%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : NUM842+2 : TPTP v8.1.0. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n026.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 08:49:04 EDT 2022 % Result : Theorem 19.83s 6.35s % Output : Proof 22.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : NUM842+2 : TPTP v8.1.0. Released v4.1.0. % 0.08/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n026.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Thu Jul 7 19:19:54 EDT 2022 % 0.13/0.34 % CPUTime : % 0.51/0.59 ____ _ % 0.51/0.59 ___ / __ \_____(_)___ ________ __________ % 0.51/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.51/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.51/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.51/0.59 % 0.51/0.59 A Theorem Prover for First-Order Logic % 0.51/0.59 (ePrincess v.1.0) % 0.51/0.59 % 0.51/0.59 (c) Philipp Rümmer, 2009-2015 % 0.51/0.59 (c) Peter Backeman, 2014-2015 % 0.51/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.51/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.51/0.59 Bug reports to peter@backeman.se % 0.51/0.59 % 0.51/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.51/0.59 % 0.51/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.76/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.79/0.95 Prover 0: Preprocessing ... % 2.76/1.24 Prover 0: Warning: ignoring some quantifiers % 2.76/1.26 Prover 0: Constructing countermodel ... % 18.09/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 18.23/6.00 Prover 1: Preprocessing ... % 18.76/6.13 Prover 1: Warning: ignoring some quantifiers % 18.76/6.13 Prover 1: Constructing countermodel ... % 19.83/6.35 Prover 1: proved (422ms) % 19.83/6.35 Prover 0: stopped % 19.83/6.35 % 19.83/6.35 No countermodel exists, formula is valid % 19.83/6.35 % SZS status Theorem for theBenchmark % 19.83/6.35 % 19.83/6.35 Generating proof ... Warning: ignoring some quantifiers % 22.25/6.91 found it (size 124) % 22.25/6.91 % 22.25/6.91 % SZS output start Proof for theBenchmark % 22.25/6.91 Assumed formulas after preprocessing and simplification: % 22.25/6.91 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & geq(vd355, vd356) = v2 & geq(vd353, vd354) = v1 & vplus(vd354, vd356) = v5 & vplus(vd353, vd355) = v4 & greater(v4, v5) = v6 & greater(vd355, vd356) = v0 & greater(vd353, vd354) = v3 & ! [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] : (v12 = 0 | ~ (less(v10, v11) = v12) | ~ (vplus(v8, v9) = v11) | ~ (vplus(v7, v9) = v10) | ? [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] : ( ~ (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] : ( ~ (less(v10, v11) = 0) | ~ (vplus(v8, v9) = v11) | ~ (vplus(v7, v9) = v10) | less(v7, v8) = 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) | ~ (greater(v10, v11) = 0) | greater(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (vplus(v7, v8) = v10) | ~ (vplus(v7, v8) = v9)) & ! [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 | ~ (less(v7, v9) = v10) | ~ (less(v7, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & less(v8, v9) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (vplus(v7, v8) = v9) | ~ (greater(v9, v7) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (less(v8, v7) = v9) | ~ (vplus(v8, v10) = v7)) & ! [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 | ~ (less(v10, v9) = v8) | ~ (less(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 | ~ (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(v7) = v9) | ~ (vplus(v9, v8) = v10) | ? [v11] : (vsucc(v11) = v10 & vplus(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) & leq(v7, v8) = v10)) & ! [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) & 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(v7, v8) = v9) | vplus(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 = 0 | ~ (geq(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (leq(v7, v7) = v8)) & ! [v7] : ! [v8] : (v7 = v1 | ~ (vskolem2(v7) = v8) | vsucc(v8) = v7) & ! [v7] : ! [v8] : ( ~ (geq(v7, v8) = 0) | leq(v8, v7) = 0) & ! [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] : ~ (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] : ( ~ (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))) % 22.60/6.95 | 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: % 22.60/6.95 | (1) ~ (all_0_0_0 = 0) & geq(vd355, vd356) = all_0_4_4 & geq(vd353, vd354) = all_0_5_5 & vplus(vd354, vd356) = all_0_1_1 & vplus(vd353, vd355) = all_0_2_2 & greater(all_0_2_2, all_0_1_1) = all_0_0_0 & greater(vd355, vd356) = all_0_6_6 & greater(vd353, vd354) = all_0_3_3 & ! [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] : (v5 = 0 | ~ (less(v3, v4) = v5) | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ? [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] : ( ~ (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] : ( ~ (less(v3, v4) = 0) | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | less(v0, v1) = 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) | ~ (greater(v3, v4) = 0) | greater(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (vplus(v0, v1) = v3) | ~ (vplus(v0, v1) = 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 | ~ (less(v0, v2) = v3) | ~ (less(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (vplus(v0, v1) = v2) | ~ (greater(v2, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (less(v1, v0) = v2) | ~ (vplus(v1, v3) = v0)) & ! [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 | ~ (less(v3, v2) = v1) | ~ (less(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 | ~ (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(v0) = v2) | ~ (vplus(v2, v1) = v3) | ? [v4] : (vsucc(v4) = v3 & vplus(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) & leq(v0, v1) = v3)) & ! [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) & 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(v0, v1) = v2) | vplus(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 = 0 | ~ (geq(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1)) & ! [v0] : ! [v1] : (v0 = v1 | ~ (vskolem2(v0) = v1) | vsucc(v1) = v0) & ! [v0] : ! [v1] : ( ~ (geq(v0, v1) = 0) | leq(v1, v0) = 0) & ! [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] : ~ (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] : ( ~ (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)) % 22.60/6.96 | % 22.60/6.96 | Applying alpha-rule on (1) yields: % 22.60/6.96 | (2) ! [v0] : ~ (greater(v0, v0) = 0) % 22.60/6.96 | (3) geq(vd355, vd356) = all_0_4_4 % 22.60/6.96 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) % 22.60/6.96 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v0, v1) = v3)) % 22.60/6.96 | (6) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v2, v1) = v3) | ? [v4] : ( ~ (v4 = v3) & vplus(v2, v0) = v4)) % 22.60/6.96 | (7) ! [v0] : ~ (vsucc(v0) = v1) % 22.60/6.96 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v1, v0) = 0) | less(v1, v0) = 0) % 22.60/6.96 | (9) greater(all_0_2_2, all_0_1_1) = all_0_0_0 % 22.60/6.96 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (less(v1, v0) = v2) | ~ (vplus(v1, v3) = v0)) % 22.60/6.96 | (11) ! [v0] : ! [v1] : ( ~ (less(v1, v0) = 0) | ? [v2] : vplus(v1, v2) = v0) % 22.60/6.96 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1)) % 22.60/6.96 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v1) = v2) | ~ (vsucc(v0) = v2)) % 22.60/6.96 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (less(v3, v4) = 0) | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | less(v0, v1) = 0) % 22.60/6.97 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) % 22.60/6.97 | (16) vplus(vd354, vd356) = all_0_1_1 % 22.60/6.97 | (17) greater(vd355, vd356) = all_0_6_6 % 22.60/6.97 | (18) geq(vd353, vd354) = all_0_5_5 % 22.60/6.97 | (19) ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1)) % 22.60/6.97 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vplus(v1, v3) = v0) | ~ (vplus(v0, v2) = v1)) % 22.60/6.97 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (vplus(v0, v3) = v1) | ~ (greater(v1, v0) = v2)) % 22.60/6.97 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v0) = v2) | ~ (vplus(v2, v1) = v3) | ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4)) % 22.60/6.97 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) % 22.60/6.97 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (geq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v1, v0) = v3)) % 22.60/6.97 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 22.60/6.97 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ? [v5] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4)) % 22.60/6.97 | (27) ! [v0] : ! [v1] : ( ~ (vplus(v0, v1) = v1) | vsucc(v0) = v1) % 22.60/6.97 | (28) ! [v0] : ! [v1] : ( ~ (geq(v0, v1) = 0) | leq(v1, v0) = 0) % 22.60/6.97 | (29) ! [v0] : ! [v1] : ( ~ (greater(v1, v0) = 0) | ? [v2] : vplus(v0, v2) = v1) % 22.60/6.97 | (30) greater(vd353, vd354) = all_0_3_3 % 22.60/6.97 | (31) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (geq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) % 22.60/6.97 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (less(v3, v4) = v5) | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ? [v6] : ( ~ (v6 = 0) & less(v0, v1) = v6)) % 22.60/6.97 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v0, v1) = v2) | vplus(v1, v0) = v2) % 22.60/6.97 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (less(v0, v2) = v3) | ~ (less(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & less(v1, v2) = v4)) % 22.60/6.97 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v1, v2) = v3) | ~ (vplus(v0, v2) = v3)) % 22.60/6.97 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (vplus(v0, v1) = v2) | ~ (greater(v2, v0) = v3)) % 22.60/6.97 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) % 22.60/6.97 | (38) ! [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)) % 22.60/6.97 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v1) = v2) | ~ (vplus(v0, v2) = v3) | ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4)) % 22.60/6.97 | (40) ! [v0] : ! [v1] : ( ~ (vplus(v1, v0) = v1) | vsucc(v0) = v1) % 22.60/6.97 | (41) ! [v0] : ! [v1] : (v1 = v0 | ~ (geq(v1, v0) = 0) | greater(v1, v0) = 0) % 22.60/6.97 | (42) vplus(vd353, vd355) = all_0_2_2 % 22.60/6.97 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ~ (greater(v3, v4) = 0) | greater(v0, v1) = 0) % 22.60/6.97 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (vplus(v0, v1) = v3) | ~ (vplus(v0, v1) = v2)) % 22.60/6.97 | (45) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ (vskolem2(v2) = v0)) % 22.60/6.97 | (46) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (less(v0, v1) = v2) | greater(v0, v1) = 0) % 22.60/6.97 | (47) ! [v0] : ! [v1] : ( ~ (less(v0, v1) = 0) | greater(v1, v0) = 0) % 22.60/6.97 | (48) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & less(v1, v0) = v3)) % 22.60/6.97 | (49) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) % 22.60/6.97 | (50) ! [v0] : ~ (vsucc(v0) = v0) % 22.60/6.97 | (51) ! [v0] : ! [v1] : ( ~ (less(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & greater(v0, v1) = v2)) % 22.60/6.97 | (52) ! [v0] : ! [v1] : (v0 = v1 | ~ (vskolem2(v0) = v1) | vsucc(v1) = v0) % 22.60/6.98 | (53) ! [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)))))) % 22.60/6.98 | (54) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ((v3 = v1 & vplus(v0, v2) = v1) | (v3 = v0 & vplus(v1, v2) = v0))) % 22.60/6.98 | (55) ~ (all_0_0_0 = 0) % 22.60/6.98 | (56) ! [v0] : ! [v1] : ~ (vplus(v0, v1) = v1) % 22.60/6.98 | (57) ! [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)))) % 22.60/6.98 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (leq(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & leq(v1, v2) = v4)) % 22.91/6.98 | (59) ! [v0] : ! [v1] : ~ (vplus(v0, v1) = v0) % 22.91/6.98 | (60) (all_0_3_3 = 0 & all_0_4_4 = 0) | (all_0_5_5 = 0 & all_0_6_6 = 0) % 22.91/6.98 | (61) ! [v0] : ~ (less(v0, v0) = 0) % 22.91/6.98 | % 22.91/6.98 | Instantiating formula (41) with vd355, vd356 yields: % 22.91/6.98 | (62) vd356 = vd355 | ~ (geq(vd355, vd356) = 0) | greater(vd355, vd356) = 0 % 22.91/6.98 | % 22.91/6.98 | Instantiating formula (28) with vd356, vd355 yields: % 22.91/6.98 | (63) ~ (geq(vd355, vd356) = 0) | leq(vd356, vd355) = 0 % 22.91/6.98 | % 22.91/6.98 | Instantiating formula (41) with vd353, vd354 yields: % 22.91/6.98 | (64) vd354 = vd353 | ~ (geq(vd353, vd354) = 0) | greater(vd353, vd354) = 0 % 22.91/6.98 | % 22.91/6.98 | Instantiating formula (28) with vd354, vd353 yields: % 22.91/6.98 | (65) ~ (geq(vd353, vd354) = 0) | leq(vd354, vd353) = 0 % 22.91/6.98 | % 22.91/6.98 | Instantiating formula (33) with all_0_1_1, vd356, vd354 and discharging atoms vplus(vd354, vd356) = all_0_1_1, yields: % 22.91/6.98 | (66) vplus(vd356, vd354) = all_0_1_1 % 22.91/6.98 | % 22.91/6.98 | Instantiating formula (33) with all_0_2_2, vd355, vd353 and discharging atoms vplus(vd353, vd355) = all_0_2_2, yields: % 22.91/6.98 | (67) vplus(vd355, vd353) = all_0_2_2 % 22.91/6.98 | % 22.91/6.98 | Instantiating formula (38) with all_0_0_0, all_0_1_1, all_0_2_2, vd355, vd354, vd353 and discharging atoms vplus(vd353, vd355) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 22.91/6.98 | (68) all_0_0_0 = 0 | ~ (vplus(vd354, vd355) = all_0_1_1) | ? [v0] : ( ~ (v0 = 0) & greater(vd353, vd354) = v0) % 22.91/6.98 | % 22.91/6.98 | Instantiating formula (57) with all_0_0_0, all_0_1_1, all_0_2_2, vd356, vd355, vd354, vd353 and discharging atoms vplus(vd354, vd356) = all_0_1_1, vplus(vd353, vd355) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 22.91/6.98 | (69) all_0_0_0 = 0 | ? [v0] : ? [v1] : (greater(vd355, vd356) = v0 & greater(vd353, vd354) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 22.91/6.98 | % 22.91/6.98 | Instantiating formula (29) with vd355, vd356 yields: % 22.91/6.98 | (70) ~ (greater(vd355, vd356) = 0) | ? [v0] : vplus(vd356, v0) = vd355 % 22.91/6.98 | % 22.91/6.98 | Instantiating formula (29) with vd353, vd354 yields: % 22.91/6.98 | (71) ~ (greater(vd353, vd354) = 0) | ? [v0] : vplus(vd354, v0) = vd353 % 22.91/6.98 | % 22.91/6.98 | Instantiating formula (57) with all_0_0_0, all_0_1_1, all_0_2_2, vd354, vd355, vd356, vd353 and discharging atoms vplus(vd356, vd354) = all_0_1_1, vplus(vd353, vd355) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 22.91/6.98 | (72) all_0_0_0 = 0 | ? [v0] : ? [v1] : (greater(vd355, vd354) = v0 & greater(vd353, vd356) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 22.91/6.98 | % 22.91/6.98 | Instantiating formula (57) with all_0_0_0, all_0_1_1, all_0_2_2, vd356, vd353, vd354, vd355 and discharging atoms vplus(vd354, vd356) = all_0_1_1, vplus(vd355, vd353) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 22.91/6.98 | (73) all_0_0_0 = 0 | ? [v0] : ? [v1] : (greater(vd355, vd354) = v1 & greater(vd353, vd356) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 22.91/6.98 | % 22.91/6.98 | Instantiating formula (57) with all_0_0_0, all_0_1_1, all_0_2_2, vd354, vd353, vd356, vd355 and discharging atoms vplus(vd356, vd354) = all_0_1_1, vplus(vd355, vd353) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 22.91/6.98 | (74) all_0_0_0 = 0 | ? [v0] : ? [v1] : (greater(vd355, vd356) = v1 & greater(vd353, vd354) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 22.91/6.98 | % 22.91/6.98 | Instantiating formula (38) with all_0_0_0, all_0_1_1, all_0_2_2, vd353, vd356, vd355 and discharging atoms vplus(vd355, vd353) = all_0_2_2, greater(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 22.91/6.98 | (75) all_0_0_0 = 0 | ~ (vplus(vd356, vd353) = all_0_1_1) | ? [v0] : ( ~ (v0 = 0) & greater(vd355, vd356) = v0) % 22.91/6.98 | % 22.91/6.98 +-Applying beta-rule and splitting (73), into two cases. % 22.91/6.98 |-Branch one: % 22.91/6.98 | (76) all_0_0_0 = 0 % 22.91/6.98 | % 22.91/6.99 | Equations (76) can reduce 55 to: % 22.91/6.99 | (77) $false % 22.91/6.99 | % 22.91/6.99 |-The branch is then unsatisfiable % 22.91/6.99 |-Branch two: % 22.91/6.99 | (55) ~ (all_0_0_0 = 0) % 22.91/6.99 | (79) ? [v0] : ? [v1] : (greater(vd355, vd354) = v1 & greater(vd353, vd356) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 22.91/6.99 | % 22.91/6.99 +-Applying beta-rule and splitting (72), into two cases. % 22.91/6.99 |-Branch one: % 22.91/6.99 | (76) all_0_0_0 = 0 % 22.91/6.99 | % 22.91/6.99 | Equations (76) can reduce 55 to: % 22.91/6.99 | (77) $false % 22.91/6.99 | % 22.91/6.99 |-The branch is then unsatisfiable % 22.91/6.99 |-Branch two: % 22.91/6.99 | (55) ~ (all_0_0_0 = 0) % 22.91/6.99 | (83) ? [v0] : ? [v1] : (greater(vd355, vd354) = v0 & greater(vd353, vd356) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 22.91/6.99 | % 22.91/6.99 +-Applying beta-rule and splitting (60), into two cases. % 22.91/6.99 |-Branch one: % 22.91/6.99 | (84) all_0_3_3 = 0 & all_0_4_4 = 0 % 22.91/6.99 | % 22.91/6.99 | Applying alpha-rule on (84) yields: % 22.91/6.99 | (85) all_0_3_3 = 0 % 22.91/6.99 | (86) all_0_4_4 = 0 % 22.91/6.99 | % 22.91/6.99 | From (86) and (3) follows: % 22.91/6.99 | (87) geq(vd355, vd356) = 0 % 22.91/6.99 | % 22.91/6.99 | From (85) and (30) follows: % 22.91/6.99 | (88) greater(vd353, vd354) = 0 % 22.91/6.99 | % 22.91/6.99 +-Applying beta-rule and splitting (69), into two cases. % 22.91/6.99 |-Branch one: % 22.91/6.99 | (76) all_0_0_0 = 0 % 22.91/6.99 | % 22.91/6.99 | Equations (76) can reduce 55 to: % 22.91/6.99 | (77) $false % 22.91/6.99 | % 22.91/6.99 |-The branch is then unsatisfiable % 22.91/6.99 |-Branch two: % 22.91/6.99 | (55) ~ (all_0_0_0 = 0) % 22.91/6.99 | (92) ? [v0] : ? [v1] : (greater(vd355, vd356) = v0 & greater(vd353, vd354) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 22.91/6.99 | % 22.91/6.99 | Instantiating (92) with all_68_0_14, all_68_1_15 yields: % 22.91/6.99 | (93) greater(vd355, vd356) = all_68_1_15 & greater(vd353, vd354) = all_68_0_14 & ( ~ (all_68_0_14 = 0) | ~ (all_68_1_15 = 0)) % 22.91/6.99 | % 22.91/6.99 | Applying alpha-rule on (93) yields: % 22.91/6.99 | (94) greater(vd355, vd356) = all_68_1_15 % 22.91/6.99 | (95) greater(vd353, vd354) = all_68_0_14 % 22.91/6.99 | (96) ~ (all_68_0_14 = 0) | ~ (all_68_1_15 = 0) % 22.91/6.99 | % 22.91/6.99 +-Applying beta-rule and splitting (63), into two cases. % 22.91/6.99 |-Branch one: % 22.91/6.99 | (97) ~ (geq(vd355, vd356) = 0) % 22.91/6.99 | % 22.91/6.99 | Using (87) and (97) yields: % 22.91/6.99 | (98) $false % 22.91/6.99 | % 22.91/6.99 |-The branch is then unsatisfiable % 22.91/6.99 |-Branch two: % 22.91/6.99 | (87) geq(vd355, vd356) = 0 % 22.91/6.99 | (100) leq(vd356, vd355) = 0 % 22.91/6.99 | % 22.91/6.99 +-Applying beta-rule and splitting (71), into two cases. % 22.91/6.99 |-Branch one: % 22.91/6.99 | (101) ~ (greater(vd353, vd354) = 0) % 22.91/6.99 | % 22.91/6.99 | Using (88) and (101) yields: % 22.91/6.99 | (98) $false % 22.91/6.99 | % 22.91/6.99 |-The branch is then unsatisfiable % 22.91/6.99 |-Branch two: % 22.91/6.99 | (88) greater(vd353, vd354) = 0 % 22.91/6.99 | (104) ? [v0] : vplus(vd354, v0) = vd353 % 22.91/6.99 | % 22.91/6.99 | Instantiating formula (37) with vd355, vd356, all_68_1_15, all_0_6_6 and discharging atoms greater(vd355, vd356) = all_68_1_15, greater(vd355, vd356) = all_0_6_6, yields: % 22.91/6.99 | (105) all_68_1_15 = all_0_6_6 % 22.91/6.99 | % 22.91/6.99 | Instantiating formula (37) with vd353, vd354, 0, all_68_0_14 and discharging atoms greater(vd353, vd354) = all_68_0_14, greater(vd353, vd354) = 0, yields: % 22.91/6.99 | (106) all_68_0_14 = 0 % 22.91/6.99 | % 22.91/6.99 | From (105) and (94) follows: % 22.91/6.99 | (17) greater(vd355, vd356) = all_0_6_6 % 22.91/6.99 | % 22.91/6.99 | From (106) and (95) follows: % 22.91/6.99 | (88) greater(vd353, vd354) = 0 % 22.91/6.99 | % 22.91/6.99 +-Applying beta-rule and splitting (74), into two cases. % 22.91/6.99 |-Branch one: % 22.91/6.99 | (76) all_0_0_0 = 0 % 22.91/6.99 | % 22.91/6.99 | Equations (76) can reduce 55 to: % 22.91/6.99 | (77) $false % 22.91/6.99 | % 22.91/6.99 |-The branch is then unsatisfiable % 22.91/6.99 |-Branch two: % 22.91/6.99 | (55) ~ (all_0_0_0 = 0) % 22.91/6.99 | (112) ? [v0] : ? [v1] : (greater(vd355, vd356) = v1 & greater(vd353, vd354) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 22.91/6.99 | % 22.91/6.99 | Instantiating (112) with all_88_0_17, all_88_1_18 yields: % 22.91/6.99 | (113) greater(vd355, vd356) = all_88_0_17 & greater(vd353, vd354) = all_88_1_18 & ( ~ (all_88_0_17 = 0) | ~ (all_88_1_18 = 0)) % 22.91/6.99 | % 22.91/6.99 | Applying alpha-rule on (113) yields: % 22.91/6.99 | (114) greater(vd355, vd356) = all_88_0_17 % 22.91/6.99 | (115) greater(vd353, vd354) = all_88_1_18 % 22.91/6.99 | (116) ~ (all_88_0_17 = 0) | ~ (all_88_1_18 = 0) % 22.91/6.99 | % 22.91/6.99 +-Applying beta-rule and splitting (96), into two cases. % 22.91/6.99 |-Branch one: % 22.91/6.99 | (117) ~ (all_68_0_14 = 0) % 22.91/6.99 | % 22.91/6.99 | Equations (106) can reduce 117 to: % 22.91/6.99 | (77) $false % 22.91/6.99 | % 22.91/6.99 |-The branch is then unsatisfiable % 22.91/6.99 |-Branch two: % 22.91/6.99 | (106) all_68_0_14 = 0 % 22.91/6.99 | (120) ~ (all_68_1_15 = 0) % 22.91/6.99 | % 22.91/6.99 | Equations (105) can reduce 120 to: % 22.91/7.00 | (121) ~ (all_0_6_6 = 0) % 22.91/7.00 | % 22.91/7.00 +-Applying beta-rule and splitting (62), into two cases. % 22.91/7.00 |-Branch one: % 22.91/7.00 | (97) ~ (geq(vd355, vd356) = 0) % 22.91/7.00 | % 22.91/7.00 | Using (87) and (97) yields: % 22.91/7.00 | (98) $false % 22.91/7.00 | % 22.91/7.00 |-The branch is then unsatisfiable % 22.91/7.00 |-Branch two: % 22.91/7.00 | (87) geq(vd355, vd356) = 0 % 22.91/7.00 | (125) vd356 = vd355 | greater(vd355, vd356) = 0 % 22.91/7.00 | % 22.91/7.00 +-Applying beta-rule and splitting (125), into two cases. % 22.91/7.00 |-Branch one: % 22.91/7.00 | (126) greater(vd355, vd356) = 0 % 22.91/7.00 | % 22.91/7.00 | Instantiating formula (37) with vd355, vd356, all_88_0_17, all_0_6_6 and discharging atoms greater(vd355, vd356) = all_88_0_17, greater(vd355, vd356) = all_0_6_6, yields: % 22.91/7.00 | (127) all_88_0_17 = all_0_6_6 % 22.91/7.00 | % 22.91/7.00 | Instantiating formula (37) with vd355, vd356, 0, all_88_0_17 and discharging atoms greater(vd355, vd356) = all_88_0_17, greater(vd355, vd356) = 0, yields: % 22.91/7.00 | (128) all_88_0_17 = 0 % 22.91/7.00 | % 22.91/7.00 | Combining equations (127,128) yields a new equation: % 22.91/7.00 | (129) all_0_6_6 = 0 % 22.91/7.00 | % 22.91/7.00 | Simplifying 129 yields: % 22.91/7.00 | (130) all_0_6_6 = 0 % 22.91/7.00 | % 22.91/7.00 | Equations (130) can reduce 121 to: % 22.91/7.00 | (77) $false % 22.91/7.00 | % 22.91/7.00 |-The branch is then unsatisfiable % 22.91/7.00 |-Branch two: % 22.91/7.00 | (132) ~ (greater(vd355, vd356) = 0) % 22.91/7.00 | (133) vd356 = vd355 % 22.91/7.00 | % 22.91/7.00 | From (133) and (16) follows: % 22.91/7.00 | (134) vplus(vd354, vd355) = all_0_1_1 % 22.91/7.00 | % 22.91/7.00 +-Applying beta-rule and splitting (68), into two cases. % 22.91/7.00 |-Branch one: % 22.91/7.00 | (135) ~ (vplus(vd354, vd355) = all_0_1_1) % 22.91/7.00 | % 22.91/7.00 | Using (134) and (135) yields: % 22.91/7.00 | (98) $false % 22.91/7.00 | % 22.91/7.00 |-The branch is then unsatisfiable % 22.91/7.00 |-Branch two: % 22.91/7.00 | (134) vplus(vd354, vd355) = all_0_1_1 % 22.91/7.00 | (138) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & greater(vd353, vd354) = v0) % 22.91/7.00 | % 22.91/7.00 +-Applying beta-rule and splitting (138), into two cases. % 22.91/7.00 |-Branch one: % 22.91/7.00 | (76) all_0_0_0 = 0 % 22.91/7.00 | % 22.91/7.00 | Equations (76) can reduce 55 to: % 22.91/7.00 | (77) $false % 22.91/7.00 | % 22.91/7.00 |-The branch is then unsatisfiable % 22.91/7.00 |-Branch two: % 22.91/7.00 | (55) ~ (all_0_0_0 = 0) % 22.91/7.00 | (142) ? [v0] : ( ~ (v0 = 0) & greater(vd353, vd354) = v0) % 22.91/7.00 | % 22.91/7.00 | Instantiating (142) with all_110_0_19 yields: % 22.91/7.00 | (143) ~ (all_110_0_19 = 0) & greater(vd353, vd354) = all_110_0_19 % 22.91/7.00 | % 22.91/7.00 | Applying alpha-rule on (143) yields: % 22.91/7.00 | (144) ~ (all_110_0_19 = 0) % 22.91/7.00 | (145) greater(vd353, vd354) = all_110_0_19 % 22.91/7.00 | % 22.91/7.00 | Instantiating formula (37) with vd353, vd354, all_110_0_19, 0 and discharging atoms greater(vd353, vd354) = all_110_0_19, greater(vd353, vd354) = 0, yields: % 22.91/7.00 | (146) all_110_0_19 = 0 % 22.91/7.00 | % 22.91/7.00 | Instantiating formula (37) with vd353, vd354, all_88_1_18, all_110_0_19 and discharging atoms greater(vd353, vd354) = all_110_0_19, greater(vd353, vd354) = all_88_1_18, yields: % 22.91/7.00 | (147) all_110_0_19 = all_88_1_18 % 22.91/7.00 | % 22.91/7.00 | Combining equations (146,147) yields a new equation: % 22.91/7.00 | (148) all_88_1_18 = 0 % 22.91/7.00 | % 22.91/7.00 | Combining equations (148,147) yields a new equation: % 22.91/7.00 | (146) all_110_0_19 = 0 % 22.91/7.00 | % 22.91/7.00 | Equations (146) can reduce 144 to: % 22.91/7.00 | (77) $false % 22.91/7.00 | % 22.91/7.00 |-The branch is then unsatisfiable % 22.91/7.00 |-Branch two: % 22.91/7.00 | (151) all_0_5_5 = 0 & all_0_6_6 = 0 % 22.91/7.00 | % 22.91/7.00 | Applying alpha-rule on (151) yields: % 22.91/7.00 | (152) all_0_5_5 = 0 % 22.91/7.00 | (130) all_0_6_6 = 0 % 22.91/7.00 | % 22.91/7.00 | From (152) and (18) follows: % 22.91/7.00 | (154) geq(vd353, vd354) = 0 % 22.91/7.00 | % 22.91/7.00 | From (130) and (17) follows: % 22.91/7.00 | (126) greater(vd355, vd356) = 0 % 22.91/7.00 | % 22.91/7.00 +-Applying beta-rule and splitting (69), into two cases. % 22.91/7.00 |-Branch one: % 22.91/7.00 | (76) all_0_0_0 = 0 % 22.91/7.00 | % 22.91/7.00 | Equations (76) can reduce 55 to: % 22.91/7.00 | (77) $false % 22.91/7.00 | % 22.91/7.00 |-The branch is then unsatisfiable % 22.91/7.00 |-Branch two: % 22.91/7.00 | (55) ~ (all_0_0_0 = 0) % 22.91/7.00 | (92) ? [v0] : ? [v1] : (greater(vd355, vd356) = v0 & greater(vd353, vd354) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 22.91/7.00 | % 22.91/7.00 | Instantiating (92) with all_68_0_20, all_68_1_21 yields: % 22.91/7.00 | (160) greater(vd355, vd356) = all_68_1_21 & greater(vd353, vd354) = all_68_0_20 & ( ~ (all_68_0_20 = 0) | ~ (all_68_1_21 = 0)) % 22.91/7.00 | % 22.91/7.00 | Applying alpha-rule on (160) yields: % 22.91/7.00 | (161) greater(vd355, vd356) = all_68_1_21 % 22.91/7.00 | (162) greater(vd353, vd354) = all_68_0_20 % 22.91/7.00 | (163) ~ (all_68_0_20 = 0) | ~ (all_68_1_21 = 0) % 22.91/7.00 | % 22.91/7.00 +-Applying beta-rule and splitting (65), into two cases. % 22.91/7.00 |-Branch one: % 22.91/7.00 | (164) ~ (geq(vd353, vd354) = 0) % 22.91/7.00 | % 22.91/7.00 | Using (154) and (164) yields: % 22.91/7.00 | (98) $false % 22.91/7.00 | % 22.91/7.00 |-The branch is then unsatisfiable % 22.91/7.00 |-Branch two: % 22.91/7.00 | (154) geq(vd353, vd354) = 0 % 22.91/7.00 | (167) leq(vd354, vd353) = 0 % 22.91/7.00 | % 22.91/7.00 +-Applying beta-rule and splitting (70), into two cases. % 22.91/7.00 |-Branch one: % 22.91/7.00 | (132) ~ (greater(vd355, vd356) = 0) % 22.91/7.00 | % 22.91/7.00 | Using (126) and (132) yields: % 22.91/7.00 | (98) $false % 22.91/7.00 | % 22.91/7.00 |-The branch is then unsatisfiable % 22.91/7.00 |-Branch two: % 22.91/7.00 | (126) greater(vd355, vd356) = 0 % 22.91/7.00 | (171) ? [v0] : vplus(vd356, v0) = vd355 % 22.91/7.00 | % 22.91/7.00 | Instantiating formula (37) with vd355, vd356, 0, all_68_1_21 and discharging atoms greater(vd355, vd356) = all_68_1_21, greater(vd355, vd356) = 0, yields: % 22.91/7.01 | (172) all_68_1_21 = 0 % 22.91/7.01 | % 22.91/7.01 | Instantiating formula (37) with vd353, vd354, all_68_0_20, all_0_3_3 and discharging atoms greater(vd353, vd354) = all_68_0_20, greater(vd353, vd354) = all_0_3_3, yields: % 22.91/7.01 | (173) all_68_0_20 = all_0_3_3 % 22.91/7.01 | % 22.91/7.01 | From (172) and (161) follows: % 22.91/7.01 | (126) greater(vd355, vd356) = 0 % 22.91/7.01 | % 22.91/7.01 | From (173) and (162) follows: % 22.91/7.01 | (30) greater(vd353, vd354) = all_0_3_3 % 22.91/7.01 | % 22.91/7.01 +-Applying beta-rule and splitting (75), into two cases. % 22.91/7.01 |-Branch one: % 22.91/7.01 | (176) ~ (vplus(vd356, vd353) = all_0_1_1) % 22.91/7.01 | % 22.91/7.01 +-Applying beta-rule and splitting (163), into two cases. % 22.91/7.01 |-Branch one: % 22.91/7.01 | (177) ~ (all_68_0_20 = 0) % 22.91/7.01 | % 22.91/7.01 | Equations (173) can reduce 177 to: % 22.91/7.01 | (178) ~ (all_0_3_3 = 0) % 22.91/7.01 | % 22.91/7.01 +-Applying beta-rule and splitting (64), into two cases. % 22.91/7.01 |-Branch one: % 22.91/7.01 | (164) ~ (geq(vd353, vd354) = 0) % 22.91/7.01 | % 22.91/7.01 | Using (154) and (164) yields: % 22.91/7.01 | (98) $false % 22.91/7.01 | % 22.91/7.01 |-The branch is then unsatisfiable % 22.91/7.01 |-Branch two: % 22.91/7.01 | (154) geq(vd353, vd354) = 0 % 22.91/7.01 | (182) vd354 = vd353 | greater(vd353, vd354) = 0 % 22.91/7.01 | % 22.91/7.01 +-Applying beta-rule and splitting (182), into two cases. % 22.91/7.01 |-Branch one: % 22.91/7.01 | (88) greater(vd353, vd354) = 0 % 22.91/7.01 | % 22.91/7.01 | Instantiating formula (37) with vd353, vd354, 0, all_0_3_3 and discharging atoms greater(vd353, vd354) = all_0_3_3, greater(vd353, vd354) = 0, yields: % 22.91/7.01 | (85) all_0_3_3 = 0 % 22.91/7.01 | % 22.91/7.01 | Equations (85) can reduce 178 to: % 22.91/7.01 | (77) $false % 22.91/7.01 | % 22.91/7.01 |-The branch is then unsatisfiable % 22.91/7.01 |-Branch two: % 22.91/7.01 | (101) ~ (greater(vd353, vd354) = 0) % 22.91/7.01 | (187) vd354 = vd353 % 22.91/7.01 | % 22.91/7.01 | From (187) and (66) follows: % 22.91/7.01 | (188) vplus(vd356, vd353) = all_0_1_1 % 22.91/7.01 | % 22.91/7.01 | Using (188) and (176) yields: % 22.91/7.01 | (98) $false % 22.91/7.01 | % 22.91/7.01 |-The branch is then unsatisfiable % 22.91/7.01 |-Branch two: % 22.91/7.01 | (190) all_68_0_20 = 0 % 22.91/7.01 | (191) ~ (all_68_1_21 = 0) % 22.91/7.01 | % 22.91/7.01 | Equations (172) can reduce 191 to: % 22.91/7.01 | (77) $false % 22.91/7.01 | % 22.91/7.01 |-The branch is then unsatisfiable % 22.91/7.01 |-Branch two: % 22.91/7.01 | (188) vplus(vd356, vd353) = all_0_1_1 % 22.91/7.01 | (194) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & greater(vd355, vd356) = v0) % 22.91/7.01 | % 22.91/7.01 +-Applying beta-rule and splitting (74), into two cases. % 22.91/7.01 |-Branch one: % 22.91/7.01 | (76) all_0_0_0 = 0 % 22.91/7.01 | % 22.91/7.01 | Equations (76) can reduce 55 to: % 22.91/7.01 | (77) $false % 22.91/7.01 | % 22.91/7.01 |-The branch is then unsatisfiable % 22.91/7.01 |-Branch two: % 22.91/7.01 | (55) ~ (all_0_0_0 = 0) % 22.91/7.01 | (112) ? [v0] : ? [v1] : (greater(vd355, vd356) = v1 & greater(vd353, vd354) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 22.91/7.01 | % 22.91/7.01 | Instantiating (112) with all_91_0_23, all_91_1_24 yields: % 22.91/7.01 | (199) greater(vd355, vd356) = all_91_0_23 & greater(vd353, vd354) = all_91_1_24 & ( ~ (all_91_0_23 = 0) | ~ (all_91_1_24 = 0)) % 22.91/7.01 | % 22.91/7.01 | Applying alpha-rule on (199) yields: % 22.91/7.01 | (200) greater(vd355, vd356) = all_91_0_23 % 22.91/7.01 | (201) greater(vd353, vd354) = all_91_1_24 % 22.91/7.01 | (202) ~ (all_91_0_23 = 0) | ~ (all_91_1_24 = 0) % 22.91/7.01 | % 22.91/7.01 +-Applying beta-rule and splitting (194), into two cases. % 22.91/7.01 |-Branch one: % 22.91/7.01 | (76) all_0_0_0 = 0 % 22.91/7.01 | % 22.91/7.01 | Equations (76) can reduce 55 to: % 22.91/7.01 | (77) $false % 22.91/7.01 | % 22.91/7.01 |-The branch is then unsatisfiable % 22.91/7.01 |-Branch two: % 22.91/7.01 | (55) ~ (all_0_0_0 = 0) % 22.91/7.01 | (206) ? [v0] : ( ~ (v0 = 0) & greater(vd355, vd356) = v0) % 22.91/7.01 | % 22.91/7.01 | Instantiating (206) with all_109_0_26 yields: % 22.91/7.01 | (207) ~ (all_109_0_26 = 0) & greater(vd355, vd356) = all_109_0_26 % 22.91/7.01 | % 22.91/7.01 | Applying alpha-rule on (207) yields: % 22.91/7.01 | (208) ~ (all_109_0_26 = 0) % 22.91/7.01 | (209) greater(vd355, vd356) = all_109_0_26 % 22.91/7.01 | % 22.91/7.01 | Instantiating formula (37) with vd355, vd356, all_109_0_26, 0 and discharging atoms greater(vd355, vd356) = all_109_0_26, greater(vd355, vd356) = 0, yields: % 22.91/7.01 | (210) all_109_0_26 = 0 % 22.91/7.01 | % 22.91/7.01 | Instantiating formula (37) with vd355, vd356, all_91_0_23, all_109_0_26 and discharging atoms greater(vd355, vd356) = all_109_0_26, greater(vd355, vd356) = all_91_0_23, yields: % 22.91/7.01 | (211) all_109_0_26 = all_91_0_23 % 22.91/7.01 | % 22.91/7.01 | Combining equations (210,211) yields a new equation: % 22.91/7.01 | (212) all_91_0_23 = 0 % 22.91/7.01 | % 22.91/7.01 | Combining equations (212,211) yields a new equation: % 22.91/7.01 | (210) all_109_0_26 = 0 % 22.91/7.01 | % 22.91/7.01 | Equations (210) can reduce 208 to: % 22.91/7.01 | (77) $false % 22.91/7.01 | % 22.91/7.01 |-The branch is then unsatisfiable % 22.91/7.01 % SZS output end Proof for theBenchmark % 22.91/7.01 % 22.91/7.01 6410ms %------------------------------------------------------------------------------