TSTP Solution File: NUM856+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM856+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 08:49:13 EDT 2022
% Result : Theorem 19.29s 6.35s
% Output : Proof 22.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM856+1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n025.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 Jul 7 12:52:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.58 ____ _
% 0.18/0.58 ___ / __ \_____(_)___ ________ __________
% 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic
% 0.18/0.58 (ePrincess v.1.0)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2015
% 0.18/0.58 (c) Peter Backeman, 2014-2015
% 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.59 Bug reports to peter@backeman.se
% 0.18/0.59
% 0.18/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.59
% 0.18/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.95/1.02 Prover 0: Preprocessing ...
% 3.07/1.36 Prover 0: Warning: ignoring some quantifiers
% 3.07/1.39 Prover 0: Constructing countermodel ...
% 17.60/5.95 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 17.87/6.03 Prover 1: Preprocessing ...
% 18.45/6.17 Prover 1: Warning: ignoring some quantifiers
% 18.45/6.17 Prover 1: Constructing countermodel ...
% 19.29/6.34 Prover 1: proved (392ms)
% 19.29/6.34 Prover 0: stopped
% 19.29/6.35
% 19.29/6.35 No countermodel exists, formula is valid
% 19.29/6.35 % SZS status Theorem for theBenchmark
% 19.29/6.35
% 19.29/6.35 Generating proof ... Warning: ignoring some quantifiers
% 21.59/6.86 found it (size 112)
% 21.59/6.86
% 21.59/6.86 % SZS output start Proof for theBenchmark
% 21.59/6.86 Assumed formulas after preprocessing and simplification:
% 21.59/6.86 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & geq(vd519, vd520) = v2 & geq(vd517, vd518) = v1 & vmul(vd518, vd520) = v5 & vmul(vd517, vd519) = v4 & greater(v4, v5) = v6 & greater(vd519, vd520) = v0 & greater(vd517, vd518) = v3 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (geq(v11, v12) = v13) | ~ (vplus(v8, v10) = v12) | ~ (vplus(v7, v9) = v11) | ? [v14] : ? [v15] : (geq(v9, v10) = v14 & geq(v7, v8) = v15 & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (vplus(v8, v10) = v12) | ~ (vplus(v7, v9) = v11) | ~ (greater(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (geq(v9, v10) = v16 & geq(v7, v8) = v15 & greater(v9, v10) = v14 & greater(v7, v8) = v17 & ( ~ (v17 = 0) | ~ (v16 = 0)) & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (vplus(v8, v10) = v12) | ~ (vplus(v7, v9) = v11) | ~ (greater(v11, v12) = v13) | ? [v14] : ? [v15] : (greater(v9, v10) = v14 & greater(v7, v8) = v15 & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (vmul(v8, v10) = v12) | ~ (vmul(v7, v9) = v11) | ~ (greater(v11, v12) = v13) | ? [v14] : ? [v15] : (greater(v9, v10) = v14 & greater(v7, v8) = v15 & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (vplus(v8, v9) = v11) | ~ (vplus(v7, v9) = v10) | ~ (less(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & less(v7, v8) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (vplus(v8, v9) = v11) | ~ (vplus(v7, v9) = v10) | ~ (greater(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & greater(v7, v8) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (less(v10, v11) = v12) | ~ (vmul(v9, v7) = v11) | ~ (vmul(v8, v7) = v10) | ? [v13] : ( ~ (v13 = 0) & less(v8, v9) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (vmul(v9, v7) = v11) | ~ (vmul(v8, v7) = v10) | ~ (greater(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & greater(v8, v9) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (vplus(v10, v11) = v12) | ~ (vmul(v7, v9) = v11) | ~ (vmul(v7, v8) = v10) | ? [v13] : (vplus(v8, v9) = v13 & vmul(v7, v13) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (leq(v8, v9) = v11) | ~ (leq(v7, v8) = v10) | ? [v12] : ? [v13] : ? [v14] : (less(v8, v9) = v12 & less(v7, v9) = v14 & less(v7, v8) = v13 & (v14 = 0 | (( ~ (v13 = 0) | ~ (v11 = 0)) & ( ~ (v12 = 0) | ~ (v10 = 0)))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (vplus(v10, v9) = v11) | ~ (vplus(v7, v8) = v10) | ? [v12] : (vplus(v8, v9) = v12 & vplus(v7, v12) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (vplus(v8, v9) = v11) | ~ (vplus(v7, v9) = v10) | ~ (less(v10, v11) = 0) | less(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (vplus(v8, v9) = v11) | ~ (vplus(v7, v9) = v10) | ~ (greater(v10, v11) = 0) | greater(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (less(v10, v11) = 0) | ~ (vmul(v9, v8) = v11) | ~ (vmul(v7, v8) = v10) | less(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (vmul(v10, v9) = v11) | ~ (vmul(v7, v8) = v10) | ? [v12] : (vmul(v8, v9) = v12 & vmul(v7, v12) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (vmul(v9, v8) = v11) | ~ (vmul(v7, v8) = v10) | ~ (greater(v10, v11) = 0) | greater(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (vplus(v7, v8) = v10) | ~ (vplus(v7, v8) = v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (vmul(v8, v7) = v10) | ~ (vmul(v8, v7) = v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (geq(v7, v9) = v10) | ~ (vplus(v8, v1) = v9) | ? [v11] : ( ~ (v11 = 0) & greater(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (leq(v7, v9) = v10) | ~ (leq(v7, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & leq(v8, v9) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (vplus(v7, v8) = v9) | ~ (greater(v9, v7) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (less(v7, v9) = v10) | ~ (less(v7, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & less(v8, v9) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v7 | ~ (vmul(v9, v8) = v10) | ~ (vmul(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (vplus(v8, v10) = v7) | ~ (less(v8, v7) = v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (vplus(v7, v10) = v8) | ~ (greater(v8, v7) = v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (geq(v10, v9) = v8) | ~ (geq(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (leq(v10, v9) = v8) | ~ (leq(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (vplus(v10, v9) = v8) | ~ (vplus(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (vplus(v8, v9) = v10) | ~ (vplus(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (less(v10, v9) = v8) | ~ (less(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (vmul(v10, v9) = v8) | ~ (vmul(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (greater(v10, v9) = v8) | ~ (greater(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (vsucc(v8) = v9) | ~ (vplus(v7, v9) = v10) | ? [v11] : (vsucc(v11) = v10 & vplus(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (vsucc(v8) = v9) | ~ (vmul(v7, v9) = v10) | ? [v11] : (vplus(v11, v7) = v10 & vmul(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (vsucc(v7) = v9) | ~ (vplus(v9, v8) = v10) | ? [v11] : (vsucc(v11) = v10 & vplus(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (vsucc(v7) = v9) | ~ (vmul(v9, v8) = v10) | ? [v11] : (vplus(v11, v8) = v10 & vmul(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (vplus(v8, v10) = v7) | ~ (vplus(v7, v9) = v8)) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (vplus(v9, v8) = v10) | ? [v11] : ( ~ (v11 = v10) & vplus(v9, v7) = v11)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = v7 | ~ (less(v7, v8) = v9) | greater(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (geq(v8, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & greater(v8, v7) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (leq(v8, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & geq(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (leq(v8, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & less(v8, v7) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (less(v8, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & greater(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (vskolem2(v9) = v8) | ~ (vskolem2(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (vsucc(v9) = v8) | ~ (vsucc(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (vsucc(v8) = v9) | ~ (vsucc(v7) = v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (vplus(v8, v1) = v9) | ~ (less(v7, v9) = 0) | leq(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (vplus(v7, v8) = v9) | vplus(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (vmul(v7, v8) = v9) | vmul(v8, v7) = v9) & ! [v7] : ! [v8] : (v8 = v7 | ~ (geq(v8, v7) = 0) | greater(v8, v7) = 0) & ! [v7] : ! [v8] : (v8 = v7 | ~ (leq(v8, v7) = 0) | less(v8, v7) = 0) & ! [v7] : ! [v8] : (v8 = v7 | ~ (vmul(v7, v1) = v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (vmul(v1, v7) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (geq(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (geq(v7, v1) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (leq(v7, v7) = v8)) & ! [v7] : ! [v8] : (v7 = v1 | ~ (vskolem2(v7) = v8) | vsucc(v8) = v7) & ! [v7] : ! [v8] : ( ~ (leq(v7, v8) = 0) | geq(v8, v7) = 0) & ! [v7] : ! [v8] : ~ (vplus(v7, v8) = v8) & ! [v7] : ! [v8] : ~ (vplus(v7, v8) = v7) & ! [v7] : ! [v8] : ( ~ (vplus(v7, v1) = v8) | vsucc(v7) = v8) & ! [v7] : ! [v8] : ( ~ (vplus(v1, v7) = v8) | vsucc(v7) = v8) & ! [v7] : ! [v8] : ( ~ (less(v8, v7) = 0) | ? [v9] : vplus(v8, v9) = v7) & ! [v7] : ! [v8] : ( ~ (less(v7, v8) = 0) | greater(v8, v7) = 0) & ! [v7] : ! [v8] : ( ~ (less(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & greater(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (greater(v8, v7) = 0) | ? [v9] : vplus(v7, v9) = v8) & ! [v7] : ~ (vsucc(v7) = v7) & ! [v7] : ~ (vsucc(v7) = v1) & ! [v7] : ~ (less(v7, v7) = 0) & ! [v7] : ~ (greater(v7, v7) = 0) & ? [v7] : ? [v8] : (v8 = v7 | ? [v9] : ? [v10] : ((v10 = v8 & vplus(v7, v9) = v8) | (v10 = v7 & vplus(v8, v9) = v7))) & ((v3 = 0 & v2 = 0) | (v1 = 0 & v0 = 0)))
% 22.05/6.91 | 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 yields:
% 22.05/6.91 | (1) ~ (all_0_0_0 = 0) & geq(vd519, vd520) = all_0_4_4 & geq(vd517, vd518) = all_0_5_5 & vmul(vd518, vd520) = all_0_1_1 & vmul(vd517, vd519) = all_0_2_2 & greater(all_0_2_2, all_0_1_1) = all_0_0_0 & greater(vd519, vd520) = all_0_6_6 & greater(vd517, vd518) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (geq(v4, v5) = v6) | ~ (vplus(v1, v3) = v5) | ~ (vplus(v0, v2) = v4) | ? [v7] : ? [v8] : (geq(v2, v3) = v7 & geq(v0, v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vplus(v1, v3) = v5) | ~ (vplus(v0, v2) = v4) | ~ (greater(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (geq(v2, v3) = v9 & geq(v0, v1) = v8 & greater(v2, v3) = v7 & greater(v0, v1) = v10 & ( ~ (v10 = 0) | ~ (v9 = 0)) & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vplus(v1, v3) = v5) | ~ (vplus(v0, v2) = v4) | ~ (greater(v4, v5) = v6) | ? [v7] : ? [v8] : (greater(v2, v3) = v7 & greater(v0, v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vmul(v1, v3) = v5) | ~ (vmul(v0, v2) = v4) | ~ (greater(v4, v5) = v6) | ? [v7] : ? [v8] : (greater(v2, v3) = v7 & greater(v0, v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ~ (less(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & less(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ~ (greater(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & greater(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (less(v3, v4) = v5) | ~ (vmul(v2, v0) = v4) | ~ (vmul(v1, v0) = v3) | ? [v6] : ( ~ (v6 = 0) & less(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (vmul(v2, v0) = v4) | ~ (vmul(v1, v0) = v3) | ~ (greater(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & greater(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vplus(v3, v4) = v5) | ~ (vmul(v0, v2) = v4) | ~ (vmul(v0, v1) = v3) | ? [v6] : (vplus(v1, v2) = v6 & vmul(v0, v6) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (leq(v1, v2) = v4) | ~ (leq(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (less(v1, v2) = v5 & less(v0, v2) = v7 & less(v0, v1) = v6 & (v7 = 0 | (( ~ (v6 = 0) | ~ (v4 = 0)) & ( ~ (v5 = 0) | ~ (v3 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ? [v5] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ~ (less(v3, v4) = 0) | less(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ~ (greater(v3, v4) = 0) | greater(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (less(v3, v4) = 0) | ~ (vmul(v2, v1) = v4) | ~ (vmul(v0, v1) = v3) | less(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vmul(v3, v2) = v4) | ~ (vmul(v0, v1) = v3) | ? [v5] : (vmul(v1, v2) = v5 & vmul(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vmul(v2, v1) = v4) | ~ (vmul(v0, v1) = v3) | ~ (greater(v3, v4) = 0) | greater(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (vplus(v0, v1) = v3) | ~ (vplus(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (vmul(v1, v0) = v3) | ~ (vmul(v1, v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (geq(v0, v2) = v3) | ~ (vplus(v1, v1) = v2) | ? [v4] : ( ~ (v4 = 0) & greater(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (leq(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & leq(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (vplus(v0, v1) = v2) | ~ (greater(v2, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less(v0, v2) = v3) | ~ (less(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | ~ (vmul(v2, v1) = v3) | ~ (vmul(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (vplus(v1, v3) = v0) | ~ (less(v1, v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (vplus(v0, v3) = v1) | ~ (greater(v1, v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v1, v2) = v3) | ~ (vplus(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v1) = v2) | ~ (vplus(v0, v2) = v3) | ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v1) = v2) | ~ (vmul(v0, v2) = v3) | ? [v4] : (vplus(v4, v0) = v3 & vmul(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v0) = v2) | ~ (vplus(v2, v1) = v3) | ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v0) = v2) | ~ (vmul(v2, v1) = v3) | ? [v4] : (vplus(v4, v1) = v3 & vmul(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vplus(v1, v3) = v0) | ~ (vplus(v0, v2) = v1)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v2, v1) = v3) | ? [v4] : ( ~ (v4 = v3) & vplus(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (less(v0, v1) = v2) | greater(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (geq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & geq(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & less(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ (vskolem2(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v1) = v2) | ~ (vsucc(v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v1, v1) = v2) | ~ (less(v0, v2) = 0) | leq(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v0, v1) = v2) | vplus(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (vmul(v0, v1) = v2) | vmul(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (geq(v1, v0) = 0) | greater(v1, v0) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v1, v0) = 0) | less(v1, v0) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (vmul(v0, v1) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (vmul(v1, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v1) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1)) & ! [v0] : ! [v1] : (v0 = v1 | ~ (vskolem2(v0) = v1) | vsucc(v1) = v0) & ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | geq(v1, v0) = 0) & ! [v0] : ! [v1] : ~ (vplus(v0, v1) = v1) & ! [v0] : ! [v1] : ~ (vplus(v0, v1) = v0) & ! [v0] : ! [v1] : ( ~ (vplus(v0, v1) = v1) | vsucc(v0) = v1) & ! [v0] : ! [v1] : ( ~ (vplus(v1, v0) = v1) | vsucc(v0) = v1) & ! [v0] : ! [v1] : ( ~ (less(v1, v0) = 0) | ? [v2] : vplus(v1, v2) = v0) & ! [v0] : ! [v1] : ( ~ (less(v0, v1) = 0) | greater(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (less(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & greater(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (greater(v1, v0) = 0) | ? [v2] : vplus(v0, v2) = v1) & ! [v0] : ~ (vsucc(v0) = v0) & ! [v0] : ~ (vsucc(v0) = v1) & ! [v0] : ~ (less(v0, v0) = 0) & ! [v0] : ~ (greater(v0, v0) = 0) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ((v3 = v1 & vplus(v0, v2) = v1) | (v3 = v0 & vplus(v1, v2) = v0))) & ((all_0_3_3 = 0 & all_0_4_4 = 0) | (all_0_5_5 = 0 & all_0_6_6 = 0))
% 22.05/6.93 |
% 22.05/6.93 | Applying alpha-rule on (1) yields:
% 22.05/6.93 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ (geq(v1, v0) = 0) | greater(v1, v0) = 0)
% 22.05/6.93 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ~ (greater(v3, v4) = 0) | greater(v0, v1) = 0)
% 22.05/6.93 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & less(v1, v0) = v3))
% 22.05/6.93 | (5) (all_0_3_3 = 0 & all_0_4_4 = 0) | (all_0_5_5 = 0 & all_0_6_6 = 0)
% 22.05/6.93 | (6) ~ (all_0_0_0 = 0)
% 22.05/6.93 | (7) ! [v0] : ! [v1] : ( ~ (vplus(v1, v0) = v1) | vsucc(v0) = v1)
% 22.05/6.93 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ (vmul(v1, v0) = v1))
% 22.05/6.93 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | ~ (vmul(v2, v1) = v3) | ~ (vmul(v0, v1) = v3))
% 22.05/6.93 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v0) = v2) | ~ (vmul(v2, v1) = v3) | ? [v4] : (vplus(v4, v1) = v3 & vmul(v0, v1) = v4))
% 22.05/6.93 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 22.05/6.93 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (geq(v4, v5) = v6) | ~ (vplus(v1, v3) = v5) | ~ (vplus(v0, v2) = v4) | ? [v7] : ? [v8] : (geq(v2, v3) = v7 & geq(v0, v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 22.05/6.93 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vplus(v1, v3) = v5) | ~ (vplus(v0, v2) = v4) | ~ (greater(v4, v5) = v6) | ? [v7] : ? [v8] : (greater(v2, v3) = v7 & greater(v0, v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 22.05/6.93 | (14) ! [v0] : ~ (greater(v0, v0) = 0)
% 22.05/6.93 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0))
% 22.05/6.93 | (16) ! [v0] : ! [v1] : (v0 = v1 | ~ (vskolem2(v0) = v1) | vsucc(v1) = v0)
% 22.05/6.93 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v1) = v2) | ~ (vmul(v0, v2) = v3) | ? [v4] : (vplus(v4, v0) = v3 & vmul(v0, v1) = v4))
% 22.05/6.93 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vplus(v1, v3) = v5) | ~ (vplus(v0, v2) = v4) | ~ (greater(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (geq(v2, v3) = v9 & geq(v0, v1) = v8 & greater(v2, v3) = v7 & greater(v0, v1) = v10 & ( ~ (v10 = 0) | ~ (v9 = 0)) & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 22.05/6.93 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ~ (greater(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & greater(v0, v1) = v6))
% 22.05/6.93 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vmul(v3, v2) = v4) | ~ (vmul(v0, v1) = v3) | ? [v5] : (vmul(v1, v2) = v5 & vmul(v0, v5) = v4))
% 22.05/6.93 | (21) geq(vd517, vd518) = all_0_5_5
% 22.05/6.93 | (22) greater(all_0_2_2, all_0_1_1) = all_0_0_0
% 22.05/6.93 | (23) ! [v0] : ~ (vsucc(v0) = v0)
% 22.05/6.93 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & geq(v0, v1) = v3))
% 22.05/6.93 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v0) = v2) | ~ (vplus(v2, v1) = v3) | ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4))
% 22.05/6.93 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (vmul(v0, v1) = v2) | vmul(v1, v0) = v2)
% 22.05/6.93 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v1, v1) = v2) | ~ (less(v0, v2) = 0) | leq(v0, v1) = 0)
% 22.05/6.93 | (28) vmul(vd518, vd520) = all_0_1_1
% 22.05/6.93 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ~ (less(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & less(v0, v1) = v6))
% 22.05/6.93 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0))
% 22.05/6.93 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ (vskolem2(v2) = v0))
% 22.05/6.93 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (vplus(v3, v4) = v5) | ~ (vmul(v0, v2) = v4) | ~ (vmul(v0, v1) = v3) | ? [v6] : (vplus(v1, v2) = v6 & vmul(v0, v6) = v5))
% 22.05/6.94 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (leq(v1, v2) = v4) | ~ (leq(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (less(v1, v2) = v5 & less(v0, v2) = v7 & less(v0, v1) = v6 & (v7 = 0 | (( ~ (v6 = 0) | ~ (v4 = 0)) & ( ~ (v5 = 0) | ~ (v3 = 0))))))
% 22.05/6.94 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0))
% 22.05/6.94 | (35) ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v1) = v1))
% 22.05/6.94 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (vmul(v2, v0) = v4) | ~ (vmul(v1, v0) = v3) | ~ (greater(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & greater(v1, v2) = v6))
% 22.05/6.94 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (vplus(v0, v1) = v2) | ~ (greater(v2, v0) = v3))
% 22.05/6.94 | (38) ! [v0] : ! [v1] : ~ (vplus(v0, v1) = v0)
% 22.05/6.94 | (39) ! [v0] : ! [v1] : ( ~ (vplus(v0, v1) = v1) | vsucc(v0) = v1)
% 22.05/6.94 | (40) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v0, v1) = v3))
% 22.05/6.94 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (geq(v0, v2) = v3) | ~ (vplus(v1, v1) = v2) | ? [v4] : ( ~ (v4 = 0) & greater(v0, v1) = v4))
% 22.05/6.94 | (42) vmul(vd517, vd519) = all_0_2_2
% 22.05/6.94 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (vplus(v1, v3) = v0) | ~ (less(v1, v0) = v2))
% 22.05/6.94 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less(v0, v2) = v3) | ~ (less(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less(v1, v2) = v4))
% 22.05/6.94 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (leq(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & leq(v1, v2) = v4))
% 22.05/6.94 | (46) ! [v0] : ! [v1] : (v1 = v0 | ~ (vmul(v0, v1) = v1))
% 22.05/6.94 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (vplus(v0, v3) = v1) | ~ (greater(v1, v0) = v2))
% 22.05/6.94 | (48) ! [v0] : ~ (vsucc(v0) = v1)
% 22.05/6.94 | (49) ! [v0] : ! [v1] : ( ~ (less(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & greater(v0, v1) = v2))
% 22.05/6.94 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vplus(v1, v3) = v0) | ~ (vplus(v0, v2) = v1))
% 22.05/6.94 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v1, v2) = v3) | ~ (vplus(v0, v2) = v3))
% 22.05/6.94 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vmul(v2, v1) = v4) | ~ (vmul(v0, v1) = v3) | ~ (greater(v3, v4) = 0) | greater(v0, v2) = 0)
% 22.05/6.94 | (53) ! [v0] : ~ (less(v0, v0) = 0)
% 22.05/6.94 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v0, v1) = v2) | vplus(v1, v0) = v2)
% 22.05/6.94 | (55) ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1))
% 22.05/6.94 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (vplus(v0, v1) = v3) | ~ (vplus(v0, v1) = v2))
% 22.05/6.94 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ~ (less(v3, v4) = 0) | less(v0, v1) = 0)
% 22.05/6.94 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0))
% 22.05/6.94 | (59) ! [v0] : ! [v1] : ~ (vplus(v0, v1) = v1)
% 22.05/6.94 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v1) = v2) | ~ (vplus(v0, v2) = v3) | ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4))
% 22.05/6.94 | (61) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0))
% 22.05/6.94 | (62) ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | geq(v1, v0) = 0)
% 22.05/6.94 | (63) ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1))
% 22.05/6.94 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vmul(v1, v3) = v5) | ~ (vmul(v0, v2) = v4) | ~ (greater(v4, v5) = v6) | ? [v7] : ? [v8] : (greater(v2, v3) = v7 & greater(v0, v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 22.05/6.94 | (65) ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v1, v0) = 0) | less(v1, v0) = 0)
% 22.05/6.94 | (66) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v2, v1) = v3) | ? [v4] : ( ~ (v4 = v3) & vplus(v2, v0) = v4))
% 22.05/6.94 | (67) geq(vd519, vd520) = all_0_4_4
% 22.05/6.94 | (68) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (less(v0, v1) = v2) | greater(v0, v1) = 0)
% 22.05/6.94 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (less(v3, v4) = v5) | ~ (vmul(v2, v0) = v4) | ~ (vmul(v1, v0) = v3) | ? [v6] : ( ~ (v6 = 0) & less(v1, v2) = v6))
% 22.05/6.94 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ? [v5] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4))
% 22.05/6.94 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (less(v3, v4) = 0) | ~ (vmul(v2, v1) = v4) | ~ (vmul(v0, v1) = v3) | less(v0, v2) = 0)
% 22.05/6.94 | (72) greater(vd519, vd520) = all_0_6_6
% 22.05/6.94 | (73) ! [v0] : ! [v1] : ( ~ (greater(v1, v0) = 0) | ? [v2] : vplus(v0, v2) = v1)
% 22.05/6.94 | (74) ! [v0] : ! [v1] : ( ~ (less(v1, v0) = 0) | ? [v2] : vplus(v1, v2) = v0)
% 22.05/6.94 | (75) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v1) = v2) | ~ (vsucc(v0) = v2))
% 22.05/6.94 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (vmul(v1, v0) = v3) | ~ (vmul(v1, v0) = v2))
% 22.05/6.94 | (77) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ((v3 = v1 & vplus(v0, v2) = v1) | (v3 = v0 & vplus(v1, v2) = v0)))
% 22.05/6.94 | (78) ! [v0] : ! [v1] : ( ~ (less(v0, v1) = 0) | greater(v1, v0) = 0)
% 22.05/6.94 | (79) greater(vd517, vd518) = all_0_3_3
% 22.05/6.94 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0))
% 22.05/6.94 | (81) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (geq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v1, v0) = v3))
% 22.05/6.95 |
% 22.05/6.95 | Instantiating formula (2) with vd519, vd520 yields:
% 22.05/6.95 | (82) vd520 = vd519 | ~ (geq(vd519, vd520) = 0) | greater(vd519, vd520) = 0
% 22.05/6.95 |
% 22.05/6.95 | Instantiating formula (2) with vd517, vd518 yields:
% 22.05/6.95 | (83) vd518 = vd517 | ~ (geq(vd517, vd518) = 0) | greater(vd517, vd518) = 0
% 22.05/6.95 |
% 22.05/6.95 | Instantiating formula (26) with all_0_1_1, vd520, vd518 and discharging atoms vmul(vd518, vd520) = all_0_1_1, yields:
% 22.05/6.95 | (84) vmul(vd520, vd518) = all_0_1_1
% 22.05/6.95 |
% 22.05/6.95 | Instantiating formula (26) with all_0_2_2, vd519, vd517 and discharging atoms vmul(vd517, vd519) = all_0_2_2, yields:
% 22.05/6.95 | (85) vmul(vd519, vd517) = all_0_2_2
% 22.05/6.95 |
% 22.05/6.95 | Instantiating formula (36) with all_0_0_0, all_0_1_1, all_0_2_2, vd518, vd517, vd519 and discharging atoms vmul(vd517, vd519) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 22.05/6.95 | (86) all_0_0_0 = 0 | ~ (vmul(vd518, vd519) = all_0_1_1) | ? [v0] : ( ~ (v0 = 0) & greater(vd517, vd518) = v0)
% 22.05/6.95 |
% 22.05/6.95 | Instantiating formula (64) with all_0_0_0, all_0_1_1, all_0_2_2, vd520, vd519, vd518, vd517 and discharging atoms vmul(vd518, vd520) = all_0_1_1, vmul(vd517, vd519) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 22.05/6.95 | (87) all_0_0_0 = 0 | ? [v0] : ? [v1] : (greater(vd519, vd520) = v0 & greater(vd517, vd518) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.05/6.95 |
% 22.05/6.95 | Instantiating formula (73) with vd519, vd520 yields:
% 22.05/6.95 | (88) ~ (greater(vd519, vd520) = 0) | ? [v0] : vplus(vd520, v0) = vd519
% 22.05/6.95 |
% 22.05/6.95 | Instantiating formula (73) with vd517, vd518 yields:
% 22.05/6.95 | (89) ~ (greater(vd517, vd518) = 0) | ? [v0] : vplus(vd518, v0) = vd517
% 22.05/6.95 |
% 22.05/6.95 | Instantiating formula (64) with all_0_0_0, all_0_1_1, all_0_2_2, vd518, vd519, vd520, vd517 and discharging atoms vmul(vd520, vd518) = all_0_1_1, vmul(vd517, vd519) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 22.05/6.95 | (90) all_0_0_0 = 0 | ? [v0] : ? [v1] : (greater(vd519, vd518) = v0 & greater(vd517, vd520) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.05/6.95 |
% 22.05/6.95 | Instantiating formula (64) with all_0_0_0, all_0_1_1, all_0_2_2, vd520, vd517, vd518, vd519 and discharging atoms vmul(vd518, vd520) = all_0_1_1, vmul(vd519, vd517) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 22.05/6.95 | (91) all_0_0_0 = 0 | ? [v0] : ? [v1] : (greater(vd519, vd518) = v1 & greater(vd517, vd520) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.05/6.95 |
% 22.05/6.95 | Instantiating formula (64) with all_0_0_0, all_0_1_1, all_0_2_2, vd518, vd517, vd520, vd519 and discharging atoms vmul(vd520, vd518) = all_0_1_1, vmul(vd519, vd517) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 22.05/6.95 | (92) all_0_0_0 = 0 | ? [v0] : ? [v1] : (greater(vd519, vd520) = v1 & greater(vd517, vd518) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.05/6.95 |
% 22.05/6.95 | Instantiating formula (36) with all_0_0_0, all_0_1_1, all_0_2_2, vd520, vd519, vd517 and discharging atoms vmul(vd519, vd517) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 22.05/6.95 | (93) all_0_0_0 = 0 | ~ (vmul(vd520, vd517) = all_0_1_1) | ? [v0] : ( ~ (v0 = 0) & greater(vd519, vd520) = v0)
% 22.05/6.95 |
% 22.05/6.95 +-Applying beta-rule and splitting (91), into two cases.
% 22.05/6.95 |-Branch one:
% 22.05/6.95 | (94) all_0_0_0 = 0
% 22.05/6.95 |
% 22.05/6.95 | Equations (94) can reduce 6 to:
% 22.05/6.95 | (95) $false
% 22.05/6.95 |
% 22.05/6.95 |-The branch is then unsatisfiable
% 22.05/6.95 |-Branch two:
% 22.05/6.95 | (6) ~ (all_0_0_0 = 0)
% 22.05/6.95 | (97) ? [v0] : ? [v1] : (greater(vd519, vd518) = v1 & greater(vd517, vd520) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.05/6.95 |
% 22.05/6.95 +-Applying beta-rule and splitting (90), into two cases.
% 22.05/6.95 |-Branch one:
% 22.05/6.95 | (94) all_0_0_0 = 0
% 22.05/6.95 |
% 22.05/6.95 | Equations (94) can reduce 6 to:
% 22.05/6.95 | (95) $false
% 22.05/6.95 |
% 22.05/6.95 |-The branch is then unsatisfiable
% 22.05/6.95 |-Branch two:
% 22.05/6.95 | (6) ~ (all_0_0_0 = 0)
% 22.05/6.95 | (101) ? [v0] : ? [v1] : (greater(vd519, vd518) = v0 & greater(vd517, vd520) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.05/6.95 |
% 22.05/6.95 +-Applying beta-rule and splitting (5), into two cases.
% 22.05/6.95 |-Branch one:
% 22.05/6.95 | (102) all_0_3_3 = 0 & all_0_4_4 = 0
% 22.05/6.95 |
% 22.05/6.95 | Applying alpha-rule on (102) yields:
% 22.05/6.95 | (103) all_0_3_3 = 0
% 22.05/6.95 | (104) all_0_4_4 = 0
% 22.05/6.95 |
% 22.05/6.95 | From (104) and (67) follows:
% 22.05/6.95 | (105) geq(vd519, vd520) = 0
% 22.05/6.95 |
% 22.05/6.95 | From (103) and (79) follows:
% 22.05/6.95 | (106) greater(vd517, vd518) = 0
% 22.05/6.95 |
% 22.05/6.95 +-Applying beta-rule and splitting (86), into two cases.
% 22.05/6.95 |-Branch one:
% 22.05/6.95 | (107) ~ (vmul(vd518, vd519) = all_0_1_1)
% 22.05/6.95 |
% 22.05/6.95 +-Applying beta-rule and splitting (89), into two cases.
% 22.05/6.95 |-Branch one:
% 22.05/6.95 | (108) ~ (greater(vd517, vd518) = 0)
% 22.05/6.95 |
% 22.05/6.95 | Using (106) and (108) yields:
% 22.05/6.95 | (109) $false
% 22.05/6.95 |
% 22.05/6.95 |-The branch is then unsatisfiable
% 22.05/6.95 |-Branch two:
% 22.05/6.95 | (106) greater(vd517, vd518) = 0
% 22.05/6.95 | (111) ? [v0] : vplus(vd518, v0) = vd517
% 22.05/6.95 |
% 22.05/6.95 +-Applying beta-rule and splitting (92), into two cases.
% 22.05/6.95 |-Branch one:
% 22.05/6.95 | (94) all_0_0_0 = 0
% 22.05/6.95 |
% 22.05/6.95 | Equations (94) can reduce 6 to:
% 22.05/6.95 | (95) $false
% 22.05/6.95 |
% 22.05/6.95 |-The branch is then unsatisfiable
% 22.05/6.95 |-Branch two:
% 22.05/6.95 | (6) ~ (all_0_0_0 = 0)
% 22.05/6.95 | (115) ? [v0] : ? [v1] : (greater(vd519, vd520) = v1 & greater(vd517, vd518) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.05/6.95 |
% 22.05/6.95 | Instantiating (115) with all_112_0_15, all_112_1_16 yields:
% 22.05/6.95 | (116) greater(vd519, vd520) = all_112_0_15 & greater(vd517, vd518) = all_112_1_16 & ( ~ (all_112_0_15 = 0) | ~ (all_112_1_16 = 0))
% 22.05/6.95 |
% 22.05/6.95 | Applying alpha-rule on (116) yields:
% 22.05/6.95 | (117) greater(vd519, vd520) = all_112_0_15
% 22.05/6.95 | (118) greater(vd517, vd518) = all_112_1_16
% 22.05/6.96 | (119) ~ (all_112_0_15 = 0) | ~ (all_112_1_16 = 0)
% 22.05/6.96 |
% 22.05/6.96 | Instantiating formula (30) with vd519, vd520, all_112_0_15, all_0_6_6 and discharging atoms greater(vd519, vd520) = all_112_0_15, greater(vd519, vd520) = all_0_6_6, yields:
% 22.05/6.96 | (120) all_112_0_15 = all_0_6_6
% 22.05/6.96 |
% 22.05/6.96 | Instantiating formula (30) with vd517, vd518, 0, all_112_1_16 and discharging atoms greater(vd517, vd518) = all_112_1_16, greater(vd517, vd518) = 0, yields:
% 22.05/6.96 | (121) all_112_1_16 = 0
% 22.05/6.96 |
% 22.05/6.96 | Using (28) and (107) yields:
% 22.05/6.96 | (122) ~ (vd520 = vd519)
% 22.05/6.96 |
% 22.05/6.96 | From (120) and (117) follows:
% 22.05/6.96 | (72) greater(vd519, vd520) = all_0_6_6
% 22.05/6.96 |
% 22.05/6.96 +-Applying beta-rule and splitting (87), into two cases.
% 22.05/6.96 |-Branch one:
% 22.05/6.96 | (94) all_0_0_0 = 0
% 22.05/6.96 |
% 22.05/6.96 | Equations (94) can reduce 6 to:
% 22.05/6.96 | (95) $false
% 22.05/6.96 |
% 22.05/6.96 |-The branch is then unsatisfiable
% 22.05/6.96 |-Branch two:
% 22.05/6.96 | (6) ~ (all_0_0_0 = 0)
% 22.05/6.96 | (127) ? [v0] : ? [v1] : (greater(vd519, vd520) = v0 & greater(vd517, vd518) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.05/6.96 |
% 22.05/6.96 | Instantiating (127) with all_122_0_17, all_122_1_18 yields:
% 22.05/6.96 | (128) greater(vd519, vd520) = all_122_1_18 & greater(vd517, vd518) = all_122_0_17 & ( ~ (all_122_0_17 = 0) | ~ (all_122_1_18 = 0))
% 22.05/6.96 |
% 22.05/6.96 | Applying alpha-rule on (128) yields:
% 22.05/6.96 | (129) greater(vd519, vd520) = all_122_1_18
% 22.05/6.96 | (130) greater(vd517, vd518) = all_122_0_17
% 22.05/6.96 | (131) ~ (all_122_0_17 = 0) | ~ (all_122_1_18 = 0)
% 22.05/6.96 |
% 22.05/6.96 +-Applying beta-rule and splitting (119), into two cases.
% 22.05/6.96 |-Branch one:
% 22.05/6.96 | (132) ~ (all_112_0_15 = 0)
% 22.05/6.96 |
% 22.05/6.96 | Equations (120) can reduce 132 to:
% 22.05/6.96 | (133) ~ (all_0_6_6 = 0)
% 22.05/6.96 |
% 22.05/6.96 +-Applying beta-rule and splitting (82), into two cases.
% 22.05/6.96 |-Branch one:
% 22.05/6.96 | (134) greater(vd519, vd520) = 0
% 22.05/6.96 |
% 22.05/6.96 | Instantiating formula (30) with vd519, vd520, all_122_1_18, all_0_6_6 and discharging atoms greater(vd519, vd520) = all_122_1_18, greater(vd519, vd520) = all_0_6_6, yields:
% 22.05/6.96 | (135) all_122_1_18 = all_0_6_6
% 22.05/6.96 |
% 22.05/6.96 | Instantiating formula (30) with vd519, vd520, 0, all_122_1_18 and discharging atoms greater(vd519, vd520) = all_122_1_18, greater(vd519, vd520) = 0, yields:
% 22.05/6.96 | (136) all_122_1_18 = 0
% 22.05/6.96 |
% 22.05/6.96 | Combining equations (135,136) yields a new equation:
% 22.05/6.96 | (137) all_0_6_6 = 0
% 22.05/6.96 |
% 22.05/6.96 | Simplifying 137 yields:
% 22.05/6.96 | (138) all_0_6_6 = 0
% 22.05/6.96 |
% 22.05/6.96 | Equations (138) can reduce 133 to:
% 22.05/6.96 | (95) $false
% 22.05/6.96 |
% 22.05/6.96 |-The branch is then unsatisfiable
% 22.05/6.96 |-Branch two:
% 22.05/6.96 | (140) ~ (greater(vd519, vd520) = 0)
% 22.05/6.96 | (141) vd520 = vd519 | ~ (geq(vd519, vd520) = 0)
% 22.05/6.96 |
% 22.05/6.96 +-Applying beta-rule and splitting (141), into two cases.
% 22.05/6.96 |-Branch one:
% 22.05/6.96 | (142) ~ (geq(vd519, vd520) = 0)
% 22.05/6.96 |
% 22.05/6.96 | Using (105) and (142) yields:
% 22.05/6.96 | (109) $false
% 22.05/6.96 |
% 22.05/6.96 |-The branch is then unsatisfiable
% 22.05/6.96 |-Branch two:
% 22.05/6.96 | (105) geq(vd519, vd520) = 0
% 22.05/6.96 | (145) vd520 = vd519
% 22.05/6.96 |
% 22.05/6.96 | Equations (145) can reduce 122 to:
% 22.05/6.96 | (95) $false
% 22.05/6.96 |
% 22.05/6.96 |-The branch is then unsatisfiable
% 22.05/6.96 |-Branch two:
% 22.05/6.96 | (147) all_112_0_15 = 0
% 22.05/6.96 | (148) ~ (all_112_1_16 = 0)
% 22.05/6.96 |
% 22.05/6.96 | Equations (121) can reduce 148 to:
% 22.05/6.96 | (95) $false
% 22.05/6.96 |
% 22.05/6.96 |-The branch is then unsatisfiable
% 22.05/6.96 |-Branch two:
% 22.05/6.96 | (150) vmul(vd518, vd519) = all_0_1_1
% 22.05/6.96 | (151) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & greater(vd517, vd518) = v0)
% 22.05/6.96 |
% 22.05/6.96 +-Applying beta-rule and splitting (89), into two cases.
% 22.05/6.96 |-Branch one:
% 22.05/6.96 | (108) ~ (greater(vd517, vd518) = 0)
% 22.05/6.96 |
% 22.05/6.96 | Using (106) and (108) yields:
% 22.05/6.96 | (109) $false
% 22.05/6.96 |
% 22.05/6.96 |-The branch is then unsatisfiable
% 22.05/6.96 |-Branch two:
% 22.05/6.96 | (106) greater(vd517, vd518) = 0
% 22.05/6.96 | (111) ? [v0] : vplus(vd518, v0) = vd517
% 22.05/6.96 |
% 22.05/6.96 +-Applying beta-rule and splitting (151), into two cases.
% 22.05/6.96 |-Branch one:
% 22.05/6.96 | (94) all_0_0_0 = 0
% 22.05/6.96 |
% 22.05/6.96 | Equations (94) can reduce 6 to:
% 22.05/6.96 | (95) $false
% 22.05/6.96 |
% 22.05/6.96 |-The branch is then unsatisfiable
% 22.05/6.96 |-Branch two:
% 22.05/6.96 | (6) ~ (all_0_0_0 = 0)
% 22.05/6.96 | (159) ? [v0] : ( ~ (v0 = 0) & greater(vd517, vd518) = v0)
% 22.05/6.96 |
% 22.05/6.96 | Instantiating (159) with all_116_0_20 yields:
% 22.05/6.96 | (160) ~ (all_116_0_20 = 0) & greater(vd517, vd518) = all_116_0_20
% 22.05/6.96 |
% 22.05/6.96 | Applying alpha-rule on (160) yields:
% 22.05/6.96 | (161) ~ (all_116_0_20 = 0)
% 22.05/6.96 | (162) greater(vd517, vd518) = all_116_0_20
% 22.05/6.96 |
% 22.05/6.96 | Instantiating formula (30) with vd517, vd518, 0, all_116_0_20 and discharging atoms greater(vd517, vd518) = all_116_0_20, greater(vd517, vd518) = 0, yields:
% 22.05/6.96 | (163) all_116_0_20 = 0
% 22.05/6.96 |
% 22.05/6.96 | Equations (163) can reduce 161 to:
% 22.05/6.96 | (95) $false
% 22.05/6.96 |
% 22.05/6.96 |-The branch is then unsatisfiable
% 22.05/6.96 |-Branch two:
% 22.05/6.96 | (165) all_0_5_5 = 0 & all_0_6_6 = 0
% 22.05/6.96 |
% 22.05/6.96 | Applying alpha-rule on (165) yields:
% 22.05/6.96 | (166) all_0_5_5 = 0
% 22.05/6.96 | (138) all_0_6_6 = 0
% 22.05/6.96 |
% 22.05/6.96 | From (166) and (21) follows:
% 22.05/6.96 | (168) geq(vd517, vd518) = 0
% 22.05/6.96 |
% 22.05/6.96 | From (138) and (72) follows:
% 22.05/6.96 | (134) greater(vd519, vd520) = 0
% 22.05/6.96 |
% 22.05/6.96 +-Applying beta-rule and splitting (93), into two cases.
% 22.05/6.96 |-Branch one:
% 22.05/6.96 | (170) ~ (vmul(vd520, vd517) = all_0_1_1)
% 22.05/6.96 |
% 22.05/6.96 +-Applying beta-rule and splitting (88), into two cases.
% 22.05/6.96 |-Branch one:
% 22.05/6.96 | (140) ~ (greater(vd519, vd520) = 0)
% 22.05/6.96 |
% 22.05/6.96 | Using (134) and (140) yields:
% 22.05/6.96 | (109) $false
% 22.05/6.96 |
% 22.05/6.96 |-The branch is then unsatisfiable
% 22.05/6.96 |-Branch two:
% 22.05/6.96 | (134) greater(vd519, vd520) = 0
% 22.05/6.97 | (174) ? [v0] : vplus(vd520, v0) = vd519
% 22.05/6.97 |
% 22.05/6.97 +-Applying beta-rule and splitting (87), into two cases.
% 22.05/6.97 |-Branch one:
% 22.05/6.97 | (94) all_0_0_0 = 0
% 22.05/6.97 |
% 22.05/6.97 | Equations (94) can reduce 6 to:
% 22.05/6.97 | (95) $false
% 22.05/6.97 |
% 22.05/6.97 |-The branch is then unsatisfiable
% 22.05/6.97 |-Branch two:
% 22.05/6.97 | (6) ~ (all_0_0_0 = 0)
% 22.05/6.97 | (127) ? [v0] : ? [v1] : (greater(vd519, vd520) = v0 & greater(vd517, vd518) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.05/6.97 |
% 22.05/6.97 | Instantiating (127) with all_116_0_22, all_116_1_23 yields:
% 22.05/6.97 | (179) greater(vd519, vd520) = all_116_1_23 & greater(vd517, vd518) = all_116_0_22 & ( ~ (all_116_0_22 = 0) | ~ (all_116_1_23 = 0))
% 22.05/6.97 |
% 22.05/6.97 | Applying alpha-rule on (179) yields:
% 22.05/6.97 | (180) greater(vd519, vd520) = all_116_1_23
% 22.05/6.97 | (181) greater(vd517, vd518) = all_116_0_22
% 22.05/6.97 | (182) ~ (all_116_0_22 = 0) | ~ (all_116_1_23 = 0)
% 22.05/6.97 |
% 22.05/6.97 | Instantiating formula (30) with vd519, vd520, 0, all_116_1_23 and discharging atoms greater(vd519, vd520) = all_116_1_23, greater(vd519, vd520) = 0, yields:
% 22.05/6.97 | (183) all_116_1_23 = 0
% 22.05/6.97 |
% 22.05/6.97 | Instantiating formula (30) with vd517, vd518, all_116_0_22, all_0_3_3 and discharging atoms greater(vd517, vd518) = all_116_0_22, greater(vd517, vd518) = all_0_3_3, yields:
% 22.05/6.97 | (184) all_116_0_22 = all_0_3_3
% 22.05/6.97 |
% 22.05/6.97 | Using (84) and (170) yields:
% 22.05/6.97 | (185) ~ (vd518 = vd517)
% 22.05/6.97 |
% 22.05/6.97 | From (184) and (181) follows:
% 22.05/6.97 | (79) greater(vd517, vd518) = all_0_3_3
% 22.05/6.97 |
% 22.05/6.97 +-Applying beta-rule and splitting (83), into two cases.
% 22.05/6.97 |-Branch one:
% 22.05/6.97 | (106) greater(vd517, vd518) = 0
% 22.05/6.97 |
% 22.05/6.97 +-Applying beta-rule and splitting (182), into two cases.
% 22.05/6.97 |-Branch one:
% 22.05/6.97 | (188) ~ (all_116_0_22 = 0)
% 22.05/6.97 |
% 22.05/6.97 | Equations (184) can reduce 188 to:
% 22.05/6.97 | (189) ~ (all_0_3_3 = 0)
% 22.05/6.97 |
% 22.05/6.97 +-Applying beta-rule and splitting (89), into two cases.
% 22.05/6.97 |-Branch one:
% 22.05/6.97 | (108) ~ (greater(vd517, vd518) = 0)
% 22.05/6.97 |
% 22.05/6.97 | Using (106) and (108) yields:
% 22.05/6.97 | (109) $false
% 22.05/6.97 |
% 22.05/6.97 |-The branch is then unsatisfiable
% 22.05/6.97 |-Branch two:
% 22.05/6.97 | (106) greater(vd517, vd518) = 0
% 22.05/6.97 | (111) ? [v0] : vplus(vd518, v0) = vd517
% 22.05/6.97 |
% 22.05/6.97 | Instantiating formula (30) with vd517, vd518, 0, all_0_3_3 and discharging atoms greater(vd517, vd518) = all_0_3_3, greater(vd517, vd518) = 0, yields:
% 22.05/6.97 | (103) all_0_3_3 = 0
% 22.05/6.97 |
% 22.05/6.97 | Equations (103) can reduce 189 to:
% 22.05/6.97 | (95) $false
% 22.05/6.97 |
% 22.05/6.97 |-The branch is then unsatisfiable
% 22.05/6.97 |-Branch two:
% 22.05/6.97 | (196) all_116_0_22 = 0
% 22.05/6.97 | (197) ~ (all_116_1_23 = 0)
% 22.05/6.97 |
% 22.05/6.97 | Equations (183) can reduce 197 to:
% 22.05/6.97 | (95) $false
% 22.05/6.97 |
% 22.05/6.97 |-The branch is then unsatisfiable
% 22.05/6.97 |-Branch two:
% 22.05/6.97 | (108) ~ (greater(vd517, vd518) = 0)
% 22.05/6.97 | (200) vd518 = vd517 | ~ (geq(vd517, vd518) = 0)
% 22.05/6.97 |
% 22.05/6.97 +-Applying beta-rule and splitting (200), into two cases.
% 22.05/6.97 |-Branch one:
% 22.05/6.97 | (201) ~ (geq(vd517, vd518) = 0)
% 22.05/6.97 |
% 22.05/6.97 | Using (168) and (201) yields:
% 22.05/6.97 | (109) $false
% 22.05/6.97 |
% 22.05/6.97 |-The branch is then unsatisfiable
% 22.05/6.97 |-Branch two:
% 22.05/6.97 | (168) geq(vd517, vd518) = 0
% 22.05/6.97 | (204) vd518 = vd517
% 22.05/6.97 |
% 22.05/6.97 | Equations (204) can reduce 185 to:
% 22.05/6.97 | (95) $false
% 22.05/6.97 |
% 22.05/6.97 |-The branch is then unsatisfiable
% 22.05/6.97 |-Branch two:
% 22.05/6.97 | (206) vmul(vd520, vd517) = all_0_1_1
% 22.05/6.97 | (207) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & greater(vd519, vd520) = v0)
% 22.05/6.97 |
% 22.05/6.97 +-Applying beta-rule and splitting (88), into two cases.
% 22.05/6.97 |-Branch one:
% 22.05/6.97 | (140) ~ (greater(vd519, vd520) = 0)
% 22.05/6.97 |
% 22.05/6.97 | Using (134) and (140) yields:
% 22.05/6.97 | (109) $false
% 22.05/6.97 |
% 22.05/6.97 |-The branch is then unsatisfiable
% 22.05/6.97 |-Branch two:
% 22.05/6.97 | (134) greater(vd519, vd520) = 0
% 22.05/6.97 | (174) ? [v0] : vplus(vd520, v0) = vd519
% 22.05/6.97 |
% 22.05/6.97 +-Applying beta-rule and splitting (207), into two cases.
% 22.05/6.97 |-Branch one:
% 22.05/6.97 | (94) all_0_0_0 = 0
% 22.05/6.97 |
% 22.05/6.97 | Equations (94) can reduce 6 to:
% 22.05/6.97 | (95) $false
% 22.05/6.97 |
% 22.05/6.97 |-The branch is then unsatisfiable
% 22.05/6.97 |-Branch two:
% 22.05/6.97 | (6) ~ (all_0_0_0 = 0)
% 22.05/6.97 | (215) ? [v0] : ( ~ (v0 = 0) & greater(vd519, vd520) = v0)
% 22.05/6.97 |
% 22.05/6.97 | Instantiating (215) with all_116_0_26 yields:
% 22.05/6.97 | (216) ~ (all_116_0_26 = 0) & greater(vd519, vd520) = all_116_0_26
% 22.05/6.97 |
% 22.05/6.97 | Applying alpha-rule on (216) yields:
% 22.05/6.97 | (217) ~ (all_116_0_26 = 0)
% 22.05/6.97 | (218) greater(vd519, vd520) = all_116_0_26
% 22.05/6.97 |
% 22.05/6.97 | Instantiating formula (30) with vd519, vd520, 0, all_116_0_26 and discharging atoms greater(vd519, vd520) = all_116_0_26, greater(vd519, vd520) = 0, yields:
% 22.05/6.97 | (219) all_116_0_26 = 0
% 22.05/6.97 |
% 22.05/6.97 | Equations (219) can reduce 217 to:
% 22.05/6.97 | (95) $false
% 22.05/6.97 |
% 22.05/6.97 |-The branch is then unsatisfiable
% 22.05/6.97 % SZS output end Proof for theBenchmark
% 22.05/6.97
% 22.05/6.97 6373ms
%------------------------------------------------------------------------------