve1 and discharging atoms vapp(all_11_6_46, all_11_7_47) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.86/13.48 | (227) all_11_6_46 = ve1
% 47.86/13.48 |
% 47.86/13.48 | Instantiating formula (66) with ve1, all_9_9_25, all_9_11_27, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(all_9_11_27, all_9_9_25) = ve1, yields:
% 47.86/13.48 | (228) ~ (vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1)
% 47.86/13.48 |
% 47.86/13.48 | From (227) and (221) follows:
% 47.86/13.48 | (229) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1
% 47.86/13.48 |
% 47.86/13.48 | Using (229) and (228) yields:
% 47.86/13.48 | (130) $false
% 47.86/13.48 |
% 47.86/13.48 |-The branch is then unsatisfiable
% 47.86/13.48 |-Branch two:
% 47.86/13.48 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.86/13.48 |
% 47.86/13.48 | Applying alpha-rule on (231) yields:
% 47.86/13.48 | (232) all_11_7_47 = all_11_9_49
% 47.86/13.48 | (219) all_0_1_1 = vnoExp
% 47.86/13.48 | (234) ~ (all_11_6_46 = 0)
% 47.86/13.48 | (235) vreduce(all_11_10_50) = all_11_9_49
% 47.86/13.48 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.86/13.48 | (212) all_11_8_48 = all_0_3_3
% 47.86/13.48 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 47.86/13.48 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 47.86/13.48 |
% 47.86/13.48 | Instantiating formula (55) with ve1, all_11_9_49, all_0_6_6 and discharging atoms vreduce(ve1) = all_0_6_6, yields:
% 47.86/13.48 | (240) all_11_9_49 = all_0_6_6 | ~ (vreduce(ve1) = all_11_9_49)
% 47.86/13.48 |
% 47.86/13.48 | Instantiating formula (47) with all_11_6_46, all_0_6_6, all_9_4_20 and discharging atoms vsomeExp(all_9_4_20) = all_0_6_6, yields:
% 47.86/13.48 | (241) all_11_6_46 = 0 | ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.86/13.48 |
% 47.86/13.48 | Instantiating formula (88) with all_0_3_3, all_11_11_51, all_11_10_50, ve2, ve1 and discharging atoms vapp(all_11_10_50, all_11_11_51) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.86/13.48 | (242) all_11_10_50 = ve1
% 47.86/13.48 |
% 47.86/13.48 | From (242) and (235) follows:
% 47.86/13.48 | (243) vreduce(ve1) = all_11_9_49
% 47.86/13.48 |
% 47.86/13.48 +-Applying beta-rule and splitting (241), into two cases.
% 47.86/13.48 |-Branch one:
% 47.86/13.48 | (244) ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.86/13.48 |
% 47.86/13.48 +-Applying beta-rule and splitting (240), into two cases.
% 47.86/13.48 |-Branch one:
% 47.86/13.48 | (245) ~ (vreduce(ve1) = all_11_9_49)
% 47.86/13.48 |
% 47.86/13.48 | Using (243) and (245) yields:
% 47.86/13.48 | (130) $false
% 47.86/13.48 |
% 47.86/13.48 |-The branch is then unsatisfiable
% 47.86/13.48 |-Branch two:
% 47.86/13.48 | (243) vreduce(ve1) = all_11_9_49
% 47.86/13.48 | (248) all_11_9_49 = all_0_6_6
% 47.86/13.48 |
% 47.86/13.48 | From (248) and (239) follows:
% 47.86/13.48 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.86/13.48 |
% 47.86/13.48 | Using (249) and (244) yields:
% 47.86/13.48 | (130) $false
% 47.86/13.48 |
% 47.86/13.48 |-The branch is then unsatisfiable
% 47.86/13.48 |-Branch two:
% 47.86/13.48 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.86/13.48 | (206) all_11_6_46 = 0
% 47.86/13.48 |
% 47.86/13.48 | Equations (206) can reduce 234 to:
% 47.86/13.48 | (165) $false
% 47.86/13.48 |
% 47.86/13.48 |-The branch is then unsatisfiable
% 47.86/13.48 |-Branch two:
% 47.86/13.48 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.86/13.48 |
% 47.86/13.48 | Applying alpha-rule on (254) yields:
% 47.86/13.48 | (212) all_11_8_48 = all_0_3_3
% 47.86/13.48 | (219) all_0_1_1 = vnoExp
% 47.86/13.48 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.86/13.48 |
% 47.86/13.48 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3, yields:
% 47.86/13.48 | (130) $false
% 47.86/13.48 |
% 47.86/13.48 |-The branch is then unsatisfiable
% 47.86/13.48 |-Branch two:
% 47.86/13.48 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 47.86/13.48 |
% 47.86/13.48 | Applying alpha-rule on (259) yields:
% 47.86/13.48 | (260) all_11_10_50 = all_0_3_3
% 47.86/13.48 | (219) all_0_1_1 = vnoExp
% 47.86/13.48 | (262) vvar(all_11_11_51) = all_0_3_3
% 47.86/13.48 |
% 47.86/13.48 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_11_11_51) = all_0_3_3, yields:
% 47.86/13.48 | (130) $false
% 47.86/13.48 |
% 47.86/13.48 |-The branch is then unsatisfiable
% 47.86/13.48 |-Branch two:
% 47.86/13.48 | (896) all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34
% 47.86/13.48 |
% 47.86/13.48 | Applying alpha-rule on (896) yields:
% 47.86/13.48 | (772) all_10_5_33 = ve2
% 47.86/13.48 | (898) vreduce(all_10_11_39) = all_10_7_35
% 47.86/13.48 | (846) all_10_3_31 = 0
% 47.86/13.48 | (900) all_10_4_32 = all_10_7_35
% 47.86/13.48 | (901) visSomeExp(all_10_7_35) = 0
% 47.86/13.48 | (902) vapp(all_10_6_34, all_10_2_30) = all_10_1_29
% 47.86/13.48 | (780) all_10_0_28 = all_0_4_4
% 47.86/13.48 | (904) vgetSomeExp(all_10_7_35) = all_10_2_30
% 47.86/13.48 | (905) vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34
% 47.86/13.48 | (906) vapp(all_10_6_34, all_10_11_39) = ve2
% 47.86/13.48 | (782) vsomeExp(all_10_1_29) = all_0_4_4
% 47.86/13.48 |
% 47.86/13.48 | From (1169) and (782) follows:
% 47.86/13.48 | (1962) vsomeExp(all_10_1_29) = all_0_6_6
% 47.86/13.48 |
% 47.86/13.48 | Instantiating formula (85) with all_0_6_6, all_10_1_29, all_9_4_20 and discharging atoms vsomeExp(all_10_1_29) = all_0_6_6, vsomeExp(all_9_4_20) = all_0_6_6, yields:
% 47.86/13.48 | (2766) all_10_1_29 = all_9_4_20
% 47.86/13.48 |
% 47.86/13.48 | From (2766) and (1962) follows:
% 47.86/13.48 | (380) vsomeExp(all_9_4_20) = all_0_6_6
% 47.86/13.48 |
% 47.86/13.48 +-Applying beta-rule and splitting (116), into two cases.
% 47.86/13.48 |-Branch one:
% 47.86/13.48 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 47.86/13.48 |
% 47.86/13.48 +-Applying beta-rule and splitting (171), into two cases.
% 47.86/13.48 |-Branch one:
% 47.86/13.48 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 47.86/13.49 |
% 47.86/13.49 +-Applying beta-rule and splitting (172), into two cases.
% 47.86/13.49 |-Branch one:
% 47.86/13.49 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 47.86/13.49 |
% 47.86/13.49 +-Applying beta-rule and splitting (173), into two cases.
% 47.86/13.49 |-Branch one:
% 47.86/13.49 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 47.86/13.49 |
% 47.86/13.49 +-Applying beta-rule and splitting (174), into two cases.
% 47.86/13.49 |-Branch one:
% 47.86/13.49 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 47.86/13.49 |
% 47.86/13.49 +-Applying beta-rule and splitting (175), into two cases.
% 47.86/13.49 |-Branch one:
% 47.86/13.49 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.86/13.49 |
% 47.86/13.49 | Applying alpha-rule on (176) yields:
% 47.86/13.49 | (177) all_11_5_45 = all_0_3_3
% 47.86/13.49 | (178) all_11_4_44 = all_11_10_50
% 47.86/13.49 | (179) visValue(all_11_8_48) = 0
% 47.86/13.49 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 47.86/13.49 | (181) all_11_0_40 = all_0_1_1
% 47.86/13.49 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.86/13.49 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.86/13.49 | (184) vreduce(all_11_8_48) = all_11_10_50
% 47.86/13.49 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 47.86/13.49 | (186) ~ (all_11_3_43 = 0)
% 47.86/13.49 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 47.86/13.49 | (188) all_11_2_42 = 0
% 47.86/13.49 |
% 47.86/13.49 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.86/13.49 | (130) $false
% 47.86/13.49 |
% 47.86/13.49 |-The branch is then unsatisfiable
% 47.86/13.49 |-Branch two:
% 47.86/13.49 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.86/13.49 |
% 47.86/13.49 | Applying alpha-rule on (190) yields:
% 47.86/13.49 | (177) all_11_5_45 = all_0_3_3
% 47.86/13.49 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 47.86/13.49 | (193) visSomeExp(all_11_7_47) = 0
% 47.86/13.49 | (181) all_11_0_40 = all_0_1_1
% 47.86/13.49 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.86/13.49 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 47.86/13.49 | (197) vreduce(all_11_11_51) = all_11_7_47
% 47.86/13.49 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 47.86/13.49 | (199) all_11_3_43 = 0
% 47.86/13.49 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.86/13.49 | (201) all_11_4_44 = all_11_7_47
% 47.86/13.49 |
% 47.86/13.49 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.86/13.49 | (130) $false
% 47.86/13.49 |
% 47.86/13.49 |-The branch is then unsatisfiable
% 47.86/13.49 |-Branch two:
% 47.86/13.49 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.86/13.49 |
% 47.86/13.49 | Applying alpha-rule on (203) yields:
% 47.86/13.49 | (204) all_11_7_47 = all_11_10_50
% 47.86/13.49 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.86/13.49 | (206) all_11_6_46 = 0
% 47.86/13.49 | (207) all_11_3_43 = all_0_1_1
% 47.86/13.49 | (208) visSomeExp(all_11_10_50) = 0
% 47.86/13.49 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 47.86/13.49 | (210) vreduce(all_11_11_51) = all_11_10_50
% 47.86/13.49 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 47.86/13.49 | (212) all_11_8_48 = all_0_3_3
% 47.86/13.49 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 47.86/13.49 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 47.86/13.49 |
% 47.86/13.49 | Instantiating formula (74) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = all_0_1_1, yields:
% 47.86/13.49 | (130) $false
% 47.86/13.49 |
% 47.86/13.49 |-The branch is then unsatisfiable
% 47.86/13.49 |-Branch two:
% 47.86/13.49 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.86/13.49 |
% 47.86/13.49 | Applying alpha-rule on (216) yields:
% 47.86/13.49 | (177) all_11_5_45 = all_0_3_3
% 47.86/13.49 | (218) visValue(all_11_7_47) = all_11_2_42
% 47.86/13.49 | (219) all_0_1_1 = vnoExp
% 47.86/13.49 | (220) vreduce(all_11_7_47) = all_11_8_48
% 47.86/13.49 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.86/13.49 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 47.86/13.49 | (186) ~ (all_11_3_43 = 0)
% 47.86/13.49 | (224) all_11_4_44 = all_11_8_48
% 47.86/13.49 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 47.86/13.49 | (226) ~ (all_11_2_42 = 0)
% 47.86/13.49 |
% 47.86/13.49 | Instantiating formula (88) with all_0_3_3, all_11_7_47, all_11_6_46, ve2, ve1 and discharging atoms vapp(all_11_6_46, all_11_7_47) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.86/13.49 | (227) all_11_6_46 = ve1
% 47.86/13.49 |
% 47.86/13.49 | Instantiating formula (66) with ve1, all_9_9_25, all_9_11_27, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(all_9_11_27, all_9_9_25) = ve1, yields:
% 47.86/13.49 | (228) ~ (vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1)
% 47.86/13.49 |
% 47.86/13.49 | From (227) and (221) follows:
% 47.86/13.49 | (229) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1
% 47.86/13.49 |
% 47.86/13.49 | Using (229) and (228) yields:
% 47.86/13.49 | (130) $false
% 47.86/13.49 |
% 47.86/13.49 |-The branch is then unsatisfiable
% 47.86/13.49 |-Branch two:
% 47.86/13.49 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.86/13.49 |
% 47.86/13.49 | Applying alpha-rule on (231) yields:
% 47.86/13.49 | (232) all_11_7_47 = all_11_9_49
% 47.86/13.49 | (219) all_0_1_1 = vnoExp
% 47.86/13.49 | (234) ~ (all_11_6_46 = 0)
% 47.86/13.49 | (235) vreduce(all_11_10_50) = all_11_9_49
% 47.86/13.49 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.86/13.49 | (212) all_11_8_48 = all_0_3_3
% 47.86/13.49 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 47.86/13.49 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 47.86/13.49 |
% 47.86/13.49 | Instantiating formula (55) with ve1, all_11_9_49, all_0_6_6 and discharging atoms vreduce(ve1) = all_0_6_6, yields:
% 47.86/13.49 | (240) all_11_9_49 = all_0_6_6 | ~ (vreduce(ve1) = all_11_9_49)
% 47.86/13.49 |
% 47.86/13.49 | Instantiating formula (47) with all_11_6_46, all_0_6_6, all_9_4_20 and discharging atoms vsomeExp(all_9_4_20) = all_0_6_6, yields:
% 47.86/13.49 | (241) all_11_6_46 = 0 | ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.86/13.49 |
% 47.86/13.49 | Instantiating formula (88) with all_0_3_3, all_11_11_51, all_11_10_50, ve2, ve1 and discharging atoms vapp(all_11_10_50, all_11_11_51) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.86/13.49 | (242) all_11_10_50 = ve1
% 47.86/13.49 |
% 47.86/13.49 | From (242) and (235) follows:
% 47.86/13.49 | (243) vreduce(ve1) = all_11_9_49
% 47.86/13.49 |
% 47.86/13.49 +-Applying beta-rule and splitting (241), into two cases.
% 47.86/13.49 |-Branch one:
% 47.86/13.49 | (244) ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.86/13.49 |
% 47.86/13.49 +-Applying beta-rule and splitting (240), into two cases.
% 47.86/13.49 |-Branch one:
% 47.86/13.49 | (245) ~ (vreduce(ve1) = all_11_9_49)
% 47.86/13.49 |
% 47.86/13.49 | Using (243) and (245) yields:
% 47.86/13.49 | (130) $false
% 47.86/13.49 |
% 47.86/13.49 |-The branch is then unsatisfiable
% 47.86/13.49 |-Branch two:
% 47.86/13.49 | (243) vreduce(ve1) = all_11_9_49
% 47.86/13.49 | (248) all_11_9_49 = all_0_6_6
% 47.86/13.49 |
% 47.86/13.49 | From (248) and (239) follows:
% 47.86/13.49 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.86/13.49 |
% 47.86/13.49 | Using (249) and (244) yields:
% 47.86/13.49 | (130) $false
% 47.86/13.49 |
% 47.86/13.49 |-The branch is then unsatisfiable
% 47.86/13.49 |-Branch two:
% 47.86/13.49 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.86/13.49 | (206) all_11_6_46 = 0
% 47.86/13.49 |
% 47.86/13.49 | Equations (206) can reduce 234 to:
% 47.86/13.49 | (165) $false
% 47.86/13.49 |
% 47.86/13.49 |-The branch is then unsatisfiable
% 47.86/13.49 |-Branch two:
% 47.86/13.49 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.86/13.49 |
% 47.86/13.49 | Applying alpha-rule on (254) yields:
% 47.86/13.49 | (212) all_11_8_48 = all_0_3_3
% 47.86/13.49 | (219) all_0_1_1 = vnoExp
% 47.86/13.49 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.86/13.49 |
% 47.86/13.49 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3, yields:
% 47.86/13.49 | (130) $false
% 47.86/13.49 |
% 47.86/13.49 |-The branch is then unsatisfiable
% 47.86/13.49 |-Branch two:
% 47.86/13.49 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 47.86/13.49 |
% 47.86/13.49 | Applying alpha-rule on (259) yields:
% 47.86/13.49 | (260) all_11_10_50 = all_0_3_3
% 47.86/13.49 | (219) all_0_1_1 = vnoExp
% 47.86/13.49 | (262) vvar(all_11_11_51) = all_0_3_3
% 47.86/13.49 |
% 47.86/13.49 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_11_11_51) = all_0_3_3, yields:
% 47.86/13.49 | (130) $false
% 47.86/13.49 |
% 47.86/13.49 |-The branch is then unsatisfiable
% 47.86/13.49 |-Branch two:
% 47.86/13.49 | (1006) all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)
% 47.86/13.49 |
% 47.86/13.49 | Applying alpha-rule on (1006) yields:
% 47.86/13.49 | (1007) all_10_7_35 = all_10_10_38
% 47.86/13.49 | (1008) vgetSomeExp(all_10_10_38) = all_10_5_33
% 47.86/13.49 | (1009) vapp(all_10_5_33, all_10_9_37) = all_10_4_32
% 47.86/13.49 | (1010) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)
% 47.86/13.49 | (1011) visSomeExp(all_10_10_38) = 0
% 47.86/13.49 | (1012) all_10_8_36 = ve2
% 47.86/13.49 | (1013) vreduce(all_10_11_39) = all_10_10_38
% 47.86/13.49 | (1014) all_10_6_34 = 0
% 47.86/13.49 | (1015) vsomeExp(all_10_4_32) = all_0_4_4
% 47.86/13.49 | (1016) vapp(all_10_11_39, all_10_9_37) = ve2
% 47.86/13.49 | (1017) all_10_3_31 = all_0_4_4
% 47.86/13.49 |
% 47.86/13.49 | From (1169) and (1015) follows:
% 47.86/13.49 | (2178) vsomeExp(all_10_4_32) = all_0_6_6
% 47.86/13.49 |
% 47.86/13.49 | Instantiating formula (85) with all_0_6_6, all_10_4_32, all_9_4_20 and discharging atoms vsomeExp(all_10_4_32) = all_0_6_6, vsomeExp(all_9_4_20) = all_0_6_6, yields:
% 47.86/13.49 | (2982) all_10_4_32 = all_9_4_20
% 47.86/13.49 |
% 47.86/13.49 | From (2982) and (2178) follows:
% 47.86/13.50 | (380) vsomeExp(all_9_4_20) = all_0_6_6
% 47.86/13.50 |
% 47.86/13.50 +-Applying beta-rule and splitting (116), into two cases.
% 47.86/13.50 |-Branch one:
% 47.86/13.50 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 47.86/13.50 |
% 47.86/13.50 +-Applying beta-rule and splitting (171), into two cases.
% 47.86/13.50 |-Branch one:
% 47.86/13.50 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 47.86/13.50 |
% 47.86/13.50 +-Applying beta-rule and splitting (172), into two cases.
% 47.86/13.50 |-Branch one:
% 47.86/13.50 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 47.86/13.50 |
% 47.86/13.50 +-Applying beta-rule and splitting (173), into two cases.
% 47.86/13.50 |-Branch one:
% 47.86/13.50 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 47.86/13.50 |
% 47.86/13.50 +-Applying beta-rule and splitting (174), into two cases.
% 47.86/13.50 |-Branch one:
% 47.86/13.50 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 47.86/13.50 |
% 47.86/13.50 +-Applying beta-rule and splitting (175), into two cases.
% 47.86/13.50 |-Branch one:
% 47.86/13.50 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.86/13.50 |
% 47.86/13.50 | Applying alpha-rule on (176) yields:
% 47.86/13.50 | (177) all_11_5_45 = all_0_3_3
% 47.86/13.50 | (178) all_11_4_44 = all_11_10_50
% 47.86/13.50 | (179) visValue(all_11_8_48) = 0
% 47.86/13.50 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 47.86/13.50 | (181) all_11_0_40 = all_0_1_1
% 47.86/13.50 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.86/13.50 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.86/13.50 | (184) vreduce(all_11_8_48) = all_11_10_50
% 47.86/13.50 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 47.86/13.50 | (186) ~ (all_11_3_43 = 0)
% 47.86/13.50 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 47.86/13.50 | (188) all_11_2_42 = 0
% 47.86/13.50 |
% 47.86/13.50 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.86/13.50 | (130) $false
% 47.86/13.50 |
% 47.86/13.50 |-The branch is then unsatisfiable
% 47.86/13.50 |-Branch two:
% 47.86/13.50 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.86/13.50 |
% 47.86/13.50 | Applying alpha-rule on (190) yields:
% 47.86/13.50 | (177) all_11_5_45 = all_0_3_3
% 47.86/13.50 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 47.86/13.50 | (193) visSomeExp(all_11_7_47) = 0
% 47.86/13.50 | (181) all_11_0_40 = all_0_1_1
% 47.86/13.50 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.86/13.50 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 47.86/13.50 | (197) vreduce(all_11_11_51) = all_11_7_47
% 47.86/13.50 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 47.86/13.50 | (199) all_11_3_43 = 0
% 47.86/13.50 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.86/13.50 | (201) all_11_4_44 = all_11_7_47
% 47.86/13.50 |
% 47.86/13.50 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.86/13.50 | (130) $false
% 47.86/13.50 |
% 47.86/13.50 |-The branch is then unsatisfiable
% 47.86/13.50 |-Branch two:
% 47.86/13.50 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.86/13.50 |
% 47.86/13.50 | Applying alpha-rule on (203) yields:
% 47.86/13.50 | (204) all_11_7_47 = all_11_10_50
% 47.86/13.50 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.86/13.50 | (206) all_11_6_46 = 0
% 47.86/13.50 | (207) all_11_3_43 = all_0_1_1
% 47.86/13.50 | (208) visSomeExp(all_11_10_50) = 0
% 47.86/13.50 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 47.86/13.50 | (210) vreduce(all_11_11_51) = all_11_10_50
% 47.86/13.50 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 47.86/13.50 | (212) all_11_8_48 = all_0_3_3
% 47.86/13.50 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 47.86/13.50 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 47.86/13.50 |
% 47.86/13.50 | Instantiating formula (74) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = all_0_1_1, yields:
% 47.86/13.50 | (130) $false
% 47.86/13.50 |
% 47.86/13.50 |-The branch is then unsatisfiable
% 47.86/13.50 |-Branch two:
% 47.86/13.50 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.86/13.50 |
% 47.86/13.50 | Applying alpha-rule on (216) yields:
% 47.86/13.50 | (177) all_11_5_45 = all_0_3_3
% 47.86/13.50 | (218) visValue(all_11_7_47) = all_11_2_42
% 47.86/13.50 | (219) all_0_1_1 = vnoExp
% 47.86/13.50 | (220) vreduce(all_11_7_47) = all_11_8_48
% 47.86/13.50 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.86/13.50 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 47.86/13.50 | (186) ~ (all_11_3_43 = 0)
% 47.86/13.50 | (224) all_11_4_44 = all_11_8_48
% 47.86/13.50 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 47.86/13.50 | (226) ~ (all_11_2_42 = 0)
% 47.86/13.50 |
% 47.86/13.50 | Instantiating formula (88) with all_0_3_3, all_11_7_47, all_11_6_46, ve2, ve1 and discharging atoms vapp(all_11_6_46, all_11_7_47) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.86/13.50 | (227) all_11_6_46 = ve1
% 47.86/13.50 |
% 47.86/13.50 | Instantiating formula (66) with ve1, all_9_9_25, all_9_11_27, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(all_9_11_27, all_9_9_25) = ve1, yields:
% 47.86/13.50 | (228) ~ (vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1)
% 47.86/13.50 |
% 47.86/13.50 | From (227) and (221) follows:
% 47.86/13.50 | (229) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = ve1
% 47.86/13.50 |
% 47.86/13.50 | Using (229) and (228) yields:
% 47.86/13.50 | (130) $false
% 47.86/13.50 |
% 47.86/13.50 |-The branch is then unsatisfiable
% 47.86/13.50 |-Branch two:
% 47.86/13.50 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.86/13.50 |
% 47.86/13.50 | Applying alpha-rule on (231) yields:
% 47.86/13.50 | (232) all_11_7_47 = all_11_9_49
% 47.86/13.50 | (219) all_0_1_1 = vnoExp
% 47.86/13.50 | (234) ~ (all_11_6_46 = 0)
% 47.86/13.50 | (235) vreduce(all_11_10_50) = all_11_9_49
% 47.86/13.50 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.86/13.50 | (212) all_11_8_48 = all_0_3_3
% 47.86/13.50 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 47.86/13.50 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 47.86/13.50 |
% 47.86/13.50 | Instantiating formula (55) with ve1, all_11_9_49, all_0_6_6 and discharging atoms vreduce(ve1) = all_0_6_6, yields:
% 47.86/13.50 | (240) all_11_9_49 = all_0_6_6 | ~ (vreduce(ve1) = all_11_9_49)
% 47.86/13.50 |
% 47.86/13.50 | Instantiating formula (47) with all_11_6_46, all_0_6_6, all_9_4_20 and discharging atoms vsomeExp(all_9_4_20) = all_0_6_6, yields:
% 47.86/13.50 | (241) all_11_6_46 = 0 | ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.86/13.50 |
% 47.86/13.50 | Instantiating formula (88) with all_0_3_3, all_11_11_51, all_11_10_50, ve2, ve1 and discharging atoms vapp(all_11_10_50, all_11_11_51) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.86/13.50 | (242) all_11_10_50 = ve1
% 47.86/13.50 |
% 47.86/13.50 | From (242) and (235) follows:
% 47.86/13.50 | (243) vreduce(ve1) = all_11_9_49
% 47.86/13.50 |
% 47.86/13.50 +-Applying beta-rule and splitting (241), into two cases.
% 47.86/13.50 |-Branch one:
% 47.86/13.50 | (244) ~ (visSomeExp(all_0_6_6) = all_11_6_46)
% 47.86/13.50 |
% 47.86/13.50 +-Applying beta-rule and splitting (240), into two cases.
% 47.86/13.50 |-Branch one:
% 47.86/13.50 | (245) ~ (vreduce(ve1) = all_11_9_49)
% 47.86/13.50 |
% 47.86/13.50 | Using (243) and (245) yields:
% 47.86/13.50 | (130) $false
% 47.86/13.50 |
% 47.86/13.50 |-The branch is then unsatisfiable
% 47.86/13.50 |-Branch two:
% 47.86/13.50 | (243) vreduce(ve1) = all_11_9_49
% 47.86/13.50 | (248) all_11_9_49 = all_0_6_6
% 47.86/13.50 |
% 47.86/13.50 | From (248) and (239) follows:
% 47.86/13.50 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.86/13.50 |
% 47.86/13.50 | Using (249) and (244) yields:
% 47.86/13.50 | (130) $false
% 47.86/13.50 |
% 47.86/13.50 |-The branch is then unsatisfiable
% 47.86/13.50 |-Branch two:
% 47.86/13.50 | (249) visSomeExp(all_0_6_6) = all_11_6_46
% 47.86/13.50 | (206) all_11_6_46 = 0
% 47.86/13.50 |
% 47.86/13.50 | Equations (206) can reduce 234 to:
% 47.86/13.50 | (165) $false
% 47.86/13.50 |
% 47.86/13.50 |-The branch is then unsatisfiable
% 47.86/13.50 |-Branch two:
% 47.86/13.50 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.86/13.50 |
% 47.86/13.50 | Applying alpha-rule on (254) yields:
% 47.86/13.50 | (212) all_11_8_48 = all_0_3_3
% 47.86/13.50 | (219) all_0_1_1 = vnoExp
% 47.86/13.50 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.86/13.50 |
% 47.86/13.50 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3, yields:
% 47.86/13.50 | (130) $false
% 47.86/13.50 |
% 47.86/13.50 |-The branch is then unsatisfiable
% 47.86/13.50 |-Branch two:
% 47.86/13.50 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 47.86/13.50 |
% 47.86/13.50 | Applying alpha-rule on (259) yields:
% 47.86/13.50 | (260) all_11_10_50 = all_0_3_3
% 47.86/13.50 | (219) all_0_1_1 = vnoExp
% 47.86/13.50 | (262) vvar(all_11_11_51) = all_0_3_3
% 47.86/13.50 |
% 47.86/13.50 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_11_11_51) = all_0_3_3, yields:
% 47.86/13.50 | (130) $false
% 47.86/13.50 |
% 47.86/13.50 |-The branch is then unsatisfiable
% 47.86/13.50 |-Branch two:
% 47.86/13.50 | (1116) all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34
% 47.86/13.51 |
% 47.86/13.51 | Applying alpha-rule on (1116) yields:
% 47.86/13.51 | (772) all_10_5_33 = ve2
% 47.86/13.51 | (1118) all_10_4_32 = all_10_8_36
% 47.86/13.51 | (775) ~ (all_10_3_31 = 0)
% 47.86/13.51 | (1120) ~ (all_10_2_30 = 0)
% 47.86/13.51 | (1121) visValue(all_10_7_35) = all_10_2_30
% 47.86/13.51 | (1122) vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34
% 47.86/13.51 | (1123) all_0_4_4 = vnoExp
% 47.86/13.51 | (1124) vreduce(all_10_7_35) = all_10_8_36
% 47.86/13.51 | (1125) visSomeExp(all_10_8_36) = all_10_3_31
% 47.86/13.51 | (1126) vapp(all_10_6_34, all_10_7_35) = ve2
% 47.86/13.51 |
% 47.86/13.51 | Combining equations (1123,1169) yields a new equation:
% 47.86/13.51 | (502) all_0_6_6 = vnoExp
% 47.86/13.51 |
% 47.86/13.51 | Equations (502) can reduce 1926 to:
% 47.86/13.51 | (165) $false
% 47.86/13.51 |
% 47.86/13.51 |-The branch is then unsatisfiable
% 47.86/13.51 |-Branch two:
% 47.86/13.51 | (1128) all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)
% 47.86/13.51 |
% 47.86/13.51 | Applying alpha-rule on (1128) yields:
% 47.86/13.51 | (1129) vreduce(all_10_10_38) = all_10_9_37
% 47.86/13.51 | (1130) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)
% 47.86/13.51 | (1123) all_0_4_4 = vnoExp
% 47.86/13.51 | (1012) all_10_8_36 = ve2
% 47.86/13.51 | (1133) ~ (all_10_6_34 = 0)
% 47.86/13.51 | (1134) vapp(all_10_10_38, all_10_11_39) = ve2
% 47.86/13.51 | (1135) visSomeExp(all_10_9_37) = all_10_6_34
% 47.86/13.51 | (1136) all_10_7_35 = all_10_9_37
% 47.86/13.51 |
% 47.86/13.51 | Combining equations (1123,1169) yields a new equation:
% 47.86/13.51 | (502) all_0_6_6 = vnoExp
% 47.86/13.51 |
% 47.86/13.51 | Equations (502) can reduce 1926 to:
% 47.86/13.51 | (165) $false
% 47.86/13.51 |
% 47.86/13.51 |-The branch is then unsatisfiable
% 47.86/13.51 |-Branch two:
% 47.86/13.51 | (1138) all_10_8_36 = ve2 & all_0_4_4 = vnoExp & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2
% 47.86/13.51 |
% 47.86/13.51 | Applying alpha-rule on (1138) yields:
% 47.86/13.51 | (1012) all_10_8_36 = ve2
% 47.86/13.51 | (1123) all_0_4_4 = vnoExp
% 47.86/13.51 | (1141) vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2
% 47.86/13.51 |
% 47.86/13.51 | Combining equations (1169,1123) yields a new equation:
% 47.86/13.51 | (2285) all_0_6_6 = vnoExp
% 47.86/13.51 |
% 47.86/13.51 | Simplifying 2285 yields:
% 47.86/13.51 | (502) all_0_6_6 = vnoExp
% 47.86/13.51 |
% 47.86/13.51 | Equations (502) can reduce 1926 to:
% 47.86/13.51 | (165) $false
% 47.86/13.51 |
% 47.86/13.51 |-The branch is then unsatisfiable
% 47.86/13.51 |-Branch two:
% 47.86/13.51 | (1143) all_10_10_38 = ve2 & all_0_4_4 = vnoExp & vvar(all_10_11_39) = ve2
% 47.86/13.51 |
% 47.86/13.51 | Applying alpha-rule on (1143) yields:
% 47.86/13.51 | (1144) all_10_10_38 = ve2
% 47.86/13.51 | (1123) all_0_4_4 = vnoExp
% 47.86/13.51 | (1146) vvar(all_10_11_39) = ve2
% 47.86/13.51 |
% 47.86/13.51 | Combining equations (1169,1123) yields a new equation:
% 47.86/13.51 | (2285) all_0_6_6 = vnoExp
% 47.86/13.51 |
% 47.86/13.51 | Simplifying 2285 yields:
% 47.86/13.51 | (502) all_0_6_6 = vnoExp
% 47.86/13.51 |
% 47.86/13.51 | Equations (502) can reduce 1926 to:
% 47.86/13.51 | (165) $false
% 47.86/13.51 |
% 47.86/13.51 |-The branch is then unsatisfiable
% 47.86/13.51 |-Branch two:
% 47.86/13.51 | (492) all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22
% 47.86/13.51 |
% 47.86/13.51 | Applying alpha-rule on (492) yields:
% 47.86/13.51 | (493) vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22
% 47.86/13.51 | (494) vapp(all_9_6_22, all_9_7_23) = ve1
% 47.86/13.51 | (495) vreduce(all_9_7_23) = all_9_8_24
% 47.86/13.51 | (496) visSomeExp(all_9_8_24) = all_9_3_19
% 47.86/13.51 | (497) visValue(all_9_7_23) = all_9_2_18
% 47.86/13.51 | (498) all_9_4_20 = all_9_8_24
% 47.86/13.51 | (156) ~ (all_9_3_19 = 0)
% 47.86/13.51 | (159) all_9_5_21 = ve1
% 47.86/13.51 | (501) ~ (all_9_2_18 = 0)
% 47.86/13.51 | (502) all_0_6_6 = vnoExp
% 47.86/13.51 |
% 47.86/13.51 | Instantiating formula (92) with ve1, all_9_7_23, all_9_6_22 and discharging atoms vapp(all_9_6_22, all_9_7_23) = ve1, yields:
% 47.86/13.51 | (162) ~ (visValue(ve1) = 0)
% 47.86/13.51 |
% 47.86/13.51 | Using (68) and (162) yields:
% 47.86/13.51 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.51 |
% 47.86/13.51 +-Applying beta-rule and splitting (143), into two cases.
% 47.86/13.51 |-Branch one:
% 47.86/13.51 | (164) all_0_7_7 = 0
% 47.86/13.51 |
% 47.86/13.51 | Equations (164) can reduce 163 to:
% 47.86/13.51 | (165) $false
% 47.86/13.51 |
% 47.86/13.51 |-The branch is then unsatisfiable
% 47.86/13.51 |-Branch two:
% 47.86/13.51 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.51 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.86/13.51 |
% 47.86/13.51 | Instantiating (167) with all_122_0_676 yields:
% 47.86/13.51 | (3132) vsomeExp(all_122_0_676) = all_0_6_6
% 47.86/13.51 |
% 47.86/13.51 | From (502) and (3132) follows:
% 47.86/13.51 | (3133) vsomeExp(all_122_0_676) = vnoExp
% 47.86/13.51 |
% 47.86/13.51 | Instantiating formula (40) with all_122_0_676 and discharging atoms vsomeExp(all_122_0_676) = vnoExp, yields:
% 47.86/13.51 | (130) $false
% 47.86/13.51 |
% 47.86/13.51 |-The branch is then unsatisfiable
% 47.86/13.51 |-Branch two:
% 47.86/13.51 | (512) all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)
% 47.86/13.51 |
% 47.86/13.51 | Applying alpha-rule on (512) yields:
% 47.86/13.51 | (383) all_9_8_24 = ve1
% 47.86/13.51 | (514) ~ (all_9_6_22 = 0)
% 47.86/13.51 | (515) all_9_7_23 = all_9_9_25
% 47.86/13.51 | (516) visSomeExp(all_9_9_25) = all_9_6_22
% 47.86/13.51 | (517) vapp(all_9_10_26, all_9_11_27) = ve1
% 47.86/13.51 | (518) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)
% 47.86/13.51 | (519) vreduce(all_9_10_26) = all_9_9_25
% 47.86/13.51 | (502) all_0_6_6 = vnoExp
% 47.86/13.51 |
% 47.86/13.51 | Instantiating formula (92) with ve1, all_9_11_27, all_9_10_26 and discharging atoms vapp(all_9_10_26, all_9_11_27) = ve1, yields:
% 47.86/13.51 | (162) ~ (visValue(ve1) = 0)
% 47.86/13.51 |
% 47.86/13.51 | Using (68) and (162) yields:
% 47.86/13.51 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.51 |
% 47.86/13.51 +-Applying beta-rule and splitting (143), into two cases.
% 47.86/13.51 |-Branch one:
% 47.86/13.51 | (164) all_0_7_7 = 0
% 47.86/13.51 |
% 47.86/13.51 | Equations (164) can reduce 163 to:
% 47.86/13.51 | (165) $false
% 47.86/13.51 |
% 47.86/13.51 |-The branch is then unsatisfiable
% 47.86/13.51 |-Branch two:
% 47.86/13.51 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.51 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.86/13.51 |
% 47.86/13.51 | Instantiating (167) with all_112_0_678 yields:
% 47.86/13.51 | (3150) vsomeExp(all_112_0_678) = all_0_6_6
% 47.86/13.51 |
% 47.86/13.51 | From (502) and (3150) follows:
% 47.86/13.51 | (3151) vsomeExp(all_112_0_678) = vnoExp
% 47.86/13.51 |
% 47.86/13.51 | Instantiating formula (40) with all_112_0_678 and discharging atoms vsomeExp(all_112_0_678) = vnoExp, yields:
% 47.86/13.51 | (130) $false
% 47.86/13.51 |
% 47.86/13.51 |-The branch is then unsatisfiable
% 47.86/13.51 |-Branch two:
% 47.86/13.51 | (530) all_9_8_24 = ve1 & all_0_6_6 = vnoExp & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1
% 47.86/13.51 |
% 47.86/13.51 | Applying alpha-rule on (530) yields:
% 47.86/13.51 | (383) all_9_8_24 = ve1
% 47.86/13.51 | (502) all_0_6_6 = vnoExp
% 47.86/13.51 | (533) vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1
% 47.86/13.51 |
% 47.86/13.51 | Equations (502) can reduce 120 to:
% 47.86/13.51 | (534) ~ (all_0_1_1 = vnoExp)
% 47.86/13.51 |
% 47.86/13.51 +-Applying beta-rule and splitting (116), into two cases.
% 47.86/13.51 |-Branch one:
% 47.86/13.51 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 47.86/13.51 |
% 47.86/13.51 +-Applying beta-rule and splitting (171), into two cases.
% 47.86/13.51 |-Branch one:
% 47.86/13.51 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 47.86/13.51 |
% 47.86/13.51 +-Applying beta-rule and splitting (172), into two cases.
% 47.86/13.51 |-Branch one:
% 47.86/13.51 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 47.86/13.51 |
% 47.86/13.51 +-Applying beta-rule and splitting (173), into two cases.
% 47.86/13.51 |-Branch one:
% 47.86/13.51 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 47.86/13.51 |
% 47.86/13.51 +-Applying beta-rule and splitting (174), into two cases.
% 47.86/13.51 |-Branch one:
% 47.86/13.51 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 47.86/13.51 |
% 47.86/13.51 +-Applying beta-rule and splitting (175), into two cases.
% 47.86/13.51 |-Branch one:
% 47.86/13.51 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.86/13.51 |
% 47.86/13.51 | Applying alpha-rule on (176) yields:
% 47.86/13.51 | (177) all_11_5_45 = all_0_3_3
% 47.86/13.51 | (178) all_11_4_44 = all_11_10_50
% 47.86/13.51 | (179) visValue(all_11_8_48) = 0
% 47.86/13.51 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 47.86/13.51 | (181) all_11_0_40 = all_0_1_1
% 47.86/13.51 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.86/13.51 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 47.86/13.51 | (184) vreduce(all_11_8_48) = all_11_10_50
% 47.86/13.51 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 47.86/13.51 | (186) ~ (all_11_3_43 = 0)
% 47.86/13.51 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 47.86/13.51 | (188) all_11_2_42 = 0
% 47.86/13.51 |
% 47.86/13.51 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.86/13.51 | (130) $false
% 47.86/13.51 |
% 47.86/13.51 |-The branch is then unsatisfiable
% 47.86/13.51 |-Branch two:
% 47.86/13.51 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.86/13.51 |
% 47.86/13.51 | Applying alpha-rule on (190) yields:
% 47.86/13.51 | (177) all_11_5_45 = all_0_3_3
% 47.86/13.51 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 47.86/13.51 | (193) visSomeExp(all_11_7_47) = 0
% 47.86/13.51 | (181) all_11_0_40 = all_0_1_1
% 47.86/13.51 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 47.86/13.51 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 47.86/13.51 | (197) vreduce(all_11_11_51) = all_11_7_47
% 47.86/13.51 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 47.86/13.51 | (199) all_11_3_43 = 0
% 47.86/13.51 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 47.86/13.51 | (201) all_11_4_44 = all_11_7_47
% 47.86/13.51 |
% 47.86/13.51 | Instantiating formula (74) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = all_0_1_1, yields:
% 47.86/13.51 | (130) $false
% 47.86/13.51 |
% 47.86/13.51 |-The branch is then unsatisfiable
% 47.86/13.51 |-Branch two:
% 47.86/13.51 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.86/13.51 |
% 47.86/13.52 | Applying alpha-rule on (203) yields:
% 47.86/13.52 | (204) all_11_7_47 = all_11_10_50
% 47.86/13.52 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 47.86/13.52 | (206) all_11_6_46 = 0
% 47.86/13.52 | (207) all_11_3_43 = all_0_1_1
% 47.86/13.52 | (208) visSomeExp(all_11_10_50) = 0
% 47.86/13.52 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 47.86/13.52 | (210) vreduce(all_11_11_51) = all_11_10_50
% 47.86/13.52 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 47.86/13.52 | (212) all_11_8_48 = all_0_3_3
% 47.86/13.52 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 47.86/13.52 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 47.86/13.52 |
% 47.86/13.52 | Instantiating formula (74) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = all_0_1_1, yields:
% 47.86/13.52 | (130) $false
% 47.86/13.52 |
% 47.86/13.52 |-The branch is then unsatisfiable
% 47.86/13.52 |-Branch two:
% 47.86/13.52 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.86/13.52 |
% 47.86/13.52 | Applying alpha-rule on (216) yields:
% 47.86/13.52 | (177) all_11_5_45 = all_0_3_3
% 47.86/13.52 | (218) visValue(all_11_7_47) = all_11_2_42
% 47.86/13.52 | (219) all_0_1_1 = vnoExp
% 47.86/13.52 | (220) vreduce(all_11_7_47) = all_11_8_48
% 47.86/13.52 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 47.86/13.52 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 47.86/13.52 | (186) ~ (all_11_3_43 = 0)
% 47.86/13.52 | (224) all_11_4_44 = all_11_8_48
% 47.86/13.52 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 47.86/13.52 | (226) ~ (all_11_2_42 = 0)
% 47.86/13.52 |
% 47.86/13.52 | Equations (219) can reduce 534 to:
% 47.86/13.52 | (165) $false
% 47.86/13.52 |
% 47.86/13.52 |-The branch is then unsatisfiable
% 47.86/13.52 |-Branch two:
% 47.86/13.52 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.86/13.52 |
% 47.86/13.52 | Applying alpha-rule on (231) yields:
% 47.86/13.52 | (232) all_11_7_47 = all_11_9_49
% 47.86/13.52 | (219) all_0_1_1 = vnoExp
% 47.86/13.52 | (234) ~ (all_11_6_46 = 0)
% 47.86/13.52 | (235) vreduce(all_11_10_50) = all_11_9_49
% 47.86/13.52 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 47.86/13.52 | (212) all_11_8_48 = all_0_3_3
% 47.86/13.52 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 47.86/13.52 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 47.86/13.52 |
% 47.86/13.52 | Equations (219) can reduce 534 to:
% 47.86/13.52 | (165) $false
% 47.86/13.52 |
% 47.86/13.52 |-The branch is then unsatisfiable
% 47.86/13.52 |-Branch two:
% 47.86/13.52 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.86/13.52 |
% 47.86/13.52 | Applying alpha-rule on (254) yields:
% 47.86/13.52 | (212) all_11_8_48 = all_0_3_3
% 47.86/13.52 | (219) all_0_1_1 = vnoExp
% 47.86/13.52 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 47.86/13.52 |
% 47.86/13.52 | Equations (219) can reduce 534 to:
% 47.86/13.52 | (165) $false
% 47.86/13.52 |
% 47.86/13.52 |-The branch is then unsatisfiable
% 47.86/13.52 |-Branch two:
% 47.86/13.52 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 47.86/13.52 |
% 47.86/13.52 | Applying alpha-rule on (259) yields:
% 47.86/13.52 | (260) all_11_10_50 = all_0_3_3
% 47.86/13.52 | (219) all_0_1_1 = vnoExp
% 47.86/13.52 | (262) vvar(all_11_11_51) = all_0_3_3
% 47.86/13.52 |
% 47.86/13.52 | Equations (219) can reduce 534 to:
% 47.86/13.52 | (165) $false
% 47.86/13.52 |
% 47.86/13.52 |-The branch is then unsatisfiable
% 47.86/13.52 |-Branch two:
% 47.86/13.52 | (612) all_9_10_26 = ve1 & all_0_6_6 = vnoExp & vvar(all_9_11_27) = ve1
% 47.86/13.52 |
% 47.86/13.52 | Applying alpha-rule on (612) yields:
% 47.86/13.52 | (613) all_9_10_26 = ve1
% 47.86/13.52 | (502) all_0_6_6 = vnoExp
% 47.86/13.52 | (615) vvar(all_9_11_27) = ve1
% 47.86/13.52 |
% 47.86/13.52 | Instantiating formula (104) with ve1, all_9_11_27 and discharging atoms vvar(all_9_11_27) = ve1, yields:
% 47.86/13.52 | (162) ~ (visValue(ve1) = 0)
% 47.86/13.52 |
% 47.86/13.52 | Using (68) and (162) yields:
% 47.86/13.52 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.52 |
% 47.86/13.52 +-Applying beta-rule and splitting (143), into two cases.
% 47.86/13.52 |-Branch one:
% 47.86/13.52 | (164) all_0_7_7 = 0
% 47.86/13.52 |
% 47.86/13.52 | Equations (164) can reduce 163 to:
% 47.86/13.52 | (165) $false
% 47.86/13.52 |
% 47.86/13.52 |-The branch is then unsatisfiable
% 47.86/13.52 |-Branch two:
% 47.86/13.52 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.52 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.86/13.52 |
% 47.86/13.52 | Instantiating (167) with all_111_0_680 yields:
% 47.86/13.52 | (3245) vsomeExp(all_111_0_680) = all_0_6_6
% 47.86/13.52 |
% 47.86/13.52 | From (502) and (3245) follows:
% 47.86/13.52 | (3246) vsomeExp(all_111_0_680) = vnoExp
% 47.86/13.52 |
% 47.86/13.52 | Instantiating formula (40) with all_111_0_680 and discharging atoms vsomeExp(all_111_0_680) = vnoExp, yields:
% 47.86/13.52 | (130) $false
% 47.86/13.52 |
% 47.86/13.52 |-The branch is then unsatisfiable
% 47.86/13.52 |-Branch two:
% 47.86/13.52 | (625) all_8_4_12 = all_8_7_15 & all_8_5_13 = all_0_3_3 & vlookup(all_8_6_14, vempty) = all_8_7_15 & vsomeType(all_0_0_0) = all_8_7_15 & vvar(all_8_6_14) = all_0_3_3
% 47.86/13.52 |
% 47.86/13.52 | Applying alpha-rule on (625) yields:
% 47.86/13.52 | (626) all_8_4_12 = all_8_7_15
% 47.86/13.52 | (627) all_8_5_13 = all_0_3_3
% 47.86/13.52 | (628) vvar(all_8_6_14) = all_0_3_3
% 47.86/13.52 | (629) vsomeType(all_0_0_0) = all_8_7_15
% 47.86/13.52 | (630) vlookup(all_8_6_14, vempty) = all_8_7_15
% 47.86/13.52 |
% 47.86/13.52 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_8_6_14 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_8_6_14) = all_0_3_3, yields:
% 47.86/13.52 | (130) $false
% 47.86/13.52 |
% 47.86/13.52 |-The branch is then unsatisfiable
% 47.86/13.52 |-Branch two:
% 47.86/13.52 | (1174) vreduce(ve2) = all_0_1_1
% 47.86/13.52 | (1175) all_0_1_1 = all_0_4_4
% 47.86/13.52 |
% 47.86/13.52 | Equations (1175) can reduce 120 to:
% 47.86/13.52 | (637) ~ (all_0_4_4 = all_0_6_6)
% 47.86/13.52 |
% 47.86/13.52 +-Applying beta-rule and splitting (113), into two cases.
% 47.86/13.52 |-Branch one:
% 47.86/13.52 | (121) (all_8_0_8 = 0 & all_8_2_10 = all_0_0_0 & all_8_3_11 = all_0_3_3 & varrow(all_8_5_13, all_8_4_12) = all_0_0_0 & vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0 & vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9 & vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3) | (all_8_1_9 = 0 & all_8_2_10 = 0 & all_8_4_12 = all_0_3_3 & varrow(all_8_5_13, all_0_0_0) = all_8_3_11 & vtcheck(vempty, all_8_6_14, all_8_5_13) = 0 & vtcheck(vempty, all_8_7_15, all_8_3_11) = 0 & vapp(all_8_7_15, all_8_6_14) = all_0_3_3)
% 47.86/13.52 |
% 47.86/13.52 +-Applying beta-rule and splitting (121), into two cases.
% 47.86/13.52 |-Branch one:
% 47.86/13.52 | (122) all_8_0_8 = 0 & all_8_2_10 = all_0_0_0 & all_8_3_11 = all_0_3_3 & varrow(all_8_5_13, all_8_4_12) = all_0_0_0 & vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0 & vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9 & vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3
% 47.86/13.52 |
% 47.86/13.52 | Applying alpha-rule on (122) yields:
% 47.86/13.52 | (123) vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3
% 47.86/13.52 | (124) vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0
% 47.86/13.52 | (125) vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9
% 47.86/13.52 | (126) all_8_3_11 = all_0_3_3
% 47.86/13.52 | (127) all_8_0_8 = 0
% 47.86/13.52 | (128) all_8_2_10 = all_0_0_0
% 47.86/13.52 | (129) varrow(all_8_5_13, all_8_4_12) = all_0_0_0
% 47.86/13.52 |
% 47.86/13.52 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_8_6_14, all_8_5_13, all_8_7_15 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3, yields:
% 47.86/13.52 | (130) $false
% 47.86/13.52 |
% 47.86/13.52 |-The branch is then unsatisfiable
% 47.86/13.52 |-Branch two:
% 47.86/13.52 | (131) all_8_1_9 = 0 & all_8_2_10 = 0 & all_8_4_12 = all_0_3_3 & varrow(all_8_5_13, all_0_0_0) = all_8_3_11 & vtcheck(vempty, all_8_6_14, all_8_5_13) = 0 & vtcheck(vempty, all_8_7_15, all_8_3_11) = 0 & vapp(all_8_7_15, all_8_6_14) = all_0_3_3
% 47.86/13.52 |
% 47.86/13.52 | Applying alpha-rule on (131) yields:
% 47.86/13.52 | (132) varrow(all_8_5_13, all_0_0_0) = all_8_3_11
% 47.86/13.52 | (133) vtcheck(vempty, all_8_6_14, all_8_5_13) = 0
% 47.86/13.52 | (134) all_8_2_10 = 0
% 47.86/13.52 | (135) vtcheck(vempty, all_8_7_15, all_8_3_11) = 0
% 47.86/13.52 | (136) all_8_4_12 = all_0_3_3
% 47.86/13.52 | (137) all_8_1_9 = 0
% 47.86/13.52 | (138) vapp(all_8_7_15, all_8_6_14) = all_0_3_3
% 47.86/13.52 |
% 47.86/13.52 | Instantiating formula (31) with all_0_3_3, all_8_6_14, all_8_7_15, ve2, ve1 and discharging atoms vapp(all_8_7_15, all_8_6_14) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.86/13.52 | (139) all_8_6_14 = ve2
% 47.86/13.52 |
% 47.86/13.52 | Instantiating formula (88) with all_0_3_3, all_8_6_14, all_8_7_15, ve2, ve1 and discharging atoms vapp(all_8_7_15, all_8_6_14) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.86/13.52 | (140) all_8_7_15 = ve1
% 47.86/13.52 |
% 47.86/13.52 | From (139) and (133) follows:
% 47.86/13.52 | (658) vtcheck(vempty, ve2, all_8_5_13) = 0
% 47.86/13.52 |
% 47.86/13.52 | From (140) and (135) follows:
% 47.86/13.52 | (141) vtcheck(vempty, ve1, all_8_3_11) = 0
% 47.86/13.52 |
% 47.86/13.52 | Instantiating formula (29) with all_8_5_13 and discharging atoms vtcheck(vempty, ve2, all_8_5_13) = 0, yields:
% 47.86/13.52 | (661) all_0_5_5 = 0 | ? [v0] : vsomeExp(v0) = all_0_4_4
% 47.86/13.52 |
% 47.86/13.52 | Instantiating formula (67) with all_8_3_11 and discharging atoms vtcheck(vempty, ve1, all_8_3_11) = 0, yields:
% 47.86/13.52 | (143) all_0_7_7 = 0 | ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.86/13.52 |
% 47.86/13.52 +-Applying beta-rule and splitting (114), into two cases.
% 47.86/13.52 |-Branch one:
% 47.86/13.52 | (144) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22) | (all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)) | (all_9_8_24 = ve1 & all_0_6_6 = vnoExp & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1)
% 47.86/13.52 |
% 47.86/13.52 +-Applying beta-rule and splitting (144), into two cases.
% 47.86/13.52 |-Branch one:
% 47.86/13.52 | (145) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22) | (all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26))
% 47.86/13.52 |
% 47.86/13.52 +-Applying beta-rule and splitting (145), into two cases.
% 47.86/13.52 |-Branch one:
% 47.86/13.52 | (146) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22)
% 47.86/13.52 |
% 47.86/13.52 +-Applying beta-rule and splitting (146), into two cases.
% 47.86/13.52 |-Branch one:
% 47.86/13.52 | (147) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27))
% 47.86/13.52 |
% 47.86/13.52 +-Applying beta-rule and splitting (147), into two cases.
% 47.86/13.52 |-Branch one:
% 47.86/13.52 | (148) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22)
% 47.86/13.52 |
% 47.86/13.52 +-Applying beta-rule and splitting (148), into two cases.
% 47.86/13.52 |-Branch one:
% 47.86/13.52 | (149) all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22
% 47.86/13.52 |
% 47.86/13.52 | Applying alpha-rule on (149) yields:
% 47.86/13.52 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 47.86/13.52 | (151) vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22
% 47.86/13.52 | (152) visSomeExp(all_9_10_26) = all_9_3_19
% 47.86/13.52 | (153) all_9_0_16 = all_0_6_6
% 47.86/13.52 | (154) vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17
% 47.86/13.52 | (155) vreduce(all_9_8_24) = all_9_10_26
% 47.86/13.52 | (156) ~ (all_9_3_19 = 0)
% 47.86/13.52 | (157) all_9_4_20 = all_9_10_26
% 47.86/13.52 | (158) vapp(all_9_6_22, all_9_8_24) = ve1
% 47.86/13.52 | (159) all_9_5_21 = ve1
% 47.86/13.52 | (160) all_9_2_18 = 0
% 47.86/13.52 | (161) visValue(all_9_8_24) = 0
% 47.86/13.52 |
% 47.86/13.52 | Instantiating formula (92) with ve1, all_9_8_24, all_9_6_22 and discharging atoms vapp(all_9_6_22, all_9_8_24) = ve1, yields:
% 47.86/13.52 | (162) ~ (visValue(ve1) = 0)
% 47.86/13.52 |
% 47.86/13.52 | Using (68) and (162) yields:
% 47.86/13.52 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.52 |
% 47.86/13.52 +-Applying beta-rule and splitting (143), into two cases.
% 47.86/13.52 |-Branch one:
% 47.86/13.52 | (164) all_0_7_7 = 0
% 47.86/13.52 |
% 47.86/13.52 | Equations (164) can reduce 163 to:
% 47.86/13.52 | (165) $false
% 47.86/13.52 |
% 47.86/13.52 |-The branch is then unsatisfiable
% 47.86/13.52 |-Branch two:
% 47.86/13.52 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.52 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.86/13.52 |
% 47.86/13.52 +-Applying beta-rule and splitting (661), into two cases.
% 47.86/13.52 |-Branch one:
% 47.86/13.52 | (761) all_0_5_5 = 0
% 47.86/13.52 |
% 47.86/13.52 | Combining equations (761,1326) yields a new equation:
% 47.86/13.52 | (164) all_0_7_7 = 0
% 47.86/13.52 |
% 47.86/13.52 | Equations (164) can reduce 163 to:
% 47.86/13.52 | (165) $false
% 47.86/13.52 |
% 47.86/13.52 |-The branch is then unsatisfiable
% 47.86/13.52 |-Branch two:
% 47.86/13.52 | (760) ~ (all_0_5_5 = 0)
% 47.86/13.52 | (764) ? [v0] : vsomeExp(v0) = all_0_4_4
% 47.86/13.52 |
% 47.86/13.52 | Instantiating (764) with all_128_0_699 yields:
% 47.86/13.52 | (3311) vsomeExp(all_128_0_699) = all_0_4_4
% 47.86/13.52 |
% 47.86/13.52 | Instantiating formula (74) with all_128_0_699 yields:
% 47.86/13.52 | (3312) ~ (vsomeExp(all_128_0_699) = all_0_1_1)
% 47.86/13.52 |
% 47.86/13.52 | From (1175) and (3312) follows:
% 47.86/13.52 | (3313) ~ (vsomeExp(all_128_0_699) = all_0_4_4)
% 47.86/13.52 |
% 47.86/13.52 | Using (3311) and (3313) yields:
% 47.86/13.52 | (130) $false
% 47.86/13.52 |
% 47.86/13.52 |-The branch is then unsatisfiable
% 47.86/13.52 |-Branch two:
% 47.86/13.52 | (264) all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22
% 47.86/13.52 |
% 47.86/13.52 | Applying alpha-rule on (264) yields:
% 47.86/13.52 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 47.86/13.52 | (266) visSomeExp(all_9_7_23) = 0
% 47.86/13.52 | (267) vapp(all_9_6_22, all_9_2_18) = all_9_1_17
% 47.86/13.52 | (268) vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22
% 47.86/13.52 | (269) vreduce(all_9_11_27) = all_9_7_23
% 47.86/13.52 | (270) vapp(all_9_6_22, all_9_11_27) = ve1
% 47.86/13.52 | (153) all_9_0_16 = all_0_6_6
% 47.86/13.52 | (272) all_9_3_19 = 0
% 47.86/13.52 | (273) vgetSomeExp(all_9_7_23) = all_9_2_18
% 47.86/13.52 | (159) all_9_5_21 = ve1
% 47.86/13.52 | (275) all_9_4_20 = all_9_7_23
% 47.86/13.52 |
% 47.86/13.52 | Instantiating formula (92) with ve1, all_9_11_27, all_9_6_22 and discharging atoms vapp(all_9_6_22, all_9_11_27) = ve1, yields:
% 47.86/13.52 | (162) ~ (visValue(ve1) = 0)
% 47.86/13.52 |
% 47.86/13.52 | Using (68) and (162) yields:
% 47.86/13.52 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.52 |
% 47.86/13.52 +-Applying beta-rule and splitting (661), into two cases.
% 47.86/13.52 |-Branch one:
% 47.86/13.52 | (761) all_0_5_5 = 0
% 47.86/13.52 |
% 47.86/13.52 | Combining equations (761,1326) yields a new equation:
% 47.86/13.52 | (164) all_0_7_7 = 0
% 47.86/13.52 |
% 47.86/13.52 | Equations (164) can reduce 163 to:
% 47.86/13.52 | (165) $false
% 47.86/13.52 |
% 47.86/13.52 |-The branch is then unsatisfiable
% 47.86/13.52 |-Branch two:
% 47.86/13.52 | (760) ~ (all_0_5_5 = 0)
% 47.86/13.52 | (764) ? [v0] : vsomeExp(v0) = all_0_4_4
% 47.86/13.52 |
% 47.86/13.52 | Instantiating (764) with all_122_0_700 yields:
% 47.86/13.52 | (3334) vsomeExp(all_122_0_700) = all_0_4_4
% 47.86/13.52 |
% 47.86/13.52 | Instantiating formula (74) with all_122_0_700 yields:
% 47.86/13.52 | (3335) ~ (vsomeExp(all_122_0_700) = all_0_1_1)
% 47.86/13.53 |
% 47.86/13.53 | From (1175) and (3335) follows:
% 47.86/13.53 | (3336) ~ (vsomeExp(all_122_0_700) = all_0_4_4)
% 47.86/13.53 |
% 47.86/13.53 | Using (3334) and (3336) yields:
% 47.86/13.53 | (130) $false
% 47.86/13.53 |
% 47.86/13.53 |-The branch is then unsatisfiable
% 47.86/13.53 |-Branch two:
% 47.86/13.53 | (378) all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)
% 47.86/13.53 |
% 47.86/13.53 | Applying alpha-rule on (378) yields:
% 47.86/13.53 | (379) vapp(all_9_5_21, all_9_9_25) = all_9_4_20
% 47.86/13.53 | (380) vsomeExp(all_9_4_20) = all_0_6_6
% 47.86/13.53 | (381) all_9_7_23 = all_9_10_26
% 47.86/13.53 | (382) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)
% 47.86/13.53 | (383) all_9_8_24 = ve1
% 47.86/13.53 | (384) all_9_6_22 = 0
% 47.86/13.53 | (385) visSomeExp(all_9_10_26) = 0
% 47.86/13.53 | (386) vapp(all_9_11_27, all_9_9_25) = ve1
% 47.86/13.53 | (387) all_9_3_19 = all_0_6_6
% 47.86/13.53 | (388) vreduce(all_9_11_27) = all_9_10_26
% 47.86/13.53 | (389) vgetSomeExp(all_9_10_26) = all_9_5_21
% 47.86/13.53 |
% 47.86/13.53 | Instantiating formula (92) with ve1, all_9_9_25, all_9_11_27 and discharging atoms vapp(all_9_11_27, all_9_9_25) = ve1, yields:
% 47.86/13.53 | (162) ~ (visValue(ve1) = 0)
% 47.86/13.53 |
% 47.86/13.53 | Using (68) and (162) yields:
% 47.86/13.53 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.53 |
% 47.86/13.53 +-Applying beta-rule and splitting (143), into two cases.
% 47.86/13.53 |-Branch one:
% 47.86/13.53 | (164) all_0_7_7 = 0
% 47.86/13.53 |
% 47.86/13.53 | Equations (164) can reduce 163 to:
% 47.86/13.53 | (165) $false
% 47.86/13.53 |
% 47.86/13.53 |-The branch is then unsatisfiable
% 47.86/13.53 |-Branch two:
% 47.86/13.53 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.53 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.86/13.53 |
% 47.86/13.53 +-Applying beta-rule and splitting (661), into two cases.
% 47.86/13.53 |-Branch one:
% 47.86/13.53 | (761) all_0_5_5 = 0
% 47.86/13.53 |
% 47.86/13.53 | Combining equations (761,1326) yields a new equation:
% 47.86/13.53 | (164) all_0_7_7 = 0
% 47.86/13.53 |
% 47.86/13.53 | Equations (164) can reduce 163 to:
% 47.86/13.53 | (165) $false
% 47.86/13.53 |
% 47.86/13.53 |-The branch is then unsatisfiable
% 47.86/13.53 |-Branch two:
% 47.86/13.53 | (760) ~ (all_0_5_5 = 0)
% 47.86/13.53 | (764) ? [v0] : vsomeExp(v0) = all_0_4_4
% 47.86/13.53 |
% 47.86/13.53 | Instantiating (764) with all_117_0_703 yields:
% 47.86/13.53 | (3361) vsomeExp(all_117_0_703) = all_0_4_4
% 47.86/13.53 |
% 47.86/13.53 | Instantiating formula (74) with all_117_0_703 yields:
% 47.86/13.53 | (3362) ~ (vsomeExp(all_117_0_703) = all_0_1_1)
% 47.86/13.53 |
% 47.86/13.53 | From (1175) and (3362) follows:
% 47.86/13.53 | (3363) ~ (vsomeExp(all_117_0_703) = all_0_4_4)
% 47.86/13.53 |
% 47.86/13.53 | Using (3361) and (3363) yields:
% 47.86/13.53 | (130) $false
% 47.86/13.53 |
% 47.86/13.53 |-The branch is then unsatisfiable
% 47.86/13.53 |-Branch two:
% 47.86/13.53 | (492) all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22
% 47.86/13.53 |
% 47.86/13.53 | Applying alpha-rule on (492) yields:
% 47.86/13.53 | (493) vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22
% 47.86/13.53 | (494) vapp(all_9_6_22, all_9_7_23) = ve1
% 47.86/13.53 | (495) vreduce(all_9_7_23) = all_9_8_24
% 47.86/13.53 | (496) visSomeExp(all_9_8_24) = all_9_3_19
% 47.86/13.53 | (497) visValue(all_9_7_23) = all_9_2_18
% 47.86/13.53 | (498) all_9_4_20 = all_9_8_24
% 47.86/13.53 | (156) ~ (all_9_3_19 = 0)
% 47.86/13.53 | (159) all_9_5_21 = ve1
% 47.86/13.53 | (501) ~ (all_9_2_18 = 0)
% 47.86/13.53 | (502) all_0_6_6 = vnoExp
% 47.86/13.53 |
% 47.86/13.53 | Instantiating formula (92) with ve1, all_9_7_23, all_9_6_22 and discharging atoms vapp(all_9_6_22, all_9_7_23) = ve1, yields:
% 47.86/13.53 | (162) ~ (visValue(ve1) = 0)
% 47.86/13.53 |
% 47.86/13.53 | Using (68) and (162) yields:
% 47.86/13.53 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.53 |
% 47.86/13.53 +-Applying beta-rule and splitting (661), into two cases.
% 47.86/13.53 |-Branch one:
% 47.86/13.53 | (761) all_0_5_5 = 0
% 47.86/13.53 |
% 47.86/13.53 | Combining equations (761,1326) yields a new equation:
% 47.86/13.53 | (164) all_0_7_7 = 0
% 47.86/13.53 |
% 47.86/13.53 | Equations (164) can reduce 163 to:
% 47.86/13.53 | (165) $false
% 47.86/13.53 |
% 47.86/13.53 |-The branch is then unsatisfiable
% 47.86/13.53 |-Branch two:
% 47.86/13.53 | (760) ~ (all_0_5_5 = 0)
% 47.86/13.53 | (764) ? [v0] : vsomeExp(v0) = all_0_4_4
% 47.86/13.53 |
% 47.86/13.53 | Equations (1326) can reduce 760 to:
% 47.86/13.53 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.53 |
% 47.86/13.53 +-Applying beta-rule and splitting (143), into two cases.
% 47.86/13.53 |-Branch one:
% 47.86/13.53 | (164) all_0_7_7 = 0
% 47.86/13.53 |
% 47.86/13.53 | Equations (164) can reduce 163 to:
% 47.86/13.53 | (165) $false
% 47.86/13.53 |
% 47.86/13.53 |-The branch is then unsatisfiable
% 47.86/13.53 |-Branch two:
% 47.86/13.53 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.53 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.86/13.53 |
% 47.86/13.53 | Instantiating (167) with all_128_0_705 yields:
% 47.86/13.53 | (3388) vsomeExp(all_128_0_705) = all_0_6_6
% 47.86/13.53 |
% 47.86/13.53 | From (502) and (3388) follows:
% 47.86/13.53 | (3389) vsomeExp(all_128_0_705) = vnoExp
% 47.86/13.53 |
% 47.86/13.53 | Instantiating formula (40) with all_128_0_705 and discharging atoms vsomeExp(all_128_0_705) = vnoExp, yields:
% 47.86/13.53 | (130) $false
% 47.86/13.53 |
% 47.86/13.53 |-The branch is then unsatisfiable
% 47.86/13.53 |-Branch two:
% 47.86/13.53 | (512) all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)
% 47.86/13.53 |
% 47.86/13.53 | Applying alpha-rule on (512) yields:
% 47.86/13.53 | (383) all_9_8_24 = ve1
% 47.86/13.53 | (514) ~ (all_9_6_22 = 0)
% 47.86/13.53 | (515) all_9_7_23 = all_9_9_25
% 47.86/13.53 | (516) visSomeExp(all_9_9_25) = all_9_6_22
% 47.86/13.53 | (517) vapp(all_9_10_26, all_9_11_27) = ve1
% 47.86/13.53 | (518) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)
% 47.86/13.53 | (519) vreduce(all_9_10_26) = all_9_9_25
% 47.86/13.53 | (502) all_0_6_6 = vnoExp
% 47.86/13.53 |
% 47.86/13.53 | Instantiating formula (92) with ve1, all_9_11_27, all_9_10_26 and discharging atoms vapp(all_9_10_26, all_9_11_27) = ve1, yields:
% 47.86/13.53 | (162) ~ (visValue(ve1) = 0)
% 47.86/13.53 |
% 47.86/13.53 | Using (68) and (162) yields:
% 47.86/13.53 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.53 |
% 47.86/13.53 +-Applying beta-rule and splitting (661), into two cases.
% 47.86/13.53 |-Branch one:
% 47.86/13.53 | (761) all_0_5_5 = 0
% 47.86/13.53 |
% 47.86/13.53 | Combining equations (761,1326) yields a new equation:
% 47.86/13.53 | (164) all_0_7_7 = 0
% 47.86/13.53 |
% 47.86/13.53 | Equations (164) can reduce 163 to:
% 47.86/13.53 | (165) $false
% 47.86/13.53 |
% 47.86/13.53 |-The branch is then unsatisfiable
% 47.86/13.53 |-Branch two:
% 47.86/13.53 | (760) ~ (all_0_5_5 = 0)
% 47.86/13.53 | (764) ? [v0] : vsomeExp(v0) = all_0_4_4
% 47.86/13.53 |
% 47.86/13.53 | Equations (1326) can reduce 760 to:
% 47.86/13.53 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.53 |
% 47.86/13.53 +-Applying beta-rule and splitting (143), into two cases.
% 47.86/13.53 |-Branch one:
% 47.86/13.53 | (164) all_0_7_7 = 0
% 47.86/13.53 |
% 47.86/13.53 | Equations (164) can reduce 163 to:
% 47.86/13.53 | (165) $false
% 47.86/13.53 |
% 47.86/13.53 |-The branch is then unsatisfiable
% 47.86/13.53 |-Branch two:
% 47.86/13.53 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.53 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.86/13.53 |
% 47.86/13.53 | Instantiating (167) with all_117_0_707 yields:
% 47.86/13.53 | (3412) vsomeExp(all_117_0_707) = all_0_6_6
% 47.86/13.53 |
% 47.86/13.53 | From (502) and (3412) follows:
% 47.86/13.53 | (3413) vsomeExp(all_117_0_707) = vnoExp
% 47.86/13.53 |
% 47.86/13.53 | Instantiating formula (40) with all_117_0_707 and discharging atoms vsomeExp(all_117_0_707) = vnoExp, yields:
% 47.86/13.53 | (130) $false
% 47.86/13.53 |
% 47.86/13.53 |-The branch is then unsatisfiable
% 47.86/13.53 |-Branch two:
% 47.86/13.53 | (530) all_9_8_24 = ve1 & all_0_6_6 = vnoExp & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1
% 47.86/13.53 |
% 47.86/13.53 | Applying alpha-rule on (530) yields:
% 47.86/13.53 | (383) all_9_8_24 = ve1
% 47.86/13.53 | (502) all_0_6_6 = vnoExp
% 47.86/13.53 | (533) vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1
% 47.86/13.53 |
% 47.86/13.53 | Equations (502) can reduce 637 to:
% 47.86/13.53 | (757) ~ (all_0_4_4 = vnoExp)
% 47.86/13.53 |
% 47.86/13.53 | Instantiating formula (22) with all_0_7_7, ve1, all_9_9_25, all_9_10_26, all_9_11_27 and discharging atoms visValue(ve1) = all_0_7_7, vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1, yields:
% 47.86/13.53 | (164) all_0_7_7 = 0
% 47.86/13.53 |
% 47.86/13.53 | From (164) and (1327) follows:
% 47.86/13.53 | (1772) visValue(ve2) = 0
% 47.86/13.53 |
% 47.86/13.53 +-Applying beta-rule and splitting (115), into two cases.
% 47.86/13.53 |-Branch one:
% 47.86/13.53 | (766) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34) | (all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)) | (all_10_8_36 = ve2 & all_0_4_4 = vnoExp & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2)
% 47.86/13.53 |
% 47.86/13.53 +-Applying beta-rule and splitting (766), into two cases.
% 47.86/13.53 |-Branch one:
% 47.86/13.53 | (767) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34) | (all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38))
% 47.86/13.53 |
% 47.86/13.53 +-Applying beta-rule and splitting (767), into two cases.
% 47.86/13.53 |-Branch one:
% 47.86/13.53 | (768) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34)
% 47.86/13.53 |
% 47.86/13.53 +-Applying beta-rule and splitting (768), into two cases.
% 47.86/13.53 |-Branch one:
% 47.86/13.53 | (769) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39))
% 47.86/13.53 |
% 47.86/13.53 +-Applying beta-rule and splitting (769), into two cases.
% 47.86/13.53 |-Branch one:
% 47.86/13.53 | (770) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34)
% 47.86/13.53 |
% 47.86/13.53 +-Applying beta-rule and splitting (770), into two cases.
% 47.86/13.53 |-Branch one:
% 47.86/13.53 | (771) all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34
% 47.86/13.53 |
% 47.86/13.53 | Applying alpha-rule on (771) yields:
% 47.86/13.53 | (772) all_10_5_33 = ve2
% 47.86/13.53 | (773) visValue(all_10_8_36) = 0
% 47.86/13.53 | (774) all_10_4_32 = all_10_10_38
% 47.86/13.53 | (775) ~ (all_10_3_31 = 0)
% 47.86/13.53 | (776) all_10_2_30 = 0
% 47.86/13.53 | (777) vapp(all_10_6_34, all_10_8_36) = ve2
% 47.86/13.53 | (778) vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29
% 47.86/13.53 | (779) vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34
% 47.86/13.53 | (780) all_10_0_28 = all_0_4_4
% 47.86/13.53 | (781) visSomeExp(all_10_10_38) = all_10_3_31
% 47.86/13.53 | (782) vsomeExp(all_10_1_29) = all_0_4_4
% 47.86/13.53 | (783) vreduce(all_10_8_36) = all_10_10_38
% 47.86/13.53 |
% 47.86/13.53 | Instantiating formula (92) with ve2, all_10_8_36, all_10_6_34 and discharging atoms visValue(ve2) = 0, vapp(all_10_6_34, all_10_8_36) = ve2, yields:
% 47.86/13.54 | (130) $false
% 47.86/13.54 |
% 47.86/13.54 |-The branch is then unsatisfiable
% 47.86/13.54 |-Branch two:
% 47.86/13.54 | (896) all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34
% 47.86/13.54 |
% 47.86/13.54 | Applying alpha-rule on (896) yields:
% 47.86/13.54 | (772) all_10_5_33 = ve2
% 47.86/13.54 | (898) vreduce(all_10_11_39) = all_10_7_35
% 47.86/13.54 | (846) all_10_3_31 = 0
% 47.86/13.54 | (900) all_10_4_32 = all_10_7_35
% 47.86/13.54 | (901) visSomeExp(all_10_7_35) = 0
% 47.86/13.54 | (902) vapp(all_10_6_34, all_10_2_30) = all_10_1_29
% 47.86/13.54 | (780) all_10_0_28 = all_0_4_4
% 47.86/13.54 | (904) vgetSomeExp(all_10_7_35) = all_10_2_30
% 47.86/13.54 | (905) vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34
% 47.86/13.54 | (906) vapp(all_10_6_34, all_10_11_39) = ve2
% 47.86/13.54 | (782) vsomeExp(all_10_1_29) = all_0_4_4
% 47.86/13.54 |
% 47.86/13.54 | Instantiating formula (92) with ve2, all_10_11_39, all_10_6_34 and discharging atoms visValue(ve2) = 0, vapp(all_10_6_34, all_10_11_39) = ve2, yields:
% 47.86/13.54 | (130) $false
% 47.86/13.54 |
% 47.86/13.54 |-The branch is then unsatisfiable
% 47.86/13.54 |-Branch two:
% 47.86/13.54 | (1006) all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)
% 47.86/13.54 |
% 47.86/13.54 | Applying alpha-rule on (1006) yields:
% 47.86/13.54 | (1007) all_10_7_35 = all_10_10_38
% 47.86/13.54 | (1008) vgetSomeExp(all_10_10_38) = all_10_5_33
% 47.86/13.54 | (1009) vapp(all_10_5_33, all_10_9_37) = all_10_4_32
% 47.86/13.54 | (1010) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)
% 47.86/13.54 | (1011) visSomeExp(all_10_10_38) = 0
% 47.86/13.54 | (1012) all_10_8_36 = ve2
% 47.86/13.54 | (1013) vreduce(all_10_11_39) = all_10_10_38
% 47.86/13.54 | (1014) all_10_6_34 = 0
% 47.86/13.54 | (1015) vsomeExp(all_10_4_32) = all_0_4_4
% 47.86/13.54 | (1016) vapp(all_10_11_39, all_10_9_37) = ve2
% 47.86/13.54 | (1017) all_10_3_31 = all_0_4_4
% 47.86/13.54 |
% 47.86/13.54 | Instantiating formula (92) with ve2, all_10_9_37, all_10_11_39 and discharging atoms visValue(ve2) = 0, vapp(all_10_11_39, all_10_9_37) = ve2, yields:
% 47.86/13.54 | (130) $false
% 47.86/13.54 |
% 47.86/13.54 |-The branch is then unsatisfiable
% 47.86/13.54 |-Branch two:
% 47.86/13.54 | (1116) all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34
% 47.86/13.54 |
% 47.86/13.54 | Applying alpha-rule on (1116) yields:
% 47.86/13.54 | (772) all_10_5_33 = ve2
% 47.86/13.54 | (1118) all_10_4_32 = all_10_8_36
% 47.86/13.54 | (775) ~ (all_10_3_31 = 0)
% 47.86/13.54 | (1120) ~ (all_10_2_30 = 0)
% 47.86/13.54 | (1121) visValue(all_10_7_35) = all_10_2_30
% 47.86/13.54 | (1122) vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34
% 47.86/13.54 | (1123) all_0_4_4 = vnoExp
% 47.86/13.54 | (1124) vreduce(all_10_7_35) = all_10_8_36
% 47.86/13.54 | (1125) visSomeExp(all_10_8_36) = all_10_3_31
% 47.86/13.54 | (1126) vapp(all_10_6_34, all_10_7_35) = ve2
% 47.86/13.54 |
% 47.86/13.54 | Equations (1123) can reduce 757 to:
% 47.86/13.54 | (165) $false
% 47.86/13.54 |
% 47.86/13.54 |-The branch is then unsatisfiable
% 47.86/13.54 |-Branch two:
% 47.86/13.54 | (1128) all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)
% 47.86/13.54 |
% 47.86/13.54 | Applying alpha-rule on (1128) yields:
% 47.86/13.54 | (1129) vreduce(all_10_10_38) = all_10_9_37
% 47.86/13.54 | (1130) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)
% 47.86/13.54 | (1123) all_0_4_4 = vnoExp
% 47.86/13.54 | (1012) all_10_8_36 = ve2
% 47.86/13.54 | (1133) ~ (all_10_6_34 = 0)
% 47.86/13.54 | (1134) vapp(all_10_10_38, all_10_11_39) = ve2
% 47.86/13.54 | (1135) visSomeExp(all_10_9_37) = all_10_6_34
% 47.86/13.54 | (1136) all_10_7_35 = all_10_9_37
% 47.86/13.54 |
% 47.86/13.54 | Equations (1123) can reduce 757 to:
% 47.86/13.54 | (165) $false
% 47.86/13.54 |
% 47.86/13.54 |-The branch is then unsatisfiable
% 47.86/13.54 |-Branch two:
% 47.86/13.54 | (1138) all_10_8_36 = ve2 & all_0_4_4 = vnoExp & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2
% 47.86/13.54 |
% 47.86/13.54 | Applying alpha-rule on (1138) yields:
% 47.86/13.54 | (1012) all_10_8_36 = ve2
% 47.86/13.54 | (1123) all_0_4_4 = vnoExp
% 47.86/13.54 | (1141) vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2
% 47.86/13.54 |
% 47.86/13.54 | Equations (1123) can reduce 757 to:
% 47.86/13.54 | (165) $false
% 47.86/13.54 |
% 47.86/13.54 |-The branch is then unsatisfiable
% 47.86/13.54 |-Branch two:
% 47.86/13.54 | (1143) all_10_10_38 = ve2 & all_0_4_4 = vnoExp & vvar(all_10_11_39) = ve2
% 47.86/13.54 |
% 47.86/13.54 | Applying alpha-rule on (1143) yields:
% 47.86/13.54 | (1144) all_10_10_38 = ve2
% 47.86/13.54 | (1123) all_0_4_4 = vnoExp
% 47.86/13.54 | (1146) vvar(all_10_11_39) = ve2
% 47.86/13.54 |
% 47.86/13.54 | Equations (1123) can reduce 757 to:
% 47.86/13.54 | (165) $false
% 47.86/13.54 |
% 47.86/13.54 |-The branch is then unsatisfiable
% 47.86/13.54 |-Branch two:
% 47.86/13.54 | (612) all_9_10_26 = ve1 & all_0_6_6 = vnoExp & vvar(all_9_11_27) = ve1
% 47.86/13.54 |
% 47.86/13.54 | Applying alpha-rule on (612) yields:
% 47.86/13.54 | (613) all_9_10_26 = ve1
% 47.86/13.54 | (502) all_0_6_6 = vnoExp
% 47.86/13.54 | (615) vvar(all_9_11_27) = ve1
% 47.86/13.54 |
% 47.86/13.54 | Instantiating formula (104) with ve1, all_9_11_27 and discharging atoms vvar(all_9_11_27) = ve1, yields:
% 47.86/13.54 | (162) ~ (visValue(ve1) = 0)
% 47.86/13.54 |
% 47.86/13.54 | Using (68) and (162) yields:
% 47.86/13.54 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.54 |
% 47.86/13.54 +-Applying beta-rule and splitting (661), into two cases.
% 47.86/13.54 |-Branch one:
% 47.86/13.54 | (761) all_0_5_5 = 0
% 47.86/13.54 |
% 47.86/13.54 | Combining equations (1326,761) yields a new equation:
% 47.86/13.54 | (1728) all_0_7_7 = 0
% 47.86/13.54 |
% 47.86/13.54 | Simplifying 1728 yields:
% 47.86/13.54 | (164) all_0_7_7 = 0
% 47.86/13.54 |
% 47.86/13.54 | Equations (164) can reduce 163 to:
% 47.86/13.54 | (165) $false
% 47.86/13.54 |
% 47.86/13.54 |-The branch is then unsatisfiable
% 47.86/13.54 |-Branch two:
% 47.86/13.54 | (760) ~ (all_0_5_5 = 0)
% 47.86/13.54 | (764) ? [v0] : vsomeExp(v0) = all_0_4_4
% 47.86/13.54 |
% 47.86/13.54 | Equations (1326) can reduce 760 to:
% 47.86/13.54 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.54 |
% 47.86/13.54 +-Applying beta-rule and splitting (143), into two cases.
% 47.86/13.54 |-Branch one:
% 47.86/13.54 | (164) all_0_7_7 = 0
% 47.86/13.54 |
% 47.86/13.54 | Equations (164) can reduce 163 to:
% 47.86/13.54 | (165) $false
% 47.86/13.54 |
% 47.86/13.54 |-The branch is then unsatisfiable
% 47.86/13.54 |-Branch two:
% 47.86/13.54 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.54 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.86/13.54 |
% 47.86/13.54 | Instantiating (167) with all_116_0_709 yields:
% 47.86/13.54 | (3516) vsomeExp(all_116_0_709) = all_0_6_6
% 47.86/13.54 |
% 47.86/13.54 | From (502) and (3516) follows:
% 47.86/13.54 | (3517) vsomeExp(all_116_0_709) = vnoExp
% 47.86/13.54 |
% 47.86/13.54 | Instantiating formula (40) with all_116_0_709 and discharging atoms vsomeExp(all_116_0_709) = vnoExp, yields:
% 47.86/13.54 | (130) $false
% 47.86/13.54 |
% 47.86/13.54 |-The branch is then unsatisfiable
% 47.86/13.54 |-Branch two:
% 47.86/13.54 | (625) all_8_4_12 = all_8_7_15 & all_8_5_13 = all_0_3_3 & vlookup(all_8_6_14, vempty) = all_8_7_15 & vsomeType(all_0_0_0) = all_8_7_15 & vvar(all_8_6_14) = all_0_3_3
% 47.86/13.54 |
% 47.86/13.54 | Applying alpha-rule on (625) yields:
% 47.86/13.54 | (626) all_8_4_12 = all_8_7_15
% 47.86/13.54 | (627) all_8_5_13 = all_0_3_3
% 47.86/13.54 | (628) vvar(all_8_6_14) = all_0_3_3
% 47.86/13.54 | (629) vsomeType(all_0_0_0) = all_8_7_15
% 47.86/13.54 | (630) vlookup(all_8_6_14, vempty) = all_8_7_15
% 47.86/13.54 |
% 47.86/13.54 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_8_6_14 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_8_6_14) = all_0_3_3, yields:
% 47.86/13.54 | (130) $false
% 47.86/13.54 |
% 47.86/13.54 |-The branch is then unsatisfiable
% 47.86/13.54 |-Branch two:
% 47.86/13.54 | (632) vreduce(ve1) = all_0_1_1
% 47.86/13.54 | (633) all_0_1_1 = all_0_6_6
% 47.86/13.54 |
% 47.86/13.54 | From (633) and (632) follows:
% 47.86/13.54 | (42) vreduce(ve1) = all_0_6_6
% 47.86/13.54 |
% 47.86/13.54 +-Applying beta-rule and splitting (105), into two cases.
% 47.86/13.54 |-Branch one:
% 47.86/13.54 | (1171) ~ (vreduce(ve2) = all_0_1_1)
% 47.86/13.54 |
% 47.86/13.54 | From (633) and (1171) follows:
% 47.86/13.54 | (1172) ~ (vreduce(ve2) = all_0_6_6)
% 47.86/13.54 |
% 47.86/13.54 | Using (81) and (1172) yields:
% 47.86/13.54 | (637) ~ (all_0_4_4 = all_0_6_6)
% 47.86/13.54 |
% 47.86/13.54 +-Applying beta-rule and splitting (113), into two cases.
% 47.86/13.54 |-Branch one:
% 47.86/13.54 | (121) (all_8_0_8 = 0 & all_8_2_10 = all_0_0_0 & all_8_3_11 = all_0_3_3 & varrow(all_8_5_13, all_8_4_12) = all_0_0_0 & vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0 & vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9 & vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3) | (all_8_1_9 = 0 & all_8_2_10 = 0 & all_8_4_12 = all_0_3_3 & varrow(all_8_5_13, all_0_0_0) = all_8_3_11 & vtcheck(vempty, all_8_6_14, all_8_5_13) = 0 & vtcheck(vempty, all_8_7_15, all_8_3_11) = 0 & vapp(all_8_7_15, all_8_6_14) = all_0_3_3)
% 47.86/13.54 |
% 47.86/13.54 +-Applying beta-rule and splitting (121), into two cases.
% 47.86/13.54 |-Branch one:
% 47.86/13.54 | (122) all_8_0_8 = 0 & all_8_2_10 = all_0_0_0 & all_8_3_11 = all_0_3_3 & varrow(all_8_5_13, all_8_4_12) = all_0_0_0 & vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0 & vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9 & vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3
% 47.86/13.54 |
% 47.86/13.54 | Applying alpha-rule on (122) yields:
% 47.86/13.54 | (123) vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3
% 47.86/13.54 | (124) vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0
% 47.86/13.54 | (125) vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9
% 47.86/13.54 | (126) all_8_3_11 = all_0_3_3
% 47.86/13.54 | (127) all_8_0_8 = 0
% 47.86/13.54 | (128) all_8_2_10 = all_0_0_0
% 47.86/13.54 | (129) varrow(all_8_5_13, all_8_4_12) = all_0_0_0
% 47.86/13.54 |
% 47.86/13.54 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_8_6_14, all_8_5_13, all_8_7_15 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3, yields:
% 47.86/13.54 | (130) $false
% 47.86/13.54 |
% 47.86/13.54 |-The branch is then unsatisfiable
% 47.86/13.54 |-Branch two:
% 47.86/13.54 | (131) all_8_1_9 = 0 & all_8_2_10 = 0 & all_8_4_12 = all_0_3_3 & varrow(all_8_5_13, all_0_0_0) = all_8_3_11 & vtcheck(vempty, all_8_6_14, all_8_5_13) = 0 & vtcheck(vempty, all_8_7_15, all_8_3_11) = 0 & vapp(all_8_7_15, all_8_6_14) = all_0_3_3
% 47.86/13.54 |
% 47.86/13.54 | Applying alpha-rule on (131) yields:
% 47.86/13.54 | (132) varrow(all_8_5_13, all_0_0_0) = all_8_3_11
% 47.86/13.54 | (133) vtcheck(vempty, all_8_6_14, all_8_5_13) = 0
% 47.86/13.54 | (134) all_8_2_10 = 0
% 47.86/13.54 | (135) vtcheck(vempty, all_8_7_15, all_8_3_11) = 0
% 47.86/13.54 | (136) all_8_4_12 = all_0_3_3
% 47.86/13.54 | (137) all_8_1_9 = 0
% 47.86/13.54 | (138) vapp(all_8_7_15, all_8_6_14) = all_0_3_3
% 47.86/13.54 |
% 47.86/13.54 | Instantiating formula (31) with all_0_3_3, all_8_6_14, all_8_7_15, ve2, ve1 and discharging atoms vapp(all_8_7_15, all_8_6_14) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.86/13.54 | (139) all_8_6_14 = ve2
% 47.86/13.54 |
% 47.86/13.54 | Instantiating formula (88) with all_0_3_3, all_8_6_14, all_8_7_15, ve2, ve1 and discharging atoms vapp(all_8_7_15, all_8_6_14) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 47.86/13.54 | (140) all_8_7_15 = ve1
% 47.86/13.54 |
% 47.86/13.54 | From (139) and (133) follows:
% 47.86/13.54 | (658) vtcheck(vempty, ve2, all_8_5_13) = 0
% 47.86/13.54 |
% 47.86/13.54 | From (140) and (135) follows:
% 47.86/13.54 | (141) vtcheck(vempty, ve1, all_8_3_11) = 0
% 47.86/13.54 |
% 47.86/13.54 | Instantiating formula (29) with all_8_5_13 and discharging atoms vtcheck(vempty, ve2, all_8_5_13) = 0, yields:
% 47.86/13.54 | (661) all_0_5_5 = 0 | ? [v0] : vsomeExp(v0) = all_0_4_4
% 47.86/13.54 |
% 47.86/13.54 | Instantiating formula (67) with all_8_3_11 and discharging atoms vtcheck(vempty, ve1, all_8_3_11) = 0, yields:
% 47.86/13.54 | (143) all_0_7_7 = 0 | ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.86/13.54 |
% 47.86/13.54 +-Applying beta-rule and splitting (114), into two cases.
% 47.86/13.54 |-Branch one:
% 47.86/13.54 | (144) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22) | (all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)) | (all_9_8_24 = ve1 & all_0_6_6 = vnoExp & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1)
% 47.86/13.54 |
% 47.86/13.54 +-Applying beta-rule and splitting (144), into two cases.
% 47.86/13.54 |-Branch one:
% 47.86/13.54 | (145) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22) | (all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26))
% 47.86/13.54 |
% 47.86/13.54 +-Applying beta-rule and splitting (145), into two cases.
% 47.86/13.54 |-Branch one:
% 47.86/13.54 | (146) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22)
% 47.86/13.54 |
% 47.86/13.54 +-Applying beta-rule and splitting (146), into two cases.
% 47.86/13.54 |-Branch one:
% 47.86/13.54 | (147) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27))
% 47.86/13.54 |
% 47.86/13.54 +-Applying beta-rule and splitting (147), into two cases.
% 47.86/13.54 |-Branch one:
% 47.86/13.54 | (148) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22)
% 47.86/13.54 |
% 47.86/13.54 +-Applying beta-rule and splitting (148), into two cases.
% 47.86/13.54 |-Branch one:
% 47.86/13.54 | (149) all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22
% 47.86/13.54 |
% 47.86/13.54 | Applying alpha-rule on (149) yields:
% 47.86/13.54 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 47.86/13.54 | (151) vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22
% 47.86/13.54 | (152) visSomeExp(all_9_10_26) = all_9_3_19
% 47.86/13.54 | (153) all_9_0_16 = all_0_6_6
% 47.86/13.54 | (154) vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17
% 47.86/13.54 | (155) vreduce(all_9_8_24) = all_9_10_26
% 47.86/13.54 | (156) ~ (all_9_3_19 = 0)
% 47.86/13.54 | (157) all_9_4_20 = all_9_10_26
% 47.86/13.54 | (158) vapp(all_9_6_22, all_9_8_24) = ve1
% 47.86/13.54 | (159) all_9_5_21 = ve1
% 47.86/13.54 | (160) all_9_2_18 = 0
% 47.86/13.54 | (161) visValue(all_9_8_24) = 0
% 47.86/13.54 |
% 47.86/13.54 | Instantiating formula (74) with all_9_1_17 yields:
% 47.86/13.54 | (681) ~ (vsomeExp(all_9_1_17) = all_0_1_1)
% 47.86/13.54 |
% 47.86/13.54 | From (633) and (681) follows:
% 47.86/13.54 | (682) ~ (vsomeExp(all_9_1_17) = all_0_6_6)
% 47.86/13.54 |
% 47.86/13.54 | Using (150) and (682) yields:
% 47.86/13.54 | (130) $false
% 47.86/13.54 |
% 47.86/13.54 |-The branch is then unsatisfiable
% 47.86/13.54 |-Branch two:
% 47.86/13.54 | (264) all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22
% 47.86/13.54 |
% 47.86/13.54 | Applying alpha-rule on (264) yields:
% 47.86/13.54 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 47.86/13.54 | (266) visSomeExp(all_9_7_23) = 0
% 47.86/13.54 | (267) vapp(all_9_6_22, all_9_2_18) = all_9_1_17
% 47.86/13.54 | (268) vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22
% 47.86/13.54 | (269) vreduce(all_9_11_27) = all_9_7_23
% 47.86/13.54 | (270) vapp(all_9_6_22, all_9_11_27) = ve1
% 47.86/13.54 | (153) all_9_0_16 = all_0_6_6
% 47.86/13.54 | (272) all_9_3_19 = 0
% 47.86/13.54 | (273) vgetSomeExp(all_9_7_23) = all_9_2_18
% 47.86/13.54 | (159) all_9_5_21 = ve1
% 47.86/13.54 | (275) all_9_4_20 = all_9_7_23
% 47.86/13.54 |
% 47.86/13.54 | Instantiating formula (74) with all_9_1_17 yields:
% 47.86/13.54 | (681) ~ (vsomeExp(all_9_1_17) = all_0_1_1)
% 47.86/13.54 |
% 47.86/13.54 | From (633) and (681) follows:
% 47.86/13.55 | (682) ~ (vsomeExp(all_9_1_17) = all_0_6_6)
% 47.86/13.55 |
% 47.86/13.55 | Using (150) and (682) yields:
% 47.86/13.55 | (130) $false
% 47.86/13.55 |
% 47.86/13.55 |-The branch is then unsatisfiable
% 47.86/13.55 |-Branch two:
% 47.86/13.55 | (378) all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)
% 47.86/13.55 |
% 47.86/13.55 | Applying alpha-rule on (378) yields:
% 47.86/13.55 | (379) vapp(all_9_5_21, all_9_9_25) = all_9_4_20
% 47.86/13.55 | (380) vsomeExp(all_9_4_20) = all_0_6_6
% 47.86/13.55 | (381) all_9_7_23 = all_9_10_26
% 47.86/13.55 | (382) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)
% 47.86/13.55 | (383) all_9_8_24 = ve1
% 47.86/13.55 | (384) all_9_6_22 = 0
% 47.86/13.55 | (385) visSomeExp(all_9_10_26) = 0
% 47.86/13.55 | (386) vapp(all_9_11_27, all_9_9_25) = ve1
% 47.86/13.55 | (387) all_9_3_19 = all_0_6_6
% 47.86/13.55 | (388) vreduce(all_9_11_27) = all_9_10_26
% 47.86/13.55 | (389) vgetSomeExp(all_9_10_26) = all_9_5_21
% 47.86/13.55 |
% 47.86/13.55 | Instantiating formula (74) with all_9_4_20 yields:
% 47.86/13.55 | (711) ~ (vsomeExp(all_9_4_20) = all_0_1_1)
% 47.86/13.55 |
% 47.86/13.55 | From (633) and (711) follows:
% 47.86/13.55 | (712) ~ (vsomeExp(all_9_4_20) = all_0_6_6)
% 47.86/13.55 |
% 47.86/13.55 | Using (380) and (712) yields:
% 47.86/13.55 | (130) $false
% 47.86/13.55 |
% 47.86/13.55 |-The branch is then unsatisfiable
% 47.86/13.55 |-Branch two:
% 47.86/13.55 | (492) all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22
% 47.86/13.55 |
% 47.86/13.55 | Applying alpha-rule on (492) yields:
% 47.86/13.55 | (493) vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22
% 47.86/13.55 | (494) vapp(all_9_6_22, all_9_7_23) = ve1
% 47.86/13.55 | (495) vreduce(all_9_7_23) = all_9_8_24
% 47.86/13.55 | (496) visSomeExp(all_9_8_24) = all_9_3_19
% 47.86/13.55 | (497) visValue(all_9_7_23) = all_9_2_18
% 47.86/13.55 | (498) all_9_4_20 = all_9_8_24
% 47.86/13.55 | (156) ~ (all_9_3_19 = 0)
% 47.86/13.55 | (159) all_9_5_21 = ve1
% 47.86/13.55 | (501) ~ (all_9_2_18 = 0)
% 47.86/13.55 | (502) all_0_6_6 = vnoExp
% 47.86/13.55 |
% 47.86/13.55 | Instantiating formula (92) with ve1, all_9_7_23, all_9_6_22 and discharging atoms vapp(all_9_6_22, all_9_7_23) = ve1, yields:
% 47.86/13.55 | (162) ~ (visValue(ve1) = 0)
% 47.86/13.55 |
% 47.86/13.55 | Using (68) and (162) yields:
% 47.86/13.55 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.55 |
% 47.86/13.55 +-Applying beta-rule and splitting (143), into two cases.
% 47.86/13.55 |-Branch one:
% 47.86/13.55 | (164) all_0_7_7 = 0
% 47.86/13.55 |
% 47.86/13.55 | Equations (164) can reduce 163 to:
% 47.86/13.55 | (165) $false
% 47.86/13.55 |
% 47.86/13.55 |-The branch is then unsatisfiable
% 47.86/13.55 |-Branch two:
% 47.86/13.55 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.55 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.86/13.55 |
% 47.86/13.55 | Instantiating (167) with all_122_0_726 yields:
% 47.86/13.55 | (3624) vsomeExp(all_122_0_726) = all_0_6_6
% 47.86/13.55 |
% 47.86/13.55 | From (502) and (3624) follows:
% 47.86/13.55 | (3625) vsomeExp(all_122_0_726) = vnoExp
% 47.86/13.55 |
% 47.86/13.55 | Instantiating formula (40) with all_122_0_726 and discharging atoms vsomeExp(all_122_0_726) = vnoExp, yields:
% 47.86/13.55 | (130) $false
% 47.86/13.55 |
% 47.86/13.55 |-The branch is then unsatisfiable
% 47.86/13.55 |-Branch two:
% 47.86/13.55 | (512) all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)
% 47.86/13.55 |
% 47.86/13.55 | Applying alpha-rule on (512) yields:
% 47.86/13.55 | (383) all_9_8_24 = ve1
% 47.86/13.55 | (514) ~ (all_9_6_22 = 0)
% 47.86/13.55 | (515) all_9_7_23 = all_9_9_25
% 47.86/13.55 | (516) visSomeExp(all_9_9_25) = all_9_6_22
% 47.86/13.55 | (517) vapp(all_9_10_26, all_9_11_27) = ve1
% 47.86/13.55 | (518) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)
% 47.86/13.55 | (519) vreduce(all_9_10_26) = all_9_9_25
% 47.86/13.55 | (502) all_0_6_6 = vnoExp
% 47.86/13.55 |
% 47.86/13.55 | Instantiating formula (92) with ve1, all_9_11_27, all_9_10_26 and discharging atoms vapp(all_9_10_26, all_9_11_27) = ve1, yields:
% 47.86/13.55 | (162) ~ (visValue(ve1) = 0)
% 47.86/13.55 |
% 47.86/13.55 | Using (68) and (162) yields:
% 47.86/13.55 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.55 |
% 47.86/13.55 +-Applying beta-rule and splitting (661), into two cases.
% 47.86/13.55 |-Branch one:
% 47.86/13.55 | (761) all_0_5_5 = 0
% 47.86/13.55 |
% 47.86/13.55 | Combining equations (761,1326) yields a new equation:
% 47.86/13.55 | (164) all_0_7_7 = 0
% 47.86/13.55 |
% 47.86/13.55 | Equations (164) can reduce 163 to:
% 47.86/13.55 | (165) $false
% 47.86/13.55 |
% 47.86/13.55 |-The branch is then unsatisfiable
% 47.86/13.55 |-Branch two:
% 47.86/13.55 | (760) ~ (all_0_5_5 = 0)
% 47.86/13.55 | (764) ? [v0] : vsomeExp(v0) = all_0_4_4
% 47.86/13.55 |
% 47.86/13.55 | Equations (1326) can reduce 760 to:
% 47.86/13.55 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.55 |
% 47.86/13.55 +-Applying beta-rule and splitting (143), into two cases.
% 47.86/13.55 |-Branch one:
% 47.86/13.55 | (164) all_0_7_7 = 0
% 47.86/13.55 |
% 47.86/13.55 | Equations (164) can reduce 163 to:
% 47.86/13.55 | (165) $false
% 47.86/13.55 |
% 47.86/13.55 |-The branch is then unsatisfiable
% 47.86/13.55 |-Branch two:
% 47.86/13.55 | (163) ~ (all_0_7_7 = 0)
% 47.86/13.55 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 47.86/13.55 |
% 47.86/13.55 | Instantiating (167) with all_117_0_729 yields:
% 47.86/13.55 | (3648) vsomeExp(all_117_0_729) = all_0_6_6
% 47.86/13.55 |
% 47.86/13.55 | From (502) and (3648) follows:
% 47.86/13.55 | (3649) vsomeExp(all_117_0_729) = vnoExp
% 47.86/13.55 |
% 47.86/13.55 | Instantiating formula (40) with all_117_0_729 and discharging atoms vsomeExp(all_117_0_729) = vnoExp, yields:
% 47.86/13.55 | (130) $false
% 47.86/13.55 |
% 47.86/13.55 |-The branch is then unsatisfiable
% 47.86/13.55 |-Branch two:
% 47.86/13.55 | (530) all_9_8_24 = ve1 & all_0_6_6 = vnoExp & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1
% 47.86/13.55 |
% 47.86/13.55 | Applying alpha-rule on (530) yields:
% 47.86/13.55 | (383) all_9_8_24 = ve1
% 47.86/13.55 | (502) all_0_6_6 = vnoExp
% 47.86/13.55 | (533) vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1
% 47.86/13.55 |
% 47.86/13.55 | Equations (502) can reduce 637 to:
% 47.86/13.55 | (757) ~ (all_0_4_4 = vnoExp)
% 47.86/13.55 |
% 47.86/13.55 | Instantiating formula (22) with all_0_7_7, ve1, all_9_9_25, all_9_10_26, all_9_11_27 and discharging atoms visValue(ve1) = all_0_7_7, vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1, yields:
% 47.86/13.55 | (164) all_0_7_7 = 0
% 47.86/13.55 |
% 47.86/13.55 | From (164) and (1327) follows:
% 47.86/13.55 | (1772) visValue(ve2) = 0
% 47.86/13.55 |
% 47.86/13.55 +-Applying beta-rule and splitting (115), into two cases.
% 47.86/13.55 |-Branch one:
% 47.86/13.55 | (766) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34) | (all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)) | (all_10_8_36 = ve2 & all_0_4_4 = vnoExp & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2)
% 47.86/13.55 |
% 47.86/13.55 +-Applying beta-rule and splitting (766), into two cases.
% 47.86/13.55 |-Branch one:
% 47.86/13.55 | (767) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34) | (all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38))
% 48.03/13.55 |
% 48.03/13.55 +-Applying beta-rule and splitting (767), into two cases.
% 48.03/13.55 |-Branch one:
% 48.03/13.55 | (768) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)) | (all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34)
% 48.03/13.55 |
% 48.03/13.55 +-Applying beta-rule and splitting (768), into two cases.
% 48.03/13.55 |-Branch one:
% 48.03/13.55 | (769) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34) | (all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39))
% 48.03/13.55 |
% 48.03/13.55 +-Applying beta-rule and splitting (769), into two cases.
% 48.03/13.55 |-Branch one:
% 48.03/13.55 | (770) (all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34) | (all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34)
% 48.03/13.55 |
% 48.03/13.55 +-Applying beta-rule and splitting (770), into two cases.
% 48.03/13.55 |-Branch one:
% 48.03/13.55 | (771) all_10_0_28 = all_0_4_4 & all_10_2_30 = 0 & all_10_4_32 = all_10_10_38 & all_10_5_33 = ve2 & ~ (all_10_3_31 = 0) & vreduce(all_10_8_36) = all_10_10_38 & visSomeExp(all_10_10_38) = all_10_3_31 & vsomeExp(all_10_1_29) = all_0_4_4 & vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29 & visValue(all_10_8_36) = 0 & vapp(all_10_6_34, all_10_8_36) = ve2 & vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34
% 48.03/13.55 |
% 48.03/13.55 | Applying alpha-rule on (771) yields:
% 48.03/13.55 | (772) all_10_5_33 = ve2
% 48.03/13.55 | (773) visValue(all_10_8_36) = 0
% 48.03/13.55 | (774) all_10_4_32 = all_10_10_38
% 48.03/13.55 | (775) ~ (all_10_3_31 = 0)
% 48.03/13.55 | (776) all_10_2_30 = 0
% 48.03/13.55 | (777) vapp(all_10_6_34, all_10_8_36) = ve2
% 48.03/13.55 | (778) vsubst(all_10_9_37, all_10_8_36, all_10_7_35) = all_10_1_29
% 48.03/13.55 | (779) vabs(all_10_9_37, all_10_11_39, all_10_7_35) = all_10_6_34
% 48.03/13.55 | (780) all_10_0_28 = all_0_4_4
% 48.03/13.55 | (781) visSomeExp(all_10_10_38) = all_10_3_31
% 48.03/13.55 | (782) vsomeExp(all_10_1_29) = all_0_4_4
% 48.03/13.55 | (783) vreduce(all_10_8_36) = all_10_10_38
% 48.03/13.55 |
% 48.03/13.55 | Instantiating formula (92) with ve2, all_10_8_36, all_10_6_34 and discharging atoms visValue(ve2) = 0, vapp(all_10_6_34, all_10_8_36) = ve2, yields:
% 48.03/13.55 | (130) $false
% 48.03/13.55 |
% 48.03/13.55 |-The branch is then unsatisfiable
% 48.03/13.55 |-Branch two:
% 48.03/13.55 | (896) all_10_0_28 = all_0_4_4 & all_10_3_31 = 0 & all_10_4_32 = all_10_7_35 & all_10_5_33 = ve2 & vreduce(all_10_11_39) = all_10_7_35 & vgetSomeExp(all_10_7_35) = all_10_2_30 & visSomeExp(all_10_7_35) = 0 & vsomeExp(all_10_1_29) = all_0_4_4 & vapp(all_10_6_34, all_10_2_30) = all_10_1_29 & vapp(all_10_6_34, all_10_11_39) = ve2 & vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34
% 48.03/13.55 |
% 48.03/13.55 | Applying alpha-rule on (896) yields:
% 48.03/13.55 | (772) all_10_5_33 = ve2
% 48.03/13.55 | (898) vreduce(all_10_11_39) = all_10_7_35
% 48.03/13.55 | (846) all_10_3_31 = 0
% 48.03/13.55 | (900) all_10_4_32 = all_10_7_35
% 48.03/13.55 | (901) visSomeExp(all_10_7_35) = 0
% 48.03/13.55 | (902) vapp(all_10_6_34, all_10_2_30) = all_10_1_29
% 48.03/13.55 | (780) all_10_0_28 = all_0_4_4
% 48.03/13.55 | (904) vgetSomeExp(all_10_7_35) = all_10_2_30
% 48.03/13.55 | (905) vabs(all_10_10_38, all_10_9_37, all_10_8_36) = all_10_6_34
% 48.03/13.55 | (906) vapp(all_10_6_34, all_10_11_39) = ve2
% 48.03/13.55 | (782) vsomeExp(all_10_1_29) = all_0_4_4
% 48.03/13.55 |
% 48.03/13.55 | Instantiating formula (92) with ve2, all_10_11_39, all_10_6_34 and discharging atoms visValue(ve2) = 0, vapp(all_10_6_34, all_10_11_39) = ve2, yields:
% 48.03/13.55 | (130) $false
% 48.03/13.55 |
% 48.03/13.55 |-The branch is then unsatisfiable
% 48.03/13.55 |-Branch two:
% 48.03/13.55 | (1006) all_10_3_31 = all_0_4_4 & all_10_6_34 = 0 & all_10_7_35 = all_10_10_38 & all_10_8_36 = ve2 & vreduce(all_10_11_39) = all_10_10_38 & vgetSomeExp(all_10_10_38) = all_10_5_33 & visSomeExp(all_10_10_38) = 0 & vsomeExp(all_10_4_32) = all_0_4_4 & vapp(all_10_5_33, all_10_9_37) = all_10_4_32 & vapp(all_10_11_39, all_10_9_37) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)
% 48.03/13.55 |
% 48.03/13.55 | Applying alpha-rule on (1006) yields:
% 48.03/13.55 | (1007) all_10_7_35 = all_10_10_38
% 48.03/13.55 | (1008) vgetSomeExp(all_10_10_38) = all_10_5_33
% 48.03/13.55 | (1009) vapp(all_10_5_33, all_10_9_37) = all_10_4_32
% 48.03/13.55 | (1010) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_11_39)
% 48.03/13.55 | (1011) visSomeExp(all_10_10_38) = 0
% 48.03/13.55 | (1012) all_10_8_36 = ve2
% 48.03/13.55 | (1013) vreduce(all_10_11_39) = all_10_10_38
% 48.03/13.55 | (1014) all_10_6_34 = 0
% 48.03/13.55 | (1015) vsomeExp(all_10_4_32) = all_0_4_4
% 48.03/13.55 | (1016) vapp(all_10_11_39, all_10_9_37) = ve2
% 48.03/13.55 | (1017) all_10_3_31 = all_0_4_4
% 48.03/13.55 |
% 48.03/13.55 | Instantiating formula (92) with ve2, all_10_9_37, all_10_11_39 and discharging atoms visValue(ve2) = 0, vapp(all_10_11_39, all_10_9_37) = ve2, yields:
% 48.03/13.55 | (130) $false
% 48.03/13.55 |
% 48.03/13.55 |-The branch is then unsatisfiable
% 48.03/13.55 |-Branch two:
% 48.03/13.55 | (1116) all_10_4_32 = all_10_8_36 & all_10_5_33 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_2_30 = 0) & ~ (all_10_3_31 = 0) & vreduce(all_10_7_35) = all_10_8_36 & visSomeExp(all_10_8_36) = all_10_3_31 & visValue(all_10_7_35) = all_10_2_30 & vapp(all_10_6_34, all_10_7_35) = ve2 & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34
% 48.03/13.55 |
% 48.03/13.55 | Applying alpha-rule on (1116) yields:
% 48.03/13.55 | (772) all_10_5_33 = ve2
% 48.03/13.55 | (1118) all_10_4_32 = all_10_8_36
% 48.03/13.55 | (775) ~ (all_10_3_31 = 0)
% 48.03/13.55 | (1120) ~ (all_10_2_30 = 0)
% 48.03/13.55 | (1121) visValue(all_10_7_35) = all_10_2_30
% 48.03/13.55 | (1122) vabs(all_10_11_39, all_10_10_38, all_10_9_37) = all_10_6_34
% 48.03/13.55 | (1123) all_0_4_4 = vnoExp
% 48.03/13.55 | (1124) vreduce(all_10_7_35) = all_10_8_36
% 48.03/13.55 | (1125) visSomeExp(all_10_8_36) = all_10_3_31
% 48.03/13.55 | (1126) vapp(all_10_6_34, all_10_7_35) = ve2
% 48.03/13.55 |
% 48.03/13.55 | Equations (1123) can reduce 757 to:
% 48.03/13.55 | (165) $false
% 48.03/13.55 |
% 48.03/13.55 |-The branch is then unsatisfiable
% 48.03/13.55 |-Branch two:
% 48.03/13.55 | (1128) all_10_7_35 = all_10_9_37 & all_10_8_36 = ve2 & all_0_4_4 = vnoExp & ~ (all_10_6_34 = 0) & vreduce(all_10_10_38) = all_10_9_37 & visSomeExp(all_10_9_37) = all_10_6_34 & vapp(all_10_10_38, all_10_11_39) = ve2 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)
% 48.03/13.55 |
% 48.03/13.55 | Applying alpha-rule on (1128) yields:
% 48.03/13.55 | (1129) vreduce(all_10_10_38) = all_10_9_37
% 48.03/13.55 | (1130) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_10_10_38)
% 48.03/13.55 | (1123) all_0_4_4 = vnoExp
% 48.03/13.55 | (1012) all_10_8_36 = ve2
% 48.03/13.55 | (1133) ~ (all_10_6_34 = 0)
% 48.03/13.55 | (1134) vapp(all_10_10_38, all_10_11_39) = ve2
% 48.03/13.55 | (1135) visSomeExp(all_10_9_37) = all_10_6_34
% 48.03/13.55 | (1136) all_10_7_35 = all_10_9_37
% 48.03/13.55 |
% 48.03/13.55 | Equations (1123) can reduce 757 to:
% 48.03/13.55 | (165) $false
% 48.03/13.55 |
% 48.03/13.55 |-The branch is then unsatisfiable
% 48.03/13.55 |-Branch two:
% 48.03/13.55 | (1138) all_10_8_36 = ve2 & all_0_4_4 = vnoExp & vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2
% 48.03/13.55 |
% 48.03/13.55 | Applying alpha-rule on (1138) yields:
% 48.03/13.55 | (1012) all_10_8_36 = ve2
% 48.03/13.55 | (1123) all_0_4_4 = vnoExp
% 48.03/13.55 | (1141) vabs(all_10_11_39, all_10_10_38, all_10_9_37) = ve2
% 48.03/13.55 |
% 48.03/13.55 | Equations (1123) can reduce 757 to:
% 48.03/13.55 | (165) $false
% 48.03/13.55 |
% 48.03/13.55 |-The branch is then unsatisfiable
% 48.03/13.55 |-Branch two:
% 48.03/13.55 | (1143) all_10_10_38 = ve2 & all_0_4_4 = vnoExp & vvar(all_10_11_39) = ve2
% 48.03/13.55 |
% 48.03/13.55 | Applying alpha-rule on (1143) yields:
% 48.03/13.55 | (1144) all_10_10_38 = ve2
% 48.03/13.55 | (1123) all_0_4_4 = vnoExp
% 48.03/13.55 | (1146) vvar(all_10_11_39) = ve2
% 48.03/13.55 |
% 48.03/13.55 | Equations (1123) can reduce 757 to:
% 48.03/13.55 | (165) $false
% 48.03/13.55 |
% 48.03/13.55 |-The branch is then unsatisfiable
% 48.03/13.55 |-Branch two:
% 48.03/13.55 | (612) all_9_10_26 = ve1 & all_0_6_6 = vnoExp & vvar(all_9_11_27) = ve1
% 48.03/13.55 |
% 48.03/13.55 | Applying alpha-rule on (612) yields:
% 48.03/13.55 | (613) all_9_10_26 = ve1
% 48.03/13.55 | (502) all_0_6_6 = vnoExp
% 48.03/13.55 | (615) vvar(all_9_11_27) = ve1
% 48.03/13.55 |
% 48.03/13.55 | Instantiating formula (104) with ve1, all_9_11_27 and discharging atoms vvar(all_9_11_27) = ve1, yields:
% 48.03/13.55 | (162) ~ (visValue(ve1) = 0)
% 48.03/13.55 |
% 48.03/13.55 | Using (68) and (162) yields:
% 48.03/13.55 | (163) ~ (all_0_7_7 = 0)
% 48.03/13.55 |
% 48.03/13.55 +-Applying beta-rule and splitting (661), into two cases.
% 48.03/13.55 |-Branch one:
% 48.03/13.55 | (761) all_0_5_5 = 0
% 48.03/13.55 |
% 48.03/13.55 | Combining equations (1326,761) yields a new equation:
% 48.03/13.55 | (1728) all_0_7_7 = 0
% 48.03/13.55 |
% 48.03/13.55 | Simplifying 1728 yields:
% 48.03/13.55 | (164) all_0_7_7 = 0
% 48.03/13.56 |
% 48.03/13.56 | Equations (164) can reduce 163 to:
% 48.03/13.56 | (165) $false
% 48.03/13.56 |
% 48.03/13.56 |-The branch is then unsatisfiable
% 48.03/13.56 |-Branch two:
% 48.03/13.56 | (760) ~ (all_0_5_5 = 0)
% 48.03/13.56 | (764) ? [v0] : vsomeExp(v0) = all_0_4_4
% 48.03/13.56 |
% 48.03/13.56 | Equations (1326) can reduce 760 to:
% 48.03/13.56 | (163) ~ (all_0_7_7 = 0)
% 48.03/13.56 |
% 48.03/13.56 +-Applying beta-rule and splitting (143), into two cases.
% 48.03/13.56 |-Branch one:
% 48.03/13.56 | (164) all_0_7_7 = 0
% 48.03/13.56 |
% 48.03/13.56 | Equations (164) can reduce 163 to:
% 48.03/13.56 | (165) $false
% 48.03/13.56 |
% 48.03/13.56 |-The branch is then unsatisfiable
% 48.03/13.56 |-Branch two:
% 48.03/13.56 | (163) ~ (all_0_7_7 = 0)
% 48.03/13.56 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 48.03/13.56 |
% 48.03/13.56 | Instantiating (167) with all_116_0_731 yields:
% 48.03/13.56 | (3752) vsomeExp(all_116_0_731) = all_0_6_6
% 48.03/13.56 |
% 48.03/13.56 | From (502) and (3752) follows:
% 48.03/13.56 | (3753) vsomeExp(all_116_0_731) = vnoExp
% 48.03/13.56 |
% 48.03/13.56 | Instantiating formula (40) with all_116_0_731 and discharging atoms vsomeExp(all_116_0_731) = vnoExp, yields:
% 48.03/13.56 | (130) $false
% 48.03/13.56 |
% 48.03/13.56 |-The branch is then unsatisfiable
% 48.03/13.56 |-Branch two:
% 48.03/13.56 | (625) all_8_4_12 = all_8_7_15 & all_8_5_13 = all_0_3_3 & vlookup(all_8_6_14, vempty) = all_8_7_15 & vsomeType(all_0_0_0) = all_8_7_15 & vvar(all_8_6_14) = all_0_3_3
% 48.03/13.56 |
% 48.03/13.56 | Applying alpha-rule on (625) yields:
% 48.03/13.56 | (626) all_8_4_12 = all_8_7_15
% 48.03/13.56 | (627) all_8_5_13 = all_0_3_3
% 48.03/13.56 | (628) vvar(all_8_6_14) = all_0_3_3
% 48.03/13.56 | (629) vsomeType(all_0_0_0) = all_8_7_15
% 48.03/13.56 | (630) vlookup(all_8_6_14, vempty) = all_8_7_15
% 48.03/13.56 |
% 48.03/13.56 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_8_6_14 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_8_6_14) = all_0_3_3, yields:
% 48.03/13.56 | (130) $false
% 48.03/13.56 |
% 48.03/13.56 |-The branch is then unsatisfiable
% 48.03/13.56 |-Branch two:
% 48.03/13.56 | (1174) vreduce(ve2) = all_0_1_1
% 48.03/13.56 | (1175) all_0_1_1 = all_0_4_4
% 48.03/13.56 |
% 48.03/13.56 | Combining equations (1175,633) yields a new equation:
% 48.03/13.56 | (1176) all_0_4_4 = all_0_6_6
% 48.03/13.56 |
% 48.03/13.56 | Simplifying 1176 yields:
% 48.03/13.56 | (1169) all_0_4_4 = all_0_6_6
% 48.03/13.56 |
% 48.03/13.56 +-Applying beta-rule and splitting (107), into two cases.
% 48.03/13.56 |-Branch one:
% 48.03/13.56 | (636) ~ (vreduce(ve1) = all_0_4_4)
% 48.03/13.56 |
% 48.03/13.56 | From (1169) and (636) follows:
% 48.03/13.56 | (3767) ~ (vreduce(ve1) = all_0_6_6)
% 48.03/13.56 |
% 48.03/13.56 | Using (42) and (3767) yields:
% 48.03/13.56 | (130) $false
% 48.03/13.56 |
% 48.03/13.56 |-The branch is then unsatisfiable
% 48.03/13.56 |-Branch two:
% 48.03/13.56 | (1168) vreduce(ve1) = all_0_4_4
% 48.03/13.56 | (1169) all_0_4_4 = all_0_6_6
% 48.03/13.56 |
% 48.03/13.56 +-Applying beta-rule and splitting (113), into two cases.
% 48.03/13.56 |-Branch one:
% 48.03/13.56 | (121) (all_8_0_8 = 0 & all_8_2_10 = all_0_0_0 & all_8_3_11 = all_0_3_3 & varrow(all_8_5_13, all_8_4_12) = all_0_0_0 & vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0 & vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9 & vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3) | (all_8_1_9 = 0 & all_8_2_10 = 0 & all_8_4_12 = all_0_3_3 & varrow(all_8_5_13, all_0_0_0) = all_8_3_11 & vtcheck(vempty, all_8_6_14, all_8_5_13) = 0 & vtcheck(vempty, all_8_7_15, all_8_3_11) = 0 & vapp(all_8_7_15, all_8_6_14) = all_0_3_3)
% 48.03/13.56 |
% 48.03/13.56 +-Applying beta-rule and splitting (121), into two cases.
% 48.03/13.56 |-Branch one:
% 48.03/13.56 | (122) all_8_0_8 = 0 & all_8_2_10 = all_0_0_0 & all_8_3_11 = all_0_3_3 & varrow(all_8_5_13, all_8_4_12) = all_0_0_0 & vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0 & vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9 & vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3
% 48.03/13.56 |
% 48.03/13.56 | Applying alpha-rule on (122) yields:
% 48.03/13.56 | (123) vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3
% 48.03/13.56 | (124) vtcheck(all_8_1_9, all_8_6_14, all_8_4_12) = 0
% 48.03/13.56 | (125) vbind(all_8_7_15, all_8_5_13, vempty) = all_8_1_9
% 48.03/13.56 | (126) all_8_3_11 = all_0_3_3
% 48.03/13.56 | (127) all_8_0_8 = 0
% 48.03/13.56 | (128) all_8_2_10 = all_0_0_0
% 48.03/13.56 | (129) varrow(all_8_5_13, all_8_4_12) = all_0_0_0
% 48.03/13.56 |
% 48.03/13.56 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_8_6_14, all_8_5_13, all_8_7_15 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_8_7_15, all_8_5_13, all_8_6_14) = all_0_3_3, yields:
% 48.03/13.56 | (130) $false
% 48.03/13.56 |
% 48.03/13.56 |-The branch is then unsatisfiable
% 48.03/13.56 |-Branch two:
% 48.03/13.56 | (131) all_8_1_9 = 0 & all_8_2_10 = 0 & all_8_4_12 = all_0_3_3 & varrow(all_8_5_13, all_0_0_0) = all_8_3_11 & vtcheck(vempty, all_8_6_14, all_8_5_13) = 0 & vtcheck(vempty, all_8_7_15, all_8_3_11) = 0 & vapp(all_8_7_15, all_8_6_14) = all_0_3_3
% 48.03/13.56 |
% 48.03/13.56 | Applying alpha-rule on (131) yields:
% 48.03/13.56 | (132) varrow(all_8_5_13, all_0_0_0) = all_8_3_11
% 48.03/13.56 | (133) vtcheck(vempty, all_8_6_14, all_8_5_13) = 0
% 48.03/13.56 | (134) all_8_2_10 = 0
% 48.03/13.56 | (135) vtcheck(vempty, all_8_7_15, all_8_3_11) = 0
% 48.03/13.56 | (136) all_8_4_12 = all_0_3_3
% 48.03/13.56 | (137) all_8_1_9 = 0
% 48.03/13.56 | (138) vapp(all_8_7_15, all_8_6_14) = all_0_3_3
% 48.03/13.56 |
% 48.03/13.56 | Instantiating formula (31) with all_0_3_3, all_8_6_14, all_8_7_15, ve2, ve1 and discharging atoms vapp(all_8_7_15, all_8_6_14) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 48.03/13.56 | (139) all_8_6_14 = ve2
% 48.03/13.56 |
% 48.03/13.56 | Instantiating formula (88) with all_0_3_3, all_8_6_14, all_8_7_15, ve2, ve1 and discharging atoms vapp(all_8_7_15, all_8_6_14) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 48.03/13.56 | (140) all_8_7_15 = ve1
% 48.03/13.56 |
% 48.03/13.56 | From (139) and (133) follows:
% 48.03/13.56 | (658) vtcheck(vempty, ve2, all_8_5_13) = 0
% 48.03/13.56 |
% 48.03/13.56 | From (140) and (135) follows:
% 48.03/13.56 | (141) vtcheck(vempty, ve1, all_8_3_11) = 0
% 48.03/13.56 |
% 48.03/13.56 | From (140)(139) and (138) follows:
% 48.03/13.56 | (35) vapp(ve1, ve2) = all_0_3_3
% 48.03/13.56 |
% 48.03/13.56 | Instantiating formula (29) with all_8_5_13 and discharging atoms vtcheck(vempty, ve2, all_8_5_13) = 0, yields:
% 48.03/13.56 | (661) all_0_5_5 = 0 | ? [v0] : vsomeExp(v0) = all_0_4_4
% 48.03/13.56 |
% 48.03/13.56 | Instantiating formula (67) with all_8_3_11 and discharging atoms vtcheck(vempty, ve1, all_8_3_11) = 0, yields:
% 48.03/13.56 | (143) all_0_7_7 = 0 | ? [v0] : vsomeExp(v0) = all_0_6_6
% 48.03/13.56 |
% 48.03/13.56 +-Applying beta-rule and splitting (114), into two cases.
% 48.03/13.56 |-Branch one:
% 48.03/13.56 | (144) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22) | (all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)) | (all_9_8_24 = ve1 & all_0_6_6 = vnoExp & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1)
% 48.03/13.56 |
% 48.03/13.56 +-Applying beta-rule and splitting (144), into two cases.
% 48.03/13.56 |-Branch one:
% 48.03/13.56 | (145) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22) | (all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26))
% 48.03/13.56 |
% 48.03/13.56 +-Applying beta-rule and splitting (145), into two cases.
% 48.03/13.56 |-Branch one:
% 48.03/13.56 | (146) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)) | (all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22)
% 48.03/13.56 |
% 48.03/13.56 +-Applying beta-rule and splitting (146), into two cases.
% 48.03/13.56 |-Branch one:
% 48.03/13.56 | (147) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22) | (all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27))
% 48.03/13.56 |
% 48.03/13.56 +-Applying beta-rule and splitting (147), into two cases.
% 48.03/13.56 |-Branch one:
% 48.03/13.56 | (148) (all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22) | (all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22)
% 48.03/13.56 |
% 48.03/13.56 +-Applying beta-rule and splitting (148), into two cases.
% 48.03/13.56 |-Branch one:
% 48.03/13.56 | (149) all_9_0_16 = all_0_6_6 & all_9_2_18 = 0 & all_9_4_20 = all_9_10_26 & all_9_5_21 = ve1 & ~ (all_9_3_19 = 0) & vreduce(all_9_8_24) = all_9_10_26 & visSomeExp(all_9_10_26) = all_9_3_19 & vsomeExp(all_9_1_17) = all_0_6_6 & vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17 & visValue(all_9_8_24) = 0 & vapp(all_9_6_22, all_9_8_24) = ve1 & vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22
% 48.03/13.56 |
% 48.03/13.56 | Applying alpha-rule on (149) yields:
% 48.03/13.56 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 48.03/13.56 | (151) vabs(all_9_9_25, all_9_11_27, all_9_7_23) = all_9_6_22
% 48.03/13.56 | (152) visSomeExp(all_9_10_26) = all_9_3_19
% 48.03/13.56 | (153) all_9_0_16 = all_0_6_6
% 48.03/13.56 | (154) vsubst(all_9_9_25, all_9_8_24, all_9_7_23) = all_9_1_17
% 48.03/13.56 | (155) vreduce(all_9_8_24) = all_9_10_26
% 48.03/13.56 | (156) ~ (all_9_3_19 = 0)
% 48.03/13.56 | (157) all_9_4_20 = all_9_10_26
% 48.03/13.56 | (158) vapp(all_9_6_22, all_9_8_24) = ve1
% 48.03/13.56 | (159) all_9_5_21 = ve1
% 48.03/13.56 | (160) all_9_2_18 = 0
% 48.03/13.56 | (161) visValue(all_9_8_24) = 0
% 48.03/13.56 |
% 48.03/13.56 | Instantiating formula (74) with all_9_1_17 yields:
% 48.03/13.56 | (681) ~ (vsomeExp(all_9_1_17) = all_0_1_1)
% 48.03/13.56 |
% 48.03/13.56 | From (633) and (681) follows:
% 48.03/13.56 | (682) ~ (vsomeExp(all_9_1_17) = all_0_6_6)
% 48.03/13.56 |
% 48.03/13.56 | Using (150) and (682) yields:
% 48.03/13.56 | (130) $false
% 48.03/13.56 |
% 48.03/13.56 |-The branch is then unsatisfiable
% 48.03/13.56 |-Branch two:
% 48.03/13.56 | (264) all_9_0_16 = all_0_6_6 & all_9_3_19 = 0 & all_9_4_20 = all_9_7_23 & all_9_5_21 = ve1 & vreduce(all_9_11_27) = all_9_7_23 & vgetSomeExp(all_9_7_23) = all_9_2_18 & visSomeExp(all_9_7_23) = 0 & vsomeExp(all_9_1_17) = all_0_6_6 & vapp(all_9_6_22, all_9_2_18) = all_9_1_17 & vapp(all_9_6_22, all_9_11_27) = ve1 & vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22
% 48.03/13.56 |
% 48.03/13.56 | Applying alpha-rule on (264) yields:
% 48.03/13.56 | (150) vsomeExp(all_9_1_17) = all_0_6_6
% 48.03/13.56 | (266) visSomeExp(all_9_7_23) = 0
% 48.03/13.56 | (267) vapp(all_9_6_22, all_9_2_18) = all_9_1_17
% 48.03/13.56 | (268) vabs(all_9_10_26, all_9_9_25, all_9_8_24) = all_9_6_22
% 48.03/13.56 | (269) vreduce(all_9_11_27) = all_9_7_23
% 48.03/13.56 | (270) vapp(all_9_6_22, all_9_11_27) = ve1
% 48.03/13.56 | (153) all_9_0_16 = all_0_6_6
% 48.03/13.56 | (272) all_9_3_19 = 0
% 48.03/13.56 | (273) vgetSomeExp(all_9_7_23) = all_9_2_18
% 48.03/13.56 | (159) all_9_5_21 = ve1
% 48.03/13.56 | (275) all_9_4_20 = all_9_7_23
% 48.03/13.56 |
% 48.03/13.56 | Instantiating formula (74) with all_9_1_17 yields:
% 48.03/13.56 | (681) ~ (vsomeExp(all_9_1_17) = all_0_1_1)
% 48.03/13.56 |
% 48.03/13.56 | From (633) and (681) follows:
% 48.03/13.56 | (682) ~ (vsomeExp(all_9_1_17) = all_0_6_6)
% 48.03/13.56 |
% 48.03/13.56 | Using (150) and (682) yields:
% 48.03/13.56 | (130) $false
% 48.03/13.56 |
% 48.03/13.56 |-The branch is then unsatisfiable
% 48.03/13.56 |-Branch two:
% 48.03/13.56 | (378) all_9_3_19 = all_0_6_6 & all_9_6_22 = 0 & all_9_7_23 = all_9_10_26 & all_9_8_24 = ve1 & vreduce(all_9_11_27) = all_9_10_26 & vgetSomeExp(all_9_10_26) = all_9_5_21 & visSomeExp(all_9_10_26) = 0 & vsomeExp(all_9_4_20) = all_0_6_6 & vapp(all_9_5_21, all_9_9_25) = all_9_4_20 & vapp(all_9_11_27, all_9_9_25) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)
% 48.03/13.56 |
% 48.03/13.56 | Applying alpha-rule on (378) yields:
% 48.03/13.56 | (379) vapp(all_9_5_21, all_9_9_25) = all_9_4_20
% 48.03/13.56 | (380) vsomeExp(all_9_4_20) = all_0_6_6
% 48.03/13.56 | (381) all_9_7_23 = all_9_10_26
% 48.03/13.56 | (382) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_11_27)
% 48.03/13.56 | (383) all_9_8_24 = ve1
% 48.03/13.56 | (384) all_9_6_22 = 0
% 48.03/13.56 | (385) visSomeExp(all_9_10_26) = 0
% 48.03/13.56 | (386) vapp(all_9_11_27, all_9_9_25) = ve1
% 48.03/13.56 | (387) all_9_3_19 = all_0_6_6
% 48.03/13.56 | (388) vreduce(all_9_11_27) = all_9_10_26
% 48.03/13.56 | (389) vgetSomeExp(all_9_10_26) = all_9_5_21
% 48.03/13.56 |
% 48.03/13.56 | Instantiating formula (74) with all_9_4_20 yields:
% 48.03/13.56 | (711) ~ (vsomeExp(all_9_4_20) = all_0_1_1)
% 48.03/13.56 |
% 48.03/13.56 | From (633) and (711) follows:
% 48.03/13.56 | (712) ~ (vsomeExp(all_9_4_20) = all_0_6_6)
% 48.03/13.56 |
% 48.03/13.56 | Using (380) and (712) yields:
% 48.03/13.56 | (130) $false
% 48.03/13.56 |
% 48.03/13.56 |-The branch is then unsatisfiable
% 48.03/13.56 |-Branch two:
% 48.03/13.56 | (492) all_9_4_20 = all_9_8_24 & all_9_5_21 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_2_18 = 0) & ~ (all_9_3_19 = 0) & vreduce(all_9_7_23) = all_9_8_24 & visSomeExp(all_9_8_24) = all_9_3_19 & visValue(all_9_7_23) = all_9_2_18 & vapp(all_9_6_22, all_9_7_23) = ve1 & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22
% 48.03/13.56 |
% 48.03/13.56 | Applying alpha-rule on (492) yields:
% 48.03/13.56 | (493) vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_9_6_22
% 48.03/13.56 | (494) vapp(all_9_6_22, all_9_7_23) = ve1
% 48.03/13.56 | (495) vreduce(all_9_7_23) = all_9_8_24
% 48.03/13.56 | (496) visSomeExp(all_9_8_24) = all_9_3_19
% 48.03/13.56 | (497) visValue(all_9_7_23) = all_9_2_18
% 48.03/13.56 | (498) all_9_4_20 = all_9_8_24
% 48.03/13.56 | (156) ~ (all_9_3_19 = 0)
% 48.03/13.56 | (159) all_9_5_21 = ve1
% 48.03/13.56 | (501) ~ (all_9_2_18 = 0)
% 48.03/13.56 | (502) all_0_6_6 = vnoExp
% 48.03/13.56 |
% 48.03/13.56 | Combining equations (502,1169) yields a new equation:
% 48.03/13.56 | (1123) all_0_4_4 = vnoExp
% 48.03/13.56 |
% 48.03/13.56 | Instantiating formula (92) with ve1, all_9_7_23, all_9_6_22 and discharging atoms vapp(all_9_6_22, all_9_7_23) = ve1, yields:
% 48.03/13.56 | (162) ~ (visValue(ve1) = 0)
% 48.03/13.56 |
% 48.03/13.56 | Using (68) and (162) yields:
% 48.03/13.56 | (163) ~ (all_0_7_7 = 0)
% 48.03/13.56 |
% 48.03/13.56 +-Applying beta-rule and splitting (661), into two cases.
% 48.03/13.56 |-Branch one:
% 48.03/13.56 | (761) all_0_5_5 = 0
% 48.03/13.56 |
% 48.03/13.56 | Combining equations (1326,761) yields a new equation:
% 48.03/13.56 | (1728) all_0_7_7 = 0
% 48.03/13.56 |
% 48.03/13.56 | Simplifying 1728 yields:
% 48.03/13.56 | (164) all_0_7_7 = 0
% 48.03/13.56 |
% 48.03/13.56 | Equations (164) can reduce 163 to:
% 48.03/13.56 | (165) $false
% 48.03/13.56 |
% 48.03/13.56 |-The branch is then unsatisfiable
% 48.03/13.56 |-Branch two:
% 48.03/13.56 | (760) ~ (all_0_5_5 = 0)
% 48.03/13.56 | (764) ? [v0] : vsomeExp(v0) = all_0_4_4
% 48.03/13.56 |
% 48.03/13.56 | Instantiating (764) with all_118_0_748 yields:
% 48.03/13.56 | (3867) vsomeExp(all_118_0_748) = all_0_4_4
% 48.03/13.56 |
% 48.03/13.56 | From (1123) and (3867) follows:
% 48.03/13.56 | (3868) vsomeExp(all_118_0_748) = vnoExp
% 48.03/13.56 |
% 48.03/13.56 | Instantiating formula (40) with all_118_0_748 and discharging atoms vsomeExp(all_118_0_748) = vnoExp, yields:
% 48.03/13.56 | (130) $false
% 48.03/13.56 |
% 48.03/13.56 |-The branch is then unsatisfiable
% 48.03/13.56 |-Branch two:
% 48.03/13.56 | (512) all_9_7_23 = all_9_9_25 & all_9_8_24 = ve1 & all_0_6_6 = vnoExp & ~ (all_9_6_22 = 0) & vreduce(all_9_10_26) = all_9_9_25 & visSomeExp(all_9_9_25) = all_9_6_22 & vapp(all_9_10_26, all_9_11_27) = ve1 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)
% 48.03/13.56 |
% 48.03/13.56 | Applying alpha-rule on (512) yields:
% 48.03/13.56 | (383) all_9_8_24 = ve1
% 48.03/13.56 | (514) ~ (all_9_6_22 = 0)
% 48.03/13.56 | (515) all_9_7_23 = all_9_9_25
% 48.03/13.56 | (516) visSomeExp(all_9_9_25) = all_9_6_22
% 48.03/13.56 | (517) vapp(all_9_10_26, all_9_11_27) = ve1
% 48.03/13.56 | (518) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_9_10_26)
% 48.03/13.56 | (519) vreduce(all_9_10_26) = all_9_9_25
% 48.03/13.56 | (502) all_0_6_6 = vnoExp
% 48.03/13.56 |
% 48.03/13.56 | Instantiating formula (92) with ve1, all_9_11_27, all_9_10_26 and discharging atoms vapp(all_9_10_26, all_9_11_27) = ve1, yields:
% 48.03/13.56 | (162) ~ (visValue(ve1) = 0)
% 48.03/13.56 |
% 48.03/13.56 | Using (68) and (162) yields:
% 48.03/13.56 | (163) ~ (all_0_7_7 = 0)
% 48.03/13.56 |
% 48.03/13.56 +-Applying beta-rule and splitting (143), into two cases.
% 48.03/13.56 |-Branch one:
% 48.03/13.56 | (164) all_0_7_7 = 0
% 48.03/13.56 |
% 48.03/13.56 | Equations (164) can reduce 163 to:
% 48.03/13.56 | (165) $false
% 48.03/13.56 |
% 48.03/13.56 |-The branch is then unsatisfiable
% 48.03/13.56 |-Branch two:
% 48.03/13.56 | (163) ~ (all_0_7_7 = 0)
% 48.03/13.56 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 48.03/13.56 |
% 48.03/13.56 | Instantiating (167) with all_108_0_750 yields:
% 48.03/13.56 | (3885) vsomeExp(all_108_0_750) = all_0_6_6
% 48.03/13.56 |
% 48.03/13.56 | From (502) and (3885) follows:
% 48.03/13.56 | (3886) vsomeExp(all_108_0_750) = vnoExp
% 48.03/13.56 |
% 48.03/13.56 | Instantiating formula (40) with all_108_0_750 and discharging atoms vsomeExp(all_108_0_750) = vnoExp, yields:
% 48.03/13.56 | (130) $false
% 48.03/13.56 |
% 48.03/13.56 |-The branch is then unsatisfiable
% 48.03/13.56 |-Branch two:
% 48.03/13.56 | (530) all_9_8_24 = ve1 & all_0_6_6 = vnoExp & vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1
% 48.03/13.56 |
% 48.03/13.56 | Applying alpha-rule on (530) yields:
% 48.03/13.56 | (383) all_9_8_24 = ve1
% 48.03/13.56 | (502) all_0_6_6 = vnoExp
% 48.03/13.56 | (533) vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1
% 48.03/13.56 |
% 48.03/13.56 | Combining equations (502,633) yields a new equation:
% 48.03/13.56 | (219) all_0_1_1 = vnoExp
% 48.03/13.56 |
% 48.03/13.56 | Instantiating formula (22) with all_0_7_7, ve1, all_9_9_25, all_9_10_26, all_9_11_27 and discharging atoms visValue(ve1) = all_0_7_7, vabs(all_9_11_27, all_9_10_26, all_9_9_25) = ve1, yields:
% 48.03/13.56 | (164) all_0_7_7 = 0
% 48.03/13.56 |
% 48.03/13.56 | From (164) and (1327) follows:
% 48.03/13.56 | (1772) visValue(ve2) = 0
% 48.03/13.56 |
% 48.03/13.56 +-Applying beta-rule and splitting (116), into two cases.
% 48.03/13.56 |-Branch one:
% 48.03/13.56 | (171) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)) | (all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3)
% 48.03/13.57 |
% 48.03/13.57 +-Applying beta-rule and splitting (171), into two cases.
% 48.03/13.57 |-Branch one:
% 48.03/13.57 | (172) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46) | (all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50))
% 48.03/13.57 |
% 48.03/13.57 +-Applying beta-rule and splitting (172), into two cases.
% 48.03/13.57 |-Branch one:
% 48.03/13.57 | (173) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)) | (all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46)
% 48.03/13.57 |
% 48.03/13.57 +-Applying beta-rule and splitting (173), into two cases.
% 48.03/13.57 |-Branch one:
% 48.03/13.57 | (174) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46) | (all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51))
% 48.03/13.57 |
% 48.03/13.57 +-Applying beta-rule and splitting (174), into two cases.
% 48.03/13.57 |-Branch one:
% 48.03/13.57 | (175) (all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46) | (all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46)
% 48.03/13.57 |
% 48.03/13.57 +-Applying beta-rule and splitting (175), into two cases.
% 48.03/13.57 |-Branch one:
% 48.03/13.57 | (176) all_11_0_40 = all_0_1_1 & all_11_2_42 = 0 & all_11_4_44 = all_11_10_50 & all_11_5_45 = all_0_3_3 & ~ (all_11_3_43 = 0) & vreduce(all_11_8_48) = all_11_10_50 & visSomeExp(all_11_10_50) = all_11_3_43 & vsomeExp(all_11_1_41) = all_0_1_1 & vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41 & visValue(all_11_8_48) = 0 & vapp(all_11_6_46, all_11_8_48) = all_0_3_3 & vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 48.03/13.57 |
% 48.03/13.57 | Applying alpha-rule on (176) yields:
% 48.03/13.57 | (177) all_11_5_45 = all_0_3_3
% 48.03/13.57 | (178) all_11_4_44 = all_11_10_50
% 48.03/13.57 | (179) visValue(all_11_8_48) = 0
% 48.03/13.57 | (180) vapp(all_11_6_46, all_11_8_48) = all_0_3_3
% 48.03/13.57 | (181) all_11_0_40 = all_0_1_1
% 48.03/13.57 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 48.03/13.57 | (183) vabs(all_11_9_49, all_11_11_51, all_11_7_47) = all_11_6_46
% 48.03/13.57 | (184) vreduce(all_11_8_48) = all_11_10_50
% 48.03/13.57 | (185) vsubst(all_11_9_49, all_11_8_48, all_11_7_47) = all_11_1_41
% 48.03/13.57 | (186) ~ (all_11_3_43 = 0)
% 48.03/13.57 | (187) visSomeExp(all_11_10_50) = all_11_3_43
% 48.03/13.57 | (188) all_11_2_42 = 0
% 48.03/13.57 |
% 48.03/13.57 | From (219) and (182) follows:
% 48.03/13.57 | (805) vsomeExp(all_11_1_41) = vnoExp
% 48.03/13.57 |
% 48.03/13.57 | Instantiating formula (40) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = vnoExp, yields:
% 48.03/13.57 | (130) $false
% 48.03/13.57 |
% 48.03/13.57 |-The branch is then unsatisfiable
% 48.03/13.57 |-Branch two:
% 48.03/13.57 | (190) all_11_0_40 = all_0_1_1 & all_11_3_43 = 0 & all_11_4_44 = all_11_7_47 & all_11_5_45 = all_0_3_3 & vreduce(all_11_11_51) = all_11_7_47 & vgetSomeExp(all_11_7_47) = all_11_2_42 & visSomeExp(all_11_7_47) = 0 & vsomeExp(all_11_1_41) = all_0_1_1 & vapp(all_11_6_46, all_11_2_42) = all_11_1_41 & vapp(all_11_6_46, all_11_11_51) = all_0_3_3 & vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 48.03/13.57 |
% 48.03/13.57 | Applying alpha-rule on (190) yields:
% 48.03/13.57 | (177) all_11_5_45 = all_0_3_3
% 48.03/13.57 | (192) vapp(all_11_6_46, all_11_11_51) = all_0_3_3
% 48.03/13.57 | (193) visSomeExp(all_11_7_47) = 0
% 48.03/13.57 | (181) all_11_0_40 = all_0_1_1
% 48.03/13.57 | (182) vsomeExp(all_11_1_41) = all_0_1_1
% 48.03/13.57 | (196) vapp(all_11_6_46, all_11_2_42) = all_11_1_41
% 48.03/13.57 | (197) vreduce(all_11_11_51) = all_11_7_47
% 48.03/13.57 | (198) vgetSomeExp(all_11_7_47) = all_11_2_42
% 48.03/13.57 | (199) all_11_3_43 = 0
% 48.03/13.57 | (200) vabs(all_11_10_50, all_11_9_49, all_11_8_48) = all_11_6_46
% 48.03/13.57 | (201) all_11_4_44 = all_11_7_47
% 48.03/13.57 |
% 48.03/13.57 | From (219) and (182) follows:
% 48.03/13.57 | (805) vsomeExp(all_11_1_41) = vnoExp
% 48.03/13.57 |
% 48.03/13.57 | Instantiating formula (40) with all_11_1_41 and discharging atoms vsomeExp(all_11_1_41) = vnoExp, yields:
% 48.03/13.57 | (130) $false
% 48.03/13.57 |
% 48.03/13.57 |-The branch is then unsatisfiable
% 48.03/13.57 |-Branch two:
% 48.03/13.57 | (203) all_11_3_43 = all_0_1_1 & all_11_6_46 = 0 & all_11_7_47 = all_11_10_50 & all_11_8_48 = all_0_3_3 & vreduce(all_11_11_51) = all_11_10_50 & vgetSomeExp(all_11_10_50) = all_11_5_45 & visSomeExp(all_11_10_50) = 0 & vsomeExp(all_11_4_44) = all_0_1_1 & vapp(all_11_5_45, all_11_9_49) = all_11_4_44 & vapp(all_11_11_51, all_11_9_49) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 48.03/13.57 |
% 48.03/13.57 | Applying alpha-rule on (203) yields:
% 48.03/13.57 | (204) all_11_7_47 = all_11_10_50
% 48.03/13.57 | (205) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_11_51)
% 48.03/13.57 | (206) all_11_6_46 = 0
% 48.03/13.57 | (207) all_11_3_43 = all_0_1_1
% 48.03/13.57 | (208) visSomeExp(all_11_10_50) = 0
% 48.03/13.57 | (209) vsomeExp(all_11_4_44) = all_0_1_1
% 48.03/13.57 | (210) vreduce(all_11_11_51) = all_11_10_50
% 48.03/13.57 | (211) vapp(all_11_11_51, all_11_9_49) = all_0_3_3
% 48.03/13.57 | (212) all_11_8_48 = all_0_3_3
% 48.03/13.57 | (213) vapp(all_11_5_45, all_11_9_49) = all_11_4_44
% 48.03/13.57 | (214) vgetSomeExp(all_11_10_50) = all_11_5_45
% 48.03/13.57 |
% 48.03/13.57 | From (219) and (209) follows:
% 48.03/13.57 | (833) vsomeExp(all_11_4_44) = vnoExp
% 48.03/13.57 |
% 48.03/13.57 | Instantiating formula (40) with all_11_4_44 and discharging atoms vsomeExp(all_11_4_44) = vnoExp, yields:
% 48.03/13.57 | (130) $false
% 48.03/13.57 |
% 48.03/13.57 |-The branch is then unsatisfiable
% 48.03/13.57 |-Branch two:
% 48.03/13.57 | (216) all_11_4_44 = all_11_8_48 & all_11_5_45 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_2_42 = 0) & ~ (all_11_3_43 = 0) & vreduce(all_11_7_47) = all_11_8_48 & visSomeExp(all_11_8_48) = all_11_3_43 & visValue(all_11_7_47) = all_11_2_42 & vapp(all_11_6_46, all_11_7_47) = all_0_3_3 & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 48.03/13.57 |
% 48.03/13.57 | Applying alpha-rule on (216) yields:
% 48.03/13.57 | (177) all_11_5_45 = all_0_3_3
% 48.03/13.57 | (218) visValue(all_11_7_47) = all_11_2_42
% 48.03/13.57 | (219) all_0_1_1 = vnoExp
% 48.03/13.57 | (220) vreduce(all_11_7_47) = all_11_8_48
% 48.03/13.57 | (221) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_11_6_46
% 48.03/13.57 | (222) vapp(all_11_6_46, all_11_7_47) = all_0_3_3
% 48.03/13.57 | (186) ~ (all_11_3_43 = 0)
% 48.03/13.57 | (224) all_11_4_44 = all_11_8_48
% 48.03/13.57 | (225) visSomeExp(all_11_8_48) = all_11_3_43
% 48.03/13.57 | (226) ~ (all_11_2_42 = 0)
% 48.03/13.57 |
% 48.03/13.57 | Instantiating formula (98) with ve2, all_11_2_42, 0 and discharging atoms visValue(ve2) = 0, yields:
% 48.03/13.57 | (3954) all_11_2_42 = 0 | ~ (visValue(ve2) = all_11_2_42)
% 48.03/13.57 |
% 48.03/13.57 | Instantiating formula (31) with all_0_3_3, all_11_7_47, all_11_6_46, ve2, ve1 and discharging atoms vapp(all_11_6_46, all_11_7_47) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 48.03/13.57 | (859) all_11_7_47 = ve2
% 48.03/13.57 |
% 48.03/13.57 | From (859) and (218) follows:
% 48.03/13.57 | (3956) visValue(ve2) = all_11_2_42
% 48.03/13.57 |
% 48.03/13.57 +-Applying beta-rule and splitting (3954), into two cases.
% 48.03/13.57 |-Branch one:
% 48.03/13.57 | (3957) ~ (visValue(ve2) = all_11_2_42)
% 48.03/13.57 |
% 48.03/13.57 | Using (3956) and (3957) yields:
% 48.03/13.57 | (130) $false
% 48.03/13.57 |
% 48.03/13.57 |-The branch is then unsatisfiable
% 48.03/13.57 |-Branch two:
% 48.03/13.57 | (3956) visValue(ve2) = all_11_2_42
% 48.03/13.57 | (188) all_11_2_42 = 0
% 48.03/13.57 |
% 48.03/13.57 | Equations (188) can reduce 226 to:
% 48.03/13.57 | (165) $false
% 48.03/13.57 |
% 48.03/13.57 |-The branch is then unsatisfiable
% 48.03/13.57 |-Branch two:
% 48.03/13.57 | (231) all_11_7_47 = all_11_9_49 & all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & ~ (all_11_6_46 = 0) & vreduce(all_11_10_50) = all_11_9_49 & visSomeExp(all_11_9_49) = all_11_6_46 & vapp(all_11_10_50, all_11_11_51) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 48.03/13.57 |
% 48.03/13.57 | Applying alpha-rule on (231) yields:
% 48.03/13.57 | (232) all_11_7_47 = all_11_9_49
% 48.03/13.57 | (219) all_0_1_1 = vnoExp
% 48.03/13.57 | (234) ~ (all_11_6_46 = 0)
% 48.03/13.57 | (235) vreduce(all_11_10_50) = all_11_9_49
% 48.03/13.57 | (236) ! [v0] : ! [v1] : ! [v2] : ~ (vabs(v0, v1, v2) = all_11_10_50)
% 48.03/13.57 | (212) all_11_8_48 = all_0_3_3
% 48.03/13.57 | (238) vapp(all_11_10_50, all_11_11_51) = all_0_3_3
% 48.03/13.57 | (239) visSomeExp(all_11_9_49) = all_11_6_46
% 48.03/13.57 |
% 48.03/13.57 | Instantiating formula (236) with all_9_9_25, all_9_10_26, all_9_11_27 yields:
% 48.03/13.57 | (882) ~ (vabs(all_9_11_27, all_9_10_26, all_9_9_25) = all_11_10_50)
% 48.03/13.57 |
% 48.03/13.57 | Instantiating formula (88) with all_0_3_3, all_11_11_51, all_11_10_50, ve2, ve1 and discharging atoms vapp(all_11_10_50, all_11_11_51) = all_0_3_3, vapp(ve1, ve2) = all_0_3_3, yields:
% 48.03/13.57 | (242) all_11_10_50 = ve1
% 48.03/13.57 |
% 48.03/13.57 | Using (533) and (882) yields:
% 48.03/13.57 | (884) ~ (all_11_10_50 = ve1)
% 48.03/13.57 |
% 48.03/13.57 | Equations (242) can reduce 884 to:
% 48.03/13.57 | (165) $false
% 48.03/13.57 |
% 48.03/13.57 |-The branch is then unsatisfiable
% 48.03/13.57 |-Branch two:
% 48.03/13.57 | (254) all_11_8_48 = all_0_3_3 & all_0_1_1 = vnoExp & vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 48.03/13.57 |
% 48.03/13.57 | Applying alpha-rule on (254) yields:
% 48.03/13.57 | (212) all_11_8_48 = all_0_3_3
% 48.03/13.57 | (219) all_0_1_1 = vnoExp
% 48.03/13.57 | (257) vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3
% 48.03/13.57 |
% 48.03/13.57 | Instantiating formula (66) with all_0_3_3, ve2, ve1, all_11_9_49, all_11_10_50, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vabs(all_11_11_51, all_11_10_50, all_11_9_49) = all_0_3_3, yields:
% 48.03/13.57 | (130) $false
% 48.03/13.57 |
% 48.03/13.57 |-The branch is then unsatisfiable
% 48.03/13.57 |-Branch two:
% 48.03/13.57 | (259) all_11_10_50 = all_0_3_3 & all_0_1_1 = vnoExp & vvar(all_11_11_51) = all_0_3_3
% 48.03/13.57 |
% 48.03/13.57 | Applying alpha-rule on (259) yields:
% 48.03/13.57 | (260) all_11_10_50 = all_0_3_3
% 48.03/13.57 | (219) all_0_1_1 = vnoExp
% 48.03/13.57 | (262) vvar(all_11_11_51) = all_0_3_3
% 48.03/13.57 |
% 48.03/13.57 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_11_11_51 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_11_11_51) = all_0_3_3, yields:
% 48.03/13.57 | (130) $false
% 48.03/13.57 |
% 48.03/13.57 |-The branch is then unsatisfiable
% 48.03/13.57 |-Branch two:
% 48.03/13.57 | (612) all_9_10_26 = ve1 & all_0_6_6 = vnoExp & vvar(all_9_11_27) = ve1
% 48.03/13.57 |
% 48.03/13.57 | Applying alpha-rule on (612) yields:
% 48.03/13.57 | (613) all_9_10_26 = ve1
% 48.03/13.57 | (502) all_0_6_6 = vnoExp
% 48.03/13.57 | (615) vvar(all_9_11_27) = ve1
% 48.03/13.57 |
% 48.03/13.57 | Instantiating formula (104) with ve1, all_9_11_27 and discharging atoms vvar(all_9_11_27) = ve1, yields:
% 48.03/13.57 | (162) ~ (visValue(ve1) = 0)
% 48.03/13.57 |
% 48.03/13.57 | Using (68) and (162) yields:
% 48.03/13.57 | (163) ~ (all_0_7_7 = 0)
% 48.03/13.57 |
% 48.03/13.57 +-Applying beta-rule and splitting (143), into two cases.
% 48.03/13.57 |-Branch one:
% 48.03/13.57 | (164) all_0_7_7 = 0
% 48.03/13.57 |
% 48.03/13.57 | Equations (164) can reduce 163 to:
% 48.03/13.57 | (165) $false
% 48.03/13.57 |
% 48.03/13.57 |-The branch is then unsatisfiable
% 48.03/13.57 |-Branch two:
% 48.03/13.57 | (163) ~ (all_0_7_7 = 0)
% 48.03/13.57 | (167) ? [v0] : vsomeExp(v0) = all_0_6_6
% 48.03/13.57 |
% 48.03/13.57 | Instantiating (167) with all_107_0_752 yields:
% 48.03/13.57 | (3995) vsomeExp(all_107_0_752) = all_0_6_6
% 48.03/13.57 |
% 48.03/13.57 | From (502) and (3995) follows:
% 48.03/13.57 | (3996) vsomeExp(all_107_0_752) = vnoExp
% 48.03/13.57 |
% 48.03/13.57 | Instantiating formula (40) with all_107_0_752 and discharging atoms vsomeExp(all_107_0_752) = vnoExp, yields:
% 48.03/13.57 | (130) $false
% 48.03/13.57 |
% 48.03/13.57 |-The branch is then unsatisfiable
% 48.03/13.57 |-Branch two:
% 48.03/13.57 | (625) all_8_4_12 = all_8_7_15 & all_8_5_13 = all_0_3_3 & vlookup(all_8_6_14, vempty) = all_8_7_15 & vsomeType(all_0_0_0) = all_8_7_15 & vvar(all_8_6_14) = all_0_3_3
% 48.03/13.57 |
% 48.03/13.57 | Applying alpha-rule on (625) yields:
% 48.03/13.57 | (626) all_8_4_12 = all_8_7_15
% 48.03/13.57 | (627) all_8_5_13 = all_0_3_3
% 48.03/13.57 | (628) vvar(all_8_6_14) = all_0_3_3
% 48.03/13.57 | (629) vsomeType(all_0_0_0) = all_8_7_15
% 48.03/13.57 | (630) vlookup(all_8_6_14, vempty) = all_8_7_15
% 48.03/13.57 |
% 48.03/13.57 | Instantiating formula (93) with all_0_3_3, ve2, ve1, all_8_6_14 and discharging atoms vapp(ve1, ve2) = all_0_3_3, vvar(all_8_6_14) = all_0_3_3, yields:
% 48.03/13.57 | (130) $false
% 48.03/13.57 |
% 48.03/13.57 |-The branch is then unsatisfiable
% 48.03/13.57 % SZS output end Proof for theBenchmark
% 48.03/13.57
% 48.03/13.57 12983ms
%------------------------------------------------------------------------------