TSTP Solution File: LCL656+1.001 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : LCL656+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.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 : Sun Jul 17 09:37:51 EDT 2022
% Result : Theorem 4.73s 1.76s
% Output : Proof 9.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL656+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n007.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 : Sun Jul 3 07:07:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.54/0.58 ____ _
% 0.54/0.58 ___ / __ \_____(_)___ ________ __________
% 0.54/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.58
% 0.54/0.58 A Theorem Prover for First-Order Logic
% 0.54/0.58 (ePrincess v.1.0)
% 0.54/0.58
% 0.54/0.58 (c) Philipp Rümmer, 2009-2015
% 0.54/0.58 (c) Peter Backeman, 2014-2015
% 0.54/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.58 Bug reports to peter@backeman.se
% 0.54/0.58
% 0.54/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.58
% 0.54/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.49/0.89 Prover 0: Preprocessing ...
% 1.61/0.99 Prover 0: Warning: ignoring some quantifiers
% 1.76/1.01 Prover 0: Constructing countermodel ...
% 1.98/1.13 Prover 0: gave up
% 1.98/1.13 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.98/1.15 Prover 1: Preprocessing ...
% 2.61/1.25 Prover 1: Constructing countermodel ...
% 2.61/1.27 Prover 1: gave up
% 2.61/1.27 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.61/1.29 Prover 2: Preprocessing ...
% 3.95/1.54 Prover 2: Warning: ignoring some quantifiers
% 3.95/1.56 Prover 2: Constructing countermodel ...
% 4.73/1.76 Prover 2: proved (495ms)
% 4.73/1.76
% 4.73/1.76 No countermodel exists, formula is valid
% 4.73/1.76 % SZS status Theorem for theBenchmark
% 4.73/1.76
% 4.73/1.76 Generating proof ... Warning: ignoring some quantifiers
% 8.16/2.58 found it (size 33)
% 8.16/2.58
% 8.16/2.58 % SZS output start Proof for theBenchmark
% 8.16/2.58 Assumed formulas after preprocessing and simplification:
% 8.16/2.58 | (0) ? [v0] : ? [v1] : ( ~ (v1 = 0) & p100(v0) = 0 & p101(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (r1(v5, v4) = v3) | ~ (r1(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (p100(v4) = v3) | ~ (p100(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (p1(v4) = v3) | ~ (p1(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (p102(v4) = v3) | ~ (p102(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (p101(v4) = v3) | ~ (p101(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (p2(v4) = v3) | ~ (p2(v4) = v2)) & ! [v2] : ! [v3] : (v3 = 0 | ~ (p2(v2) = v3) | ? [v4] : ( ~ (v4 = 0) & r1(v0, v2) = v4)) & ! [v2] : ! [v3] : (v3 = 0 | ~ (r1(v2, v2) = v3)) & ! [v2] : ! [v3] : ( ~ (p100(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (( ~ (v4 = 0) & r1(v0, v2) = v4) | (( ~ (v3 = 0) | (v17 = 0 & v14 = 0 & v12 = 0 & v10 = 0 & v9 = 0 & ~ (v16 = 0) & ~ (v15 = 0) & ~ (v11 = 0) & p102(v13) = v16 & p102(v8) = v11 & p101(v13) = 0 & p101(v8) = 0 & p2(v13) = v15 & p2(v8) = 0 & r1(v2, v13) = 0 & r1(v2, v8) = 0) | (v4 = 0 & p101(v2) = 0)) & ( ~ (v3 = 0) | (((v6 = 0 & p1(v2) = 0) | ( ! [v18] : ( ~ (p100(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p1(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (p1(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p100(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p100(v18) = v19) | ( ~ (v19 = 0) & p1(v18) = v19))))) & (( ~ (v6 = 0) & p1(v2) = v6) | ( ! [v18] : ! [v19] : (v19 = 0 | ~ (p1(v18) = v19) | ? [v20] : (( ~ (v20 = 0) & p100(v18) = v20) | ( ~ (v20 = 0) & r1(v2, v18) = v20))) & ! [v18] : ( ~ (p100(v18) = 0) | ? [v19] : ((v19 = 0 & p1(v18) = 0) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : ((v19 = 0 & p1(v18) = 0) | ( ~ (v19 = 0) & p100(v18) = v19))))))) & (v3 = 0 | ( ~ (v4 = 0) & p101(v2) = v4)) & ((v4 = 0 & p101(v2) = 0) | ( ~ (v5 = 0) & p102(v2) = v5)) & (( ~ (v4 = 0) & p101(v2) = v4) | (((v7 = 0 & p2(v2) = 0) | ( ! [v18] : ( ~ (p101(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p2(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (p2(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p101(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p101(v18) = v19) | ( ~ (v19 = 0) & p2(v18) = v19))))) & (( ~ (v7 = 0) & p2(v2) = v7) | ( ! [v18] : ! [v19] : (v19 = 0 | ~ (p2(v18) = v19) | ? [v20] : (( ~ (v20 = 0) & p101(v18) = v20) | ( ~ (v20 = 0) & r1(v2, v18) = v20))) & ! [v18] : ( ~ (p101(v18) = 0) | ? [v19] : ((v19 = 0 & p2(v18) = 0) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : ((v19 = 0 & p2(v18) = 0) | ( ~ (v19 = 0) & p101(v18) = v19)))))))))) & ! [v2] : ! [v3] : ( ~ (p1(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (( ~ (v4 = 0) & r1(v0, v2) = v4) | (((v17 = 0 & v14 = 0 & v12 = 0 & v10 = 0 & v9 = 0 & ~ (v16 = 0) & ~ (v15 = 0) & ~ (v11 = 0) & p102(v13) = v16 & p102(v8) = v11 & p101(v13) = 0 & p101(v8) = 0 & p2(v13) = v15 & p2(v8) = 0 & r1(v2, v13) = 0 & r1(v2, v8) = 0) | (v4 = 0 & p101(v2) = 0) | ( ~ (v5 = 0) & p100(v2) = v5)) & ((v5 = 0 & p100(v2) = 0) | ( ~ (v4 = 0) & p101(v2) = v4)) & ((v4 = 0 & p101(v2) = 0) | ( ~ (v6 = 0) & p102(v2) = v6)) & (( ~ (v5 = 0) & p100(v2) = v5) | (( ~ (v3 = 0) | ( ! [v18] : ! [v19] : (v19 = 0 | ~ (p1(v18) = v19) | ? [v20] : (( ~ (v20 = 0) & p100(v18) = v20) | ( ~ (v20 = 0) & r1(v2, v18) = v20))) & ! [v18] : ( ~ (p100(v18) = 0) | ? [v19] : ((v19 = 0 & p1(v18) = 0) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : ((v19 = 0 & p1(v18) = 0) | ( ~ (v19 = 0) & p100(v18) = v19))))) & (v3 = 0 | ( ! [v18] : ( ~ (p100(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p1(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (p1(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p100(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p100(v18) = v19) | ( ~ (v19 = 0) & p1(v18) = v19))))))) & (( ~ (v4 = 0) & p101(v2) = v4) | (((v7 = 0 & p2(v2) = 0) | ( ! [v18] : ( ~ (p101(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p2(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (p2(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p101(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p101(v18) = v19) | ( ~ (v19 = 0) & p2(v18) = v19))))) & (( ~ (v7 = 0) & p2(v2) = v7) | ( ! [v18] : ! [v19] : (v19 = 0 | ~ (p2(v18) = v19) | ? [v20] : (( ~ (v20 = 0) & p101(v18) = v20) | ( ~ (v20 = 0) & r1(v2, v18) = v20))) & ! [v18] : ( ~ (p101(v18) = 0) | ? [v19] : ((v19 = 0 & p2(v18) = 0) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : ((v19 = 0 & p2(v18) = 0) | ( ~ (v19 = 0) & p101(v18) = v19)))))))))) & ! [v2] : ! [v3] : ( ~ (p102(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (( ~ (v4 = 0) & r1(v0, v2) = v4) | (( ~ (v3 = 0) | (v4 = 0 & p101(v2) = 0)) & ((v17 = 0 & v14 = 0 & v12 = 0 & v10 = 0 & v9 = 0 & ~ (v16 = 0) & ~ (v15 = 0) & ~ (v11 = 0) & p102(v13) = v16 & p102(v8) = v11 & p101(v13) = 0 & p101(v8) = 0 & p2(v13) = v15 & p2(v8) = 0 & r1(v2, v13) = 0 & r1(v2, v8) = 0) | (v4 = 0 & p101(v2) = 0) | ( ~ (v5 = 0) & p100(v2) = v5)) & ((v5 = 0 & p100(v2) = 0) | ( ~ (v4 = 0) & p101(v2) = v4)) & (( ~ (v5 = 0) & p100(v2) = v5) | (((v6 = 0 & p1(v2) = 0) | ( ! [v18] : ( ~ (p100(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p1(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (p1(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p100(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p100(v18) = v19) | ( ~ (v19 = 0) & p1(v18) = v19))))) & (( ~ (v6 = 0) & p1(v2) = v6) | ( ! [v18] : ! [v19] : (v19 = 0 | ~ (p1(v18) = v19) | ? [v20] : (( ~ (v20 = 0) & p100(v18) = v20) | ( ~ (v20 = 0) & r1(v2, v18) = v20))) & ! [v18] : ( ~ (p100(v18) = 0) | ? [v19] : ((v19 = 0 & p1(v18) = 0) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : ((v19 = 0 & p1(v18) = 0) | ( ~ (v19 = 0) & p100(v18) = v19))))))) & (( ~ (v4 = 0) & p101(v2) = v4) | (((v7 = 0 & p2(v2) = 0) | ( ! [v18] : ( ~ (p101(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p2(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (p2(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p101(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p101(v18) = v19) | ( ~ (v19 = 0) & p2(v18) = v19))))) & (( ~ (v7 = 0) & p2(v2) = v7) | ( ! [v18] : ! [v19] : (v19 = 0 | ~ (p2(v18) = v19) | ? [v20] : (( ~ (v20 = 0) & p101(v18) = v20) | ( ~ (v20 = 0) & r1(v2, v18) = v20))) & ! [v18] : ( ~ (p101(v18) = 0) | ? [v19] : ((v19 = 0 & p2(v18) = 0) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : ((v19 = 0 & p2(v18) = 0) | ( ~ (v19 = 0) & p101(v18) = v19)))))))))) & ! [v2] : ! [v3] : ( ~ (p101(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (( ~ (v4 = 0) & r1(v0, v2) = v4) | (( ~ (v3 = 0) | (v4 = 0 & p100(v2) = 0)) & ( ~ (v3 = 0) | (((v7 = 0 & p2(v2) = 0) | ( ! [v18] : ( ~ (p101(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p2(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (p2(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p101(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p101(v18) = v19) | ( ~ (v19 = 0) & p2(v18) = v19))))) & (( ~ (v7 = 0) & p2(v2) = v7) | ( ! [v18] : ! [v19] : (v19 = 0 | ~ (p2(v18) = v19) | ? [v20] : (( ~ (v20 = 0) & p101(v18) = v20) | ( ~ (v20 = 0) & r1(v2, v18) = v20))) & ! [v18] : ( ~ (p101(v18) = 0) | ? [v19] : ((v19 = 0 & p2(v18) = 0) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : ((v19 = 0 & p2(v18) = 0) | ( ~ (v19 = 0) & p101(v18) = v19))))))) & (v3 = 0 | (v17 = 0 & v14 = 0 & v12 = 0 & v10 = 0 & v9 = 0 & ~ (v16 = 0) & ~ (v15 = 0) & ~ (v11 = 0) & p102(v13) = v16 & p102(v8) = v11 & p101(v13) = 0 & p101(v8) = 0 & p2(v13) = v15 & p2(v8) = 0 & r1(v2, v13) = 0 & r1(v2, v8) = 0) | ( ~ (v4 = 0) & p100(v2) = v4)) & (v3 = 0 | ( ~ (v5 = 0) & p102(v2) = v5)) & (( ~ (v4 = 0) & p100(v2) = v4) | (((v6 = 0 & p1(v2) = 0) | ( ! [v18] : ( ~ (p100(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p1(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (p1(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p100(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p100(v18) = v19) | ( ~ (v19 = 0) & p1(v18) = v19))))) & (( ~ (v6 = 0) & p1(v2) = v6) | ( ! [v18] : ! [v19] : (v19 = 0 | ~ (p1(v18) = v19) | ? [v20] : (( ~ (v20 = 0) & p100(v18) = v20) | ( ~ (v20 = 0) & r1(v2, v18) = v20))) & ! [v18] : ( ~ (p100(v18) = 0) | ? [v19] : ((v19 = 0 & p1(v18) = 0) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : ((v19 = 0 & p1(v18) = 0) | ( ~ (v19 = 0) & p100(v18) = v19)))))))))) & ! [v2] : ! [v3] : ( ~ (p2(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (( ~ (v4 = 0) & r1(v0, v2) = v4) | (((v17 = 0 & v14 = 0 & v12 = 0 & v10 = 0 & v9 = 0 & ~ (v16 = 0) & ~ (v15 = 0) & ~ (v11 = 0) & p102(v13) = v16 & p102(v8) = v11 & p101(v13) = 0 & p101(v8) = 0 & p2(v13) = v15 & p2(v8) = 0 & r1(v2, v13) = 0 & r1(v2, v8) = 0) | (v4 = 0 & p101(v2) = 0) | ( ~ (v5 = 0) & p100(v2) = v5)) & ((v5 = 0 & p100(v2) = 0) | ( ~ (v4 = 0) & p101(v2) = v4)) & ((v4 = 0 & p101(v2) = 0) | ( ~ (v6 = 0) & p102(v2) = v6)) & (( ~ (v5 = 0) & p100(v2) = v5) | (((v7 = 0 & p1(v2) = 0) | ( ! [v18] : ( ~ (p100(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p1(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (p1(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p100(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p100(v18) = v19) | ( ~ (v19 = 0) & p1(v18) = v19))))) & (( ~ (v7 = 0) & p1(v2) = v7) | ( ! [v18] : ! [v19] : (v19 = 0 | ~ (p1(v18) = v19) | ? [v20] : (( ~ (v20 = 0) & p100(v18) = v20) | ( ~ (v20 = 0) & r1(v2, v18) = v20))) & ! [v18] : ( ~ (p100(v18) = 0) | ? [v19] : ((v19 = 0 & p1(v18) = 0) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : ((v19 = 0 & p1(v18) = 0) | ( ~ (v19 = 0) & p100(v18) = v19))))))) & (( ~ (v4 = 0) & p101(v2) = v4) | (( ~ (v3 = 0) | ( ! [v18] : ! [v19] : (v19 = 0 | ~ (p2(v18) = v19) | ? [v20] : (( ~ (v20 = 0) & p101(v18) = v20) | ( ~ (v20 = 0) & r1(v2, v18) = v20))) & ! [v18] : ( ~ (p101(v18) = 0) | ? [v19] : ((v19 = 0 & p2(v18) = 0) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : ((v19 = 0 & p2(v18) = 0) | ( ~ (v19 = 0) & p101(v18) = v19))))) & (v3 = 0 | ( ! [v18] : ( ~ (p101(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p2(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (p2(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p101(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p101(v18) = v19) | ( ~ (v19 = 0) & p2(v18) = v19)))))))))) & ! [v2] : ( ~ (r1(v0, v2) = 0) | p2(v2) = 0) & ! [v2] : ( ~ (r1(v0, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (((v17 = 0 & v14 = 0 & v12 = 0 & v10 = 0 & v9 = 0 & ~ (v16 = 0) & ~ (v15 = 0) & ~ (v11 = 0) & p102(v13) = v16 & p102(v8) = v11 & p101(v13) = 0 & p101(v8) = 0 & p2(v13) = v15 & p2(v8) = 0 & r1(v2, v13) = 0 & r1(v2, v8) = 0) | (v3 = 0 & p101(v2) = 0) | ( ~ (v4 = 0) & p100(v2) = v4)) & ((v4 = 0 & p100(v2) = 0) | ( ~ (v3 = 0) & p101(v2) = v3)) & ((v3 = 0 & p101(v2) = 0) | ( ~ (v5 = 0) & p102(v2) = v5)) & (( ~ (v4 = 0) & p100(v2) = v4) | (((v6 = 0 & p1(v2) = 0) | ( ! [v18] : ( ~ (p100(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p1(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (p1(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p100(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p100(v18) = v19) | ( ~ (v19 = 0) & p1(v18) = v19))))) & (( ~ (v6 = 0) & p1(v2) = v6) | ( ! [v18] : ! [v19] : (v19 = 0 | ~ (p1(v18) = v19) | ? [v20] : (( ~ (v20 = 0) & p100(v18) = v20) | ( ~ (v20 = 0) & r1(v2, v18) = v20))) & ! [v18] : ( ~ (p100(v18) = 0) | ? [v19] : ((v19 = 0 & p1(v18) = 0) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : ((v19 = 0 & p1(v18) = 0) | ( ~ (v19 = 0) & p100(v18) = v19))))))) & (( ~ (v3 = 0) & p101(v2) = v3) | (((v7 = 0 & p2(v2) = 0) | ( ! [v18] : ( ~ (p101(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p2(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (p2(v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p101(v18) = v19) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : (( ~ (v19 = 0) & p101(v18) = v19) | ( ~ (v19 = 0) & p2(v18) = v19))))) & (( ~ (v7 = 0) & p2(v2) = v7) | ( ! [v18] : ! [v19] : (v19 = 0 | ~ (p2(v18) = v19) | ? [v20] : (( ~ (v20 = 0) & p101(v18) = v20) | ( ~ (v20 = 0) & r1(v2, v18) = v20))) & ! [v18] : ( ~ (p101(v18) = 0) | ? [v19] : ((v19 = 0 & p2(v18) = 0) | ( ~ (v19 = 0) & r1(v2, v18) = v19))) & ! [v18] : ( ~ (r1(v2, v18) = 0) | ? [v19] : ((v19 = 0 & p2(v18) = 0) | ( ~ (v19 = 0) & p101(v18) = v19))))))))) & ? [v2] : ? [v3] : ? [v4] : r1(v3, v2) = v4 & ? [v2] : ? [v3] : p100(v2) = v3 & ? [v2] : ? [v3] : p1(v2) = v3 & ? [v2] : ? [v3] : p102(v2) = v3 & ? [v2] : ? [v3] : p101(v2) = v3 & ? [v2] : ? [v3] : p2(v2) = v3)
% 8.61/2.64 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 8.61/2.64 | (1) ~ (all_0_0_0 = 0) & p100(all_0_1_1) = 0 & p101(all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p100(v2) = v1) | ~ (p100(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p1(v2) = v1) | ~ (p1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p102(v2) = v1) | ~ (p102(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p101(v2) = v1) | ~ (p101(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p2(v2) = v1) | ~ (p2(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (p2(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & r1(all_0_1_1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (r1(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (p100(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (( ~ (v2 = 0) & r1(all_0_1_1, v0) = v2) | (( ~ (v1 = 0) | (v15 = 0 & v12 = 0 & v10 = 0 & v8 = 0 & v7 = 0 & ~ (v14 = 0) & ~ (v13 = 0) & ~ (v9 = 0) & p102(v11) = v14 & p102(v6) = v9 & p101(v11) = 0 & p101(v6) = 0 & p2(v11) = v13 & p2(v6) = 0 & r1(v0, v11) = 0 & r1(v0, v6) = 0) | (v2 = 0 & p101(v0) = 0)) & ( ~ (v1 = 0) | (((v4 = 0 & p1(v0) = 0) | ( ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p1(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p1(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & p1(v16) = v17))))) & (( ~ (v4 = 0) & p1(v0) = v4) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p1(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p100(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & p100(v16) = v17))))))) & (v1 = 0 | ( ~ (v2 = 0) & p101(v0) = v2)) & ((v2 = 0 & p101(v0) = 0) | ( ~ (v3 = 0) & p102(v0) = v3)) & (( ~ (v2 = 0) & p101(v0) = v2) | (((v5 = 0 & p2(v0) = 0) | ( ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p2(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p2(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & p2(v16) = v17))))) & (( ~ (v5 = 0) & p2(v0) = v5) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p2(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p101(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & p101(v16) = v17)))))))))) & ! [v0] : ! [v1] : ( ~ (p1(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (( ~ (v2 = 0) & r1(all_0_1_1, v0) = v2) | (((v15 = 0 & v12 = 0 & v10 = 0 & v8 = 0 & v7 = 0 & ~ (v14 = 0) & ~ (v13 = 0) & ~ (v9 = 0) & p102(v11) = v14 & p102(v6) = v9 & p101(v11) = 0 & p101(v6) = 0 & p2(v11) = v13 & p2(v6) = 0 & r1(v0, v11) = 0 & r1(v0, v6) = 0) | (v2 = 0 & p101(v0) = 0) | ( ~ (v3 = 0) & p100(v0) = v3)) & ((v3 = 0 & p100(v0) = 0) | ( ~ (v2 = 0) & p101(v0) = v2)) & ((v2 = 0 & p101(v0) = 0) | ( ~ (v4 = 0) & p102(v0) = v4)) & (( ~ (v3 = 0) & p100(v0) = v3) | (( ~ (v1 = 0) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p1(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p100(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & p100(v16) = v17))))) & (v1 = 0 | ( ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p1(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p1(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & p1(v16) = v17))))))) & (( ~ (v2 = 0) & p101(v0) = v2) | (((v5 = 0 & p2(v0) = 0) | ( ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p2(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p2(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & p2(v16) = v17))))) & (( ~ (v5 = 0) & p2(v0) = v5) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p2(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p101(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & p101(v16) = v17)))))))))) & ! [v0] : ! [v1] : ( ~ (p102(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (( ~ (v2 = 0) & r1(all_0_1_1, v0) = v2) | (( ~ (v1 = 0) | (v2 = 0 & p101(v0) = 0)) & ((v15 = 0 & v12 = 0 & v10 = 0 & v8 = 0 & v7 = 0 & ~ (v14 = 0) & ~ (v13 = 0) & ~ (v9 = 0) & p102(v11) = v14 & p102(v6) = v9 & p101(v11) = 0 & p101(v6) = 0 & p2(v11) = v13 & p2(v6) = 0 & r1(v0, v11) = 0 & r1(v0, v6) = 0) | (v2 = 0 & p101(v0) = 0) | ( ~ (v3 = 0) & p100(v0) = v3)) & ((v3 = 0 & p100(v0) = 0) | ( ~ (v2 = 0) & p101(v0) = v2)) & (( ~ (v3 = 0) & p100(v0) = v3) | (((v4 = 0 & p1(v0) = 0) | ( ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p1(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p1(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & p1(v16) = v17))))) & (( ~ (v4 = 0) & p1(v0) = v4) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p1(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p100(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & p100(v16) = v17))))))) & (( ~ (v2 = 0) & p101(v0) = v2) | (((v5 = 0 & p2(v0) = 0) | ( ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p2(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p2(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & p2(v16) = v17))))) & (( ~ (v5 = 0) & p2(v0) = v5) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p2(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p101(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & p101(v16) = v17)))))))))) & ! [v0] : ! [v1] : ( ~ (p101(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (( ~ (v2 = 0) & r1(all_0_1_1, v0) = v2) | (( ~ (v1 = 0) | (v2 = 0 & p100(v0) = 0)) & ( ~ (v1 = 0) | (((v5 = 0 & p2(v0) = 0) | ( ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p2(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p2(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & p2(v16) = v17))))) & (( ~ (v5 = 0) & p2(v0) = v5) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p2(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p101(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & p101(v16) = v17))))))) & (v1 = 0 | (v15 = 0 & v12 = 0 & v10 = 0 & v8 = 0 & v7 = 0 & ~ (v14 = 0) & ~ (v13 = 0) & ~ (v9 = 0) & p102(v11) = v14 & p102(v6) = v9 & p101(v11) = 0 & p101(v6) = 0 & p2(v11) = v13 & p2(v6) = 0 & r1(v0, v11) = 0 & r1(v0, v6) = 0) | ( ~ (v2 = 0) & p100(v0) = v2)) & (v1 = 0 | ( ~ (v3 = 0) & p102(v0) = v3)) & (( ~ (v2 = 0) & p100(v0) = v2) | (((v4 = 0 & p1(v0) = 0) | ( ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p1(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p1(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & p1(v16) = v17))))) & (( ~ (v4 = 0) & p1(v0) = v4) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p1(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p100(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & p100(v16) = v17)))))))))) & ! [v0] : ! [v1] : ( ~ (p2(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (( ~ (v2 = 0) & r1(all_0_1_1, v0) = v2) | (((v15 = 0 & v12 = 0 & v10 = 0 & v8 = 0 & v7 = 0 & ~ (v14 = 0) & ~ (v13 = 0) & ~ (v9 = 0) & p102(v11) = v14 & p102(v6) = v9 & p101(v11) = 0 & p101(v6) = 0 & p2(v11) = v13 & p2(v6) = 0 & r1(v0, v11) = 0 & r1(v0, v6) = 0) | (v2 = 0 & p101(v0) = 0) | ( ~ (v3 = 0) & p100(v0) = v3)) & ((v3 = 0 & p100(v0) = 0) | ( ~ (v2 = 0) & p101(v0) = v2)) & ((v2 = 0 & p101(v0) = 0) | ( ~ (v4 = 0) & p102(v0) = v4)) & (( ~ (v3 = 0) & p100(v0) = v3) | (((v5 = 0 & p1(v0) = 0) | ( ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p1(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p1(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & p1(v16) = v17))))) & (( ~ (v5 = 0) & p1(v0) = v5) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p1(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p100(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & p100(v16) = v17))))))) & (( ~ (v2 = 0) & p101(v0) = v2) | (( ~ (v1 = 0) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p2(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p101(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & p101(v16) = v17))))) & (v1 = 0 | ( ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p2(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p2(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & p2(v16) = v17)))))))))) & ! [v0] : ( ~ (r1(all_0_1_1, v0) = 0) | p2(v0) = 0) & ! [v0] : ( ~ (r1(all_0_1_1, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (((v15 = 0 & v12 = 0 & v10 = 0 & v8 = 0 & v7 = 0 & ~ (v14 = 0) & ~ (v13 = 0) & ~ (v9 = 0) & p102(v11) = v14 & p102(v6) = v9 & p101(v11) = 0 & p101(v6) = 0 & p2(v11) = v13 & p2(v6) = 0 & r1(v0, v11) = 0 & r1(v0, v6) = 0) | (v1 = 0 & p101(v0) = 0) | ( ~ (v2 = 0) & p100(v0) = v2)) & ((v2 = 0 & p100(v0) = 0) | ( ~ (v1 = 0) & p101(v0) = v1)) & ((v1 = 0 & p101(v0) = 0) | ( ~ (v3 = 0) & p102(v0) = v3)) & (( ~ (v2 = 0) & p100(v0) = v2) | (((v4 = 0 & p1(v0) = 0) | ( ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p1(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p1(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & p1(v16) = v17))))) & (( ~ (v4 = 0) & p1(v0) = v4) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p1(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p100(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & p100(v16) = v17))))))) & (( ~ (v1 = 0) & p101(v0) = v1) | (((v5 = 0 & p2(v0) = 0) | ( ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p2(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p2(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & p2(v16) = v17))))) & (( ~ (v5 = 0) & p2(v0) = v5) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p2(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p101(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & p101(v16) = v17))))))))) & ? [v0] : ? [v1] : ? [v2] : r1(v1, v0) = v2 & ? [v0] : ? [v1] : p100(v0) = v1 & ? [v0] : ? [v1] : p1(v0) = v1 & ? [v0] : ? [v1] : p102(v0) = v1 & ? [v0] : ? [v1] : p101(v0) = v1 & ? [v0] : ? [v1] : p2(v0) = v1
% 8.61/2.67 |
% 8.61/2.67 | Applying alpha-rule on (1) yields:
% 8.61/2.67 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p101(v2) = v1) | ~ (p101(v2) = v0))
% 8.61/2.67 | (3) ! [v0] : ! [v1] : ( ~ (p2(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (( ~ (v2 = 0) & r1(all_0_1_1, v0) = v2) | (((v15 = 0 & v12 = 0 & v10 = 0 & v8 = 0 & v7 = 0 & ~ (v14 = 0) & ~ (v13 = 0) & ~ (v9 = 0) & p102(v11) = v14 & p102(v6) = v9 & p101(v11) = 0 & p101(v6) = 0 & p2(v11) = v13 & p2(v6) = 0 & r1(v0, v11) = 0 & r1(v0, v6) = 0) | (v2 = 0 & p101(v0) = 0) | ( ~ (v3 = 0) & p100(v0) = v3)) & ((v3 = 0 & p100(v0) = 0) | ( ~ (v2 = 0) & p101(v0) = v2)) & ((v2 = 0 & p101(v0) = 0) | ( ~ (v4 = 0) & p102(v0) = v4)) & (( ~ (v3 = 0) & p100(v0) = v3) | (((v5 = 0 & p1(v0) = 0) | ( ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p1(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p1(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & p1(v16) = v17))))) & (( ~ (v5 = 0) & p1(v0) = v5) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p1(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p100(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & p100(v16) = v17))))))) & (( ~ (v2 = 0) & p101(v0) = v2) | (( ~ (v1 = 0) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p2(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p101(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & p101(v16) = v17))))) & (v1 = 0 | ( ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p2(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p2(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & p2(v16) = v17))))))))))
% 8.61/2.68 | (4) ? [v0] : ? [v1] : ? [v2] : r1(v1, v0) = v2
% 8.61/2.68 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p2(v2) = v1) | ~ (p2(v2) = v0))
% 8.61/2.68 | (6) p101(all_0_1_1) = all_0_0_0
% 8.61/2.68 | (7) p100(all_0_1_1) = 0
% 8.61/2.68 | (8) ! [v0] : ! [v1] : ( ~ (p100(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (( ~ (v2 = 0) & r1(all_0_1_1, v0) = v2) | (( ~ (v1 = 0) | (v15 = 0 & v12 = 0 & v10 = 0 & v8 = 0 & v7 = 0 & ~ (v14 = 0) & ~ (v13 = 0) & ~ (v9 = 0) & p102(v11) = v14 & p102(v6) = v9 & p101(v11) = 0 & p101(v6) = 0 & p2(v11) = v13 & p2(v6) = 0 & r1(v0, v11) = 0 & r1(v0, v6) = 0) | (v2 = 0 & p101(v0) = 0)) & ( ~ (v1 = 0) | (((v4 = 0 & p1(v0) = 0) | ( ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p1(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p1(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & p1(v16) = v17))))) & (( ~ (v4 = 0) & p1(v0) = v4) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p1(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p100(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & p100(v16) = v17))))))) & (v1 = 0 | ( ~ (v2 = 0) & p101(v0) = v2)) & ((v2 = 0 & p101(v0) = 0) | ( ~ (v3 = 0) & p102(v0) = v3)) & (( ~ (v2 = 0) & p101(v0) = v2) | (((v5 = 0 & p2(v0) = 0) | ( ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p2(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p2(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & p2(v16) = v17))))) & (( ~ (v5 = 0) & p2(v0) = v5) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p2(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p101(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & p101(v16) = v17))))))))))
% 8.61/2.68 | (9) ! [v0] : ! [v1] : ( ~ (p101(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (( ~ (v2 = 0) & r1(all_0_1_1, v0) = v2) | (( ~ (v1 = 0) | (v2 = 0 & p100(v0) = 0)) & ( ~ (v1 = 0) | (((v5 = 0 & p2(v0) = 0) | ( ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p2(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p2(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & p2(v16) = v17))))) & (( ~ (v5 = 0) & p2(v0) = v5) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p2(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p101(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & p101(v16) = v17))))))) & (v1 = 0 | (v15 = 0 & v12 = 0 & v10 = 0 & v8 = 0 & v7 = 0 & ~ (v14 = 0) & ~ (v13 = 0) & ~ (v9 = 0) & p102(v11) = v14 & p102(v6) = v9 & p101(v11) = 0 & p101(v6) = 0 & p2(v11) = v13 & p2(v6) = 0 & r1(v0, v11) = 0 & r1(v0, v6) = 0) | ( ~ (v2 = 0) & p100(v0) = v2)) & (v1 = 0 | ( ~ (v3 = 0) & p102(v0) = v3)) & (( ~ (v2 = 0) & p100(v0) = v2) | (((v4 = 0 & p1(v0) = 0) | ( ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p1(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p1(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & p1(v16) = v17))))) & (( ~ (v4 = 0) & p1(v0) = v4) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p1(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p100(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & p100(v16) = v17))))))))))
% 8.61/2.68 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (p2(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & r1(all_0_1_1, v0) = v2))
% 8.61/2.68 | (11) ~ (all_0_0_0 = 0)
% 8.61/2.68 | (12) ? [v0] : ? [v1] : p101(v0) = v1
% 8.61/2.68 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p102(v2) = v1) | ~ (p102(v2) = v0))
% 8.61/2.68 | (14) ? [v0] : ? [v1] : p2(v0) = v1
% 8.61/2.68 | (15) ? [v0] : ? [v1] : p100(v0) = v1
% 8.61/2.68 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0))
% 8.61/2.68 | (17) ! [v0] : ! [v1] : ( ~ (p1(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (( ~ (v2 = 0) & r1(all_0_1_1, v0) = v2) | (((v15 = 0 & v12 = 0 & v10 = 0 & v8 = 0 & v7 = 0 & ~ (v14 = 0) & ~ (v13 = 0) & ~ (v9 = 0) & p102(v11) = v14 & p102(v6) = v9 & p101(v11) = 0 & p101(v6) = 0 & p2(v11) = v13 & p2(v6) = 0 & r1(v0, v11) = 0 & r1(v0, v6) = 0) | (v2 = 0 & p101(v0) = 0) | ( ~ (v3 = 0) & p100(v0) = v3)) & ((v3 = 0 & p100(v0) = 0) | ( ~ (v2 = 0) & p101(v0) = v2)) & ((v2 = 0 & p101(v0) = 0) | ( ~ (v4 = 0) & p102(v0) = v4)) & (( ~ (v3 = 0) & p100(v0) = v3) | (( ~ (v1 = 0) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p1(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p100(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & p100(v16) = v17))))) & (v1 = 0 | ( ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p1(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p1(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & p1(v16) = v17))))))) & (( ~ (v2 = 0) & p101(v0) = v2) | (((v5 = 0 & p2(v0) = 0) | ( ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p2(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p2(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & p2(v16) = v17))))) & (( ~ (v5 = 0) & p2(v0) = v5) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p2(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p101(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & p101(v16) = v17))))))))))
% 8.61/2.69 | (18) ! [v0] : ( ~ (r1(all_0_1_1, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (((v15 = 0 & v12 = 0 & v10 = 0 & v8 = 0 & v7 = 0 & ~ (v14 = 0) & ~ (v13 = 0) & ~ (v9 = 0) & p102(v11) = v14 & p102(v6) = v9 & p101(v11) = 0 & p101(v6) = 0 & p2(v11) = v13 & p2(v6) = 0 & r1(v0, v11) = 0 & r1(v0, v6) = 0) | (v1 = 0 & p101(v0) = 0) | ( ~ (v2 = 0) & p100(v0) = v2)) & ((v2 = 0 & p100(v0) = 0) | ( ~ (v1 = 0) & p101(v0) = v1)) & ((v1 = 0 & p101(v0) = 0) | ( ~ (v3 = 0) & p102(v0) = v3)) & (( ~ (v2 = 0) & p100(v0) = v2) | (((v4 = 0 & p1(v0) = 0) | ( ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p1(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p1(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & p1(v16) = v17))))) & (( ~ (v4 = 0) & p1(v0) = v4) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p1(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p100(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & p100(v16) = v17))))))) & (( ~ (v1 = 0) & p101(v0) = v1) | (((v5 = 0 & p2(v0) = 0) | ( ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p2(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p2(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & p2(v16) = v17))))) & (( ~ (v5 = 0) & p2(v0) = v5) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p2(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p101(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & p101(v16) = v17)))))))))
% 8.61/2.69 | (19) ! [v0] : ( ~ (r1(all_0_1_1, v0) = 0) | p2(v0) = 0)
% 8.61/2.69 | (20) ? [v0] : ? [v1] : p102(v0) = v1
% 8.61/2.69 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p1(v2) = v1) | ~ (p1(v2) = v0))
% 8.61/2.69 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p100(v2) = v1) | ~ (p100(v2) = v0))
% 8.61/2.69 | (23) ! [v0] : ! [v1] : ( ~ (p102(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (( ~ (v2 = 0) & r1(all_0_1_1, v0) = v2) | (( ~ (v1 = 0) | (v2 = 0 & p101(v0) = 0)) & ((v15 = 0 & v12 = 0 & v10 = 0 & v8 = 0 & v7 = 0 & ~ (v14 = 0) & ~ (v13 = 0) & ~ (v9 = 0) & p102(v11) = v14 & p102(v6) = v9 & p101(v11) = 0 & p101(v6) = 0 & p2(v11) = v13 & p2(v6) = 0 & r1(v0, v11) = 0 & r1(v0, v6) = 0) | (v2 = 0 & p101(v0) = 0) | ( ~ (v3 = 0) & p100(v0) = v3)) & ((v3 = 0 & p100(v0) = 0) | ( ~ (v2 = 0) & p101(v0) = v2)) & (( ~ (v3 = 0) & p100(v0) = v3) | (((v4 = 0 & p1(v0) = 0) | ( ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p1(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p1(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p100(v16) = v17) | ( ~ (v17 = 0) & p1(v16) = v17))))) & (( ~ (v4 = 0) & p1(v0) = v4) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p1(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p100(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p100(v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p1(v16) = 0) | ( ~ (v17 = 0) & p100(v16) = v17))))))) & (( ~ (v2 = 0) & p101(v0) = v2) | (((v5 = 0 & p2(v0) = 0) | ( ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p2(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (p2(v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & p101(v16) = v17) | ( ~ (v17 = 0) & p2(v16) = v17))))) & (( ~ (v5 = 0) & p2(v0) = v5) | ( ! [v16] : ! [v17] : (v17 = 0 | ~ (p2(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & p101(v16) = v18) | ( ~ (v18 = 0) & r1(v0, v16) = v18))) & ! [v16] : ( ~ (p101(v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & r1(v0, v16) = v17))) & ! [v16] : ( ~ (r1(v0, v16) = 0) | ? [v17] : ((v17 = 0 & p2(v16) = 0) | ( ~ (v17 = 0) & p101(v16) = v17))))))))))
% 8.61/2.69 | (24) ? [v0] : ? [v1] : p1(v0) = v1
% 8.61/2.69 | (25) ! [v0] : ! [v1] : (v1 = 0 | ~ (r1(v0, v0) = v1))
% 8.61/2.69 |
% 8.61/2.70 | Instantiating formula (9) with all_0_0_0, all_0_1_1 and discharging atoms p101(all_0_1_1) = all_0_0_0, yields:
% 8.61/2.70 | (26) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (( ~ (v0 = 0) & r1(all_0_1_1, all_0_1_1) = v0) | (( ~ (all_0_0_0 = 0) | (v0 = 0 & p100(all_0_1_1) = 0)) & ( ~ (all_0_0_0 = 0) | (((v3 = 0 & p2(all_0_1_1) = 0) | ( ! [v14] : ( ~ (p101(v14) = 0) | ? [v15] : (( ~ (v15 = 0) & p2(v14) = v15) | ( ~ (v15 = 0) & r1(all_0_1_1, v14) = v15))) & ! [v14] : ( ~ (p2(v14) = 0) | ? [v15] : (( ~ (v15 = 0) & p101(v14) = v15) | ( ~ (v15 = 0) & r1(all_0_1_1, v14) = v15))) & ! [v14] : ( ~ (r1(all_0_1_1, v14) = 0) | ? [v15] : (( ~ (v15 = 0) & p101(v14) = v15) | ( ~ (v15 = 0) & p2(v14) = v15))))) & (( ~ (v3 = 0) & p2(all_0_1_1) = v3) | ( ! [v14] : ! [v15] : (v15 = 0 | ~ (p2(v14) = v15) | ? [v16] : (( ~ (v16 = 0) & p101(v14) = v16) | ( ~ (v16 = 0) & r1(all_0_1_1, v14) = v16))) & ! [v14] : ( ~ (p101(v14) = 0) | ? [v15] : ((v15 = 0 & p2(v14) = 0) | ( ~ (v15 = 0) & r1(all_0_1_1, v14) = v15))) & ! [v14] : ( ~ (r1(all_0_1_1, v14) = 0) | ? [v15] : ((v15 = 0 & p2(v14) = 0) | ( ~ (v15 = 0) & p101(v14) = v15))))))) & (all_0_0_0 = 0 | (v13 = 0 & v10 = 0 & v8 = 0 & v6 = 0 & v5 = 0 & ~ (v12 = 0) & ~ (v11 = 0) & ~ (v7 = 0) & p102(v9) = v12 & p102(v4) = v7 & p101(v9) = 0 & p101(v4) = 0 & p2(v9) = v11 & p2(v4) = 0 & r1(all_0_1_1, v9) = 0 & r1(all_0_1_1, v4) = 0) | ( ~ (v0 = 0) & p100(all_0_1_1) = v0)) & (all_0_0_0 = 0 | ( ~ (v1 = 0) & p102(all_0_1_1) = v1)) & (( ~ (v0 = 0) & p100(all_0_1_1) = v0) | (((v2 = 0 & p1(all_0_1_1) = 0) | ( ! [v14] : ( ~ (p100(v14) = 0) | ? [v15] : (( ~ (v15 = 0) & p1(v14) = v15) | ( ~ (v15 = 0) & r1(all_0_1_1, v14) = v15))) & ! [v14] : ( ~ (p1(v14) = 0) | ? [v15] : (( ~ (v15 = 0) & p100(v14) = v15) | ( ~ (v15 = 0) & r1(all_0_1_1, v14) = v15))) & ! [v14] : ( ~ (r1(all_0_1_1, v14) = 0) | ? [v15] : (( ~ (v15 = 0) & p100(v14) = v15) | ( ~ (v15 = 0) & p1(v14) = v15))))) & (( ~ (v2 = 0) & p1(all_0_1_1) = v2) | ( ! [v14] : ! [v15] : (v15 = 0 | ~ (p1(v14) = v15) | ? [v16] : (( ~ (v16 = 0) & p100(v14) = v16) | ( ~ (v16 = 0) & r1(all_0_1_1, v14) = v16))) & ! [v14] : ( ~ (p100(v14) = 0) | ? [v15] : ((v15 = 0 & p1(v14) = 0) | ( ~ (v15 = 0) & r1(all_0_1_1, v14) = v15))) & ! [v14] : ( ~ (r1(all_0_1_1, v14) = 0) | ? [v15] : ((v15 = 0 & p1(v14) = 0) | ( ~ (v15 = 0) & p100(v14) = v15)))))))))
% 9.04/2.70 |
% 9.04/2.70 | Instantiating (26) with all_20_0_15, all_20_1_16, all_20_2_17, all_20_3_18, all_20_4_19, all_20_5_20, all_20_6_21, all_20_7_22, all_20_8_23, all_20_9_24, all_20_10_25, all_20_11_26, all_20_12_27, all_20_13_28 yields:
% 9.04/2.70 | (27) ( ~ (all_20_13_28 = 0) & r1(all_0_1_1, all_0_1_1) = all_20_13_28) | (( ~ (all_0_0_0 = 0) | (all_20_13_28 = 0 & p100(all_0_1_1) = 0)) & ( ~ (all_0_0_0 = 0) | (((all_20_10_25 = 0 & p2(all_0_1_1) = 0) | ( ! [v0] : ( ~ (p101(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p2(v0) = v1) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (p2(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p101(v0) = v1) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (r1(all_0_1_1, v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p101(v0) = v1) | ( ~ (v1 = 0) & p2(v0) = v1))))) & (( ~ (all_20_10_25 = 0) & p2(all_0_1_1) = all_20_10_25) | ( ! [v0] : ! [v1] : (v1 = 0 | ~ (p2(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & p101(v0) = v2) | ( ~ (v2 = 0) & r1(all_0_1_1, v0) = v2))) & ! [v0] : ( ~ (p101(v0) = 0) | ? [v1] : ((v1 = 0 & p2(v0) = 0) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (r1(all_0_1_1, v0) = 0) | ? [v1] : ((v1 = 0 & p2(v0) = 0) | ( ~ (v1 = 0) & p101(v0) = v1))))))) & (all_0_0_0 = 0 | (all_20_0_15 = 0 & all_20_3_18 = 0 & all_20_5_20 = 0 & all_20_7_22 = 0 & all_20_8_23 = 0 & ~ (all_20_1_16 = 0) & ~ (all_20_2_17 = 0) & ~ (all_20_6_21 = 0) & p102(all_20_4_19) = all_20_1_16 & p102(all_20_9_24) = all_20_6_21 & p101(all_20_4_19) = 0 & p101(all_20_9_24) = 0 & p2(all_20_4_19) = all_20_2_17 & p2(all_20_9_24) = 0 & r1(all_0_1_1, all_20_4_19) = 0 & r1(all_0_1_1, all_20_9_24) = 0) | ( ~ (all_20_13_28 = 0) & p100(all_0_1_1) = all_20_13_28)) & (all_0_0_0 = 0 | ( ~ (all_20_12_27 = 0) & p102(all_0_1_1) = all_20_12_27)) & (( ~ (all_20_13_28 = 0) & p100(all_0_1_1) = all_20_13_28) | (((all_20_11_26 = 0 & p1(all_0_1_1) = 0) | ( ! [v0] : ( ~ (p100(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p1(v0) = v1) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (p1(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p100(v0) = v1) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (r1(all_0_1_1, v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p100(v0) = v1) | ( ~ (v1 = 0) & p1(v0) = v1))))) & (( ~ (all_20_11_26 = 0) & p1(all_0_1_1) = all_20_11_26) | ( ! [v0] : ! [v1] : (v1 = 0 | ~ (p1(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & p100(v0) = v2) | ( ~ (v2 = 0) & r1(all_0_1_1, v0) = v2))) & ! [v0] : ( ~ (p100(v0) = 0) | ? [v1] : ((v1 = 0 & p1(v0) = 0) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (r1(all_0_1_1, v0) = 0) | ? [v1] : ((v1 = 0 & p1(v0) = 0) | ( ~ (v1 = 0) & p100(v0) = v1))))))))
% 9.04/2.70 |
% 9.04/2.70 +-Applying beta-rule and splitting (27), into two cases.
% 9.04/2.70 |-Branch one:
% 9.04/2.70 | (28) ~ (all_20_13_28 = 0) & r1(all_0_1_1, all_0_1_1) = all_20_13_28
% 9.04/2.70 |
% 9.04/2.70 | Applying alpha-rule on (28) yields:
% 9.04/2.70 | (29) ~ (all_20_13_28 = 0)
% 9.04/2.70 | (30) r1(all_0_1_1, all_0_1_1) = all_20_13_28
% 9.04/2.70 |
% 9.04/2.70 | Instantiating formula (25) with all_20_13_28, all_0_1_1 and discharging atoms r1(all_0_1_1, all_0_1_1) = all_20_13_28, yields:
% 9.04/2.70 | (31) all_20_13_28 = 0
% 9.04/2.70 |
% 9.04/2.70 | Equations (31) can reduce 29 to:
% 9.04/2.70 | (32) $false
% 9.04/2.70 |
% 9.04/2.70 |-The branch is then unsatisfiable
% 9.04/2.70 |-Branch two:
% 9.04/2.70 | (33) ( ~ (all_0_0_0 = 0) | (all_20_13_28 = 0 & p100(all_0_1_1) = 0)) & ( ~ (all_0_0_0 = 0) | (((all_20_10_25 = 0 & p2(all_0_1_1) = 0) | ( ! [v0] : ( ~ (p101(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p2(v0) = v1) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (p2(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p101(v0) = v1) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (r1(all_0_1_1, v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p101(v0) = v1) | ( ~ (v1 = 0) & p2(v0) = v1))))) & (( ~ (all_20_10_25 = 0) & p2(all_0_1_1) = all_20_10_25) | ( ! [v0] : ! [v1] : (v1 = 0 | ~ (p2(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & p101(v0) = v2) | ( ~ (v2 = 0) & r1(all_0_1_1, v0) = v2))) & ! [v0] : ( ~ (p101(v0) = 0) | ? [v1] : ((v1 = 0 & p2(v0) = 0) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (r1(all_0_1_1, v0) = 0) | ? [v1] : ((v1 = 0 & p2(v0) = 0) | ( ~ (v1 = 0) & p101(v0) = v1))))))) & (all_0_0_0 = 0 | (all_20_0_15 = 0 & all_20_3_18 = 0 & all_20_5_20 = 0 & all_20_7_22 = 0 & all_20_8_23 = 0 & ~ (all_20_1_16 = 0) & ~ (all_20_2_17 = 0) & ~ (all_20_6_21 = 0) & p102(all_20_4_19) = all_20_1_16 & p102(all_20_9_24) = all_20_6_21 & p101(all_20_4_19) = 0 & p101(all_20_9_24) = 0 & p2(all_20_4_19) = all_20_2_17 & p2(all_20_9_24) = 0 & r1(all_0_1_1, all_20_4_19) = 0 & r1(all_0_1_1, all_20_9_24) = 0) | ( ~ (all_20_13_28 = 0) & p100(all_0_1_1) = all_20_13_28)) & (all_0_0_0 = 0 | ( ~ (all_20_12_27 = 0) & p102(all_0_1_1) = all_20_12_27)) & (( ~ (all_20_13_28 = 0) & p100(all_0_1_1) = all_20_13_28) | (((all_20_11_26 = 0 & p1(all_0_1_1) = 0) | ( ! [v0] : ( ~ (p100(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p1(v0) = v1) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (p1(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p100(v0) = v1) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (r1(all_0_1_1, v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p100(v0) = v1) | ( ~ (v1 = 0) & p1(v0) = v1))))) & (( ~ (all_20_11_26 = 0) & p1(all_0_1_1) = all_20_11_26) | ( ! [v0] : ! [v1] : (v1 = 0 | ~ (p1(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & p100(v0) = v2) | ( ~ (v2 = 0) & r1(all_0_1_1, v0) = v2))) & ! [v0] : ( ~ (p100(v0) = 0) | ? [v1] : ((v1 = 0 & p1(v0) = 0) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (r1(all_0_1_1, v0) = 0) | ? [v1] : ((v1 = 0 & p1(v0) = 0) | ( ~ (v1 = 0) & p100(v0) = v1)))))))
% 9.04/2.71 |
% 9.04/2.71 | Applying alpha-rule on (33) yields:
% 9.04/2.71 | (34) ~ (all_0_0_0 = 0) | (all_20_13_28 = 0 & p100(all_0_1_1) = 0)
% 9.04/2.71 | (35) ( ~ (all_20_13_28 = 0) & p100(all_0_1_1) = all_20_13_28) | (((all_20_11_26 = 0 & p1(all_0_1_1) = 0) | ( ! [v0] : ( ~ (p100(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p1(v0) = v1) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (p1(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p100(v0) = v1) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (r1(all_0_1_1, v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p100(v0) = v1) | ( ~ (v1 = 0) & p1(v0) = v1))))) & (( ~ (all_20_11_26 = 0) & p1(all_0_1_1) = all_20_11_26) | ( ! [v0] : ! [v1] : (v1 = 0 | ~ (p1(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & p100(v0) = v2) | ( ~ (v2 = 0) & r1(all_0_1_1, v0) = v2))) & ! [v0] : ( ~ (p100(v0) = 0) | ? [v1] : ((v1 = 0 & p1(v0) = 0) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (r1(all_0_1_1, v0) = 0) | ? [v1] : ((v1 = 0 & p1(v0) = 0) | ( ~ (v1 = 0) & p100(v0) = v1))))))
% 9.04/2.71 | (36) all_0_0_0 = 0 | (all_20_0_15 = 0 & all_20_3_18 = 0 & all_20_5_20 = 0 & all_20_7_22 = 0 & all_20_8_23 = 0 & ~ (all_20_1_16 = 0) & ~ (all_20_2_17 = 0) & ~ (all_20_6_21 = 0) & p102(all_20_4_19) = all_20_1_16 & p102(all_20_9_24) = all_20_6_21 & p101(all_20_4_19) = 0 & p101(all_20_9_24) = 0 & p2(all_20_4_19) = all_20_2_17 & p2(all_20_9_24) = 0 & r1(all_0_1_1, all_20_4_19) = 0 & r1(all_0_1_1, all_20_9_24) = 0) | ( ~ (all_20_13_28 = 0) & p100(all_0_1_1) = all_20_13_28)
% 9.04/2.71 | (37) all_0_0_0 = 0 | ( ~ (all_20_12_27 = 0) & p102(all_0_1_1) = all_20_12_27)
% 9.04/2.71 | (38) ~ (all_0_0_0 = 0) | (((all_20_10_25 = 0 & p2(all_0_1_1) = 0) | ( ! [v0] : ( ~ (p101(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p2(v0) = v1) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (p2(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p101(v0) = v1) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (r1(all_0_1_1, v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p101(v0) = v1) | ( ~ (v1 = 0) & p2(v0) = v1))))) & (( ~ (all_20_10_25 = 0) & p2(all_0_1_1) = all_20_10_25) | ( ! [v0] : ! [v1] : (v1 = 0 | ~ (p2(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & p101(v0) = v2) | ( ~ (v2 = 0) & r1(all_0_1_1, v0) = v2))) & ! [v0] : ( ~ (p101(v0) = 0) | ? [v1] : ((v1 = 0 & p2(v0) = 0) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (r1(all_0_1_1, v0) = 0) | ? [v1] : ((v1 = 0 & p2(v0) = 0) | ( ~ (v1 = 0) & p101(v0) = v1))))))
% 9.04/2.71 |
% 9.04/2.71 +-Applying beta-rule and splitting (38), into two cases.
% 9.04/2.71 |-Branch one:
% 9.04/2.71 | (11) ~ (all_0_0_0 = 0)
% 9.04/2.71 |
% 9.04/2.71 +-Applying beta-rule and splitting (37), into two cases.
% 9.04/2.71 |-Branch one:
% 9.04/2.71 | (40) all_0_0_0 = 0
% 9.04/2.71 |
% 9.04/2.71 | Equations (40) can reduce 11 to:
% 9.04/2.71 | (32) $false
% 9.04/2.71 |
% 9.04/2.71 |-The branch is then unsatisfiable
% 9.04/2.71 |-Branch two:
% 9.04/2.71 | (11) ~ (all_0_0_0 = 0)
% 9.04/2.71 | (43) ~ (all_20_12_27 = 0) & p102(all_0_1_1) = all_20_12_27
% 9.04/2.71 |
% 9.04/2.71 +-Applying beta-rule and splitting (36), into two cases.
% 9.04/2.71 |-Branch one:
% 9.04/2.71 | (40) all_0_0_0 = 0
% 9.04/2.71 |
% 9.04/2.71 | Equations (40) can reduce 11 to:
% 9.04/2.71 | (32) $false
% 9.04/2.71 |
% 9.04/2.71 |-The branch is then unsatisfiable
% 9.04/2.71 |-Branch two:
% 9.04/2.71 | (11) ~ (all_0_0_0 = 0)
% 9.04/2.71 | (47) (all_20_0_15 = 0 & all_20_3_18 = 0 & all_20_5_20 = 0 & all_20_7_22 = 0 & all_20_8_23 = 0 & ~ (all_20_1_16 = 0) & ~ (all_20_2_17 = 0) & ~ (all_20_6_21 = 0) & p102(all_20_4_19) = all_20_1_16 & p102(all_20_9_24) = all_20_6_21 & p101(all_20_4_19) = 0 & p101(all_20_9_24) = 0 & p2(all_20_4_19) = all_20_2_17 & p2(all_20_9_24) = 0 & r1(all_0_1_1, all_20_4_19) = 0 & r1(all_0_1_1, all_20_9_24) = 0) | ( ~ (all_20_13_28 = 0) & p100(all_0_1_1) = all_20_13_28)
% 9.04/2.71 |
% 9.04/2.71 +-Applying beta-rule and splitting (47), into two cases.
% 9.04/2.71 |-Branch one:
% 9.04/2.71 | (48) all_20_0_15 = 0 & all_20_3_18 = 0 & all_20_5_20 = 0 & all_20_7_22 = 0 & all_20_8_23 = 0 & ~ (all_20_1_16 = 0) & ~ (all_20_2_17 = 0) & ~ (all_20_6_21 = 0) & p102(all_20_4_19) = all_20_1_16 & p102(all_20_9_24) = all_20_6_21 & p101(all_20_4_19) = 0 & p101(all_20_9_24) = 0 & p2(all_20_4_19) = all_20_2_17 & p2(all_20_9_24) = 0 & r1(all_0_1_1, all_20_4_19) = 0 & r1(all_0_1_1, all_20_9_24) = 0
% 9.04/2.71 |
% 9.04/2.71 | Applying alpha-rule on (48) yields:
% 9.04/2.71 | (49) p2(all_20_4_19) = all_20_2_17
% 9.04/2.71 | (50) p2(all_20_9_24) = 0
% 9.04/2.71 | (51) all_20_8_23 = 0
% 9.04/2.71 | (52) p102(all_20_4_19) = all_20_1_16
% 9.04/2.71 | (53) p102(all_20_9_24) = all_20_6_21
% 9.04/2.71 | (54) ~ (all_20_1_16 = 0)
% 9.04/2.71 | (55) all_20_7_22 = 0
% 9.04/2.71 | (56) all_20_0_15 = 0
% 9.04/2.71 | (57) all_20_3_18 = 0
% 9.04/2.71 | (58) ~ (all_20_2_17 = 0)
% 9.04/2.71 | (59) all_20_5_20 = 0
% 9.04/2.71 | (60) r1(all_0_1_1, all_20_9_24) = 0
% 9.04/2.71 | (61) p101(all_20_9_24) = 0
% 9.04/2.71 | (62) ~ (all_20_6_21 = 0)
% 9.04/2.71 | (63) p101(all_20_4_19) = 0
% 9.04/2.71 | (64) r1(all_0_1_1, all_20_4_19) = 0
% 9.04/2.71 |
% 9.04/2.71 | Instantiating formula (10) with all_20_2_17, all_20_4_19 and discharging atoms p2(all_20_4_19) = all_20_2_17, yields:
% 9.04/2.71 | (65) all_20_2_17 = 0 | ? [v0] : ( ~ (v0 = 0) & r1(all_0_1_1, all_20_4_19) = v0)
% 9.04/2.71 |
% 9.04/2.71 | Instantiating formula (19) with all_20_4_19 and discharging atoms r1(all_0_1_1, all_20_4_19) = 0, yields:
% 9.04/2.71 | (66) p2(all_20_4_19) = 0
% 9.04/2.71 |
% 9.04/2.71 +-Applying beta-rule and splitting (65), into two cases.
% 9.04/2.71 |-Branch one:
% 9.04/2.71 | (67) all_20_2_17 = 0
% 9.04/2.71 |
% 9.04/2.71 | Equations (67) can reduce 58 to:
% 9.04/2.71 | (32) $false
% 9.04/2.71 |
% 9.04/2.71 |-The branch is then unsatisfiable
% 9.04/2.71 |-Branch two:
% 9.04/2.71 | (58) ~ (all_20_2_17 = 0)
% 9.04/2.71 | (70) ? [v0] : ( ~ (v0 = 0) & r1(all_0_1_1, all_20_4_19) = v0)
% 9.04/2.71 |
% 9.04/2.71 | Instantiating formula (5) with all_20_4_19, 0, all_20_2_17 and discharging atoms p2(all_20_4_19) = all_20_2_17, p2(all_20_4_19) = 0, yields:
% 9.04/2.71 | (67) all_20_2_17 = 0
% 9.04/2.71 |
% 9.04/2.71 | Equations (67) can reduce 58 to:
% 9.04/2.71 | (32) $false
% 9.04/2.71 |
% 9.04/2.71 |-The branch is then unsatisfiable
% 9.04/2.71 |-Branch two:
% 9.04/2.71 | (73) ~ (all_20_13_28 = 0) & p100(all_0_1_1) = all_20_13_28
% 9.04/2.71 |
% 9.04/2.71 | Applying alpha-rule on (73) yields:
% 9.04/2.71 | (29) ~ (all_20_13_28 = 0)
% 9.04/2.71 | (75) p100(all_0_1_1) = all_20_13_28
% 9.04/2.71 |
% 9.04/2.71 | Instantiating formula (22) with all_0_1_1, all_20_13_28, 0 and discharging atoms p100(all_0_1_1) = all_20_13_28, p100(all_0_1_1) = 0, yields:
% 9.04/2.72 | (31) all_20_13_28 = 0
% 9.04/2.72 |
% 9.04/2.72 | Equations (31) can reduce 29 to:
% 9.04/2.72 | (32) $false
% 9.04/2.72 |
% 9.04/2.72 |-The branch is then unsatisfiable
% 9.04/2.72 |-Branch two:
% 9.04/2.72 | (40) all_0_0_0 = 0
% 9.04/2.72 | (79) ((all_20_10_25 = 0 & p2(all_0_1_1) = 0) | ( ! [v0] : ( ~ (p101(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p2(v0) = v1) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (p2(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p101(v0) = v1) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (r1(all_0_1_1, v0) = 0) | ? [v1] : (( ~ (v1 = 0) & p101(v0) = v1) | ( ~ (v1 = 0) & p2(v0) = v1))))) & (( ~ (all_20_10_25 = 0) & p2(all_0_1_1) = all_20_10_25) | ( ! [v0] : ! [v1] : (v1 = 0 | ~ (p2(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & p101(v0) = v2) | ( ~ (v2 = 0) & r1(all_0_1_1, v0) = v2))) & ! [v0] : ( ~ (p101(v0) = 0) | ? [v1] : ((v1 = 0 & p2(v0) = 0) | ( ~ (v1 = 0) & r1(all_0_1_1, v0) = v1))) & ! [v0] : ( ~ (r1(all_0_1_1, v0) = 0) | ? [v1] : ((v1 = 0 & p2(v0) = 0) | ( ~ (v1 = 0) & p101(v0) = v1)))))
% 9.04/2.72 |
% 9.04/2.72 | Equations (40) can reduce 11 to:
% 9.04/2.72 | (32) $false
% 9.04/2.72 |
% 9.04/2.72 |-The branch is then unsatisfiable
% 9.04/2.72 % SZS output end Proof for theBenchmark
% 9.04/2.72
% 9.04/2.72 2123ms
%------------------------------------------------------------------------------