%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU132+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n004.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 08:46:49 EDT 2022 % Result : Theorem 8.46s 2.61s % Output : Proof 10.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.11 % Problem : SEU132+2 : TPTP v8.1.0. Released v3.3.0. % 0.08/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n004.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sat Jun 18 20:55:23 EDT 2022 % 0.12/0.33 % CPUTime : % 0.49/0.60 ____ _ % 0.49/0.60 ___ / __ \_____(_)___ ________ __________ % 0.49/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.49/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.49/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.49/0.60 % 0.49/0.60 A Theorem Prover for First-Order Logic % 0.49/0.61 (ePrincess v.1.0) % 0.49/0.61 % 0.49/0.61 (c) Philipp Rümmer, 2009-2015 % 0.49/0.61 (c) Peter Backeman, 2014-2015 % 0.49/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.49/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.49/0.61 Bug reports to peter@backeman.se % 0.49/0.61 % 0.49/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.49/0.61 % 0.49/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.79/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.65/1.00 Prover 0: Preprocessing ... % 2.57/1.28 Prover 0: Warning: ignoring some quantifiers % 2.57/1.31 Prover 0: Constructing countermodel ... % 4.72/1.77 Prover 0: gave up % 4.72/1.77 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 4.72/1.81 Prover 1: Preprocessing ... % 5.08/1.92 Prover 1: Warning: ignoring some quantifiers % 5.08/1.93 Prover 1: Constructing countermodel ... % 7.33/2.37 Prover 1: gave up % 7.33/2.37 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 7.33/2.40 Prover 2: Preprocessing ... % 7.97/2.50 Prover 2: Warning: ignoring some quantifiers % 7.97/2.51 Prover 2: Constructing countermodel ... % 8.46/2.61 Prover 2: proved (240ms) % 8.46/2.61 % 8.46/2.61 No countermodel exists, formula is valid % 8.46/2.61 % SZS status Theorem for theBenchmark % 8.46/2.61 % 8.46/2.61 Generating proof ... Warning: ignoring some quantifiers % 9.95/2.97 found it (size 57) % 9.95/2.97 % 9.95/2.97 % SZS output start Proof for theBenchmark % 9.95/2.97 Assumed formulas after preprocessing and simplification: % 9.95/2.97 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v7 = 0) & ~ (v5 = 0) & empty(v8) = 0 & empty(v6) = v7 & empty(empty_set) = 0 & set_difference(v1, v2) = v4 & set_difference(v0, v2) = v3 & subset(v3, v4) = v5 & subset(v0, v1) = 0 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v12, v13) = v14) | ~ (set_intersection2(v10, v11) = v13) | ~ (set_intersection2(v9, v11) = v12) | ? [v15] : ( ~ (v15 = 0) & subset(v9, v10) = v15)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (set_difference(v9, v10) = v11) | ~ (in(v12, v11) = v13) | ? [v14] : ((v14 = 0 & in(v12, v10) = 0) | ( ~ (v14 = 0) & in(v12, v9) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (set_difference(v9, v10) = v11) | ~ (in(v12, v10) = v13) | ? [v14] : ((v14 = 0 & in(v12, v11) = 0) | ( ~ (v14 = 0) & in(v12, v9) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v12, v10) = v13) | ~ (set_union2(v9, v11) = v12) | ? [v14] : (( ~ (v14 = 0) & subset(v11, v10) = v14) | ( ~ (v14 = 0) & subset(v9, v10) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v9, v12) = v13) | ~ (set_intersection2(v10, v11) = v12) | ? [v14] : (( ~ (v14 = 0) & subset(v9, v11) = v14) | ( ~ (v14 = 0) & subset(v9, v10) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (set_intersection2(v9, v10) = v11) | ~ (in(v12, v11) = v13) | ? [v14] : (( ~ (v14 = 0) & in(v12, v10) = v14) | ( ~ (v14 = 0) & in(v12, v9) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (set_union2(v9, v10) = v11) | ~ (in(v12, v11) = v13) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & ~ (v14 = 0) & in(v12, v10) = v15 & in(v12, v9) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (set_union2(v9, v10) = v11) | ~ (in(v12, v10) = v13) | ? [v14] : ((v14 = 0 & in(v12, v9) = 0) | ( ~ (v14 = 0) & in(v12, v11) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (set_union2(v9, v10) = v11) | ~ (in(v12, v9) = v13) | ? [v14] : ((v14 = 0 & in(v12, v10) = 0) | ( ~ (v14 = 0) & in(v12, v11) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v9, v10) = v11) | ~ (in(v12, v10) = v13) | ? [v14] : ((v14 = 0 & ~ (v13 = 0) & in(v12, v9) = 0) | ( ~ (v14 = 0) & in(v12, v11) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v9, v10) = v11) | ~ (in(v12, v9) = v13) | ? [v14] : ((v13 = 0 & ~ (v14 = 0) & in(v12, v10) = v14) | ( ~ (v14 = 0) & in(v12, v11) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v9, v10) = v11) | ~ (in(v12, v10) = v13) | ? [v14] : ((v14 = 0 & v13 = 0 & in(v12, v9) = 0) | ( ~ (v14 = 0) & in(v12, v11) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v9, v10) = v11) | ~ (in(v12, v9) = v13) | ? [v14] : ((v14 = 0 & v13 = 0 & in(v12, v10) = 0) | ( ~ (v14 = 0) & in(v12, v11) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v9, v10) = v11) | ~ (in(v12, v10) = v13) | ? [v14] : ((v14 = 0 & in(v12, v11) = 0) | ( ~ (v14 = 0) & ~ (v13 = 0) & in(v12, v9) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v9, v10) = v11) | ~ (in(v12, v9) = v13) | ? [v14] : ((v14 = 0 & in(v12, v11) = 0) | ( ~ (v14 = 0) & ~ (v13 = 0) & in(v12, v10) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v10, v11) = 0) | ~ (subset(v9, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & subset(v9, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v9, v11) = v12) | ~ (subset(v9, v10) = 0) | ? [v13] : ( ~ (v13 = 0) & subset(v10, v11) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v9, v10) = 0) | ~ (in(v11, v10) = v12) | ? [v13] : ( ~ (v13 = 0) & in(v11, v9) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (disjoint(v12, v11) = v10) | ~ (disjoint(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (set_difference(v12, v11) = v10) | ~ (set_difference(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (subset(v12, v11) = v10) | ~ (subset(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (set_intersection2(v12, v11) = v10) | ~ (set_intersection2(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (set_union2(v12, v11) = v10) | ~ (set_union2(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (in(v12, v11) = v10) | ~ (in(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v9, v10) = v11) | ~ (in(v12, v11) = 0) | ? [v13] : ( ~ (v13 = 0) & in(v12, v10) = v13 & in(v12, v9) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v9, v10) = v11) | ~ (in(v12, v9) = 0) | ? [v13] : ((v13 = 0 & in(v12, v11) = 0) | (v13 = 0 & in(v12, v10) = 0))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v9, v10) = v11) | ~ (in(v12, v11) = 0) | ? [v13] : ( ~ (v13 = 0) & disjoint(v9, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v9, v10) = v11) | ~ (in(v12, v11) = 0) | (in(v12, v10) = 0 & in(v12, v9) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v9, v10) = v11) | ~ (in(v12, v10) = 0) | ? [v13] : ((v13 = 0 & in(v12, v11) = 0) | ( ~ (v13 = 0) & in(v12, v9) = v13))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v9, v10) = v11) | ~ (in(v12, v9) = 0) | ? [v13] : ((v13 = 0 & in(v12, v11) = 0) | ( ~ (v13 = 0) & in(v12, v10) = v13))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v9, v10) = v11) | ~ (in(v12, v11) = 0) | ? [v13] : ((v13 = 0 & in(v12, v10) = 0) | (v13 = 0 & in(v12, v9) = 0))) & ? [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (set_difference(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (((v16 = 0 & in(v13, v11) = 0) | ( ~ (v15 = 0) & in(v13, v10) = v15) | ( ~ (v14 = 0) & in(v13, v9) = v14)) & ((v15 = 0 & ~ (v16 = 0) & in(v13, v11) = v16 & in(v13, v10) = 0) | (v14 = 0 & in(v13, v9) = 0)))) & ? [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (set_intersection2(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (((v16 = 0 & v15 = 0 & in(v13, v11) = 0 & in(v13, v10) = 0) | (v14 = 0 & in(v13, v9) = 0)) & (( ~ (v16 = 0) & in(v13, v11) = v16) | ( ~ (v15 = 0) & in(v13, v10) = v15) | ( ~ (v14 = 0) & in(v13, v9) = v14)))) & ? [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (set_union2(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (((v16 = 0 & in(v13, v11) = 0) | (v15 = 0 & in(v13, v10) = 0) | (v14 = 0 & in(v13, v9) = 0)) & (( ~ (v16 = 0) & ~ (v15 = 0) & in(v13, v11) = v16 & in(v13, v10) = v15) | ( ~ (v14 = 0) & in(v13, v9) = v14)))) & ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (set_union2(v9, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (set_intersection2(v9, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : (v11 = empty_set | ~ (set_difference(v9, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : (v11 = empty_set | ~ (set_intersection2(v9, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & disjoint(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (disjoint(v10, v9) = v11) | ? [v12] : ( ~ (v12 = 0) & disjoint(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (disjoint(v9, v10) = v11) | ? [v12] : ? [v13] : (set_intersection2(v9, v10) = v12 & in(v13, v12) = 0)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (disjoint(v9, v10) = v11) | ? [v12] : ( ~ (v12 = empty_set) & set_intersection2(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (disjoint(v9, v10) = v11) | ? [v12] : (in(v12, v10) = 0 & in(v12, v9) = 0)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v9, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & in(v12, v10) = v13 & in(v12, v9) = 0)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v9, v10) = v11) | ? [v12] : ( ~ (v12 = empty_set) & set_difference(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (empty(v11) = v10) | ~ (empty(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (disjoint(v9, v10) = 0) | ~ (in(v11, v10) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v11, v9) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (disjoint(v9, v10) = 0) | ~ (in(v11, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v11, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset(v10, v11) = 0) | ~ (subset(v9, v10) = 0) | subset(v9, v11) = 0) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset(v9, v10) = 0) | ~ (in(v11, v9) = 0) | in(v11, v10) = 0) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v9) = v11) | set_intersection2(v9, v10) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | subset(v11, v9) = 0) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | set_intersection2(v10, v9) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | ? [v12] : ? [v13] : ((v13 = 0 & in(v12, v11) = 0) | (v12 = 0 & disjoint(v9, v10) = 0))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v10, v9) = v11) | set_union2(v9, v10) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v10, v9) = v11) | ? [v12] : ((v12 = 0 & empty(v9) = 0) | ( ~ (v12 = 0) & empty(v11) = v12))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v9, v10) = v11) | subset(v9, v11) = 0) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v9, v10) = v11) | set_union2(v10, v9) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v9, v10) = v11) | ? [v12] : ((v12 = 0 & empty(v9) = 0) | ( ~ (v12 = 0) & empty(v11) = v12))) & ! [v9] : ! [v10] : (v10 = v9 | ~ (empty(v10) = 0) | ~ (empty(v9) = 0)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (set_difference(v9, empty_set) = v10)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (subset(v10, v9) = 0) | ? [v11] : ( ~ (v11 = 0) & subset(v9, v10) = v11)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (subset(v9, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & subset(v10, v9) = v11)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (set_intersection2(v9, v9) = v10)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (set_union2(v9, v9) = v10)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (set_union2(v9, empty_set) = v10)) & ! [v9] : ! [v10] : (v10 = empty_set | ~ (set_difference(empty_set, v9) = v10)) & ! [v9] : ! [v10] : (v10 = empty_set | ~ (set_intersection2(v9, empty_set) = v10)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v9, v9) = v10)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(empty_set, v9) = v10)) & ! [v9] : ! [v10] : ( ~ (disjoint(v9, v10) = 0) | disjoint(v10, v9) = 0) & ! [v9] : ! [v10] : ( ~ (disjoint(v9, v10) = 0) | set_intersection2(v9, v10) = empty_set) & ! [v9] : ! [v10] : ( ~ (disjoint(v9, v10) = 0) | ? [v11] : (set_intersection2(v9, v10) = v11 & ! [v12] : ~ (in(v12, v11) = 0))) & ! [v9] : ! [v10] : ( ~ (set_difference(v9, v10) = empty_set) | subset(v9, v10) = 0) & ! [v9] : ! [v10] : ( ~ (subset(v9, v10) = 0) | set_difference(v9, v10) = empty_set) & ! [v9] : ! [v10] : ( ~ (subset(v9, v10) = 0) | set_intersection2(v9, v10) = v9) & ! [v9] : ! [v10] : ( ~ (subset(v9, v10) = 0) | set_union2(v9, v10) = v10) & ! [v9] : ! [v10] : ( ~ (set_intersection2(v9, v10) = empty_set) | disjoint(v9, v10) = 0) & ! [v9] : ! [v10] : ( ~ (in(v10, v9) = 0) | ? [v11] : ( ~ (v11 = 0) & in(v9, v10) = v11)) & ! [v9] : ! [v10] : ( ~ (in(v9, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & empty(v10) = v11)) & ! [v9] : ! [v10] : ( ~ (in(v9, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & in(v10, v9) = v11)) & ! [v9] : (v9 = empty_set | ~ (empty(v9) = 0)) & ! [v9] : (v9 = empty_set | ~ (subset(v9, empty_set) = 0)) & ! [v9] : ~ (in(v9, empty_set) = 0) & ? [v9] : ? [v10] : ? [v11] : disjoint(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : set_difference(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : subset(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : set_intersection2(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : set_union2(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : in(v10, v9) = v11 & ? [v9] : ? [v10] : (v10 = v9 | ? [v11] : ? [v12] : ? [v13] : (((v13 = 0 & in(v11, v10) = 0) | (v12 = 0 & in(v11, v9) = 0)) & (( ~ (v13 = 0) & in(v11, v10) = v13) | ( ~ (v12 = 0) & in(v11, v9) = v12)))) & ? [v9] : ? [v10] : empty(v9) = v10 & ? [v9] : (v9 = empty_set | ? [v10] : in(v10, v9) = 0)) % 9.95/3.02 | 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, all_0_7_7, all_0_8_8 yields: % 9.95/3.02 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & set_difference(all_0_7_7, all_0_6_6) = all_0_4_4 & set_difference(all_0_8_8, all_0_6_6) = all_0_5_5 & subset(all_0_5_5, all_0_4_4) = all_0_3_3 & subset(all_0_8_8, all_0_7_7) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & in(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ? [v5] : (( ~ (v5 = 0) & subset(v2, v1) = v5) | ( ~ (v5 = 0) & subset(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (set_intersection2(v1, v2) = v3) | ? [v5] : (( ~ (v5 = 0) & subset(v0, v2) = v5) | ( ~ (v5 = 0) & subset(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : (( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & ~ (v4 = 0) & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v4 = 0 & ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v4 = 0 & in(v3, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ((v4 = 0 & in(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)) & ((v6 = 0 & ~ (v7 = 0) & in(v4, v2) = v7 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v6 = 0 & in(v4, v2) = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & in(v4, v2) = v7) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | (v6 = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & ~ (v6 = 0) & in(v4, v2) = v7 & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0))) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_difference(v0, v1) = empty_set) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_intersection2(v0, v1) = v0) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_union2(v0, v1) = v1) & ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0)) & ! [v0] : ~ (in(v0, empty_set) = 0) & ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_difference(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & in(v2, v1) = 0) | (v3 = 0 & in(v2, v0) = 0)) & (( ~ (v4 = 0) & in(v2, v1) = v4) | ( ~ (v3 = 0) & in(v2, v0) = v3)))) & ? [v0] : ? [v1] : empty(v0) = v1 & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0) % 10.39/3.04 | % 10.39/3.04 | Applying alpha-rule on (1) yields: % 10.39/3.04 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0) = 0) % 10.39/3.04 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & ~ (v4 = 0) & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) % 10.39/3.04 | (4) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) % 10.39/3.05 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0)) % 10.39/3.05 | (6) ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2 % 10.39/3.05 | (7) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0) % 10.39/3.05 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4)) % 10.39/3.05 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (set_intersection2(v1, v2) = v3) | ? [v5] : (( ~ (v5 = 0) & subset(v0, v2) = v5) | ( ~ (v5 = 0) & subset(v0, v1) = v5))) % 10.39/3.05 | (10) subset(all_0_5_5, all_0_4_4) = all_0_3_3 % 10.39/3.05 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 10.39/3.05 | (12) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 10.39/3.05 | (13) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v6 = 0 & in(v4, v2) = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & in(v4, v2) = v7) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)))) % 10.39/3.05 | (14) ? [v0] : ? [v1] : empty(v0) = v1 % 10.39/3.05 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 10.39/3.05 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) % 10.39/3.05 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) % 10.39/3.05 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v0) = v5))) % 10.39/3.05 | (19) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & in(v2, v1) = 0) | (v3 = 0 & in(v2, v0) = 0)) & (( ~ (v4 = 0) & in(v2, v1) = v4) | ( ~ (v3 = 0) & in(v2, v0) = v3)))) % 10.39/3.05 | (20) ! [v0] : ~ (in(v0, empty_set) = 0) % 10.39/3.05 | (21) ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2 % 10.39/3.05 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) % 10.39/3.05 | (23) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_union2(v0, v1) = v1) % 10.39/3.05 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0) % 10.39/3.05 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 10.39/3.05 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) % 10.39/3.05 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 10.39/3.05 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ? [v5] : (( ~ (v5 = 0) & subset(v2, v1) = v5) | ( ~ (v5 = 0) & subset(v0, v1) = v5))) % 10.39/3.05 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | (in(v3, v1) = 0 & in(v3, v0) = 0)) % 10.39/3.05 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) % 10.39/3.05 | (31) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) % 10.39/3.05 | (32) empty(all_0_0_0) = 0 % 10.39/3.05 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 10.39/3.05 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v4 = 0 & in(v3, v1) = 0))) % 10.39/3.05 | (35) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | (v6 = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & ~ (v6 = 0) & in(v4, v2) = v7 & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)))) % 10.39/3.06 | (36) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) % 10.39/3.06 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v1) = v4))) % 10.39/3.06 | (38) ~ (all_0_3_3 = 0) % 10.39/3.06 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 10.39/3.06 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 10.39/3.06 | (41) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_difference(v0, v1) = v3)) % 10.39/3.06 | (42) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 10.39/3.06 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v0) = v3)) % 10.39/3.06 | (44) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) % 10.39/3.06 | (45) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) % 10.39/3.06 | (46) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_intersection2(v0, v1) = v0) % 10.39/3.06 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) % 10.39/3.06 | (48) ? [v0] : ? [v1] : ? [v2] : set_difference(v1, v0) = v2 % 10.39/3.06 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 10.39/3.06 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) % 10.39/3.06 | (51) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 10.39/3.06 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ((v4 = 0 & in(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0))) % 10.39/3.06 | (53) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 10.39/3.06 | (54) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 10.39/3.06 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : (( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v0) = v5))) % 10.39/3.06 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v0) = v4))) % 10.39/3.06 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2) = 0) % 10.39/3.06 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 10.39/3.06 | (59) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 10.39/3.06 | (60) empty(empty_set) = 0 % 10.39/3.06 | (61) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 10.39/3.06 | (62) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 % 10.39/3.06 | (63) set_difference(all_0_7_7, all_0_6_6) = all_0_4_4 % 10.39/3.06 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) % 10.39/3.06 | (65) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 10.39/3.06 | (66) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 % 10.39/3.06 | (67) ~ (all_0_1_1 = 0) % 10.39/3.06 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 10.39/3.06 | (69) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)) & ((v6 = 0 & ~ (v7 = 0) & in(v4, v2) = v7 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)))) % 10.39/3.06 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v0) = v5))) % 10.39/3.06 | (71) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) % 10.39/3.06 | (72) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0) % 10.39/3.06 | (73) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) % 10.39/3.06 | (74) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) % 10.39/3.06 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0))) % 10.39/3.06 | (76) empty(all_0_2_2) = all_0_1_1 % 10.39/3.06 | (77) subset(all_0_8_8, all_0_7_7) = 0 % 10.39/3.07 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) % 10.39/3.07 | (79) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0)) % 10.39/3.07 | (80) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) % 10.39/3.07 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 10.39/3.07 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) % 10.39/3.07 | (83) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 10.39/3.07 | (84) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 10.39/3.07 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) % 10.39/3.07 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 10.39/3.07 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 10.39/3.07 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) % 10.39/3.07 | (89) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 10.39/3.07 | (90) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0))) % 10.39/3.07 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 10.39/3.07 | (92) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 10.39/3.07 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v4 = 0 & ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v2) = v5))) % 10.39/3.07 | (94) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) % 10.39/3.07 | (95) ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2 % 10.39/3.07 | (96) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_difference(v0, v1) = empty_set) % 10.39/3.07 | (97) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0) % 10.39/3.07 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) % 10.39/3.07 | (99) set_difference(all_0_8_8, all_0_6_6) = all_0_5_5 % 10.39/3.07 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & in(v3, v0) = v5))) % 10.39/3.07 | (101) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 10.39/3.07 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v1) = v5))) % 10.39/3.07 | % 10.39/3.07 | Instantiating formula (11) with all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 10.39/3.07 | (103) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_5_5) = 0) % 10.39/3.07 | % 10.39/3.07 | Instantiating formula (41) with all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 10.39/3.07 | (104) all_0_3_3 = 0 | ? [v0] : ( ~ (v0 = empty_set) & set_difference(all_0_5_5, all_0_4_4) = v0) % 10.39/3.07 | % 10.39/3.07 | Instantiating formula (96) with all_0_7_7, all_0_8_8 and discharging atoms subset(all_0_8_8, all_0_7_7) = 0, yields: % 10.39/3.07 | (105) set_difference(all_0_8_8, all_0_7_7) = empty_set % 10.39/3.07 | % 10.39/3.07 | Instantiating formula (23) with all_0_7_7, all_0_8_8 and discharging atoms subset(all_0_8_8, all_0_7_7) = 0, yields: % 10.39/3.07 | (106) set_union2(all_0_8_8, all_0_7_7) = all_0_7_7 % 10.39/3.07 | % 10.39/3.07 +-Applying beta-rule and splitting (103), into two cases. % 10.39/3.07 |-Branch one: % 10.39/3.07 | (107) all_0_3_3 = 0 % 10.39/3.07 | % 10.39/3.07 | Equations (107) can reduce 38 to: % 10.39/3.07 | (108) $false % 10.39/3.07 | % 10.39/3.07 |-The branch is then unsatisfiable % 10.39/3.07 |-Branch two: % 10.39/3.07 | (38) ~ (all_0_3_3 = 0) % 10.39/3.07 | (110) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_5_5) = 0) % 10.39/3.07 | % 10.39/3.07 | Instantiating (110) with all_39_0_35, all_39_1_36 yields: % 10.39/3.07 | (111) ~ (all_39_0_35 = 0) & in(all_39_1_36, all_0_4_4) = all_39_0_35 & in(all_39_1_36, all_0_5_5) = 0 % 10.39/3.07 | % 10.39/3.07 | Applying alpha-rule on (111) yields: % 10.39/3.07 | (112) ~ (all_39_0_35 = 0) % 10.39/3.07 | (113) in(all_39_1_36, all_0_4_4) = all_39_0_35 % 10.39/3.07 | (114) in(all_39_1_36, all_0_5_5) = 0 % 10.39/3.08 | % 10.39/3.08 +-Applying beta-rule and splitting (104), into two cases. % 10.39/3.08 |-Branch one: % 10.39/3.08 | (107) all_0_3_3 = 0 % 10.39/3.08 | % 10.39/3.08 | Equations (107) can reduce 38 to: % 10.39/3.08 | (108) $false % 10.39/3.08 | % 10.39/3.08 |-The branch is then unsatisfiable % 10.39/3.08 |-Branch two: % 10.39/3.08 | (38) ~ (all_0_3_3 = 0) % 10.39/3.08 | (118) ? [v0] : ( ~ (v0 = empty_set) & set_difference(all_0_5_5, all_0_4_4) = v0) % 10.39/3.08 | % 10.39/3.08 | Instantiating (118) with all_44_0_37 yields: % 10.39/3.08 | (119) ~ (all_44_0_37 = empty_set) & set_difference(all_0_5_5, all_0_4_4) = all_44_0_37 % 10.39/3.08 | % 10.39/3.08 | Applying alpha-rule on (119) yields: % 10.39/3.08 | (120) ~ (all_44_0_37 = empty_set) % 10.39/3.08 | (121) set_difference(all_0_5_5, all_0_4_4) = all_44_0_37 % 10.39/3.08 | % 10.39/3.08 | Instantiating formula (40) with all_0_7_7, all_0_8_8, all_0_7_7 and discharging atoms set_union2(all_0_8_8, all_0_7_7) = all_0_7_7, yields: % 10.39/3.08 | (122) set_union2(all_0_7_7, all_0_8_8) = all_0_7_7 % 10.39/3.08 | % 10.39/3.08 | Instantiating formula (70) with all_39_0_35, all_39_1_36, all_0_4_4, all_0_6_6, all_0_7_7 and discharging atoms set_difference(all_0_7_7, all_0_6_6) = all_0_4_4, in(all_39_1_36, all_0_4_4) = all_39_0_35, yields: % 10.39/3.08 | (123) all_39_0_35 = 0 | ? [v0] : ((v0 = 0 & in(all_39_1_36, all_0_6_6) = 0) | ( ~ (v0 = 0) & in(all_39_1_36, all_0_7_7) = v0)) % 10.39/3.08 | % 10.39/3.08 | Instantiating formula (100) with all_39_0_35, all_39_1_36, all_44_0_37, all_0_4_4, all_0_5_5 and discharging atoms set_difference(all_0_5_5, all_0_4_4) = all_44_0_37, in(all_39_1_36, all_0_4_4) = all_39_0_35, yields: % 10.39/3.08 | (124) all_39_0_35 = 0 | ? [v0] : ((v0 = 0 & in(all_39_1_36, all_44_0_37) = 0) | ( ~ (v0 = 0) & in(all_39_1_36, all_0_5_5) = v0)) % 10.39/3.08 | % 10.39/3.08 | Instantiating formula (33) with all_39_1_36, all_0_5_5, all_0_6_6, all_0_8_8 and discharging atoms set_difference(all_0_8_8, all_0_6_6) = all_0_5_5, in(all_39_1_36, all_0_5_5) = 0, yields: % 10.39/3.08 | (125) ? [v0] : ( ~ (v0 = 0) & in(all_39_1_36, all_0_6_6) = v0 & in(all_39_1_36, all_0_8_8) = 0) % 10.39/3.08 | % 10.39/3.08 | Instantiating (125) with all_59_0_44 yields: % 10.39/3.08 | (126) ~ (all_59_0_44 = 0) & in(all_39_1_36, all_0_6_6) = all_59_0_44 & in(all_39_1_36, all_0_8_8) = 0 % 10.39/3.08 | % 10.39/3.08 | Applying alpha-rule on (126) yields: % 10.39/3.08 | (127) ~ (all_59_0_44 = 0) % 10.39/3.08 | (128) in(all_39_1_36, all_0_6_6) = all_59_0_44 % 10.39/3.08 | (129) in(all_39_1_36, all_0_8_8) = 0 % 10.39/3.08 | % 10.39/3.08 +-Applying beta-rule and splitting (124), into two cases. % 10.39/3.08 |-Branch one: % 10.39/3.08 | (130) all_39_0_35 = 0 % 10.39/3.08 | % 10.39/3.08 | Equations (130) can reduce 112 to: % 10.39/3.08 | (108) $false % 10.39/3.08 | % 10.39/3.08 |-The branch is then unsatisfiable % 10.39/3.08 |-Branch two: % 10.39/3.08 | (112) ~ (all_39_0_35 = 0) % 10.39/3.08 | (133) ? [v0] : ((v0 = 0 & in(all_39_1_36, all_44_0_37) = 0) | ( ~ (v0 = 0) & in(all_39_1_36, all_0_5_5) = v0)) % 10.39/3.08 | % 10.39/3.08 +-Applying beta-rule and splitting (123), into two cases. % 10.39/3.08 |-Branch one: % 10.39/3.08 | (130) all_39_0_35 = 0 % 10.39/3.08 | % 10.39/3.08 | Equations (130) can reduce 112 to: % 10.39/3.08 | (108) $false % 10.39/3.08 | % 10.39/3.08 |-The branch is then unsatisfiable % 10.39/3.08 |-Branch two: % 10.39/3.08 | (112) ~ (all_39_0_35 = 0) % 10.39/3.08 | (137) ? [v0] : ((v0 = 0 & in(all_39_1_36, all_0_6_6) = 0) | ( ~ (v0 = 0) & in(all_39_1_36, all_0_7_7) = v0)) % 10.39/3.08 | % 10.39/3.08 | Instantiating (137) with all_72_0_49 yields: % 10.39/3.08 | (138) (all_72_0_49 = 0 & in(all_39_1_36, all_0_6_6) = 0) | ( ~ (all_72_0_49 = 0) & in(all_39_1_36, all_0_7_7) = all_72_0_49) % 10.39/3.08 | % 10.39/3.08 +-Applying beta-rule and splitting (138), into two cases. % 10.39/3.08 |-Branch one: % 10.39/3.08 | (139) all_72_0_49 = 0 & in(all_39_1_36, all_0_6_6) = 0 % 10.39/3.08 | % 10.39/3.08 | Applying alpha-rule on (139) yields: % 10.39/3.08 | (140) all_72_0_49 = 0 % 10.39/3.08 | (141) in(all_39_1_36, all_0_6_6) = 0 % 10.39/3.08 | % 10.39/3.08 | Instantiating formula (91) with all_39_1_36, all_0_6_6, 0, all_59_0_44 and discharging atoms in(all_39_1_36, all_0_6_6) = all_59_0_44, in(all_39_1_36, all_0_6_6) = 0, yields: % 10.39/3.08 | (142) all_59_0_44 = 0 % 10.39/3.08 | % 10.39/3.08 | Equations (142) can reduce 127 to: % 10.39/3.08 | (108) $false % 10.39/3.08 | % 10.39/3.08 |-The branch is then unsatisfiable % 10.39/3.08 |-Branch two: % 10.39/3.08 | (144) ~ (all_72_0_49 = 0) & in(all_39_1_36, all_0_7_7) = all_72_0_49 % 10.39/3.08 | % 10.39/3.08 | Applying alpha-rule on (144) yields: % 10.39/3.08 | (145) ~ (all_72_0_49 = 0) % 10.39/3.08 | (146) in(all_39_1_36, all_0_7_7) = all_72_0_49 % 10.39/3.08 | % 10.39/3.08 | Instantiating formula (100) with all_72_0_49, all_39_1_36, empty_set, all_0_7_7, all_0_8_8 and discharging atoms set_difference(all_0_8_8, all_0_7_7) = empty_set, in(all_39_1_36, all_0_7_7) = all_72_0_49, yields: % 10.39/3.08 | (147) all_72_0_49 = 0 | ? [v0] : ((v0 = 0 & in(all_39_1_36, empty_set) = 0) | ( ~ (v0 = 0) & in(all_39_1_36, all_0_8_8) = v0)) % 10.39/3.08 | % 10.39/3.08 | Instantiating formula (98) with all_72_0_49, all_39_1_36, all_0_7_7, all_0_8_8, all_0_7_7 and discharging atoms set_union2(all_0_7_7, all_0_8_8) = all_0_7_7, in(all_39_1_36, all_0_7_7) = all_72_0_49, yields: % 10.39/3.08 | (148) all_72_0_49 = 0 | ? [v0] : ((v0 = 0 & in(all_39_1_36, all_0_8_8) = 0) | ( ~ (v0 = 0) & in(all_39_1_36, all_0_7_7) = v0)) % 10.39/3.08 | % 10.39/3.08 | Instantiating formula (78) with all_72_0_49, all_39_1_36, all_0_7_7, all_0_8_8 and discharging atoms subset(all_0_8_8, all_0_7_7) = 0, in(all_39_1_36, all_0_7_7) = all_72_0_49, yields: % 10.39/3.08 | (149) all_72_0_49 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_39_1_36, all_0_8_8) = v0) % 10.39/3.08 | % 10.39/3.08 | Instantiating formula (34) with all_39_1_36, empty_set, all_0_7_7, all_0_8_8 and discharging atoms set_difference(all_0_8_8, all_0_7_7) = empty_set, in(all_39_1_36, all_0_8_8) = 0, yields: % 10.39/3.08 | (150) ? [v0] : ((v0 = 0 & in(all_39_1_36, all_0_7_7) = 0) | (v0 = 0 & in(all_39_1_36, empty_set) = 0)) % 10.39/3.08 | % 10.39/3.08 | Instantiating (150) with all_123_0_65 yields: % 10.39/3.08 | (151) (all_123_0_65 = 0 & in(all_39_1_36, all_0_7_7) = 0) | (all_123_0_65 = 0 & in(all_39_1_36, empty_set) = 0) % 10.39/3.08 | % 10.39/3.08 +-Applying beta-rule and splitting (149), into two cases. % 10.39/3.08 |-Branch one: % 10.39/3.08 | (140) all_72_0_49 = 0 % 10.39/3.08 | % 10.39/3.08 | Equations (140) can reduce 145 to: % 10.39/3.08 | (108) $false % 10.39/3.08 | % 10.39/3.08 |-The branch is then unsatisfiable % 10.39/3.08 |-Branch two: % 10.39/3.08 | (145) ~ (all_72_0_49 = 0) % 10.39/3.08 | (155) ? [v0] : ( ~ (v0 = 0) & in(all_39_1_36, all_0_8_8) = v0) % 10.39/3.08 | % 10.39/3.08 +-Applying beta-rule and splitting (147), into two cases. % 10.39/3.08 |-Branch one: % 10.39/3.08 | (140) all_72_0_49 = 0 % 10.39/3.08 | % 10.39/3.08 | Equations (140) can reduce 145 to: % 10.39/3.08 | (108) $false % 10.39/3.08 | % 10.39/3.08 |-The branch is then unsatisfiable % 10.39/3.08 |-Branch two: % 10.39/3.08 | (145) ~ (all_72_0_49 = 0) % 10.39/3.08 | (159) ? [v0] : ((v0 = 0 & in(all_39_1_36, empty_set) = 0) | ( ~ (v0 = 0) & in(all_39_1_36, all_0_8_8) = v0)) % 10.39/3.08 | % 10.39/3.08 +-Applying beta-rule and splitting (151), into two cases. % 10.39/3.08 |-Branch one: % 10.39/3.08 | (160) all_123_0_65 = 0 & in(all_39_1_36, all_0_7_7) = 0 % 10.39/3.08 | % 10.39/3.08 | Applying alpha-rule on (160) yields: % 10.39/3.08 | (161) all_123_0_65 = 0 % 10.39/3.08 | (162) in(all_39_1_36, all_0_7_7) = 0 % 10.39/3.08 | % 10.39/3.08 +-Applying beta-rule and splitting (148), into two cases. % 10.39/3.08 |-Branch one: % 10.39/3.08 | (140) all_72_0_49 = 0 % 10.39/3.08 | % 10.39/3.08 | Equations (140) can reduce 145 to: % 10.39/3.08 | (108) $false % 10.39/3.08 | % 10.39/3.08 |-The branch is then unsatisfiable % 10.39/3.08 |-Branch two: % 10.39/3.08 | (145) ~ (all_72_0_49 = 0) % 10.39/3.08 | (166) ? [v0] : ((v0 = 0 & in(all_39_1_36, all_0_8_8) = 0) | ( ~ (v0 = 0) & in(all_39_1_36, all_0_7_7) = v0)) % 10.39/3.08 | % 10.39/3.08 | Instantiating formula (91) with all_39_1_36, all_0_7_7, 0, all_72_0_49 and discharging atoms in(all_39_1_36, all_0_7_7) = all_72_0_49, in(all_39_1_36, all_0_7_7) = 0, yields: % 10.39/3.08 | (140) all_72_0_49 = 0 % 10.39/3.08 | % 10.39/3.08 | Equations (140) can reduce 145 to: % 10.39/3.08 | (108) $false % 10.39/3.08 | % 10.39/3.08 |-The branch is then unsatisfiable % 10.39/3.08 |-Branch two: % 10.39/3.08 | (169) all_123_0_65 = 0 & in(all_39_1_36, empty_set) = 0 % 10.39/3.08 | % 10.39/3.08 | Applying alpha-rule on (169) yields: % 10.39/3.08 | (161) all_123_0_65 = 0 % 10.39/3.08 | (171) in(all_39_1_36, empty_set) = 0 % 10.39/3.08 | % 10.39/3.08 | Instantiating formula (20) with all_39_1_36 and discharging atoms in(all_39_1_36, empty_set) = 0, yields: % 10.39/3.08 | (172) $false % 10.39/3.08 | % 10.39/3.08 |-The branch is then unsatisfiable % 10.39/3.09 % SZS output end Proof for theBenchmark % 10.39/3.09 % 10.39/3.09 2463ms %------------------------------------------------------------------------------