%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU264+1 : TPTP v8.1.0. Released v3.3.0. % 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 08:48:17 EDT 2022 % Result : Theorem 3.80s 1.55s % Output : Proof 5.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU264+1 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n019.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sun Jun 19 16:59:24 EDT 2022 % 0.12/0.34 % CPUTime : % 0.49/0.58 ____ _ % 0.49/0.58 ___ / __ \_____(_)___ ________ __________ % 0.49/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.49/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.49/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.49/0.58 % 0.49/0.58 A Theorem Prover for First-Order Logic % 0.49/0.58 (ePrincess v.1.0) % 0.49/0.58 % 0.49/0.58 (c) Philipp Rümmer, 2009-2015 % 0.49/0.58 (c) Peter Backeman, 2014-2015 % 0.49/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.49/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.49/0.58 Bug reports to peter@backeman.se % 0.49/0.58 % 0.49/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.49/0.58 % 0.49/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.49/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.34/0.90 Prover 0: Preprocessing ... % 1.70/1.03 Prover 0: Warning: ignoring some quantifiers % 1.70/1.05 Prover 0: Constructing countermodel ... % 2.25/1.18 Prover 0: gave up % 2.25/1.18 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.25/1.20 Prover 1: Preprocessing ... % 2.69/1.28 Prover 1: Warning: ignoring some quantifiers % 2.69/1.29 Prover 1: Constructing countermodel ... % 2.90/1.35 Prover 1: gave up % 2.90/1.36 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.97/1.37 Prover 2: Preprocessing ... % 3.24/1.45 Prover 2: Warning: ignoring some quantifiers % 3.24/1.46 Prover 2: Constructing countermodel ... % 3.80/1.55 Prover 2: proved (196ms) % 3.80/1.55 % 3.80/1.55 No countermodel exists, formula is valid % 3.80/1.55 % SZS status Theorem for theBenchmark % 3.80/1.55 % 3.80/1.55 Generating proof ... Warning: ignoring some quantifiers % 4.97/1.84 found it (size 29) % 4.97/1.84 % 4.97/1.84 % SZS output start Proof for theBenchmark % 4.97/1.84 Assumed formulas after preprocessing and simplification: % 4.97/1.84 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = 0 & relation_of2_as_subset(v3, v2, v1) = v4 & relation_of2_as_subset(v3, v2, v0) = 0 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (cartesian_product2(v5, v6) = v8) | ~ (powerset(v8) = v9) | ~ (element(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & relation_of2_as_subset(v7, v5, v6) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (relation_of2_as_subset(v8, v7, v6) = v9) | ~ (relation_of2_as_subset(v8, v7, v5) = 0) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & relation_rng(v8) = v10 & subset(v10, v6) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (relation_of2(v9, v8, v7) = v6) | ~ (relation_of2(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (relation_of2_as_subset(v9, v8, v7) = v6) | ~ (relation_of2_as_subset(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (relation_rng(v8) = v9) | ~ (subset(v9, v6) = 0) | ~ (relation_of2_as_subset(v8, v7, v5) = 0) | relation_of2_as_subset(v8, v7, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (cartesian_product2(v5, v6) = v8) | ~ (powerset(v8) = v9) | ~ (element(v7, v9) = 0) | relation(v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v6, v7) = 0) | ~ (subset(v5, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & subset(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v5, v7) = v8) | ~ (subset(v5, v6) = 0) | ? [v9] : ( ~ (v9 = 0) & subset(v6, v7) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (relation_of2(v7, v5, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & relation_of2_as_subset(v7, v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (relation_of2_as_subset(v7, v5, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & relation_of2(v7, v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (powerset(v6) = v7) | ~ (element(v5, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & subset(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (subset(v8, v7) = v6) | ~ (subset(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (cartesian_product2(v8, v7) = v6) | ~ (cartesian_product2(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (element(v8, v7) = v6) | ~ (element(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & powerset(v6) = v8 & element(v5, v8) = v9)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (relation_dom(v7) = v6) | ~ (relation_dom(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (relation_rng(v7) = v6) | ~ (relation_rng(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (powerset(v7) = v6) | ~ (powerset(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (relation(v7) = v6) | ~ (relation(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (subset(v6, v7) = 0) | ~ (subset(v5, v6) = 0) | subset(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_of2(v7, v5, v6) = 0) | relation_of2_as_subset(v7, v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_of2_as_subset(v7, v5, v6) = 0) | relation_of2(v7, v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_of2_as_subset(v7, v5, v6) = 0) | ? [v8] : ? [v9] : (relation_dom(v7) = v8 & relation_rng(v7) = v9 & subset(v9, v6) = 0 & subset(v8, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_of2_as_subset(v7, v5, v6) = 0) | ? [v8] : ? [v9] : (cartesian_product2(v5, v6) = v8 & powerset(v8) = v9 & element(v7, v9) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (powerset(v6) = v7) | ~ (element(v5, v7) = 0) | subset(v5, v6) = 0) & ! [v5] : ! [v6] : (v6 = 0 | ~ (subset(v5, v5) = v6)) & ! [v5] : ! [v6] : ( ~ (subset(v5, v6) = 0) | ? [v7] : (powerset(v6) = v7 & element(v5, v7) = 0)) & ? [v5] : ? [v6] : ? [v7] : ? [v8] : relation_of2(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : relation_of2_as_subset(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : subset(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : relation_of2(v7, v5, v6) = 0 & ? [v5] : ? [v6] : ? [v7] : relation_of2_as_subset(v7, v5, v6) = 0 & ? [v5] : ? [v6] : ? [v7] : cartesian_product2(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : element(v6, v5) = v7 & ? [v5] : ? [v6] : relation_dom(v5) = v6 & ? [v5] : ? [v6] : relation_rng(v5) = v6 & ? [v5] : ? [v6] : powerset(v5) = v6 & ? [v5] : ? [v6] : element(v6, v5) = 0 & ? [v5] : ? [v6] : relation(v5) = v6) % 5.14/1.88 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 5.14/1.88 | (1) ~ (all_0_0_0 = 0) & subset(all_0_4_4, all_0_3_3) = 0 & relation_of2_as_subset(all_0_1_1, all_0_2_2, all_0_3_3) = all_0_0_0 & relation_of2_as_subset(all_0_1_1, all_0_2_2, all_0_4_4) = 0 & ! [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 | ~ (relation_of2_as_subset(v3, v2, v1) = v4) | ~ (relation_of2_as_subset(v3, v2, v0) = 0) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & relation_rng(v3) = v5 & subset(v5, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ (relation_of2(v4, v3, v2) = v0)) & ! [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] : ( ~ (relation_rng(v3) = v4) | ~ (subset(v4, v1) = 0) | ~ (relation_of2_as_subset(v3, v2, v0) = 0) | relation_of2_as_subset(v3, v2, v1) = 0) & ! [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 | ~ (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] : ( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4)) & ! [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 | ~ (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] : (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] : ( ~ (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_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] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2_as_subset(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) = 0 & ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(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 % 5.14/1.89 | % 5.14/1.89 | Applying alpha-rule on (1) yields: % 5.14/1.89 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 5.14/1.89 | (3) ? [v0] : ? [v1] : relation_rng(v0) = v1 % 5.14/1.89 | (4) ? [v0] : ? [v1] : relation_dom(v0) = v1 % 5.14/1.89 | (5) relation_of2_as_subset(all_0_1_1, all_0_2_2, all_0_4_4) = 0 % 5.14/1.89 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 5.14/1.89 | (7) ? [v0] : ? [v1] : ? [v2] : cartesian_product2(v1, v0) = v2 % 5.14/1.89 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 5.14/1.89 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0) % 5.14/1.89 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) % 5.14/1.89 | (11) ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2(v2, v1, v0) = v3 % 5.14/1.89 | (12) ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) = 0 % 5.14/1.89 | (13) ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) = 0 % 5.14/1.89 | (14) subset(all_0_4_4, all_0_3_3) = 0 % 5.14/1.89 | (15) ~ (all_0_0_0 = 0) % 5.14/1.89 | (16) ? [v0] : ? [v1] : powerset(v0) = v1 % 5.14/1.89 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | relation_of2(v2, v0, v1) = 0) % 5.14/1.89 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | relation_of2_as_subset(v2, v0, v1) = 0) % 5.14/1.89 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) % 5.14/1.89 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 5.14/1.90 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 5.14/1.90 | (22) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) % 5.14/1.90 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_of2_as_subset(v3, v2, v1) = v4) | ~ (relation_of2_as_subset(v3, v2, v0) = 0) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & relation_rng(v3) = v5 & subset(v5, v1) = v6)) % 5.14/1.90 | (24) ! [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)) % 5.14/1.90 | (25) relation_of2_as_subset(all_0_1_1, all_0_2_2, all_0_3_3) = all_0_0_0 % 5.14/1.90 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4, v3, v2) = v0)) % 5.14/1.90 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 5.14/1.90 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 5.14/1.90 | (29) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) % 5.14/1.90 | (30) ! [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)) % 5.14/1.90 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 5.14/1.90 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = 0) | relation(v2) = 0) % 5.14/1.90 | (33) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 % 5.14/1.90 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ (subset(v4, v1) = 0) | ~ (relation_of2_as_subset(v3, v2, v0) = 0) | relation_of2_as_subset(v3, v2, v1) = 0) % 5.14/1.90 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 5.14/1.90 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 5.14/1.90 | (37) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 % 5.14/1.90 | (38) ? [v0] : ? [v1] : relation(v0) = v1 % 5.14/1.90 | (39) ! [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)) % 5.14/1.90 | (40) ? [v0] : ? [v1] : element(v1, v0) = 0 % 5.14/1.90 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2_as_subset(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4)) % 5.14/1.91 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4)) % 5.14/1.91 | (43) ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2_as_subset(v2, v1, v0) = v3 % 5.14/1.91 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ (relation_of2(v4, v3, v2) = v0)) % 5.14/1.91 | % 5.14/1.91 | Instantiating formula (23) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms relation_of2_as_subset(all_0_1_1, all_0_2_2, all_0_3_3) = all_0_0_0, relation_of2_as_subset(all_0_1_1, all_0_2_2, all_0_4_4) = 0, yields: % 5.14/1.91 | (45) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & relation_rng(all_0_1_1) = v0 & subset(v0, all_0_3_3) = v1) % 5.14/1.91 | % 5.14/1.91 | Instantiating formula (30) with all_0_1_1, all_0_4_4, all_0_2_2 and discharging atoms relation_of2_as_subset(all_0_1_1, all_0_2_2, all_0_4_4) = 0, yields: % 5.14/1.91 | (46) ? [v0] : ? [v1] : (relation_dom(all_0_1_1) = v0 & relation_rng(all_0_1_1) = v1 & subset(v1, all_0_4_4) = 0 & subset(v0, all_0_2_2) = 0) % 5.14/1.91 | % 5.14/1.91 | Instantiating (46) with all_37_0_42, all_37_1_43 yields: % 5.14/1.91 | (47) relation_dom(all_0_1_1) = all_37_1_43 & relation_rng(all_0_1_1) = all_37_0_42 & subset(all_37_0_42, all_0_4_4) = 0 & subset(all_37_1_43, all_0_2_2) = 0 % 5.14/1.91 | % 5.14/1.91 | Applying alpha-rule on (47) yields: % 5.14/1.91 | (48) relation_dom(all_0_1_1) = all_37_1_43 % 5.14/1.91 | (49) relation_rng(all_0_1_1) = all_37_0_42 % 5.14/1.91 | (50) subset(all_37_0_42, all_0_4_4) = 0 % 5.14/1.91 | (51) subset(all_37_1_43, all_0_2_2) = 0 % 5.14/1.91 | % 5.14/1.91 +-Applying beta-rule and splitting (45), into two cases. % 5.14/1.91 |-Branch one: % 5.14/1.91 | (52) all_0_0_0 = 0 % 5.14/1.91 | % 5.14/1.91 | Equations (52) can reduce 15 to: % 5.14/1.91 | (53) $false % 5.14/1.91 | % 5.14/1.91 |-The branch is then unsatisfiable % 5.14/1.91 |-Branch two: % 5.14/1.91 | (15) ~ (all_0_0_0 = 0) % 5.14/1.91 | (55) ? [v0] : ? [v1] : ( ~ (v1 = 0) & relation_rng(all_0_1_1) = v0 & subset(v0, all_0_3_3) = v1) % 5.14/1.91 | % 5.14/1.91 | Instantiating (55) with all_47_0_47, all_47_1_48 yields: % 5.14/1.91 | (56) ~ (all_47_0_47 = 0) & relation_rng(all_0_1_1) = all_47_1_48 & subset(all_47_1_48, all_0_3_3) = all_47_0_47 % 5.14/1.91 | % 5.14/1.91 | Applying alpha-rule on (56) yields: % 5.14/1.91 | (57) ~ (all_47_0_47 = 0) % 5.14/1.91 | (58) relation_rng(all_0_1_1) = all_47_1_48 % 5.14/1.91 | (59) subset(all_47_1_48, all_0_3_3) = all_47_0_47 % 5.14/1.91 | % 5.14/1.91 | Instantiating formula (8) with all_0_1_1, all_37_0_42, all_47_1_48 and discharging atoms relation_rng(all_0_1_1) = all_47_1_48, relation_rng(all_0_1_1) = all_37_0_42, yields: % 5.14/1.91 | (60) all_47_1_48 = all_37_0_42 % 5.14/1.91 | % 5.14/1.91 | From (60) and (59) follows: % 5.14/1.91 | (61) subset(all_37_0_42, all_0_3_3) = all_47_0_47 % 5.14/1.91 | % 5.14/1.91 | Instantiating formula (31) with all_47_0_47, all_0_3_3, all_0_4_4, all_37_0_42 and discharging atoms subset(all_37_0_42, all_0_3_3) = all_47_0_47, subset(all_0_4_4, all_0_3_3) = 0, yields: % 5.14/1.91 | (62) all_47_0_47 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_37_0_42, all_0_4_4) = v0) % 5.14/1.92 | % 5.14/1.92 | Instantiating formula (29) with all_47_0_47, all_0_3_3, all_37_0_42 and discharging atoms subset(all_37_0_42, all_0_3_3) = all_47_0_47, yields: % 5.14/1.92 | (63) all_47_0_47 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_0_3_3) = v0 & element(all_37_0_42, v0) = v1) % 5.14/1.92 | % 5.14/1.92 | Instantiating formula (9) with all_0_3_3, all_0_4_4, all_37_0_42 and discharging atoms subset(all_37_0_42, all_0_4_4) = 0, subset(all_0_4_4, all_0_3_3) = 0, yields: % 5.14/1.92 | (64) subset(all_37_0_42, all_0_3_3) = 0 % 5.14/1.92 | % 5.14/1.92 | Instantiating formula (19) with all_47_0_47, all_0_3_3, all_0_4_4, all_37_0_42 and discharging atoms subset(all_37_0_42, all_0_3_3) = all_47_0_47, subset(all_37_0_42, all_0_4_4) = 0, yields: % 5.14/1.92 | (65) all_47_0_47 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_0_4_4, all_0_3_3) = v0) % 5.14/1.92 | % 5.14/1.92 +-Applying beta-rule and splitting (62), into two cases. % 5.14/1.92 |-Branch one: % 5.14/1.92 | (66) all_47_0_47 = 0 % 5.14/1.92 | % 5.14/1.92 | Equations (66) can reduce 57 to: % 5.14/1.92 | (53) $false % 5.14/1.92 | % 5.14/1.92 |-The branch is then unsatisfiable % 5.14/1.92 |-Branch two: % 5.14/1.92 | (57) ~ (all_47_0_47 = 0) % 5.14/1.92 | (69) ? [v0] : ( ~ (v0 = 0) & subset(all_37_0_42, all_0_4_4) = v0) % 5.14/1.92 | % 5.14/1.92 +-Applying beta-rule and splitting (65), into two cases. % 5.14/1.92 |-Branch one: % 5.14/1.92 | (66) all_47_0_47 = 0 % 5.14/1.92 | % 5.14/1.92 | Equations (66) can reduce 57 to: % 5.14/1.92 | (53) $false % 5.14/1.92 | % 5.14/1.92 |-The branch is then unsatisfiable % 5.14/1.92 |-Branch two: % 5.14/1.92 | (57) ~ (all_47_0_47 = 0) % 5.14/1.92 | (73) ? [v0] : ( ~ (v0 = 0) & subset(all_0_4_4, all_0_3_3) = v0) % 5.14/1.92 | % 5.14/1.92 +-Applying beta-rule and splitting (63), into two cases. % 5.14/1.92 |-Branch one: % 5.14/1.92 | (66) all_47_0_47 = 0 % 5.14/1.92 | % 5.14/1.92 | Equations (66) can reduce 57 to: % 5.14/1.92 | (53) $false % 5.14/1.92 | % 5.14/1.92 |-The branch is then unsatisfiable % 5.14/1.92 |-Branch two: % 5.14/1.92 | (57) ~ (all_47_0_47 = 0) % 5.14/1.92 | (77) ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_0_3_3) = v0 & element(all_37_0_42, v0) = v1) % 5.14/1.92 | % 5.14/1.92 | Instantiating formula (2) with all_37_0_42, all_0_3_3, 0, all_47_0_47 and discharging atoms subset(all_37_0_42, all_0_3_3) = all_47_0_47, subset(all_37_0_42, all_0_3_3) = 0, yields: % 5.14/1.92 | (66) all_47_0_47 = 0 % 5.14/1.92 | % 5.14/1.92 | Equations (66) can reduce 57 to: % 5.14/1.92 | (53) $false % 5.14/1.92 | % 5.14/1.92 |-The branch is then unsatisfiable % 5.14/1.92 % SZS output end Proof for theBenchmark % 5.14/1.92 % 5.14/1.92 1330ms %------------------------------------------------------------------------------