%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : NUM857+1 : TPTP v8.1.0. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n006.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Mon Jul 18 08:49:14 EDT 2022 % Result : Theorem 18.90s 6.26s % Output : Proof 21.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : NUM857+1 : TPTP v8.1.0. Released v4.1.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n006.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 00:55:21 EDT 2022 % 0.12/0.33 % CPUTime : % 0.55/0.61 ____ _ % 0.55/0.61 ___ / __ \_____(_)___ ________ __________ % 0.55/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.55/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.55/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.55/0.61 % 0.55/0.61 A Theorem Prover for First-Order Logic % 0.55/0.61 (ePrincess v.1.0) % 0.55/0.61 % 0.55/0.61 (c) Philipp Rümmer, 2009-2015 % 0.55/0.61 (c) Peter Backeman, 2014-2015 % 0.55/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.55/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.55/0.61 Bug reports to peter@backeman.se % 0.55/0.61 % 0.55/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.55/0.61 % 0.55/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.71/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.82/1.06 Prover 0: Preprocessing ... % 3.11/1.42 Prover 0: Warning: ignoring some quantifiers % 3.11/1.45 Prover 0: Constructing countermodel ... % 17.62/5.98 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 17.77/6.06 Prover 1: Preprocessing ... % 18.62/6.20 Prover 1: Warning: ignoring some quantifiers % 18.62/6.20 Prover 1: Constructing countermodel ... % 18.90/6.26 Prover 1: proved (278ms) % 18.90/6.26 Prover 0: stopped % 18.90/6.26 % 18.90/6.26 No countermodel exists, formula is valid % 18.90/6.26 % SZS status Theorem for theBenchmark % 18.90/6.26 % 18.90/6.26 Generating proof ... Warning: ignoring some quantifiers % 20.91/6.75 found it (size 99) % 20.91/6.75 % 20.91/6.75 % SZS output start Proof for theBenchmark % 20.91/6.75 Assumed formulas after preprocessing and simplification: % 20.91/6.75 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & vmul(vd527, vd530) = v1 & vmul(vd526, vd529) = v0 & geq(v0, v1) = v2 & geq(vd529, vd530) = 0 & geq(vd526, vd527) = 0 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (vplus(v4, v6) = v8) | ~ (vplus(v3, v5) = v7) | ~ (geq(v7, v8) = v9) | ? [v10] : ? [v11] : (geq(v5, v6) = v10 & geq(v3, v4) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (vplus(v4, v6) = v8) | ~ (vplus(v3, v5) = v7) | ~ (greater(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (geq(v5, v6) = v12 & geq(v3, v4) = v11 & greater(v5, v6) = v10 & greater(v3, v4) = v13 & ( ~ (v13 = 0) | ~ (v12 = 0)) & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (vplus(v4, v6) = v8) | ~ (vplus(v3, v5) = v7) | ~ (greater(v7, v8) = v9) | ? [v10] : ? [v11] : (greater(v5, v6) = v10 & greater(v3, v4) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (vmul(v4, v6) = v8) | ~ (vmul(v3, v5) = v7) | ~ (greater(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (geq(v5, v6) = v12 & geq(v3, v4) = v11 & greater(v5, v6) = v10 & greater(v3, v4) = v13 & ( ~ (v13 = 0) | ~ (v12 = 0)) & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (vmul(v4, v6) = v8) | ~ (vmul(v3, v5) = v7) | ~ (greater(v7, v8) = v9) | ? [v10] : ? [v11] : (greater(v5, v6) = v10 & greater(v3, v4) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (vplus(v4, v5) = v7) | ~ (vplus(v3, v5) = v6) | ~ (less(v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & less(v3, v4) = v9)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (vplus(v4, v5) = v7) | ~ (vplus(v3, v5) = v6) | ~ (greater(v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & greater(v3, v4) = v9)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (less(v6, v7) = v8) | ~ (vmul(v5, v3) = v7) | ~ (vmul(v4, v3) = v6) | ? [v9] : ( ~ (v9 = 0) & less(v4, v5) = v9)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (vmul(v5, v3) = v7) | ~ (vmul(v4, v3) = v6) | ~ (greater(v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & greater(v4, v5) = v9)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (vplus(v6, v7) = v8) | ~ (vmul(v3, v5) = v7) | ~ (vmul(v3, v4) = v6) | ? [v9] : (vplus(v4, v5) = v9 & vmul(v3, v9) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (leq(v4, v5) = v7) | ~ (leq(v3, v4) = v6) | ? [v8] : ? [v9] : ? [v10] : (less(v4, v5) = v8 & less(v3, v5) = v10 & less(v3, v4) = v9 & (v10 = 0 | (( ~ (v9 = 0) | ~ (v7 = 0)) & ( ~ (v8 = 0) | ~ (v6 = 0)))))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (vplus(v6, v5) = v7) | ~ (vplus(v3, v4) = v6) | ? [v8] : (vplus(v4, v5) = v8 & vplus(v3, v8) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (vplus(v4, v5) = v7) | ~ (vplus(v3, v5) = v6) | ~ (less(v6, v7) = 0) | less(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (vplus(v4, v5) = v7) | ~ (vplus(v3, v5) = v6) | ~ (greater(v6, v7) = 0) | greater(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (less(v6, v7) = 0) | ~ (vmul(v5, v4) = v7) | ~ (vmul(v3, v4) = v6) | less(v3, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (vmul(v6, v5) = v7) | ~ (vmul(v3, v4) = v6) | ? [v8] : (vmul(v4, v5) = v8 & vmul(v3, v8) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (vmul(v5, v4) = v7) | ~ (vmul(v3, v4) = v6) | ~ (greater(v6, v7) = 0) | greater(v3, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (vplus(v3, v4) = v6) | ~ (vplus(v3, v4) = v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (vmul(v4, v3) = v6) | ~ (vmul(v4, v3) = v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (leq(v3, v5) = v6) | ~ (leq(v3, v4) = 0) | ? [v7] : ( ~ (v7 = 0) & leq(v4, v5) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vplus(v4, v1) = v5) | ~ (geq(v3, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & greater(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vplus(v3, v4) = v5) | ~ (greater(v5, v3) = v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (less(v3, v5) = v6) | ~ (less(v3, v4) = 0) | ? [v7] : ( ~ (v7 = 0) & less(v4, v5) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v3 | ~ (vmul(v5, v4) = v6) | ~ (vmul(v3, v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (vplus(v4, v6) = v3) | ~ (less(v4, v3) = v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (vplus(v3, v6) = v4) | ~ (greater(v4, v3) = v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (leq(v6, v5) = v4) | ~ (leq(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (vplus(v6, v5) = v4) | ~ (vplus(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (vplus(v4, v5) = v6) | ~ (vplus(v3, v5) = v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (less(v6, v5) = v4) | ~ (less(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (vmul(v6, v5) = v4) | ~ (vmul(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (geq(v6, v5) = v4) | ~ (geq(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (greater(v6, v5) = v4) | ~ (greater(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (vsucc(v4) = v5) | ~ (vplus(v3, v5) = v6) | ? [v7] : (vsucc(v7) = v6 & vplus(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (vsucc(v4) = v5) | ~ (vmul(v3, v5) = v6) | ? [v7] : (vplus(v7, v3) = v6 & vmul(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (vsucc(v3) = v5) | ~ (vplus(v5, v4) = v6) | ? [v7] : (vsucc(v7) = v6 & vplus(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (vsucc(v3) = v5) | ~ (vmul(v5, v4) = v6) | ? [v7] : (vplus(v7, v4) = v6 & vmul(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (vplus(v4, v6) = v3) | ~ (vplus(v3, v5) = v4)) & ? [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (vplus(v5, v4) = v6) | ? [v7] : ( ~ (v7 = v6) & vplus(v5, v3) = v7)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = v3 | ~ (less(v3, v4) = v5) | greater(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (leq(v4, v3) = v5) | ? [v6] : ( ~ (v6 = 0) & less(v4, v3) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (leq(v4, v3) = v5) | ? [v6] : ( ~ (v6 = 0) & geq(v3, v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (less(v4, v3) = v5) | ? [v6] : ( ~ (v6 = 0) & greater(v3, v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (geq(v4, v3) = v5) | ? [v6] : ( ~ (v6 = 0) & greater(v4, v3) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (vskolem2(v5) = v4) | ~ (vskolem2(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (vsucc(v5) = v4) | ~ (vsucc(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (vsucc(v4) = v5) | ~ (vsucc(v3) = v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (vplus(v4, v1) = v5) | ~ (less(v3, v5) = 0) | leq(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : ( ~ (vplus(v3, v4) = v5) | vplus(v4, v3) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (vmul(v3, v4) = v5) | vmul(v4, v3) = v5) & ! [v3] : ! [v4] : (v4 = v3 | ~ (leq(v4, v3) = 0) | less(v4, v3) = 0) & ! [v3] : ! [v4] : (v4 = v3 | ~ (vmul(v3, v1) = v4)) & ! [v3] : ! [v4] : (v4 = v3 | ~ (vmul(v1, v3) = v4)) & ! [v3] : ! [v4] : (v4 = v3 | ~ (geq(v4, v3) = 0) | greater(v4, v3) = 0) & ! [v3] : ! [v4] : (v4 = 0 | ~ (leq(v3, v3) = v4)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (geq(v3, v3) = v4)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (geq(v3, v1) = v4)) & ! [v3] : ! [v4] : (v3 = v1 | ~ (vskolem2(v3) = v4) | vsucc(v4) = v3) & ! [v3] : ! [v4] : ( ~ (leq(v3, v4) = 0) | geq(v4, v3) = 0) & ! [v3] : ! [v4] : ~ (vplus(v3, v4) = v4) & ! [v3] : ! [v4] : ~ (vplus(v3, v4) = v3) & ! [v3] : ! [v4] : ( ~ (vplus(v3, v1) = v4) | vsucc(v3) = v4) & ! [v3] : ! [v4] : ( ~ (vplus(v1, v3) = v4) | vsucc(v3) = v4) & ! [v3] : ! [v4] : ( ~ (less(v4, v3) = 0) | ? [v5] : vplus(v4, v5) = v3) & ! [v3] : ! [v4] : ( ~ (less(v3, v4) = 0) | greater(v4, v3) = 0) & ! [v3] : ! [v4] : ( ~ (less(v3, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & greater(v3, v4) = v5)) & ! [v3] : ! [v4] : ( ~ (greater(v4, v3) = 0) | ? [v5] : vplus(v3, v5) = v4) & ! [v3] : ~ (vsucc(v3) = v3) & ! [v3] : ~ (vsucc(v3) = v1) & ! [v3] : ~ (less(v3, v3) = 0) & ! [v3] : ~ (greater(v3, v3) = 0) & ? [v3] : ? [v4] : (v4 = v3 | ? [v5] : ? [v6] : ((v6 = v4 & vplus(v3, v5) = v4) | (v6 = v3 & vplus(v4, v5) = v3)))) % 21.37/6.81 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 21.37/6.81 | (1) ~ (all_0_0_0 = 0) & vmul(vd527, vd530) = all_0_1_1 & vmul(vd526, vd529) = all_0_2_2 & geq(all_0_2_2, all_0_1_1) = all_0_0_0 & geq(vd529, vd530) = 0 & geq(vd526, vd527) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vplus(v1, v3) = v5) | ~ (vplus(v0, v2) = v4) | ~ (geq(v4, v5) = v6) | ? [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] : ? [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 | ~ (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 | ~ (leq(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & leq(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (vplus(v1, v1) = v2) | ~ (geq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & greater(v0, v1) = 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 | ~ (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 | ~ (geq(v3, v2) = v1) | ~ (geq(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 | ~ (leq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & less(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & geq(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (geq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v1, v0) = 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 | ~ (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 = v0 | ~ (geq(v1, v0) = 0) | greater(v1, v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v1) = 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))) % 21.54/6.83 | % 21.54/6.83 | Applying alpha-rule on (1) yields: % 21.54/6.83 | (2) ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1)) % 21.54/6.83 | (3) ! [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)) % 21.54/6.83 | (4) ! [v0] : ! [v1] : ~ (vplus(v0, v1) = v1) % 21.54/6.83 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v1, v2) = v3) | ~ (vplus(v0, v2) = v3)) % 21.54/6.83 | (6) ! [v0] : ! [v1] : ( ~ (less(v0, v1) = 0) | greater(v1, v0) = 0) % 21.54/6.83 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (less(v0, v1) = v2) | greater(v0, v1) = 0) % 21.54/6.83 | (8) ! [v0] : ! [v1] : ~ (vplus(v0, v1) = v0) % 21.54/6.83 | (9) ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | geq(v1, v0) = 0) % 21.54/6.83 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (vmul(v0, v1) = v2) | vmul(v1, v0) = v2) % 21.54/6.83 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v0, v1) = v2) | vplus(v1, v0) = v2) % 21.54/6.83 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | ~ (vmul(v2, v1) = v3) | ~ (vmul(v0, v1) = v3)) % 21.54/6.83 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) % 21.54/6.83 | (14) ! [v0] : ! [v1] : ( ~ (less(v1, v0) = 0) | ? [v2] : vplus(v1, v2) = v0) % 21.54/6.83 | (15) ! [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)))) % 21.54/6.83 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (vmul(v1, v0) = v3) | ~ (vmul(v1, v0) = v2)) % 21.54/6.83 | (17) vmul(vd527, vd530) = all_0_1_1 % 21.54/6.83 | (18) ! [v0] : ! [v1] : ( ~ (less(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & greater(v0, v1) = v2)) % 21.54/6.83 | (19) ! [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)))))) % 21.54/6.83 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 21.54/6.83 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ (vskolem2(v2) = v0)) % 21.54/6.83 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ~ (greater(v3, v4) = 0) | greater(v0, v1) = 0) % 21.54/6.83 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (vplus(v0, v1) = v2) | ~ (greater(v2, v0) = v3)) % 21.54/6.83 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (vplus(v1, v3) = v0) | ~ (less(v1, v0) = v2)) % 21.54/6.83 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v0) = v2) | ~ (vmul(v2, v1) = v3) | ? [v4] : (vplus(v4, v1) = v3 & vmul(v0, v1) = v4)) % 21.54/6.83 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vmul(v3, v2) = v4) | ~ (vmul(v0, v1) = v3) | ? [v5] : (vmul(v1, v2) = v5 & vmul(v0, v5) = v4)) % 21.54/6.83 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) % 21.54/6.83 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v1, v1) = v2) | ~ (less(v0, v2) = 0) | leq(v0, v1) = 0) % 21.54/6.83 | (29) geq(all_0_2_2, all_0_1_1) = all_0_0_0 % 21.54/6.84 | (30) ~ (all_0_0_0 = 0) % 21.54/6.84 | (31) ! [v0] : ! [v1] : (v1 = v0 | ~ (vmul(v0, v1) = v1)) % 21.54/6.84 | (32) ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v1, v0) = 0) | less(v1, v0) = 0) % 21.54/6.84 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (vplus(v1, v1) = v2) | ~ (geq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & greater(v0, v1) = v4)) % 21.54/6.84 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ? [v5] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4)) % 21.54/6.84 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) % 21.54/6.84 | (36) ! [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)) % 21.54/6.84 | (37) ! [v0] : ~ (greater(v0, v0) = 0) % 21.54/6.84 | (38) ! [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)) % 21.54/6.84 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) % 21.54/6.84 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vmul(v1, v3) = v5) | ~ (vmul(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)))) % 21.54/6.84 | (41) vmul(vd526, vd529) = all_0_2_2 % 21.54/6.84 | (42) ! [v0] : ~ (less(v0, v0) = 0) % 21.54/6.84 | (43) ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1)) % 21.54/6.84 | (44) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & less(v1, v0) = v3)) % 21.54/6.84 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ~ (less(v3, v4) = 0) | less(v0, v1) = 0) % 21.54/6.84 | (46) ! [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)))) % 21.54/6.84 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (less(v3, v4) = 0) | ~ (vmul(v2, v1) = v4) | ~ (vmul(v0, v1) = v3) | less(v0, v2) = 0) % 21.54/6.84 | (48) ! [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)) % 21.54/6.84 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (vplus(v0, v1) = v3) | ~ (vplus(v0, v1) = v2)) % 21.54/6.84 | (50) ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v1) = v1)) % 21.54/6.84 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v1) = v2) | ~ (vmul(v0, v2) = v3) | ? [v4] : (vplus(v4, v0) = v3 & vmul(v0, v1) = v4)) % 21.54/6.84 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less(v0, v2) = v3) | ~ (less(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less(v1, v2) = v4)) % 21.54/6.84 | (53) geq(vd529, vd530) = 0 % 21.54/6.84 | (54) geq(vd526, vd527) = 0 % 21.54/6.84 | (55) ! [v0] : ! [v1] : ( ~ (vplus(v1, v0) = v1) | vsucc(v0) = v1) % 21.54/6.84 | (56) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v2, v1) = v3) | ? [v4] : ( ~ (v4 = v3) & vplus(v2, v0) = v4)) % 21.54/6.84 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vmul(v2, v1) = v4) | ~ (vmul(v0, v1) = v3) | ~ (greater(v3, v4) = 0) | greater(v0, v2) = 0) % 21.54/6.84 | (58) ! [v0] : ! [v1] : ( ~ (greater(v1, v0) = 0) | ? [v2] : vplus(v0, v2) = v1) % 21.54/6.84 | (59) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v1) = v2) | ~ (vsucc(v0) = v2)) % 21.54/6.84 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (vplus(v0, v3) = v1) | ~ (greater(v1, v0) = v2)) % 21.54/6.84 | (61) ! [v0] : ~ (vsucc(v0) = v0) % 21.54/6.84 | (62) ! [v0] : ! [v1] : (v1 = v0 | ~ (geq(v1, v0) = 0) | greater(v1, v0) = 0) % 21.54/6.84 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v0) = v2) | ~ (vplus(v2, v1) = v3) | ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4)) % 21.54/6.84 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v1) = v2) | ~ (vplus(v0, v2) = v3) | ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4)) % 21.54/6.84 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vplus(v1, v3) = v0) | ~ (vplus(v0, v2) = v1)) % 21.54/6.84 | (66) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ((v3 = v1 & vplus(v0, v2) = v1) | (v3 = v0 & vplus(v1, v2) = v0))) % 21.54/6.84 | (67) ! [v0] : ! [v1] : (v0 = v1 | ~ (vskolem2(v0) = v1) | vsucc(v1) = v0) % 21.54/6.84 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) % 21.54/6.84 | (69) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & geq(v0, v1) = v3)) % 21.54/6.84 | (70) ! [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)) % 21.54/6.84 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (vplus(v1, v3) = v5) | ~ (vplus(v0, v2) = v4) | ~ (geq(v4, v5) = v6) | ? [v7] : ? [v8] : (geq(v2, v3) = v7 & geq(v0, v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0)))) % 21.72/6.84 | (72) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v0, v1) = v3)) % 21.72/6.84 | (73) ! [v0] : ~ (vsucc(v0) = v1) % 21.72/6.84 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (leq(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & leq(v1, v2) = v4)) % 21.72/6.84 | (75) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) % 21.72/6.84 | (76) ! [v0] : ! [v1] : ( ~ (vplus(v0, v1) = v1) | vsucc(v0) = v1) % 21.72/6.84 | (77) ! [v0] : ! [v1] : (v1 = v0 | ~ (vmul(v1, v0) = v1)) % 21.72/6.84 | (78) ! [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)))) % 21.72/6.84 | (79) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (geq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v1, v0) = v3)) % 21.72/6.84 | % 21.72/6.85 | Instantiating formula (43) with all_0_0_0, all_0_2_2 yields: % 21.72/6.85 | (80) all_0_0_0 = 0 | ~ (geq(all_0_2_2, all_0_2_2) = all_0_0_0) % 21.72/6.85 | % 21.72/6.85 | Instantiating formula (10) with all_0_1_1, vd530, vd527 and discharging atoms vmul(vd527, vd530) = all_0_1_1, yields: % 21.72/6.85 | (81) vmul(vd530, vd527) = all_0_1_1 % 21.72/6.85 | % 21.72/6.85 | Instantiating formula (10) with all_0_2_2, vd529, vd526 and discharging atoms vmul(vd526, vd529) = all_0_2_2, yields: % 21.72/6.85 | (82) vmul(vd529, vd526) = all_0_2_2 % 21.72/6.85 | % 21.72/6.85 | Instantiating formula (79) with all_0_0_0, all_0_2_2, all_0_1_1 and discharging atoms geq(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 21.72/6.85 | (83) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & greater(all_0_2_2, all_0_1_1) = v0) % 21.72/6.85 | % 21.72/6.85 | Instantiating formula (62) with vd529, vd530 and discharging atoms geq(vd529, vd530) = 0, yields: % 21.72/6.85 | (84) vd530 = vd529 | greater(vd529, vd530) = 0 % 21.72/6.85 | % 21.72/6.85 | Instantiating formula (62) with vd526, vd527 and discharging atoms geq(vd526, vd527) = 0, yields: % 21.72/6.85 | (85) vd527 = vd526 | greater(vd526, vd527) = 0 % 21.72/6.85 | % 21.72/6.85 +-Applying beta-rule and splitting (80), into two cases. % 21.72/6.85 |-Branch one: % 21.72/6.85 | (86) ~ (geq(all_0_2_2, all_0_2_2) = all_0_0_0) % 21.72/6.85 | % 21.72/6.85 +-Applying beta-rule and splitting (83), into two cases. % 21.72/6.85 |-Branch one: % 21.72/6.85 | (87) all_0_0_0 = 0 % 21.72/6.85 | % 21.72/6.85 | Equations (87) can reduce 30 to: % 21.72/6.85 | (88) $false % 21.72/6.85 | % 21.72/6.85 |-The branch is then unsatisfiable % 21.72/6.85 |-Branch two: % 21.72/6.85 | (30) ~ (all_0_0_0 = 0) % 21.72/6.85 | (90) ? [v0] : ( ~ (v0 = 0) & greater(all_0_2_2, all_0_1_1) = v0) % 21.72/6.85 | % 21.72/6.85 | Instantiating (90) with all_24_0_6 yields: % 21.72/6.85 | (91) ~ (all_24_0_6 = 0) & greater(all_0_2_2, all_0_1_1) = all_24_0_6 % 21.72/6.85 | % 21.72/6.85 | Applying alpha-rule on (91) yields: % 21.72/6.85 | (92) ~ (all_24_0_6 = 0) % 21.72/6.85 | (93) greater(all_0_2_2, all_0_1_1) = all_24_0_6 % 21.72/6.85 | % 21.72/6.85 | Using (29) and (86) yields: % 21.72/6.85 | (94) ~ (all_0_1_1 = all_0_2_2) % 21.72/6.85 | % 21.72/6.85 | Instantiating formula (40) with all_24_0_6, all_0_1_1, all_0_2_2, vd530, vd529, vd527, vd526 and discharging atoms vmul(vd527, vd530) = all_0_1_1, vmul(vd526, vd529) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_24_0_6, yields: % 21.72/6.85 | (95) all_24_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (geq(vd529, vd530) = v2 & geq(vd526, vd527) = v1 & greater(vd529, vd530) = v0 & greater(vd526, vd527) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)) & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.72/6.85 | % 21.72/6.85 | Instantiating formula (15) with all_24_0_6, all_0_1_1, all_0_2_2, vd530, vd529, vd527, vd526 and discharging atoms vmul(vd527, vd530) = all_0_1_1, vmul(vd526, vd529) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_24_0_6, yields: % 21.72/6.85 | (96) all_24_0_6 = 0 | ? [v0] : ? [v1] : (greater(vd529, vd530) = v0 & greater(vd526, vd527) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.72/6.85 | % 21.72/6.85 | Instantiating formula (40) with all_24_0_6, all_0_1_1, all_0_2_2, vd530, vd526, vd527, vd529 and discharging atoms vmul(vd527, vd530) = all_0_1_1, vmul(vd529, vd526) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_24_0_6, yields: % 21.72/6.85 | (97) all_24_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (geq(vd529, vd527) = v1 & geq(vd526, vd530) = v2 & greater(vd529, vd527) = v3 & greater(vd526, vd530) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0)) & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.72/6.85 | % 21.72/6.85 | Instantiating formula (15) with all_24_0_6, all_0_1_1, all_0_2_2, vd530, vd526, vd527, vd529 and discharging atoms vmul(vd527, vd530) = all_0_1_1, vmul(vd529, vd526) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_24_0_6, yields: % 21.72/6.85 | (98) all_24_0_6 = 0 | ? [v0] : ? [v1] : (greater(vd529, vd527) = v1 & greater(vd526, vd530) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.72/6.85 | % 21.72/6.85 | Instantiating formula (40) with all_24_0_6, all_0_1_1, all_0_2_2, vd527, vd529, vd530, vd526 and discharging atoms vmul(vd530, vd527) = all_0_1_1, vmul(vd526, vd529) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_24_0_6, yields: % 21.72/6.85 | (99) all_24_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (geq(vd529, vd527) = v2 & geq(vd526, vd530) = v1 & greater(vd529, vd527) = v0 & greater(vd526, vd530) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)) & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.72/6.85 | % 21.72/6.85 | Instantiating formula (15) with all_24_0_6, all_0_1_1, all_0_2_2, vd527, vd529, vd530, vd526 and discharging atoms vmul(vd530, vd527) = all_0_1_1, vmul(vd526, vd529) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_24_0_6, yields: % 21.72/6.85 | (100) all_24_0_6 = 0 | ? [v0] : ? [v1] : (greater(vd529, vd527) = v0 & greater(vd526, vd530) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.72/6.85 | % 21.72/6.85 | Instantiating formula (40) with all_24_0_6, all_0_1_1, all_0_2_2, vd527, vd526, vd530, vd529 and discharging atoms vmul(vd530, vd527) = all_0_1_1, vmul(vd529, vd526) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_24_0_6, yields: % 21.72/6.85 | (101) all_24_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (geq(vd529, vd530) = v1 & geq(vd526, vd527) = v2 & greater(vd529, vd530) = v3 & greater(vd526, vd527) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0)) & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.72/6.85 | % 21.72/6.85 | Instantiating formula (15) with all_24_0_6, all_0_1_1, all_0_2_2, vd527, vd526, vd530, vd529 and discharging atoms vmul(vd530, vd527) = all_0_1_1, vmul(vd529, vd526) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_24_0_6, yields: % 21.72/6.85 | (102) all_24_0_6 = 0 | ? [v0] : ? [v1] : (greater(vd529, vd530) = v1 & greater(vd526, vd527) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.72/6.85 | % 21.72/6.85 +-Applying beta-rule and splitting (95), into two cases. % 21.72/6.85 |-Branch one: % 21.72/6.85 | (103) all_24_0_6 = 0 % 21.72/6.85 | % 21.72/6.85 | Equations (103) can reduce 92 to: % 21.72/6.85 | (88) $false % 21.72/6.85 | % 21.72/6.85 |-The branch is then unsatisfiable % 21.72/6.85 |-Branch two: % 21.72/6.85 | (92) ~ (all_24_0_6 = 0) % 21.72/6.85 | (106) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (geq(vd529, vd530) = v2 & geq(vd526, vd527) = v1 & greater(vd529, vd530) = v0 & greater(vd526, vd527) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)) & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.72/6.85 | % 21.72/6.85 | Instantiating (106) with all_41_0_7, all_41_1_8, all_41_2_9, all_41_3_10 yields: % 21.72/6.85 | (107) geq(vd529, vd530) = all_41_1_8 & geq(vd526, vd527) = all_41_2_9 & greater(vd529, vd530) = all_41_3_10 & greater(vd526, vd527) = all_41_0_7 & ( ~ (all_41_0_7 = 0) | ~ (all_41_1_8 = 0)) & ( ~ (all_41_2_9 = 0) | ~ (all_41_3_10 = 0)) % 21.72/6.85 | % 21.72/6.85 | Applying alpha-rule on (107) yields: % 21.72/6.85 | (108) greater(vd526, vd527) = all_41_0_7 % 21.72/6.85 | (109) ~ (all_41_2_9 = 0) | ~ (all_41_3_10 = 0) % 21.72/6.85 | (110) geq(vd529, vd530) = all_41_1_8 % 21.72/6.85 | (111) greater(vd529, vd530) = all_41_3_10 % 21.72/6.85 | (112) geq(vd526, vd527) = all_41_2_9 % 21.72/6.85 | (113) ~ (all_41_0_7 = 0) | ~ (all_41_1_8 = 0) % 21.72/6.85 | % 21.72/6.85 +-Applying beta-rule and splitting (96), into two cases. % 21.72/6.85 |-Branch one: % 21.72/6.85 | (103) all_24_0_6 = 0 % 21.72/6.85 | % 21.72/6.85 | Equations (103) can reduce 92 to: % 21.72/6.85 | (88) $false % 21.72/6.85 | % 21.72/6.85 |-The branch is then unsatisfiable % 21.72/6.85 |-Branch two: % 21.72/6.85 | (92) ~ (all_24_0_6 = 0) % 21.72/6.85 | (117) ? [v0] : ? [v1] : (greater(vd529, vd530) = v0 & greater(vd526, vd527) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.72/6.85 | % 21.72/6.85 | Instantiating (117) with all_46_0_11, all_46_1_12 yields: % 21.72/6.85 | (118) greater(vd529, vd530) = all_46_1_12 & greater(vd526, vd527) = all_46_0_11 & ( ~ (all_46_0_11 = 0) | ~ (all_46_1_12 = 0)) % 21.72/6.85 | % 21.72/6.85 | Applying alpha-rule on (118) yields: % 21.72/6.85 | (119) greater(vd529, vd530) = all_46_1_12 % 21.72/6.86 | (120) greater(vd526, vd527) = all_46_0_11 % 21.72/6.86 | (121) ~ (all_46_0_11 = 0) | ~ (all_46_1_12 = 0) % 21.72/6.86 | % 21.72/6.86 +-Applying beta-rule and splitting (97), into two cases. % 21.72/6.86 |-Branch one: % 21.72/6.86 | (103) all_24_0_6 = 0 % 21.72/6.86 | % 21.72/6.86 | Equations (103) can reduce 92 to: % 21.72/6.86 | (88) $false % 21.72/6.86 | % 21.72/6.86 |-The branch is then unsatisfiable % 21.72/6.86 |-Branch two: % 21.72/6.86 | (92) ~ (all_24_0_6 = 0) % 21.72/6.86 | (125) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (geq(vd529, vd527) = v1 & geq(vd526, vd530) = v2 & greater(vd529, vd527) = v3 & greater(vd526, vd530) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0)) & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.72/6.86 | % 21.72/6.86 +-Applying beta-rule and splitting (98), into two cases. % 21.72/6.86 |-Branch one: % 21.72/6.86 | (103) all_24_0_6 = 0 % 21.72/6.86 | % 21.72/6.86 | Equations (103) can reduce 92 to: % 21.72/6.86 | (88) $false % 21.72/6.86 | % 21.72/6.86 |-The branch is then unsatisfiable % 21.72/6.86 |-Branch two: % 21.72/6.86 | (92) ~ (all_24_0_6 = 0) % 21.72/6.86 | (129) ? [v0] : ? [v1] : (greater(vd529, vd527) = v1 & greater(vd526, vd530) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.72/6.86 | % 21.72/6.86 +-Applying beta-rule and splitting (99), into two cases. % 21.72/6.86 |-Branch one: % 21.72/6.86 | (103) all_24_0_6 = 0 % 21.72/6.86 | % 21.72/6.86 | Equations (103) can reduce 92 to: % 21.72/6.86 | (88) $false % 21.72/6.86 | % 21.72/6.86 |-The branch is then unsatisfiable % 21.72/6.86 |-Branch two: % 21.72/6.86 | (92) ~ (all_24_0_6 = 0) % 21.72/6.86 | (133) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (geq(vd529, vd527) = v2 & geq(vd526, vd530) = v1 & greater(vd529, vd527) = v0 & greater(vd526, vd530) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)) & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.72/6.86 | % 21.72/6.86 +-Applying beta-rule and splitting (100), into two cases. % 21.72/6.86 |-Branch one: % 21.72/6.86 | (103) all_24_0_6 = 0 % 21.72/6.86 | % 21.72/6.86 | Equations (103) can reduce 92 to: % 21.72/6.86 | (88) $false % 21.72/6.86 | % 21.72/6.86 |-The branch is then unsatisfiable % 21.72/6.86 |-Branch two: % 21.72/6.86 | (92) ~ (all_24_0_6 = 0) % 21.72/6.86 | (137) ? [v0] : ? [v1] : (greater(vd529, vd527) = v0 & greater(vd526, vd530) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.72/6.86 | % 21.72/6.86 +-Applying beta-rule and splitting (101), into two cases. % 21.72/6.86 |-Branch one: % 21.72/6.86 | (103) all_24_0_6 = 0 % 21.72/6.86 | % 21.72/6.86 | Equations (103) can reduce 92 to: % 21.72/6.86 | (88) $false % 21.72/6.86 | % 21.72/6.86 |-The branch is then unsatisfiable % 21.72/6.86 |-Branch two: % 21.72/6.86 | (92) ~ (all_24_0_6 = 0) % 21.72/6.86 | (141) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (geq(vd529, vd530) = v1 & geq(vd526, vd527) = v2 & greater(vd529, vd530) = v3 & greater(vd526, vd527) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0)) & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.72/6.86 | % 21.72/6.86 | Instantiating (141) with all_71_0_25, all_71_1_26, all_71_2_27, all_71_3_28 yields: % 21.72/6.86 | (142) geq(vd529, vd530) = all_71_2_27 & geq(vd526, vd527) = all_71_1_26 & greater(vd529, vd530) = all_71_0_25 & greater(vd526, vd527) = all_71_3_28 & ( ~ (all_71_0_25 = 0) | ~ (all_71_1_26 = 0)) & ( ~ (all_71_2_27 = 0) | ~ (all_71_3_28 = 0)) % 21.72/6.86 | % 21.72/6.86 | Applying alpha-rule on (142) yields: % 21.72/6.86 | (143) ~ (all_71_2_27 = 0) | ~ (all_71_3_28 = 0) % 21.72/6.86 | (144) greater(vd529, vd530) = all_71_0_25 % 21.72/6.86 | (145) greater(vd526, vd527) = all_71_3_28 % 21.72/6.86 | (146) geq(vd529, vd530) = all_71_2_27 % 21.72/6.86 | (147) ~ (all_71_0_25 = 0) | ~ (all_71_1_26 = 0) % 21.72/6.86 | (148) geq(vd526, vd527) = all_71_1_26 % 21.72/6.86 | % 21.72/6.86 +-Applying beta-rule and splitting (102), into two cases. % 21.72/6.86 |-Branch one: % 21.72/6.86 | (103) all_24_0_6 = 0 % 21.72/6.86 | % 21.72/6.86 | Equations (103) can reduce 92 to: % 21.72/6.86 | (88) $false % 21.72/6.86 | % 21.72/6.86 |-The branch is then unsatisfiable % 21.72/6.86 |-Branch two: % 21.72/6.86 | (92) ~ (all_24_0_6 = 0) % 21.72/6.86 | (152) ? [v0] : ? [v1] : (greater(vd529, vd530) = v1 & greater(vd526, vd527) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.72/6.86 | % 21.72/6.86 | Instantiating (152) with all_76_0_29, all_76_1_30 yields: % 21.72/6.86 | (153) greater(vd529, vd530) = all_76_0_29 & greater(vd526, vd527) = all_76_1_30 & ( ~ (all_76_0_29 = 0) | ~ (all_76_1_30 = 0)) % 21.72/6.86 | % 21.72/6.86 | Applying alpha-rule on (153) yields: % 21.72/6.86 | (154) greater(vd529, vd530) = all_76_0_29 % 21.72/6.86 | (155) greater(vd526, vd527) = all_76_1_30 % 21.72/6.86 | (156) ~ (all_76_0_29 = 0) | ~ (all_76_1_30 = 0) % 21.72/6.86 | % 21.72/6.86 | Instantiating formula (13) with vd529, vd530, all_71_2_27, 0 and discharging atoms geq(vd529, vd530) = all_71_2_27, geq(vd529, vd530) = 0, yields: % 21.72/6.86 | (157) all_71_2_27 = 0 % 21.72/6.86 | % 21.72/6.86 | Instantiating formula (13) with vd529, vd530, all_41_1_8, all_71_2_27 and discharging atoms geq(vd529, vd530) = all_71_2_27, geq(vd529, vd530) = all_41_1_8, yields: % 21.72/6.86 | (158) all_71_2_27 = all_41_1_8 % 21.72/6.86 | % 21.72/6.86 | Instantiating formula (13) with vd526, vd527, all_71_1_26, 0 and discharging atoms geq(vd526, vd527) = all_71_1_26, geq(vd526, vd527) = 0, yields: % 21.72/6.86 | (159) all_71_1_26 = 0 % 21.72/6.86 | % 21.72/6.86 | Instantiating formula (13) with vd526, vd527, all_41_2_9, all_71_1_26 and discharging atoms geq(vd526, vd527) = all_71_1_26, geq(vd526, vd527) = all_41_2_9, yields: % 21.72/6.86 | (160) all_71_1_26 = all_41_2_9 % 21.72/6.86 | % 21.72/6.86 | Instantiating formula (68) with vd529, vd530, all_71_0_25, all_76_0_29 and discharging atoms greater(vd529, vd530) = all_76_0_29, greater(vd529, vd530) = all_71_0_25, yields: % 21.72/6.86 | (161) all_76_0_29 = all_71_0_25 % 21.72/6.86 | % 21.72/6.86 | Instantiating formula (68) with vd529, vd530, all_46_1_12, all_71_0_25 and discharging atoms greater(vd529, vd530) = all_71_0_25, greater(vd529, vd530) = all_46_1_12, yields: % 21.72/6.86 | (162) all_71_0_25 = all_46_1_12 % 21.72/6.86 | % 21.72/6.86 | Instantiating formula (68) with vd529, vd530, all_41_3_10, all_76_0_29 and discharging atoms greater(vd529, vd530) = all_76_0_29, greater(vd529, vd530) = all_41_3_10, yields: % 21.72/6.86 | (163) all_76_0_29 = all_41_3_10 % 21.72/6.86 | % 21.72/6.86 | Instantiating formula (68) with vd526, vd527, all_71_3_28, all_76_1_30 and discharging atoms greater(vd526, vd527) = all_76_1_30, greater(vd526, vd527) = all_71_3_28, yields: % 21.72/6.86 | (164) all_76_1_30 = all_71_3_28 % 21.72/6.86 | % 21.72/6.86 | Instantiating formula (68) with vd526, vd527, all_46_0_11, all_76_1_30 and discharging atoms greater(vd526, vd527) = all_76_1_30, greater(vd526, vd527) = all_46_0_11, yields: % 21.72/6.86 | (165) all_76_1_30 = all_46_0_11 % 21.72/6.86 | % 21.72/6.86 | Instantiating formula (68) with vd526, vd527, all_41_0_7, all_76_1_30 and discharging atoms greater(vd526, vd527) = all_76_1_30, greater(vd526, vd527) = all_41_0_7, yields: % 21.72/6.86 | (166) all_76_1_30 = all_41_0_7 % 21.72/6.86 | % 21.72/6.86 | Combining equations (161,163) yields a new equation: % 21.72/6.86 | (167) all_71_0_25 = all_41_3_10 % 21.72/6.86 | % 21.72/6.86 | Simplifying 167 yields: % 21.72/6.86 | (168) all_71_0_25 = all_41_3_10 % 21.72/6.86 | % 21.72/6.86 | Combining equations (165,164) yields a new equation: % 21.72/6.86 | (169) all_71_3_28 = all_46_0_11 % 21.72/6.86 | % 21.72/6.86 | Combining equations (166,164) yields a new equation: % 21.72/6.86 | (170) all_71_3_28 = all_41_0_7 % 21.72/6.86 | % 21.72/6.86 | Combining equations (168,162) yields a new equation: % 21.72/6.86 | (171) all_46_1_12 = all_41_3_10 % 21.72/6.86 | % 21.72/6.86 | Combining equations (159,160) yields a new equation: % 21.72/6.86 | (172) all_41_2_9 = 0 % 21.72/6.86 | % 21.72/6.86 | Combining equations (157,158) yields a new equation: % 21.72/6.86 | (173) all_41_1_8 = 0 % 21.72/6.86 | % 21.72/6.86 | Combining equations (170,169) yields a new equation: % 21.72/6.86 | (174) all_46_0_11 = all_41_0_7 % 21.72/6.86 | % 21.72/6.86 | Combining equations (172,160) yields a new equation: % 21.72/6.86 | (159) all_71_1_26 = 0 % 21.72/6.86 | % 21.72/6.86 | Combining equations (171,162) yields a new equation: % 21.72/6.86 | (168) all_71_0_25 = all_41_3_10 % 21.72/6.86 | % 21.72/6.86 | From (171) and (119) follows: % 21.72/6.86 | (111) greater(vd529, vd530) = all_41_3_10 % 21.72/6.86 | % 21.72/6.86 | From (174) and (120) follows: % 21.72/6.86 | (108) greater(vd526, vd527) = all_41_0_7 % 21.72/6.86 | % 21.72/6.86 +-Applying beta-rule and splitting (147), into two cases. % 21.72/6.86 |-Branch one: % 21.72/6.86 | (179) ~ (all_71_0_25 = 0) % 21.72/6.86 | % 21.72/6.86 | Equations (168) can reduce 179 to: % 21.72/6.86 | (180) ~ (all_41_3_10 = 0) % 21.72/6.86 | % 21.72/6.86 +-Applying beta-rule and splitting (84), into two cases. % 21.72/6.86 |-Branch one: % 21.72/6.86 | (181) greater(vd529, vd530) = 0 % 21.72/6.86 | % 21.72/6.86 | Instantiating formula (68) with vd529, vd530, 0, all_41_3_10 and discharging atoms greater(vd529, vd530) = all_41_3_10, greater(vd529, vd530) = 0, yields: % 21.72/6.86 | (182) all_41_3_10 = 0 % 21.72/6.86 | % 21.72/6.86 | Equations (182) can reduce 180 to: % 21.72/6.86 | (88) $false % 21.72/6.86 | % 21.72/6.86 |-The branch is then unsatisfiable % 21.72/6.86 |-Branch two: % 21.72/6.86 | (184) ~ (greater(vd529, vd530) = 0) % 21.72/6.86 | (185) vd530 = vd529 % 21.72/6.86 | % 21.72/6.86 | From (185) and (17) follows: % 21.72/6.86 | (186) vmul(vd527, vd529) = all_0_1_1 % 21.72/6.86 | % 21.72/6.86 +-Applying beta-rule and splitting (113), into two cases. % 21.72/6.86 |-Branch one: % 21.72/6.86 | (187) ~ (all_41_0_7 = 0) % 21.72/6.86 | % 21.72/6.86 +-Applying beta-rule and splitting (85), into two cases. % 21.72/6.86 |-Branch one: % 21.72/6.86 | (188) greater(vd526, vd527) = 0 % 21.72/6.86 | % 21.72/6.86 | Instantiating formula (68) with vd526, vd527, 0, all_41_0_7 and discharging atoms greater(vd526, vd527) = all_41_0_7, greater(vd526, vd527) = 0, yields: % 21.72/6.86 | (189) all_41_0_7 = 0 % 21.72/6.86 | % 21.72/6.86 | Equations (189) can reduce 187 to: % 21.72/6.86 | (88) $false % 21.72/6.86 | % 21.72/6.86 |-The branch is then unsatisfiable % 21.72/6.86 |-Branch two: % 21.72/6.86 | (191) ~ (greater(vd526, vd527) = 0) % 21.72/6.86 | (192) vd527 = vd526 % 21.72/6.86 | % 21.72/6.86 | From (192) and (186) follows: % 21.72/6.87 | (193) vmul(vd526, vd529) = all_0_1_1 % 21.72/6.87 | % 21.72/6.87 | Instantiating formula (16) with all_0_1_1, all_0_2_2, vd526, vd529 and discharging atoms vmul(vd526, vd529) = all_0_1_1, vmul(vd526, vd529) = all_0_2_2, yields: % 21.72/6.87 | (194) all_0_1_1 = all_0_2_2 % 21.72/6.87 | % 21.72/6.87 | Equations (194) can reduce 94 to: % 21.72/6.87 | (88) $false % 21.72/6.87 | % 21.72/6.87 |-The branch is then unsatisfiable % 21.72/6.87 |-Branch two: % 21.72/6.87 | (189) all_41_0_7 = 0 % 21.72/6.87 | (197) ~ (all_41_1_8 = 0) % 21.72/6.87 | % 21.72/6.87 | Equations (173) can reduce 197 to: % 21.72/6.87 | (88) $false % 21.72/6.87 | % 21.72/6.87 |-The branch is then unsatisfiable % 21.72/6.87 |-Branch two: % 21.72/6.87 | (199) all_71_0_25 = 0 % 21.72/6.87 | (200) ~ (all_71_1_26 = 0) % 21.72/6.87 | % 21.72/6.87 | Equations (159) can reduce 200 to: % 21.72/6.87 | (88) $false % 21.72/6.87 | % 21.72/6.87 |-The branch is then unsatisfiable % 21.72/6.87 |-Branch two: % 21.72/6.87 | (202) geq(all_0_2_2, all_0_2_2) = all_0_0_0 % 21.72/6.87 | (87) all_0_0_0 = 0 % 21.72/6.87 | % 21.72/6.87 | Equations (87) can reduce 30 to: % 21.72/6.87 | (88) $false % 21.72/6.87 | % 21.72/6.87 |-The branch is then unsatisfiable % 21.72/6.87 % SZS output end Proof for theBenchmark % 21.72/6.87 % 21.72/6.87 6237ms %------------------------------------------------------------------------------