TSTP Solution File: COM135+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : COM135+1 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n006.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 01:08:16 EDT 2022
% Result : Theorem 7.81s 2.41s
% Output : Proof 12.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM135+1 : TPTP v8.1.0. Released v6.4.0.
% 0.13/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 18:24:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.58/0.60 ____ _
% 0.58/0.60 ___ / __ \_____(_)___ ________ __________
% 0.58/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.60
% 0.58/0.60 A Theorem Prover for First-Order Logic
% 0.58/0.60 (ePrincess v.1.0)
% 0.58/0.60
% 0.58/0.60 (c) Philipp Rümmer, 2009-2015
% 0.58/0.60 (c) Peter Backeman, 2014-2015
% 0.58/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.60 Bug reports to peter@backeman.se
% 0.58/0.60
% 0.58/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.60
% 0.58/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.77/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.15/1.06 Prover 0: Preprocessing ...
% 4.10/1.58 Prover 0: Warning: ignoring some quantifiers
% 4.10/1.61 Prover 0: Constructing countermodel ...
% 5.55/1.91 Prover 0: gave up
% 5.55/1.91 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.93/2.00 Prover 1: Preprocessing ...
% 6.56/2.20 Prover 1: Constructing countermodel ...
% 7.81/2.41 Prover 1: proved (500ms)
% 7.81/2.41
% 7.81/2.41 No countermodel exists, formula is valid
% 7.81/2.41 % SZS status Theorem for theBenchmark
% 7.81/2.41
% 7.81/2.41 Generating proof ... found it (size 137)
% 11.76/3.31
% 11.76/3.31 % SZS output start Proof for theBenchmark
% 11.76/3.31 Assumed formulas after preprocessing and simplification:
% 11.76/3.31 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = 0) & vsubst(v2, v3, v7) = v8 & vtcheck(v6, v7, v5) = 0 & vtcheck(v1, v8, v5) = v9 & vtcheck(v1, v3, v0) = 0 & vbind(v2, v0, v1) = v6 & vvar(v4) = v7 & ~ (visSomeExp(vnoExp) = 0) & ~ (visSomeType(vnoType) = 0) & ! [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) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (vgensym(v26) = v27 & visFreeVar(v15, v11) = v23 & vapp(v24, v25) = v26 & vapp(v11, v17) = v24 & vabs(v15, v14, v17) = v22 & vvar(v10) = v25 & ( ~ (v27 = v16) | ~ (v23 = 0) | ~ (v22 = v12)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | v12 = v10 | ~ (vtcheck(v18, v15, v16) = v19) | ~ (vbind(v12, v13, v14) = v17) | ~ (vbind(v10, v11, v17) = v18) | ? [v20] : ? [v21] : ? [v22] : ( ~ (v22 = 0) & vtcheck(v21, v15, v16) = v22 & vbind(v12, v13, v20) = v21 & vbind(v10, v11, v14) = v20)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (vreduce(v11) = v12) | ~ (vgetSomeExp(v16) = v18) | ~ (vapp(v17, v18) = v19) | ~ (vapp(v17, v10) = v11) | ~ (vabs(v13, v14, v15) = v17) | ? [v20] : ? [v21] : ? [v22] : (vreduce(v10) = v20 & visSomeExp(v16) = v21 & vsomeExp(v19) = v22 & ( ~ (v21 = 0) | ~ (v20 = v16) | v22 = v12))) & ! [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) | ? [v19] : ? [v20] : (visFreeVar(v14, v11) = v20 & vabs(v14, v15, v16) = v19 & ( ~ (v19 = v12) | v20 = 0))) & ! [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] : ! [v18] : (v18 = 0 | v16 = vnoExp | ~ (vreduce(v15) = v16) | ~ (visSomeExp(v13) = v18) | ~ (vapp(v17, v14) = v15) | ~ (vabs(v10, v11, v12) = v17) | ? [v19] : ? [v20] : (vreduce(v14) = v19 & visValue(v14) = v20 & ( ~ (v19 = v13) | v20 = 0))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (vreduce(v12) = v13) | ~ (visSomeExp(v11) = v18) | ~ (vapp(v17, v15) = v12) | ~ (vabs(v14, v10, v16) = v17) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (vreduce(v15) = v19 & vsomeExp(v21) = v22 & vsubst(v14, v15, v16) = v21 & visValue(v15) = v20 & ( ~ (v20 = 0) | ~ (v19 = v11) | v22 = v13))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (varrow(v13, v14) = v16) | ~ (vtcheck(v10, v15, v16) = v17) | ~ (vabs(v11, v13, v12) = v15) | ? [v18] : ? [v19] : ( ~ (v19 = 0) & vtcheck(v18, v12, v14) = v19 & vbind(v11, v13, v10) = v18)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (varrow(v10, v14) = v15) | ~ (vtcheck(v11, v16, v14) = v17) | ~ (vtcheck(v11, v12, v15) = 0) | ~ (vapp(v12, v13) = v16) | ? [v18] : ( ~ (v18 = 0) & vtcheck(v11, v13, v10) = v18)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (vtcheck(v17, v14, v15) = 0) | ~ (vbind(v10, v12, v16) = v17) | ~ (vbind(v10, v11, v13) = v16) | ? [v18] : (vtcheck(v18, v14, v15) = 0 & vbind(v10, v12, v13) = v18)) & ! [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] : (v16 = 0 | ~ (vtcheck(v15, v13, v14) = v16) | ~ (vbind(v10, v11, v12) = v15) | ? [v17] : ? [v18] : (vtcheck(v12, v13, v14) = v18 & vlookup(v10, v12) = v17 & ( ~ (v18 = 0) | ~ (v17 = vnoType)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (vtcheck(v15, v13, v14) = v16) | ~ (vbind(v10, v11, v12) = v15) | ? [v17] : ? [v18] : (vtcheck(v12, v13, v14) = v18 & visFreeVar(v10, v13) = v17 & ( ~ (v18 = 0) | v17 = 0))) & ! [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] : ( ~ (vreduce(v11) = v12) | ~ (vreduce(v10) = v13) | ~ (vgetSomeExp(v13) = v15) | ~ (vapp(v15, v14) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ((v20 = v10 & vabs(v17, v18, v19) = v10) | (visSomeExp(v13) = v18 & vsomeExp(v16) = v19 & vapp(v10, v14) = v17 & ( ~ (v18 = 0) | ~ (v17 = v11) | v19 = v12)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = vnoExp | ~ (vreduce(v13) = v14) | ~ (visSomeExp(v12) = v15) | ~ (vapp(v11, v10) = v13) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = v11 & vabs(v16, v17, v18) = v11) | ( ~ (v16 = v12) & vreduce(v11) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (visFreeVar(v10, v13) = v15) | ~ (visFreeVar(v10, v12) = v14) | ~ (visFreeVar(v10, v11) = 0) | ? [v16] : ( ~ (v16 = v11) & vapp(v12, v13) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v13 = v11 | ~ (visFreeVar(v11, v14) = 0) | ~ (visFreeVar(v11, v12) = v15) | ~ (vabs(v13, v10, v14) = v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (visFreeVar(v11, v14) = v15) | ~ (visFreeVar(v11, v12) = 0) | ~ (vabs(v13, v10, v14) = v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (visFreeVar(v10, v13) = v14) | ~ (visFreeVar(v10, v12) = 0) | ~ (visFreeVar(v10, v11) = v15) | ? [v16] : ( ~ (v16 = v11) & vapp(v12, v13) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (visFreeVar(v10, v13) = 0) | ~ (visFreeVar(v10, v12) = v14) | ~ (visFreeVar(v10, v11) = v15) | ? [v16] : ( ~ (v16 = v11) & vapp(v12, v13) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (vsubst(v11, v10, v12) = v13) | ~ (vabs(v11, v14, v15) = v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (vtcheck(v15, v13, v14) = 0) | ~ (vbind(v10, v11, v12) = v15) | ? [v16] : ? [v17] : (vtcheck(v12, v13, v14) = v17 & visFreeVar(v10, v13) = v16 & (v17 = 0 | v16 = 0))) & ! [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] : (v14 = vnoExp | ~ (vreduce(v13) = v14) | ~ (vabs(v10, v11, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (vtcheck(v10, v13, v12) = v14) | ~ (vvar(v11) = v13) | ? [v15] : ? [v16] : ( ~ (v16 = v15) & vlookup(v11, v10) = v15 & vsomeType(v12) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (visValue(v13) = v14) | ~ (vabs(v10, v11, v12) = v13)) & ! [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] : (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 | ~ (vtcheck(v14, v13, v12) = v11) | ~ (vtcheck(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] : ( ~ (visFreeVar(v11, v13) = v14) | ~ (visFreeVar(v11, v12) = 0) | ~ (vabs(v11, v10, v13) = v12)) & ! [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 | ~ (visFreeVar(v13, v12) = v11) | ~ (visFreeVar(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] : ? [v29] : ((v29 = v13 & v25 = v18 & v21 = 0 & v20 = v12 & v15 = v11 & v14 = v10 & ~ (v17 = v10) & vsubst(v17, v26, v19) = v27 & vsubst(v10, v11, v28) = v13 & vgensym(v24) = v18 & visFreeVar(v17, v11) = 0 & vapp(v22, v23) = v24 & vapp(v11, v19) = v22 & vabs(v18, v16, v27) = v28 & vabs(v17, v16, v19) = v12 & vvar(v18) = v26 & vvar(v10) = v23) | (v22 = v13 & v19 = v12 & v17 = v11 & v16 = v10 & ~ (v20 = 0) & ~ (v14 = v10) & vsubst(v10, v11, v18) = v21 & visFreeVar(v14, v11) = v20 & vabs(v14, v15, v21) = v13 & vabs(v14, v15, v18) = v12) | (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] : ( ~ (vapp(v11, v12) = v13) | ~ (vvar(v10) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (vgetSomeExp(v10) = v11) | ~ (vsomeExp(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (vsomeExp(v10) = v12) | ~ (vsomeExp(v10) = v11)) & ! [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 | ~ (visFreeVar(v10, v11) = 0) | ~ (vvar(v12) = v11)) & ! [v10] : ! [v11] : ! [v12] : (v12 = vnoExp | ~ (vreduce(v11) = v12) | ~ (vvar(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] : (v12 = 0 | ~ (visSomeExp(v11) = v12) | ~ (vsomeExp(v10) = v11)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (visSomeType(v11) = v12) | ~ (vsomeType(v10) = v11)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (visFreeVar(v10, v11) = v12) | ~ (vvar(v10) = v11)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (vreduce(v12) = v11) | ~ (vreduce(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (vgetSomeExp(v12) = v11) | ~ (vgetSomeExp(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (visSomeExp(v12) = v11) | ~ (visSomeExp(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (vsomeExp(v12) = v11) | ~ (vsomeExp(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (vsomeExp(v11) = v12) | ~ (vsomeExp(v10) = v12)) & ! [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 | ~ (visSomeType(v12) = v11) | ~ (visSomeType(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 | ~ (visValue(v12) = v11) | ~ (visValue(v12) = v10)) & ! [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] : ( ~ (vtcheck(v12, v10, v11) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ((v20 = 0 & v18 = v11 & v17 = v10 & varrow(v15, v16) = v11 & vtcheck(v19, v14, v16) = 0 & vbind(v13, v15, v12) = v19 & vabs(v13, v15, v14) = v10) | (v19 = 0 & v18 = 0 & v16 = v10 & varrow(v15, v11) = v17 & vtcheck(v12, v14, v15) = 0 & vtcheck(v12, v13, v17) = 0 & vapp(v13, v14) = v10) | (v16 = v13 & v15 = v10 & vlookup(v14, v12) = v13 & vsomeType(v11) = v13 & vvar(v14) = v10))) & ! [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] : ( ~ (visValue(v12) = 0) | ~ (vapp(v10, v11) = v12)) & ! [v10] : ! [v11] : (v11 = vnoType | ~ (vlookup(v10, vempty) = v11)) & ! [v10] : ! [v11] : ( ~ (vreduce(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ((v23 = v11 & v21 = 0 & v19 = v13 & v18 = v10 & ~ (v20 = 0) & vreduce(v15) = v13 & visSomeExp(v13) = v20 & vsomeExp(v22) = v11 & vsubst(v14, v15, v16) = v22 & visValue(v15) = 0 & vapp(v17, v15) = v10 & vabs(v14, v12, v16) = v17) | (v23 = v11 & v20 = 0 & v19 = v16 & v18 = v10 & vreduce(v12) = v16 & vgetSomeExp(v16) = v21 & visSomeExp(v16) = 0 & vsomeExp(v22) = v11 & vapp(v17, v21) = v22 & vapp(v17, v12) = v10 & vabs(v13, v14, v15) = v17) | (v20 = v11 & v17 = 0 & v16 = v13 & v15 = v10 & vreduce(v12) = v13 & vgetSomeExp(v13) = v18 & visSomeExp(v13) = 0 & vsomeExp(v19) = v11 & vapp(v18, v14) = v19 & vapp(v12, v14) = v10 & ! [v24] : ! [v25] : ! [v26] : ~ (vabs(v24, v25, v26) = v12)) | (v19 = v15 & v18 = v10 & v11 = vnoExp & ~ (v21 = 0) & ~ (v20 = 0) & vreduce(v16) = v15 & visSomeExp(v15) = v20 & visValue(v16) = v21 & vapp(v17, v16) = v10 & vabs(v12, v13, v14) = v17) | (v16 = v14 & v15 = v10 & v11 = vnoExp & ~ (v17 = 0) & vreduce(v13) = v14 & visSomeExp(v14) = v17 & vapp(v13, v12) = v10 & ! [v24] : ! [v25] : ! [v26] : ~ (vabs(v24, v25, v26) = v13)) | (v15 = v10 & v11 = vnoExp & vabs(v12, v13, v14) = v10) | (v13 = v10 & v11 = vnoExp & vvar(v12) = v10))) & ! [v10] : ! [v11] : ( ~ (visFreeVar(v10, v11) = 0) | ? [v12] : ( ~ (v12 = v10) & vgensym(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (visValue(v11) = 0) | ~ (vvar(v10) = v11)) & ! [v10] : ~ (vsomeExp(v10) = vnoExp) & ! [v10] : ~ (vsomeType(v10) = vnoType))
% 12.12/3.37 | 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:
% 12.12/3.37 | (1) ~ (all_0_0_0 = 0) & vsubst(all_0_7_7, all_0_6_6, all_0_2_2) = all_0_1_1 & vtcheck(all_0_3_3, all_0_2_2, all_0_4_4) = 0 & vtcheck(all_0_8_8, all_0_1_1, all_0_4_4) = all_0_0_0 & vtcheck(all_0_8_8, all_0_6_6, all_0_9_9) = 0 & vbind(all_0_7_7, all_0_9_9, all_0_8_8) = all_0_3_3 & vvar(all_0_5_5) = all_0_2_2 & ~ (visSomeExp(vnoExp) = 0) & ~ (visSomeType(vnoType) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v3 | v5 = v0 | ~ (vsubst(v5, v8, v7) = v9) | ~ (vsubst(v0, v1, v10) = v11) | ~ (vsubst(v0, v1, v2) = v3) | ~ (vabs(v6, v4, v9) = v10) | ~ (vvar(v6) = v8) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (vgensym(v16) = v17 & visFreeVar(v5, v1) = v13 & vapp(v14, v15) = v16 & vapp(v1, v7) = v14 & vabs(v5, v4, v7) = v12 & vvar(v0) = v15 & ( ~ (v17 = v6) | ~ (v13 = 0) | ~ (v12 = v2)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v2 = v0 | ~ (vtcheck(v8, v5, v6) = v9) | ~ (vbind(v2, v3, v4) = v7) | ~ (vbind(v0, v1, v7) = v8) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = 0) & vtcheck(v11, v5, v6) = v12 & vbind(v2, v3, v10) = v11 & vbind(v0, v1, v4) = v10)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (vreduce(v1) = v2) | ~ (vgetSomeExp(v6) = v8) | ~ (vapp(v7, v8) = v9) | ~ (vapp(v7, v0) = v1) | ~ (vabs(v3, v4, v5) = v7) | ? [v10] : ? [v11] : ? [v12] : (vreduce(v0) = v10 & visSomeExp(v6) = v11 & vsomeExp(v9) = v12 & ( ~ (v11 = 0) | ~ (v10 = v6) | v12 = v2))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v3 | v4 = v0 | ~ (vsubst(v0, v1, v6) = v7) | ~ (vsubst(v0, v1, v2) = v3) | ~ (vabs(v4, v5, v7) = v8) | ? [v9] : ? [v10] : (visFreeVar(v4, v1) = v10 & vabs(v4, v5, v6) = v9 & ( ~ (v9 = v2) | v10 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v3 | ~ (vsubst(v0, v1, v5) = v7) | ~ (vsubst(v0, v1, v4) = v6) | ~ (vsubst(v0, v1, v2) = v3) | ~ (vapp(v6, v7) = v8) | ? [v9] : ( ~ (v9 = v2) & vapp(v4, v5) = v9)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v6 = vnoExp | ~ (vreduce(v5) = v6) | ~ (visSomeExp(v3) = v8) | ~ (vapp(v7, v4) = v5) | ~ (vabs(v0, v1, v2) = v7) | ? [v9] : ? [v10] : (vreduce(v4) = v9 & visValue(v4) = v10 & ( ~ (v9 = v3) | v10 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (vreduce(v2) = v3) | ~ (visSomeExp(v1) = v8) | ~ (vapp(v7, v5) = v2) | ~ (vabs(v4, v0, v6) = v7) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (vreduce(v5) = v9 & vsomeExp(v11) = v12 & vsubst(v4, v5, v6) = v11 & visValue(v5) = v10 & ( ~ (v10 = 0) | ~ (v9 = v1) | v12 = v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (varrow(v3, v4) = v6) | ~ (vtcheck(v0, v5, v6) = v7) | ~ (vabs(v1, v3, v2) = v5) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & vtcheck(v8, v2, v4) = v9 & vbind(v1, v3, v0) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (varrow(v0, v4) = v5) | ~ (vtcheck(v1, v6, v4) = v7) | ~ (vtcheck(v1, v2, v5) = 0) | ~ (vapp(v2, v3) = v6) | ? [v8] : ( ~ (v8 = 0) & vtcheck(v1, v3, v0) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (vtcheck(v7, v4, v5) = 0) | ~ (vbind(v0, v2, v6) = v7) | ~ (vbind(v0, v1, v3) = v6) | ? [v8] : (vtcheck(v8, v4, v5) = 0 & vbind(v0, v2, v3) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v4 | v2 = v1 | ~ (vlookup(v2, v5) = v6) | ~ (vlookup(v2, v3) = v4) | ~ (vbind(v1, v0, v5) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vtcheck(v5, v3, v4) = v6) | ~ (vbind(v0, v1, v2) = v5) | ? [v7] : ? [v8] : (vtcheck(v2, v3, v4) = v8 & vlookup(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = vnoType)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vtcheck(v5, v3, v4) = v6) | ~ (vbind(v0, v1, v2) = v5) | ? [v7] : ? [v8] : (vtcheck(v2, v3, v4) = v8 & visFreeVar(v0, v3) = v7 & ( ~ (v8 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v2 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v2 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v1 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v1 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v0 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v0 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (vreduce(v1) = v2) | ~ (vreduce(v0) = v3) | ~ (vgetSomeExp(v3) = v5) | ~ (vapp(v5, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v10 = v0 & vabs(v7, v8, v9) = v0) | (visSomeExp(v3) = v8 & vsomeExp(v6) = v9 & vapp(v0, v4) = v7 & ( ~ (v8 = 0) | ~ (v7 = v1) | v9 = v2)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = vnoExp | ~ (vreduce(v3) = v4) | ~ (visSomeExp(v2) = v5) | ~ (vapp(v1, v0) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v9 = v1 & vabs(v6, v7, v8) = v1) | ( ~ (v6 = v2) & vreduce(v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (visFreeVar(v0, v3) = v5) | ~ (visFreeVar(v0, v2) = v4) | ~ (visFreeVar(v0, v1) = 0) | ? [v6] : ( ~ (v6 = v1) & vapp(v2, v3) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v3 = v1 | ~ (visFreeVar(v1, v4) = 0) | ~ (visFreeVar(v1, v2) = v5) | ~ (vabs(v3, v0, v4) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (visFreeVar(v1, v4) = v5) | ~ (visFreeVar(v1, v2) = 0) | ~ (vabs(v3, v0, v4) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (visFreeVar(v0, v3) = v4) | ~ (visFreeVar(v0, v2) = 0) | ~ (visFreeVar(v0, v1) = v5) | ? [v6] : ( ~ (v6 = v1) & vapp(v2, v3) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (visFreeVar(v0, v3) = 0) | ~ (visFreeVar(v0, v2) = v4) | ~ (visFreeVar(v0, v1) = v5) | ? [v6] : ( ~ (v6 = v1) & vapp(v2, v3) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (vsubst(v1, v0, v2) = v3) | ~ (vabs(v1, v4, v5) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vtcheck(v5, v3, v4) = 0) | ~ (vbind(v0, v1, v2) = v5) | ? [v6] : ? [v7] : (vtcheck(v2, v3, v4) = v7 & visFreeVar(v0, v3) = v6 & (v7 = 0 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vapp(v3, v4) = v5) | ~ (vabs(v0, v1, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (vbind(v0, v1, v2) = v4) | ~ (vbind(v0, v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (vabs(v0, v1, v2) = v4) | ~ (vabs(v0, v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v1 | v3 = v2 | ~ (vsubst(v1, v0, v2) = v3) | ~ (vvar(v4) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = vnoExp | ~ (vreduce(v3) = v4) | ~ (vabs(v0, v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (vtcheck(v0, v3, v2) = v4) | ~ (vvar(v1) = v3) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & vlookup(v1, v0) = v5 & vsomeType(v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (visValue(v3) = v4) | ~ (vabs(v0, v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (varrow(v2, v3) = v4) | ~ (varrow(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (varrow(v2, v3) = v4) | ~ (varrow(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vlookup(v1, v2) = v3) | ~ (vbind(v1, v4, v0) = v2) | vsomeType(v4) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (visFreeVar(v1, v3) = v4) | ~ (visFreeVar(v1, v2) = 0) | ~ (vabs(v1, v0, v3) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vabs(v1, v2, v3) = v4) | ~ (vvar(v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (varrow(v0, v1) = v3) | ~ (varrow(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (vapp(v0, v1) = v3) | ~ (vapp(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (vsubst(v0, v1, v2) = v3) | ~ (vvar(v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (varrow(v3, v2) = v1) | ~ (varrow(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~ (vlookup(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~ (vapp(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsubst(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = v3 & v15 = v8 & v11 = 0 & v10 = v2 & v5 = v1 & v4 = v0 & ~ (v7 = v0) & vsubst(v7, v16, v9) = v17 & vsubst(v0, v1, v18) = v3 & vgensym(v14) = v8 & visFreeVar(v7, v1) = 0 & vapp(v12, v13) = v14 & vapp(v1, v9) = v12 & vabs(v8, v6, v17) = v18 & vabs(v7, v6, v9) = v2 & vvar(v8) = v16 & vvar(v0) = v13) | (v12 = v3 & v9 = v2 & v7 = v1 & v6 = v0 & ~ (v10 = 0) & ~ (v4 = v0) & vsubst(v0, v1, v8) = v11 & visFreeVar(v4, v1) = v10 & vabs(v4, v5, v11) = v3 & vabs(v4, v5, v8) = v2) | (v11 = v3 & v8 = v2 & v6 = v1 & v5 = v0 & vsubst(v0, v1, v7) = v10 & vsubst(v0, v1, v4) = v9 & vapp(v9, v10) = v3 & vapp(v4, v7) = v2) | (v9 = v2 & v6 = v0 & v5 = v0 & v4 = v1 & v3 = v2 & vabs(v0, v7, v8) = v2) | (v7 = v2 & v6 = v1 & v5 = v0 & v4 = v0 & v3 = v1 & vvar(v0) = v2) | (v7 = v2 & v5 = v0 & v4 = v1 & v3 = v2 & ~ (v6 = v0) & vvar(v6) = v2))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vapp(v1, v2) = v3) | ~ (vvar(v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vgetSomeExp(v0) = v1) | ~ (vsomeExp(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vsomeExp(v0) = v2) | ~ (vsomeExp(v0) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vgetSomeType(v0) = v1) | ~ (vsomeType(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vsomeType(v0) = v2) | ~ (vsomeType(v0) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vvar(v0) = v2) | ~ (vvar(v0) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (visFreeVar(v0, v1) = 0) | ~ (vvar(v2) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = vnoExp | ~ (vreduce(v1) = v2) | ~ (vvar(v0) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = vnoType | ~ (vlookup(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = v2 & v7 = v1 & v5 = v0 & v4 = v0 & vsomeType(v6) = v2 & vbind(v0, v6, v3) = v1) | (v8 = v2 & v7 = v1 & v5 = v0 & ~ (v4 = v0) & vlookup(v0, v6) = v2 & vbind(v4, v3, v6) = v1))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (visSomeExp(v1) = v2) | ~ (vsomeExp(v0) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (visSomeType(v1) = v2) | ~ (vsomeType(v0) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (visFreeVar(v0, v1) = v2) | ~ (vvar(v0) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~ (vsomeExp(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeExp(v1) = v2) | ~ (vsomeExp(v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~ (vsomeType(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeType(v1) = v2) | ~ (vsomeType(v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (visValue(v2) = v1) | ~ (visValue(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vvar(v1) = v2) | ~ (vvar(v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = vempty | ~ (vlookup(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = v2 & v7 = v1 & v5 = v0 & v4 = v0 & vsomeType(v6) = v2 & vbind(v0, v6, v3) = v1) | (v8 = v2 & v7 = v1 & v5 = v0 & ~ (v4 = v0) & vlookup(v0, v6) = v2 & vbind(v4, v3, v6) = v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (vtcheck(v2, v0, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v8 = v1 & v7 = v0 & varrow(v5, v6) = v1 & vtcheck(v9, v4, v6) = 0 & vbind(v3, v5, v2) = v9 & vabs(v3, v5, v4) = v0) | (v9 = 0 & v8 = 0 & v6 = v0 & varrow(v5, v1) = v7 & vtcheck(v2, v4, v5) = 0 & vtcheck(v2, v3, v7) = 0 & vapp(v3, v4) = v0) | (v6 = v3 & v5 = v0 & vlookup(v4, v2) = v3 & vsomeType(v1) = v3 & vvar(v4) = v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (vlookup(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (v3 = v0 | (v8 = v2 & v7 = v1 & v5 = v0 & v4 = v0 & vsomeType(v6) = v2 & vbind(v0, v6, v3) = v1) | (v8 = v2 & v7 = v1 & v5 = v0 & ~ (v4 = v0) & vlookup(v0, v6) = v2 & vbind(v4, v3, v6) = v1))) & ! [v0] : ! [v1] : ! [v2] : ~ (vbind(v0, v1, v2) = vempty) & ! [v0] : ! [v1] : ! [v2] : ( ~ (visValue(v2) = 0) | ~ (vapp(v0, v1) = v2)) & ! [v0] : ! [v1] : (v1 = vnoType | ~ (vlookup(v0, vempty) = v1)) & ! [v0] : ! [v1] : ( ~ (vreduce(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v13 = v1 & v11 = 0 & v9 = v3 & v8 = v0 & ~ (v10 = 0) & vreduce(v5) = v3 & visSomeExp(v3) = v10 & vsomeExp(v12) = v1 & vsubst(v4, v5, v6) = v12 & visValue(v5) = 0 & vapp(v7, v5) = v0 & vabs(v4, v2, v6) = v7) | (v13 = v1 & v10 = 0 & v9 = v6 & v8 = v0 & vreduce(v2) = v6 & vgetSomeExp(v6) = v11 & visSomeExp(v6) = 0 & vsomeExp(v12) = v1 & vapp(v7, v11) = v12 & vapp(v7, v2) = v0 & vabs(v3, v4, v5) = v7) | (v10 = v1 & v7 = 0 & v6 = v3 & v5 = v0 & vreduce(v2) = v3 & vgetSomeExp(v3) = v8 & visSomeExp(v3) = 0 & vsomeExp(v9) = v1 & vapp(v8, v4) = v9 & vapp(v2, v4) = v0 & ! [v14] : ! [v15] : ! [v16] : ~ (vabs(v14, v15, v16) = v2)) | (v9 = v5 & v8 = v0 & v1 = vnoExp & ~ (v11 = 0) & ~ (v10 = 0) & vreduce(v6) = v5 & visSomeExp(v5) = v10 & visValue(v6) = v11 & vapp(v7, v6) = v0 & vabs(v2, v3, v4) = v7) | (v6 = v4 & v5 = v0 & v1 = vnoExp & ~ (v7 = 0) & vreduce(v3) = v4 & visSomeExp(v4) = v7 & vapp(v3, v2) = v0 & ! [v14] : ! [v15] : ! [v16] : ~ (vabs(v14, v15, v16) = v3)) | (v5 = v0 & v1 = vnoExp & vabs(v2, v3, v4) = v0) | (v3 = v0 & v1 = vnoExp & vvar(v2) = v0))) & ! [v0] : ! [v1] : ( ~ (visFreeVar(v0, v1) = 0) | ? [v2] : ( ~ (v2 = v0) & vgensym(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (visValue(v1) = 0) | ~ (vvar(v0) = v1)) & ! [v0] : ~ (vsomeExp(v0) = vnoExp) & ! [v0] : ~ (vsomeType(v0) = vnoType)
% 12.19/3.40 |
% 12.19/3.40 | Applying alpha-rule on (1) yields:
% 12.19/3.40 | (2) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (visSomeExp(v1) = v2) | ~ (vsomeExp(v0) = v1))
% 12.19/3.40 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (visFreeVar(v0, v3) = 0) | ~ (visFreeVar(v0, v2) = v4) | ~ (visFreeVar(v0, v1) = v5) | ? [v6] : ( ~ (v6 = v1) & vapp(v2, v3) = v6))
% 12.19/3.40 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4))
% 12.19/3.40 | (5) vtcheck(all_0_8_8, all_0_1_1, all_0_4_4) = all_0_0_0
% 12.19/3.40 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (varrow(v2, v3) = v4) | ~ (varrow(v0, v1) = v4))
% 12.19/3.40 | (7) ! [v0] : ! [v1] : ( ~ (visFreeVar(v0, v1) = 0) | ? [v2] : ( ~ (v2 = v0) & vgensym(v1) = v2))
% 12.19/3.40 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v6 = vnoExp | ~ (vreduce(v5) = v6) | ~ (visSomeExp(v3) = v8) | ~ (vapp(v7, v4) = v5) | ~ (vabs(v0, v1, v2) = v7) | ? [v9] : ? [v10] : (vreduce(v4) = v9 & visValue(v4) = v10 & ( ~ (v9 = v3) | v10 = 0)))
% 12.19/3.40 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (vsubst(v0, v1, v2) = v3) | ~ (vvar(v0) = v2))
% 12.19/3.40 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vtcheck(v5, v3, v4) = v6) | ~ (vbind(v0, v1, v2) = v5) | ? [v7] : ? [v8] : (vtcheck(v2, v3, v4) = v8 & visFreeVar(v0, v3) = v7 & ( ~ (v8 = 0) | v7 = 0)))
% 12.19/3.40 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (visFreeVar(v1, v3) = v4) | ~ (visFreeVar(v1, v2) = 0) | ~ (vabs(v1, v0, v3) = v2))
% 12.19/3.40 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vlookup(v1, v2) = v3) | ~ (vbind(v1, v4, v0) = v2) | vsomeType(v4) = v3)
% 12.19/3.40 | (13) ! [v0] : ~ (vsomeExp(v0) = vnoExp)
% 12.19/3.40 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~ (vlookup(v3, v2) = v0))
% 12.19/3.40 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (visValue(v3) = v4) | ~ (vabs(v0, v1, v2) = v3))
% 12.19/3.40 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (vreduce(v1) = v2) | ~ (vgetSomeExp(v6) = v8) | ~ (vapp(v7, v8) = v9) | ~ (vapp(v7, v0) = v1) | ~ (vabs(v3, v4, v5) = v7) | ? [v10] : ? [v11] : ? [v12] : (vreduce(v0) = v10 & visSomeExp(v6) = v11 & vsomeExp(v9) = v12 & ( ~ (v11 = 0) | ~ (v10 = v6) | v12 = v2)))
% 12.19/3.40 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (vreduce(v2) = v3) | ~ (visSomeExp(v1) = v8) | ~ (vapp(v7, v5) = v2) | ~ (vabs(v4, v0, v6) = v7) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (vreduce(v5) = v9 & vsomeExp(v11) = v12 & vsubst(v4, v5, v6) = v11 & visValue(v5) = v10 & ( ~ (v10 = 0) | ~ (v9 = v1) | v12 = v3)))
% 12.19/3.40 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (visFreeVar(v0, v1) = v2) | ~ (vvar(v0) = v1))
% 12.19/3.40 | (19) ! [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)))
% 12.19/3.40 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v0 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6))
% 12.19/3.40 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0))
% 12.19/3.40 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vabs(v1, v2, v3) = v4) | ~ (vvar(v0) = v4))
% 12.19/3.40 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v1 | v3 = v2 | ~ (vsubst(v1, v0, v2) = v3) | ~ (vvar(v4) = v2))
% 12.19/3.40 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0))
% 12.19/3.40 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v3 | v4 = v0 | ~ (vsubst(v0, v1, v6) = v7) | ~ (vsubst(v0, v1, v2) = v3) | ~ (vabs(v4, v5, v7) = v8) | ? [v9] : ? [v10] : (visFreeVar(v4, v1) = v10 & vabs(v4, v5, v6) = v9 & ( ~ (v9 = v2) | v10 = 0)))
% 12.19/3.41 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vvar(v0) = v2) | ~ (vvar(v0) = v1))
% 12.19/3.41 | (27) vvar(all_0_5_5) = all_0_2_2
% 12.19/3.41 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v4 | v2 = v1 | ~ (vlookup(v2, v5) = v6) | ~ (vlookup(v2, v3) = v4) | ~ (vbind(v1, v0, v5) = v3))
% 12.19/3.41 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v2 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6))
% 12.19/3.41 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (vsubst(v1, v0, v2) = v3) | ~ (vabs(v1, v4, v5) = v2))
% 12.19/3.41 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v2 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6))
% 12.19/3.41 | (32) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeType(v1) = v2) | ~ (vsomeType(v0) = v2))
% 12.19/3.41 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) = v0))
% 12.19/3.41 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v1 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6))
% 12.19/3.41 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (varrow(v0, v1) = v3) | ~ (varrow(v0, v1) = v2))
% 12.19/3.41 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vapp(v3, v4) = v5) | ~ (vabs(v0, v1, v2) = v5))
% 12.19/3.41 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0))
% 12.19/3.41 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0))
% 12.19/3.41 | (39) ! [v0] : ! [v1] : ! [v2] : (v2 = vnoExp | ~ (vreduce(v1) = v2) | ~ (vvar(v0) = v1))
% 12.19/3.41 | (40) vbind(all_0_7_7, all_0_9_9, all_0_8_8) = all_0_3_3
% 12.19/3.41 | (41) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vsomeExp(v0) = v2) | ~ (vsomeExp(v0) = v1))
% 12.19/3.41 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0))
% 12.19/3.41 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0))
% 12.19/3.41 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v1 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6))
% 12.19/3.41 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (vabs(v0, v1, v2) = v4) | ~ (vabs(v0, v1, v2) = v3))
% 12.19/3.41 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vapp(v1, v2) = v3) | ~ (vvar(v0) = v3))
% 12.19/3.41 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (vtcheck(v0, v3, v2) = v4) | ~ (vvar(v1) = v3) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & vlookup(v1, v0) = v5 & vsomeType(v2) = v6))
% 12.19/3.41 | (48) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (visFreeVar(v0, v1) = 0) | ~ (vvar(v2) = v1))
% 12.19/3.41 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (varrow(v2, v3) = v4) | ~ (varrow(v0, v1) = v4))
% 12.19/3.41 | (50) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~ (vsomeExp(v2) = v0))
% 12.19/3.41 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = vnoExp | ~ (vreduce(v3) = v4) | ~ (visSomeExp(v2) = v5) | ~ (vapp(v1, v0) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v9 = v1 & vabs(v6, v7, v8) = v1) | ( ~ (v6 = v2) & vreduce(v1) = v6)))
% 12.19/3.41 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (varrow(v3, v4) = v6) | ~ (vtcheck(v0, v5, v6) = v7) | ~ (vabs(v1, v3, v2) = v5) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & vtcheck(v8, v2, v4) = v9 & vbind(v1, v3, v0) = v8))
% 12.19/3.41 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v0 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6))
% 12.19/3.41 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (visFreeVar(v1, v4) = v5) | ~ (visFreeVar(v1, v2) = 0) | ~ (vabs(v3, v0, v4) = v2))
% 12.19/3.41 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (vbind(v0, v1, v2) = v4) | ~ (vbind(v0, v1, v2) = v3))
% 12.19/3.41 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsubst(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = v3 & v15 = v8 & v11 = 0 & v10 = v2 & v5 = v1 & v4 = v0 & ~ (v7 = v0) & vsubst(v7, v16, v9) = v17 & vsubst(v0, v1, v18) = v3 & vgensym(v14) = v8 & visFreeVar(v7, v1) = 0 & vapp(v12, v13) = v14 & vapp(v1, v9) = v12 & vabs(v8, v6, v17) = v18 & vabs(v7, v6, v9) = v2 & vvar(v8) = v16 & vvar(v0) = v13) | (v12 = v3 & v9 = v2 & v7 = v1 & v6 = v0 & ~ (v10 = 0) & ~ (v4 = v0) & vsubst(v0, v1, v8) = v11 & visFreeVar(v4, v1) = v10 & vabs(v4, v5, v11) = v3 & vabs(v4, v5, v8) = v2) | (v11 = v3 & v8 = v2 & v6 = v1 & v5 = v0 & vsubst(v0, v1, v7) = v10 & vsubst(v0, v1, v4) = v9 & vapp(v9, v10) = v3 & vapp(v4, v7) = v2) | (v9 = v2 & v6 = v0 & v5 = v0 & v4 = v1 & v3 = v2 & vabs(v0, v7, v8) = v2) | (v7 = v2 & v6 = v1 & v5 = v0 & v4 = v0 & v3 = v1 & vvar(v0) = v2) | (v7 = v2 & v5 = v0 & v4 = v1 & v3 = v2 & ~ (v6 = v0) & vvar(v6) = v2)))
% 12.19/3.41 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3, v2) = v0))
% 12.19/3.41 | (58) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0))
% 12.19/3.41 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = vnoExp | ~ (vreduce(v3) = v4) | ~ (vabs(v0, v1, v2) = v3))
% 12.19/3.41 | (60) vtcheck(all_0_8_8, all_0_6_6, all_0_9_9) = 0
% 12.19/3.41 | (61) ! [v0] : ! [v1] : ( ~ (vreduce(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v13 = v1 & v11 = 0 & v9 = v3 & v8 = v0 & ~ (v10 = 0) & vreduce(v5) = v3 & visSomeExp(v3) = v10 & vsomeExp(v12) = v1 & vsubst(v4, v5, v6) = v12 & visValue(v5) = 0 & vapp(v7, v5) = v0 & vabs(v4, v2, v6) = v7) | (v13 = v1 & v10 = 0 & v9 = v6 & v8 = v0 & vreduce(v2) = v6 & vgetSomeExp(v6) = v11 & visSomeExp(v6) = 0 & vsomeExp(v12) = v1 & vapp(v7, v11) = v12 & vapp(v7, v2) = v0 & vabs(v3, v4, v5) = v7) | (v10 = v1 & v7 = 0 & v6 = v3 & v5 = v0 & vreduce(v2) = v3 & vgetSomeExp(v3) = v8 & visSomeExp(v3) = 0 & vsomeExp(v9) = v1 & vapp(v8, v4) = v9 & vapp(v2, v4) = v0 & ! [v14] : ! [v15] : ! [v16] : ~ (vabs(v14, v15, v16) = v2)) | (v9 = v5 & v8 = v0 & v1 = vnoExp & ~ (v11 = 0) & ~ (v10 = 0) & vreduce(v6) = v5 & visSomeExp(v5) = v10 & visValue(v6) = v11 & vapp(v7, v6) = v0 & vabs(v2, v3, v4) = v7) | (v6 = v4 & v5 = v0 & v1 = vnoExp & ~ (v7 = 0) & vreduce(v3) = v4 & visSomeExp(v4) = v7 & vapp(v3, v2) = v0 & ! [v14] : ! [v15] : ! [v16] : ~ (vabs(v14, v15, v16) = v3)) | (v5 = v0 & v1 = vnoExp & vabs(v2, v3, v4) = v0) | (v3 = v0 & v1 = vnoExp & vvar(v2) = v0)))
% 12.37/3.42 | (62) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vgetSomeType(v0) = v1) | ~ (vsomeType(v2) = v0))
% 12.37/3.42 | (63) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (visSomeType(v1) = v2) | ~ (vsomeType(v0) = v1))
% 12.37/3.42 | (64) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vsomeType(v0) = v2) | ~ (vsomeType(v0) = v1))
% 12.37/3.42 | (65) ! [v0] : ~ (vsomeType(v0) = vnoType)
% 12.37/3.42 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4))
% 12.37/3.42 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vtcheck(v5, v3, v4) = 0) | ~ (vbind(v0, v1, v2) = v5) | ? [v6] : ? [v7] : (vtcheck(v2, v3, v4) = v7 & visFreeVar(v0, v3) = v6 & (v7 = 0 | v6 = 0)))
% 12.37/3.42 | (68) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) = v0))
% 12.37/3.42 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (varrow(v0, v4) = v5) | ~ (vtcheck(v1, v6, v4) = v7) | ~ (vtcheck(v1, v2, v5) = 0) | ~ (vapp(v2, v3) = v6) | ? [v8] : ( ~ (v8 = 0) & vtcheck(v1, v3, v0) = v8))
% 12.37/3.42 | (70) vsubst(all_0_7_7, all_0_6_6, all_0_2_2) = all_0_1_1
% 12.37/3.42 | (71) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vgetSomeExp(v0) = v1) | ~ (vsomeExp(v2) = v0))
% 12.37/3.42 | (72) ~ (all_0_0_0 = 0)
% 12.37/3.42 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (vtcheck(v2, v0, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v8 = v1 & v7 = v0 & varrow(v5, v6) = v1 & vtcheck(v9, v4, v6) = 0 & vbind(v3, v5, v2) = v9 & vabs(v3, v5, v4) = v0) | (v9 = 0 & v8 = 0 & v6 = v0 & varrow(v5, v1) = v7 & vtcheck(v2, v4, v5) = 0 & vtcheck(v2, v3, v7) = 0 & vapp(v3, v4) = v0) | (v6 = v3 & v5 = v0 & vlookup(v4, v2) = v3 & vsomeType(v1) = v3 & vvar(v4) = v0)))
% 12.37/3.42 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (visValue(v2) = 0) | ~ (vapp(v0, v1) = v2))
% 12.37/3.42 | (75) ! [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)))
% 12.37/3.42 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (vtcheck(v7, v4, v5) = 0) | ~ (vbind(v0, v2, v6) = v7) | ~ (vbind(v0, v1, v3) = v6) | ? [v8] : (vtcheck(v8, v4, v5) = 0 & vbind(v0, v2, v3) = v8))
% 12.37/3.42 | (77) vtcheck(all_0_3_3, all_0_2_2, all_0_4_4) = 0
% 12.37/3.42 | (78) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeExp(v1) = v2) | ~ (vsomeExp(v0) = v2))
% 12.37/3.42 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v3 = v1 | ~ (visFreeVar(v1, v4) = 0) | ~ (visFreeVar(v1, v2) = v5) | ~ (vabs(v3, v0, v4) = v2))
% 12.37/3.42 | (80) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~ (vsomeType(v2) = v0))
% 12.37/3.42 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (vapp(v0, v1) = v3) | ~ (vapp(v0, v1) = v2))
% 12.37/3.42 | (82) ! [v0] : ! [v1] : (v1 = vnoType | ~ (vlookup(v0, vempty) = v1))
% 12.37/3.42 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (visFreeVar(v0, v3) = v4) | ~ (visFreeVar(v0, v2) = 0) | ~ (visFreeVar(v0, v1) = v5) | ? [v6] : ( ~ (v6 = v1) & vapp(v2, v3) = v6))
% 12.37/3.42 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (varrow(v3, v2) = v1) | ~ (varrow(v3, v2) = v0))
% 12.37/3.42 | (85) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vvar(v1) = v2) | ~ (vvar(v0) = v2))
% 12.37/3.42 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vtcheck(v5, v3, v4) = v6) | ~ (vbind(v0, v1, v2) = v5) | ? [v7] : ? [v8] : (vtcheck(v2, v3, v4) = v8 & vlookup(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = vnoType))))
% 12.37/3.42 | (87) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (visValue(v2) = v1) | ~ (visValue(v2) = v0))
% 12.37/3.42 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0))
% 12.37/3.42 | (89) ! [v0] : ! [v1] : ! [v2] : ~ (vbind(v0, v1, v2) = vempty)
% 12.37/3.42 | (90) ! [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)))
% 12.37/3.42 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v3 | v5 = v0 | ~ (vsubst(v5, v8, v7) = v9) | ~ (vsubst(v0, v1, v10) = v11) | ~ (vsubst(v0, v1, v2) = v3) | ~ (vabs(v6, v4, v9) = v10) | ~ (vvar(v6) = v8) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (vgensym(v16) = v17 & visFreeVar(v5, v1) = v13 & vapp(v14, v15) = v16 & vapp(v1, v7) = v14 & vabs(v5, v4, v7) = v12 & vvar(v0) = v15 & ( ~ (v17 = v6) | ~ (v13 = 0) | ~ (v12 = v2))))
% 12.37/3.42 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v2 = v0 | ~ (vtcheck(v8, v5, v6) = v9) | ~ (vbind(v2, v3, v4) = v7) | ~ (vbind(v0, v1, v7) = v8) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = 0) & vtcheck(v11, v5, v6) = v12 & vbind(v2, v3, v10) = v11 & vbind(v0, v1, v4) = v10))
% 12.37/3.42 | (93) ~ (visSomeType(vnoType) = 0)
% 12.37/3.42 | (94) ! [v0] : ! [v1] : ( ~ (visValue(v1) = 0) | ~ (vvar(v0) = v1))
% 12.37/3.42 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (vreduce(v1) = v2) | ~ (vreduce(v0) = v3) | ~ (vgetSomeExp(v3) = v5) | ~ (vapp(v5, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v10 = v0 & vabs(v7, v8, v9) = v0) | (visSomeExp(v3) = v8 & vsomeExp(v6) = v9 & vapp(v0, v4) = v7 & ( ~ (v8 = 0) | ~ (v7 = v1) | v9 = v2))))
% 12.37/3.42 | (96) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0))
% 12.37/3.42 | (97) ~ (visSomeExp(vnoExp) = 0)
% 12.37/3.42 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (visFreeVar(v0, v3) = v5) | ~ (visFreeVar(v0, v2) = v4) | ~ (visFreeVar(v0, v1) = 0) | ? [v6] : ( ~ (v6 = v1) & vapp(v2, v3) = v6))
% 12.37/3.42 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~ (vapp(v3, v2) = v0))
% 12.37/3.42 | (100) ! [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))
% 12.37/3.42 |
% 12.37/3.43 | Instantiating formula (9) with all_0_1_1, all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms vsubst(all_0_7_7, all_0_6_6, all_0_2_2) = all_0_1_1, yields:
% 12.37/3.43 | (101) all_0_1_1 = all_0_6_6 | ~ (vvar(all_0_7_7) = all_0_2_2)
% 12.37/3.43 |
% 12.37/3.43 | Instantiating formula (23) with all_0_5_5, all_0_1_1, all_0_2_2, all_0_7_7, all_0_6_6 and discharging atoms vsubst(all_0_7_7, all_0_6_6, all_0_2_2) = all_0_1_1, vvar(all_0_5_5) = all_0_2_2, yields:
% 12.37/3.43 | (102) all_0_1_1 = all_0_2_2 | all_0_5_5 = all_0_7_7
% 12.37/3.43 |
% 12.37/3.43 | Instantiating formula (73) with all_0_3_3, all_0_4_4, all_0_2_2 and discharging atoms vtcheck(all_0_3_3, all_0_2_2, all_0_4_4) = 0, yields:
% 12.37/3.43 | (103) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v5 = all_0_4_4 & v4 = all_0_2_2 & varrow(v2, v3) = all_0_4_4 & vtcheck(v6, v1, v3) = 0 & vbind(v0, v2, all_0_3_3) = v6 & vabs(v0, v2, v1) = all_0_2_2) | (v6 = 0 & v5 = 0 & v3 = all_0_2_2 & varrow(v2, all_0_4_4) = v4 & vtcheck(all_0_3_3, v1, v2) = 0 & vtcheck(all_0_3_3, v0, v4) = 0 & vapp(v0, v1) = all_0_2_2) | (v3 = v0 & v2 = all_0_2_2 & vlookup(v1, all_0_3_3) = v0 & vsomeType(all_0_4_4) = v0 & vvar(v1) = all_0_2_2))
% 12.37/3.43 |
% 12.37/3.43 | Instantiating formula (67) with all_0_3_3, all_0_4_4, all_0_2_2, all_0_8_8, all_0_9_9, all_0_7_7 and discharging atoms vtcheck(all_0_3_3, all_0_2_2, all_0_4_4) = 0, vbind(all_0_7_7, all_0_9_9, all_0_8_8) = all_0_3_3, yields:
% 12.37/3.43 | (104) ? [v0] : ? [v1] : (vtcheck(all_0_8_8, all_0_2_2, all_0_4_4) = v1 & visFreeVar(all_0_7_7, all_0_2_2) = v0 & (v1 = 0 | v0 = 0))
% 12.37/3.43 |
% 12.37/3.43 | Instantiating formula (47) with all_0_0_0, all_0_2_2, all_0_4_4, all_0_5_5, all_0_8_8 and discharging atoms vvar(all_0_5_5) = all_0_2_2, yields:
% 12.37/3.43 | (105) all_0_0_0 = 0 | ~ (vtcheck(all_0_8_8, all_0_2_2, all_0_4_4) = all_0_0_0) | ? [v0] : ? [v1] : ( ~ (v1 = v0) & vlookup(all_0_5_5, all_0_8_8) = v0 & vsomeType(all_0_4_4) = v1)
% 12.37/3.43 |
% 12.37/3.43 | Instantiating (104) with all_16_0_10, all_16_1_11 yields:
% 12.37/3.43 | (106) vtcheck(all_0_8_8, all_0_2_2, all_0_4_4) = all_16_0_10 & visFreeVar(all_0_7_7, all_0_2_2) = all_16_1_11 & (all_16_0_10 = 0 | all_16_1_11 = 0)
% 12.37/3.43 |
% 12.37/3.43 | Applying alpha-rule on (106) yields:
% 12.37/3.43 | (107) vtcheck(all_0_8_8, all_0_2_2, all_0_4_4) = all_16_0_10
% 12.37/3.43 | (108) visFreeVar(all_0_7_7, all_0_2_2) = all_16_1_11
% 12.37/3.43 | (109) all_16_0_10 = 0 | all_16_1_11 = 0
% 12.37/3.43 |
% 12.37/3.43 | Instantiating (103) with all_19_0_20, all_19_1_21, all_19_2_22, all_19_3_23, all_19_4_24, all_19_5_25, all_19_6_26, all_19_7_27 yields:
% 12.37/3.43 | (110) (all_19_0_20 = 0 & all_19_2_22 = all_0_4_4 & all_19_3_23 = all_0_2_2 & varrow(all_19_5_25, all_19_4_24) = all_0_4_4 & vtcheck(all_19_1_21, all_19_6_26, all_19_4_24) = 0 & vbind(all_19_7_27, all_19_5_25, all_0_3_3) = all_19_1_21 & vabs(all_19_7_27, all_19_5_25, all_19_6_26) = all_0_2_2) | (all_19_1_21 = 0 & all_19_2_22 = 0 & all_19_4_24 = all_0_2_2 & varrow(all_19_5_25, all_0_4_4) = all_19_3_23 & vtcheck(all_0_3_3, all_19_6_26, all_19_5_25) = 0 & vtcheck(all_0_3_3, all_19_7_27, all_19_3_23) = 0 & vapp(all_19_7_27, all_19_6_26) = all_0_2_2) | (all_19_4_24 = all_19_7_27 & all_19_5_25 = all_0_2_2 & vlookup(all_19_6_26, all_0_3_3) = all_19_7_27 & vsomeType(all_0_4_4) = all_19_7_27 & vvar(all_19_6_26) = all_0_2_2)
% 12.37/3.43 |
% 12.37/3.43 | Instantiating formula (57) with all_0_8_8, all_0_2_2, all_0_4_4, all_16_0_10, 0 and discharging atoms vtcheck(all_0_8_8, all_0_2_2, all_0_4_4) = all_16_0_10, yields:
% 12.37/3.43 | (111) all_16_0_10 = 0 | ~ (vtcheck(all_0_8_8, all_0_2_2, all_0_4_4) = 0)
% 12.37/3.43 |
% 12.37/3.43 | Instantiating formula (57) with all_0_8_8, all_0_2_2, all_0_4_4, all_16_0_10, all_0_0_0 and discharging atoms vtcheck(all_0_8_8, all_0_2_2, all_0_4_4) = all_16_0_10, yields:
% 12.37/3.43 | (112) all_16_0_10 = all_0_0_0 | ~ (vtcheck(all_0_8_8, all_0_2_2, all_0_4_4) = all_0_0_0)
% 12.37/3.43 |
% 12.37/3.43 | Instantiating formula (18) with all_16_1_11, all_0_2_2, all_0_7_7 and discharging atoms visFreeVar(all_0_7_7, all_0_2_2) = all_16_1_11, yields:
% 12.37/3.43 | (113) all_16_1_11 = 0 | ~ (vvar(all_0_7_7) = all_0_2_2)
% 12.37/3.43 |
% 12.37/3.43 | Instantiating formula (48) with all_0_5_5, all_0_2_2, all_0_7_7 and discharging atoms vvar(all_0_5_5) = all_0_2_2, yields:
% 12.37/3.43 | (114) all_0_5_5 = all_0_7_7 | ~ (visFreeVar(all_0_7_7, all_0_2_2) = 0)
% 12.37/3.43 |
% 12.37/3.43 | Instantiating formula (47) with all_16_0_10, all_0_2_2, all_0_4_4, all_0_5_5, all_0_8_8 and discharging atoms vtcheck(all_0_8_8, all_0_2_2, all_0_4_4) = all_16_0_10, vvar(all_0_5_5) = all_0_2_2, yields:
% 12.37/3.43 | (115) all_16_0_10 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & vlookup(all_0_5_5, all_0_8_8) = v0 & vsomeType(all_0_4_4) = v1)
% 12.37/3.43 |
% 12.37/3.43 | Instantiating formula (7) with all_0_2_2, all_0_7_7 yields:
% 12.37/3.43 | (116) ~ (visFreeVar(all_0_7_7, all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = all_0_7_7) & vgensym(all_0_2_2) = v0)
% 12.37/3.43 |
% 12.37/3.43 +-Applying beta-rule and splitting (101), into two cases.
% 12.37/3.43 |-Branch one:
% 12.37/3.43 | (117) ~ (vvar(all_0_7_7) = all_0_2_2)
% 12.37/3.43 |
% 12.37/3.43 | Using (27) and (117) yields:
% 12.37/3.43 | (118) ~ (all_0_5_5 = all_0_7_7)
% 12.37/3.43 |
% 12.37/3.43 +-Applying beta-rule and splitting (102), into two cases.
% 12.37/3.43 |-Branch one:
% 12.37/3.43 | (119) all_0_1_1 = all_0_2_2
% 12.37/3.43 |
% 12.37/3.43 | From (119) and (5) follows:
% 12.37/3.43 | (120) vtcheck(all_0_8_8, all_0_2_2, all_0_4_4) = all_0_0_0
% 12.37/3.43 |
% 12.37/3.43 +-Applying beta-rule and splitting (112), into two cases.
% 12.37/3.43 |-Branch one:
% 12.37/3.43 | (121) ~ (vtcheck(all_0_8_8, all_0_2_2, all_0_4_4) = all_0_0_0)
% 12.37/3.43 |
% 12.37/3.43 | Using (120) and (121) yields:
% 12.37/3.43 | (122) $false
% 12.37/3.43 |
% 12.37/3.43 |-The branch is then unsatisfiable
% 12.37/3.43 |-Branch two:
% 12.37/3.43 | (120) vtcheck(all_0_8_8, all_0_2_2, all_0_4_4) = all_0_0_0
% 12.37/3.43 | (124) all_16_0_10 = all_0_0_0
% 12.37/3.43 |
% 12.37/3.43 +-Applying beta-rule and splitting (109), into two cases.
% 12.37/3.43 |-Branch one:
% 12.37/3.43 | (125) all_16_0_10 = 0
% 12.37/3.43 |
% 12.37/3.43 | Combining equations (125,124) yields a new equation:
% 12.37/3.43 | (126) all_0_0_0 = 0
% 12.37/3.43 |
% 12.37/3.43 | Equations (126) can reduce 72 to:
% 12.37/3.43 | (127) $false
% 12.37/3.43 |
% 12.37/3.43 |-The branch is then unsatisfiable
% 12.37/3.43 |-Branch two:
% 12.37/3.43 | (128) ~ (all_16_0_10 = 0)
% 12.37/3.43 | (129) all_16_1_11 = 0
% 12.37/3.43 |
% 12.37/3.43 | From (129) and (108) follows:
% 12.37/3.43 | (130) visFreeVar(all_0_7_7, all_0_2_2) = 0
% 12.37/3.43 |
% 12.37/3.43 +-Applying beta-rule and splitting (114), into two cases.
% 12.37/3.43 |-Branch one:
% 12.37/3.43 | (131) ~ (visFreeVar(all_0_7_7, all_0_2_2) = 0)
% 12.37/3.43 |
% 12.37/3.43 | Using (130) and (131) yields:
% 12.37/3.43 | (122) $false
% 12.37/3.43 |
% 12.37/3.43 |-The branch is then unsatisfiable
% 12.37/3.43 |-Branch two:
% 12.37/3.43 | (130) visFreeVar(all_0_7_7, all_0_2_2) = 0
% 12.37/3.43 | (134) all_0_5_5 = all_0_7_7
% 12.37/3.43 |
% 12.37/3.43 | Equations (134) can reduce 118 to:
% 12.37/3.43 | (127) $false
% 12.37/3.43 |
% 12.37/3.43 |-The branch is then unsatisfiable
% 12.37/3.43 |-Branch two:
% 12.37/3.43 | (136) ~ (all_0_1_1 = all_0_2_2)
% 12.37/3.43 | (134) all_0_5_5 = all_0_7_7
% 12.37/3.43 |
% 12.37/3.43 | Equations (134) can reduce 118 to:
% 12.37/3.43 | (127) $false
% 12.37/3.43 |
% 12.37/3.43 |-The branch is then unsatisfiable
% 12.37/3.43 |-Branch two:
% 12.37/3.43 | (139) vvar(all_0_7_7) = all_0_2_2
% 12.37/3.43 | (140) all_0_1_1 = all_0_6_6
% 12.37/3.43 |
% 12.37/3.43 | From (140) and (5) follows:
% 12.37/3.43 | (141) vtcheck(all_0_8_8, all_0_6_6, all_0_4_4) = all_0_0_0
% 12.37/3.43 |
% 12.37/3.43 +-Applying beta-rule and splitting (113), into two cases.
% 12.37/3.43 |-Branch one:
% 12.37/3.43 | (117) ~ (vvar(all_0_7_7) = all_0_2_2)
% 12.37/3.43 |
% 12.37/3.43 | Using (139) and (117) yields:
% 12.37/3.43 | (122) $false
% 12.37/3.43 |
% 12.37/3.43 |-The branch is then unsatisfiable
% 12.37/3.43 |-Branch two:
% 12.37/3.43 | (139) vvar(all_0_7_7) = all_0_2_2
% 12.37/3.43 | (129) all_16_1_11 = 0
% 12.37/3.43 |
% 12.37/3.43 | From (129) and (108) follows:
% 12.37/3.43 | (130) visFreeVar(all_0_7_7, all_0_2_2) = 0
% 12.37/3.43 |
% 12.37/3.43 +-Applying beta-rule and splitting (114), into two cases.
% 12.37/3.43 |-Branch one:
% 12.37/3.43 | (131) ~ (visFreeVar(all_0_7_7, all_0_2_2) = 0)
% 12.37/3.43 |
% 12.37/3.43 | Using (130) and (131) yields:
% 12.37/3.43 | (122) $false
% 12.37/3.43 |
% 12.37/3.43 |-The branch is then unsatisfiable
% 12.37/3.43 |-Branch two:
% 12.37/3.43 | (130) visFreeVar(all_0_7_7, all_0_2_2) = 0
% 12.37/3.43 | (134) all_0_5_5 = all_0_7_7
% 12.37/3.43 |
% 12.37/3.43 | From (134) and (27) follows:
% 12.37/3.43 | (139) vvar(all_0_7_7) = all_0_2_2
% 12.37/3.43 |
% 12.37/3.43 +-Applying beta-rule and splitting (116), into two cases.
% 12.37/3.43 |-Branch one:
% 12.37/3.43 | (131) ~ (visFreeVar(all_0_7_7, all_0_2_2) = 0)
% 12.37/3.43 |
% 12.37/3.43 | Using (130) and (131) yields:
% 12.37/3.43 | (122) $false
% 12.37/3.43 |
% 12.37/3.43 |-The branch is then unsatisfiable
% 12.37/3.43 |-Branch two:
% 12.37/3.43 | (130) visFreeVar(all_0_7_7, all_0_2_2) = 0
% 12.37/3.43 | (155) ? [v0] : ( ~ (v0 = all_0_7_7) & vgensym(all_0_2_2) = v0)
% 12.37/3.43 |
% 12.37/3.44 | Instantiating formula (57) with all_0_8_8, all_0_6_6, all_0_9_9, all_0_0_0, 0 and discharging atoms vtcheck(all_0_8_8, all_0_6_6, all_0_9_9) = 0, yields:
% 12.37/3.44 | (156) all_0_0_0 = 0 | ~ (vtcheck(all_0_8_8, all_0_6_6, all_0_9_9) = all_0_0_0)
% 12.37/3.44 |
% 12.37/3.44 +-Applying beta-rule and splitting (105), into two cases.
% 12.37/3.44 |-Branch one:
% 12.37/3.44 | (121) ~ (vtcheck(all_0_8_8, all_0_2_2, all_0_4_4) = all_0_0_0)
% 12.37/3.44 |
% 12.37/3.44 | Using (107) and (121) yields:
% 12.37/3.44 | (158) ~ (all_16_0_10 = all_0_0_0)
% 12.37/3.44 |
% 12.37/3.44 +-Applying beta-rule and splitting (111), into two cases.
% 12.37/3.44 |-Branch one:
% 12.37/3.44 | (159) ~ (vtcheck(all_0_8_8, all_0_2_2, all_0_4_4) = 0)
% 12.37/3.44 |
% 12.37/3.44 | Using (107) and (159) yields:
% 12.37/3.44 | (128) ~ (all_16_0_10 = 0)
% 12.37/3.44 |
% 12.37/3.44 +-Applying beta-rule and splitting (115), into two cases.
% 12.37/3.44 |-Branch one:
% 12.37/3.44 | (125) all_16_0_10 = 0
% 12.37/3.44 |
% 12.37/3.44 | Equations (125) can reduce 128 to:
% 12.37/3.44 | (127) $false
% 12.37/3.44 |
% 12.37/3.44 |-The branch is then unsatisfiable
% 12.37/3.44 |-Branch two:
% 12.37/3.44 | (128) ~ (all_16_0_10 = 0)
% 12.37/3.44 | (164) ? [v0] : ? [v1] : ( ~ (v1 = v0) & vlookup(all_0_5_5, all_0_8_8) = v0 & vsomeType(all_0_4_4) = v1)
% 12.37/3.44 |
% 12.37/3.44 | Instantiating (164) with all_86_0_45, all_86_1_46 yields:
% 12.37/3.44 | (165) ~ (all_86_0_45 = all_86_1_46) & vlookup(all_0_5_5, all_0_8_8) = all_86_1_46 & vsomeType(all_0_4_4) = all_86_0_45
% 12.37/3.44 |
% 12.37/3.44 | Applying alpha-rule on (165) yields:
% 12.37/3.44 | (166) ~ (all_86_0_45 = all_86_1_46)
% 12.37/3.44 | (167) vlookup(all_0_5_5, all_0_8_8) = all_86_1_46
% 12.37/3.44 | (168) vsomeType(all_0_4_4) = all_86_0_45
% 12.37/3.44 |
% 12.37/3.44 +-Applying beta-rule and splitting (110), into two cases.
% 12.37/3.44 |-Branch one:
% 12.37/3.44 | (169) (all_19_0_20 = 0 & all_19_2_22 = all_0_4_4 & all_19_3_23 = all_0_2_2 & varrow(all_19_5_25, all_19_4_24) = all_0_4_4 & vtcheck(all_19_1_21, all_19_6_26, all_19_4_24) = 0 & vbind(all_19_7_27, all_19_5_25, all_0_3_3) = all_19_1_21 & vabs(all_19_7_27, all_19_5_25, all_19_6_26) = all_0_2_2) | (all_19_1_21 = 0 & all_19_2_22 = 0 & all_19_4_24 = all_0_2_2 & varrow(all_19_5_25, all_0_4_4) = all_19_3_23 & vtcheck(all_0_3_3, all_19_6_26, all_19_5_25) = 0 & vtcheck(all_0_3_3, all_19_7_27, all_19_3_23) = 0 & vapp(all_19_7_27, all_19_6_26) = all_0_2_2)
% 12.37/3.44 |
% 12.37/3.44 +-Applying beta-rule and splitting (169), into two cases.
% 12.37/3.44 |-Branch one:
% 12.37/3.44 | (170) all_19_0_20 = 0 & all_19_2_22 = all_0_4_4 & all_19_3_23 = all_0_2_2 & varrow(all_19_5_25, all_19_4_24) = all_0_4_4 & vtcheck(all_19_1_21, all_19_6_26, all_19_4_24) = 0 & vbind(all_19_7_27, all_19_5_25, all_0_3_3) = all_19_1_21 & vabs(all_19_7_27, all_19_5_25, all_19_6_26) = all_0_2_2
% 12.37/3.44 |
% 12.37/3.44 | Applying alpha-rule on (170) yields:
% 12.37/3.44 | (171) all_19_3_23 = all_0_2_2
% 12.37/3.44 | (172) vbind(all_19_7_27, all_19_5_25, all_0_3_3) = all_19_1_21
% 12.37/3.44 | (173) varrow(all_19_5_25, all_19_4_24) = all_0_4_4
% 12.37/3.44 | (174) vabs(all_19_7_27, all_19_5_25, all_19_6_26) = all_0_2_2
% 12.37/3.44 | (175) vtcheck(all_19_1_21, all_19_6_26, all_19_4_24) = 0
% 12.37/3.44 | (176) all_19_2_22 = all_0_4_4
% 12.37/3.44 | (177) all_19_0_20 = 0
% 12.37/3.44 |
% 12.37/3.44 | Instantiating formula (22) with all_0_2_2, all_19_6_26, all_19_5_25, all_19_7_27, all_0_7_7 and discharging atoms vabs(all_19_7_27, all_19_5_25, all_19_6_26) = all_0_2_2, vvar(all_0_7_7) = all_0_2_2, yields:
% 12.37/3.44 | (122) $false
% 12.37/3.44 |
% 12.37/3.44 |-The branch is then unsatisfiable
% 12.37/3.44 |-Branch two:
% 12.37/3.44 | (179) all_19_1_21 = 0 & all_19_2_22 = 0 & all_19_4_24 = all_0_2_2 & varrow(all_19_5_25, all_0_4_4) = all_19_3_23 & vtcheck(all_0_3_3, all_19_6_26, all_19_5_25) = 0 & vtcheck(all_0_3_3, all_19_7_27, all_19_3_23) = 0 & vapp(all_19_7_27, all_19_6_26) = all_0_2_2
% 12.37/3.44 |
% 12.37/3.44 | Applying alpha-rule on (179) yields:
% 12.37/3.44 | (180) vapp(all_19_7_27, all_19_6_26) = all_0_2_2
% 12.37/3.44 | (181) vtcheck(all_0_3_3, all_19_6_26, all_19_5_25) = 0
% 12.37/3.44 | (182) varrow(all_19_5_25, all_0_4_4) = all_19_3_23
% 12.37/3.44 | (183) all_19_1_21 = 0
% 12.37/3.44 | (184) vtcheck(all_0_3_3, all_19_7_27, all_19_3_23) = 0
% 12.37/3.44 | (185) all_19_4_24 = all_0_2_2
% 12.37/3.44 | (186) all_19_2_22 = 0
% 12.37/3.44 |
% 12.37/3.44 | Instantiating formula (46) with all_0_2_2, all_19_6_26, all_19_7_27, all_0_7_7 and discharging atoms vapp(all_19_7_27, all_19_6_26) = all_0_2_2, vvar(all_0_7_7) = all_0_2_2, yields:
% 12.37/3.44 | (122) $false
% 12.37/3.44 |
% 12.37/3.44 |-The branch is then unsatisfiable
% 12.37/3.44 |-Branch two:
% 12.37/3.44 | (188) all_19_4_24 = all_19_7_27 & all_19_5_25 = all_0_2_2 & vlookup(all_19_6_26, all_0_3_3) = all_19_7_27 & vsomeType(all_0_4_4) = all_19_7_27 & vvar(all_19_6_26) = all_0_2_2
% 12.37/3.44 |
% 12.37/3.44 | Applying alpha-rule on (188) yields:
% 12.37/3.44 | (189) all_19_4_24 = all_19_7_27
% 12.37/3.44 | (190) all_19_5_25 = all_0_2_2
% 12.37/3.44 | (191) vvar(all_19_6_26) = all_0_2_2
% 12.37/3.44 | (192) vsomeType(all_0_4_4) = all_19_7_27
% 12.37/3.44 | (193) vlookup(all_19_6_26, all_0_3_3) = all_19_7_27
% 12.37/3.44 |
% 12.37/3.44 | Instantiating formula (64) with all_19_7_27, all_86_0_45, all_0_4_4 and discharging atoms vsomeType(all_0_4_4) = all_86_0_45, vsomeType(all_0_4_4) = all_19_7_27, yields:
% 12.37/3.44 | (194) all_86_0_45 = all_19_7_27
% 12.37/3.44 |
% 12.37/3.44 | Instantiating formula (48) with all_19_6_26, all_0_2_2, all_0_7_7 and discharging atoms visFreeVar(all_0_7_7, all_0_2_2) = 0, vvar(all_19_6_26) = all_0_2_2, yields:
% 12.37/3.44 | (195) all_19_6_26 = all_0_7_7
% 12.37/3.44 |
% 12.37/3.44 | From (195) and (193) follows:
% 12.37/3.44 | (196) vlookup(all_0_7_7, all_0_3_3) = all_19_7_27
% 12.37/3.44 |
% 12.37/3.44 | From (194) and (168) follows:
% 12.48/3.44 | (192) vsomeType(all_0_4_4) = all_19_7_27
% 12.48/3.44 |
% 12.48/3.44 | Instantiating formula (12) with all_0_9_9, all_19_7_27, all_0_3_3, all_0_7_7, all_0_8_8 and discharging atoms vlookup(all_0_7_7, all_0_3_3) = all_19_7_27, vbind(all_0_7_7, all_0_9_9, all_0_8_8) = all_0_3_3, yields:
% 12.48/3.44 | (198) vsomeType(all_0_9_9) = all_19_7_27
% 12.48/3.44 |
% 12.48/3.44 | Instantiating formula (32) with all_19_7_27, all_0_9_9, all_0_4_4 and discharging atoms vsomeType(all_0_4_4) = all_19_7_27, vsomeType(all_0_9_9) = all_19_7_27, yields:
% 12.48/3.44 | (199) all_0_4_4 = all_0_9_9
% 12.48/3.44 |
% 12.48/3.44 | From (199) and (141) follows:
% 12.48/3.44 | (200) vtcheck(all_0_8_8, all_0_6_6, all_0_9_9) = all_0_0_0
% 12.48/3.44 |
% 12.48/3.44 +-Applying beta-rule and splitting (156), into two cases.
% 12.48/3.44 |-Branch one:
% 12.48/3.44 | (201) ~ (vtcheck(all_0_8_8, all_0_6_6, all_0_9_9) = all_0_0_0)
% 12.48/3.44 |
% 12.48/3.44 | Using (200) and (201) yields:
% 12.48/3.44 | (122) $false
% 12.48/3.44 |
% 12.48/3.44 |-The branch is then unsatisfiable
% 12.48/3.44 |-Branch two:
% 12.48/3.44 | (200) vtcheck(all_0_8_8, all_0_6_6, all_0_9_9) = all_0_0_0
% 12.48/3.44 | (126) all_0_0_0 = 0
% 12.48/3.44 |
% 12.48/3.44 | Equations (126) can reduce 72 to:
% 12.48/3.44 | (127) $false
% 12.48/3.44 |
% 12.48/3.44 |-The branch is then unsatisfiable
% 12.48/3.44 |-Branch two:
% 12.48/3.44 | (206) vtcheck(all_0_8_8, all_0_2_2, all_0_4_4) = 0
% 12.48/3.44 | (125) all_16_0_10 = 0
% 12.48/3.44 |
% 12.48/3.44 | Equations (125) can reduce 158 to:
% 12.48/3.44 | (208) ~ (all_0_0_0 = 0)
% 12.48/3.44 |
% 12.48/3.44 | Simplifying 208 yields:
% 12.48/3.44 | (72) ~ (all_0_0_0 = 0)
% 12.48/3.44 |
% 12.48/3.44 +-Applying beta-rule and splitting (110), into two cases.
% 12.48/3.44 |-Branch one:
% 12.48/3.44 | (169) (all_19_0_20 = 0 & all_19_2_22 = all_0_4_4 & all_19_3_23 = all_0_2_2 & varrow(all_19_5_25, all_19_4_24) = all_0_4_4 & vtcheck(all_19_1_21, all_19_6_26, all_19_4_24) = 0 & vbind(all_19_7_27, all_19_5_25, all_0_3_3) = all_19_1_21 & vabs(all_19_7_27, all_19_5_25, all_19_6_26) = all_0_2_2) | (all_19_1_21 = 0 & all_19_2_22 = 0 & all_19_4_24 = all_0_2_2 & varrow(all_19_5_25, all_0_4_4) = all_19_3_23 & vtcheck(all_0_3_3, all_19_6_26, all_19_5_25) = 0 & vtcheck(all_0_3_3, all_19_7_27, all_19_3_23) = 0 & vapp(all_19_7_27, all_19_6_26) = all_0_2_2)
% 12.48/3.44 |
% 12.48/3.44 +-Applying beta-rule and splitting (169), into two cases.
% 12.48/3.44 |-Branch one:
% 12.48/3.44 | (170) all_19_0_20 = 0 & all_19_2_22 = all_0_4_4 & all_19_3_23 = all_0_2_2 & varrow(all_19_5_25, all_19_4_24) = all_0_4_4 & vtcheck(all_19_1_21, all_19_6_26, all_19_4_24) = 0 & vbind(all_19_7_27, all_19_5_25, all_0_3_3) = all_19_1_21 & vabs(all_19_7_27, all_19_5_25, all_19_6_26) = all_0_2_2
% 12.48/3.44 |
% 12.48/3.44 | Applying alpha-rule on (170) yields:
% 12.48/3.44 | (171) all_19_3_23 = all_0_2_2
% 12.48/3.44 | (172) vbind(all_19_7_27, all_19_5_25, all_0_3_3) = all_19_1_21
% 12.48/3.44 | (173) varrow(all_19_5_25, all_19_4_24) = all_0_4_4
% 12.48/3.44 | (174) vabs(all_19_7_27, all_19_5_25, all_19_6_26) = all_0_2_2
% 12.48/3.44 | (175) vtcheck(all_19_1_21, all_19_6_26, all_19_4_24) = 0
% 12.48/3.44 | (176) all_19_2_22 = all_0_4_4
% 12.48/3.44 | (177) all_19_0_20 = 0
% 12.48/3.44 |
% 12.48/3.44 | Instantiating formula (22) with all_0_2_2, all_19_6_26, all_19_5_25, all_19_7_27, all_0_7_7 and discharging atoms vabs(all_19_7_27, all_19_5_25, all_19_6_26) = all_0_2_2, vvar(all_0_7_7) = all_0_2_2, yields:
% 12.48/3.44 | (122) $false
% 12.48/3.44 |
% 12.48/3.44 |-The branch is then unsatisfiable
% 12.48/3.44 |-Branch two:
% 12.48/3.44 | (179) all_19_1_21 = 0 & all_19_2_22 = 0 & all_19_4_24 = all_0_2_2 & varrow(all_19_5_25, all_0_4_4) = all_19_3_23 & vtcheck(all_0_3_3, all_19_6_26, all_19_5_25) = 0 & vtcheck(all_0_3_3, all_19_7_27, all_19_3_23) = 0 & vapp(all_19_7_27, all_19_6_26) = all_0_2_2
% 12.48/3.44 |
% 12.48/3.44 | Applying alpha-rule on (179) yields:
% 12.48/3.44 | (180) vapp(all_19_7_27, all_19_6_26) = all_0_2_2
% 12.48/3.44 | (181) vtcheck(all_0_3_3, all_19_6_26, all_19_5_25) = 0
% 12.48/3.44 | (182) varrow(all_19_5_25, all_0_4_4) = all_19_3_23
% 12.48/3.44 | (183) all_19_1_21 = 0
% 12.48/3.44 | (184) vtcheck(all_0_3_3, all_19_7_27, all_19_3_23) = 0
% 12.48/3.44 | (185) all_19_4_24 = all_0_2_2
% 12.48/3.44 | (186) all_19_2_22 = 0
% 12.48/3.44 |
% 12.48/3.44 | Instantiating formula (46) with all_0_2_2, all_19_6_26, all_19_7_27, all_0_7_7 and discharging atoms vapp(all_19_7_27, all_19_6_26) = all_0_2_2, vvar(all_0_7_7) = all_0_2_2, yields:
% 12.48/3.44 | (122) $false
% 12.48/3.44 |
% 12.48/3.44 |-The branch is then unsatisfiable
% 12.48/3.44 |-Branch two:
% 12.48/3.44 | (188) all_19_4_24 = all_19_7_27 & all_19_5_25 = all_0_2_2 & vlookup(all_19_6_26, all_0_3_3) = all_19_7_27 & vsomeType(all_0_4_4) = all_19_7_27 & vvar(all_19_6_26) = all_0_2_2
% 12.48/3.44 |
% 12.48/3.44 | Applying alpha-rule on (188) yields:
% 12.48/3.44 | (189) all_19_4_24 = all_19_7_27
% 12.48/3.44 | (190) all_19_5_25 = all_0_2_2
% 12.48/3.44 | (191) vvar(all_19_6_26) = all_0_2_2
% 12.48/3.44 | (192) vsomeType(all_0_4_4) = all_19_7_27
% 12.48/3.44 | (193) vlookup(all_19_6_26, all_0_3_3) = all_19_7_27
% 12.48/3.44 |
% 12.48/3.44 | Instantiating formula (48) with all_19_6_26, all_0_2_2, all_0_7_7 and discharging atoms visFreeVar(all_0_7_7, all_0_2_2) = 0, vvar(all_19_6_26) = all_0_2_2, yields:
% 12.48/3.44 | (195) all_19_6_26 = all_0_7_7
% 12.48/3.44 |
% 12.48/3.44 | From (195) and (193) follows:
% 12.48/3.44 | (196) vlookup(all_0_7_7, all_0_3_3) = all_19_7_27
% 12.48/3.44 |
% 12.48/3.44 | Instantiating formula (12) with all_0_9_9, all_19_7_27, all_0_3_3, all_0_7_7, all_0_8_8 and discharging atoms vlookup(all_0_7_7, all_0_3_3) = all_19_7_27, vbind(all_0_7_7, all_0_9_9, all_0_8_8) = all_0_3_3, yields:
% 12.48/3.44 | (198) vsomeType(all_0_9_9) = all_19_7_27
% 12.48/3.44 |
% 12.48/3.44 | Instantiating formula (32) with all_19_7_27, all_0_9_9, all_0_4_4 and discharging atoms vsomeType(all_0_4_4) = all_19_7_27, vsomeType(all_0_9_9) = all_19_7_27, yields:
% 12.48/3.44 | (199) all_0_4_4 = all_0_9_9
% 12.48/3.44 |
% 12.48/3.44 | From (199) and (141) follows:
% 12.48/3.44 | (200) vtcheck(all_0_8_8, all_0_6_6, all_0_9_9) = all_0_0_0
% 12.48/3.44 |
% 12.48/3.44 +-Applying beta-rule and splitting (156), into two cases.
% 12.48/3.44 |-Branch one:
% 12.48/3.44 | (201) ~ (vtcheck(all_0_8_8, all_0_6_6, all_0_9_9) = all_0_0_0)
% 12.48/3.44 |
% 12.48/3.44 | Using (200) and (201) yields:
% 12.48/3.44 | (122) $false
% 12.48/3.44 |
% 12.48/3.44 |-The branch is then unsatisfiable
% 12.48/3.44 |-Branch two:
% 12.48/3.44 | (200) vtcheck(all_0_8_8, all_0_6_6, all_0_9_9) = all_0_0_0
% 12.48/3.44 | (126) all_0_0_0 = 0
% 12.48/3.44 |
% 12.48/3.44 | Equations (126) can reduce 72 to:
% 12.48/3.44 | (127) $false
% 12.48/3.45 |
% 12.48/3.45 |-The branch is then unsatisfiable
% 12.48/3.45 |-Branch two:
% 12.48/3.45 | (120) vtcheck(all_0_8_8, all_0_2_2, all_0_4_4) = all_0_0_0
% 12.48/3.45 | (246) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & vlookup(all_0_5_5, all_0_8_8) = v0 & vsomeType(all_0_4_4) = v1)
% 12.48/3.45 |
% 12.48/3.45 +-Applying beta-rule and splitting (112), into two cases.
% 12.48/3.45 |-Branch one:
% 12.48/3.45 | (121) ~ (vtcheck(all_0_8_8, all_0_2_2, all_0_4_4) = all_0_0_0)
% 12.48/3.45 |
% 12.48/3.45 | Using (120) and (121) yields:
% 12.48/3.45 | (122) $false
% 12.48/3.45 |
% 12.48/3.45 |-The branch is then unsatisfiable
% 12.48/3.45 |-Branch two:
% 12.48/3.45 | (120) vtcheck(all_0_8_8, all_0_2_2, all_0_4_4) = all_0_0_0
% 12.48/3.45 | (124) all_16_0_10 = all_0_0_0
% 12.48/3.45 |
% 12.48/3.45 +-Applying beta-rule and splitting (115), into two cases.
% 12.48/3.45 |-Branch one:
% 12.48/3.45 | (125) all_16_0_10 = 0
% 12.48/3.45 |
% 12.48/3.45 | Combining equations (125,124) yields a new equation:
% 12.48/3.45 | (126) all_0_0_0 = 0
% 12.48/3.45 |
% 12.48/3.45 | Equations (126) can reduce 72 to:
% 12.48/3.45 | (127) $false
% 12.48/3.45 |
% 12.48/3.45 |-The branch is then unsatisfiable
% 12.48/3.45 |-Branch two:
% 12.48/3.45 | (128) ~ (all_16_0_10 = 0)
% 12.48/3.45 | (164) ? [v0] : ? [v1] : ( ~ (v1 = v0) & vlookup(all_0_5_5, all_0_8_8) = v0 & vsomeType(all_0_4_4) = v1)
% 12.48/3.45 |
% 12.48/3.45 | Instantiating (164) with all_68_0_117, all_68_1_118 yields:
% 12.48/3.45 | (256) ~ (all_68_0_117 = all_68_1_118) & vlookup(all_0_5_5, all_0_8_8) = all_68_1_118 & vsomeType(all_0_4_4) = all_68_0_117
% 12.48/3.45 |
% 12.48/3.45 | Applying alpha-rule on (256) yields:
% 12.48/3.45 | (257) ~ (all_68_0_117 = all_68_1_118)
% 12.48/3.45 | (258) vlookup(all_0_5_5, all_0_8_8) = all_68_1_118
% 12.48/3.45 | (259) vsomeType(all_0_4_4) = all_68_0_117
% 12.48/3.45 |
% 12.48/3.45 | Equations (124) can reduce 128 to:
% 12.48/3.45 | (72) ~ (all_0_0_0 = 0)
% 12.48/3.45 |
% 12.48/3.45 +-Applying beta-rule and splitting (246), into two cases.
% 12.48/3.45 |-Branch one:
% 12.48/3.45 | (126) all_0_0_0 = 0
% 12.48/3.45 |
% 12.48/3.45 | Equations (126) can reduce 72 to:
% 12.48/3.45 | (127) $false
% 12.48/3.45 |
% 12.48/3.45 |-The branch is then unsatisfiable
% 12.48/3.45 |-Branch two:
% 12.48/3.45 | (72) ~ (all_0_0_0 = 0)
% 12.48/3.45 | (164) ? [v0] : ? [v1] : ( ~ (v1 = v0) & vlookup(all_0_5_5, all_0_8_8) = v0 & vsomeType(all_0_4_4) = v1)
% 12.48/3.45 |
% 12.48/3.45 | Instantiating (164) with all_73_0_119, all_73_1_120 yields:
% 12.48/3.45 | (265) ~ (all_73_0_119 = all_73_1_120) & vlookup(all_0_5_5, all_0_8_8) = all_73_1_120 & vsomeType(all_0_4_4) = all_73_0_119
% 12.48/3.45 |
% 12.48/3.45 | Applying alpha-rule on (265) yields:
% 12.48/3.45 | (266) ~ (all_73_0_119 = all_73_1_120)
% 12.48/3.45 | (267) vlookup(all_0_5_5, all_0_8_8) = all_73_1_120
% 12.48/3.45 | (268) vsomeType(all_0_4_4) = all_73_0_119
% 12.48/3.45 |
% 12.48/3.45 | Instantiating formula (64) with all_68_0_117, all_73_0_119, all_0_4_4 and discharging atoms vsomeType(all_0_4_4) = all_73_0_119, vsomeType(all_0_4_4) = all_68_0_117, yields:
% 12.48/3.45 | (269) all_73_0_119 = all_68_0_117
% 12.48/3.45 |
% 12.48/3.45 | From (269) and (268) follows:
% 12.48/3.45 | (259) vsomeType(all_0_4_4) = all_68_0_117
% 12.48/3.45 |
% 12.48/3.45 +-Applying beta-rule and splitting (110), into two cases.
% 12.48/3.45 |-Branch one:
% 12.48/3.45 | (169) (all_19_0_20 = 0 & all_19_2_22 = all_0_4_4 & all_19_3_23 = all_0_2_2 & varrow(all_19_5_25, all_19_4_24) = all_0_4_4 & vtcheck(all_19_1_21, all_19_6_26, all_19_4_24) = 0 & vbind(all_19_7_27, all_19_5_25, all_0_3_3) = all_19_1_21 & vabs(all_19_7_27, all_19_5_25, all_19_6_26) = all_0_2_2) | (all_19_1_21 = 0 & all_19_2_22 = 0 & all_19_4_24 = all_0_2_2 & varrow(all_19_5_25, all_0_4_4) = all_19_3_23 & vtcheck(all_0_3_3, all_19_6_26, all_19_5_25) = 0 & vtcheck(all_0_3_3, all_19_7_27, all_19_3_23) = 0 & vapp(all_19_7_27, all_19_6_26) = all_0_2_2)
% 12.48/3.45 |
% 12.48/3.45 +-Applying beta-rule and splitting (169), into two cases.
% 12.48/3.45 |-Branch one:
% 12.48/3.45 | (170) all_19_0_20 = 0 & all_19_2_22 = all_0_4_4 & all_19_3_23 = all_0_2_2 & varrow(all_19_5_25, all_19_4_24) = all_0_4_4 & vtcheck(all_19_1_21, all_19_6_26, all_19_4_24) = 0 & vbind(all_19_7_27, all_19_5_25, all_0_3_3) = all_19_1_21 & vabs(all_19_7_27, all_19_5_25, all_19_6_26) = all_0_2_2
% 12.48/3.45 |
% 12.48/3.45 | Applying alpha-rule on (170) yields:
% 12.48/3.45 | (171) all_19_3_23 = all_0_2_2
% 12.48/3.45 | (172) vbind(all_19_7_27, all_19_5_25, all_0_3_3) = all_19_1_21
% 12.48/3.45 | (173) varrow(all_19_5_25, all_19_4_24) = all_0_4_4
% 12.48/3.45 | (174) vabs(all_19_7_27, all_19_5_25, all_19_6_26) = all_0_2_2
% 12.48/3.45 | (175) vtcheck(all_19_1_21, all_19_6_26, all_19_4_24) = 0
% 12.48/3.45 | (176) all_19_2_22 = all_0_4_4
% 12.48/3.45 | (177) all_19_0_20 = 0
% 12.48/3.45 |
% 12.48/3.45 | Instantiating formula (22) with all_0_2_2, all_19_6_26, all_19_5_25, all_19_7_27, all_0_7_7 and discharging atoms vabs(all_19_7_27, all_19_5_25, all_19_6_26) = all_0_2_2, vvar(all_0_7_7) = all_0_2_2, yields:
% 12.48/3.45 | (122) $false
% 12.48/3.45 |
% 12.48/3.45 |-The branch is then unsatisfiable
% 12.48/3.45 |-Branch two:
% 12.48/3.45 | (179) all_19_1_21 = 0 & all_19_2_22 = 0 & all_19_4_24 = all_0_2_2 & varrow(all_19_5_25, all_0_4_4) = all_19_3_23 & vtcheck(all_0_3_3, all_19_6_26, all_19_5_25) = 0 & vtcheck(all_0_3_3, all_19_7_27, all_19_3_23) = 0 & vapp(all_19_7_27, all_19_6_26) = all_0_2_2
% 12.48/3.45 |
% 12.48/3.45 | Applying alpha-rule on (179) yields:
% 12.48/3.45 | (180) vapp(all_19_7_27, all_19_6_26) = all_0_2_2
% 12.48/3.45 | (181) vtcheck(all_0_3_3, all_19_6_26, all_19_5_25) = 0
% 12.48/3.45 | (182) varrow(all_19_5_25, all_0_4_4) = all_19_3_23
% 12.48/3.45 | (183) all_19_1_21 = 0
% 12.48/3.45 | (184) vtcheck(all_0_3_3, all_19_7_27, all_19_3_23) = 0
% 12.48/3.45 | (185) all_19_4_24 = all_0_2_2
% 12.48/3.45 | (186) all_19_2_22 = 0
% 12.48/3.45 |
% 12.48/3.45 | Instantiating formula (46) with all_0_2_2, all_19_6_26, all_19_7_27, all_0_7_7 and discharging atoms vapp(all_19_7_27, all_19_6_26) = all_0_2_2, vvar(all_0_7_7) = all_0_2_2, yields:
% 12.48/3.45 | (122) $false
% 12.48/3.45 |
% 12.48/3.45 |-The branch is then unsatisfiable
% 12.48/3.45 |-Branch two:
% 12.48/3.45 | (188) all_19_4_24 = all_19_7_27 & all_19_5_25 = all_0_2_2 & vlookup(all_19_6_26, all_0_3_3) = all_19_7_27 & vsomeType(all_0_4_4) = all_19_7_27 & vvar(all_19_6_26) = all_0_2_2
% 12.48/3.45 |
% 12.48/3.45 | Applying alpha-rule on (188) yields:
% 12.48/3.45 | (189) all_19_4_24 = all_19_7_27
% 12.48/3.45 | (190) all_19_5_25 = all_0_2_2
% 12.48/3.45 | (191) vvar(all_19_6_26) = all_0_2_2
% 12.48/3.45 | (192) vsomeType(all_0_4_4) = all_19_7_27
% 12.48/3.45 | (193) vlookup(all_19_6_26, all_0_3_3) = all_19_7_27
% 12.48/3.45 |
% 12.48/3.45 | Instantiating formula (64) with all_19_7_27, all_68_0_117, all_0_4_4 and discharging atoms vsomeType(all_0_4_4) = all_68_0_117, vsomeType(all_0_4_4) = all_19_7_27, yields:
% 12.48/3.45 | (296) all_68_0_117 = all_19_7_27
% 12.48/3.45 |
% 12.48/3.45 | Instantiating formula (48) with all_19_6_26, all_0_2_2, all_0_7_7 and discharging atoms visFreeVar(all_0_7_7, all_0_2_2) = 0, vvar(all_19_6_26) = all_0_2_2, yields:
% 12.48/3.45 | (195) all_19_6_26 = all_0_7_7
% 12.48/3.45 |
% 12.48/3.45 | From (195) and (193) follows:
% 12.48/3.45 | (196) vlookup(all_0_7_7, all_0_3_3) = all_19_7_27
% 12.48/3.45 |
% 12.48/3.45 | From (296) and (259) follows:
% 12.48/3.45 | (192) vsomeType(all_0_4_4) = all_19_7_27
% 12.48/3.45 |
% 12.48/3.45 | Instantiating formula (12) with all_0_9_9, all_19_7_27, all_0_3_3, all_0_7_7, all_0_8_8 and discharging atoms vlookup(all_0_7_7, all_0_3_3) = all_19_7_27, vbind(all_0_7_7, all_0_9_9, all_0_8_8) = all_0_3_3, yields:
% 12.48/3.45 | (198) vsomeType(all_0_9_9) = all_19_7_27
% 12.48/3.45 |
% 12.48/3.45 | Instantiating formula (32) with all_19_7_27, all_0_9_9, all_0_4_4 and discharging atoms vsomeType(all_0_4_4) = all_19_7_27, vsomeType(all_0_9_9) = all_19_7_27, yields:
% 12.48/3.45 | (199) all_0_4_4 = all_0_9_9
% 12.48/3.45 |
% 12.48/3.45 | From (199) and (141) follows:
% 12.48/3.45 | (200) vtcheck(all_0_8_8, all_0_6_6, all_0_9_9) = all_0_0_0
% 12.48/3.45 |
% 12.48/3.45 +-Applying beta-rule and splitting (156), into two cases.
% 12.48/3.45 |-Branch one:
% 12.48/3.45 | (201) ~ (vtcheck(all_0_8_8, all_0_6_6, all_0_9_9) = all_0_0_0)
% 12.48/3.45 |
% 12.48/3.45 | Using (200) and (201) yields:
% 12.48/3.45 | (122) $false
% 12.48/3.45 |
% 12.48/3.45 |-The branch is then unsatisfiable
% 12.48/3.45 |-Branch two:
% 12.48/3.45 | (200) vtcheck(all_0_8_8, all_0_6_6, all_0_9_9) = all_0_0_0
% 12.48/3.45 | (126) all_0_0_0 = 0
% 12.48/3.45 |
% 12.48/3.45 | Equations (126) can reduce 72 to:
% 12.48/3.45 | (127) $false
% 12.48/3.45 |
% 12.48/3.45 |-The branch is then unsatisfiable
% 12.48/3.45 % SZS output end Proof for theBenchmark
% 12.48/3.45
% 12.48/3.45 2842ms
%------------------------------------------------------------------------------