%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU263+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n009.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 08:48:17 EDT 2022 % Result : Theorem 7.64s 2.54s % Output : Proof 9.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.14 % Problem : SEU263+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.36 % Computer : n009.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Sun Jun 19 20:35:07 EDT 2022 % 0.14/0.36 % CPUTime : % 0.63/0.66 ____ _ % 0.63/0.66 ___ / __ \_____(_)___ ________ __________ % 0.63/0.66 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.63/0.66 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.63/0.66 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.63/0.66 % 0.63/0.66 A Theorem Prover for First-Order Logic % 0.63/0.66 (ePrincess v.1.0) % 0.63/0.66 % 0.63/0.66 (c) Philipp Rümmer, 2009-2015 % 0.63/0.66 (c) Peter Backeman, 2014-2015 % 0.63/0.66 (contributions by Angelo Brillout, Peter Baumgartner) % 0.63/0.66 Free software under GNU Lesser General Public License (LGPL). % 0.63/0.66 Bug reports to peter@backeman.se % 0.63/0.66 % 0.63/0.66 For more information, visit http://user.uu.se/~petba168/breu/ % 0.63/0.66 % 0.63/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.80/0.71 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.40/1.00 Prover 0: Preprocessing ... % 1.79/1.17 Prover 0: Warning: ignoring some quantifiers % 2.03/1.19 Prover 0: Constructing countermodel ... % 5.87/2.20 Prover 0: gave up % 5.87/2.20 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 6.34/2.22 Prover 1: Preprocessing ... % 6.34/2.29 Prover 1: Warning: ignoring some quantifiers % 6.34/2.29 Prover 1: Constructing countermodel ... % 6.77/2.34 Prover 1: gave up % 6.77/2.34 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 6.77/2.35 Prover 2: Preprocessing ... % 7.23/2.42 Prover 2: Warning: ignoring some quantifiers % 7.23/2.43 Prover 2: Constructing countermodel ... % 7.64/2.54 Prover 2: proved (200ms) % 7.64/2.54 % 7.64/2.54 No countermodel exists, formula is valid % 7.64/2.54 % SZS status Theorem for theBenchmark % 7.64/2.54 % 7.64/2.54 Generating proof ... Warning: ignoring some quantifiers % 9.52/2.94 found it (size 80) % 9.52/2.94 % 9.52/2.94 % SZS output start Proof for theBenchmark % 9.52/2.94 Assumed formulas after preprocessing and simplification: % 9.52/2.94 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & relation_rng(v3) = v4 & relation_of2_as_subset(v3, v2, v1) = v5 & relation_of2_as_subset(v3, v2, v0) = 0 & subset(v4, v1) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v10, v11) = v12) | ~ (cartesian_product2(v7, v9) = v11) | ~ (cartesian_product2(v6, v8) = v10) | ? [v13] : (( ~ (v13 = 0) & subset(v8, v9) = v13) | ( ~ (v13 = 0) & subset(v6, v7) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (cartesian_product2(v6, v7) = v9) | ~ (powerset(v9) = v10) | ~ (element(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & relation_of2_as_subset(v8, v6, v7) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = v10) | ~ (cartesian_product2(v6, v7) = v9) | ? [v11] : ( ~ (v11 = 0) & relation_of2(v8, v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (relation_of2_as_subset(v10, v9, v8) = v7) | ~ (relation_of2_as_subset(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (relation_of2(v10, v9, v8) = v7) | ~ (relation_of2(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (cartesian_product2(v6, v7) = v9) | ~ (powerset(v9) = v10) | ~ (element(v8, v10) = 0) | relation(v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (relation_of2_as_subset(v8, v6, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & relation_of2(v8, v6, v7) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = 0) | ~ (subset(v6, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & subset(v6, v7) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v6, v8) = v9) | ~ (subset(v6, v7) = 0) | ? [v10] : ( ~ (v10 = 0) & subset(v7, v8) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (relation_of2(v8, v6, v7) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & subset(v8, v10) = v11 & cartesian_product2(v6, v7) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (relation_of2(v8, v6, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & relation_of2_as_subset(v8, v6, v7) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (powerset(v7) = v8) | ~ (element(v6, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & subset(v6, v7) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (subset(v9, v8) = v7) | ~ (subset(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (cartesian_product2(v9, v8) = v7) | ~ (cartesian_product2(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (element(v9, v8) = v7) | ~ (element(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v8, v9) = 0) | ~ (cartesian_product2(v6, v7) = v9) | relation_of2(v8, v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v6, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & powerset(v7) = v9 & element(v6, v9) = v10)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (relation_dom(v8) = v7) | ~ (relation_dom(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (relation_rng(v8) = v7) | ~ (relation_rng(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (powerset(v8) = v7) | ~ (powerset(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (relation(v8) = v7) | ~ (relation(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (relation_of2_as_subset(v8, v6, v7) = 0) | relation_of2(v8, v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ( ~ (relation_of2_as_subset(v8, v6, v7) = 0) | ? [v9] : ? [v10] : (relation_dom(v8) = v9 & relation_rng(v8) = v10 & subset(v10, v7) = 0 & subset(v9, v6) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (relation_of2_as_subset(v8, v6, v7) = 0) | ? [v9] : ? [v10] : (cartesian_product2(v6, v7) = v9 & powerset(v9) = v10 & element(v8, v10) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (subset(v7, v8) = 0) | ~ (subset(v6, v7) = 0) | subset(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ( ~ (relation_of2(v8, v6, v7) = 0) | relation_of2_as_subset(v8, v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ( ~ (relation_of2(v8, v6, v7) = 0) | ? [v9] : (subset(v8, v9) = 0 & cartesian_product2(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ~ (element(v6, v8) = 0) | subset(v6, v7) = 0) & ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v6, v6) = v7)) & ! [v6] : ! [v7] : ( ~ (relation_dom(v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & relation_rng(v6) = v8 & subset(v6, v9) = 0 & cartesian_product2(v7, v8) = v9) | ( ~ (v8 = 0) & relation(v6) = v8))) & ! [v6] : ! [v7] : ( ~ (relation_rng(v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & relation_dom(v6) = v8 & subset(v6, v9) = 0 & cartesian_product2(v8, v7) = v9) | ( ~ (v8 = 0) & relation(v6) = v8))) & ! [v6] : ! [v7] : ( ~ (subset(v6, v7) = 0) | ? [v8] : (powerset(v7) = v8 & element(v6, v8) = 0)) & ! [v6] : ( ~ (relation(v6) = 0) | ? [v7] : ? [v8] : ? [v9] : (relation_dom(v6) = v7 & relation_rng(v6) = v8 & subset(v6, v9) = 0 & cartesian_product2(v7, v8) = v9)) & ? [v6] : ? [v7] : ? [v8] : ? [v9] : relation_of2_as_subset(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : relation_of2(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : relation_of2_as_subset(v8, v6, v7) = 0 & ? [v6] : ? [v7] : ? [v8] : subset(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : relation_of2(v8, v6, v7) = 0 & ? [v6] : ? [v7] : ? [v8] : cartesian_product2(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : element(v7, v6) = v8 & ? [v6] : ? [v7] : relation_dom(v6) = v7 & ? [v6] : ? [v7] : relation_rng(v6) = v7 & ? [v6] : ? [v7] : powerset(v6) = v7 & ? [v6] : ? [v7] : element(v7, v6) = 0 & ? [v6] : ? [v7] : relation(v6) = v7) % 9.52/2.98 | 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 yields: % 9.52/2.98 | (1) ~ (all_0_0_0 = 0) & relation_rng(all_0_2_2) = all_0_1_1 & relation_of2_as_subset(all_0_2_2, all_0_3_3, all_0_4_4) = all_0_0_0 & relation_of2_as_subset(all_0_2_2, all_0_3_3, all_0_5_5) = 0 & subset(all_0_1_1, all_0_4_4) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (subset(v4, v5) = v6) | ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ? [v7] : (( ~ (v7 = 0) & subset(v2, v3) = v7) | ( ~ (v7 = 0) & subset(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & relation_of2_as_subset(v2, v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v2, v3) = v4) | ~ (cartesian_product2(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & relation_of2(v2, v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ (relation_of2(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = 0) | relation(v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2_as_subset(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4)) & ! [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 | ~ (relation_of2(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & subset(v2, v4) = v5 & cartesian_product2(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v2, v3) = 0) | ~ (cartesian_product2(v0, v1) = v3) | relation_of2(v2, v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | relation_of2(v2, v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & relation_rng(v2) = v4 & subset(v4, v1) = 0 & subset(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | ? [v3] : ? [v4] : (cartesian_product2(v0, v1) = v3 & powerset(v3) = v4 & element(v2, v4) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | relation_of2_as_subset(v2, v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | ? [v3] : (subset(v2, v3) = 0 & cartesian_product2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & relation_rng(v0) = v2 & subset(v0, v3) = 0 & cartesian_product2(v1, v2) = v3) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & relation_dom(v0) = v2 & subset(v0, v3) = 0 & cartesian_product2(v2, v1) = v3) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_dom(v0) = v1 & relation_rng(v0) = v2 & subset(v0, v3) = 0 & cartesian_product2(v1, v2) = v3)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2_as_subset(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) = 0 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) = 0 & ? [v0] : ? [v1] : ? [v2] : cartesian_product2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : relation_dom(v0) = v1 & ? [v0] : ? [v1] : relation_rng(v0) = v1 & ? [v0] : ? [v1] : powerset(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : relation(v0) = v1 % 9.52/2.99 | % 9.52/2.99 | Applying alpha-rule on (1) yields: % 9.52/2.99 | (2) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 % 9.52/2.99 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = 0) | relation(v2) = 0) % 9.52/3.00 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (subset(v4, v5) = v6) | ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ? [v7] : (( ~ (v7 = 0) & subset(v2, v3) = v7) | ( ~ (v7 = 0) & subset(v0, v1) = v7))) % 9.52/3.00 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | ? [v3] : (subset(v2, v3) = 0 & cartesian_product2(v0, v1) = v3)) % 9.52/3.00 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & relation_of2_as_subset(v2, v0, v1) = v6)) % 9.52/3.00 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 9.52/3.00 | (8) ? [v0] : ? [v1] : relation(v0) = v1 % 9.52/3.00 | (9) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) % 9.52/3.00 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 9.52/3.00 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4, v3, v2) = v0)) % 9.52/3.00 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 9.52/3.00 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4)) % 9.52/3.00 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2_as_subset(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4)) % 9.52/3.00 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 9.52/3.00 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | relation_of2_as_subset(v2, v0, v1) = 0) % 9.52/3.00 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | relation_of2(v2, v0, v1) = 0) % 9.52/3.00 | (18) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & relation_dom(v0) = v2 & subset(v0, v3) = 0 & cartesian_product2(v2, v1) = v3) | ( ~ (v2 = 0) & relation(v0) = v2))) % 9.52/3.00 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 9.52/3.00 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | ? [v3] : ? [v4] : (cartesian_product2(v0, v1) = v3 & powerset(v3) = v4 & element(v2, v4) = 0)) % 9.52/3.00 | (21) ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2(v2, v1, v0) = v3 % 9.52/3.00 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 9.52/3.00 | (23) ? [v0] : ? [v1] : ? [v2] : cartesian_product2(v1, v0) = v2 % 9.52/3.00 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v2, v3) = 0) | ~ (cartesian_product2(v0, v1) = v3) | relation_of2(v2, v0, v1) = 0) % 9.52/3.00 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & subset(v2, v4) = v5 & cartesian_product2(v0, v1) = v4)) % 9.89/3.00 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v2, v3) = v4) | ~ (cartesian_product2(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & relation_of2(v2, v0, v1) = v5)) % 9.89/3.00 | (27) ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) = 0 % 9.89/3.00 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) % 9.89/3.00 | (29) ~ (all_0_0_0 = 0) % 9.89/3.00 | (30) relation_of2_as_subset(all_0_2_2, all_0_3_3, all_0_5_5) = 0 % 9.89/3.00 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0) % 9.89/3.00 | (32) ? [v0] : ? [v1] : powerset(v0) = v1 % 9.89/3.00 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 9.89/3.00 | (34) ? [v0] : ? [v1] : element(v1, v0) = 0 % 9.89/3.00 | (35) relation_of2_as_subset(all_0_2_2, all_0_3_3, all_0_4_4) = all_0_0_0 % 9.89/3.00 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 9.89/3.00 | (37) relation_rng(all_0_2_2) = all_0_1_1 % 9.89/3.00 | (38) ? [v0] : ? [v1] : relation_rng(v0) = v1 % 9.89/3.00 | (39) ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) = 0 % 9.89/3.00 | (40) ? [v0] : ? [v1] : relation_dom(v0) = v1 % 9.89/3.00 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ (relation_of2(v4, v3, v2) = v0)) % 9.89/3.00 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) % 9.89/3.00 | (43) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & relation_rng(v0) = v2 & subset(v0, v3) = 0 & cartesian_product2(v1, v2) = v3) | ( ~ (v2 = 0) & relation(v0) = v2))) % 9.89/3.01 | (44) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 9.89/3.01 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & relation_rng(v2) = v4 & subset(v4, v1) = 0 & subset(v3, v0) = 0)) % 9.89/3.01 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 9.89/3.01 | (47) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_dom(v0) = v1 & relation_rng(v0) = v2 & subset(v0, v3) = 0 & cartesian_product2(v1, v2) = v3)) % 9.89/3.01 | (48) subset(all_0_1_1, all_0_4_4) = 0 % 9.89/3.01 | (49) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 % 9.89/3.01 | (50) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) % 9.89/3.01 | (51) ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2_as_subset(v2, v1, v0) = v3 % 9.89/3.01 | % 9.89/3.01 | Instantiating formula (18) with all_0_1_1, all_0_2_2 and discharging atoms relation_rng(all_0_2_2) = all_0_1_1, yields: % 9.89/3.01 | (52) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & relation_dom(all_0_2_2) = v0 & subset(all_0_2_2, v1) = 0 & cartesian_product2(v0, all_0_1_1) = v1) | ( ~ (v0 = 0) & relation(all_0_2_2) = v0)) % 9.89/3.01 | % 9.89/3.01 | Instantiating formula (14) with all_0_0_0, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms relation_of2_as_subset(all_0_2_2, all_0_3_3, all_0_4_4) = all_0_0_0, yields: % 9.89/3.01 | (53) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & relation_of2(all_0_2_2, all_0_3_3, all_0_4_4) = v0) % 9.89/3.01 | % 9.89/3.01 | Instantiating formula (17) with all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms relation_of2_as_subset(all_0_2_2, all_0_3_3, all_0_5_5) = 0, yields: % 9.89/3.01 | (54) relation_of2(all_0_2_2, all_0_3_3, all_0_5_5) = 0 % 9.89/3.01 | % 9.89/3.01 | Instantiating formula (45) with all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms relation_of2_as_subset(all_0_2_2, all_0_3_3, all_0_5_5) = 0, yields: % 9.89/3.01 | (55) ? [v0] : ? [v1] : (relation_dom(all_0_2_2) = v0 & relation_rng(all_0_2_2) = v1 & subset(v1, all_0_5_5) = 0 & subset(v0, all_0_3_3) = 0) % 9.89/3.01 | % 9.89/3.01 | Instantiating formula (20) with all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms relation_of2_as_subset(all_0_2_2, all_0_3_3, all_0_5_5) = 0, yields: % 9.89/3.01 | (56) ? [v0] : ? [v1] : (cartesian_product2(all_0_3_3, all_0_5_5) = v0 & powerset(v0) = v1 & element(all_0_2_2, v1) = 0) % 9.89/3.01 | % 9.89/3.01 | Instantiating (52) with all_37_0_41, all_37_1_42, all_37_2_43 yields: % 9.89/3.01 | (57) (all_37_0_41 = 0 & relation_dom(all_0_2_2) = all_37_2_43 & subset(all_0_2_2, all_37_1_42) = 0 & cartesian_product2(all_37_2_43, all_0_1_1) = all_37_1_42) | ( ~ (all_37_2_43 = 0) & relation(all_0_2_2) = all_37_2_43) % 9.89/3.01 | % 9.89/3.01 | Instantiating (56) with all_38_0_44, all_38_1_45 yields: % 9.89/3.01 | (58) cartesian_product2(all_0_3_3, all_0_5_5) = all_38_1_45 & powerset(all_38_1_45) = all_38_0_44 & element(all_0_2_2, all_38_0_44) = 0 % 9.89/3.01 | % 9.89/3.01 | Applying alpha-rule on (58) yields: % 9.89/3.01 | (59) cartesian_product2(all_0_3_3, all_0_5_5) = all_38_1_45 % 9.89/3.01 | (60) powerset(all_38_1_45) = all_38_0_44 % 9.89/3.01 | (61) element(all_0_2_2, all_38_0_44) = 0 % 9.89/3.01 | % 9.89/3.01 | Instantiating (55) with all_44_0_50, all_44_1_51 yields: % 9.89/3.01 | (62) relation_dom(all_0_2_2) = all_44_1_51 & relation_rng(all_0_2_2) = all_44_0_50 & subset(all_44_0_50, all_0_5_5) = 0 & subset(all_44_1_51, all_0_3_3) = 0 % 9.89/3.01 | % 9.89/3.01 | Applying alpha-rule on (62) yields: % 9.89/3.01 | (63) relation_dom(all_0_2_2) = all_44_1_51 % 9.89/3.01 | (64) relation_rng(all_0_2_2) = all_44_0_50 % 9.89/3.01 | (65) subset(all_44_0_50, all_0_5_5) = 0 % 9.89/3.01 | (66) subset(all_44_1_51, all_0_3_3) = 0 % 9.89/3.01 | % 9.89/3.01 +-Applying beta-rule and splitting (53), into two cases. % 9.89/3.01 |-Branch one: % 9.89/3.01 | (67) all_0_0_0 = 0 % 9.89/3.01 | % 9.89/3.01 | Equations (67) can reduce 29 to: % 9.89/3.01 | (68) $false % 9.89/3.01 | % 9.89/3.01 |-The branch is then unsatisfiable % 9.89/3.01 |-Branch two: % 9.89/3.01 | (29) ~ (all_0_0_0 = 0) % 9.89/3.01 | (70) ? [v0] : ( ~ (v0 = 0) & relation_of2(all_0_2_2, all_0_3_3, all_0_4_4) = v0) % 9.89/3.01 | % 9.89/3.01 | Instantiating (70) with all_50_0_52 yields: % 9.89/3.01 | (71) ~ (all_50_0_52 = 0) & relation_of2(all_0_2_2, all_0_3_3, all_0_4_4) = all_50_0_52 % 9.89/3.01 | % 9.89/3.01 | Applying alpha-rule on (71) yields: % 9.89/3.01 | (72) ~ (all_50_0_52 = 0) % 9.89/3.01 | (73) relation_of2(all_0_2_2, all_0_3_3, all_0_4_4) = all_50_0_52 % 9.89/3.01 | % 9.89/3.01 | Instantiating formula (7) with all_0_2_2, all_44_0_50, all_0_1_1 and discharging atoms relation_rng(all_0_2_2) = all_44_0_50, relation_rng(all_0_2_2) = all_0_1_1, yields: % 9.89/3.01 | (74) all_44_0_50 = all_0_1_1 % 9.89/3.01 | % 9.89/3.01 | From (74) and (64) follows: % 9.89/3.02 | (37) relation_rng(all_0_2_2) = all_0_1_1 % 9.89/3.02 | % 9.89/3.02 | Instantiating formula (43) with all_44_1_51, all_0_2_2 and discharging atoms relation_dom(all_0_2_2) = all_44_1_51, yields: % 9.89/3.02 | (76) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & relation_rng(all_0_2_2) = v0 & subset(all_0_2_2, v1) = 0 & cartesian_product2(all_44_1_51, v0) = v1) | ( ~ (v0 = 0) & relation(all_0_2_2) = v0)) % 9.89/3.02 | % 9.89/3.02 | Instantiating formula (25) with all_50_0_52, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms relation_of2(all_0_2_2, all_0_3_3, all_0_4_4) = all_50_0_52, yields: % 9.89/3.02 | (77) all_50_0_52 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & subset(all_0_2_2, v0) = v1 & cartesian_product2(all_0_3_3, all_0_4_4) = v0) % 9.89/3.02 | % 9.89/3.02 | Instantiating formula (5) with all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms relation_of2(all_0_2_2, all_0_3_3, all_0_5_5) = 0, yields: % 9.89/3.02 | (78) ? [v0] : (subset(all_0_2_2, v0) = 0 & cartesian_product2(all_0_3_3, all_0_5_5) = v0) % 9.89/3.02 | % 9.89/3.02 | Instantiating formula (3) with all_38_0_44, all_38_1_45, all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms cartesian_product2(all_0_3_3, all_0_5_5) = all_38_1_45, powerset(all_38_1_45) = all_38_0_44, element(all_0_2_2, all_38_0_44) = 0, yields: % 9.89/3.02 | (79) relation(all_0_2_2) = 0 % 9.89/3.02 | % 9.89/3.02 | Instantiating (78) with all_70_0_57 yields: % 9.89/3.02 | (80) subset(all_0_2_2, all_70_0_57) = 0 & cartesian_product2(all_0_3_3, all_0_5_5) = all_70_0_57 % 9.89/3.02 | % 9.89/3.02 | Applying alpha-rule on (80) yields: % 9.89/3.02 | (81) subset(all_0_2_2, all_70_0_57) = 0 % 9.89/3.02 | (82) cartesian_product2(all_0_3_3, all_0_5_5) = all_70_0_57 % 9.89/3.02 | % 9.89/3.02 | Instantiating (76) with all_81_0_67, all_81_1_68, all_81_2_69 yields: % 9.89/3.02 | (83) (all_81_0_67 = 0 & relation_rng(all_0_2_2) = all_81_2_69 & subset(all_0_2_2, all_81_1_68) = 0 & cartesian_product2(all_44_1_51, all_81_2_69) = all_81_1_68) | ( ~ (all_81_2_69 = 0) & relation(all_0_2_2) = all_81_2_69) % 9.89/3.02 | % 9.89/3.02 +-Applying beta-rule and splitting (57), into two cases. % 9.89/3.02 |-Branch one: % 9.89/3.02 | (84) all_37_0_41 = 0 & relation_dom(all_0_2_2) = all_37_2_43 & subset(all_0_2_2, all_37_1_42) = 0 & cartesian_product2(all_37_2_43, all_0_1_1) = all_37_1_42 % 9.89/3.02 | % 9.89/3.02 | Applying alpha-rule on (84) yields: % 9.89/3.02 | (85) all_37_0_41 = 0 % 9.89/3.02 | (86) relation_dom(all_0_2_2) = all_37_2_43 % 9.89/3.02 | (87) subset(all_0_2_2, all_37_1_42) = 0 % 9.89/3.02 | (88) cartesian_product2(all_37_2_43, all_0_1_1) = all_37_1_42 % 9.89/3.02 | % 9.89/3.02 +-Applying beta-rule and splitting (83), into two cases. % 9.89/3.02 |-Branch one: % 9.89/3.02 | (89) all_81_0_67 = 0 & relation_rng(all_0_2_2) = all_81_2_69 & subset(all_0_2_2, all_81_1_68) = 0 & cartesian_product2(all_44_1_51, all_81_2_69) = all_81_1_68 % 9.89/3.02 | % 9.89/3.02 | Applying alpha-rule on (89) yields: % 9.89/3.02 | (90) all_81_0_67 = 0 % 9.89/3.02 | (91) relation_rng(all_0_2_2) = all_81_2_69 % 9.89/3.02 | (92) subset(all_0_2_2, all_81_1_68) = 0 % 9.89/3.02 | (93) cartesian_product2(all_44_1_51, all_81_2_69) = all_81_1_68 % 9.89/3.02 | % 9.89/3.02 +-Applying beta-rule and splitting (77), into two cases. % 9.89/3.02 |-Branch one: % 9.89/3.02 | (94) all_50_0_52 = 0 % 9.89/3.02 | % 9.89/3.02 | Equations (94) can reduce 72 to: % 9.89/3.02 | (68) $false % 9.89/3.02 | % 9.89/3.02 |-The branch is then unsatisfiable % 9.89/3.02 |-Branch two: % 9.89/3.02 | (72) ~ (all_50_0_52 = 0) % 9.89/3.02 | (97) ? [v0] : ? [v1] : ( ~ (v1 = 0) & subset(all_0_2_2, v0) = v1 & cartesian_product2(all_0_3_3, all_0_4_4) = v0) % 9.89/3.02 | % 9.89/3.02 | Instantiating (97) with all_102_0_73, all_102_1_74 yields: % 9.89/3.02 | (98) ~ (all_102_0_73 = 0) & subset(all_0_2_2, all_102_1_74) = all_102_0_73 & cartesian_product2(all_0_3_3, all_0_4_4) = all_102_1_74 % 9.89/3.02 | % 9.89/3.02 | Applying alpha-rule on (98) yields: % 9.89/3.02 | (99) ~ (all_102_0_73 = 0) % 9.89/3.02 | (100) subset(all_0_2_2, all_102_1_74) = all_102_0_73 % 9.89/3.02 | (101) cartesian_product2(all_0_3_3, all_0_4_4) = all_102_1_74 % 9.89/3.02 | % 9.89/3.02 | Instantiating formula (33) with all_0_2_2, all_37_2_43, all_44_1_51 and discharging atoms relation_dom(all_0_2_2) = all_44_1_51, relation_dom(all_0_2_2) = all_37_2_43, yields: % 9.89/3.02 | (102) all_44_1_51 = all_37_2_43 % 9.89/3.02 | % 9.89/3.02 | Instantiating formula (7) with all_0_2_2, all_81_2_69, all_0_1_1 and discharging atoms relation_rng(all_0_2_2) = all_81_2_69, relation_rng(all_0_2_2) = all_0_1_1, yields: % 9.89/3.02 | (103) all_81_2_69 = all_0_1_1 % 9.89/3.02 | % 9.89/3.02 | Instantiating formula (19) with all_0_3_3, all_0_5_5, all_70_0_57, all_38_1_45 and discharging atoms cartesian_product2(all_0_3_3, all_0_5_5) = all_70_0_57, cartesian_product2(all_0_3_3, all_0_5_5) = all_38_1_45, yields: % 9.89/3.02 | (104) all_70_0_57 = all_38_1_45 % 9.89/3.02 | % 9.89/3.02 | From (102) and (66) follows: % 9.89/3.02 | (105) subset(all_37_2_43, all_0_3_3) = 0 % 9.89/3.02 | % 9.89/3.02 | From (104) and (81) follows: % 9.89/3.02 | (106) subset(all_0_2_2, all_38_1_45) = 0 % 9.89/3.02 | % 9.89/3.02 | From (102)(103) and (93) follows: % 9.89/3.02 | (107) cartesian_product2(all_37_2_43, all_0_1_1) = all_81_1_68 % 9.89/3.02 | % 9.89/3.02 | Instantiating formula (19) with all_37_2_43, all_0_1_1, all_81_1_68, all_37_1_42 and discharging atoms cartesian_product2(all_37_2_43, all_0_1_1) = all_81_1_68, cartesian_product2(all_37_2_43, all_0_1_1) = all_37_1_42, yields: % 9.89/3.02 | (108) all_81_1_68 = all_37_1_42 % 9.89/3.02 | % 9.89/3.02 | From (108) and (92) follows: % 9.89/3.02 | (87) subset(all_0_2_2, all_37_1_42) = 0 % 9.89/3.02 | % 9.89/3.02 | From (108) and (107) follows: % 9.89/3.02 | (88) cartesian_product2(all_37_2_43, all_0_1_1) = all_37_1_42 % 9.89/3.02 | % 9.89/3.02 | Instantiating formula (50) with all_102_0_73, all_102_1_74, all_0_2_2 and discharging atoms subset(all_0_2_2, all_102_1_74) = all_102_0_73, yields: % 9.89/3.02 | (111) all_102_0_73 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_102_1_74) = v0 & element(all_0_2_2, v0) = v1) % 9.89/3.02 | % 9.89/3.02 | Instantiating formula (28) with all_102_0_73, all_102_1_74, all_38_1_45, all_0_2_2 and discharging atoms subset(all_0_2_2, all_102_1_74) = all_102_0_73, subset(all_0_2_2, all_38_1_45) = 0, yields: % 9.89/3.02 | (112) all_102_0_73 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_38_1_45, all_102_1_74) = v0) % 9.89/3.02 | % 9.89/3.02 | Instantiating formula (28) with all_102_0_73, all_102_1_74, all_37_1_42, all_0_2_2 and discharging atoms subset(all_0_2_2, all_102_1_74) = all_102_0_73, subset(all_0_2_2, all_37_1_42) = 0, yields: % 9.89/3.02 | (113) all_102_0_73 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_37_1_42, all_102_1_74) = v0) % 9.89/3.02 | % 9.89/3.02 +-Applying beta-rule and splitting (111), into two cases. % 9.89/3.02 |-Branch one: % 9.89/3.02 | (114) all_102_0_73 = 0 % 9.89/3.02 | % 9.89/3.02 | Equations (114) can reduce 99 to: % 9.89/3.03 | (68) $false % 9.89/3.03 | % 9.89/3.03 |-The branch is then unsatisfiable % 9.89/3.03 |-Branch two: % 9.89/3.03 | (99) ~ (all_102_0_73 = 0) % 9.89/3.03 | (117) ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_102_1_74) = v0 & element(all_0_2_2, v0) = v1) % 9.89/3.03 | % 9.89/3.03 +-Applying beta-rule and splitting (112), into two cases. % 9.89/3.03 |-Branch one: % 9.89/3.03 | (114) all_102_0_73 = 0 % 9.89/3.03 | % 9.89/3.03 | Equations (114) can reduce 99 to: % 9.89/3.03 | (68) $false % 9.89/3.03 | % 9.89/3.03 |-The branch is then unsatisfiable % 9.89/3.03 |-Branch two: % 9.89/3.03 | (99) ~ (all_102_0_73 = 0) % 9.89/3.03 | (121) ? [v0] : ( ~ (v0 = 0) & subset(all_38_1_45, all_102_1_74) = v0) % 9.89/3.03 | % 9.89/3.03 +-Applying beta-rule and splitting (113), into two cases. % 9.89/3.03 |-Branch one: % 9.89/3.03 | (114) all_102_0_73 = 0 % 9.89/3.03 | % 9.89/3.03 | Equations (114) can reduce 99 to: % 9.89/3.03 | (68) $false % 9.89/3.03 | % 9.89/3.03 |-The branch is then unsatisfiable % 9.89/3.03 |-Branch two: % 9.89/3.03 | (99) ~ (all_102_0_73 = 0) % 9.89/3.03 | (125) ? [v0] : ( ~ (v0 = 0) & subset(all_37_1_42, all_102_1_74) = v0) % 9.89/3.03 | % 9.89/3.03 | Instantiating (125) with all_149_0_88 yields: % 9.89/3.03 | (126) ~ (all_149_0_88 = 0) & subset(all_37_1_42, all_102_1_74) = all_149_0_88 % 9.89/3.03 | % 9.89/3.03 | Applying alpha-rule on (126) yields: % 9.89/3.03 | (127) ~ (all_149_0_88 = 0) % 9.89/3.03 | (128) subset(all_37_1_42, all_102_1_74) = all_149_0_88 % 9.89/3.03 | % 9.89/3.03 | Instantiating formula (4) with all_149_0_88, all_102_1_74, all_37_1_42, all_0_4_4, all_0_1_1, all_0_3_3, all_37_2_43 and discharging atoms subset(all_37_1_42, all_102_1_74) = all_149_0_88, cartesian_product2(all_37_2_43, all_0_1_1) = all_37_1_42, cartesian_product2(all_0_3_3, all_0_4_4) = all_102_1_74, yields: % 9.89/3.03 | (129) all_149_0_88 = 0 | ? [v0] : (( ~ (v0 = 0) & subset(all_37_2_43, all_0_3_3) = v0) | ( ~ (v0 = 0) & subset(all_0_1_1, all_0_4_4) = v0)) % 9.89/3.03 | % 9.89/3.03 +-Applying beta-rule and splitting (129), into two cases. % 9.89/3.03 |-Branch one: % 9.89/3.03 | (130) all_149_0_88 = 0 % 9.89/3.03 | % 9.89/3.03 | Equations (130) can reduce 127 to: % 9.89/3.03 | (68) $false % 9.89/3.03 | % 9.89/3.03 |-The branch is then unsatisfiable % 9.89/3.03 |-Branch two: % 9.89/3.03 | (127) ~ (all_149_0_88 = 0) % 9.89/3.03 | (133) ? [v0] : (( ~ (v0 = 0) & subset(all_37_2_43, all_0_3_3) = v0) | ( ~ (v0 = 0) & subset(all_0_1_1, all_0_4_4) = v0)) % 9.89/3.03 | % 9.89/3.03 | Instantiating (133) with all_171_0_90 yields: % 9.89/3.03 | (134) ( ~ (all_171_0_90 = 0) & subset(all_37_2_43, all_0_3_3) = all_171_0_90) | ( ~ (all_171_0_90 = 0) & subset(all_0_1_1, all_0_4_4) = all_171_0_90) % 9.89/3.03 | % 9.89/3.03 +-Applying beta-rule and splitting (134), into two cases. % 9.89/3.03 |-Branch one: % 9.89/3.03 | (135) ~ (all_171_0_90 = 0) & subset(all_37_2_43, all_0_3_3) = all_171_0_90 % 9.89/3.03 | % 9.89/3.03 | Applying alpha-rule on (135) yields: % 9.89/3.03 | (136) ~ (all_171_0_90 = 0) % 9.89/3.03 | (137) subset(all_37_2_43, all_0_3_3) = all_171_0_90 % 9.89/3.03 | % 9.89/3.03 | Instantiating formula (22) with all_37_2_43, all_0_3_3, all_171_0_90, 0 and discharging atoms subset(all_37_2_43, all_0_3_3) = all_171_0_90, subset(all_37_2_43, all_0_3_3) = 0, yields: % 9.89/3.03 | (138) all_171_0_90 = 0 % 9.89/3.03 | % 9.89/3.03 | Equations (138) can reduce 136 to: % 9.89/3.03 | (68) $false % 9.89/3.03 | % 9.89/3.03 |-The branch is then unsatisfiable % 9.89/3.03 |-Branch two: % 9.89/3.03 | (140) ~ (all_171_0_90 = 0) & subset(all_0_1_1, all_0_4_4) = all_171_0_90 % 9.89/3.03 | % 9.89/3.03 | Applying alpha-rule on (140) yields: % 9.89/3.03 | (136) ~ (all_171_0_90 = 0) % 9.89/3.03 | (142) subset(all_0_1_1, all_0_4_4) = all_171_0_90 % 9.89/3.03 | % 9.89/3.03 | Instantiating formula (22) with all_0_1_1, all_0_4_4, all_171_0_90, 0 and discharging atoms subset(all_0_1_1, all_0_4_4) = all_171_0_90, subset(all_0_1_1, all_0_4_4) = 0, yields: % 9.89/3.03 | (138) all_171_0_90 = 0 % 9.89/3.03 | % 9.89/3.03 | Equations (138) can reduce 136 to: % 9.89/3.03 | (68) $false % 9.89/3.03 | % 9.89/3.03 |-The branch is then unsatisfiable % 9.89/3.03 |-Branch two: % 9.89/3.03 | (145) ~ (all_81_2_69 = 0) & relation(all_0_2_2) = all_81_2_69 % 9.89/3.03 | % 9.89/3.03 | Applying alpha-rule on (145) yields: % 9.89/3.03 | (146) ~ (all_81_2_69 = 0) % 9.89/3.03 | (147) relation(all_0_2_2) = all_81_2_69 % 9.89/3.03 | % 9.89/3.03 | Instantiating formula (36) with all_0_2_2, 0, all_81_2_69 and discharging atoms relation(all_0_2_2) = all_81_2_69, relation(all_0_2_2) = 0, yields: % 9.89/3.03 | (148) all_81_2_69 = 0 % 9.89/3.03 | % 9.89/3.03 | Equations (148) can reduce 146 to: % 9.89/3.03 | (68) $false % 9.89/3.03 | % 9.89/3.03 |-The branch is then unsatisfiable % 9.89/3.03 |-Branch two: % 9.89/3.03 | (150) ~ (all_37_2_43 = 0) & relation(all_0_2_2) = all_37_2_43 % 9.89/3.03 | % 9.89/3.03 | Applying alpha-rule on (150) yields: % 9.89/3.03 | (151) ~ (all_37_2_43 = 0) % 9.89/3.03 | (152) relation(all_0_2_2) = all_37_2_43 % 9.89/3.03 | % 9.89/3.03 | Instantiating formula (36) with all_0_2_2, 0, all_37_2_43 and discharging atoms relation(all_0_2_2) = all_37_2_43, relation(all_0_2_2) = 0, yields: % 9.89/3.03 | (153) all_37_2_43 = 0 % 9.89/3.03 | % 9.89/3.03 | Equations (153) can reduce 151 to: % 9.89/3.03 | (68) $false % 9.89/3.03 | % 9.89/3.03 |-The branch is then unsatisfiable % 9.89/3.03 % SZS output end Proof for theBenchmark % 9.89/3.03 % 9.89/3.03 2363ms %------------------------------------------------------------------------------