%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU113+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n016.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 08:46:39 EDT 2022 % Result : Theorem 5.55s 1.94s % Output : Proof 9.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU113+1 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n016.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sun Jun 19 04:29:38 EDT 2022 % 0.13/0.34 % CPUTime : % 0.53/0.59 ____ _ % 0.53/0.59 ___ / __ \_____(_)___ ________ __________ % 0.53/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.53/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.53/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.53/0.59 % 0.53/0.59 A Theorem Prover for First-Order Logic % 0.53/0.59 (ePrincess v.1.0) % 0.53/0.59 % 0.53/0.59 (c) Philipp Rümmer, 2009-2015 % 0.53/0.59 (c) Peter Backeman, 2014-2015 % 0.53/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.53/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.53/0.59 Bug reports to peter@backeman.se % 0.53/0.59 % 0.53/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.53/0.59 % 0.53/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.64/0.94 Prover 0: Preprocessing ... % 2.04/1.15 Prover 0: Warning: ignoring some quantifiers % 2.25/1.17 Prover 0: Constructing countermodel ... % 3.58/1.49 Prover 0: gave up % 3.58/1.49 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.58/1.52 Prover 1: Preprocessing ... % 4.24/1.65 Prover 1: Warning: ignoring some quantifiers % 4.24/1.65 Prover 1: Constructing countermodel ... % 5.55/1.94 Prover 1: proved (452ms) % 5.55/1.94 % 5.55/1.94 No countermodel exists, formula is valid % 5.55/1.94 % SZS status Theorem for theBenchmark % 5.55/1.94 % 5.55/1.94 Generating proof ... Warning: ignoring some quantifiers % 8.75/2.65 found it (size 39) % 8.75/2.65 % 8.75/2.65 % SZS output start Proof for theBenchmark % 8.75/2.66 Assumed formulas after preprocessing and simplification: % 8.75/2.66 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & ~ (v8 = 0) & ~ (v5 = 0) & ~ (v3 = 0) & cap_closed(v7) = 0 & subset(v1, v2) = v3 & finite_subsets(v0) = v1 & powerset(v0) = v2 & diff_closed(v7) = 0 & preboolean(v7) = 0 & cup_closed(v7) = 0 & finite(v9) = 0 & empty(v9) = v10 & empty(v7) = v8 & empty(v6) = 0 & empty(v4) = v5 & empty(empty_set) = 0 & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (powerset(v12) = v13) | ~ (element(v11, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & subset(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (subset(v14, v13) = v12) | ~ (subset(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (element(v14, v13) = v12) | ~ (element(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (in(v14, v13) = v12) | ~ (in(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (subset(v13, v11) = v14) | ~ (finite_subsets(v11) = v12) | ~ (preboolean(v12) = 0) | ? [v15] : ? [v16] : (finite(v13) = v16 & in(v13, v12) = v15 & ( ~ (v15 = 0) | (v16 = 0 & v14 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ (element(v12, v14) = 0) | ~ (in(v11, v12) = 0) | element(v11, v13) = 0) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ (element(v12, v14) = 0) | ~ (in(v11, v12) = 0) | ? [v15] : ( ~ (v15 = 0) & empty(v13) = v15)) & ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (finite_subsets(v11) = v13) | ~ (preboolean(v12) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (subset(v14, v11) = v16 & finite(v14) = v17 & in(v14, v12) = v15 & ( ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0)) & (v15 = 0 | (v17 = 0 & v16 = 0)))) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v11, v12) = v13) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & in(v14, v12) = v15 & in(v14, v11) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (in(v11, v12) = v13) | ? [v14] : ? [v15] : (element(v11, v12) = v14 & empty(v12) = v15 & ( ~ (v14 = 0) | v15 = 0))) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation(v13) = v12) | ~ (relation(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (function(v13) = v12) | ~ (function(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (one_to_one(v13) = v12) | ~ (one_to_one(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (epsilon_transitive(v13) = v12) | ~ (epsilon_transitive(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (epsilon_connected(v13) = v12) | ~ (epsilon_connected(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (ordinal(v13) = v12) | ~ (ordinal(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (natural(v13) = v12) | ~ (natural(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (cap_closed(v13) = v12) | ~ (cap_closed(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (finite_subsets(v13) = v12) | ~ (finite_subsets(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (powerset(v13) = v12) | ~ (powerset(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (diff_closed(v13) = v12) | ~ (diff_closed(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (preboolean(v13) = v12) | ~ (preboolean(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (cup_closed(v13) = v12) | ~ (cup_closed(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (finite(v13) = v12) | ~ (finite(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (empty(v13) = v12) | ~ (empty(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (subset(v13, v11) = 0) | ~ (finite_subsets(v11) = v12) | ~ (preboolean(v12) = 0) | ? [v14] : ? [v15] : (finite(v13) = v14 & in(v13, v12) = v15 & ( ~ (v14 = 0) | v15 = 0))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (subset(v11, v12) = 0) | ~ (in(v13, v11) = 0) | in(v13, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (finite_subsets(v11) = v13) | ~ (element(v12, v13) = 0) | finite(v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ (element(v11, v13) = 0) | subset(v11, v12) = 0) & ! [v11] : ! [v12] : (v12 = v11 | ~ (empty(v12) = 0) | ~ (empty(v11) = 0)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v11, v11) = v12)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (finite(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v11) = v13)) & ! [v11] : ! [v12] : ( ~ (finite_subsets(v11) = v12) | diff_closed(v12) = 0) & ! [v11] : ! [v12] : ( ~ (finite_subsets(v11) = v12) | preboolean(v12) = 0) & ! [v11] : ! [v12] : ( ~ (finite_subsets(v11) = v12) | cup_closed(v12) = 0) & ! [v11] : ! [v12] : ( ~ (finite_subsets(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | diff_closed(v12) = 0) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | preboolean(v12) = 0) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | cup_closed(v12) = 0) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = 0 & v14 = 0 & ~ (v15 = 0) & element(v13, v12) = 0 & finite(v13) = 0 & empty(v13) = v15) | (v13 = 0 & empty(v11) = 0))) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ((v14 = 0 & ~ (v15 = 0) & element(v13, v12) = 0 & empty(v13) = v15) | (v13 = 0 & empty(v11) = 0))) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : (relation(v13) = 0 & function(v13) = 0 & one_to_one(v13) = 0 & epsilon_transitive(v13) = 0 & epsilon_connected(v13) = 0 & ordinal(v13) = 0 & natural(v13) = 0 & element(v13, v12) = 0 & finite(v13) = 0 & empty(v13) = 0)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : (element(v13, v12) = 0 & empty(v13) = 0)) & ! [v11] : ! [v12] : ( ~ (diff_closed(v11) = v12) | ? [v13] : ? [v14] : (preboolean(v11) = v13 & cup_closed(v11) = v14 & ( ~ (v13 = 0) | (v14 = 0 & v12 = 0)))) & ! [v11] : ! [v12] : ( ~ (in(v11, v12) = 0) | element(v11, v12) = 0) & ! [v11] : ! [v12] : ( ~ (in(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (in(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & in(v12, v11) = v13)) & ! [v11] : (v11 = empty_set | ~ (empty(v11) = 0)) & ! [v11] : ( ~ (diff_closed(v11) = 0) | ? [v12] : ? [v13] : (preboolean(v11) = v13 & cup_closed(v11) = v12 & ( ~ (v12 = 0) | v13 = 0))) & ! [v11] : ( ~ (finite(v11) = 0) | ? [v12] : (powerset(v11) = v12 & ! [v13] : ( ~ (element(v13, v12) = 0) | finite(v13) = 0))) & ? [v11] : ? [v12] : element(v12, v11) = 0) % 9.06/2.70 | 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, all_0_9_9, all_0_10_10 yields: % 9.06/2.70 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_2_2 = 0) & ~ (all_0_5_5 = 0) & ~ (all_0_7_7 = 0) & cap_closed(all_0_3_3) = 0 & subset(all_0_9_9, all_0_8_8) = all_0_7_7 & finite_subsets(all_0_10_10) = all_0_9_9 & powerset(all_0_10_10) = all_0_8_8 & diff_closed(all_0_3_3) = 0 & preboolean(all_0_3_3) = 0 & cup_closed(all_0_3_3) = 0 & finite(all_0_1_1) = 0 & empty(all_0_1_1) = all_0_0_0 & empty(all_0_3_3) = all_0_2_2 & empty(all_0_4_4) = 0 & empty(all_0_6_6) = all_0_5_5 & empty(empty_set) = 0 & ! [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 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v2, v0) = v3) | ~ (finite_subsets(v0) = v1) | ~ (preboolean(v1) = 0) | ? [v4] : ? [v5] : (finite(v2) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (finite_subsets(v0) = v2) | ~ (preboolean(v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (subset(v3, v0) = v5 & finite(v3) = v6 & in(v3, v1) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v6 = 0 & v5 = 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 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (natural(v2) = v1) | ~ (natural(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cap_closed(v2) = v1) | ~ (cap_closed(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite_subsets(v2) = v1) | ~ (finite_subsets(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (diff_closed(v2) = v1) | ~ (diff_closed(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (preboolean(v2) = v1) | ~ (preboolean(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cup_closed(v2) = v1) | ~ (cup_closed(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite(v2) = v1) | ~ (finite(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v2, v0) = 0) | ~ (finite_subsets(v0) = v1) | ~ (preboolean(v1) = 0) | ? [v3] : ? [v4] : (finite(v2) = v3 & in(v2, v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v2) | ~ (element(v1, v2) = 0) | finite(v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (finite(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | diff_closed(v1) = 0) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | preboolean(v1) = 0) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | cup_closed(v1) = 0) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | diff_closed(v1) = 0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | preboolean(v1) = 0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | cup_closed(v1) = 0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & finite(v2) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (relation(v2) = 0 & function(v2) = 0 & one_to_one(v2) = 0 & epsilon_transitive(v2) = 0 & epsilon_connected(v2) = 0 & ordinal(v2) = 0 & natural(v2) = 0 & element(v2, v1) = 0 & finite(v2) = 0 & empty(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (diff_closed(v0) = v1) | ? [v2] : ? [v3] : (preboolean(v0) = v2 & cup_closed(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) & ! [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] : ( ~ (diff_closed(v0) = 0) | ? [v1] : ? [v2] : (preboolean(v0) = v2 & cup_closed(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))) & ! [v0] : ( ~ (finite(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | finite(v2) = 0))) & ? [v0] : ? [v1] : element(v1, v0) = 0 % 9.06/2.72 | % 9.06/2.72 | Applying alpha-rule on (1) yields: % 9.06/2.72 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cap_closed(v2) = v1) | ~ (cap_closed(v2) = v0)) % 9.06/2.72 | (3) ~ (all_0_7_7 = 0) % 9.06/2.72 | (4) ~ (all_0_5_5 = 0) % 9.06/2.72 | (5) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) % 9.06/2.72 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 9.06/2.72 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 9.06/2.72 | (8) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 9.06/2.72 | (9) subset(all_0_9_9, all_0_8_8) = all_0_7_7 % 9.06/2.72 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (finite_subsets(v0) = v2) | ~ (preboolean(v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (subset(v3, v0) = v5 & finite(v3) = v6 & in(v3, v1) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v6 = 0 & v5 = 0)))) % 9.06/2.72 | (11) empty(all_0_1_1) = all_0_0_0 % 9.06/2.72 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 9.06/2.72 | (13) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 9.06/2.72 | (14) ? [v0] : ? [v1] : element(v1, v0) = 0 % 9.06/2.72 | (15) powerset(all_0_10_10) = all_0_8_8 % 9.06/2.72 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) % 9.06/2.72 | (17) ~ (all_0_2_2 = 0) % 9.06/2.72 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cup_closed(v2) = v1) | ~ (cup_closed(v2) = v0)) % 9.06/2.72 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 9.06/2.72 | (20) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 9.06/2.72 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (diff_closed(v2) = v1) | ~ (diff_closed(v2) = v0)) % 9.06/2.72 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) % 9.06/2.72 | (23) empty(all_0_6_6) = all_0_5_5 % 9.06/2.72 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 9.06/2.72 | (25) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & finite(v2) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) % 9.06/2.72 | (26) ~ (all_0_0_0 = 0) % 9.06/2.72 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) % 9.06/2.72 | (28) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) % 9.06/2.72 | (29) cap_closed(all_0_3_3) = 0 % 9.06/2.72 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (preboolean(v2) = v1) | ~ (preboolean(v2) = v0)) % 9.06/2.72 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 9.06/2.72 | (32) empty(all_0_4_4) = 0 % 9.06/2.72 | (33) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | cup_closed(v1) = 0) % 9.06/2.72 | (34) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | preboolean(v1) = 0) % 9.06/2.72 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) % 9.06/2.72 | (36) preboolean(all_0_3_3) = 0 % 9.06/2.72 | (37) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 9.06/2.72 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v2, v0) = 0) | ~ (finite_subsets(v0) = v1) | ~ (preboolean(v1) = 0) | ? [v3] : ? [v4] : (finite(v2) = v3 & in(v2, v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) % 9.06/2.73 | (39) finite_subsets(all_0_10_10) = all_0_9_9 % 9.06/2.73 | (40) empty(empty_set) = 0 % 9.06/2.73 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) % 9.06/2.73 | (42) cup_closed(all_0_3_3) = 0 % 9.06/2.73 | (43) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | diff_closed(v1) = 0) % 9.06/2.73 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 9.06/2.73 | (45) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (natural(v2) = v1) | ~ (natural(v2) = v0)) % 9.06/2.73 | (46) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite(v2) = v1) | ~ (finite(v2) = v0)) % 9.06/2.73 | (47) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 9.06/2.73 | (48) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) % 9.06/2.73 | (49) finite(all_0_1_1) = 0 % 9.06/2.73 | (50) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 9.06/2.73 | (51) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 9.06/2.73 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) % 9.06/2.73 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) % 9.06/2.73 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v2) | ~ (element(v1, v2) = 0) | finite(v1) = 0) % 9.06/2.73 | (55) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 9.06/2.73 | (56) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | preboolean(v1) = 0) % 9.06/2.73 | (57) ! [v0] : ! [v1] : (v1 = 0 | ~ (finite(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 9.06/2.73 | (58) ! [v0] : ( ~ (finite(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | finite(v2) = 0))) % 9.06/2.73 | (59) ! [v0] : ! [v1] : ( ~ (diff_closed(v0) = v1) | ? [v2] : ? [v3] : (preboolean(v0) = v2 & cup_closed(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) % 9.06/2.73 | (60) ! [v0] : ( ~ (diff_closed(v0) = 0) | ? [v1] : ? [v2] : (preboolean(v0) = v2 & cup_closed(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))) % 9.06/2.73 | (61) diff_closed(all_0_3_3) = 0 % 9.06/2.73 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 9.06/2.73 | (63) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite_subsets(v2) = v1) | ~ (finite_subsets(v2) = v0)) % 9.06/2.73 | (64) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | diff_closed(v1) = 0) % 9.06/2.73 | (65) empty(all_0_3_3) = all_0_2_2 % 9.06/2.73 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v2, v0) = v3) | ~ (finite_subsets(v0) = v1) | ~ (preboolean(v1) = 0) | ? [v4] : ? [v5] : (finite(v2) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) % 9.06/2.73 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 9.06/2.73 | (68) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (relation(v2) = 0 & function(v2) = 0 & one_to_one(v2) = 0 & epsilon_transitive(v2) = 0 & epsilon_connected(v2) = 0 & ordinal(v2) = 0 & natural(v2) = 0 & element(v2, v1) = 0 & finite(v2) = 0 & empty(v2) = 0)) % 9.06/2.73 | (69) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) % 9.06/2.74 | (70) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | cup_closed(v1) = 0) % 9.06/2.74 | % 9.06/2.74 | Instantiating formula (51) with all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms subset(all_0_9_9, all_0_8_8) = all_0_7_7, yields: % 9.06/2.74 | (71) all_0_7_7 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_8_8) = v1 & in(v0, all_0_9_9) = 0) % 9.06/2.74 | % 9.06/2.74 | Instantiating formula (34) with all_0_9_9, all_0_10_10 and discharging atoms finite_subsets(all_0_10_10) = all_0_9_9, yields: % 9.06/2.74 | (72) preboolean(all_0_9_9) = 0 % 9.06/2.74 | % 9.06/2.74 | Instantiating formula (13) with all_0_8_8, all_0_10_10 and discharging atoms powerset(all_0_10_10) = all_0_8_8, yields: % 9.06/2.74 | (73) ? [v0] : ( ~ (v0 = 0) & empty(all_0_8_8) = v0) % 9.06/2.74 | % 9.06/2.74 | Instantiating (73) with all_34_0_24 yields: % 9.06/2.74 | (74) ~ (all_34_0_24 = 0) & empty(all_0_8_8) = all_34_0_24 % 9.06/2.74 | % 9.06/2.74 | Applying alpha-rule on (74) yields: % 9.06/2.74 | (75) ~ (all_34_0_24 = 0) % 9.06/2.74 | (76) empty(all_0_8_8) = all_34_0_24 % 9.06/2.74 | % 9.06/2.74 +-Applying beta-rule and splitting (71), into two cases. % 9.06/2.74 |-Branch one: % 9.06/2.74 | (77) all_0_7_7 = 0 % 9.06/2.74 | % 9.06/2.74 | Equations (77) can reduce 3 to: % 9.06/2.74 | (78) $false % 9.06/2.74 | % 9.06/2.74 |-The branch is then unsatisfiable % 9.06/2.74 |-Branch two: % 9.06/2.74 | (3) ~ (all_0_7_7 = 0) % 9.06/2.74 | (80) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_8_8) = v1 & in(v0, all_0_9_9) = 0) % 9.06/2.74 | % 9.06/2.74 | Instantiating (80) with all_40_0_25, all_40_1_26 yields: % 9.06/2.74 | (81) ~ (all_40_0_25 = 0) & in(all_40_1_26, all_0_8_8) = all_40_0_25 & in(all_40_1_26, all_0_9_9) = 0 % 9.06/2.74 | % 9.06/2.74 | Applying alpha-rule on (81) yields: % 9.06/2.74 | (82) ~ (all_40_0_25 = 0) % 9.06/2.74 | (83) in(all_40_1_26, all_0_8_8) = all_40_0_25 % 9.06/2.74 | (84) in(all_40_1_26, all_0_9_9) = 0 % 9.06/2.74 | % 9.06/2.74 | Instantiating formula (69) with all_40_0_25, all_0_8_8, all_40_1_26 and discharging atoms in(all_40_1_26, all_0_8_8) = all_40_0_25, yields: % 9.06/2.74 | (85) all_40_0_25 = 0 | ? [v0] : ? [v1] : (element(all_40_1_26, all_0_8_8) = v0 & empty(all_0_8_8) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 9.06/2.74 | % 9.06/2.74 +-Applying beta-rule and splitting (85), into two cases. % 9.06/2.74 |-Branch one: % 9.06/2.74 | (86) all_40_0_25 = 0 % 9.06/2.74 | % 9.06/2.74 | Equations (86) can reduce 82 to: % 9.06/2.74 | (78) $false % 9.06/2.74 | % 9.06/2.74 |-The branch is then unsatisfiable % 9.06/2.74 |-Branch two: % 9.06/2.74 | (82) ~ (all_40_0_25 = 0) % 9.06/2.74 | (89) ? [v0] : ? [v1] : (element(all_40_1_26, all_0_8_8) = v0 & empty(all_0_8_8) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 9.06/2.74 | % 9.06/2.74 | Instantiating (89) with all_76_0_39, all_76_1_40 yields: % 9.06/2.74 | (90) element(all_40_1_26, all_0_8_8) = all_76_1_40 & empty(all_0_8_8) = all_76_0_39 & ( ~ (all_76_1_40 = 0) | all_76_0_39 = 0) % 9.06/2.74 | % 9.06/2.74 | Applying alpha-rule on (90) yields: % 9.06/2.74 | (91) element(all_40_1_26, all_0_8_8) = all_76_1_40 % 9.06/2.74 | (92) empty(all_0_8_8) = all_76_0_39 % 9.06/2.74 | (93) ~ (all_76_1_40 = 0) | all_76_0_39 = 0 % 9.06/2.74 | % 9.06/2.74 | Instantiating formula (12) with all_0_8_8, all_76_0_39, all_34_0_24 and discharging atoms empty(all_0_8_8) = all_76_0_39, empty(all_0_8_8) = all_34_0_24, yields: % 9.06/2.74 | (94) all_76_0_39 = all_34_0_24 % 9.06/2.74 | % 9.06/2.74 +-Applying beta-rule and splitting (93), into two cases. % 9.06/2.74 |-Branch one: % 9.06/2.74 | (95) ~ (all_76_1_40 = 0) % 9.06/2.74 | % 9.06/2.74 | Instantiating formula (31) with all_76_1_40, all_0_8_8, all_0_10_10, all_40_1_26 and discharging atoms powerset(all_0_10_10) = all_0_8_8, element(all_40_1_26, all_0_8_8) = all_76_1_40, yields: % 9.06/2.74 | (96) all_76_1_40 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_40_1_26, all_0_10_10) = v0) % 9.06/2.74 | % 9.06/2.74 +-Applying beta-rule and splitting (96), into two cases. % 9.06/2.74 |-Branch one: % 9.06/2.74 | (97) all_76_1_40 = 0 % 9.06/2.74 | % 9.06/2.74 | Equations (97) can reduce 95 to: % 9.06/2.74 | (78) $false % 9.06/2.74 | % 9.06/2.74 |-The branch is then unsatisfiable % 9.06/2.74 |-Branch two: % 9.06/2.74 | (95) ~ (all_76_1_40 = 0) % 9.06/2.74 | (100) ? [v0] : ( ~ (v0 = 0) & subset(all_40_1_26, all_0_10_10) = v0) % 9.06/2.74 | % 9.06/2.74 | Instantiating (100) with all_123_0_64 yields: % 9.06/2.74 | (101) ~ (all_123_0_64 = 0) & subset(all_40_1_26, all_0_10_10) = all_123_0_64 % 9.06/2.74 | % 9.06/2.74 | Applying alpha-rule on (101) yields: % 9.06/2.74 | (102) ~ (all_123_0_64 = 0) % 9.06/2.74 | (103) subset(all_40_1_26, all_0_10_10) = all_123_0_64 % 9.06/2.74 | % 9.06/2.74 | Instantiating formula (66) with all_123_0_64, all_40_1_26, all_0_9_9, all_0_10_10 and discharging atoms subset(all_40_1_26, all_0_10_10) = all_123_0_64, finite_subsets(all_0_10_10) = all_0_9_9, preboolean(all_0_9_9) = 0, yields: % 9.06/2.75 | (104) ? [v0] : ? [v1] : (finite(all_40_1_26) = v1 & in(all_40_1_26, all_0_9_9) = v0 & ( ~ (v0 = 0) | (v1 = 0 & all_123_0_64 = 0))) % 9.06/2.75 | % 9.06/2.75 | Instantiating (104) with all_159_0_70, all_159_1_71 yields: % 9.06/2.75 | (105) finite(all_40_1_26) = all_159_0_70 & in(all_40_1_26, all_0_9_9) = all_159_1_71 & ( ~ (all_159_1_71 = 0) | (all_159_0_70 = 0 & all_123_0_64 = 0)) % 9.06/2.75 | % 9.06/2.75 | Applying alpha-rule on (105) yields: % 9.06/2.75 | (106) finite(all_40_1_26) = all_159_0_70 % 9.06/2.75 | (107) in(all_40_1_26, all_0_9_9) = all_159_1_71 % 9.06/2.75 | (108) ~ (all_159_1_71 = 0) | (all_159_0_70 = 0 & all_123_0_64 = 0) % 9.06/2.75 | % 9.06/2.75 +-Applying beta-rule and splitting (108), into two cases. % 9.06/2.75 |-Branch one: % 9.06/2.75 | (109) ~ (all_159_1_71 = 0) % 9.06/2.75 | % 9.06/2.75 | Instantiating formula (19) with all_40_1_26, all_0_9_9, all_159_1_71, 0 and discharging atoms in(all_40_1_26, all_0_9_9) = all_159_1_71, in(all_40_1_26, all_0_9_9) = 0, yields: % 9.06/2.75 | (110) all_159_1_71 = 0 % 9.06/2.75 | % 9.06/2.75 | Equations (110) can reduce 109 to: % 9.06/2.75 | (78) $false % 9.06/2.75 | % 9.06/2.75 |-The branch is then unsatisfiable % 9.06/2.75 |-Branch two: % 9.06/2.75 | (110) all_159_1_71 = 0 % 9.06/2.75 | (113) all_159_0_70 = 0 & all_123_0_64 = 0 % 9.06/2.75 | % 9.06/2.75 | Applying alpha-rule on (113) yields: % 9.06/2.75 | (114) all_159_0_70 = 0 % 9.06/2.75 | (115) all_123_0_64 = 0 % 9.06/2.75 | % 9.06/2.75 | Equations (115) can reduce 102 to: % 9.06/2.75 | (78) $false % 9.06/2.75 | % 9.06/2.75 |-The branch is then unsatisfiable % 9.06/2.75 |-Branch two: % 9.06/2.75 | (97) all_76_1_40 = 0 % 9.06/2.75 | (118) all_76_0_39 = 0 % 9.06/2.75 | % 9.06/2.75 | Combining equations (118,94) yields a new equation: % 9.06/2.75 | (119) all_34_0_24 = 0 % 9.06/2.75 | % 9.06/2.75 | Equations (119) can reduce 75 to: % 9.06/2.75 | (78) $false % 9.06/2.75 | % 9.06/2.75 |-The branch is then unsatisfiable % 9.06/2.75 % SZS output end Proof for theBenchmark % 9.06/2.75 % 9.06/2.75 2147ms %------------------------------------------------------------------------------