%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : NUM840+2 : TPTP v8.1.0. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n019.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 08:49:03 EDT 2022 % Result : Theorem 19.53s 6.14s % Output : Proof 20.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM840+2 : TPTP v8.1.0. Released v4.1.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n019.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 : Tue Jul 5 05:55:38 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.59 ____ _ % 0.19/0.59 ___ / __ \_____(_)___ ________ __________ % 0.19/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic % 0.19/0.59 (ePrincess v.1.0) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2015 % 0.19/0.59 (c) Peter Backeman, 2014-2015 % 0.19/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.59 Bug reports to peter@backeman.se % 0.19/0.59 % 0.19/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.59 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.63/0.95 Prover 0: Preprocessing ... % 2.40/1.18 Prover 0: Warning: ignoring some quantifiers % 2.40/1.20 Prover 0: Constructing countermodel ... % 18.60/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 18.60/5.98 Prover 1: Preprocessing ... % 19.23/6.09 Prover 1: Warning: ignoring some quantifiers % 19.35/6.09 Prover 1: Constructing countermodel ... % 19.53/6.13 Prover 1: proved (198ms) % 19.53/6.14 Prover 0: stopped % 19.53/6.14 % 19.53/6.14 No countermodel exists, formula is valid % 19.53/6.14 % SZS status Theorem for theBenchmark % 19.53/6.14 % 19.53/6.14 Generating proof ... Warning: ignoring some quantifiers % 20.21/6.30 found it (size 37) % 20.21/6.30 % 20.21/6.30 % SZS output start Proof for theBenchmark % 20.21/6.30 Assumed formulas after preprocessing and simplification: % 20.21/6.30 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & greater(v0, v1) = v2 & greater(vd328, vd329) = v3 & vplus(vd329, vd330) = v1 & vplus(vd328, vd330) = v0 & less(v0, v1) = 0 & less(vd328, vd329) = v4 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (greater(v8, v9) = v10) | ~ (vplus(v6, v7) = v9) | ~ (vplus(v5, v7) = v8) | ? [v11] : ( ~ (v11 = 0) & greater(v5, v6) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (vplus(v6, v7) = v9) | ~ (vplus(v5, v7) = v8) | ~ (less(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & less(v5, v6) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (vplus(v8, v7) = v9) | ~ (vplus(v5, v6) = v8) | ? [v10] : (vplus(v6, v7) = v10 & vplus(v5, v10) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ (vplus(v5, v6) = v8) | ~ (vplus(v5, v6) = v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | ~ (greater(v6, v5) = v7) | ~ (vplus(v5, v8) = v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | ~ (vplus(v6, v8) = v5) | ~ (less(v6, v5) = v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (greater(v8, v7) = v6) | ~ (greater(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (vplus(v8, v7) = v6) | ~ (vplus(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (less(v8, v7) = v6) | ~ (less(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (vsucc(v6) = v7) | ~ (vplus(v5, v7) = v8) | ? [v9] : (vsucc(v9) = v8 & vplus(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (vsucc(v5) = v7) | ~ (vplus(v7, v6) = v8) | ? [v9] : (vsucc(v9) = v8 & vplus(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (vplus(v6, v8) = v5) | ~ (vplus(v5, v7) = v6)) & ? [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (vplus(v7, v6) = v8) | ? [v9] : ( ~ (v9 = v8) & vplus(v7, v5) = v9)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = v5 | ~ (less(v5, v6) = v7) | greater(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (less(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & greater(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (vsucc(v7) = v6) | ~ (vsucc(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (vplus(v5, v6) = v7) | vplus(v6, v5) = v7) & ! [v5] : ! [v6] : ( ~ (greater(v6, v5) = 0) | ? [v7] : vplus(v5, v7) = v6) & ! [v5] : ! [v6] : ~ (vplus(v5, v6) = v6) & ! [v5] : ! [v6] : ~ (vplus(v5, v6) = v5) & ! [v5] : ! [v6] : ( ~ (vplus(v5, v1) = v6) | vsucc(v5) = v6) & ! [v5] : ! [v6] : ( ~ (vplus(v1, v5) = v6) | vsucc(v5) = v6) & ! [v5] : ! [v6] : ( ~ (less(v6, v5) = 0) | ? [v7] : vplus(v6, v7) = v5) & ! [v5] : ! [v6] : ( ~ (less(v5, v6) = 0) | greater(v6, v5) = 0) & ! [v5] : ! [v6] : ( ~ (less(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & greater(v5, v6) = v7)) & ! [v5] : ~ (greater(v5, v5) = 0) & ! [v5] : ~ (less(v5, v5) = 0) & ? [v5] : ? [v6] : (v6 = v5 | ? [v7] : ? [v8] : ((v8 = v6 & vplus(v5, v7) = v6) | (v8 = v5 & vplus(v6, v7) = v5))) & ( ~ (v2 = 0) | v3 = 0) & ( ~ (v1 = v0) | vd329 = vd328)) % 20.21/6.33 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 20.21/6.33 | (1) ~ (all_0_0_0 = 0) & greater(all_0_4_4, all_0_3_3) = all_0_2_2 & greater(vd328, vd329) = all_0_1_1 & vplus(vd329, vd330) = all_0_3_3 & vplus(vd328, vd330) = all_0_4_4 & less(all_0_4_4, all_0_3_3) = 0 & less(vd328, vd329) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (greater(v3, v4) = v5) | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ? [v6] : ( ~ (v6 = 0) & greater(v0, v1) = v6)) & ! [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] : ( ~ (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ? [v5] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (vplus(v0, v1) = v3) | ~ (vplus(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (greater(v1, v0) = v2) | ~ (vplus(v0, v3) = v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (vplus(v1, v3) = v0) | ~ (less(v1, v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(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 | ~ (less(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v0, v1) = v2) | vplus(v1, v0) = v2) & ! [v0] : ! [v1] : ( ~ (greater(v1, v0) = 0) | ? [v2] : vplus(v0, v2) = v1) & ! [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] : ~ (greater(v0, v0) = 0) & ! [v0] : ~ (less(v0, v0) = 0) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ((v3 = v1 & vplus(v0, v2) = v1) | (v3 = v0 & vplus(v1, v2) = v0))) & ( ~ (all_0_2_2 = 0) | all_0_1_1 = 0) & ( ~ (all_0_3_3 = all_0_4_4) | vd329 = vd328) % 20.21/6.34 | % 20.21/6.34 | Applying alpha-rule on (1) yields: % 20.21/6.34 | (2) ! [v0] : ! [v1] : ( ~ (greater(v1, v0) = 0) | ? [v2] : vplus(v0, v2) = v1) % 20.21/6.34 | (3) ! [v0] : ! [v1] : ( ~ (less(v0, v1) = 0) | greater(v1, v0) = 0) % 20.21/6.34 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) % 20.21/6.34 | (5) vplus(vd329, vd330) = all_0_3_3 % 20.21/6.34 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vplus(v1, v3) = v0) | ~ (vplus(v0, v2) = v1)) % 20.21/6.34 | (7) ! [v0] : ~ (greater(v0, v0) = 0) % 20.21/6.34 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (vplus(v1, v3) = v0) | ~ (less(v1, v0) = v2)) % 20.21/6.34 | (9) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ((v3 = v1 & vplus(v0, v2) = v1) | (v3 = v0 & vplus(v1, v2) = v0))) % 20.21/6.34 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (greater(v1, v0) = v2) | ~ (vplus(v0, v3) = v1)) % 20.21/6.34 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v1) = v2) | ~ (vplus(v0, v2) = v3) | ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4)) % 20.21/6.34 | (12) ! [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)) % 20.21/6.34 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & greater(v0, v1) = v3)) % 20.21/6.34 | (14) ! [v0] : ~ (less(v0, v0) = 0) % 20.21/6.34 | (15) ~ (all_0_2_2 = 0) | all_0_1_1 = 0 % 20.21/6.34 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v0, v1) = v2) | vplus(v1, v0) = v2) % 20.21/6.34 | (17) ! [v0] : ! [v1] : ( ~ (less(v1, v0) = 0) | ? [v2] : vplus(v1, v2) = v0) % 20.21/6.34 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) % 20.21/6.34 | (19) ! [v0] : ! [v1] : ~ (vplus(v0, v1) = v1) % 20.21/6.34 | (20) less(all_0_4_4, all_0_3_3) = 0 % 20.21/6.34 | (21) ! [v0] : ! [v1] : ( ~ (vplus(v1, v0) = v1) | vsucc(v0) = v1) % 20.21/6.34 | (22) vplus(vd328, vd330) = all_0_4_4 % 20.21/6.34 | (23) greater(all_0_4_4, all_0_3_3) = all_0_2_2 % 20.21/6.34 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) % 20.21/6.34 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (less(v0, v1) = v2) | greater(v0, v1) = 0) % 20.21/6.34 | (26) less(vd328, vd329) = all_0_0_0 % 20.21/6.34 | (27) ! [v0] : ! [v1] : ( ~ (vplus(v0, v1) = v1) | vsucc(v0) = v1) % 20.21/6.34 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ? [v5] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4)) % 20.21/6.34 | (29) ! [v0] : ! [v1] : ( ~ (less(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & greater(v0, v1) = v2)) % 20.21/6.34 | (30) greater(vd328, vd329) = all_0_1_1 % 20.21/6.34 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) % 20.21/6.34 | (32) ! [v0] : ! [v1] : ~ (vplus(v0, v1) = v0) % 20.21/6.34 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v0) = v2) | ~ (vplus(v2, v1) = v3) | ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4)) % 20.21/6.34 | (34) ~ (all_0_3_3 = all_0_4_4) | vd329 = vd328 % 20.21/6.34 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (greater(v3, v4) = v5) | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ? [v6] : ( ~ (v6 = 0) & greater(v0, v1) = v6)) % 20.21/6.34 | (36) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v2, v1) = v3) | ? [v4] : ( ~ (v4 = v3) & vplus(v2, v0) = v4)) % 20.21/6.34 | (37) ~ (all_0_0_0 = 0) % 20.21/6.34 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (vplus(v0, v1) = v3) | ~ (vplus(v0, v1) = v2)) % 20.21/6.35 | % 20.21/6.35 | Instantiating formula (38) with all_0_4_4, all_0_3_3, vd330, vd328 and discharging atoms vplus(vd328, vd330) = all_0_4_4, yields: % 20.21/6.35 | (39) all_0_3_3 = all_0_4_4 | ~ (vplus(vd328, vd330) = all_0_3_3) % 20.21/6.35 | % 20.21/6.35 | Instantiating formula (14) with all_0_4_4 yields: % 20.21/6.35 | (40) ~ (less(all_0_4_4, all_0_4_4) = 0) % 20.21/6.35 | % 20.21/6.35 | Using (20) and (40) yields: % 20.21/6.35 | (41) ~ (all_0_3_3 = all_0_4_4) % 20.21/6.35 | % 20.21/6.35 | Instantiating formula (35) with all_0_2_2, all_0_3_3, all_0_4_4, vd330, vd329, vd328 and discharging atoms greater(all_0_4_4, all_0_3_3) = all_0_2_2, vplus(vd329, vd330) = all_0_3_3, vplus(vd328, vd330) = all_0_4_4, yields: % 20.21/6.35 | (42) all_0_2_2 = 0 | ? [v0] : ( ~ (v0 = 0) & greater(vd328, vd329) = v0) % 20.21/6.35 | % 20.21/6.35 | Instantiating formula (29) with all_0_3_3, all_0_4_4 and discharging atoms less(all_0_4_4, all_0_3_3) = 0, yields: % 20.21/6.35 | (43) ? [v0] : ( ~ (v0 = 0) & greater(all_0_4_4, all_0_3_3) = v0) % 20.21/6.35 | % 20.21/6.35 | Instantiating formula (25) with all_0_0_0, vd329, vd328 and discharging atoms less(vd328, vd329) = all_0_0_0, yields: % 20.21/6.35 | (44) all_0_0_0 = 0 | vd329 = vd328 | greater(vd328, vd329) = 0 % 20.21/6.35 | % 20.21/6.35 | Instantiating formula (13) with all_0_0_0, vd328, vd329 and discharging atoms less(vd328, vd329) = all_0_0_0, yields: % 20.21/6.35 | (45) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & greater(vd329, vd328) = v0) % 20.21/6.35 | % 20.21/6.35 | Instantiating (43) with all_26_0_9 yields: % 20.21/6.35 | (46) ~ (all_26_0_9 = 0) & greater(all_0_4_4, all_0_3_3) = all_26_0_9 % 20.21/6.35 | % 20.21/6.35 | Applying alpha-rule on (46) yields: % 20.21/6.35 | (47) ~ (all_26_0_9 = 0) % 20.21/6.35 | (48) greater(all_0_4_4, all_0_3_3) = all_26_0_9 % 20.21/6.35 | % 20.21/6.35 +-Applying beta-rule and splitting (45), into two cases. % 20.21/6.35 |-Branch one: % 20.21/6.35 | (49) all_0_0_0 = 0 % 20.21/6.35 | % 20.21/6.35 | Equations (49) can reduce 37 to: % 20.21/6.35 | (50) $false % 20.21/6.35 | % 20.21/6.35 |-The branch is then unsatisfiable % 20.21/6.35 |-Branch two: % 20.21/6.35 | (37) ~ (all_0_0_0 = 0) % 20.21/6.35 | (52) ? [v0] : ( ~ (v0 = 0) & greater(vd329, vd328) = v0) % 20.21/6.35 | % 20.21/6.35 | Instantiating formula (24) with all_0_4_4, all_0_3_3, all_26_0_9, all_0_2_2 and discharging atoms greater(all_0_4_4, all_0_3_3) = all_26_0_9, greater(all_0_4_4, all_0_3_3) = all_0_2_2, yields: % 20.21/6.35 | (53) all_26_0_9 = all_0_2_2 % 20.21/6.35 | % 20.21/6.35 | Equations (53) can reduce 47 to: % 20.21/6.35 | (54) ~ (all_0_2_2 = 0) % 20.21/6.35 | % 20.21/6.35 +-Applying beta-rule and splitting (42), into two cases. % 20.21/6.35 |-Branch one: % 20.21/6.35 | (55) all_0_2_2 = 0 % 20.21/6.35 | % 20.21/6.35 | Equations (55) can reduce 54 to: % 20.21/6.35 | (50) $false % 20.21/6.35 | % 20.21/6.35 |-The branch is then unsatisfiable % 20.21/6.35 |-Branch two: % 20.21/6.35 | (54) ~ (all_0_2_2 = 0) % 20.21/6.35 | (58) ? [v0] : ( ~ (v0 = 0) & greater(vd328, vd329) = v0) % 20.21/6.35 | % 20.21/6.35 | Instantiating (58) with all_42_0_11 yields: % 20.21/6.35 | (59) ~ (all_42_0_11 = 0) & greater(vd328, vd329) = all_42_0_11 % 20.21/6.35 | % 20.21/6.35 | Applying alpha-rule on (59) yields: % 20.21/6.35 | (60) ~ (all_42_0_11 = 0) % 20.21/6.35 | (61) greater(vd328, vd329) = all_42_0_11 % 20.21/6.35 | % 20.21/6.35 | Instantiating formula (24) with vd328, vd329, all_42_0_11, all_0_1_1 and discharging atoms greater(vd328, vd329) = all_42_0_11, greater(vd328, vd329) = all_0_1_1, yields: % 20.21/6.35 | (62) all_42_0_11 = all_0_1_1 % 20.21/6.35 | % 20.21/6.35 | Equations (62) can reduce 60 to: % 20.21/6.35 | (63) ~ (all_0_1_1 = 0) % 20.21/6.35 | % 20.21/6.35 | From (62) and (61) follows: % 20.21/6.35 | (30) greater(vd328, vd329) = all_0_1_1 % 20.21/6.35 | % 20.21/6.35 +-Applying beta-rule and splitting (44), into two cases. % 20.21/6.35 |-Branch one: % 20.21/6.35 | (65) greater(vd328, vd329) = 0 % 20.21/6.35 | % 20.21/6.35 | Instantiating formula (24) with vd328, vd329, 0, all_0_1_1 and discharging atoms greater(vd328, vd329) = all_0_1_1, greater(vd328, vd329) = 0, yields: % 20.21/6.35 | (66) all_0_1_1 = 0 % 20.21/6.35 | % 20.21/6.35 | Equations (66) can reduce 63 to: % 20.21/6.35 | (50) $false % 20.21/6.35 | % 20.21/6.35 |-The branch is then unsatisfiable % 20.21/6.35 |-Branch two: % 20.21/6.35 | (68) ~ (greater(vd328, vd329) = 0) % 20.21/6.35 | (69) all_0_0_0 = 0 | vd329 = vd328 % 20.21/6.35 | % 20.21/6.35 +-Applying beta-rule and splitting (69), into two cases. % 20.21/6.35 |-Branch one: % 20.21/6.35 | (70) vd329 = vd328 % 20.21/6.35 | % 20.21/6.35 | From (70) and (5) follows: % 20.21/6.35 | (71) vplus(vd328, vd330) = all_0_3_3 % 20.21/6.35 | % 20.21/6.35 +-Applying beta-rule and splitting (39), into two cases. % 20.21/6.35 |-Branch one: % 20.21/6.35 | (72) ~ (vplus(vd328, vd330) = all_0_3_3) % 20.21/6.35 | % 20.21/6.35 | Using (71) and (72) yields: % 20.21/6.35 | (73) $false % 20.21/6.35 | % 20.21/6.35 |-The branch is then unsatisfiable % 20.21/6.35 |-Branch two: % 20.21/6.35 | (71) vplus(vd328, vd330) = all_0_3_3 % 20.21/6.35 | (75) all_0_3_3 = all_0_4_4 % 20.21/6.36 | % 20.21/6.36 | Equations (75) can reduce 41 to: % 20.21/6.36 | (50) $false % 20.21/6.36 | % 20.21/6.36 |-The branch is then unsatisfiable % 20.21/6.36 |-Branch two: % 20.21/6.36 | (77) ~ (vd329 = vd328) % 20.21/6.36 | (49) all_0_0_0 = 0 % 20.21/6.36 | % 20.21/6.36 | Equations (49) can reduce 37 to: % 20.21/6.36 | (50) $false % 20.21/6.36 | % 20.21/6.36 |-The branch is then unsatisfiable % 20.21/6.36 % SZS output end Proof for theBenchmark % 20.21/6.36 % 20.21/6.36 5751ms %------------------------------------------------------------------------------