TSTP Solution File: COM132+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : COM132+2 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.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 01:08:15 EDT 2022
% Result : Theorem 39.27s 12.25s
% Output : Proof 46.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : COM132+2 : TPTP v8.1.0. Released v6.4.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n025.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 19:18:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.52/0.61 ____ _
% 0.52/0.61 ___ / __ \_____(_)___ ________ __________
% 0.52/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.52/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.52/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.52/0.61
% 0.52/0.61 A Theorem Prover for First-Order Logic
% 0.52/0.61 (ePrincess v.1.0)
% 0.52/0.61
% 0.52/0.61 (c) Philipp Rümmer, 2009-2015
% 0.52/0.61 (c) Peter Backeman, 2014-2015
% 0.52/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.52/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.52/0.61 Bug reports to peter@backeman.se
% 0.52/0.61
% 0.52/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.52/0.61
% 0.52/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.69/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.05/1.06 Prover 0: Preprocessing ...
% 3.84/1.51 Prover 0: Warning: ignoring some quantifiers
% 4.02/1.54 Prover 0: Constructing countermodel ...
% 22.17/5.95 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 22.48/6.04 Prover 1: Preprocessing ...
% 23.13/6.22 Prover 1: Constructing countermodel ...
% 30.80/8.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 30.83/8.61 Prover 2: Preprocessing ...
% 31.81/8.78 Prover 2: Warning: ignoring some quantifiers
% 31.90/8.79 Prover 2: Constructing countermodel ...
% 37.34/11.56 Prover 0: stopped
% 37.61/11.76 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 37.72/11.82 Prover 3: Preprocessing ...
% 37.92/11.89 Prover 3: Warning: ignoring some quantifiers
% 37.92/11.89 Prover 3: Constructing countermodel ...
% 39.27/12.24 Prover 3: proved (485ms)
% 39.27/12.24 Prover 1: stopped
% 39.27/12.25 Prover 2: stopped
% 39.27/12.25
% 39.27/12.25 No countermodel exists, formula is valid
% 39.27/12.25 % SZS status Theorem for theBenchmark
% 39.27/12.25
% 39.27/12.25 Generating proof ... Warning: ignoring some quantifiers
% 45.63/13.77 found it (size 163)
% 45.63/13.77
% 45.63/13.77 % SZS output start Proof for theBenchmark
% 45.63/13.78 Assumed formulas after preprocessing and simplification:
% 45.63/13.78 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v4 = v2) & vsubst(v2, v3, v8) = v9 & vbind(v2, v0, v1) = v7 & vabs(v4, v5, veabs) = v8 & vtcheck(v7, v8, v6) & vtcheck(v1, v3, v0) & visFreeVar(v4, v3) & ~ vtcheck(v1, v9, v6) & ~ visSomeType(vnoType) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = v13 | v15 = v10 | ~ (vsubst(v15, v18, v17) = v19) | ~ (vsubst(v10, v11, v20) = v21) | ~ (vsubst(v10, v11, v12) = v13) | ~ (vabs(v16, v14, v19) = v20) | ~ (vvar(v16) = v18) | ~ visFreeVar(v15, v11) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (( ~ (v25 = v16) & vgensym(v24) = v25 & vapp(v22, v23) = v24 & vapp(v11, v17) = v22 & vvar(v10) = v23) | ( ~ (v22 = v12) & vabs(v15, v14, v17) = v22))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v14 = v12 | ~ (vsubst(v12, v13, v19) = v20) | ~ (vbind(v12, v10, v11) = v18) | ~ (vabs(v14, v15, v16) = v19) | ~ vtcheck(v18, v19, v17) | ~ vtcheck(v11, v13, v10) | vtcheck(v11, v20, v17) | visFreeVar(v14, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v13 | v14 = v10 | ~ (vsubst(v10, v11, v16) = v17) | ~ (vsubst(v10, v11, v12) = v13) | ~ (vabs(v14, v15, v17) = v18) | visFreeVar(v14, v11) | ? [v19] : ( ~ (v19 = v12) & vabs(v14, v15, v16) = v19)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v13 | ~ (vsubst(v10, v11, v15) = v17) | ~ (vsubst(v10, v11, v14) = v16) | ~ (vsubst(v10, v11, v12) = v13) | ~ (vapp(v16, v17) = v18) | ? [v19] : ( ~ (v19 = v12) & vapp(v14, v15) = v19)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (varrow(v13, v14) = v17) | ~ (vbind(v11, v13, v10) = v15) | ~ (vabs(v11, v13, v12) = v16) | ~ vtcheck(v15, v12, v14) | vtcheck(v10, v16, v17)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (vbind(v10, v12, v16) = v17) | ~ (vbind(v10, v11, v13) = v16) | ~ vtcheck(v17, v14, v15) | ? [v18] : (vbind(v10, v12, v13) = v18 & vtcheck(v18, v14, v15))) & ? [v10] : ? [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v14 = v12 | ~ (vbind(v14, v15, v16) = v17) | ~ (vbind(v12, v13, v17) = v18) | vtcheck(v18, v10, v11) | ? [v19] : ? [v20] : (vbind(v14, v15, v19) = v20 & vbind(v12, v13, v16) = v19 & ~ vtcheck(v20, v10, v11))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v14 | v12 = v11 | ~ (vlookup(v12, v15) = v16) | ~ (vlookup(v12, v13) = v14) | ~ (vbind(v11, v10, v15) = v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = v12 | ~ (vbind(v13, v14, v15) = v16) | ~ (vbind(v10, v11, v12) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = v12 | ~ (vabs(v13, v14, v15) = v16) | ~ (vabs(v10, v11, v12) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v11 | ~ (vbind(v13, v14, v15) = v16) | ~ (vbind(v10, v11, v12) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v11 | ~ (vabs(v13, v14, v15) = v16) | ~ (vabs(v10, v11, v12) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = v10 | ~ (vbind(v13, v14, v15) = v16) | ~ (vbind(v10, v11, v12) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = v10 | ~ (vabs(v13, v14, v15) = v16) | ~ (vabs(v10, v11, v12) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (varrow(v10, v14) = v15) | ~ (vapp(v12, v13) = v16) | ~ vtcheck(v11, v13, v10) | ~ vtcheck(v11, v12, v15) | vtcheck(v11, v16, v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (vsubst(v11, v14, v13) = v15) | ~ (vabs(v12, v10, v15) = v16) | ~ (vvar(v12) = v14) | visFreeVar(v12, v13) | ? [v17] : (vabs(v11, v10, v13) = v17 & valphaEquivalent(v17, v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (vapp(v14, v15) = v16) | ~ (vapp(v10, v13) = v14) | ~ (vvar(v11) = v15) | ~ visFreeVar(v12, v13) | ? [v17] : ( ~ (v17 = v12) & vgensym(v16) = v17)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (vsubst(v11, v10, v12) = v13) | ~ (vabs(v11, v14, v15) = v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (vbind(v10, v11, v12) = v15) | ~ vtcheck(v15, v13, v14) | vtcheck(v12, v13, v14) | visFreeVar(v10, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (vbind(v10, v11, v12) = v15) | ~ vtcheck(v12, v13, v14) | vtcheck(v15, v13, v14) | visFreeVar(v10, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (vbind(v10, v11, v12) = v15) | ~ vtcheck(v12, v13, v14) | vtcheck(v15, v13, v14) | ? [v16] : ( ~ (v16 = vnoType) & vlookup(v10, v12) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (vapp(v13, v14) = v15) | ~ (vapp(v10, v11) = v13) | ~ (vvar(v12) = v14) | ? [v16] : ( ~ (v16 = v12) & vgensym(v15) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (vapp(v13, v14) = v15) | ~ (vabs(v10, v11, v12) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (vbind(v10, v11, v12) = v14) | ~ (vbind(v10, v11, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (vabs(v10, v11, v12) = v14) | ~ (vabs(v10, v11, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | v13 = v12 | ~ (vsubst(v11, v10, v12) = v13) | ~ (vvar(v14) = v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = v11 | ~ (varrow(v12, v13) = v14) | ~ (varrow(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = v11 | ~ (vapp(v12, v13) = v14) | ~ (vapp(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = v11 | ~ (vabs(v13, v10, v14) = v12) | ~ visFreeVar(v11, v14) | visFreeVar(v11, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v10 | ~ (varrow(v12, v13) = v14) | ~ (varrow(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v10 | ~ (vapp(v12, v13) = v14) | ~ (vapp(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | ~ (vsubst(v14, v13, v12) = v11) | ~ (vsubst(v14, v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | ~ (vbind(v14, v13, v12) = v11) | ~ (vbind(v14, v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | ~ (vabs(v14, v13, v12) = v11) | ~ (vabs(v14, v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (vlookup(v11, v12) = v13) | ~ (vbind(v11, v14, v10) = v12) | vsomeType(v14) = v13) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (vabs(v13, v10, v14) = v12) | ~ visFreeVar(v11, v12) | visFreeVar(v11, v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (vabs(v11, v12, v13) = v14) | ~ (vvar(v10) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (varrow(v10, v11) = v13) | ~ (varrow(v10, v11) = v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (vapp(v10, v11) = v13) | ~ (vapp(v10, v11) = v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (vsubst(v10, v11, v12) = v13) | ~ (vvar(v10) = v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (varrow(v13, v12) = v11) | ~ (varrow(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (vlookup(v13, v12) = v11) | ~ (vlookup(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (vapp(v13, v12) = v11) | ~ (vapp(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (vsubst(v10, v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ((v28 = v13 & v24 = v18 & v20 = v12 & v15 = v11 & v14 = v10 & ~ (v17 = v10) & vsubst(v17, v25, v19) = v26 & vsubst(v10, v11, v27) = v13 & vgensym(v23) = v18 & vapp(v21, v22) = v23 & vapp(v11, v19) = v21 & vabs(v18, v16, v26) = v27 & vabs(v17, v16, v19) = v12 & vvar(v18) = v25 & vvar(v10) = v22 & visFreeVar(v17, v11)) | (v21 = v13 & v19 = v12 & v17 = v11 & v16 = v10 & ~ (v14 = v10) & vsubst(v10, v11, v18) = v20 & vabs(v14, v15, v20) = v13 & vabs(v14, v15, v18) = v12 & ~ visFreeVar(v14, v11)) | (v21 = v13 & v18 = v12 & v16 = v11 & v15 = v10 & vsubst(v10, v11, v17) = v20 & vsubst(v10, v11, v14) = v19 & vapp(v19, v20) = v13 & vapp(v14, v17) = v12) | (v19 = v12 & v16 = v10 & v15 = v10 & v14 = v11 & v13 = v12 & vabs(v10, v17, v18) = v12) | (v17 = v12 & v16 = v11 & v15 = v10 & v14 = v10 & v13 = v11 & vvar(v10) = v12) | (v17 = v12 & v15 = v10 & v14 = v11 & v13 = v12 & ~ (v16 = v10) & vvar(v16) = v12))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (vlookup(v11, v10) = v13) | ~ (vsomeType(v12) = v13) | ? [v14] : (vvar(v11) = v14 & vtcheck(v10, v14, v12))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (vsomeType(v11) = v13) | ~ vtcheck(v12, v10, v11) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ((v19 = v11 & v18 = v10 & varrow(v16, v17) = v11 & vbind(v14, v16, v12) = v20 & vabs(v14, v16, v15) = v10 & vtcheck(v20, v15, v17)) | (v17 = v10 & varrow(v16, v11) = v18 & vapp(v14, v15) = v10 & vtcheck(v12, v15, v16) & vtcheck(v12, v14, v18)) | (v16 = v13 & v15 = v10 & vlookup(v14, v12) = v13 & vvar(v14) = v10))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (vapp(v12, v13) = v11) | ~ visFreeVar(v10, v13) | visFreeVar(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (vapp(v12, v13) = v11) | ~ visFreeVar(v10, v12) | visFreeVar(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (vapp(v12, v13) = v11) | ~ visFreeVar(v10, v11) | visFreeVar(v10, v13) | visFreeVar(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (vapp(v11, v12) = v13) | ~ (vvar(v10) = v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (vabs(v11, v10, v13) = v12) | ~ visFreeVar(v11, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (vabs(v10, v11, v12) = v13) | visValue(v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ valphaEquivalent(v10, v12) | ~ vtcheck(v11, v10, v13) | vtcheck(v11, v12, v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (vgetSomeType(v10) = v11) | ~ (vsomeType(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (vsomeType(v10) = v12) | ~ (vsomeType(v10) = v11)) & ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (vvar(v10) = v12) | ~ (vvar(v10) = v11)) & ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (vvar(v12) = v11) | ~ visFreeVar(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : (v12 = vnoType | ~ (vlookup(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = v12 & v17 = v11 & v15 = v10 & v14 = v10 & vsomeType(v16) = v12 & vbind(v10, v16, v13) = v11) | (v18 = v12 & v17 = v11 & v15 = v10 & ~ (v14 = v10) & vlookup(v10, v16) = v12 & vbind(v14, v13, v16) = v11))) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (vgensym(v12) = v11) | ~ (vgensym(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (vgetSomeType(v12) = v11) | ~ (vgetSomeType(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (vsomeType(v12) = v11) | ~ (vsomeType(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (vsomeType(v11) = v12) | ~ (vsomeType(v10) = v12)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (vvar(v12) = v11) | ~ (vvar(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (vvar(v11) = v12) | ~ (vvar(v10) = v12)) & ! [v10] : ! [v11] : ! [v12] : (v11 = vempty | ~ (vlookup(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = v12 & v17 = v11 & v15 = v10 & v14 = v10 & vsomeType(v16) = v12 & vbind(v10, v16, v13) = v11) | (v18 = v12 & v17 = v11 & v15 = v10 & ~ (v14 = v10) & vlookup(v10, v16) = v12 & vbind(v14, v13, v16) = v11))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (vlookup(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (v13 = v10 | (v18 = v12 & v17 = v11 & v15 = v10 & v14 = v10 & vsomeType(v16) = v12 & vbind(v10, v16, v13) = v11) | (v18 = v12 & v17 = v11 & v15 = v10 & ~ (v14 = v10) & vlookup(v10, v16) = v12 & vbind(v14, v13, v16) = v11))) & ! [v10] : ! [v11] : ! [v12] : ~ (vbind(v10, v11, v12) = vempty) & ! [v10] : ! [v11] : ! [v12] : ( ~ (vapp(v10, v11) = v12) | ~ visValue(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ valphaEquivalent(v11, v10) | ~ valphaEquivalent(v10, v12) | valphaEquivalent(v11, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ valphaEquivalent(v10, v12) | ~ visFreeVar(v11, v12) | visFreeVar(v11, v10)) & ! [v10] : ! [v11] : (v11 = vnoType | ~ (vlookup(v10, vempty) = v11)) & ! [v10] : ! [v11] : ( ~ (vgensym(v11) = v10) | ~ visFreeVar(v10, v11)) & ! [v10] : ! [v11] : ( ~ (vsomeType(v10) = v11) | visSomeType(v11)) & ! [v10] : ! [v11] : ( ~ (vvar(v10) = v11) | ~ visValue(v11)) & ! [v10] : ! [v11] : ( ~ (vvar(v10) = v11) | visFreeVar(v10, v11)) & ! [v10] : ! [v11] : ( ~ valphaEquivalent(v11, v10) | valphaEquivalent(v10, v11)) & ! [v10] : ~ (vsomeType(v10) = vnoType) & ? [v10] : valphaEquivalent(v10, v10))
% 46.04/13.84 | 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, all_0_8_8, all_0_9_9 yields:
% 46.04/13.84 | (1) ~ (all_0_5_5 = all_0_7_7) & vsubst(all_0_7_7, all_0_6_6, all_0_1_1) = all_0_0_0 & vbind(all_0_7_7, all_0_9_9, all_0_8_8) = all_0_2_2 & vabs(all_0_5_5, all_0_4_4, veabs) = all_0_1_1 & vtcheck(all_0_2_2, all_0_1_1, all_0_3_3) & vtcheck(all_0_8_8, all_0_6_6, all_0_9_9) & visFreeVar(all_0_5_5, all_0_6_6) & ~ vtcheck(all_0_8_8, all_0_0_0, all_0_3_3) & ~ visSomeType(vnoType) & ! [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) | ~ visFreeVar(v5, v1) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (( ~ (v15 = v6) & vgensym(v14) = v15 & vapp(v12, v13) = v14 & vapp(v1, v7) = v12 & vvar(v0) = v13) | ( ~ (v12 = v2) & vabs(v5, v4, v7) = v12))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v4 = v2 | ~ (vsubst(v2, v3, v9) = v10) | ~ (vbind(v2, v0, v1) = v8) | ~ (vabs(v4, v5, v6) = v9) | ~ vtcheck(v8, v9, v7) | ~ vtcheck(v1, v3, v0) | vtcheck(v1, v10, v7) | visFreeVar(v4, v3)) & ! [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) | visFreeVar(v4, v1) | ? [v9] : ( ~ (v9 = v2) & vabs(v4, v5, v6) = v9)) & ! [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] : ( ~ (varrow(v3, v4) = v7) | ~ (vbind(v1, v3, v0) = v5) | ~ (vabs(v1, v3, v2) = v6) | ~ vtcheck(v5, v2, v4) | vtcheck(v0, v6, v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (vbind(v0, v2, v6) = v7) | ~ (vbind(v0, v1, v3) = v6) | ~ vtcheck(v7, v4, v5) | ? [v8] : (vbind(v0, v2, v3) = v8 & vtcheck(v8, v4, v5))) & ? [v0] : ? [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v4 = v2 | ~ (vbind(v4, v5, v6) = v7) | ~ (vbind(v2, v3, v7) = v8) | vtcheck(v8, v0, v1) | ? [v9] : ? [v10] : (vbind(v4, v5, v9) = v10 & vbind(v2, v3, v6) = v9 & ~ vtcheck(v10, v0, v1))) & ! [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] : (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] : ( ~ (varrow(v0, v4) = v5) | ~ (vapp(v2, v3) = v6) | ~ vtcheck(v1, v3, v0) | ~ vtcheck(v1, v2, v5) | vtcheck(v1, v6, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (vsubst(v1, v4, v3) = v5) | ~ (vabs(v2, v0, v5) = v6) | ~ (vvar(v2) = v4) | visFreeVar(v2, v3) | ? [v7] : (vabs(v1, v0, v3) = v7 & valphaEquivalent(v7, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (vapp(v4, v5) = v6) | ~ (vapp(v0, v3) = v4) | ~ (vvar(v1) = v5) | ~ visFreeVar(v2, v3) | ? [v7] : ( ~ (v7 = v2) & vgensym(v6) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (vsubst(v1, v0, v2) = v3) | ~ (vabs(v1, v4, v5) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vbind(v0, v1, v2) = v5) | ~ vtcheck(v5, v3, v4) | vtcheck(v2, v3, v4) | visFreeVar(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vbind(v0, v1, v2) = v5) | ~ vtcheck(v2, v3, v4) | vtcheck(v5, v3, v4) | visFreeVar(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vbind(v0, v1, v2) = v5) | ~ vtcheck(v2, v3, v4) | vtcheck(v5, v3, v4) | ? [v6] : ( ~ (v6 = vnoType) & vlookup(v0, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vapp(v3, v4) = v5) | ~ (vapp(v0, v1) = v3) | ~ (vvar(v2) = v4) | ? [v6] : ( ~ (v6 = v2) & vgensym(v5) = v6)) & ! [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] : (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] : (v3 = v1 | ~ (vabs(v3, v0, v4) = v2) | ~ visFreeVar(v1, v4) | visFreeVar(v1, v2)) & ! [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 | ~ (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] : ( ~ (vabs(v3, v0, v4) = v2) | ~ visFreeVar(v1, v2) | visFreeVar(v1, v4)) & ! [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 | ~ (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] : ((v18 = v3 & v14 = v8 & v10 = v2 & v5 = v1 & v4 = v0 & ~ (v7 = v0) & vsubst(v7, v15, v9) = v16 & vsubst(v0, v1, v17) = v3 & vgensym(v13) = v8 & vapp(v11, v12) = v13 & vapp(v1, v9) = v11 & vabs(v8, v6, v16) = v17 & vabs(v7, v6, v9) = v2 & vvar(v8) = v15 & vvar(v0) = v12 & visFreeVar(v7, v1)) | (v11 = v3 & v9 = v2 & v7 = v1 & v6 = v0 & ~ (v4 = v0) & vsubst(v0, v1, v8) = v10 & vabs(v4, v5, v10) = v3 & vabs(v4, v5, v8) = v2 & ~ visFreeVar(v4, v1)) | (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] : ( ~ (vlookup(v1, v0) = v3) | ~ (vsomeType(v2) = v3) | ? [v4] : (vvar(v1) = v4 & vtcheck(v0, v4, v2))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsomeType(v1) = v3) | ~ vtcheck(v2, v0, v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v9 = v1 & v8 = v0 & varrow(v6, v7) = v1 & vbind(v4, v6, v2) = v10 & vabs(v4, v6, v5) = v0 & vtcheck(v10, v5, v7)) | (v7 = v0 & varrow(v6, v1) = v8 & vapp(v4, v5) = v0 & vtcheck(v2, v5, v6) & vtcheck(v2, v4, v8)) | (v6 = v3 & v5 = v0 & vlookup(v4, v2) = v3 & vvar(v4) = v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vapp(v2, v3) = v1) | ~ visFreeVar(v0, v3) | visFreeVar(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vapp(v2, v3) = v1) | ~ visFreeVar(v0, v2) | visFreeVar(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vapp(v2, v3) = v1) | ~ visFreeVar(v0, v1) | visFreeVar(v0, v3) | visFreeVar(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vapp(v1, v2) = v3) | ~ (vvar(v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vabs(v1, v0, v3) = v2) | ~ visFreeVar(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vabs(v0, v1, v2) = v3) | visValue(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ valphaEquivalent(v0, v2) | ~ vtcheck(v1, v0, v3) | vtcheck(v1, v2, v3)) & ! [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 | ~ (vvar(v2) = v1) | ~ visFreeVar(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] : (v1 = v0 | ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(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 | ~ (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] : ( ~ (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] : ( ~ (vapp(v0, v1) = v2) | ~ visValue(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ valphaEquivalent(v1, v0) | ~ valphaEquivalent(v0, v2) | valphaEquivalent(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ valphaEquivalent(v0, v2) | ~ visFreeVar(v1, v2) | visFreeVar(v1, v0)) & ! [v0] : ! [v1] : (v1 = vnoType | ~ (vlookup(v0, vempty) = v1)) & ! [v0] : ! [v1] : ( ~ (vgensym(v1) = v0) | ~ visFreeVar(v0, v1)) & ! [v0] : ! [v1] : ( ~ (vsomeType(v0) = v1) | visSomeType(v1)) & ! [v0] : ! [v1] : ( ~ (vvar(v0) = v1) | ~ visValue(v1)) & ! [v0] : ! [v1] : ( ~ (vvar(v0) = v1) | visFreeVar(v0, v1)) & ! [v0] : ! [v1] : ( ~ valphaEquivalent(v1, v0) | valphaEquivalent(v0, v1)) & ! [v0] : ~ (vsomeType(v0) = vnoType) & ? [v0] : valphaEquivalent(v0, v0)
% 46.14/13.86 |
% 46.14/13.86 | Applying alpha-rule on (1) yields:
% 46.14/13.86 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v1 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6))
% 46.14/13.86 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (vapp(v4, v5) = v6) | ~ (vapp(v0, v3) = v4) | ~ (vvar(v1) = v5) | ~ visFreeVar(v2, v3) | ? [v7] : ( ~ (v7 = v2) & vgensym(v6) = v7))
% 46.14/13.86 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v4 | v2 = v1 | ~ (vlookup(v2, v5) = v6) | ~ (vlookup(v2, v3) = v4) | ~ (vbind(v1, v0, v5) = v3))
% 46.14/13.86 | (5) vtcheck(all_0_8_8, all_0_6_6, all_0_9_9)
% 46.14/13.86 | (6) visFreeVar(all_0_5_5, all_0_6_6)
% 46.14/13.86 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vabs(v1, v2, v3) = v4) | ~ (vvar(v0) = v4))
% 46.14/13.86 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v1 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6))
% 46.14/13.86 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~ (vlookup(v3, v2) = v0))
% 46.14/13.86 | (10) ? [v0] : valphaEquivalent(v0, v0)
% 46.14/13.86 | (11) vtcheck(all_0_2_2, all_0_1_1, all_0_3_3)
% 46.14/13.86 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsubst(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = v3 & v14 = v8 & v10 = v2 & v5 = v1 & v4 = v0 & ~ (v7 = v0) & vsubst(v7, v15, v9) = v16 & vsubst(v0, v1, v17) = v3 & vgensym(v13) = v8 & vapp(v11, v12) = v13 & vapp(v1, v9) = v11 & vabs(v8, v6, v16) = v17 & vabs(v7, v6, v9) = v2 & vvar(v8) = v15 & vvar(v0) = v12 & visFreeVar(v7, v1)) | (v11 = v3 & v9 = v2 & v7 = v1 & v6 = v0 & ~ (v4 = v0) & vsubst(v0, v1, v8) = v10 & vabs(v4, v5, v10) = v3 & vabs(v4, v5, v8) = v2 & ~ visFreeVar(v4, v1)) | (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)))
% 46.14/13.87 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) = v0))
% 46.14/13.87 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (varrow(v3, v2) = v1) | ~ (varrow(v3, v2) = v0))
% 46.14/13.87 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (vsubst(v1, v0, v2) = v3) | ~ (vabs(v1, v4, v5) = v2))
% 46.14/13.87 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vapp(v2, v3) = v1) | ~ visFreeVar(v0, v2) | visFreeVar(v0, v1))
% 46.14/13.87 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0))
% 46.14/13.87 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vvar(v0) = v2) | ~ (vvar(v0) = v1))
% 46.14/13.87 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vapp(v2, v3) = v1) | ~ visFreeVar(v0, v1) | visFreeVar(v0, v3) | visFreeVar(v0, v2))
% 46.14/13.87 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vbind(v0, v1, v2) = v5) | ~ vtcheck(v5, v3, v4) | vtcheck(v2, v3, v4) | visFreeVar(v0, v3))
% 46.14/13.87 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0))
% 46.14/13.87 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (varrow(v2, v3) = v4) | ~ (varrow(v0, v1) = v4))
% 46.14/13.87 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~ (vapp(v3, v2) = v0))
% 46.14/13.87 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (vapp(v0, v1) = v3) | ~ (vapp(v0, v1) = v2))
% 46.14/13.87 | (25) ! [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)))
% 46.14/13.87 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vabs(v3, v0, v4) = v2) | ~ visFreeVar(v1, v2) | visFreeVar(v1, v4))
% 46.14/13.87 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~ (vsomeType(v2) = v0))
% 46.14/13.87 | (28) ! [v0] : ! [v1] : ( ~ (vgensym(v1) = v0) | ~ visFreeVar(v0, v1))
% 46.14/13.87 | (29) ! [v0] : ! [v1] : ! [v2] : ~ (vbind(v0, v1, v2) = vempty)
% 46.14/13.87 | (30) ! [v0] : ! [v1] : ( ~ (vvar(v0) = v1) | ~ visValue(v1))
% 46.14/13.87 | (31) ! [v0] : ! [v1] : ( ~ (vsomeType(v0) = v1) | visSomeType(v1))
% 46.14/13.87 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4))
% 46.14/13.87 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v2 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6))
% 46.14/13.87 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (vvar(v2) = v1) | ~ visFreeVar(v0, v1))
% 46.14/13.87 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (varrow(v3, v4) = v7) | ~ (vbind(v1, v3, v0) = v5) | ~ (vabs(v1, v3, v2) = v6) | ~ vtcheck(v5, v2, v4) | vtcheck(v0, v6, v7))
% 46.14/13.87 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ valphaEquivalent(v1, v0) | ~ valphaEquivalent(v0, v2) | valphaEquivalent(v1, v2))
% 46.14/13.87 | (37) ! [v0] : ~ (vsomeType(v0) = vnoType)
% 46.14/13.87 | (38) ! [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) | ~ visFreeVar(v5, v1) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (( ~ (v15 = v6) & vgensym(v14) = v15 & vapp(v12, v13) = v14 & vapp(v1, v7) = v12 & vvar(v0) = v13) | ( ~ (v12 = v2) & vabs(v5, v4, v7) = v12)))
% 46.14/13.87 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (varrow(v0, v1) = v3) | ~ (varrow(v0, v1) = v2))
% 46.14/13.87 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vabs(v0, v1, v2) = v3) | visValue(v3))
% 46.14/13.87 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vabs(v1, v0, v3) = v2) | ~ visFreeVar(v1, v2))
% 46.14/13.87 | (42) ~ visSomeType(vnoType)
% 46.14/13.87 | (43) ! [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)))
% 46.14/13.87 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeType(v1) = v2) | ~ (vsomeType(v0) = v2))
% 46.14/13.87 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (varrow(v0, v4) = v5) | ~ (vapp(v2, v3) = v6) | ~ vtcheck(v1, v3, v0) | ~ vtcheck(v1, v2, v5) | vtcheck(v1, v6, v4))
% 46.14/13.88 | (46) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vvar(v1) = v2) | ~ (vvar(v0) = v2))
% 46.14/13.88 | (47) ~ (all_0_5_5 = all_0_7_7)
% 46.14/13.88 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0))
% 46.14/13.88 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ valphaEquivalent(v0, v2) | ~ vtcheck(v1, v0, v3) | vtcheck(v1, v2, v3))
% 46.14/13.88 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsomeType(v1) = v3) | ~ vtcheck(v2, v0, v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v9 = v1 & v8 = v0 & varrow(v6, v7) = v1 & vbind(v4, v6, v2) = v10 & vabs(v4, v6, v5) = v0 & vtcheck(v10, v5, v7)) | (v7 = v0 & varrow(v6, v1) = v8 & vapp(v4, v5) = v0 & vtcheck(v2, v5, v6) & vtcheck(v2, v4, v8)) | (v6 = v3 & v5 = v0 & vlookup(v4, v2) = v3 & vvar(v4) = v0)))
% 46.14/13.88 | (51) vbind(all_0_7_7, all_0_9_9, all_0_8_8) = all_0_2_2
% 46.14/13.88 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0))
% 46.14/13.88 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vapp(v2, v3) = v1) | ~ visFreeVar(v0, v3) | visFreeVar(v0, v1))
% 46.14/13.88 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vapp(v1, v2) = v3) | ~ (vvar(v0) = v3))
% 46.14/13.88 | (55) ! [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) | visFreeVar(v4, v1) | ? [v9] : ( ~ (v9 = v2) & vabs(v4, v5, v6) = v9))
% 46.14/13.88 | (56) ! [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))
% 46.14/13.88 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (vsubst(v0, v1, v2) = v3) | ~ (vvar(v0) = v2))
% 46.14/13.88 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v0 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6))
% 46.14/13.88 | (59) vabs(all_0_5_5, all_0_4_4, veabs) = all_0_1_1
% 46.14/13.88 | (60) ! [v0] : ! [v1] : ( ~ valphaEquivalent(v1, v0) | valphaEquivalent(v0, v1))
% 46.14/13.88 | (61) ! [v0] : ! [v1] : ( ~ (vvar(v0) = v1) | visFreeVar(v0, v1))
% 46.14/13.88 | (62) ~ vtcheck(all_0_8_8, all_0_0_0, all_0_3_3)
% 46.14/13.88 | (63) ! [v0] : ! [v1] : (v1 = vnoType | ~ (vlookup(v0, vempty) = v1))
% 46.14/13.88 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (vbind(v0, v2, v6) = v7) | ~ (vbind(v0, v1, v3) = v6) | ~ vtcheck(v7, v4, v5) | ? [v8] : (vbind(v0, v2, v3) = v8 & vtcheck(v8, v4, v5)))
% 46.14/13.88 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vbind(v0, v1, v2) = v5) | ~ vtcheck(v2, v3, v4) | vtcheck(v5, v3, v4) | ? [v6] : ( ~ (v6 = vnoType) & vlookup(v0, v2) = v6))
% 46.14/13.88 | (66) ! [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)))
% 46.14/13.88 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (vabs(v0, v1, v2) = v4) | ~ (vabs(v0, v1, v2) = v3))
% 46.14/13.88 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (vbind(v0, v1, v2) = v4) | ~ (vbind(v0, v1, v2) = v3))
% 46.14/13.88 | (69) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vgetSomeType(v0) = v1) | ~ (vsomeType(v2) = v0))
% 46.14/13.88 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vlookup(v1, v0) = v3) | ~ (vsomeType(v2) = v3) | ? [v4] : (vvar(v1) = v4 & vtcheck(v0, v4, v2)))
% 46.14/13.88 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (vabs(v3, v0, v4) = v2) | ~ visFreeVar(v1, v4) | visFreeVar(v1, v2))
% 46.14/13.88 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v0 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6))
% 46.14/13.88 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) = v0))
% 46.14/13.88 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v4 = v2 | ~ (vsubst(v2, v3, v9) = v10) | ~ (vbind(v2, v0, v1) = v8) | ~ (vabs(v4, v5, v6) = v9) | ~ vtcheck(v8, v9, v7) | ~ vtcheck(v1, v3, v0) | vtcheck(v1, v10, v7) | visFreeVar(v4, v3))
% 46.14/13.88 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v1 | v3 = v2 | ~ (vsubst(v1, v0, v2) = v3) | ~ (vvar(v4) = v2))
% 46.14/13.88 | (76) ? [v0] : ? [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v4 = v2 | ~ (vbind(v4, v5, v6) = v7) | ~ (vbind(v2, v3, v7) = v8) | vtcheck(v8, v0, v1) | ? [v9] : ? [v10] : (vbind(v4, v5, v9) = v10 & vbind(v2, v3, v6) = v9 & ~ vtcheck(v10, v0, v1)))
% 46.14/13.89 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (varrow(v2, v3) = v4) | ~ (varrow(v0, v1) = v4))
% 46.14/13.89 | (78) ! [v0] : ! [v1] : ! [v2] : ( ~ (vapp(v0, v1) = v2) | ~ visValue(v2))
% 46.14/13.89 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vapp(v3, v4) = v5) | ~ (vapp(v0, v1) = v3) | ~ (vvar(v2) = v4) | ? [v6] : ( ~ (v6 = v2) & vgensym(v5) = v6))
% 46.14/13.89 | (80) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vsomeType(v0) = v2) | ~ (vsomeType(v0) = v1))
% 46.14/13.89 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4))
% 46.14/13.89 | (82) ! [v0] : ! [v1] : ! [v2] : ( ~ valphaEquivalent(v0, v2) | ~ visFreeVar(v1, v2) | visFreeVar(v1, v0))
% 46.14/13.89 | (83) vsubst(all_0_7_7, all_0_6_6, all_0_1_1) = all_0_0_0
% 46.14/13.89 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v2 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6))
% 46.14/13.89 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vapp(v3, v4) = v5) | ~ (vabs(v0, v1, v2) = v5))
% 46.14/13.89 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vbind(v0, v1, v2) = v5) | ~ vtcheck(v2, v3, v4) | vtcheck(v5, v3, v4) | visFreeVar(v0, v3))
% 46.14/13.89 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vlookup(v1, v2) = v3) | ~ (vbind(v1, v4, v0) = v2) | vsomeType(v4) = v3)
% 46.14/13.89 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (vsubst(v1, v4, v3) = v5) | ~ (vabs(v2, v0, v5) = v6) | ~ (vvar(v2) = v4) | visFreeVar(v2, v3) | ? [v7] : (vabs(v1, v0, v3) = v7 & valphaEquivalent(v7, v6)))
% 46.14/13.89 |
% 46.14/13.89 | Instantiating formula (12) with all_0_0_0, all_0_1_1, all_0_6_6, all_0_7_7 and discharging atoms vsubst(all_0_7_7, all_0_6_6, all_0_1_1) = all_0_0_0, yields:
% 46.14/13.89 | (89) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = all_0_0_0 & v10 = v4 & v6 = all_0_1_1 & v1 = all_0_6_6 & v0 = all_0_7_7 & ~ (v3 = all_0_7_7) & vsubst(v3, v11, v5) = v12 & vsubst(all_0_7_7, all_0_6_6, v13) = all_0_0_0 & vgensym(v9) = v4 & vapp(v7, v8) = v9 & vapp(all_0_6_6, v5) = v7 & vabs(v4, v2, v12) = v13 & vabs(v3, v2, v5) = all_0_1_1 & vvar(v4) = v11 & vvar(all_0_7_7) = v8 & visFreeVar(v3, all_0_6_6)) | (v7 = all_0_0_0 & v5 = all_0_1_1 & v3 = all_0_6_6 & v2 = all_0_7_7 & ~ (v0 = all_0_7_7) & vsubst(all_0_7_7, all_0_6_6, v4) = v6 & vabs(v0, v1, v6) = all_0_0_0 & vabs(v0, v1, v4) = all_0_1_1 & ~ visFreeVar(v0, all_0_6_6)) | (v7 = all_0_0_0 & v4 = all_0_1_1 & v2 = all_0_6_6 & v1 = all_0_7_7 & vsubst(all_0_7_7, all_0_6_6, v3) = v6 & vsubst(all_0_7_7, all_0_6_6, v0) = v5 & vapp(v5, v6) = all_0_0_0 & vapp(v0, v3) = all_0_1_1) | (v5 = all_0_1_1 & v2 = all_0_7_7 & v1 = all_0_7_7 & v0 = all_0_6_6 & all_0_0_0 = all_0_1_1 & vabs(all_0_7_7, v3, v4) = all_0_1_1) | (v3 = all_0_1_1 & v2 = all_0_6_6 & v1 = all_0_7_7 & v0 = all_0_7_7 & all_0_0_0 = all_0_6_6 & vvar(all_0_7_7) = all_0_1_1) | (v3 = all_0_1_1 & v1 = all_0_7_7 & v0 = all_0_6_6 & all_0_0_0 = all_0_1_1 & ~ (v2 = all_0_7_7) & vvar(v2) = all_0_1_1))
% 46.14/13.89 |
% 46.14/13.89 | Instantiating formula (40) with all_0_1_1, veabs, all_0_4_4, all_0_5_5 and discharging atoms vabs(all_0_5_5, all_0_4_4, veabs) = all_0_1_1, yields:
% 46.14/13.89 | (90) visValue(all_0_1_1)
% 46.14/13.89 |
% 46.14/13.89 | Instantiating formula (20) with all_0_2_2, all_0_3_3, all_0_1_1, all_0_8_8, all_0_9_9, all_0_7_7 and discharging atoms vbind(all_0_7_7, all_0_9_9, all_0_8_8) = all_0_2_2, vtcheck(all_0_2_2, all_0_1_1, all_0_3_3), yields:
% 46.14/13.89 | (91) vtcheck(all_0_8_8, all_0_1_1, all_0_3_3) | visFreeVar(all_0_7_7, all_0_1_1)
% 46.14/13.89 |
% 46.14/13.89 | Instantiating (89) with all_21_0_13, all_21_1_14, all_21_2_15, all_21_3_16, all_21_4_17, all_21_5_18, all_21_6_19, all_21_7_20, all_21_8_21, all_21_9_22, all_21_10_23, all_21_11_24, all_21_12_25, all_21_13_26, all_21_14_27 yields:
% 46.14/13.89 | (92) (all_21_0_13 = all_0_0_0 & all_21_4_17 = all_21_10_23 & all_21_8_21 = all_0_1_1 & all_21_13_26 = all_0_6_6 & all_21_14_27 = all_0_7_7 & ~ (all_21_11_24 = all_0_7_7) & vsubst(all_21_11_24, all_21_3_16, all_21_9_22) = all_21_2_15 & vsubst(all_0_7_7, all_0_6_6, all_21_1_14) = all_0_0_0 & vgensym(all_21_5_18) = all_21_10_23 & vapp(all_21_7_20, all_21_6_19) = all_21_5_18 & vapp(all_0_6_6, all_21_9_22) = all_21_7_20 & vabs(all_21_10_23, all_21_12_25, all_21_2_15) = all_21_1_14 & vabs(all_21_11_24, all_21_12_25, all_21_9_22) = all_0_1_1 & vvar(all_21_10_23) = all_21_3_16 & vvar(all_0_7_7) = all_21_6_19 & visFreeVar(all_21_11_24, all_0_6_6)) | (all_21_7_20 = all_0_0_0 & all_21_9_22 = all_0_1_1 & all_21_11_24 = all_0_6_6 & all_21_12_25 = all_0_7_7 & ~ (all_21_14_27 = all_0_7_7) & vsubst(all_0_7_7, all_0_6_6, all_21_10_23) = all_21_8_21 & vabs(all_21_14_27, all_21_13_26, all_21_8_21) = all_0_0_0 & vabs(all_21_14_27, all_21_13_26, all_21_10_23) = all_0_1_1 & ~ visFreeVar(all_21_14_27, all_0_6_6)) | (all_21_7_20 = all_0_0_0 & all_21_10_23 = all_0_1_1 & all_21_12_25 = all_0_6_6 & all_21_13_26 = all_0_7_7 & vsubst(all_0_7_7, all_0_6_6, all_21_11_24) = all_21_8_21 & vsubst(all_0_7_7, all_0_6_6, all_21_14_27) = all_21_9_22 & vapp(all_21_9_22, all_21_8_21) = all_0_0_0 & vapp(all_21_14_27, all_21_11_24) = all_0_1_1) | (all_21_9_22 = all_0_1_1 & all_21_12_25 = all_0_7_7 & all_21_13_26 = all_0_7_7 & all_21_14_27 = all_0_6_6 & all_0_0_0 = all_0_1_1 & vabs(all_0_7_7, all_21_11_24, all_21_10_23) = all_0_1_1) | (all_21_11_24 = all_0_1_1 & all_21_12_25 = all_0_6_6 & all_21_13_26 = all_0_7_7 & all_21_14_27 = all_0_7_7 & all_0_0_0 = all_0_6_6 & vvar(all_0_7_7) = all_0_1_1) | (all_21_11_24 = all_0_1_1 & all_21_13_26 = all_0_7_7 & all_21_14_27 = all_0_6_6 & all_0_0_0 = all_0_1_1 & ~ (all_21_12_25 = all_0_7_7) & vvar(all_21_12_25) = all_0_1_1)
% 46.14/13.89 |
% 46.14/13.89 +-Applying beta-rule and splitting (91), into two cases.
% 46.14/13.89 |-Branch one:
% 46.14/13.89 | (93) vtcheck(all_0_8_8, all_0_1_1, all_0_3_3)
% 46.14/13.89 |
% 46.14/13.89 | Using (93) and (62) yields:
% 46.14/13.89 | (94) ~ (all_0_0_0 = all_0_1_1)
% 46.14/13.89 |
% 46.14/13.89 +-Applying beta-rule and splitting (92), into two cases.
% 46.14/13.89 |-Branch one:
% 46.14/13.89 | (95) (all_21_0_13 = all_0_0_0 & all_21_4_17 = all_21_10_23 & all_21_8_21 = all_0_1_1 & all_21_13_26 = all_0_6_6 & all_21_14_27 = all_0_7_7 & ~ (all_21_11_24 = all_0_7_7) & vsubst(all_21_11_24, all_21_3_16, all_21_9_22) = all_21_2_15 & vsubst(all_0_7_7, all_0_6_6, all_21_1_14) = all_0_0_0 & vgensym(all_21_5_18) = all_21_10_23 & vapp(all_21_7_20, all_21_6_19) = all_21_5_18 & vapp(all_0_6_6, all_21_9_22) = all_21_7_20 & vabs(all_21_10_23, all_21_12_25, all_21_2_15) = all_21_1_14 & vabs(all_21_11_24, all_21_12_25, all_21_9_22) = all_0_1_1 & vvar(all_21_10_23) = all_21_3_16 & vvar(all_0_7_7) = all_21_6_19 & visFreeVar(all_21_11_24, all_0_6_6)) | (all_21_7_20 = all_0_0_0 & all_21_9_22 = all_0_1_1 & all_21_11_24 = all_0_6_6 & all_21_12_25 = all_0_7_7 & ~ (all_21_14_27 = all_0_7_7) & vsubst(all_0_7_7, all_0_6_6, all_21_10_23) = all_21_8_21 & vabs(all_21_14_27, all_21_13_26, all_21_8_21) = all_0_0_0 & vabs(all_21_14_27, all_21_13_26, all_21_10_23) = all_0_1_1 & ~ visFreeVar(all_21_14_27, all_0_6_6)) | (all_21_7_20 = all_0_0_0 & all_21_10_23 = all_0_1_1 & all_21_12_25 = all_0_6_6 & all_21_13_26 = all_0_7_7 & vsubst(all_0_7_7, all_0_6_6, all_21_11_24) = all_21_8_21 & vsubst(all_0_7_7, all_0_6_6, all_21_14_27) = all_21_9_22 & vapp(all_21_9_22, all_21_8_21) = all_0_0_0 & vapp(all_21_14_27, all_21_11_24) = all_0_1_1) | (all_21_9_22 = all_0_1_1 & all_21_12_25 = all_0_7_7 & all_21_13_26 = all_0_7_7 & all_21_14_27 = all_0_6_6 & all_0_0_0 = all_0_1_1 & vabs(all_0_7_7, all_21_11_24, all_21_10_23) = all_0_1_1) | (all_21_11_24 = all_0_1_1 & all_21_12_25 = all_0_6_6 & all_21_13_26 = all_0_7_7 & all_21_14_27 = all_0_7_7 & all_0_0_0 = all_0_6_6 & vvar(all_0_7_7) = all_0_1_1)
% 46.14/13.90 |
% 46.14/13.90 +-Applying beta-rule and splitting (95), into two cases.
% 46.14/13.90 |-Branch one:
% 46.14/13.90 | (96) (all_21_0_13 = all_0_0_0 & all_21_4_17 = all_21_10_23 & all_21_8_21 = all_0_1_1 & all_21_13_26 = all_0_6_6 & all_21_14_27 = all_0_7_7 & ~ (all_21_11_24 = all_0_7_7) & vsubst(all_21_11_24, all_21_3_16, all_21_9_22) = all_21_2_15 & vsubst(all_0_7_7, all_0_6_6, all_21_1_14) = all_0_0_0 & vgensym(all_21_5_18) = all_21_10_23 & vapp(all_21_7_20, all_21_6_19) = all_21_5_18 & vapp(all_0_6_6, all_21_9_22) = all_21_7_20 & vabs(all_21_10_23, all_21_12_25, all_21_2_15) = all_21_1_14 & vabs(all_21_11_24, all_21_12_25, all_21_9_22) = all_0_1_1 & vvar(all_21_10_23) = all_21_3_16 & vvar(all_0_7_7) = all_21_6_19 & visFreeVar(all_21_11_24, all_0_6_6)) | (all_21_7_20 = all_0_0_0 & all_21_9_22 = all_0_1_1 & all_21_11_24 = all_0_6_6 & all_21_12_25 = all_0_7_7 & ~ (all_21_14_27 = all_0_7_7) & vsubst(all_0_7_7, all_0_6_6, all_21_10_23) = all_21_8_21 & vabs(all_21_14_27, all_21_13_26, all_21_8_21) = all_0_0_0 & vabs(all_21_14_27, all_21_13_26, all_21_10_23) = all_0_1_1 & ~ visFreeVar(all_21_14_27, all_0_6_6)) | (all_21_7_20 = all_0_0_0 & all_21_10_23 = all_0_1_1 & all_21_12_25 = all_0_6_6 & all_21_13_26 = all_0_7_7 & vsubst(all_0_7_7, all_0_6_6, all_21_11_24) = all_21_8_21 & vsubst(all_0_7_7, all_0_6_6, all_21_14_27) = all_21_9_22 & vapp(all_21_9_22, all_21_8_21) = all_0_0_0 & vapp(all_21_14_27, all_21_11_24) = all_0_1_1) | (all_21_9_22 = all_0_1_1 & all_21_12_25 = all_0_7_7 & all_21_13_26 = all_0_7_7 & all_21_14_27 = all_0_6_6 & all_0_0_0 = all_0_1_1 & vabs(all_0_7_7, all_21_11_24, all_21_10_23) = all_0_1_1)
% 46.14/13.90 |
% 46.14/13.90 +-Applying beta-rule and splitting (96), into two cases.
% 46.14/13.90 |-Branch one:
% 46.14/13.90 | (97) (all_21_0_13 = all_0_0_0 & all_21_4_17 = all_21_10_23 & all_21_8_21 = all_0_1_1 & all_21_13_26 = all_0_6_6 & all_21_14_27 = all_0_7_7 & ~ (all_21_11_24 = all_0_7_7) & vsubst(all_21_11_24, all_21_3_16, all_21_9_22) = all_21_2_15 & vsubst(all_0_7_7, all_0_6_6, all_21_1_14) = all_0_0_0 & vgensym(all_21_5_18) = all_21_10_23 & vapp(all_21_7_20, all_21_6_19) = all_21_5_18 & vapp(all_0_6_6, all_21_9_22) = all_21_7_20 & vabs(all_21_10_23, all_21_12_25, all_21_2_15) = all_21_1_14 & vabs(all_21_11_24, all_21_12_25, all_21_9_22) = all_0_1_1 & vvar(all_21_10_23) = all_21_3_16 & vvar(all_0_7_7) = all_21_6_19 & visFreeVar(all_21_11_24, all_0_6_6)) | (all_21_7_20 = all_0_0_0 & all_21_9_22 = all_0_1_1 & all_21_11_24 = all_0_6_6 & all_21_12_25 = all_0_7_7 & ~ (all_21_14_27 = all_0_7_7) & vsubst(all_0_7_7, all_0_6_6, all_21_10_23) = all_21_8_21 & vabs(all_21_14_27, all_21_13_26, all_21_8_21) = all_0_0_0 & vabs(all_21_14_27, all_21_13_26, all_21_10_23) = all_0_1_1 & ~ visFreeVar(all_21_14_27, all_0_6_6)) | (all_21_7_20 = all_0_0_0 & all_21_10_23 = all_0_1_1 & all_21_12_25 = all_0_6_6 & all_21_13_26 = all_0_7_7 & vsubst(all_0_7_7, all_0_6_6, all_21_11_24) = all_21_8_21 & vsubst(all_0_7_7, all_0_6_6, all_21_14_27) = all_21_9_22 & vapp(all_21_9_22, all_21_8_21) = all_0_0_0 & vapp(all_21_14_27, all_21_11_24) = all_0_1_1)
% 46.14/13.90 |
% 46.14/13.90 +-Applying beta-rule and splitting (97), into two cases.
% 46.14/13.90 |-Branch one:
% 46.14/13.90 | (98) (all_21_0_13 = all_0_0_0 & all_21_4_17 = all_21_10_23 & all_21_8_21 = all_0_1_1 & all_21_13_26 = all_0_6_6 & all_21_14_27 = all_0_7_7 & ~ (all_21_11_24 = all_0_7_7) & vsubst(all_21_11_24, all_21_3_16, all_21_9_22) = all_21_2_15 & vsubst(all_0_7_7, all_0_6_6, all_21_1_14) = all_0_0_0 & vgensym(all_21_5_18) = all_21_10_23 & vapp(all_21_7_20, all_21_6_19) = all_21_5_18 & vapp(all_0_6_6, all_21_9_22) = all_21_7_20 & vabs(all_21_10_23, all_21_12_25, all_21_2_15) = all_21_1_14 & vabs(all_21_11_24, all_21_12_25, all_21_9_22) = all_0_1_1 & vvar(all_21_10_23) = all_21_3_16 & vvar(all_0_7_7) = all_21_6_19 & visFreeVar(all_21_11_24, all_0_6_6)) | (all_21_7_20 = all_0_0_0 & all_21_9_22 = all_0_1_1 & all_21_11_24 = all_0_6_6 & all_21_12_25 = all_0_7_7 & ~ (all_21_14_27 = all_0_7_7) & vsubst(all_0_7_7, all_0_6_6, all_21_10_23) = all_21_8_21 & vabs(all_21_14_27, all_21_13_26, all_21_8_21) = all_0_0_0 & vabs(all_21_14_27, all_21_13_26, all_21_10_23) = all_0_1_1 & ~ visFreeVar(all_21_14_27, all_0_6_6))
% 46.14/13.90 |
% 46.14/13.90 +-Applying beta-rule and splitting (98), into two cases.
% 46.14/13.90 |-Branch one:
% 46.14/13.90 | (99) all_21_0_13 = all_0_0_0 & all_21_4_17 = all_21_10_23 & all_21_8_21 = all_0_1_1 & all_21_13_26 = all_0_6_6 & all_21_14_27 = all_0_7_7 & ~ (all_21_11_24 = all_0_7_7) & vsubst(all_21_11_24, all_21_3_16, all_21_9_22) = all_21_2_15 & vsubst(all_0_7_7, all_0_6_6, all_21_1_14) = all_0_0_0 & vgensym(all_21_5_18) = all_21_10_23 & vapp(all_21_7_20, all_21_6_19) = all_21_5_18 & vapp(all_0_6_6, all_21_9_22) = all_21_7_20 & vabs(all_21_10_23, all_21_12_25, all_21_2_15) = all_21_1_14 & vabs(all_21_11_24, all_21_12_25, all_21_9_22) = all_0_1_1 & vvar(all_21_10_23) = all_21_3_16 & vvar(all_0_7_7) = all_21_6_19 & visFreeVar(all_21_11_24, all_0_6_6)
% 46.14/13.90 |
% 46.14/13.90 | Applying alpha-rule on (99) yields:
% 46.14/13.90 | (100) ~ (all_21_11_24 = all_0_7_7)
% 46.14/13.90 | (101) all_21_4_17 = all_21_10_23
% 46.14/13.90 | (102) vvar(all_0_7_7) = all_21_6_19
% 46.14/13.90 | (103) vabs(all_21_11_24, all_21_12_25, all_21_9_22) = all_0_1_1
% 46.14/13.90 | (104) vapp(all_0_6_6, all_21_9_22) = all_21_7_20
% 46.14/13.90 | (105) vgensym(all_21_5_18) = all_21_10_23
% 46.14/13.90 | (106) vsubst(all_0_7_7, all_0_6_6, all_21_1_14) = all_0_0_0
% 46.14/13.90 | (107) vsubst(all_21_11_24, all_21_3_16, all_21_9_22) = all_21_2_15
% 46.14/13.90 | (108) all_21_14_27 = all_0_7_7
% 46.14/13.90 | (109) vapp(all_21_7_20, all_21_6_19) = all_21_5_18
% 46.14/13.90 | (110) all_21_13_26 = all_0_6_6
% 46.14/13.90 | (111) all_21_8_21 = all_0_1_1
% 46.14/13.90 | (112) all_21_0_13 = all_0_0_0
% 46.14/13.90 | (113) visFreeVar(all_21_11_24, all_0_6_6)
% 46.14/13.90 | (114) vabs(all_21_10_23, all_21_12_25, all_21_2_15) = all_21_1_14
% 46.14/13.90 | (115) vvar(all_21_10_23) = all_21_3_16
% 46.14/13.90 |
% 46.14/13.90 | Instantiating formula (84) with all_0_1_1, all_21_9_22, all_21_12_25, all_21_11_24, veabs, all_0_4_4, all_0_5_5 and discharging atoms vabs(all_21_11_24, all_21_12_25, all_21_9_22) = all_0_1_1, vabs(all_0_5_5, all_0_4_4, veabs) = all_0_1_1, yields:
% 46.14/13.90 | (116) all_21_9_22 = veabs
% 46.14/13.90 |
% 46.14/13.90 | Instantiating formula (2) with all_0_1_1, all_21_9_22, all_21_12_25, all_21_11_24, veabs, all_0_4_4, all_0_5_5 and discharging atoms vabs(all_21_11_24, all_21_12_25, all_21_9_22) = all_0_1_1, vabs(all_0_5_5, all_0_4_4, veabs) = all_0_1_1, yields:
% 46.14/13.90 | (117) all_21_12_25 = all_0_4_4
% 46.14/13.90 |
% 46.14/13.90 | Instantiating formula (58) with all_0_1_1, all_21_9_22, all_21_12_25, all_21_11_24, veabs, all_0_4_4, all_0_5_5 and discharging atoms vabs(all_21_11_24, all_21_12_25, all_21_9_22) = all_0_1_1, vabs(all_0_5_5, all_0_4_4, veabs) = all_0_1_1, yields:
% 46.14/13.90 | (118) all_21_11_24 = all_0_5_5
% 46.14/13.90 |
% 46.14/13.90 | From (118)(116) and (107) follows:
% 46.14/13.90 | (119) vsubst(all_0_5_5, all_21_3_16, veabs) = all_21_2_15
% 46.14/13.90 |
% 46.14/13.90 | From (116) and (104) follows:
% 46.14/13.90 | (120) vapp(all_0_6_6, veabs) = all_21_7_20
% 46.14/13.90 |
% 46.14/13.90 | From (117) and (114) follows:
% 46.14/13.90 | (121) vabs(all_21_10_23, all_0_4_4, all_21_2_15) = all_21_1_14
% 46.14/13.90 |
% 46.14/13.90 | From (118)(117)(116) and (103) follows:
% 46.14/13.90 | (59) vabs(all_0_5_5, all_0_4_4, veabs) = all_0_1_1
% 46.14/13.90 |
% 46.14/13.90 | Instantiating formula (88) with all_21_1_14, all_21_2_15, all_21_3_16, veabs, all_21_10_23, all_0_5_5, all_0_4_4 and discharging atoms vsubst(all_0_5_5, all_21_3_16, veabs) = all_21_2_15, vabs(all_21_10_23, all_0_4_4, all_21_2_15) = all_21_1_14, vvar(all_21_10_23) = all_21_3_16, yields:
% 46.14/13.90 | (123) visFreeVar(all_21_10_23, veabs) | ? [v0] : (vabs(all_0_5_5, all_0_4_4, veabs) = v0 & valphaEquivalent(v0, all_21_1_14))
% 46.14/13.90 |
% 46.14/13.90 | Instantiating formula (79) with all_21_5_18, all_21_6_19, all_21_7_20, all_0_7_7, veabs, all_0_6_6 and discharging atoms vapp(all_21_7_20, all_21_6_19) = all_21_5_18, vapp(all_0_6_6, veabs) = all_21_7_20, vvar(all_0_7_7) = all_21_6_19, yields:
% 46.14/13.90 | (124) ? [v0] : ( ~ (v0 = all_0_7_7) & vgensym(all_21_5_18) = v0)
% 46.14/13.90 |
% 46.14/13.90 | Instantiating (124) with all_66_0_43 yields:
% 46.14/13.90 | (125) ~ (all_66_0_43 = all_0_7_7) & vgensym(all_21_5_18) = all_66_0_43
% 46.14/13.90 |
% 46.14/13.90 | Applying alpha-rule on (125) yields:
% 46.14/13.90 | (126) ~ (all_66_0_43 = all_0_7_7)
% 46.14/13.90 | (127) vgensym(all_21_5_18) = all_66_0_43
% 46.14/13.90 |
% 46.14/13.90 | Instantiating formula (21) with all_21_5_18, all_66_0_43, all_21_10_23 and discharging atoms vgensym(all_21_5_18) = all_66_0_43, vgensym(all_21_5_18) = all_21_10_23, yields:
% 46.14/13.90 | (128) all_66_0_43 = all_21_10_23
% 46.14/13.90 |
% 46.14/13.90 | Equations (128) can reduce 126 to:
% 46.14/13.90 | (129) ~ (all_21_10_23 = all_0_7_7)
% 46.14/13.90 |
% 46.14/13.90 | From (128) and (127) follows:
% 46.14/13.90 | (105) vgensym(all_21_5_18) = all_21_10_23
% 46.14/13.90 |
% 46.14/13.90 | Instantiating formula (3) with all_21_5_18, all_21_6_19, all_21_7_20, veabs, all_21_10_23, all_0_7_7, all_0_6_6 and discharging atoms vapp(all_21_7_20, all_21_6_19) = all_21_5_18, vapp(all_0_6_6, veabs) = all_21_7_20, vvar(all_0_7_7) = all_21_6_19, yields:
% 46.14/13.90 | (131) ~ visFreeVar(all_21_10_23, veabs) | ? [v0] : ( ~ (v0 = all_21_10_23) & vgensym(all_21_5_18) = v0)
% 46.14/13.90 |
% 46.14/13.90 | Instantiating formula (16) with veabs, all_0_6_6, all_21_7_20, all_21_10_23 and discharging atoms vapp(all_0_6_6, veabs) = all_21_7_20, yields:
% 46.14/13.90 | (132) ~ visFreeVar(all_21_10_23, all_0_6_6) | visFreeVar(all_21_10_23, all_21_7_20)
% 46.14/13.90 |
% 46.14/13.90 +-Applying beta-rule and splitting (131), into two cases.
% 46.14/13.90 |-Branch one:
% 46.14/13.90 | (133) ~ visFreeVar(all_21_10_23, veabs)
% 46.14/13.90 |
% 46.14/13.90 +-Applying beta-rule and splitting (123), into two cases.
% 46.14/13.90 |-Branch one:
% 46.14/13.90 | (134) visFreeVar(all_21_10_23, veabs)
% 46.14/13.90 |
% 46.14/13.90 | Using (134) and (133) yields:
% 46.14/13.90 | (135) $false
% 46.14/13.90 |
% 46.14/13.91 |-The branch is then unsatisfiable
% 46.14/13.91 |-Branch two:
% 46.14/13.91 | (133) ~ visFreeVar(all_21_10_23, veabs)
% 46.14/13.91 | (137) ? [v0] : (vabs(all_0_5_5, all_0_4_4, veabs) = v0 & valphaEquivalent(v0, all_21_1_14))
% 46.14/13.91 |
% 46.14/13.91 | Instantiating (137) with all_99_0_59 yields:
% 46.14/13.91 | (138) vabs(all_0_5_5, all_0_4_4, veabs) = all_99_0_59 & valphaEquivalent(all_99_0_59, all_21_1_14)
% 46.14/13.91 |
% 46.14/13.91 | Applying alpha-rule on (138) yields:
% 46.14/13.91 | (139) vabs(all_0_5_5, all_0_4_4, veabs) = all_99_0_59
% 46.14/13.91 | (140) valphaEquivalent(all_99_0_59, all_21_1_14)
% 46.14/13.91 |
% 46.14/13.91 | Instantiating formula (67) with all_99_0_59, all_0_1_1, veabs, all_0_4_4, all_0_5_5 and discharging atoms vabs(all_0_5_5, all_0_4_4, veabs) = all_99_0_59, vabs(all_0_5_5, all_0_4_4, veabs) = all_0_1_1, yields:
% 46.14/13.91 | (141) all_99_0_59 = all_0_1_1
% 46.14/13.91 |
% 46.14/13.91 | From (141) and (140) follows:
% 46.14/13.91 | (142) valphaEquivalent(all_0_1_1, all_21_1_14)
% 46.14/13.91 |
% 46.14/13.91 | Instantiating formula (49) with all_0_3_3, all_21_1_14, all_0_2_2, all_0_1_1 and discharging atoms valphaEquivalent(all_0_1_1, all_21_1_14), vtcheck(all_0_2_2, all_0_1_1, all_0_3_3), yields:
% 46.14/13.91 | (143) vtcheck(all_0_2_2, all_21_1_14, all_0_3_3)
% 46.14/13.91 |
% 46.14/13.91 | Instantiating formula (74) with all_0_0_0, all_21_1_14, all_0_2_2, all_0_3_3, all_21_2_15, all_0_4_4, all_21_10_23, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms vsubst(all_0_7_7, all_0_6_6, all_21_1_14) = all_0_0_0, vbind(all_0_7_7, all_0_9_9, all_0_8_8) = all_0_2_2, vabs(all_21_10_23, all_0_4_4, all_21_2_15) = all_21_1_14, vtcheck(all_0_2_2, all_21_1_14, all_0_3_3), vtcheck(all_0_8_8, all_0_6_6, all_0_9_9), ~ vtcheck(all_0_8_8, all_0_0_0, all_0_3_3), yields:
% 46.14/13.91 | (144) all_21_10_23 = all_0_7_7 | visFreeVar(all_21_10_23, all_0_6_6)
% 46.14/13.91 |
% 46.14/13.91 +-Applying beta-rule and splitting (144), into two cases.
% 46.14/13.91 |-Branch one:
% 46.14/13.91 | (145) visFreeVar(all_21_10_23, all_0_6_6)
% 46.14/13.91 |
% 46.14/13.91 +-Applying beta-rule and splitting (132), into two cases.
% 46.14/13.91 |-Branch one:
% 46.14/13.91 | (146) ~ visFreeVar(all_21_10_23, all_0_6_6)
% 46.14/13.91 |
% 46.14/13.91 | Using (145) and (146) yields:
% 46.14/13.91 | (135) $false
% 46.14/13.91 |
% 46.14/13.91 |-The branch is then unsatisfiable
% 46.14/13.91 |-Branch two:
% 46.14/13.91 | (145) visFreeVar(all_21_10_23, all_0_6_6)
% 46.14/13.91 | (149) visFreeVar(all_21_10_23, all_21_7_20)
% 46.14/13.91 |
% 46.14/13.91 | Instantiating formula (16) with all_21_6_19, all_21_7_20, all_21_5_18, all_21_10_23 and discharging atoms vapp(all_21_7_20, all_21_6_19) = all_21_5_18, visFreeVar(all_21_10_23, all_21_7_20), yields:
% 46.14/13.91 | (150) visFreeVar(all_21_10_23, all_21_5_18)
% 46.14/13.91 |
% 46.14/13.91 | Instantiating formula (28) with all_21_5_18, all_21_10_23 and discharging atoms vgensym(all_21_5_18) = all_21_10_23, visFreeVar(all_21_10_23, all_21_5_18), yields:
% 46.14/13.91 | (135) $false
% 46.14/13.91 |
% 46.14/13.91 |-The branch is then unsatisfiable
% 46.14/13.91 |-Branch two:
% 46.14/13.91 | (146) ~ visFreeVar(all_21_10_23, all_0_6_6)
% 46.14/13.91 | (153) all_21_10_23 = all_0_7_7
% 46.14/13.91 |
% 46.14/13.91 | Equations (153) can reduce 129 to:
% 46.14/13.91 | (154) $false
% 46.14/13.91 |
% 46.14/13.91 |-The branch is then unsatisfiable
% 46.14/13.91 |-Branch two:
% 46.14/13.91 | (134) visFreeVar(all_21_10_23, veabs)
% 46.14/13.91 | (156) ? [v0] : ( ~ (v0 = all_21_10_23) & vgensym(all_21_5_18) = v0)
% 46.14/13.91 |
% 46.14/13.91 | Instantiating (156) with all_95_0_60 yields:
% 46.14/13.91 | (157) ~ (all_95_0_60 = all_21_10_23) & vgensym(all_21_5_18) = all_95_0_60
% 46.14/13.91 |
% 46.14/13.91 | Applying alpha-rule on (157) yields:
% 46.14/13.91 | (158) ~ (all_95_0_60 = all_21_10_23)
% 46.14/13.91 | (159) vgensym(all_21_5_18) = all_95_0_60
% 46.14/13.91 |
% 46.14/13.91 | Instantiating formula (21) with all_21_5_18, all_95_0_60, all_21_10_23 and discharging atoms vgensym(all_21_5_18) = all_95_0_60, vgensym(all_21_5_18) = all_21_10_23, yields:
% 46.14/13.91 | (160) all_95_0_60 = all_21_10_23
% 46.14/13.91 |
% 46.14/13.91 | Equations (160) can reduce 158 to:
% 46.14/13.91 | (154) $false
% 46.14/13.91 |
% 46.14/13.91 |-The branch is then unsatisfiable
% 46.14/13.91 |-Branch two:
% 46.14/13.91 | (162) all_21_7_20 = all_0_0_0 & all_21_9_22 = all_0_1_1 & all_21_11_24 = all_0_6_6 & all_21_12_25 = all_0_7_7 & ~ (all_21_14_27 = all_0_7_7) & vsubst(all_0_7_7, all_0_6_6, all_21_10_23) = all_21_8_21 & vabs(all_21_14_27, all_21_13_26, all_21_8_21) = all_0_0_0 & vabs(all_21_14_27, all_21_13_26, all_21_10_23) = all_0_1_1 & ~ visFreeVar(all_21_14_27, all_0_6_6)
% 46.14/13.91 |
% 46.14/13.91 | Applying alpha-rule on (162) yields:
% 46.14/13.91 | (163) all_21_12_25 = all_0_7_7
% 46.14/13.91 | (164) vabs(all_21_14_27, all_21_13_26, all_21_8_21) = all_0_0_0
% 46.14/13.91 | (165) vabs(all_21_14_27, all_21_13_26, all_21_10_23) = all_0_1_1
% 46.14/13.91 | (166) vsubst(all_0_7_7, all_0_6_6, all_21_10_23) = all_21_8_21
% 46.14/13.91 | (167) all_21_7_20 = all_0_0_0
% 46.14/13.91 | (168) ~ visFreeVar(all_21_14_27, all_0_6_6)
% 46.14/13.91 | (169) all_21_9_22 = all_0_1_1
% 46.14/13.91 | (170) all_21_11_24 = all_0_6_6
% 46.14/13.91 | (171) ~ (all_21_14_27 = all_0_7_7)
% 46.14/13.91 |
% 46.14/13.91 | Instantiating formula (58) with all_0_1_1, all_21_10_23, all_21_13_26, all_21_14_27, veabs, all_0_4_4, all_0_5_5 and discharging atoms vabs(all_21_14_27, all_21_13_26, all_21_10_23) = all_0_1_1, vabs(all_0_5_5, all_0_4_4, veabs) = all_0_1_1, yields:
% 46.14/13.91 | (172) all_21_14_27 = all_0_5_5
% 46.14/13.91 |
% 46.14/13.91 | Using (6) and (168) yields:
% 46.14/13.91 | (173) ~ (all_21_14_27 = all_0_5_5)
% 46.14/13.91 |
% 46.14/13.91 | Equations (172) can reduce 173 to:
% 46.14/13.91 | (154) $false
% 46.14/13.91 |
% 46.14/13.91 |-The branch is then unsatisfiable
% 46.14/13.91 |-Branch two:
% 46.14/13.91 | (175) all_21_7_20 = all_0_0_0 & all_21_10_23 = all_0_1_1 & all_21_12_25 = all_0_6_6 & all_21_13_26 = all_0_7_7 & vsubst(all_0_7_7, all_0_6_6, all_21_11_24) = all_21_8_21 & vsubst(all_0_7_7, all_0_6_6, all_21_14_27) = all_21_9_22 & vapp(all_21_9_22, all_21_8_21) = all_0_0_0 & vapp(all_21_14_27, all_21_11_24) = all_0_1_1
% 46.14/13.91 |
% 46.14/13.91 | Applying alpha-rule on (175) yields:
% 46.14/13.91 | (176) vapp(all_21_9_22, all_21_8_21) = all_0_0_0
% 46.14/13.91 | (177) vapp(all_21_14_27, all_21_11_24) = all_0_1_1
% 46.14/13.91 | (178) all_21_10_23 = all_0_1_1
% 46.14/13.91 | (179) all_21_13_26 = all_0_7_7
% 46.14/13.91 | (167) all_21_7_20 = all_0_0_0
% 46.14/13.91 | (181) vsubst(all_0_7_7, all_0_6_6, all_21_14_27) = all_21_9_22
% 46.14/13.91 | (182) vsubst(all_0_7_7, all_0_6_6, all_21_11_24) = all_21_8_21
% 46.14/13.91 | (183) all_21_12_25 = all_0_6_6
% 46.14/13.91 |
% 46.14/13.91 | Instantiating formula (78) with all_0_1_1, all_21_11_24, all_21_14_27 and discharging atoms vapp(all_21_14_27, all_21_11_24) = all_0_1_1, visValue(all_0_1_1), yields:
% 46.14/13.91 | (135) $false
% 46.14/13.91 |
% 46.14/13.91 |-The branch is then unsatisfiable
% 46.14/13.91 |-Branch two:
% 46.14/13.91 | (185) all_21_9_22 = all_0_1_1 & all_21_12_25 = all_0_7_7 & all_21_13_26 = all_0_7_7 & all_21_14_27 = all_0_6_6 & all_0_0_0 = all_0_1_1 & vabs(all_0_7_7, all_21_11_24, all_21_10_23) = all_0_1_1
% 46.14/13.91 |
% 46.14/13.91 | Applying alpha-rule on (185) yields:
% 46.14/13.91 | (163) all_21_12_25 = all_0_7_7
% 46.14/13.91 | (187) all_21_14_27 = all_0_6_6
% 46.14/13.91 | (179) all_21_13_26 = all_0_7_7
% 46.14/13.91 | (169) all_21_9_22 = all_0_1_1
% 46.14/13.91 | (190) all_0_0_0 = all_0_1_1
% 46.14/13.91 | (191) vabs(all_0_7_7, all_21_11_24, all_21_10_23) = all_0_1_1
% 46.14/13.91 |
% 46.14/13.91 | Equations (190) can reduce 94 to:
% 46.14/13.91 | (154) $false
% 46.14/13.91 |
% 46.14/13.91 |-The branch is then unsatisfiable
% 46.14/13.91 |-Branch two:
% 46.14/13.91 | (193) all_21_11_24 = all_0_1_1 & all_21_12_25 = all_0_6_6 & all_21_13_26 = all_0_7_7 & all_21_14_27 = all_0_7_7 & all_0_0_0 = all_0_6_6 & vvar(all_0_7_7) = all_0_1_1
% 46.14/13.91 |
% 46.14/13.91 | Applying alpha-rule on (193) yields:
% 46.14/13.91 | (194) vvar(all_0_7_7) = all_0_1_1
% 46.14/13.91 | (179) all_21_13_26 = all_0_7_7
% 46.14/13.91 | (108) all_21_14_27 = all_0_7_7
% 46.14/13.91 | (197) all_0_0_0 = all_0_6_6
% 46.14/13.91 | (183) all_21_12_25 = all_0_6_6
% 46.14/13.91 | (199) all_21_11_24 = all_0_1_1
% 46.14/13.91 |
% 46.14/13.91 | Instantiating formula (30) with all_0_1_1, all_0_7_7 and discharging atoms vvar(all_0_7_7) = all_0_1_1, visValue(all_0_1_1), yields:
% 46.14/13.91 | (135) $false
% 46.14/13.91 |
% 46.14/13.91 |-The branch is then unsatisfiable
% 46.14/13.91 |-Branch two:
% 46.14/13.91 | (201) all_21_11_24 = all_0_1_1 & all_21_13_26 = all_0_7_7 & all_21_14_27 = all_0_6_6 & all_0_0_0 = all_0_1_1 & ~ (all_21_12_25 = all_0_7_7) & vvar(all_21_12_25) = all_0_1_1
% 46.14/13.91 |
% 46.14/13.91 | Applying alpha-rule on (201) yields:
% 46.14/13.91 | (202) ~ (all_21_12_25 = all_0_7_7)
% 46.14/13.91 | (187) all_21_14_27 = all_0_6_6
% 46.14/13.91 | (204) vvar(all_21_12_25) = all_0_1_1
% 46.14/13.91 | (179) all_21_13_26 = all_0_7_7
% 46.14/13.91 | (190) all_0_0_0 = all_0_1_1
% 46.14/13.91 | (199) all_21_11_24 = all_0_1_1
% 46.14/13.91 |
% 46.14/13.91 | Equations (190) can reduce 94 to:
% 46.14/13.91 | (154) $false
% 46.14/13.91 |
% 46.14/13.91 |-The branch is then unsatisfiable
% 46.14/13.91 |-Branch two:
% 46.14/13.91 | (209) ~ vtcheck(all_0_8_8, all_0_1_1, all_0_3_3)
% 46.14/13.91 | (210) visFreeVar(all_0_7_7, all_0_1_1)
% 46.14/13.91 |
% 46.14/13.91 +-Applying beta-rule and splitting (92), into two cases.
% 46.14/13.91 |-Branch one:
% 46.14/13.91 | (95) (all_21_0_13 = all_0_0_0 & all_21_4_17 = all_21_10_23 & all_21_8_21 = all_0_1_1 & all_21_13_26 = all_0_6_6 & all_21_14_27 = all_0_7_7 & ~ (all_21_11_24 = all_0_7_7) & vsubst(all_21_11_24, all_21_3_16, all_21_9_22) = all_21_2_15 & vsubst(all_0_7_7, all_0_6_6, all_21_1_14) = all_0_0_0 & vgensym(all_21_5_18) = all_21_10_23 & vapp(all_21_7_20, all_21_6_19) = all_21_5_18 & vapp(all_0_6_6, all_21_9_22) = all_21_7_20 & vabs(all_21_10_23, all_21_12_25, all_21_2_15) = all_21_1_14 & vabs(all_21_11_24, all_21_12_25, all_21_9_22) = all_0_1_1 & vvar(all_21_10_23) = all_21_3_16 & vvar(all_0_7_7) = all_21_6_19 & visFreeVar(all_21_11_24, all_0_6_6)) | (all_21_7_20 = all_0_0_0 & all_21_9_22 = all_0_1_1 & all_21_11_24 = all_0_6_6 & all_21_12_25 = all_0_7_7 & ~ (all_21_14_27 = all_0_7_7) & vsubst(all_0_7_7, all_0_6_6, all_21_10_23) = all_21_8_21 & vabs(all_21_14_27, all_21_13_26, all_21_8_21) = all_0_0_0 & vabs(all_21_14_27, all_21_13_26, all_21_10_23) = all_0_1_1 & ~ visFreeVar(all_21_14_27, all_0_6_6)) | (all_21_7_20 = all_0_0_0 & all_21_10_23 = all_0_1_1 & all_21_12_25 = all_0_6_6 & all_21_13_26 = all_0_7_7 & vsubst(all_0_7_7, all_0_6_6, all_21_11_24) = all_21_8_21 & vsubst(all_0_7_7, all_0_6_6, all_21_14_27) = all_21_9_22 & vapp(all_21_9_22, all_21_8_21) = all_0_0_0 & vapp(all_21_14_27, all_21_11_24) = all_0_1_1) | (all_21_9_22 = all_0_1_1 & all_21_12_25 = all_0_7_7 & all_21_13_26 = all_0_7_7 & all_21_14_27 = all_0_6_6 & all_0_0_0 = all_0_1_1 & vabs(all_0_7_7, all_21_11_24, all_21_10_23) = all_0_1_1) | (all_21_11_24 = all_0_1_1 & all_21_12_25 = all_0_6_6 & all_21_13_26 = all_0_7_7 & all_21_14_27 = all_0_7_7 & all_0_0_0 = all_0_6_6 & vvar(all_0_7_7) = all_0_1_1)
% 46.14/13.91 |
% 46.14/13.91 +-Applying beta-rule and splitting (95), into two cases.
% 46.14/13.91 |-Branch one:
% 46.14/13.91 | (96) (all_21_0_13 = all_0_0_0 & all_21_4_17 = all_21_10_23 & all_21_8_21 = all_0_1_1 & all_21_13_26 = all_0_6_6 & all_21_14_27 = all_0_7_7 & ~ (all_21_11_24 = all_0_7_7) & vsubst(all_21_11_24, all_21_3_16, all_21_9_22) = all_21_2_15 & vsubst(all_0_7_7, all_0_6_6, all_21_1_14) = all_0_0_0 & vgensym(all_21_5_18) = all_21_10_23 & vapp(all_21_7_20, all_21_6_19) = all_21_5_18 & vapp(all_0_6_6, all_21_9_22) = all_21_7_20 & vabs(all_21_10_23, all_21_12_25, all_21_2_15) = all_21_1_14 & vabs(all_21_11_24, all_21_12_25, all_21_9_22) = all_0_1_1 & vvar(all_21_10_23) = all_21_3_16 & vvar(all_0_7_7) = all_21_6_19 & visFreeVar(all_21_11_24, all_0_6_6)) | (all_21_7_20 = all_0_0_0 & all_21_9_22 = all_0_1_1 & all_21_11_24 = all_0_6_6 & all_21_12_25 = all_0_7_7 & ~ (all_21_14_27 = all_0_7_7) & vsubst(all_0_7_7, all_0_6_6, all_21_10_23) = all_21_8_21 & vabs(all_21_14_27, all_21_13_26, all_21_8_21) = all_0_0_0 & vabs(all_21_14_27, all_21_13_26, all_21_10_23) = all_0_1_1 & ~ visFreeVar(all_21_14_27, all_0_6_6)) | (all_21_7_20 = all_0_0_0 & all_21_10_23 = all_0_1_1 & all_21_12_25 = all_0_6_6 & all_21_13_26 = all_0_7_7 & vsubst(all_0_7_7, all_0_6_6, all_21_11_24) = all_21_8_21 & vsubst(all_0_7_7, all_0_6_6, all_21_14_27) = all_21_9_22 & vapp(all_21_9_22, all_21_8_21) = all_0_0_0 & vapp(all_21_14_27, all_21_11_24) = all_0_1_1) | (all_21_9_22 = all_0_1_1 & all_21_12_25 = all_0_7_7 & all_21_13_26 = all_0_7_7 & all_21_14_27 = all_0_6_6 & all_0_0_0 = all_0_1_1 & vabs(all_0_7_7, all_21_11_24, all_21_10_23) = all_0_1_1)
% 46.14/13.91 |
% 46.14/13.91 +-Applying beta-rule and splitting (96), into two cases.
% 46.14/13.91 |-Branch one:
% 46.14/13.91 | (97) (all_21_0_13 = all_0_0_0 & all_21_4_17 = all_21_10_23 & all_21_8_21 = all_0_1_1 & all_21_13_26 = all_0_6_6 & all_21_14_27 = all_0_7_7 & ~ (all_21_11_24 = all_0_7_7) & vsubst(all_21_11_24, all_21_3_16, all_21_9_22) = all_21_2_15 & vsubst(all_0_7_7, all_0_6_6, all_21_1_14) = all_0_0_0 & vgensym(all_21_5_18) = all_21_10_23 & vapp(all_21_7_20, all_21_6_19) = all_21_5_18 & vapp(all_0_6_6, all_21_9_22) = all_21_7_20 & vabs(all_21_10_23, all_21_12_25, all_21_2_15) = all_21_1_14 & vabs(all_21_11_24, all_21_12_25, all_21_9_22) = all_0_1_1 & vvar(all_21_10_23) = all_21_3_16 & vvar(all_0_7_7) = all_21_6_19 & visFreeVar(all_21_11_24, all_0_6_6)) | (all_21_7_20 = all_0_0_0 & all_21_9_22 = all_0_1_1 & all_21_11_24 = all_0_6_6 & all_21_12_25 = all_0_7_7 & ~ (all_21_14_27 = all_0_7_7) & vsubst(all_0_7_7, all_0_6_6, all_21_10_23) = all_21_8_21 & vabs(all_21_14_27, all_21_13_26, all_21_8_21) = all_0_0_0 & vabs(all_21_14_27, all_21_13_26, all_21_10_23) = all_0_1_1 & ~ visFreeVar(all_21_14_27, all_0_6_6)) | (all_21_7_20 = all_0_0_0 & all_21_10_23 = all_0_1_1 & all_21_12_25 = all_0_6_6 & all_21_13_26 = all_0_7_7 & vsubst(all_0_7_7, all_0_6_6, all_21_11_24) = all_21_8_21 & vsubst(all_0_7_7, all_0_6_6, all_21_14_27) = all_21_9_22 & vapp(all_21_9_22, all_21_8_21) = all_0_0_0 & vapp(all_21_14_27, all_21_11_24) = all_0_1_1)
% 46.14/13.92 |
% 46.14/13.92 +-Applying beta-rule and splitting (97), into two cases.
% 46.14/13.92 |-Branch one:
% 46.14/13.92 | (98) (all_21_0_13 = all_0_0_0 & all_21_4_17 = all_21_10_23 & all_21_8_21 = all_0_1_1 & all_21_13_26 = all_0_6_6 & all_21_14_27 = all_0_7_7 & ~ (all_21_11_24 = all_0_7_7) & vsubst(all_21_11_24, all_21_3_16, all_21_9_22) = all_21_2_15 & vsubst(all_0_7_7, all_0_6_6, all_21_1_14) = all_0_0_0 & vgensym(all_21_5_18) = all_21_10_23 & vapp(all_21_7_20, all_21_6_19) = all_21_5_18 & vapp(all_0_6_6, all_21_9_22) = all_21_7_20 & vabs(all_21_10_23, all_21_12_25, all_21_2_15) = all_21_1_14 & vabs(all_21_11_24, all_21_12_25, all_21_9_22) = all_0_1_1 & vvar(all_21_10_23) = all_21_3_16 & vvar(all_0_7_7) = all_21_6_19 & visFreeVar(all_21_11_24, all_0_6_6)) | (all_21_7_20 = all_0_0_0 & all_21_9_22 = all_0_1_1 & all_21_11_24 = all_0_6_6 & all_21_12_25 = all_0_7_7 & ~ (all_21_14_27 = all_0_7_7) & vsubst(all_0_7_7, all_0_6_6, all_21_10_23) = all_21_8_21 & vabs(all_21_14_27, all_21_13_26, all_21_8_21) = all_0_0_0 & vabs(all_21_14_27, all_21_13_26, all_21_10_23) = all_0_1_1 & ~ visFreeVar(all_21_14_27, all_0_6_6))
% 46.46/13.92 |
% 46.46/13.92 +-Applying beta-rule and splitting (98), into two cases.
% 46.46/13.92 |-Branch one:
% 46.46/13.92 | (99) all_21_0_13 = all_0_0_0 & all_21_4_17 = all_21_10_23 & all_21_8_21 = all_0_1_1 & all_21_13_26 = all_0_6_6 & all_21_14_27 = all_0_7_7 & ~ (all_21_11_24 = all_0_7_7) & vsubst(all_21_11_24, all_21_3_16, all_21_9_22) = all_21_2_15 & vsubst(all_0_7_7, all_0_6_6, all_21_1_14) = all_0_0_0 & vgensym(all_21_5_18) = all_21_10_23 & vapp(all_21_7_20, all_21_6_19) = all_21_5_18 & vapp(all_0_6_6, all_21_9_22) = all_21_7_20 & vabs(all_21_10_23, all_21_12_25, all_21_2_15) = all_21_1_14 & vabs(all_21_11_24, all_21_12_25, all_21_9_22) = all_0_1_1 & vvar(all_21_10_23) = all_21_3_16 & vvar(all_0_7_7) = all_21_6_19 & visFreeVar(all_21_11_24, all_0_6_6)
% 46.46/13.92 |
% 46.46/13.92 | Applying alpha-rule on (99) yields:
% 46.46/13.92 | (100) ~ (all_21_11_24 = all_0_7_7)
% 46.46/13.92 | (101) all_21_4_17 = all_21_10_23
% 46.46/13.92 | (102) vvar(all_0_7_7) = all_21_6_19
% 46.46/13.92 | (103) vabs(all_21_11_24, all_21_12_25, all_21_9_22) = all_0_1_1
% 46.46/13.92 | (104) vapp(all_0_6_6, all_21_9_22) = all_21_7_20
% 46.46/13.92 | (105) vgensym(all_21_5_18) = all_21_10_23
% 46.46/13.92 | (106) vsubst(all_0_7_7, all_0_6_6, all_21_1_14) = all_0_0_0
% 46.46/13.92 | (107) vsubst(all_21_11_24, all_21_3_16, all_21_9_22) = all_21_2_15
% 46.46/13.92 | (108) all_21_14_27 = all_0_7_7
% 46.46/13.92 | (109) vapp(all_21_7_20, all_21_6_19) = all_21_5_18
% 46.46/13.92 | (110) all_21_13_26 = all_0_6_6
% 46.46/13.92 | (111) all_21_8_21 = all_0_1_1
% 46.46/13.92 | (112) all_21_0_13 = all_0_0_0
% 46.46/13.92 | (113) visFreeVar(all_21_11_24, all_0_6_6)
% 46.46/13.92 | (114) vabs(all_21_10_23, all_21_12_25, all_21_2_15) = all_21_1_14
% 46.46/13.92 | (115) vvar(all_21_10_23) = all_21_3_16
% 46.46/13.92 |
% 46.46/13.92 | Instantiating formula (84) with all_0_1_1, all_21_9_22, all_21_12_25, all_21_11_24, veabs, all_0_4_4, all_0_5_5 and discharging atoms vabs(all_21_11_24, all_21_12_25, all_21_9_22) = all_0_1_1, vabs(all_0_5_5, all_0_4_4, veabs) = all_0_1_1, yields:
% 46.46/13.92 | (116) all_21_9_22 = veabs
% 46.46/13.92 |
% 46.46/13.92 | Instantiating formula (2) with all_0_1_1, all_21_9_22, all_21_12_25, all_21_11_24, veabs, all_0_4_4, all_0_5_5 and discharging atoms vabs(all_21_11_24, all_21_12_25, all_21_9_22) = all_0_1_1, vabs(all_0_5_5, all_0_4_4, veabs) = all_0_1_1, yields:
% 46.46/13.92 | (117) all_21_12_25 = all_0_4_4
% 46.46/13.92 |
% 46.46/13.92 | Instantiating formula (58) with all_0_1_1, all_21_9_22, all_21_12_25, all_21_11_24, veabs, all_0_4_4, all_0_5_5 and discharging atoms vabs(all_21_11_24, all_21_12_25, all_21_9_22) = all_0_1_1, vabs(all_0_5_5, all_0_4_4, veabs) = all_0_1_1, yields:
% 46.46/13.92 | (118) all_21_11_24 = all_0_5_5
% 46.46/13.92 |
% 46.46/13.92 | From (118)(116) and (107) follows:
% 46.46/13.92 | (119) vsubst(all_0_5_5, all_21_3_16, veabs) = all_21_2_15
% 46.46/13.92 |
% 46.46/13.92 | From (116) and (104) follows:
% 46.46/13.92 | (120) vapp(all_0_6_6, veabs) = all_21_7_20
% 46.46/13.92 |
% 46.46/13.92 | From (117) and (114) follows:
% 46.46/13.92 | (121) vabs(all_21_10_23, all_0_4_4, all_21_2_15) = all_21_1_14
% 46.46/13.92 |
% 46.46/13.92 | From (118)(117)(116) and (103) follows:
% 46.46/13.92 | (59) vabs(all_0_5_5, all_0_4_4, veabs) = all_0_1_1
% 46.46/13.92 |
% 46.46/13.92 | Instantiating formula (12) with all_0_0_0, all_21_1_14, all_0_6_6, all_0_7_7 and discharging atoms vsubst(all_0_7_7, all_0_6_6, all_21_1_14) = all_0_0_0, yields:
% 46.46/13.92 | (239) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = all_0_0_0 & v10 = v4 & v6 = all_21_1_14 & v1 = all_0_6_6 & v0 = all_0_7_7 & ~ (v3 = all_0_7_7) & vsubst(v3, v11, v5) = v12 & vsubst(all_0_7_7, all_0_6_6, v13) = all_0_0_0 & vgensym(v9) = v4 & vapp(v7, v8) = v9 & vapp(all_0_6_6, v5) = v7 & vabs(v4, v2, v12) = v13 & vabs(v3, v2, v5) = all_21_1_14 & vvar(v4) = v11 & vvar(all_0_7_7) = v8 & visFreeVar(v3, all_0_6_6)) | (v7 = all_0_0_0 & v5 = all_21_1_14 & v3 = all_0_6_6 & v2 = all_0_7_7 & ~ (v0 = all_0_7_7) & vsubst(all_0_7_7, all_0_6_6, v4) = v6 & vabs(v0, v1, v6) = all_0_0_0 & vabs(v0, v1, v4) = all_21_1_14 & ~ visFreeVar(v0, all_0_6_6)) | (v7 = all_0_0_0 & v4 = all_21_1_14 & v2 = all_0_6_6 & v1 = all_0_7_7 & vsubst(all_0_7_7, all_0_6_6, v3) = v6 & vsubst(all_0_7_7, all_0_6_6, v0) = v5 & vapp(v5, v6) = all_0_0_0 & vapp(v0, v3) = all_21_1_14) | (v5 = all_0_0_0 & v2 = all_0_7_7 & v1 = all_0_7_7 & v0 = all_0_6_6 & all_21_1_14 = all_0_0_0 & vabs(all_0_7_7, v3, v4) = all_0_0_0) | (v3 = all_21_1_14 & v2 = all_0_6_6 & v1 = all_0_7_7 & v0 = all_0_7_7 & all_0_0_0 = all_0_6_6 & vvar(all_0_7_7) = all_21_1_14) | (v3 = all_0_0_0 & v1 = all_0_7_7 & v0 = all_0_6_6 & all_21_1_14 = all_0_0_0 & ~ (v2 = all_0_7_7) & vvar(v2) = all_0_0_0))
% 46.46/13.92 |
% 46.46/13.92 | Instantiating formula (40) with all_21_1_14, all_21_2_15, all_0_4_4, all_21_10_23 and discharging atoms vabs(all_21_10_23, all_0_4_4, all_21_2_15) = all_21_1_14, yields:
% 46.46/13.92 | (240) visValue(all_21_1_14)
% 46.46/13.92 |
% 46.46/13.92 | Instantiating formula (88) with all_21_1_14, all_21_2_15, all_21_3_16, veabs, all_21_10_23, all_0_5_5, all_0_4_4 and discharging atoms vsubst(all_0_5_5, all_21_3_16, veabs) = all_21_2_15, vabs(all_21_10_23, all_0_4_4, all_21_2_15) = all_21_1_14, vvar(all_21_10_23) = all_21_3_16, yields:
% 46.46/13.92 | (123) visFreeVar(all_21_10_23, veabs) | ? [v0] : (vabs(all_0_5_5, all_0_4_4, veabs) = v0 & valphaEquivalent(v0, all_21_1_14))
% 46.46/13.92 |
% 46.46/13.92 | Instantiating formula (79) with all_21_5_18, all_21_6_19, all_21_7_20, all_0_7_7, veabs, all_0_6_6 and discharging atoms vapp(all_21_7_20, all_21_6_19) = all_21_5_18, vapp(all_0_6_6, veabs) = all_21_7_20, vvar(all_0_7_7) = all_21_6_19, yields:
% 46.46/13.92 | (124) ? [v0] : ( ~ (v0 = all_0_7_7) & vgensym(all_21_5_18) = v0)
% 46.46/13.92 |
% 46.46/13.92 | Instantiating (239) with all_71_0_61, all_71_1_62, all_71_2_63, all_71_3_64, all_71_4_65, all_71_5_66, all_71_6_67, all_71_7_68, all_71_8_69, all_71_9_70, all_71_10_71, all_71_11_72, all_71_12_73, all_71_13_74, all_71_14_75 yields:
% 46.46/13.92 | (243) (all_71_0_61 = all_0_0_0 & all_71_4_65 = all_71_10_71 & all_71_8_69 = all_21_1_14 & all_71_13_74 = all_0_6_6 & all_71_14_75 = all_0_7_7 & ~ (all_71_11_72 = all_0_7_7) & vsubst(all_71_11_72, all_71_3_64, all_71_9_70) = all_71_2_63 & vsubst(all_0_7_7, all_0_6_6, all_71_1_62) = all_0_0_0 & vgensym(all_71_5_66) = all_71_10_71 & vapp(all_71_7_68, all_71_6_67) = all_71_5_66 & vapp(all_0_6_6, all_71_9_70) = all_71_7_68 & vabs(all_71_10_71, all_71_12_73, all_71_2_63) = all_71_1_62 & vabs(all_71_11_72, all_71_12_73, all_71_9_70) = all_21_1_14 & vvar(all_71_10_71) = all_71_3_64 & vvar(all_0_7_7) = all_71_6_67 & visFreeVar(all_71_11_72, all_0_6_6)) | (all_71_7_68 = all_0_0_0 & all_71_9_70 = all_21_1_14 & all_71_11_72 = all_0_6_6 & all_71_12_73 = all_0_7_7 & ~ (all_71_14_75 = all_0_7_7) & vsubst(all_0_7_7, all_0_6_6, all_71_10_71) = all_71_8_69 & vabs(all_71_14_75, all_71_13_74, all_71_8_69) = all_0_0_0 & vabs(all_71_14_75, all_71_13_74, all_71_10_71) = all_21_1_14 & ~ visFreeVar(all_71_14_75, all_0_6_6)) | (all_71_7_68 = all_0_0_0 & all_71_10_71 = all_21_1_14 & all_71_12_73 = all_0_6_6 & all_71_13_74 = all_0_7_7 & vsubst(all_0_7_7, all_0_6_6, all_71_11_72) = all_71_8_69 & vsubst(all_0_7_7, all_0_6_6, all_71_14_75) = all_71_9_70 & vapp(all_71_9_70, all_71_8_69) = all_0_0_0 & vapp(all_71_14_75, all_71_11_72) = all_21_1_14) | (all_71_9_70 = all_0_0_0 & all_71_12_73 = all_0_7_7 & all_71_13_74 = all_0_7_7 & all_71_14_75 = all_0_6_6 & all_21_1_14 = all_0_0_0 & vabs(all_0_7_7, all_71_11_72, all_71_10_71) = all_0_0_0) | (all_71_11_72 = all_21_1_14 & all_71_12_73 = all_0_6_6 & all_71_13_74 = all_0_7_7 & all_71_14_75 = all_0_7_7 & all_0_0_0 = all_0_6_6 & vvar(all_0_7_7) = all_21_1_14) | (all_71_11_72 = all_0_0_0 & all_71_13_74 = all_0_7_7 & all_71_14_75 = all_0_6_6 & all_21_1_14 = all_0_0_0 & ~ (all_71_12_73 = all_0_7_7) & vvar(all_71_12_73) = all_0_0_0)
% 46.46/13.92 |
% 46.46/13.92 | Instantiating (124) with all_72_0_76 yields:
% 46.46/13.92 | (244) ~ (all_72_0_76 = all_0_7_7) & vgensym(all_21_5_18) = all_72_0_76
% 46.46/13.92 |
% 46.46/13.92 | Applying alpha-rule on (244) yields:
% 46.46/13.92 | (245) ~ (all_72_0_76 = all_0_7_7)
% 46.46/13.92 | (246) vgensym(all_21_5_18) = all_72_0_76
% 46.46/13.92 |
% 46.46/13.92 | Instantiating formula (21) with all_21_5_18, all_72_0_76, all_21_10_23 and discharging atoms vgensym(all_21_5_18) = all_72_0_76, vgensym(all_21_5_18) = all_21_10_23, yields:
% 46.46/13.92 | (247) all_72_0_76 = all_21_10_23
% 46.46/13.92 |
% 46.46/13.92 | Equations (247) can reduce 245 to:
% 46.46/13.92 | (129) ~ (all_21_10_23 = all_0_7_7)
% 46.46/13.92 |
% 46.46/13.92 | From (247) and (246) follows:
% 46.46/13.92 | (105) vgensym(all_21_5_18) = all_21_10_23
% 46.46/13.92 |
% 46.46/13.92 | Instantiating formula (16) with veabs, all_0_6_6, all_21_7_20, all_21_10_23 and discharging atoms vapp(all_0_6_6, veabs) = all_21_7_20, yields:
% 46.46/13.92 | (132) ~ visFreeVar(all_21_10_23, all_0_6_6) | visFreeVar(all_21_10_23, all_21_7_20)
% 46.46/13.92 |
% 46.46/13.92 +-Applying beta-rule and splitting (123), into two cases.
% 46.46/13.92 |-Branch one:
% 46.46/13.92 | (134) visFreeVar(all_21_10_23, veabs)
% 46.46/13.92 |
% 46.46/13.92 | Instantiating formula (3) with all_21_5_18, all_21_6_19, all_21_7_20, veabs, all_21_10_23, all_0_7_7, all_0_6_6 and discharging atoms vapp(all_21_7_20, all_21_6_19) = all_21_5_18, vapp(all_0_6_6, veabs) = all_21_7_20, vvar(all_0_7_7) = all_21_6_19, visFreeVar(all_21_10_23, veabs), yields:
% 46.46/13.92 | (156) ? [v0] : ( ~ (v0 = all_21_10_23) & vgensym(all_21_5_18) = v0)
% 46.46/13.92 |
% 46.46/13.92 | Instantiating (156) with all_386_0_154 yields:
% 46.46/13.92 | (253) ~ (all_386_0_154 = all_21_10_23) & vgensym(all_21_5_18) = all_386_0_154
% 46.46/13.92 |
% 46.46/13.92 | Applying alpha-rule on (253) yields:
% 46.46/13.92 | (254) ~ (all_386_0_154 = all_21_10_23)
% 46.46/13.92 | (255) vgensym(all_21_5_18) = all_386_0_154
% 46.46/13.92 |
% 46.46/13.92 | Instantiating formula (21) with all_21_5_18, all_386_0_154, all_21_10_23 and discharging atoms vgensym(all_21_5_18) = all_386_0_154, vgensym(all_21_5_18) = all_21_10_23, yields:
% 46.46/13.92 | (256) all_386_0_154 = all_21_10_23
% 46.46/13.92 |
% 46.46/13.92 | Equations (256) can reduce 254 to:
% 46.46/13.92 | (154) $false
% 46.46/13.92 |
% 46.46/13.92 |-The branch is then unsatisfiable
% 46.46/13.92 |-Branch two:
% 46.46/13.92 | (133) ~ visFreeVar(all_21_10_23, veabs)
% 46.46/13.92 | (137) ? [v0] : (vabs(all_0_5_5, all_0_4_4, veabs) = v0 & valphaEquivalent(v0, all_21_1_14))
% 46.46/13.92 |
% 46.46/13.92 | Instantiating (137) with all_273_0_170 yields:
% 46.46/13.92 | (260) vabs(all_0_5_5, all_0_4_4, veabs) = all_273_0_170 & valphaEquivalent(all_273_0_170, all_21_1_14)
% 46.46/13.92 |
% 46.46/13.92 | Applying alpha-rule on (260) yields:
% 46.46/13.92 | (261) vabs(all_0_5_5, all_0_4_4, veabs) = all_273_0_170
% 46.46/13.92 | (262) valphaEquivalent(all_273_0_170, all_21_1_14)
% 46.46/13.92 |
% 46.46/13.92 | Instantiating formula (67) with all_273_0_170, all_0_1_1, veabs, all_0_4_4, all_0_5_5 and discharging atoms vabs(all_0_5_5, all_0_4_4, veabs) = all_273_0_170, vabs(all_0_5_5, all_0_4_4, veabs) = all_0_1_1, yields:
% 46.46/13.92 | (263) all_273_0_170 = all_0_1_1
% 46.46/13.92 |
% 46.46/13.92 | From (263) and (262) follows:
% 46.46/13.92 | (142) valphaEquivalent(all_0_1_1, all_21_1_14)
% 46.46/13.92 |
% 46.46/13.92 +-Applying beta-rule and splitting (243), into two cases.
% 46.46/13.92 |-Branch one:
% 46.46/13.92 | (265) (all_71_0_61 = all_0_0_0 & all_71_4_65 = all_71_10_71 & all_71_8_69 = all_21_1_14 & all_71_13_74 = all_0_6_6 & all_71_14_75 = all_0_7_7 & ~ (all_71_11_72 = all_0_7_7) & vsubst(all_71_11_72, all_71_3_64, all_71_9_70) = all_71_2_63 & vsubst(all_0_7_7, all_0_6_6, all_71_1_62) = all_0_0_0 & vgensym(all_71_5_66) = all_71_10_71 & vapp(all_71_7_68, all_71_6_67) = all_71_5_66 & vapp(all_0_6_6, all_71_9_70) = all_71_7_68 & vabs(all_71_10_71, all_71_12_73, all_71_2_63) = all_71_1_62 & vabs(all_71_11_72, all_71_12_73, all_71_9_70) = all_21_1_14 & vvar(all_71_10_71) = all_71_3_64 & vvar(all_0_7_7) = all_71_6_67 & visFreeVar(all_71_11_72, all_0_6_6)) | (all_71_7_68 = all_0_0_0 & all_71_9_70 = all_21_1_14 & all_71_11_72 = all_0_6_6 & all_71_12_73 = all_0_7_7 & ~ (all_71_14_75 = all_0_7_7) & vsubst(all_0_7_7, all_0_6_6, all_71_10_71) = all_71_8_69 & vabs(all_71_14_75, all_71_13_74, all_71_8_69) = all_0_0_0 & vabs(all_71_14_75, all_71_13_74, all_71_10_71) = all_21_1_14 & ~ visFreeVar(all_71_14_75, all_0_6_6)) | (all_71_7_68 = all_0_0_0 & all_71_10_71 = all_21_1_14 & all_71_12_73 = all_0_6_6 & all_71_13_74 = all_0_7_7 & vsubst(all_0_7_7, all_0_6_6, all_71_11_72) = all_71_8_69 & vsubst(all_0_7_7, all_0_6_6, all_71_14_75) = all_71_9_70 & vapp(all_71_9_70, all_71_8_69) = all_0_0_0 & vapp(all_71_14_75, all_71_11_72) = all_21_1_14) | (all_71_9_70 = all_0_0_0 & all_71_12_73 = all_0_7_7 & all_71_13_74 = all_0_7_7 & all_71_14_75 = all_0_6_6 & all_21_1_14 = all_0_0_0 & vabs(all_0_7_7, all_71_11_72, all_71_10_71) = all_0_0_0) | (all_71_11_72 = all_21_1_14 & all_71_12_73 = all_0_6_6 & all_71_13_74 = all_0_7_7 & all_71_14_75 = all_0_7_7 & all_0_0_0 = all_0_6_6 & vvar(all_0_7_7) = all_21_1_14)
% 46.46/13.93 |
% 46.46/13.93 +-Applying beta-rule and splitting (265), into two cases.
% 46.46/13.93 |-Branch one:
% 46.46/13.93 | (266) (all_71_0_61 = all_0_0_0 & all_71_4_65 = all_71_10_71 & all_71_8_69 = all_21_1_14 & all_71_13_74 = all_0_6_6 & all_71_14_75 = all_0_7_7 & ~ (all_71_11_72 = all_0_7_7) & vsubst(all_71_11_72, all_71_3_64, all_71_9_70) = all_71_2_63 & vsubst(all_0_7_7, all_0_6_6, all_71_1_62) = all_0_0_0 & vgensym(all_71_5_66) = all_71_10_71 & vapp(all_71_7_68, all_71_6_67) = all_71_5_66 & vapp(all_0_6_6, all_71_9_70) = all_71_7_68 & vabs(all_71_10_71, all_71_12_73, all_71_2_63) = all_71_1_62 & vabs(all_71_11_72, all_71_12_73, all_71_9_70) = all_21_1_14 & vvar(all_71_10_71) = all_71_3_64 & vvar(all_0_7_7) = all_71_6_67 & visFreeVar(all_71_11_72, all_0_6_6)) | (all_71_7_68 = all_0_0_0 & all_71_9_70 = all_21_1_14 & all_71_11_72 = all_0_6_6 & all_71_12_73 = all_0_7_7 & ~ (all_71_14_75 = all_0_7_7) & vsubst(all_0_7_7, all_0_6_6, all_71_10_71) = all_71_8_69 & vabs(all_71_14_75, all_71_13_74, all_71_8_69) = all_0_0_0 & vabs(all_71_14_75, all_71_13_74, all_71_10_71) = all_21_1_14 & ~ visFreeVar(all_71_14_75, all_0_6_6)) | (all_71_7_68 = all_0_0_0 & all_71_10_71 = all_21_1_14 & all_71_12_73 = all_0_6_6 & all_71_13_74 = all_0_7_7 & vsubst(all_0_7_7, all_0_6_6, all_71_11_72) = all_71_8_69 & vsubst(all_0_7_7, all_0_6_6, all_71_14_75) = all_71_9_70 & vapp(all_71_9_70, all_71_8_69) = all_0_0_0 & vapp(all_71_14_75, all_71_11_72) = all_21_1_14) | (all_71_9_70 = all_0_0_0 & all_71_12_73 = all_0_7_7 & all_71_13_74 = all_0_7_7 & all_71_14_75 = all_0_6_6 & all_21_1_14 = all_0_0_0 & vabs(all_0_7_7, all_71_11_72, all_71_10_71) = all_0_0_0)
% 46.46/13.93 |
% 46.46/13.93 +-Applying beta-rule and splitting (266), into two cases.
% 46.46/13.93 |-Branch one:
% 46.46/13.93 | (267) (all_71_0_61 = all_0_0_0 & all_71_4_65 = all_71_10_71 & all_71_8_69 = all_21_1_14 & all_71_13_74 = all_0_6_6 & all_71_14_75 = all_0_7_7 & ~ (all_71_11_72 = all_0_7_7) & vsubst(all_71_11_72, all_71_3_64, all_71_9_70) = all_71_2_63 & vsubst(all_0_7_7, all_0_6_6, all_71_1_62) = all_0_0_0 & vgensym(all_71_5_66) = all_71_10_71 & vapp(all_71_7_68, all_71_6_67) = all_71_5_66 & vapp(all_0_6_6, all_71_9_70) = all_71_7_68 & vabs(all_71_10_71, all_71_12_73, all_71_2_63) = all_71_1_62 & vabs(all_71_11_72, all_71_12_73, all_71_9_70) = all_21_1_14 & vvar(all_71_10_71) = all_71_3_64 & vvar(all_0_7_7) = all_71_6_67 & visFreeVar(all_71_11_72, all_0_6_6)) | (all_71_7_68 = all_0_0_0 & all_71_9_70 = all_21_1_14 & all_71_11_72 = all_0_6_6 & all_71_12_73 = all_0_7_7 & ~ (all_71_14_75 = all_0_7_7) & vsubst(all_0_7_7, all_0_6_6, all_71_10_71) = all_71_8_69 & vabs(all_71_14_75, all_71_13_74, all_71_8_69) = all_0_0_0 & vabs(all_71_14_75, all_71_13_74, all_71_10_71) = all_21_1_14 & ~ visFreeVar(all_71_14_75, all_0_6_6)) | (all_71_7_68 = all_0_0_0 & all_71_10_71 = all_21_1_14 & all_71_12_73 = all_0_6_6 & all_71_13_74 = all_0_7_7 & vsubst(all_0_7_7, all_0_6_6, all_71_11_72) = all_71_8_69 & vsubst(all_0_7_7, all_0_6_6, all_71_14_75) = all_71_9_70 & vapp(all_71_9_70, all_71_8_69) = all_0_0_0 & vapp(all_71_14_75, all_71_11_72) = all_21_1_14)
% 46.46/13.93 |
% 46.46/13.93 +-Applying beta-rule and splitting (267), into two cases.
% 46.46/13.93 |-Branch one:
% 46.46/13.93 | (268) (all_71_0_61 = all_0_0_0 & all_71_4_65 = all_71_10_71 & all_71_8_69 = all_21_1_14 & all_71_13_74 = all_0_6_6 & all_71_14_75 = all_0_7_7 & ~ (all_71_11_72 = all_0_7_7) & vsubst(all_71_11_72, all_71_3_64, all_71_9_70) = all_71_2_63 & vsubst(all_0_7_7, all_0_6_6, all_71_1_62) = all_0_0_0 & vgensym(all_71_5_66) = all_71_10_71 & vapp(all_71_7_68, all_71_6_67) = all_71_5_66 & vapp(all_0_6_6, all_71_9_70) = all_71_7_68 & vabs(all_71_10_71, all_71_12_73, all_71_2_63) = all_71_1_62 & vabs(all_71_11_72, all_71_12_73, all_71_9_70) = all_21_1_14 & vvar(all_71_10_71) = all_71_3_64 & vvar(all_0_7_7) = all_71_6_67 & visFreeVar(all_71_11_72, all_0_6_6)) | (all_71_7_68 = all_0_0_0 & all_71_9_70 = all_21_1_14 & all_71_11_72 = all_0_6_6 & all_71_12_73 = all_0_7_7 & ~ (all_71_14_75 = all_0_7_7) & vsubst(all_0_7_7, all_0_6_6, all_71_10_71) = all_71_8_69 & vabs(all_71_14_75, all_71_13_74, all_71_8_69) = all_0_0_0 & vabs(all_71_14_75, all_71_13_74, all_71_10_71) = all_21_1_14 & ~ visFreeVar(all_71_14_75, all_0_6_6))
% 46.46/13.93 |
% 46.46/13.93 +-Applying beta-rule and splitting (268), into two cases.
% 46.46/13.93 |-Branch one:
% 46.46/13.93 | (269) all_71_0_61 = all_0_0_0 & all_71_4_65 = all_71_10_71 & all_71_8_69 = all_21_1_14 & all_71_13_74 = all_0_6_6 & all_71_14_75 = all_0_7_7 & ~ (all_71_11_72 = all_0_7_7) & vsubst(all_71_11_72, all_71_3_64, all_71_9_70) = all_71_2_63 & vsubst(all_0_7_7, all_0_6_6, all_71_1_62) = all_0_0_0 & vgensym(all_71_5_66) = all_71_10_71 & vapp(all_71_7_68, all_71_6_67) = all_71_5_66 & vapp(all_0_6_6, all_71_9_70) = all_71_7_68 & vabs(all_71_10_71, all_71_12_73, all_71_2_63) = all_71_1_62 & vabs(all_71_11_72, all_71_12_73, all_71_9_70) = all_21_1_14 & vvar(all_71_10_71) = all_71_3_64 & vvar(all_0_7_7) = all_71_6_67 & visFreeVar(all_71_11_72, all_0_6_6)
% 46.46/13.93 |
% 46.46/13.93 | Applying alpha-rule on (269) yields:
% 46.46/13.93 | (270) vsubst(all_0_7_7, all_0_6_6, all_71_1_62) = all_0_0_0
% 46.46/13.93 | (271) vgensym(all_71_5_66) = all_71_10_71
% 46.46/13.93 | (272) vabs(all_71_11_72, all_71_12_73, all_71_9_70) = all_21_1_14
% 46.46/13.93 | (273) ~ (all_71_11_72 = all_0_7_7)
% 46.46/13.93 | (274) all_71_14_75 = all_0_7_7
% 46.46/13.93 | (275) all_71_4_65 = all_71_10_71
% 46.46/13.93 | (276) visFreeVar(all_71_11_72, all_0_6_6)
% 46.46/13.93 | (277) all_71_8_69 = all_21_1_14
% 46.46/13.93 | (278) vsubst(all_71_11_72, all_71_3_64, all_71_9_70) = all_71_2_63
% 46.46/13.93 | (279) vvar(all_0_7_7) = all_71_6_67
% 46.46/13.93 | (280) vvar(all_71_10_71) = all_71_3_64
% 46.46/13.93 | (281) all_71_0_61 = all_0_0_0
% 46.46/13.93 | (282) vapp(all_0_6_6, all_71_9_70) = all_71_7_68
% 46.46/13.93 | (283) all_71_13_74 = all_0_6_6
% 46.46/13.93 | (284) vabs(all_71_10_71, all_71_12_73, all_71_2_63) = all_71_1_62
% 46.46/13.93 | (285) vapp(all_71_7_68, all_71_6_67) = all_71_5_66
% 46.46/13.93 |
% 46.46/13.93 | Instantiating formula (58) with all_21_1_14, all_71_9_70, all_71_12_73, all_71_11_72, all_21_2_15, all_0_4_4, all_21_10_23 and discharging atoms vabs(all_71_11_72, all_71_12_73, all_71_9_70) = all_21_1_14, vabs(all_21_10_23, all_0_4_4, all_21_2_15) = all_21_1_14, yields:
% 46.46/13.93 | (286) all_71_11_72 = all_21_10_23
% 46.46/13.93 |
% 46.46/13.93 | From (286) and (276) follows:
% 46.46/13.93 | (145) visFreeVar(all_21_10_23, all_0_6_6)
% 46.46/13.93 |
% 46.46/13.93 +-Applying beta-rule and splitting (132), into two cases.
% 46.46/13.93 |-Branch one:
% 46.46/13.93 | (146) ~ visFreeVar(all_21_10_23, all_0_6_6)
% 46.46/13.93 |
% 46.46/13.93 | Using (145) and (146) yields:
% 46.46/13.93 | (135) $false
% 46.46/13.93 |
% 46.46/13.93 |-The branch is then unsatisfiable
% 46.46/13.93 |-Branch two:
% 46.46/13.93 | (145) visFreeVar(all_21_10_23, all_0_6_6)
% 46.46/13.93 | (149) visFreeVar(all_21_10_23, all_21_7_20)
% 46.46/13.93 |
% 46.46/13.93 | Instantiating formula (16) with all_21_6_19, all_21_7_20, all_21_5_18, all_21_10_23 and discharging atoms vapp(all_21_7_20, all_21_6_19) = all_21_5_18, visFreeVar(all_21_10_23, all_21_7_20), yields:
% 46.46/13.93 | (150) visFreeVar(all_21_10_23, all_21_5_18)
% 46.46/13.93 |
% 46.46/13.93 | Instantiating formula (28) with all_21_5_18, all_21_10_23 and discharging atoms vgensym(all_21_5_18) = all_21_10_23, visFreeVar(all_21_10_23, all_21_5_18), yields:
% 46.46/13.93 | (135) $false
% 46.46/13.93 |
% 46.46/13.93 |-The branch is then unsatisfiable
% 46.46/13.93 |-Branch two:
% 46.46/13.93 | (294) all_71_7_68 = all_0_0_0 & all_71_9_70 = all_21_1_14 & all_71_11_72 = all_0_6_6 & all_71_12_73 = all_0_7_7 & ~ (all_71_14_75 = all_0_7_7) & vsubst(all_0_7_7, all_0_6_6, all_71_10_71) = all_71_8_69 & vabs(all_71_14_75, all_71_13_74, all_71_8_69) = all_0_0_0 & vabs(all_71_14_75, all_71_13_74, all_71_10_71) = all_21_1_14 & ~ visFreeVar(all_71_14_75, all_0_6_6)
% 46.46/13.93 |
% 46.46/13.93 | Applying alpha-rule on (294) yields:
% 46.46/13.93 | (295) ~ visFreeVar(all_71_14_75, all_0_6_6)
% 46.46/13.93 | (296) all_71_9_70 = all_21_1_14
% 46.46/13.93 | (297) all_71_7_68 = all_0_0_0
% 46.46/13.93 | (298) all_71_11_72 = all_0_6_6
% 46.46/13.93 | (299) ~ (all_71_14_75 = all_0_7_7)
% 46.46/13.93 | (300) vabs(all_71_14_75, all_71_13_74, all_71_8_69) = all_0_0_0
% 46.46/13.93 | (301) all_71_12_73 = all_0_7_7
% 46.46/13.93 | (302) vabs(all_71_14_75, all_71_13_74, all_71_10_71) = all_21_1_14
% 46.46/13.93 | (303) vsubst(all_0_7_7, all_0_6_6, all_71_10_71) = all_71_8_69
% 46.46/13.93 |
% 46.46/13.93 | Instantiating formula (84) with all_21_1_14, all_71_10_71, all_71_13_74, all_71_14_75, all_21_2_15, all_0_4_4, all_21_10_23 and discharging atoms vabs(all_71_14_75, all_71_13_74, all_71_10_71) = all_21_1_14, vabs(all_21_10_23, all_0_4_4, all_21_2_15) = all_21_1_14, yields:
% 46.46/13.93 | (304) all_71_10_71 = all_21_2_15
% 46.46/13.93 |
% 46.46/13.93 | Instantiating formula (2) with all_21_1_14, all_71_10_71, all_71_13_74, all_71_14_75, all_21_2_15, all_0_4_4, all_21_10_23 and discharging atoms vabs(all_71_14_75, all_71_13_74, all_71_10_71) = all_21_1_14, vabs(all_21_10_23, all_0_4_4, all_21_2_15) = all_21_1_14, yields:
% 46.46/13.93 | (305) all_71_13_74 = all_0_4_4
% 46.46/13.93 |
% 46.46/13.93 | Instantiating formula (58) with all_21_1_14, all_71_10_71, all_71_13_74, all_71_14_75, all_21_2_15, all_0_4_4, all_21_10_23 and discharging atoms vabs(all_71_14_75, all_71_13_74, all_71_10_71) = all_21_1_14, vabs(all_21_10_23, all_0_4_4, all_21_2_15) = all_21_1_14, yields:
% 46.46/13.93 | (306) all_71_14_75 = all_21_10_23
% 46.46/13.93 |
% 46.46/13.93 | Equations (306) can reduce 299 to:
% 46.46/13.93 | (129) ~ (all_21_10_23 = all_0_7_7)
% 46.46/13.93 |
% 46.46/13.93 | From (306)(305)(304) and (302) follows:
% 46.46/13.93 | (121) vabs(all_21_10_23, all_0_4_4, all_21_2_15) = all_21_1_14
% 46.46/13.93 |
% 46.46/13.93 | From (306) and (295) follows:
% 46.46/13.93 | (146) ~ visFreeVar(all_21_10_23, all_0_6_6)
% 46.46/13.93 |
% 46.46/13.93 | Instantiating formula (49) with all_0_3_3, all_21_1_14, all_0_2_2, all_0_1_1 and discharging atoms valphaEquivalent(all_0_1_1, all_21_1_14), vtcheck(all_0_2_2, all_0_1_1, all_0_3_3), yields:
% 46.46/13.93 | (143) vtcheck(all_0_2_2, all_21_1_14, all_0_3_3)
% 46.46/13.93 |
% 46.46/13.93 | Instantiating formula (74) with all_0_0_0, all_21_1_14, all_0_2_2, all_0_3_3, all_21_2_15, all_0_4_4, all_21_10_23, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms vsubst(all_0_7_7, all_0_6_6, all_21_1_14) = all_0_0_0, vbind(all_0_7_7, all_0_9_9, all_0_8_8) = all_0_2_2, vabs(all_21_10_23, all_0_4_4, all_21_2_15) = all_21_1_14, vtcheck(all_0_2_2, all_21_1_14, all_0_3_3), vtcheck(all_0_8_8, all_0_6_6, all_0_9_9), ~ vtcheck(all_0_8_8, all_0_0_0, all_0_3_3), ~ visFreeVar(all_21_10_23, all_0_6_6), yields:
% 46.46/13.93 | (153) all_21_10_23 = all_0_7_7
% 46.46/13.93 |
% 46.46/13.93 | Equations (153) can reduce 129 to:
% 46.46/13.93 | (154) $false
% 46.46/13.93 |
% 46.46/13.93 |-The branch is then unsatisfiable
% 46.46/13.93 |-Branch two:
% 46.46/13.93 | (313) all_71_7_68 = all_0_0_0 & all_71_10_71 = all_21_1_14 & all_71_12_73 = all_0_6_6 & all_71_13_74 = all_0_7_7 & vsubst(all_0_7_7, all_0_6_6, all_71_11_72) = all_71_8_69 & vsubst(all_0_7_7, all_0_6_6, all_71_14_75) = all_71_9_70 & vapp(all_71_9_70, all_71_8_69) = all_0_0_0 & vapp(all_71_14_75, all_71_11_72) = all_21_1_14
% 46.46/13.93 |
% 46.46/13.93 | Applying alpha-rule on (313) yields:
% 46.46/13.93 | (314) vapp(all_71_9_70, all_71_8_69) = all_0_0_0
% 46.46/13.93 | (297) all_71_7_68 = all_0_0_0
% 46.46/13.93 | (316) all_71_13_74 = all_0_7_7
% 46.46/13.93 | (317) all_71_10_71 = all_21_1_14
% 46.46/13.93 | (318) all_71_12_73 = all_0_6_6
% 46.46/13.93 | (319) vsubst(all_0_7_7, all_0_6_6, all_71_11_72) = all_71_8_69
% 46.46/13.93 | (320) vapp(all_71_14_75, all_71_11_72) = all_21_1_14
% 46.46/13.93 | (321) vsubst(all_0_7_7, all_0_6_6, all_71_14_75) = all_71_9_70
% 46.46/13.93 |
% 46.46/13.93 | Instantiating formula (78) with all_21_1_14, all_71_11_72, all_71_14_75 and discharging atoms vapp(all_71_14_75, all_71_11_72) = all_21_1_14, visValue(all_21_1_14), yields:
% 46.46/13.93 | (135) $false
% 46.46/13.93 |
% 46.46/13.93 |-The branch is then unsatisfiable
% 46.46/13.93 |-Branch two:
% 46.46/13.93 | (323) all_71_9_70 = all_0_0_0 & all_71_12_73 = all_0_7_7 & all_71_13_74 = all_0_7_7 & all_71_14_75 = all_0_6_6 & all_21_1_14 = all_0_0_0 & vabs(all_0_7_7, all_71_11_72, all_71_10_71) = all_0_0_0
% 46.46/13.93 |
% 46.46/13.93 | Applying alpha-rule on (323) yields:
% 46.46/13.93 | (324) all_71_9_70 = all_0_0_0
% 46.46/13.93 | (325) vabs(all_0_7_7, all_71_11_72, all_71_10_71) = all_0_0_0
% 46.46/13.93 | (326) all_71_14_75 = all_0_6_6
% 46.46/13.93 | (316) all_71_13_74 = all_0_7_7
% 46.46/13.93 | (301) all_71_12_73 = all_0_7_7
% 46.46/13.93 | (329) all_21_1_14 = all_0_0_0
% 46.46/13.93 |
% 46.46/13.93 | From (329) and (121) follows:
% 46.46/13.93 | (330) vabs(all_21_10_23, all_0_4_4, all_21_2_15) = all_0_0_0
% 46.46/13.93 |
% 46.46/13.93 | Instantiating formula (58) with all_0_0_0, all_71_10_71, all_71_11_72, all_0_7_7, all_21_2_15, all_0_4_4, all_21_10_23 and discharging atoms vabs(all_21_10_23, all_0_4_4, all_21_2_15) = all_0_0_0, vabs(all_0_7_7, all_71_11_72, all_71_10_71) = all_0_0_0, yields:
% 46.46/13.93 | (153) all_21_10_23 = all_0_7_7
% 46.46/13.93 |
% 46.46/13.93 | Equations (153) can reduce 129 to:
% 46.46/13.93 | (154) $false
% 46.46/13.93 |
% 46.46/13.93 |-The branch is then unsatisfiable
% 46.46/13.93 |-Branch two:
% 46.46/13.93 | (333) all_71_11_72 = all_21_1_14 & all_71_12_73 = all_0_6_6 & all_71_13_74 = all_0_7_7 & all_71_14_75 = all_0_7_7 & all_0_0_0 = all_0_6_6 & vvar(all_0_7_7) = all_21_1_14
% 46.46/13.94 |
% 46.46/13.94 | Applying alpha-rule on (333) yields:
% 46.46/13.94 | (274) all_71_14_75 = all_0_7_7
% 46.46/13.94 | (335) all_71_11_72 = all_21_1_14
% 46.46/13.94 | (316) all_71_13_74 = all_0_7_7
% 46.46/13.94 | (318) all_71_12_73 = all_0_6_6
% 46.46/13.94 | (197) all_0_0_0 = all_0_6_6
% 46.46/13.94 | (339) vvar(all_0_7_7) = all_21_1_14
% 46.46/13.94 |
% 46.46/13.94 | Instantiating formula (30) with all_21_1_14, all_0_7_7 and discharging atoms vvar(all_0_7_7) = all_21_1_14, visValue(all_21_1_14), yields:
% 46.46/13.94 | (135) $false
% 46.46/13.94 |
% 46.46/13.94 |-The branch is then unsatisfiable
% 46.46/13.94 |-Branch two:
% 46.46/13.94 | (341) all_71_11_72 = all_0_0_0 & all_71_13_74 = all_0_7_7 & all_71_14_75 = all_0_6_6 & all_21_1_14 = all_0_0_0 & ~ (all_71_12_73 = all_0_7_7) & vvar(all_71_12_73) = all_0_0_0
% 46.46/13.94 |
% 46.46/13.94 | Applying alpha-rule on (341) yields:
% 46.46/13.94 | (326) all_71_14_75 = all_0_6_6
% 46.46/13.94 | (343) all_71_11_72 = all_0_0_0
% 46.46/13.94 | (316) all_71_13_74 = all_0_7_7
% 46.46/13.94 | (345) vvar(all_71_12_73) = all_0_0_0
% 46.46/13.94 | (346) ~ (all_71_12_73 = all_0_7_7)
% 46.46/13.94 | (329) all_21_1_14 = all_0_0_0
% 46.46/13.94 |
% 46.46/13.94 | From (329) and (240) follows:
% 46.46/13.94 | (348) visValue(all_0_0_0)
% 46.46/13.94 |
% 46.46/13.94 | Instantiating formula (30) with all_0_0_0, all_71_12_73 and discharging atoms vvar(all_71_12_73) = all_0_0_0, visValue(all_0_0_0), yields:
% 46.46/13.94 | (135) $false
% 46.46/13.94 |
% 46.46/13.94 |-The branch is then unsatisfiable
% 46.46/13.94 |-Branch two:
% 46.46/13.94 | (162) all_21_7_20 = all_0_0_0 & all_21_9_22 = all_0_1_1 & all_21_11_24 = all_0_6_6 & all_21_12_25 = all_0_7_7 & ~ (all_21_14_27 = all_0_7_7) & vsubst(all_0_7_7, all_0_6_6, all_21_10_23) = all_21_8_21 & vabs(all_21_14_27, all_21_13_26, all_21_8_21) = all_0_0_0 & vabs(all_21_14_27, all_21_13_26, all_21_10_23) = all_0_1_1 & ~ visFreeVar(all_21_14_27, all_0_6_6)
% 46.46/13.94 |
% 46.46/13.94 | Applying alpha-rule on (162) yields:
% 46.46/13.94 | (163) all_21_12_25 = all_0_7_7
% 46.46/13.94 | (164) vabs(all_21_14_27, all_21_13_26, all_21_8_21) = all_0_0_0
% 46.46/13.94 | (165) vabs(all_21_14_27, all_21_13_26, all_21_10_23) = all_0_1_1
% 46.46/13.94 | (166) vsubst(all_0_7_7, all_0_6_6, all_21_10_23) = all_21_8_21
% 46.46/13.94 | (167) all_21_7_20 = all_0_0_0
% 46.46/13.94 | (168) ~ visFreeVar(all_21_14_27, all_0_6_6)
% 46.46/13.94 | (169) all_21_9_22 = all_0_1_1
% 46.46/13.94 | (170) all_21_11_24 = all_0_6_6
% 46.46/13.94 | (171) ~ (all_21_14_27 = all_0_7_7)
% 46.46/13.94 |
% 46.46/13.94 | Instantiating formula (58) with all_0_1_1, all_21_10_23, all_21_13_26, all_21_14_27, veabs, all_0_4_4, all_0_5_5 and discharging atoms vabs(all_21_14_27, all_21_13_26, all_21_10_23) = all_0_1_1, vabs(all_0_5_5, all_0_4_4, veabs) = all_0_1_1, yields:
% 46.46/13.94 | (172) all_21_14_27 = all_0_5_5
% 46.46/13.94 |
% 46.46/13.94 | Using (6) and (168) yields:
% 46.46/13.94 | (173) ~ (all_21_14_27 = all_0_5_5)
% 46.46/13.94 |
% 46.46/13.94 | Equations (172) can reduce 173 to:
% 46.46/13.94 | (154) $false
% 46.46/13.94 |
% 46.46/13.94 |-The branch is then unsatisfiable
% 46.46/13.94 |-Branch two:
% 46.46/13.94 | (175) all_21_7_20 = all_0_0_0 & all_21_10_23 = all_0_1_1 & all_21_12_25 = all_0_6_6 & all_21_13_26 = all_0_7_7 & vsubst(all_0_7_7, all_0_6_6, all_21_11_24) = all_21_8_21 & vsubst(all_0_7_7, all_0_6_6, all_21_14_27) = all_21_9_22 & vapp(all_21_9_22, all_21_8_21) = all_0_0_0 & vapp(all_21_14_27, all_21_11_24) = all_0_1_1
% 46.46/13.94 |
% 46.46/13.94 | Applying alpha-rule on (175) yields:
% 46.46/13.94 | (176) vapp(all_21_9_22, all_21_8_21) = all_0_0_0
% 46.46/13.94 | (177) vapp(all_21_14_27, all_21_11_24) = all_0_1_1
% 46.46/13.94 | (178) all_21_10_23 = all_0_1_1
% 46.46/13.94 | (179) all_21_13_26 = all_0_7_7
% 46.46/13.94 | (167) all_21_7_20 = all_0_0_0
% 46.46/13.94 | (181) vsubst(all_0_7_7, all_0_6_6, all_21_14_27) = all_21_9_22
% 46.46/13.94 | (182) vsubst(all_0_7_7, all_0_6_6, all_21_11_24) = all_21_8_21
% 46.46/13.94 | (183) all_21_12_25 = all_0_6_6
% 46.46/13.94 |
% 46.46/13.94 | Instantiating formula (78) with all_0_1_1, all_21_11_24, all_21_14_27 and discharging atoms vapp(all_21_14_27, all_21_11_24) = all_0_1_1, visValue(all_0_1_1), yields:
% 46.46/13.94 | (135) $false
% 46.46/13.94 |
% 46.46/13.94 |-The branch is then unsatisfiable
% 46.46/13.94 |-Branch two:
% 46.46/13.94 | (185) all_21_9_22 = all_0_1_1 & all_21_12_25 = all_0_7_7 & all_21_13_26 = all_0_7_7 & all_21_14_27 = all_0_6_6 & all_0_0_0 = all_0_1_1 & vabs(all_0_7_7, all_21_11_24, all_21_10_23) = all_0_1_1
% 46.46/13.94 |
% 46.46/13.94 | Applying alpha-rule on (185) yields:
% 46.46/13.94 | (163) all_21_12_25 = all_0_7_7
% 46.46/13.94 | (187) all_21_14_27 = all_0_6_6
% 46.46/13.94 | (179) all_21_13_26 = all_0_7_7
% 46.46/13.94 | (169) all_21_9_22 = all_0_1_1
% 46.46/13.94 | (190) all_0_0_0 = all_0_1_1
% 46.46/13.94 | (191) vabs(all_0_7_7, all_21_11_24, all_21_10_23) = all_0_1_1
% 46.46/13.94 |
% 46.46/13.94 | Instantiating formula (41) with all_21_10_23, all_0_1_1, all_0_7_7, all_21_11_24 and discharging atoms vabs(all_0_7_7, all_21_11_24, all_21_10_23) = all_0_1_1, visFreeVar(all_0_7_7, all_0_1_1), yields:
% 46.46/13.94 | (135) $false
% 46.46/13.94 |
% 46.46/13.94 |-The branch is then unsatisfiable
% 46.46/13.94 |-Branch two:
% 46.46/13.94 | (193) all_21_11_24 = all_0_1_1 & all_21_12_25 = all_0_6_6 & all_21_13_26 = all_0_7_7 & all_21_14_27 = all_0_7_7 & all_0_0_0 = all_0_6_6 & vvar(all_0_7_7) = all_0_1_1
% 46.46/13.94 |
% 46.46/13.94 | Applying alpha-rule on (193) yields:
% 46.46/13.94 | (194) vvar(all_0_7_7) = all_0_1_1
% 46.46/13.94 | (179) all_21_13_26 = all_0_7_7
% 46.46/13.94 | (108) all_21_14_27 = all_0_7_7
% 46.46/13.94 | (197) all_0_0_0 = all_0_6_6
% 46.46/13.94 | (183) all_21_12_25 = all_0_6_6
% 46.46/13.94 | (199) all_21_11_24 = all_0_1_1
% 46.46/13.94 |
% 46.46/13.94 | Instantiating formula (30) with all_0_1_1, all_0_7_7 and discharging atoms vvar(all_0_7_7) = all_0_1_1, visValue(all_0_1_1), yields:
% 46.46/13.94 | (135) $false
% 46.46/13.94 |
% 46.46/13.94 |-The branch is then unsatisfiable
% 46.46/13.94 |-Branch two:
% 46.46/13.94 | (201) all_21_11_24 = all_0_1_1 & all_21_13_26 = all_0_7_7 & all_21_14_27 = all_0_6_6 & all_0_0_0 = all_0_1_1 & ~ (all_21_12_25 = all_0_7_7) & vvar(all_21_12_25) = all_0_1_1
% 46.46/13.94 |
% 46.46/13.94 | Applying alpha-rule on (201) yields:
% 46.46/13.94 | (202) ~ (all_21_12_25 = all_0_7_7)
% 46.46/13.94 | (187) all_21_14_27 = all_0_6_6
% 46.46/13.94 | (204) vvar(all_21_12_25) = all_0_1_1
% 46.46/13.94 | (179) all_21_13_26 = all_0_7_7
% 46.46/13.94 | (190) all_0_0_0 = all_0_1_1
% 46.46/13.94 | (199) all_21_11_24 = all_0_1_1
% 46.46/13.94 |
% 46.46/13.94 | Instantiating formula (30) with all_0_1_1, all_21_12_25 and discharging atoms vvar(all_21_12_25) = all_0_1_1, visValue(all_0_1_1), yields:
% 46.46/13.94 | (135) $false
% 46.46/13.94 |
% 46.46/13.94 |-The branch is then unsatisfiable
% 46.46/13.94 % SZS output end Proof for theBenchmark
% 46.46/13.94
% 46.46/13.94 13324ms
%------------------------------------------------------------------------------