TSTP Solution File: COM123+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : COM123+1 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.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 01:08:12 EDT 2022
% Result : Theorem 7.64s 2.38s
% Output : Proof 11.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : COM123+1 : TPTP v8.1.0. Released v6.4.0.
% 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 18:21:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.57 ____ _
% 0.19/0.57 ___ / __ \_____(_)___ ________ __________
% 0.19/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.57
% 0.19/0.57 A Theorem Prover for First-Order Logic
% 0.19/0.58 (ePrincess v.1.0)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2015
% 0.19/0.58 (c) Peter Backeman, 2014-2015
% 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58 Bug reports to peter@backeman.se
% 0.19/0.58
% 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.64/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.22/1.02 Prover 0: Preprocessing ...
% 4.16/1.52 Prover 0: Warning: ignoring some quantifiers
% 4.16/1.55 Prover 0: Constructing countermodel ...
% 5.72/1.93 Prover 0: gave up
% 5.72/1.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 6.27/2.02 Prover 1: Preprocessing ...
% 7.06/2.23 Prover 1: Constructing countermodel ...
% 7.64/2.38 Prover 1: proved (446ms)
% 7.64/2.38
% 7.64/2.38 No countermodel exists, formula is valid
% 7.64/2.38 % SZS status Theorem for theBenchmark
% 7.64/2.38
% 7.64/2.38 Generating proof ... found it (size 87)
% 10.65/3.05
% 10.65/3.05 % SZS output start Proof for theBenchmark
% 10.65/3.05 Assumed formulas after preprocessing and simplification:
% 10.65/3.05 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = 0) & ~ (v7 = 0) & ~ (v3 = v0) & vtcheck(v8, v6, v5) = v9 & vtcheck(v2, v6, v5) = 0 & vbind(v0, v1, v2) = v8 & visFreeVar(v0, v6) = v7 & vabs(v3, v4, veabs) = v6 & ~ (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] : (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 | ~ (vtcheck(v14, veabs, v13) = v15) | ~ (vbind(v10, v11, v12) = v14) | ? [v16] : ? [v17] : (vtcheck(v12, veabs, v13) = v17 & visFreeVar(v10, veabs) = v16 & ( ~ (v17 = 0) | v16 = 0))) & ! [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))
% 11.18/3.13 | 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:
% 11.18/3.13 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_2_2 = 0) & ~ (all_0_6_6 = all_0_9_9) & vtcheck(all_0_1_1, all_0_3_3, all_0_4_4) = all_0_0_0 & vtcheck(all_0_7_7, all_0_3_3, all_0_4_4) = 0 & vbind(all_0_9_9, all_0_8_8, all_0_7_7) = all_0_1_1 & visFreeVar(all_0_9_9, all_0_3_3) = all_0_2_2 & vabs(all_0_6_6, all_0_5_5, veabs) = all_0_3_3 & ~ (visSomeExp(vnoExp) = 0) & ~ (visSomeType(vnoType) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v3 | v5 = v0 | ~ (vsubst(v5, v8, v7) = v9) | ~ (vsubst(v0, v1, v10) = v11) | ~ (vsubst(v0, v1, v2) = v3) | ~ (vabs(v6, v4, v9) = v10) | ~ (vvar(v6) = v8) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (vgensym(v16) = v17 & visFreeVar(v5, v1) = v13 & vapp(v14, v15) = v16 & vapp(v1, v7) = v14 & vabs(v5, v4, v7) = v12 & vvar(v0) = v15 & ( ~ (v17 = v6) | ~ (v13 = 0) | ~ (v12 = v2)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v2 = v0 | ~ (vtcheck(v8, v5, v6) = v9) | ~ (vbind(v2, v3, v4) = v7) | ~ (vbind(v0, v1, v7) = v8) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = 0) & vtcheck(v11, v5, v6) = v12 & vbind(v2, v3, v10) = v11 & vbind(v0, v1, v4) = v10)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (vreduce(v1) = v2) | ~ (vgetSomeExp(v6) = v8) | ~ (vapp(v7, v8) = v9) | ~ (vapp(v7, v0) = v1) | ~ (vabs(v3, v4, v5) = v7) | ? [v10] : ? [v11] : ? [v12] : (vreduce(v0) = v10 & visSomeExp(v6) = v11 & vsomeExp(v9) = v12 & ( ~ (v11 = 0) | ~ (v10 = v6) | v12 = v2))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v3 | v4 = v0 | ~ (vsubst(v0, v1, v6) = v7) | ~ (vsubst(v0, v1, v2) = v3) | ~ (vabs(v4, v5, v7) = v8) | ? [v9] : ? [v10] : (visFreeVar(v4, v1) = v10 & vabs(v4, v5, v6) = v9 & ( ~ (v9 = v2) | v10 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v3 | ~ (vsubst(v0, v1, v5) = v7) | ~ (vsubst(v0, v1, v4) = v6) | ~ (vsubst(v0, v1, v2) = v3) | ~ (vapp(v6, v7) = v8) | ? [v9] : ( ~ (v9 = v2) & vapp(v4, v5) = v9)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v6 = vnoExp | ~ (vreduce(v5) = v6) | ~ (visSomeExp(v3) = v8) | ~ (vapp(v7, v4) = v5) | ~ (vabs(v0, v1, v2) = v7) | ? [v9] : ? [v10] : (vreduce(v4) = v9 & visValue(v4) = v10 & ( ~ (v9 = v3) | v10 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (vreduce(v2) = v3) | ~ (visSomeExp(v1) = v8) | ~ (vapp(v7, v5) = v2) | ~ (vabs(v4, v0, v6) = v7) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (vreduce(v5) = v9 & vsomeExp(v11) = v12 & vsubst(v4, v5, v6) = v11 & visValue(v5) = v10 & ( ~ (v10 = 0) | ~ (v9 = v1) | v12 = v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (varrow(v3, v4) = v6) | ~ (vtcheck(v0, v5, v6) = v7) | ~ (vabs(v1, v3, v2) = v5) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & vtcheck(v8, v2, v4) = v9 & vbind(v1, v3, v0) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (varrow(v0, v4) = v5) | ~ (vtcheck(v1, v6, v4) = v7) | ~ (vtcheck(v1, v2, v5) = 0) | ~ (vapp(v2, v3) = v6) | ? [v8] : ( ~ (v8 = 0) & vtcheck(v1, v3, v0) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (vtcheck(v7, v4, v5) = 0) | ~ (vbind(v0, v2, v6) = v7) | ~ (vbind(v0, v1, v3) = v6) | ? [v8] : (vtcheck(v8, v4, v5) = 0 & vbind(v0, v2, v3) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v4 | v2 = v1 | ~ (vlookup(v2, v5) = v6) | ~ (vlookup(v2, v3) = v4) | ~ (vbind(v1, v0, v5) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vtcheck(v5, v3, v4) = v6) | ~ (vbind(v0, v1, v2) = v5) | ? [v7] : ? [v8] : (vtcheck(v2, v3, v4) = v8 & vlookup(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = vnoType)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v2 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v2 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v1 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v1 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v0 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v0 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (vreduce(v1) = v2) | ~ (vreduce(v0) = v3) | ~ (vgetSomeExp(v3) = v5) | ~ (vapp(v5, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v10 = v0 & vabs(v7, v8, v9) = v0) | (visSomeExp(v3) = v8 & vsomeExp(v6) = v9 & vapp(v0, v4) = v7 & ( ~ (v8 = 0) | ~ (v7 = v1) | v9 = v2)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = vnoExp | ~ (vreduce(v3) = v4) | ~ (visSomeExp(v2) = v5) | ~ (vapp(v1, v0) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v9 = v1 & vabs(v6, v7, v8) = v1) | ( ~ (v6 = v2) & vreduce(v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (visFreeVar(v0, v3) = v5) | ~ (visFreeVar(v0, v2) = v4) | ~ (visFreeVar(v0, v1) = 0) | ? [v6] : ( ~ (v6 = v1) & vapp(v2, v3) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v3 = v1 | ~ (visFreeVar(v1, v4) = 0) | ~ (visFreeVar(v1, v2) = v5) | ~ (vabs(v3, v0, v4) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (vtcheck(v4, veabs, v3) = v5) | ~ (vbind(v0, v1, v2) = v4) | ? [v6] : ? [v7] : (vtcheck(v2, veabs, v3) = v7 & visFreeVar(v0, veabs) = v6 & ( ~ (v7 = 0) | v6 = 0))) & ! [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)
% 11.18/3.16 |
% 11.18/3.16 | Applying alpha-rule on (1) yields:
% 11.18/3.16 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v2 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6))
% 11.18/3.16 | (3) ! [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))
% 11.18/3.16 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~ (vsomeType(v2) = v0))
% 11.18/3.16 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeType(v1) = v2) | ~ (vsomeType(v0) = v2))
% 11.18/3.16 | (6) ! [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)))
% 11.18/3.16 | (7) ! [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)))
% 11.18/3.18 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0))
% 11.18/3.18 | (9) ! [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)))
% 11.18/3.18 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = vnoExp | ~ (vreduce(v3) = v4) | ~ (vabs(v0, v1, v2) = v3))
% 11.18/3.18 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (varrow(v2, v3) = v4) | ~ (varrow(v0, v1) = v4))
% 11.18/3.18 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vvar(v1) = v2) | ~ (vvar(v0) = v2))
% 11.18/3.18 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~ (vlookup(v3, v2) = v0))
% 11.18/3.18 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0))
% 11.18/3.18 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (visSomeType(v1) = v2) | ~ (vsomeType(v0) = v1))
% 11.18/3.18 | (16) ~ (visSomeExp(vnoExp) = 0)
% 11.18/3.18 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vsomeExp(v0) = v2) | ~ (vsomeExp(v0) = v1))
% 11.18/3.18 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (varrow(v0, v1) = v3) | ~ (varrow(v0, v1) = v2))
% 11.18/3.18 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vgetSomeExp(v0) = v1) | ~ (vsomeExp(v2) = v0))
% 11.18/3.18 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v0 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6))
% 11.18/3.18 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vsomeType(v0) = v2) | ~ (vsomeType(v0) = v1))
% 11.18/3.18 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (varrow(v3, v2) = v1) | ~ (varrow(v3, v2) = v0))
% 11.18/3.18 | (23) ! [v0] : ~ (vsomeType(v0) = vnoType)
% 11.18/3.18 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~ (vapp(v3, v2) = v0))
% 11.18/3.18 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v2 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6))
% 11.18/3.18 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (visValue(v2) = 0) | ~ (vapp(v0, v1) = v2))
% 11.18/3.18 | (27) ! [v0] : ~ (vsomeExp(v0) = vnoExp)
% 11.18/3.18 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (visFreeVar(v1, v3) = v4) | ~ (visFreeVar(v1, v2) = 0) | ~ (vabs(v1, v0, v3) = v2))
% 11.18/3.18 | (29) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (visFreeVar(v0, v1) = 0) | ~ (vvar(v2) = v1))
% 11.18/3.18 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0))
% 11.18/3.18 | (31) ! [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))))
% 11.18/3.18 | (32) ! [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)))
% 11.18/3.18 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0))
% 11.18/3.18 | (34) ~ (visSomeType(vnoType) = 0)
% 11.18/3.18 | (35) ! [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)))
% 11.18/3.18 | (36) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vvar(v0) = v2) | ~ (vvar(v0) = v1))
% 11.18/3.18 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v3 = v1 | ~ (visFreeVar(v1, v4) = 0) | ~ (visFreeVar(v1, v2) = v5) | ~ (vabs(v3, v0, v4) = v2))
% 11.18/3.18 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v1 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6))
% 11.18/3.18 | (39) ~ (all_0_0_0 = 0)
% 11.18/3.18 | (40) ! [v0] : ! [v1] : ! [v2] : (v2 = vnoExp | ~ (vreduce(v1) = v2) | ~ (vvar(v0) = v1))
% 11.18/3.18 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (vapp(v0, v1) = v3) | ~ (vapp(v0, v1) = v2))
% 11.18/3.18 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (vbind(v0, v1, v2) = v4) | ~ (vbind(v0, v1, v2) = v3))
% 11.18/3.18 | (43) vabs(all_0_6_6, all_0_5_5, veabs) = all_0_3_3
% 11.18/3.18 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v4 | v2 = v1 | ~ (vlookup(v2, v5) = v6) | ~ (vlookup(v2, v3) = v4) | ~ (vbind(v1, v0, v5) = v3))
% 11.18/3.18 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vapp(v1, v2) = v3) | ~ (vvar(v0) = v3))
% 11.18/3.18 | (46) ! [v0] : ! [v1] : ( ~ (visFreeVar(v0, v1) = 0) | ? [v2] : ( ~ (v2 = v0) & vgensym(v1) = v2))
% 11.18/3.19 | (47) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (visSomeExp(v1) = v2) | ~ (vsomeExp(v0) = v1))
% 11.18/3.19 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0))
% 11.18/3.19 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) = v0))
% 11.18/3.19 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vapp(v3, v4) = v5) | ~ (vabs(v0, v1, v2) = v5))
% 11.18/3.19 | (51) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (visFreeVar(v0, v1) = v2) | ~ (vvar(v0) = v1))
% 11.18/3.19 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) = v0))
% 11.18/3.19 | (53) ! [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))))
% 11.18/3.19 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (vabs(v0, v1, v2) = v4) | ~ (vabs(v0, v1, v2) = v3))
% 11.18/3.19 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v1 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6))
% 11.18/3.19 | (56) vtcheck(all_0_7_7, all_0_3_3, all_0_4_4) = 0
% 11.18/3.19 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (vtcheck(v4, veabs, v3) = v5) | ~ (vbind(v0, v1, v2) = v4) | ? [v6] : ? [v7] : (vtcheck(v2, veabs, v3) = v7 & visFreeVar(v0, veabs) = v6 & ( ~ (v7 = 0) | v6 = 0)))
% 11.18/3.19 | (58) ! [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))
% 11.18/3.19 | (59) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0))
% 11.18/3.19 | (60) ! [v0] : ! [v1] : (v1 = vnoType | ~ (vlookup(v0, vempty) = v1))
% 11.18/3.19 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (visValue(v3) = v4) | ~ (vabs(v0, v1, v2) = v3))
% 11.18/3.19 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (vsubst(v1, v0, v2) = v3) | ~ (vabs(v1, v4, v5) = v2))
% 11.18/3.19 | (63) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0))
% 11.18/3.19 | (64) ! [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))
% 11.18/3.19 | (65) ~ (all_0_6_6 = all_0_9_9)
% 11.18/3.19 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v1 | v3 = v2 | ~ (vsubst(v1, v0, v2) = v3) | ~ (vvar(v4) = v2))
% 11.18/3.19 | (67) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeExp(v1) = v2) | ~ (vsomeExp(v0) = v2))
% 11.18/3.19 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vlookup(v1, v2) = v3) | ~ (vbind(v1, v4, v0) = v2) | vsomeType(v4) = v3)
% 11.18/3.19 | (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))
% 11.18/3.19 | (70) ! [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))
% 11.18/3.19 | (71) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0))
% 11.18/3.19 | (72) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (vgetSomeType(v0) = v1) | ~ (vsomeType(v2) = v0))
% 11.18/3.19 | (73) ! [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)))
% 11.18/3.19 | (74) ! [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))))
% 11.18/3.19 | (75) ! [v0] : ! [v1] : ( ~ (visValue(v1) = 0) | ~ (vvar(v0) = v1))
% 11.18/3.19 | (76) vtcheck(all_0_1_1, all_0_3_3, all_0_4_4) = all_0_0_0
% 11.18/3.20 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4))
% 11.18/3.20 | (78) ! [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)))
% 11.18/3.20 | (79) ! [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))
% 11.18/3.20 | (80) ! [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)))
% 11.18/3.20 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (visFreeVar(v1, v4) = v5) | ~ (visFreeVar(v1, v2) = 0) | ~ (vabs(v3, v0, v4) = v2))
% 11.18/3.20 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3, v2) = v0))
% 11.18/3.20 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v0 | ~ (vbind(v3, v4, v5) = v6) | ~ (vbind(v0, v1, v2) = v6))
% 11.18/3.20 | (84) ! [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)))
% 11.18/3.20 | (85) ! [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)))
% 11.18/3.20 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (vsubst(v0, v1, v2) = v3) | ~ (vvar(v0) = v2))
% 11.18/3.20 | (87) vbind(all_0_9_9, all_0_8_8, all_0_7_7) = all_0_1_1
% 11.18/3.20 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (varrow(v2, v3) = v4) | ~ (varrow(v0, v1) = v4))
% 11.18/3.20 | (89) ! [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))
% 11.18/3.20 | (90) ! [v0] : ! [v1] : ! [v2] : ~ (vbind(v0, v1, v2) = vempty)
% 11.18/3.20 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4))
% 11.18/3.20 | (92) ~ (all_0_2_2 = 0)
% 11.18/3.20 | (93) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~ (vsomeExp(v2) = v0))
% 11.18/3.20 | (94) ! [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))
% 11.18/3.20 | (95) ! [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)))
% 11.18/3.20 | (96) ! [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)))
% 11.18/3.20 | (97) ! [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))
% 11.18/3.20 | (98) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (visValue(v2) = v1) | ~ (visValue(v2) = v0))
% 11.18/3.20 | (99) visFreeVar(all_0_9_9, all_0_3_3) = all_0_2_2
% 11.18/3.20 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0))
% 11.18/3.20 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vabs(v1, v2, v3) = v4) | ~ (vvar(v0) = v4))
% 11.18/3.20 |
% 11.18/3.20 | Instantiating formula (82) with all_0_7_7, all_0_3_3, all_0_4_4, 0, all_0_0_0 and discharging atoms vtcheck(all_0_7_7, all_0_3_3, all_0_4_4) = 0, yields:
% 11.18/3.20 | (102) all_0_0_0 = 0 | ~ (vtcheck(all_0_7_7, all_0_3_3, all_0_4_4) = all_0_0_0)
% 11.18/3.21 |
% 11.18/3.21 | Instantiating formula (9) with all_0_7_7, all_0_4_4, all_0_3_3 and discharging atoms vtcheck(all_0_7_7, all_0_3_3, all_0_4_4) = 0, yields:
% 11.18/3.21 | (103) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v5 = all_0_4_4 & v4 = all_0_3_3 & varrow(v2, v3) = all_0_4_4 & vtcheck(v6, v1, v3) = 0 & vbind(v0, v2, all_0_7_7) = v6 & vabs(v0, v2, v1) = all_0_3_3) | (v6 = 0 & v5 = 0 & v3 = all_0_3_3 & varrow(v2, all_0_4_4) = v4 & vtcheck(all_0_7_7, v1, v2) = 0 & vtcheck(all_0_7_7, v0, v4) = 0 & vapp(v0, v1) = all_0_3_3) | (v3 = v0 & v2 = all_0_3_3 & vlookup(v1, all_0_7_7) = v0 & vsomeType(all_0_4_4) = v0 & vvar(v1) = all_0_3_3))
% 11.18/3.21 |
% 11.18/3.21 | Instantiating formula (74) with all_0_0_0, all_0_1_1, all_0_4_4, all_0_3_3, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms vtcheck(all_0_1_1, all_0_3_3, all_0_4_4) = all_0_0_0, vbind(all_0_9_9, all_0_8_8, all_0_7_7) = all_0_1_1, yields:
% 11.18/3.21 | (104) all_0_0_0 = 0 | ? [v0] : ? [v1] : (vtcheck(all_0_7_7, all_0_3_3, all_0_4_4) = v1 & vlookup(all_0_9_9, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = vnoType)))
% 11.18/3.21 |
% 11.18/3.21 | Instantiating (103) with all_16_0_10, all_16_1_11, all_16_2_12, all_16_3_13, all_16_4_14, all_16_5_15, all_16_6_16, all_16_7_17 yields:
% 11.18/3.21 | (105) (all_16_0_10 = 0 & all_16_2_12 = all_0_4_4 & all_16_3_13 = all_0_3_3 & varrow(all_16_5_15, all_16_4_14) = all_0_4_4 & vtcheck(all_16_1_11, all_16_6_16, all_16_4_14) = 0 & vbind(all_16_7_17, all_16_5_15, all_0_7_7) = all_16_1_11 & vabs(all_16_7_17, all_16_5_15, all_16_6_16) = all_0_3_3) | (all_16_1_11 = 0 & all_16_2_12 = 0 & all_16_4_14 = all_0_3_3 & varrow(all_16_5_15, all_0_4_4) = all_16_3_13 & vtcheck(all_0_7_7, all_16_6_16, all_16_5_15) = 0 & vtcheck(all_0_7_7, all_16_7_17, all_16_3_13) = 0 & vapp(all_16_7_17, all_16_6_16) = all_0_3_3) | (all_16_4_14 = all_16_7_17 & all_16_5_15 = all_0_3_3 & vlookup(all_16_6_16, all_0_7_7) = all_16_7_17 & vsomeType(all_0_4_4) = all_16_7_17 & vvar(all_16_6_16) = all_0_3_3)
% 11.18/3.21 |
% 11.18/3.21 +-Applying beta-rule and splitting (102), into two cases.
% 11.18/3.21 |-Branch one:
% 11.18/3.21 | (106) ~ (vtcheck(all_0_7_7, all_0_3_3, all_0_4_4) = all_0_0_0)
% 11.18/3.21 |
% 11.18/3.21 +-Applying beta-rule and splitting (104), into two cases.
% 11.18/3.21 |-Branch one:
% 11.18/3.21 | (107) all_0_0_0 = 0
% 11.18/3.21 |
% 11.18/3.21 | Equations (107) can reduce 39 to:
% 11.18/3.21 | (108) $false
% 11.18/3.21 |
% 11.18/3.21 |-The branch is then unsatisfiable
% 11.18/3.21 |-Branch two:
% 11.18/3.21 | (39) ~ (all_0_0_0 = 0)
% 11.18/3.21 | (110) ? [v0] : ? [v1] : (vtcheck(all_0_7_7, all_0_3_3, all_0_4_4) = v1 & vlookup(all_0_9_9, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = vnoType)))
% 11.18/3.21 |
% 11.18/3.21 | Instantiating (110) with all_23_0_18, all_23_1_19 yields:
% 11.18/3.21 | (111) vtcheck(all_0_7_7, all_0_3_3, all_0_4_4) = all_23_0_18 & vlookup(all_0_9_9, all_0_7_7) = all_23_1_19 & ( ~ (all_23_0_18 = 0) | ~ (all_23_1_19 = vnoType))
% 11.18/3.21 |
% 11.18/3.21 | Applying alpha-rule on (111) yields:
% 11.18/3.21 | (112) vtcheck(all_0_7_7, all_0_3_3, all_0_4_4) = all_23_0_18
% 11.18/3.21 | (113) vlookup(all_0_9_9, all_0_7_7) = all_23_1_19
% 11.18/3.21 | (114) ~ (all_23_0_18 = 0) | ~ (all_23_1_19 = vnoType)
% 11.18/3.21 |
% 11.18/3.21 | Instantiating formula (82) with all_0_7_7, all_0_3_3, all_0_4_4, all_23_0_18, 0 and discharging atoms vtcheck(all_0_7_7, all_0_3_3, all_0_4_4) = all_23_0_18, vtcheck(all_0_7_7, all_0_3_3, all_0_4_4) = 0, yields:
% 11.18/3.21 | (115) all_23_0_18 = 0
% 11.18/3.21 |
% 11.18/3.21 | Using (112) and (106) yields:
% 11.18/3.21 | (116) ~ (all_23_0_18 = all_0_0_0)
% 11.18/3.21 |
% 11.18/3.21 | Equations (115) can reduce 116 to:
% 11.18/3.21 | (117) ~ (all_0_0_0 = 0)
% 11.18/3.21 |
% 11.18/3.21 | Simplifying 117 yields:
% 11.18/3.21 | (39) ~ (all_0_0_0 = 0)
% 11.18/3.21 |
% 11.18/3.21 +-Applying beta-rule and splitting (105), into two cases.
% 11.18/3.21 |-Branch one:
% 11.18/3.21 | (119) (all_16_0_10 = 0 & all_16_2_12 = all_0_4_4 & all_16_3_13 = all_0_3_3 & varrow(all_16_5_15, all_16_4_14) = all_0_4_4 & vtcheck(all_16_1_11, all_16_6_16, all_16_4_14) = 0 & vbind(all_16_7_17, all_16_5_15, all_0_7_7) = all_16_1_11 & vabs(all_16_7_17, all_16_5_15, all_16_6_16) = all_0_3_3) | (all_16_1_11 = 0 & all_16_2_12 = 0 & all_16_4_14 = all_0_3_3 & varrow(all_16_5_15, all_0_4_4) = all_16_3_13 & vtcheck(all_0_7_7, all_16_6_16, all_16_5_15) = 0 & vtcheck(all_0_7_7, all_16_7_17, all_16_3_13) = 0 & vapp(all_16_7_17, all_16_6_16) = all_0_3_3)
% 11.18/3.21 |
% 11.18/3.21 +-Applying beta-rule and splitting (119), into two cases.
% 11.18/3.21 |-Branch one:
% 11.18/3.21 | (120) all_16_0_10 = 0 & all_16_2_12 = all_0_4_4 & all_16_3_13 = all_0_3_3 & varrow(all_16_5_15, all_16_4_14) = all_0_4_4 & vtcheck(all_16_1_11, all_16_6_16, all_16_4_14) = 0 & vbind(all_16_7_17, all_16_5_15, all_0_7_7) = all_16_1_11 & vabs(all_16_7_17, all_16_5_15, all_16_6_16) = all_0_3_3
% 11.18/3.21 |
% 11.18/3.21 | Applying alpha-rule on (120) yields:
% 11.18/3.21 | (121) vbind(all_16_7_17, all_16_5_15, all_0_7_7) = all_16_1_11
% 11.18/3.21 | (122) vtcheck(all_16_1_11, all_16_6_16, all_16_4_14) = 0
% 11.18/3.21 | (123) all_16_0_10 = 0
% 11.18/3.21 | (124) varrow(all_16_5_15, all_16_4_14) = all_0_4_4
% 11.18/3.21 | (125) all_16_2_12 = all_0_4_4
% 11.18/3.21 | (126) all_16_3_13 = all_0_3_3
% 11.18/3.21 | (127) vabs(all_16_7_17, all_16_5_15, all_16_6_16) = all_0_3_3
% 11.18/3.21 |
% 11.18/3.21 | Instantiating formula (25) with all_0_3_3, all_16_6_16, all_16_5_15, all_16_7_17, veabs, all_0_5_5, all_0_6_6 and discharging atoms vabs(all_16_7_17, all_16_5_15, all_16_6_16) = all_0_3_3, vabs(all_0_6_6, all_0_5_5, veabs) = all_0_3_3, yields:
% 11.18/3.21 | (128) all_16_6_16 = veabs
% 11.18/3.21 |
% 11.18/3.21 | Instantiating formula (38) with all_0_3_3, all_16_6_16, all_16_5_15, all_16_7_17, veabs, all_0_5_5, all_0_6_6 and discharging atoms vabs(all_16_7_17, all_16_5_15, all_16_6_16) = all_0_3_3, vabs(all_0_6_6, all_0_5_5, veabs) = all_0_3_3, yields:
% 11.18/3.21 | (129) all_16_5_15 = all_0_5_5
% 11.18/3.21 |
% 11.18/3.21 | Instantiating formula (20) with all_0_3_3, all_16_6_16, all_16_5_15, all_16_7_17, veabs, all_0_5_5, all_0_6_6 and discharging atoms vabs(all_16_7_17, all_16_5_15, all_16_6_16) = all_0_3_3, vabs(all_0_6_6, all_0_5_5, veabs) = all_0_3_3, yields:
% 11.18/3.21 | (130) all_16_7_17 = all_0_6_6
% 11.18/3.21 |
% 11.18/3.21 | From (129) and (124) follows:
% 11.18/3.21 | (131) varrow(all_0_5_5, all_16_4_14) = all_0_4_4
% 11.18/3.21 |
% 11.18/3.21 | From (128) and (122) follows:
% 11.18/3.21 | (132) vtcheck(all_16_1_11, veabs, all_16_4_14) = 0
% 11.18/3.21 |
% 11.18/3.21 | From (130)(129) and (121) follows:
% 11.18/3.21 | (133) vbind(all_0_6_6, all_0_5_5, all_0_7_7) = all_16_1_11
% 11.18/3.21 |
% 11.18/3.21 | From (130)(129)(128) and (127) follows:
% 11.18/3.21 | (43) vabs(all_0_6_6, all_0_5_5, veabs) = all_0_3_3
% 11.18/3.21 |
% 11.18/3.21 | Instantiating formula (64) with all_0_0_0, all_0_4_4, all_0_3_3, all_16_4_14, all_0_5_5, veabs, all_0_6_6, all_0_1_1 and discharging atoms varrow(all_0_5_5, all_16_4_14) = all_0_4_4, vtcheck(all_0_1_1, all_0_3_3, all_0_4_4) = all_0_0_0, vabs(all_0_6_6, all_0_5_5, veabs) = all_0_3_3, yields:
% 11.18/3.21 | (135) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & vtcheck(v0, veabs, all_16_4_14) = v1 & vbind(all_0_6_6, all_0_5_5, all_0_1_1) = v0)
% 11.18/3.21 |
% 11.18/3.21 +-Applying beta-rule and splitting (135), into two cases.
% 11.18/3.21 |-Branch one:
% 11.18/3.21 | (107) all_0_0_0 = 0
% 11.18/3.22 |
% 11.18/3.22 | Equations (107) can reduce 39 to:
% 11.18/3.22 | (108) $false
% 11.18/3.22 |
% 11.18/3.22 |-The branch is then unsatisfiable
% 11.18/3.22 |-Branch two:
% 11.18/3.22 | (39) ~ (all_0_0_0 = 0)
% 11.18/3.22 | (139) ? [v0] : ? [v1] : ( ~ (v1 = 0) & vtcheck(v0, veabs, all_16_4_14) = v1 & vbind(all_0_6_6, all_0_5_5, all_0_1_1) = v0)
% 11.18/3.22 |
% 11.18/3.22 | Instantiating (139) with all_93_0_48, all_93_1_49 yields:
% 11.18/3.22 | (140) ~ (all_93_0_48 = 0) & vtcheck(all_93_1_49, veabs, all_16_4_14) = all_93_0_48 & vbind(all_0_6_6, all_0_5_5, all_0_1_1) = all_93_1_49
% 11.18/3.22 |
% 11.18/3.22 | Applying alpha-rule on (140) yields:
% 11.18/3.22 | (141) ~ (all_93_0_48 = 0)
% 11.18/3.22 | (142) vtcheck(all_93_1_49, veabs, all_16_4_14) = all_93_0_48
% 11.18/3.22 | (143) vbind(all_0_6_6, all_0_5_5, all_0_1_1) = all_93_1_49
% 11.18/3.22 |
% 11.71/3.22 | Instantiating formula (3) with all_93_0_48, all_93_1_49, all_0_1_1, all_16_4_14, veabs, all_0_7_7, all_0_8_8, all_0_9_9, all_0_5_5, all_0_6_6 and discharging atoms vtcheck(all_93_1_49, veabs, all_16_4_14) = all_93_0_48, vbind(all_0_6_6, all_0_5_5, all_0_1_1) = all_93_1_49, vbind(all_0_9_9, all_0_8_8, all_0_7_7) = all_0_1_1, yields:
% 11.71/3.22 | (144) all_93_0_48 = 0 | all_0_6_6 = all_0_9_9 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & vtcheck(v1, veabs, all_16_4_14) = v2 & vbind(all_0_6_6, all_0_5_5, all_0_7_7) = v0 & vbind(all_0_9_9, all_0_8_8, v0) = v1)
% 11.71/3.22 |
% 11.71/3.22 | Instantiating formula (57) with all_93_0_48, all_93_1_49, all_16_4_14, all_0_1_1, all_0_5_5, all_0_6_6 and discharging atoms vtcheck(all_93_1_49, veabs, all_16_4_14) = all_93_0_48, vbind(all_0_6_6, all_0_5_5, all_0_1_1) = all_93_1_49, yields:
% 11.71/3.22 | (145) all_93_0_48 = 0 | ? [v0] : ? [v1] : (vtcheck(all_0_1_1, veabs, all_16_4_14) = v1 & visFreeVar(all_0_6_6, veabs) = v0 & ( ~ (v1 = 0) | v0 = 0))
% 11.71/3.22 |
% 11.71/3.22 | Instantiating formula (74) with all_93_0_48, all_93_1_49, all_16_4_14, veabs, all_0_1_1, all_0_5_5, all_0_6_6 and discharging atoms vtcheck(all_93_1_49, veabs, all_16_4_14) = all_93_0_48, vbind(all_0_6_6, all_0_5_5, all_0_1_1) = all_93_1_49, yields:
% 11.71/3.22 | (146) all_93_0_48 = 0 | ? [v0] : ? [v1] : (vtcheck(all_0_1_1, veabs, all_16_4_14) = v1 & vlookup(all_0_6_6, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = vnoType)))
% 11.71/3.22 |
% 11.71/3.22 +-Applying beta-rule and splitting (145), into two cases.
% 11.71/3.22 |-Branch one:
% 11.71/3.22 | (147) all_93_0_48 = 0
% 11.71/3.22 |
% 11.71/3.22 | Equations (147) can reduce 141 to:
% 11.71/3.22 | (108) $false
% 11.71/3.22 |
% 11.71/3.22 |-The branch is then unsatisfiable
% 11.71/3.22 |-Branch two:
% 11.71/3.22 | (141) ~ (all_93_0_48 = 0)
% 11.71/3.22 | (150) ? [v0] : ? [v1] : (vtcheck(all_0_1_1, veabs, all_16_4_14) = v1 & visFreeVar(all_0_6_6, veabs) = v0 & ( ~ (v1 = 0) | v0 = 0))
% 11.71/3.22 |
% 11.71/3.22 +-Applying beta-rule and splitting (146), into two cases.
% 11.71/3.22 |-Branch one:
% 11.71/3.22 | (147) all_93_0_48 = 0
% 11.71/3.22 |
% 11.71/3.22 | Equations (147) can reduce 141 to:
% 11.71/3.22 | (108) $false
% 11.71/3.22 |
% 11.71/3.22 |-The branch is then unsatisfiable
% 11.71/3.22 |-Branch two:
% 11.71/3.22 | (141) ~ (all_93_0_48 = 0)
% 11.71/3.22 | (154) ? [v0] : ? [v1] : (vtcheck(all_0_1_1, veabs, all_16_4_14) = v1 & vlookup(all_0_6_6, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = vnoType)))
% 11.71/3.22 |
% 11.71/3.22 +-Applying beta-rule and splitting (144), into two cases.
% 11.71/3.22 |-Branch one:
% 11.71/3.22 | (147) all_93_0_48 = 0
% 11.71/3.22 |
% 11.71/3.22 | Equations (147) can reduce 141 to:
% 11.71/3.22 | (108) $false
% 11.71/3.22 |
% 11.71/3.22 |-The branch is then unsatisfiable
% 11.71/3.22 |-Branch two:
% 11.71/3.22 | (141) ~ (all_93_0_48 = 0)
% 11.71/3.22 | (158) all_0_6_6 = all_0_9_9 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & vtcheck(v1, veabs, all_16_4_14) = v2 & vbind(all_0_6_6, all_0_5_5, all_0_7_7) = v0 & vbind(all_0_9_9, all_0_8_8, v0) = v1)
% 11.71/3.22 |
% 11.71/3.22 +-Applying beta-rule and splitting (158), into two cases.
% 11.71/3.22 |-Branch one:
% 11.71/3.22 | (159) all_0_6_6 = all_0_9_9
% 11.71/3.22 |
% 11.71/3.22 | Equations (159) can reduce 65 to:
% 11.71/3.22 | (108) $false
% 11.71/3.22 |
% 11.71/3.22 |-The branch is then unsatisfiable
% 11.71/3.22 |-Branch two:
% 11.71/3.22 | (65) ~ (all_0_6_6 = all_0_9_9)
% 11.71/3.22 | (162) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & vtcheck(v1, veabs, all_16_4_14) = v2 & vbind(all_0_6_6, all_0_5_5, all_0_7_7) = v0 & vbind(all_0_9_9, all_0_8_8, v0) = v1)
% 11.71/3.22 |
% 11.71/3.22 | Instantiating (162) with all_136_0_54, all_136_1_55, all_136_2_56 yields:
% 11.71/3.22 | (163) ~ (all_136_0_54 = 0) & vtcheck(all_136_1_55, veabs, all_16_4_14) = all_136_0_54 & vbind(all_0_6_6, all_0_5_5, all_0_7_7) = all_136_2_56 & vbind(all_0_9_9, all_0_8_8, all_136_2_56) = all_136_1_55
% 11.71/3.22 |
% 11.71/3.22 | Applying alpha-rule on (163) yields:
% 11.71/3.22 | (164) ~ (all_136_0_54 = 0)
% 11.71/3.22 | (165) vtcheck(all_136_1_55, veabs, all_16_4_14) = all_136_0_54
% 11.71/3.22 | (166) vbind(all_0_6_6, all_0_5_5, all_0_7_7) = all_136_2_56
% 11.71/3.22 | (167) vbind(all_0_9_9, all_0_8_8, all_136_2_56) = all_136_1_55
% 11.71/3.22 |
% 11.71/3.22 | Instantiating formula (42) with all_136_2_56, all_16_1_11, all_0_7_7, all_0_5_5, all_0_6_6 and discharging atoms vbind(all_0_6_6, all_0_5_5, all_0_7_7) = all_136_2_56, vbind(all_0_6_6, all_0_5_5, all_0_7_7) = all_16_1_11, yields:
% 11.71/3.22 | (168) all_136_2_56 = all_16_1_11
% 11.71/3.22 |
% 11.71/3.22 | From (168) and (167) follows:
% 11.71/3.22 | (169) vbind(all_0_9_9, all_0_8_8, all_16_1_11) = all_136_1_55
% 11.71/3.22 |
% 11.71/3.22 | Instantiating formula (57) with all_136_0_54, all_136_1_55, all_16_4_14, all_16_1_11, all_0_8_8, all_0_9_9 and discharging atoms vtcheck(all_136_1_55, veabs, all_16_4_14) = all_136_0_54, vbind(all_0_9_9, all_0_8_8, all_16_1_11) = all_136_1_55, yields:
% 11.71/3.22 | (170) all_136_0_54 = 0 | ? [v0] : ? [v1] : (vtcheck(all_16_1_11, veabs, all_16_4_14) = v1 & visFreeVar(all_0_9_9, veabs) = v0 & ( ~ (v1 = 0) | v0 = 0))
% 11.71/3.22 |
% 11.71/3.22 | Instantiating formula (74) with all_136_0_54, all_136_1_55, all_16_4_14, veabs, all_16_1_11, all_0_8_8, all_0_9_9 and discharging atoms vtcheck(all_136_1_55, veabs, all_16_4_14) = all_136_0_54, vbind(all_0_9_9, all_0_8_8, all_16_1_11) = all_136_1_55, yields:
% 11.71/3.22 | (171) all_136_0_54 = 0 | ? [v0] : ? [v1] : (vtcheck(all_16_1_11, veabs, all_16_4_14) = v1 & vlookup(all_0_9_9, all_16_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = vnoType)))
% 11.71/3.22 |
% 11.71/3.22 +-Applying beta-rule and splitting (170), into two cases.
% 11.71/3.22 |-Branch one:
% 11.71/3.22 | (172) all_136_0_54 = 0
% 11.71/3.22 |
% 11.71/3.22 | Equations (172) can reduce 164 to:
% 11.71/3.22 | (108) $false
% 11.71/3.22 |
% 11.71/3.22 |-The branch is then unsatisfiable
% 11.71/3.22 |-Branch two:
% 11.71/3.22 | (164) ~ (all_136_0_54 = 0)
% 11.71/3.22 | (175) ? [v0] : ? [v1] : (vtcheck(all_16_1_11, veabs, all_16_4_14) = v1 & visFreeVar(all_0_9_9, veabs) = v0 & ( ~ (v1 = 0) | v0 = 0))
% 11.71/3.22 |
% 11.71/3.22 | Instantiating (175) with all_166_0_63, all_166_1_64 yields:
% 11.71/3.22 | (176) vtcheck(all_16_1_11, veabs, all_16_4_14) = all_166_0_63 & visFreeVar(all_0_9_9, veabs) = all_166_1_64 & ( ~ (all_166_0_63 = 0) | all_166_1_64 = 0)
% 11.71/3.22 |
% 11.71/3.22 | Applying alpha-rule on (176) yields:
% 11.71/3.22 | (177) vtcheck(all_16_1_11, veabs, all_16_4_14) = all_166_0_63
% 11.71/3.22 | (178) visFreeVar(all_0_9_9, veabs) = all_166_1_64
% 11.71/3.22 | (179) ~ (all_166_0_63 = 0) | all_166_1_64 = 0
% 11.71/3.22 |
% 11.71/3.22 +-Applying beta-rule and splitting (171), into two cases.
% 11.71/3.22 |-Branch one:
% 11.71/3.22 | (172) all_136_0_54 = 0
% 11.71/3.22 |
% 11.71/3.22 | Equations (172) can reduce 164 to:
% 11.71/3.22 | (108) $false
% 11.71/3.22 |
% 11.71/3.22 |-The branch is then unsatisfiable
% 11.71/3.22 |-Branch two:
% 11.71/3.22 | (164) ~ (all_136_0_54 = 0)
% 11.71/3.22 | (183) ? [v0] : ? [v1] : (vtcheck(all_16_1_11, veabs, all_16_4_14) = v1 & vlookup(all_0_9_9, all_16_1_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = vnoType)))
% 11.71/3.22 |
% 11.71/3.22 | Instantiating (183) with all_179_0_71, all_179_1_72 yields:
% 11.71/3.22 | (184) vtcheck(all_16_1_11, veabs, all_16_4_14) = all_179_0_71 & vlookup(all_0_9_9, all_16_1_11) = all_179_1_72 & ( ~ (all_179_0_71 = 0) | ~ (all_179_1_72 = vnoType))
% 11.71/3.22 |
% 11.71/3.22 | Applying alpha-rule on (184) yields:
% 11.71/3.22 | (185) vtcheck(all_16_1_11, veabs, all_16_4_14) = all_179_0_71
% 11.71/3.22 | (186) vlookup(all_0_9_9, all_16_1_11) = all_179_1_72
% 11.71/3.22 | (187) ~ (all_179_0_71 = 0) | ~ (all_179_1_72 = vnoType)
% 11.71/3.22 |
% 11.71/3.22 | Instantiating formula (82) with all_16_1_11, veabs, all_16_4_14, all_179_0_71, 0 and discharging atoms vtcheck(all_16_1_11, veabs, all_16_4_14) = all_179_0_71, vtcheck(all_16_1_11, veabs, all_16_4_14) = 0, yields:
% 11.71/3.22 | (188) all_179_0_71 = 0
% 11.71/3.22 |
% 11.71/3.22 | Instantiating formula (82) with all_16_1_11, veabs, all_16_4_14, all_166_0_63, all_179_0_71 and discharging atoms vtcheck(all_16_1_11, veabs, all_16_4_14) = all_179_0_71, vtcheck(all_16_1_11, veabs, all_16_4_14) = all_166_0_63, yields:
% 11.71/3.22 | (189) all_179_0_71 = all_166_0_63
% 11.71/3.22 |
% 11.71/3.22 | Instantiating formula (37) with all_0_2_2, veabs, all_0_6_6, all_0_3_3, all_0_9_9, all_0_5_5 and discharging atoms visFreeVar(all_0_9_9, all_0_3_3) = all_0_2_2, vabs(all_0_6_6, all_0_5_5, veabs) = all_0_3_3, yields:
% 11.71/3.22 | (190) all_0_2_2 = 0 | all_0_6_6 = all_0_9_9 | ~ (visFreeVar(all_0_9_9, veabs) = 0)
% 11.71/3.22 |
% 11.71/3.22 | Combining equations (188,189) yields a new equation:
% 11.71/3.22 | (191) all_166_0_63 = 0
% 11.71/3.22 |
% 11.71/3.22 +-Applying beta-rule and splitting (179), into two cases.
% 11.71/3.22 |-Branch one:
% 11.71/3.22 | (192) ~ (all_166_0_63 = 0)
% 11.71/3.22 |
% 11.71/3.22 | Equations (191) can reduce 192 to:
% 11.71/3.22 | (108) $false
% 11.71/3.22 |
% 11.71/3.22 |-The branch is then unsatisfiable
% 11.71/3.22 |-Branch two:
% 11.71/3.22 | (191) all_166_0_63 = 0
% 11.71/3.22 | (195) all_166_1_64 = 0
% 11.71/3.22 |
% 11.71/3.22 | From (195) and (178) follows:
% 11.71/3.22 | (196) visFreeVar(all_0_9_9, veabs) = 0
% 11.71/3.22 |
% 11.71/3.23 +-Applying beta-rule and splitting (190), into two cases.
% 11.71/3.23 |-Branch one:
% 11.71/3.23 | (197) ~ (visFreeVar(all_0_9_9, veabs) = 0)
% 11.71/3.23 |
% 11.71/3.23 | Using (196) and (197) yields:
% 11.71/3.23 | (198) $false
% 11.71/3.23 |
% 11.71/3.23 |-The branch is then unsatisfiable
% 11.71/3.23 |-Branch two:
% 11.71/3.23 | (196) visFreeVar(all_0_9_9, veabs) = 0
% 11.71/3.23 | (200) all_0_2_2 = 0 | all_0_6_6 = all_0_9_9
% 11.71/3.23 |
% 11.71/3.23 +-Applying beta-rule and splitting (200), into two cases.
% 11.71/3.23 |-Branch one:
% 11.71/3.23 | (201) all_0_2_2 = 0
% 11.71/3.23 |
% 11.71/3.23 | Equations (201) can reduce 92 to:
% 11.71/3.23 | (108) $false
% 11.71/3.23 |
% 11.71/3.23 |-The branch is then unsatisfiable
% 11.71/3.23 |-Branch two:
% 11.71/3.23 | (92) ~ (all_0_2_2 = 0)
% 11.71/3.23 | (159) all_0_6_6 = all_0_9_9
% 11.71/3.23 |
% 11.71/3.23 | Equations (159) can reduce 65 to:
% 11.71/3.23 | (108) $false
% 11.71/3.23 |
% 11.71/3.23 |-The branch is then unsatisfiable
% 11.71/3.23 |-Branch two:
% 11.71/3.23 | (206) all_16_1_11 = 0 & all_16_2_12 = 0 & all_16_4_14 = all_0_3_3 & varrow(all_16_5_15, all_0_4_4) = all_16_3_13 & vtcheck(all_0_7_7, all_16_6_16, all_16_5_15) = 0 & vtcheck(all_0_7_7, all_16_7_17, all_16_3_13) = 0 & vapp(all_16_7_17, all_16_6_16) = all_0_3_3
% 11.71/3.23 |
% 11.71/3.23 | Applying alpha-rule on (206) yields:
% 11.71/3.23 | (207) varrow(all_16_5_15, all_0_4_4) = all_16_3_13
% 11.71/3.23 | (208) all_16_1_11 = 0
% 11.71/3.23 | (209) all_16_4_14 = all_0_3_3
% 11.71/3.23 | (210) all_16_2_12 = 0
% 11.71/3.23 | (211) vtcheck(all_0_7_7, all_16_7_17, all_16_3_13) = 0
% 11.71/3.23 | (212) vtcheck(all_0_7_7, all_16_6_16, all_16_5_15) = 0
% 11.71/3.23 | (213) vapp(all_16_7_17, all_16_6_16) = all_0_3_3
% 11.71/3.23 |
% 11.71/3.23 | Instantiating formula (50) with all_0_3_3, all_16_6_16, all_16_7_17, veabs, all_0_5_5, all_0_6_6 and discharging atoms vapp(all_16_7_17, all_16_6_16) = all_0_3_3, vabs(all_0_6_6, all_0_5_5, veabs) = all_0_3_3, yields:
% 11.71/3.23 | (198) $false
% 11.71/3.23 |
% 11.71/3.23 |-The branch is then unsatisfiable
% 11.71/3.23 |-Branch two:
% 11.71/3.23 | (215) all_16_4_14 = all_16_7_17 & all_16_5_15 = all_0_3_3 & vlookup(all_16_6_16, all_0_7_7) = all_16_7_17 & vsomeType(all_0_4_4) = all_16_7_17 & vvar(all_16_6_16) = all_0_3_3
% 11.71/3.23 |
% 11.71/3.23 | Applying alpha-rule on (215) yields:
% 11.71/3.23 | (216) vsomeType(all_0_4_4) = all_16_7_17
% 11.71/3.23 | (217) vvar(all_16_6_16) = all_0_3_3
% 11.71/3.23 | (218) vlookup(all_16_6_16, all_0_7_7) = all_16_7_17
% 11.71/3.23 | (219) all_16_4_14 = all_16_7_17
% 11.71/3.23 | (220) all_16_5_15 = all_0_3_3
% 11.71/3.23 |
% 11.71/3.23 | Instantiating formula (101) with all_0_3_3, veabs, all_0_5_5, all_0_6_6, all_16_6_16 and discharging atoms vabs(all_0_6_6, all_0_5_5, veabs) = all_0_3_3, vvar(all_16_6_16) = all_0_3_3, yields:
% 11.71/3.23 | (198) $false
% 11.71/3.23 |
% 11.71/3.23 |-The branch is then unsatisfiable
% 11.71/3.23 |-Branch two:
% 11.71/3.23 | (222) vtcheck(all_0_7_7, all_0_3_3, all_0_4_4) = all_0_0_0
% 11.71/3.23 | (107) all_0_0_0 = 0
% 11.71/3.23 |
% 11.71/3.23 | Equations (107) can reduce 39 to:
% 11.71/3.23 | (108) $false
% 11.71/3.23 |
% 11.71/3.23 |-The branch is then unsatisfiable
% 11.71/3.23 % SZS output end Proof for theBenchmark
% 11.71/3.23
% 11.71/3.23 2643ms
%------------------------------------------------------------------------------