%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET700+4 : TPTP v8.1.0. Released v2.2.0. % 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 : Tue Jul 19 00:21:29 EDT 2022 % Result : Theorem 6.20s 2.19s % Output : Proof 8.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.08 % Problem : SET700+4 : TPTP v8.1.0. Released v2.2.0. % 0.08/0.09 % Command : ePrincess-casc -timeout=%d %s % 0.08/0.28 % Computer : n019.cluster.edu % 0.08/0.28 % Model : x86_64 x86_64 % 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.28 % Memory : 8042.1875MB % 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.28 % CPULimit : 300 % 0.08/0.28 % WCLimit : 600 % 0.08/0.28 % DateTime : Sun Jul 10 01:35:53 EDT 2022 % 0.08/0.28 % CPUTime : % 0.51/0.52 ____ _ % 0.51/0.52 ___ / __ \_____(_)___ ________ __________ % 0.51/0.52 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.51/0.52 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.51/0.52 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.51/0.52 % 0.51/0.52 A Theorem Prover for First-Order Logic % 0.51/0.53 (ePrincess v.1.0) % 0.51/0.53 % 0.51/0.53 (c) Philipp Rümmer, 2009-2015 % 0.51/0.53 (c) Peter Backeman, 2014-2015 % 0.51/0.53 (contributions by Angelo Brillout, Peter Baumgartner) % 0.51/0.53 Free software under GNU Lesser General Public License (LGPL). % 0.51/0.53 Bug reports to peter@backeman.se % 0.51/0.53 % 0.51/0.53 For more information, visit http://user.uu.se/~petba168/breu/ % 0.51/0.53 % 0.51/0.53 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.53/0.59 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.35/0.92 Prover 0: Preprocessing ... % 2.01/1.17 Prover 0: Warning: ignoring some quantifiers % 2.01/1.21 Prover 0: Constructing countermodel ... % 2.96/1.52 Prover 0: gave up % 3.26/1.52 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.26/1.56 Prover 1: Preprocessing ... % 3.91/1.72 Prover 1: Constructing countermodel ... % 4.54/1.86 Prover 1: gave up % 4.54/1.86 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.78/1.88 Prover 2: Preprocessing ... % 5.30/2.01 Prover 2: Warning: ignoring some quantifiers % 5.30/2.02 Prover 2: Constructing countermodel ... % 6.20/2.19 Prover 2: proved (336ms) % 6.20/2.19 % 6.20/2.19 No countermodel exists, formula is valid % 6.20/2.19 % SZS status Theorem for theBenchmark % 6.20/2.19 % 6.20/2.19 Generating proof ... Warning: ignoring some quantifiers % 8.08/2.60 found it (size 70) % 8.08/2.60 % 8.08/2.60 % SZS output start Proof for theBenchmark % 8.08/2.60 Assumed formulas after preprocessing and simplification: % 8.08/2.60 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (difference(v2, v1) = v4 & intersection(v0, v4) = v5 & subset(v5, v1) = v6 & subset(v1, v2) = 0 & subset(v0, v2) = 0 & subset(v0, v1) = v3 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (product(v8) = v9) | ~ (member(v7, v10) = v11) | ~ (member(v7, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v10, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (difference(v9, v8) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ((v12 = 0 & member(v7, v8) = 0) | ( ~ (v12 = 0) & member(v7, v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (union(v8, v9) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & ~ (v12 = 0) & member(v7, v9) = v13 & member(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (intersection(v8, v9) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : (( ~ (v12 = 0) & member(v7, v9) = v12) | ( ~ (v12 = 0) & member(v7, v8) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (sum(v8) = v9) | ~ (member(v11, v8) = 0) | ~ (member(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v7, v11) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (sum(v8) = v9) | ~ (member(v7, v11) = 0) | ~ (member(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (product(v8) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = 0 & member(v7, v11) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v8, v7) = v9) | ~ (member(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v7, v8) = v9) | ~ (member(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (power_set(v8) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v7, v8) = 0) | ~ (member(v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & member(v9, v7) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v7 | v8 = v7 | ~ (unordered_pair(v8, v9) = v10) | ~ (member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (difference(v10, v9) = v8) | ~ (difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (union(v10, v9) = v8) | ~ (union(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (intersection(v10, v9) = v8) | ~ (intersection(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (equal_set(v10, v9) = v8) | ~ (equal_set(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (member(v10, v9) = v8) | ~ (member(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (product(v8) = v9) | ~ (member(v10, v8) = 0) | ~ (member(v7, v9) = 0) | member(v7, v10) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (difference(v9, v8) = v10) | ~ (member(v7, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v7, v9) = 0 & member(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v8, v9) = v10) | ~ (member(v7, v10) = 0) | ? [v11] : ((v11 = 0 & member(v7, v9) = 0) | (v11 = 0 & member(v7, v8) = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection(v8, v9) = v10) | ~ (member(v7, v10) = 0) | (member(v7, v9) = 0 & member(v7, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (singleton(v7) = v8) | ~ (member(v7, v8) = v9)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (equal_set(v7, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & subset(v8, v7) = v10) | ( ~ (v10 = 0) & subset(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & power_set(v8) = v10 & member(v7, v10) = v11)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & member(v10, v8) = v11 & member(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (product(v9) = v8) | ~ (product(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (sum(v9) = v8) | ~ (sum(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v8) = v9) | ~ (member(v7, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (power_set(v9) = v8) | ~ (power_set(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sum(v8) = v9) | ~ (member(v7, v9) = 0) | ? [v10] : (member(v10, v8) = 0 & member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (power_set(v8) = v9) | ~ (member(v7, v9) = 0) | subset(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v8, v7) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & subset(v7, v8) = 0) | ( ~ (v10 = 0) & equal_set(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & subset(v8, v7) = 0) | ( ~ (v10 = 0) & equal_set(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (member(v9, v7) = 0) | member(v9, v8) = 0) & ! [v7] : ! [v8] : ( ~ (equal_set(v7, v8) = 0) | (subset(v8, v7) = 0 & subset(v7, v8) = 0)) & ! [v7] : ! [v8] : ( ~ (subset(v8, v7) = 0) | ? [v9] : ((v9 = 0 & equal_set(v7, v8) = 0) | ( ~ (v9 = 0) & subset(v7, v8) = v9))) & ! [v7] : ! [v8] : ( ~ (subset(v7, v8) = 0) | ? [v9] : (power_set(v8) = v9 & member(v7, v9) = 0)) & ! [v7] : ! [v8] : ( ~ (subset(v7, v8) = 0) | ? [v9] : ((v9 = 0 & equal_set(v7, v8) = 0) | ( ~ (v9 = 0) & subset(v8, v7) = v9))) & ! [v7] : ~ (member(v7, empty_set) = 0) & ? [v7] : ? [v8] : ? [v9] : unordered_pair(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : difference(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : union(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : intersection(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : equal_set(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : subset(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : member(v8, v7) = v9 & ? [v7] : ? [v8] : product(v7) = v8 & ? [v7] : ? [v8] : sum(v7) = v8 & ? [v7] : ? [v8] : singleton(v7) = v8 & ? [v7] : ? [v8] : power_set(v7) = v8 & ((v6 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v6 = 0)))) % 8.25/2.66 | 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: % 8.25/2.66 | (1) difference(all_0_4_4, all_0_5_5) = all_0_2_2 & intersection(all_0_6_6, all_0_2_2) = all_0_1_1 & subset(all_0_1_1, all_0_5_5) = all_0_0_0 & subset(all_0_5_5, all_0_4_4) = 0 & subset(all_0_6_6, all_0_4_4) = 0 & subset(all_0_6_6, all_0_5_5) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ((v5 = 0 & member(v0, v1) = 0) | ( ~ (v5 = 0) & member(v0, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & member(v0, v2) = v5) | ( ~ (v5 = 0) & member(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v4, v1) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ((v4 = 0 & member(v0, v2) = 0) | (v4 = 0 & member(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2))) & ! [v0] : ~ (member(v0, empty_set) = 0) & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2 & ? [v0] : ? [v1] : product(v0) = v1 & ? [v0] : ? [v1] : sum(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : power_set(v0) = v1 & ((all_0_0_0 = 0 & ~ (all_0_3_3 = 0)) | (all_0_3_3 = 0 & ~ (all_0_0_0 = 0))) % 8.25/2.68 | % 8.25/2.68 | Applying alpha-rule on (1) yields: % 8.25/2.68 | (2) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 % 8.25/2.68 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 8.25/2.68 | (4) ! [v0] : ~ (member(v0, empty_set) = 0) % 8.25/2.68 | (5) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0)) % 8.25/2.68 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 8.25/2.68 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 8.25/2.68 | (8) intersection(all_0_6_6, all_0_2_2) = all_0_1_1 % 8.25/2.68 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 8.25/2.68 | (10) ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2 % 8.25/2.68 | (11) subset(all_0_6_6, all_0_4_4) = 0 % 8.25/2.68 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) % 8.25/2.68 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) % 8.25/2.68 | (14) (all_0_0_0 = 0 & ~ (all_0_3_3 = 0)) | (all_0_3_3 = 0 & ~ (all_0_0_0 = 0)) % 8.25/2.68 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) % 8.25/2.69 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ((v4 = 0 & member(v0, v2) = 0) | (v4 = 0 & member(v0, v1) = 0))) % 8.25/2.69 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ((v5 = 0 & member(v0, v1) = 0) | ( ~ (v5 = 0) & member(v0, v2) = v5))) % 8.25/2.69 | (18) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2 % 8.25/2.69 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) % 8.25/2.69 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3))) % 8.25/2.69 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 8.25/2.69 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 8.25/2.69 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 8.25/2.69 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 8.25/2.69 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 8.25/2.69 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 8.25/2.69 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 8.25/2.69 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 8.25/2.69 | (29) ? [v0] : ? [v1] : singleton(v0) = v1 % 8.25/2.69 | (30) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4)) % 8.25/2.69 | (31) subset(all_0_1_1, all_0_5_5) = all_0_0_0 % 8.25/2.69 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0) % 8.25/2.69 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 8.25/2.70 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 8.25/2.70 | (35) ? [v0] : ? [v1] : sum(v0) = v1 % 8.25/2.70 | (36) difference(all_0_4_4, all_0_5_5) = all_0_2_2 % 8.25/2.70 | (37) ? [v0] : ? [v1] : power_set(v0) = v1 % 8.25/2.70 | (38) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 8.25/2.70 | (39) ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2))) % 8.25/2.70 | (40) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 8.25/2.70 | (41) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2 % 8.25/2.70 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 8.25/2.70 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 8.25/2.70 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 8.25/2.70 | (45) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 8.25/2.70 | (46) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2))) % 8.25/2.70 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v4, v1) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v0, v4) = v5)) % 8.25/2.70 | (48) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 % 8.25/2.70 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) % 8.25/2.70 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & member(v0, v2) = v5) | ( ~ (v5 = 0) & member(v0, v1) = v5))) % 8.25/2.70 | (51) subset(all_0_5_5, all_0_4_4) = 0 % 8.25/2.70 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 8.25/2.71 | (53) ? [v0] : ? [v1] : product(v0) = v1 % 8.25/2.71 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) % 8.25/2.71 | (55) ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2 % 8.25/2.71 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 8.25/2.71 | (57) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 8.25/2.71 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) % 8.25/2.71 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 8.25/2.71 | (60) subset(all_0_6_6, all_0_5_5) = all_0_3_3 % 8.25/2.71 | (61) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2 % 8.25/2.71 | % 8.25/2.71 | Instantiating formula (30) with all_0_0_0, all_0_5_5, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 8.25/2.71 | (62) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & power_set(all_0_5_5) = v0 & member(all_0_1_1, v0) = v1) % 8.25/2.71 | % 8.25/2.71 | Instantiating formula (40) with all_0_0_0, all_0_5_5, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 8.25/2.71 | (63) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_5_5) = v1) % 8.25/2.71 | % 8.25/2.71 | Instantiating formula (30) with all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_5_5) = all_0_3_3, yields: % 8.25/2.71 | (64) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & power_set(all_0_5_5) = v0 & member(all_0_6_6, v0) = v1) % 8.25/2.71 | % 8.25/2.71 | Instantiating formula (40) with all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_5_5) = all_0_3_3, yields: % 8.25/2.71 | (65) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_5_5) = v1 & member(v0, all_0_6_6) = 0) % 8.25/2.71 | % 8.25/2.71 +-Applying beta-rule and splitting (14), into two cases. % 8.25/2.71 |-Branch one: % 8.25/2.71 | (66) all_0_0_0 = 0 & ~ (all_0_3_3 = 0) % 8.25/2.71 | % 8.25/2.71 | Applying alpha-rule on (66) yields: % 8.25/2.71 | (67) all_0_0_0 = 0 % 8.25/2.71 | (68) ~ (all_0_3_3 = 0) % 8.25/2.71 | % 8.25/2.71 | From (67) and (31) follows: % 8.25/2.71 | (69) subset(all_0_1_1, all_0_5_5) = 0 % 8.25/2.72 | % 8.25/2.72 +-Applying beta-rule and splitting (64), into two cases. % 8.25/2.72 |-Branch one: % 8.25/2.72 | (70) all_0_3_3 = 0 % 8.25/2.72 | % 8.25/2.72 | Equations (70) can reduce 68 to: % 8.25/2.72 | (71) $false % 8.25/2.72 | % 8.65/2.72 |-The branch is then unsatisfiable % 8.65/2.72 |-Branch two: % 8.65/2.72 | (68) ~ (all_0_3_3 = 0) % 8.65/2.72 | (73) ? [v0] : ? [v1] : ( ~ (v1 = 0) & power_set(all_0_5_5) = v0 & member(all_0_6_6, v0) = v1) % 8.65/2.72 | % 8.65/2.72 +-Applying beta-rule and splitting (65), into two cases. % 8.65/2.72 |-Branch one: % 8.65/2.72 | (70) all_0_3_3 = 0 % 8.65/2.72 | % 8.65/2.72 | Equations (70) can reduce 68 to: % 8.65/2.72 | (71) $false % 8.65/2.72 | % 8.65/2.72 |-The branch is then unsatisfiable % 8.65/2.72 |-Branch two: % 8.65/2.72 | (68) ~ (all_0_3_3 = 0) % 8.65/2.72 | (77) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_5_5) = v1 & member(v0, all_0_6_6) = 0) % 8.65/2.72 | % 8.65/2.72 | Instantiating (77) with all_73_0_52, all_73_1_53 yields: % 8.65/2.72 | (78) ~ (all_73_0_52 = 0) & member(all_73_1_53, all_0_5_5) = all_73_0_52 & member(all_73_1_53, all_0_6_6) = 0 % 8.65/2.72 | % 8.65/2.72 | Applying alpha-rule on (78) yields: % 8.65/2.72 | (79) ~ (all_73_0_52 = 0) % 8.65/2.72 | (80) member(all_73_1_53, all_0_5_5) = all_73_0_52 % 8.65/2.72 | (81) member(all_73_1_53, all_0_6_6) = 0 % 8.65/2.72 | % 8.65/2.72 | Instantiating formula (12) with all_73_0_52, all_73_1_53, all_0_5_5, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_5_5) = 0, member(all_73_1_53, all_0_5_5) = all_73_0_52, yields: % 8.65/2.72 | (82) all_73_0_52 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_73_1_53, all_0_1_1) = v0) % 8.65/2.72 | % 8.65/2.72 | Instantiating formula (27) with all_73_1_53, all_0_4_4, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_4_4) = 0, member(all_73_1_53, all_0_6_6) = 0, yields: % 8.65/2.72 | (83) member(all_73_1_53, all_0_4_4) = 0 % 8.65/2.72 | % 8.65/2.72 +-Applying beta-rule and splitting (82), into two cases. % 8.65/2.72 |-Branch one: % 8.65/2.72 | (84) all_73_0_52 = 0 % 8.65/2.72 | % 8.65/2.72 | Equations (84) can reduce 79 to: % 8.65/2.72 | (71) $false % 8.65/2.72 | % 8.65/2.72 |-The branch is then unsatisfiable % 8.65/2.72 |-Branch two: % 8.65/2.72 | (79) ~ (all_73_0_52 = 0) % 8.65/2.72 | (87) ? [v0] : ( ~ (v0 = 0) & member(all_73_1_53, all_0_1_1) = v0) % 8.65/2.72 | % 8.65/2.72 | Instantiating (87) with all_89_0_57 yields: % 8.65/2.72 | (88) ~ (all_89_0_57 = 0) & member(all_73_1_53, all_0_1_1) = all_89_0_57 % 8.65/2.72 | % 8.65/2.72 | Applying alpha-rule on (88) yields: % 8.65/2.72 | (89) ~ (all_89_0_57 = 0) % 8.65/2.72 | (90) member(all_73_1_53, all_0_1_1) = all_89_0_57 % 8.65/2.72 | % 8.65/2.72 | Instantiating formula (50) with all_89_0_57, all_0_1_1, all_0_2_2, all_0_6_6, all_73_1_53 and discharging atoms intersection(all_0_6_6, all_0_2_2) = all_0_1_1, member(all_73_1_53, all_0_1_1) = all_89_0_57, yields: % 8.65/2.72 | (91) all_89_0_57 = 0 | ? [v0] : (( ~ (v0 = 0) & member(all_73_1_53, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_73_1_53, all_0_6_6) = v0)) % 8.65/2.72 | % 8.65/2.72 +-Applying beta-rule and splitting (91), into two cases. % 8.65/2.72 |-Branch one: % 8.65/2.72 | (92) all_89_0_57 = 0 % 8.65/2.72 | % 8.65/2.72 | Equations (92) can reduce 89 to: % 8.65/2.72 | (71) $false % 8.65/2.72 | % 8.65/2.72 |-The branch is then unsatisfiable % 8.65/2.72 |-Branch two: % 8.65/2.72 | (89) ~ (all_89_0_57 = 0) % 8.65/2.72 | (95) ? [v0] : (( ~ (v0 = 0) & member(all_73_1_53, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_73_1_53, all_0_6_6) = v0)) % 8.65/2.72 | % 8.65/2.72 | Instantiating (95) with all_117_0_60 yields: % 8.65/2.72 | (96) ( ~ (all_117_0_60 = 0) & member(all_73_1_53, all_0_2_2) = all_117_0_60) | ( ~ (all_117_0_60 = 0) & member(all_73_1_53, all_0_6_6) = all_117_0_60) % 8.65/2.73 | % 8.65/2.73 +-Applying beta-rule and splitting (96), into two cases. % 8.65/2.73 |-Branch one: % 8.65/2.73 | (97) ~ (all_117_0_60 = 0) & member(all_73_1_53, all_0_2_2) = all_117_0_60 % 8.65/2.73 | % 8.65/2.73 | Applying alpha-rule on (97) yields: % 8.65/2.73 | (98) ~ (all_117_0_60 = 0) % 8.65/2.73 | (99) member(all_73_1_53, all_0_2_2) = all_117_0_60 % 8.65/2.73 | % 8.65/2.73 | Instantiating formula (17) with all_117_0_60, all_0_2_2, all_0_4_4, all_0_5_5, all_73_1_53 and discharging atoms difference(all_0_4_4, all_0_5_5) = all_0_2_2, member(all_73_1_53, all_0_2_2) = all_117_0_60, yields: % 8.65/2.73 | (100) all_117_0_60 = 0 | ? [v0] : ((v0 = 0 & member(all_73_1_53, all_0_5_5) = 0) | ( ~ (v0 = 0) & member(all_73_1_53, all_0_4_4) = v0)) % 8.65/2.73 | % 8.65/2.73 +-Applying beta-rule and splitting (100), into two cases. % 8.65/2.73 |-Branch one: % 8.65/2.73 | (101) all_117_0_60 = 0 % 8.65/2.73 | % 8.65/2.73 | Equations (101) can reduce 98 to: % 8.65/2.73 | (71) $false % 8.65/2.73 | % 8.65/2.73 |-The branch is then unsatisfiable % 8.65/2.73 |-Branch two: % 8.65/2.73 | (98) ~ (all_117_0_60 = 0) % 8.65/2.73 | (104) ? [v0] : ((v0 = 0 & member(all_73_1_53, all_0_5_5) = 0) | ( ~ (v0 = 0) & member(all_73_1_53, all_0_4_4) = v0)) % 8.65/2.73 | % 8.65/2.73 | Instantiating (104) with all_141_0_62 yields: % 8.65/2.73 | (105) (all_141_0_62 = 0 & member(all_73_1_53, all_0_5_5) = 0) | ( ~ (all_141_0_62 = 0) & member(all_73_1_53, all_0_4_4) = all_141_0_62) % 8.65/2.73 | % 8.65/2.73 +-Applying beta-rule and splitting (105), into two cases. % 8.65/2.73 |-Branch one: % 8.65/2.73 | (106) all_141_0_62 = 0 & member(all_73_1_53, all_0_5_5) = 0 % 8.65/2.73 | % 8.65/2.73 | Applying alpha-rule on (106) yields: % 8.65/2.73 | (107) all_141_0_62 = 0 % 8.65/2.73 | (108) member(all_73_1_53, all_0_5_5) = 0 % 8.65/2.73 | % 8.65/2.73 | Instantiating formula (44) with all_73_1_53, all_0_5_5, 0, all_73_0_52 and discharging atoms member(all_73_1_53, all_0_5_5) = all_73_0_52, member(all_73_1_53, all_0_5_5) = 0, yields: % 8.65/2.73 | (84) all_73_0_52 = 0 % 8.65/2.73 | % 8.65/2.73 | Equations (84) can reduce 79 to: % 8.65/2.73 | (71) $false % 8.65/2.73 | % 8.65/2.73 |-The branch is then unsatisfiable % 8.65/2.73 |-Branch two: % 8.65/2.73 | (111) ~ (all_141_0_62 = 0) & member(all_73_1_53, all_0_4_4) = all_141_0_62 % 8.65/2.73 | % 8.65/2.73 | Applying alpha-rule on (111) yields: % 8.65/2.73 | (112) ~ (all_141_0_62 = 0) % 8.65/2.73 | (113) member(all_73_1_53, all_0_4_4) = all_141_0_62 % 8.65/2.73 | % 8.65/2.73 | Instantiating formula (44) with all_73_1_53, all_0_4_4, all_141_0_62, 0 and discharging atoms member(all_73_1_53, all_0_4_4) = all_141_0_62, member(all_73_1_53, all_0_4_4) = 0, yields: % 8.65/2.74 | (107) all_141_0_62 = 0 % 8.65/2.74 | % 8.65/2.74 | Equations (107) can reduce 112 to: % 8.65/2.74 | (71) $false % 8.65/2.74 | % 8.65/2.74 |-The branch is then unsatisfiable % 8.65/2.74 |-Branch two: % 8.65/2.74 | (116) ~ (all_117_0_60 = 0) & member(all_73_1_53, all_0_6_6) = all_117_0_60 % 8.65/2.74 | % 8.65/2.74 | Applying alpha-rule on (116) yields: % 8.65/2.74 | (98) ~ (all_117_0_60 = 0) % 8.65/2.74 | (118) member(all_73_1_53, all_0_6_6) = all_117_0_60 % 8.65/2.74 | % 8.65/2.74 | Instantiating formula (44) with all_73_1_53, all_0_6_6, all_117_0_60, 0 and discharging atoms member(all_73_1_53, all_0_6_6) = all_117_0_60, member(all_73_1_53, all_0_6_6) = 0, yields: % 8.65/2.74 | (101) all_117_0_60 = 0 % 8.65/2.74 | % 8.65/2.74 | Equations (101) can reduce 98 to: % 8.65/2.74 | (71) $false % 8.65/2.74 | % 8.65/2.74 |-The branch is then unsatisfiable % 8.65/2.74 |-Branch two: % 8.65/2.74 | (121) all_0_3_3 = 0 & ~ (all_0_0_0 = 0) % 8.65/2.74 | % 8.65/2.74 | Applying alpha-rule on (121) yields: % 8.65/2.74 | (70) all_0_3_3 = 0 % 8.65/2.74 | (123) ~ (all_0_0_0 = 0) % 8.65/2.74 | % 8.65/2.74 | From (70) and (60) follows: % 8.65/2.74 | (124) subset(all_0_6_6, all_0_5_5) = 0 % 8.65/2.74 | % 8.65/2.74 +-Applying beta-rule and splitting (62), into two cases. % 8.65/2.74 |-Branch one: % 8.65/2.74 | (67) all_0_0_0 = 0 % 8.65/2.74 | % 8.65/2.74 | Equations (67) can reduce 123 to: % 8.65/2.74 | (71) $false % 8.65/2.74 | % 8.65/2.74 |-The branch is then unsatisfiable % 8.65/2.74 |-Branch two: % 8.65/2.74 | (123) ~ (all_0_0_0 = 0) % 8.65/2.74 | (128) ? [v0] : ? [v1] : ( ~ (v1 = 0) & power_set(all_0_5_5) = v0 & member(all_0_1_1, v0) = v1) % 8.65/2.74 | % 8.65/2.74 +-Applying beta-rule and splitting (63), into two cases. % 8.65/2.74 |-Branch one: % 8.65/2.74 | (67) all_0_0_0 = 0 % 8.65/2.74 | % 8.65/2.74 | Equations (67) can reduce 123 to: % 8.65/2.74 | (71) $false % 8.65/2.74 | % 8.65/2.74 |-The branch is then unsatisfiable % 8.65/2.74 |-Branch two: % 8.65/2.74 | (123) ~ (all_0_0_0 = 0) % 8.65/2.74 | (132) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_5_5) = v1) % 8.65/2.74 | % 8.65/2.74 | Instantiating (132) with all_69_0_65, all_69_1_66 yields: % 8.65/2.74 | (133) ~ (all_69_0_65 = 0) & member(all_69_1_66, all_0_1_1) = 0 & member(all_69_1_66, all_0_5_5) = all_69_0_65 % 8.65/2.74 | % 8.65/2.74 | Applying alpha-rule on (133) yields: % 8.65/2.74 | (134) ~ (all_69_0_65 = 0) % 8.65/2.74 | (135) member(all_69_1_66, all_0_1_1) = 0 % 8.65/2.74 | (136) member(all_69_1_66, all_0_5_5) = all_69_0_65 % 8.65/2.74 | % 8.65/2.74 | Instantiating formula (26) with all_0_1_1, all_0_2_2, all_0_6_6, all_69_1_66 and discharging atoms intersection(all_0_6_6, all_0_2_2) = all_0_1_1, member(all_69_1_66, all_0_1_1) = 0, yields: % 8.65/2.74 | (137) member(all_69_1_66, all_0_2_2) = 0 & member(all_69_1_66, all_0_6_6) = 0 % 8.65/2.74 | % 8.65/2.74 | Applying alpha-rule on (137) yields: % 8.65/2.74 | (138) member(all_69_1_66, all_0_2_2) = 0 % 8.65/2.74 | (139) member(all_69_1_66, all_0_6_6) = 0 % 8.65/2.74 | % 8.65/2.74 | Instantiating formula (12) with all_69_0_65, all_69_1_66, all_0_5_5, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_5_5) = 0, member(all_69_1_66, all_0_5_5) = all_69_0_65, yields: % 8.65/2.74 | (140) all_69_0_65 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_69_1_66, all_0_6_6) = v0) % 8.65/2.74 | % 8.65/2.74 +-Applying beta-rule and splitting (140), into two cases. % 8.65/2.74 |-Branch one: % 8.65/2.74 | (141) all_69_0_65 = 0 % 8.65/2.74 | % 8.65/2.74 | Equations (141) can reduce 134 to: % 8.65/2.74 | (71) $false % 8.65/2.74 | % 8.65/2.74 |-The branch is then unsatisfiable % 8.65/2.74 |-Branch two: % 8.65/2.75 | (134) ~ (all_69_0_65 = 0) % 8.65/2.75 | (144) ? [v0] : ( ~ (v0 = 0) & member(all_69_1_66, all_0_6_6) = v0) % 8.65/2.75 | % 8.65/2.75 | Instantiating (144) with all_89_0_70 yields: % 8.65/2.75 | (145) ~ (all_89_0_70 = 0) & member(all_69_1_66, all_0_6_6) = all_89_0_70 % 8.65/2.75 | % 8.65/2.75 | Applying alpha-rule on (145) yields: % 8.65/2.75 | (146) ~ (all_89_0_70 = 0) % 8.65/2.75 | (147) member(all_69_1_66, all_0_6_6) = all_89_0_70 % 8.65/2.75 | % 8.65/2.75 | Instantiating formula (44) with all_69_1_66, all_0_6_6, 0, all_89_0_70 and discharging atoms member(all_69_1_66, all_0_6_6) = all_89_0_70, member(all_69_1_66, all_0_6_6) = 0, yields: % 8.65/2.75 | (148) all_89_0_70 = 0 % 8.65/2.75 | % 8.65/2.75 | Equations (148) can reduce 146 to: % 8.65/2.75 | (71) $false % 8.65/2.75 | % 8.65/2.75 |-The branch is then unsatisfiable % 8.65/2.75 % SZS output end Proof for theBenchmark % 8.65/2.75 % 8.65/2.75 2209ms %------------------------------------------------------------------------------