%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU010+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n006.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 08:46:10 EDT 2022 % Result : Theorem 37.74s 10.98s % Output : Proof 41.26s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU010+1 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n006.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 : Mon Jun 20 00:14:55 EDT 2022 % 0.13/0.34 % CPUTime : % 0.67/0.63 ____ _ % 0.67/0.63 ___ / __ \_____(_)___ ________ __________ % 0.67/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.67/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.67/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.67/0.63 % 0.67/0.63 A Theorem Prover for First-Order Logic % 0.67/0.63 (ePrincess v.1.0) % 0.67/0.63 % 0.67/0.63 (c) Philipp Rümmer, 2009-2015 % 0.67/0.63 (c) Peter Backeman, 2014-2015 % 0.67/0.63 (contributions by Angelo Brillout, Peter Baumgartner) % 0.67/0.63 Free software under GNU Lesser General Public License (LGPL). % 0.67/0.63 Bug reports to peter@backeman.se % 0.67/0.63 % 0.67/0.63 For more information, visit http://user.uu.se/~petba168/breu/ % 0.67/0.63 % 0.67/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.73/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.58/1.00 Prover 0: Preprocessing ... % 2.16/1.21 Prover 0: Warning: ignoring some quantifiers % 2.28/1.23 Prover 0: Constructing countermodel ... % 9.03/2.84 Prover 0: gave up % 9.03/2.84 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 9.05/2.87 Prover 1: Preprocessing ... % 9.59/2.96 Prover 1: Warning: ignoring some quantifiers % 9.59/2.97 Prover 1: Constructing countermodel ... % 21.47/5.88 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 21.58/5.91 Prover 2: Preprocessing ... % 21.72/5.98 Prover 2: Warning: ignoring some quantifiers % 21.72/5.98 Prover 2: Constructing countermodel ... % 27.77/7.64 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 27.91/7.68 Prover 3: Preprocessing ... % 27.91/7.71 Prover 3: Warning: ignoring some quantifiers % 27.91/7.72 Prover 3: Constructing countermodel ... % 28.80/7.87 Prover 3: gave up % 28.80/7.87 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 28.80/7.89 Prover 4: Preprocessing ... % 29.17/7.95 Prover 4: Warning: ignoring some quantifiers % 29.17/7.95 Prover 4: Constructing countermodel ... % 37.74/10.98 Prover 4: proved (1615ms) % 37.74/10.98 Prover 2: stopped % 37.74/10.98 Prover 1: stopped % 37.74/10.98 % 37.74/10.98 No countermodel exists, formula is valid % 37.74/10.98 % SZS status Theorem for theBenchmark % 37.74/10.98 % 37.74/10.98 Generating proof ... Warning: ignoring some quantifiers % 40.70/11.64 found it (size 123) % 40.70/11.64 % 40.70/11.64 % SZS output start Proof for theBenchmark % 40.70/11.64 Assumed formulas after preprocessing and simplification: % 40.70/11.64 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ( ~ (v12 = 0) & ~ (v8 = 0) & relation_empty_yielding(v10) = 0 & relation_empty_yielding(empty_set) = 0 & identity_relation(v4) = v5 & identity_relation(v1) = v2 & relation_composition(v2, v0) = v3 & relation_composition(v0, v5) = v6 & relation_rng(v0) = v4 & relation(v14) = 0 & relation(v13) = 0 & relation(v11) = 0 & relation(v10) = 0 & relation(v0) = 0 & relation(empty_set) = 0 & relation_dom(v0) = v1 & function(v14) = 0 & function(v0) = 0 & empty(v13) = 0 & empty(v11) = v12 & empty(v9) = 0 & empty(v7) = v8 & empty(empty_set) = 0 & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (powerset(v17) = v18) | ~ (element(v16, v18) = 0) | ~ (element(v15, v17) = v19) | ? [v20] : ( ~ (v20 = 0) & in(v15, v16) = v20)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (identity_relation(v15) = v17) | ~ (relation_composition(v17, v16) = v18) | ? [v19] : ? [v20] : ? [v21] : (subset(v20, v15) = v21 & relation(v16) = v19 & relation_dom(v16) = v20 & ( ~ (v21 = 0) | ~ (v19 = 0)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (identity_relation(v15) = v17) | ~ (relation_composition(v16, v17) = v18) | ? [v19] : ? [v20] : ? [v21] : (subset(v20, v15) = v21 & relation_rng(v16) = v20 & relation(v16) = v19 & ( ~ (v21 = 0) | ~ (v19 = 0)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (powerset(v16) = v17) | ~ (element(v15, v17) = v18) | ? [v19] : ( ~ (v19 = 0) & subset(v15, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (element(v15, v17) = v18) | ~ (in(v15, v16) = 0) | ? [v19] : ? [v20] : ( ~ (v20 = 0) & powerset(v17) = v19 & element(v16, v19) = v20)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (subset(v18, v17) = v16) | ~ (subset(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_composition(v18, v17) = v16) | ~ (relation_composition(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (element(v18, v17) = v16) | ~ (element(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (in(v18, v17) = v16) | ~ (in(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ (element(v16, v18) = 0) | ~ (in(v15, v16) = 0) | element(v15, v17) = 0) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ (element(v16, v18) = 0) | ~ (in(v15, v16) = 0) | ? [v19] : ( ~ (v19 = 0) & empty(v17) = v19)) & ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (subset(v15, v16) = v17) | ? [v18] : ? [v19] : ( ~ (v19 = 0) & powerset(v16) = v18 & element(v15, v18) = v19)) & ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (element(v15, v16) = v17) | ? [v18] : ( ~ (v18 = 0) & in(v15, v16) = v18)) & ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (in(v15, v16) = v17) | ? [v18] : ? [v19] : (empty(v16) = v19 & element(v15, v16) = v18 & ( ~ (v18 = 0) | v19 = 0))) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation_empty_yielding(v17) = v16) | ~ (relation_empty_yielding(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (identity_relation(v17) = v16) | ~ (identity_relation(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation_rng(v17) = v16) | ~ (relation_rng(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation(v17) = v16) | ~ (relation(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation_dom(v17) = v16) | ~ (relation_dom(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (function(v17) = v16) | ~ (function(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (empty(v17) = v16) | ~ (empty(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (powerset(v17) = v16) | ~ (powerset(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (subset(v17, v15) = 0) | ~ (relation_rng(v16) = v17) | ? [v18] : ? [v19] : ? [v20] : (identity_relation(v15) = v19 & relation_composition(v16, v19) = v20 & relation(v16) = v18 & ( ~ (v18 = 0) | v20 = v16))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (subset(v17, v15) = 0) | ~ (relation_dom(v16) = v17) | ? [v18] : ? [v19] : ? [v20] : (identity_relation(v15) = v19 & relation_composition(v19, v16) = v20 & relation(v16) = v18 & ( ~ (v18 = 0) | v20 = v16))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v16, v15) = v17) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (relation(v17) = v21 & relation(v16) = v19 & empty(v17) = v20 & empty(v15) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0) | (v21 = 0 & v20 = 0)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation(v17) = v22 & relation(v16) = v20 & relation(v15) = v18 & function(v17) = v23 & function(v16) = v21 & function(v15) = v19 & ( ~ (v21 = 0) | ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0) | (v23 = 0 & v22 = 0)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (relation(v17) = v21 & relation(v16) = v19 & empty(v17) = v20 & empty(v15) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0) | (v21 = 0 & v20 = 0)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : (relation(v17) = v20 & relation(v16) = v19 & relation(v15) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0) | v20 = 0))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (empty(v17) = 0) | ~ (in(v15, v16) = 0) | ? [v18] : ? [v19] : ( ~ (v19 = 0) & powerset(v17) = v18 & element(v16, v18) = v19)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ (element(v15, v17) = 0) | subset(v15, v16) = 0) & ! [v15] : ! [v16] : (v16 = v15 | ~ (empty(v16) = 0) | ~ (empty(v15) = 0)) & ! [v15] : ! [v16] : (v16 = 0 | ~ (subset(v15, v15) = v16)) & ! [v15] : ! [v16] : (v16 = 0 | ~ (relation(v15) = v16) | ? [v17] : ( ~ (v17 = 0) & empty(v15) = v17)) & ! [v15] : ! [v16] : (v16 = 0 | ~ (function(v15) = v16) | ? [v17] : ( ~ (v17 = 0) & empty(v15) = v17)) & ! [v15] : ! [v16] : (v16 = 0 | ~ (empty(v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ( ~ (v19 = 0) & empty(v18) = v19 & powerset(v15) = v17 & element(v18, v17) = 0)) & ! [v15] : ! [v16] : (v16 = 0 | ~ (empty(v15) = v16) | ? [v17] : ? [v18] : ? [v19] : (relation_rng(v15) = v18 & relation(v15) = v17 & empty(v18) = v19 & ( ~ (v19 = 0) | ~ (v17 = 0)))) & ! [v15] : ! [v16] : (v16 = 0 | ~ (empty(v15) = v16) | ? [v17] : ? [v18] : ? [v19] : (relation(v15) = v17 & relation_dom(v15) = v18 & empty(v18) = v19 & ( ~ (v19 = 0) | ~ (v17 = 0)))) & ! [v15] : ! [v16] : ( ~ (identity_relation(v15) = v16) | relation(v16) = 0) & ! [v15] : ! [v16] : ( ~ (identity_relation(v15) = v16) | function(v16) = 0) & ! [v15] : ! [v16] : ( ~ (subset(v15, v16) = 0) | ? [v17] : (powerset(v16) = v17 & element(v15, v17) = 0)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ? [v17] : ? [v18] : ? [v19] : (relation(v16) = v19 & empty(v16) = v18 & empty(v15) = v17 & ( ~ (v17 = 0) | (v19 = 0 & v18 = 0)))) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ? [v17] : ? [v18] : ? [v19] : (relation(v15) = v18 & empty(v16) = v19 & empty(v15) = v17 & ( ~ (v19 = 0) | ~ (v18 = 0) | v17 = 0))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ? [v17] : ? [v18] : ? [v19] : (relation(v16) = v19 & empty(v16) = v18 & empty(v15) = v17 & ( ~ (v17 = 0) | (v19 = 0 & v18 = 0)))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ? [v17] : ? [v18] : ? [v19] : (relation(v15) = v18 & empty(v16) = v19 & empty(v15) = v17 & ( ~ (v19 = 0) | ~ (v18 = 0) | v17 = 0))) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ((v18 = 0 & ~ (v19 = 0) & empty(v17) = v19 & element(v17, v16) = 0) | (v17 = 0 & empty(v15) = 0))) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ? [v17] : ( ~ (v17 = 0) & empty(v16) = v17)) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ? [v17] : (empty(v17) = 0 & element(v17, v16) = 0)) & ! [v15] : ! [v16] : ( ~ (element(v15, v16) = 0) | ? [v17] : ? [v18] : (empty(v16) = v17 & in(v15, v16) = v18 & (v18 = 0 | v17 = 0))) & ! [v15] : ! [v16] : ( ~ (in(v16, v15) = 0) | ? [v17] : ( ~ (v17 = 0) & in(v15, v16) = v17)) & ! [v15] : ! [v16] : ( ~ (in(v15, v16) = 0) | element(v15, v16) = 0) & ! [v15] : ! [v16] : ( ~ (in(v15, v16) = 0) | ? [v17] : ( ~ (v17 = 0) & empty(v16) = v17)) & ! [v15] : ! [v16] : ( ~ (in(v15, v16) = 0) | ? [v17] : ( ~ (v17 = 0) & in(v16, v15) = v17)) & ! [v15] : (v15 = empty_set | ~ (empty(v15) = 0)) & ! [v15] : ( ~ (relation(v15) = 0) | ? [v16] : ? [v17] : ? [v18] : (relation_rng(v15) = v17 & empty(v17) = v18 & empty(v15) = v16 & ( ~ (v18 = 0) | v16 = 0))) & ! [v15] : ( ~ (relation(v15) = 0) | ? [v16] : ? [v17] : ? [v18] : (relation_dom(v15) = v17 & empty(v17) = v18 & empty(v15) = v16 & ( ~ (v18 = 0) | v16 = 0))) & ! [v15] : ( ~ (empty(v15) = 0) | relation(v15) = 0) & ! [v15] : ( ~ (empty(v15) = 0) | function(v15) = 0) & ! [v15] : ( ~ (empty(v15) = 0) | ? [v16] : (relation_rng(v15) = v16 & relation(v16) = 0 & empty(v16) = 0)) & ! [v15] : ( ~ (empty(v15) = 0) | ? [v16] : (relation(v16) = 0 & relation_dom(v15) = v16 & empty(v16) = 0)) & ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_composition(v15, v16) = v21 & relation(v21) = v22 & relation(v16) = v19 & relation(v15) = v17 & function(v21) = v23 & function(v16) = v20 & function(v15) = v18 & ( ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | (v23 = 0 & v22 = 0))) & ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (identity_relation(v15) = v20 & subset(v18, v15) = v19 & relation_composition(v20, v16) = v21 & relation(v16) = v17 & relation_dom(v16) = v18 & ( ~ (v19 = 0) | ~ (v17 = 0) | v21 = v16)) & ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (identity_relation(v15) = v20 & subset(v18, v15) = v19 & relation_composition(v16, v20) = v21 & relation_rng(v16) = v18 & relation(v16) = v17 & ( ~ (v19 = 0) | ~ (v17 = 0) | v21 = v16)) & ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (subset(v15, v16) = v17 & powerset(v16) = v18 & element(v15, v18) = v19 & ( ~ (v17 = 0) | v19 = 0)) & ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (empty(v16) = v18 & element(v15, v16) = v17 & in(v15, v16) = v19 & ( ~ (v17 = 0) | v19 = 0 | v18 = 0)) & ? [v15] : ? [v16] : element(v16, v15) = 0 & ( ~ (v6 = v0) | ~ (v3 = v0))) % 40.85/11.70 | 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, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14 yields: % 40.85/11.70 | (1) ~ (all_0_2_2 = 0) & ~ (all_0_6_6 = 0) & relation_empty_yielding(all_0_4_4) = 0 & relation_empty_yielding(empty_set) = 0 & identity_relation(all_0_10_10) = all_0_9_9 & identity_relation(all_0_13_13) = all_0_12_12 & relation_composition(all_0_12_12, all_0_14_14) = all_0_11_11 & relation_composition(all_0_14_14, all_0_9_9) = all_0_8_8 & relation_rng(all_0_14_14) = all_0_10_10 & relation(all_0_0_0) = 0 & relation(all_0_1_1) = 0 & relation(all_0_3_3) = 0 & relation(all_0_4_4) = 0 & relation(all_0_14_14) = 0 & relation(empty_set) = 0 & relation_dom(all_0_14_14) = all_0_13_13 & function(all_0_0_0) = 0 & function(all_0_14_14) = 0 & empty(all_0_1_1) = 0 & empty(all_0_3_3) = all_0_2_2 & empty(all_0_5_5) = 0 & empty(all_0_7_7) = all_0_6_6 & empty(empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (identity_relation(v0) = v2) | ~ (relation_composition(v2, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : (subset(v5, v0) = v6 & relation(v1) = v4 & relation_dom(v1) = v5 & ( ~ (v6 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (identity_relation(v0) = v2) | ~ (relation_composition(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (subset(v5, v0) = v6 & relation_rng(v1) = v5 & relation(v1) = v4 & ( ~ (v6 = 0) | ~ (v4 = 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] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & powerset(v2) = v4 & element(v1, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(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] : ( ~ (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 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v1) = v4 & element(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v2, v0) = 0) | ~ (relation_rng(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (identity_relation(v0) = v4 & relation_composition(v1, v4) = v5 & relation(v1) = v3 & ( ~ (v3 = 0) | v5 = v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v2, v0) = 0) | ~ (relation_dom(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (identity_relation(v0) = v4 & relation_composition(v4, v1) = v5 & relation(v1) = v3 & ( ~ (v3 = 0) | v5 = v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation(v2) = v6 & relation(v1) = v4 & empty(v2) = v5 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation(v2) = v7 & relation(v1) = v5 & relation(v0) = v3 & function(v2) = v8 & function(v1) = v6 & function(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | (v8 = 0 & v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation(v2) = v6 & relation(v1) = v4 & empty(v2) = v5 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4)) & ! [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 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & empty(v3) = v4 & powerset(v0) = v2 & element(v3, v2) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation_rng(v0) = v3 & relation(v0) = v2 & empty(v3) = v4 & ( ~ (v4 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v2 & relation_dom(v0) = v3 & empty(v3) = v4 & ( ~ (v4 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1) = 0) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1) = 0) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [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] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_rng(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 & ( ~ (v3 = 0) | v1 = 0))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_dom(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 & ( ~ (v3 = 0) | v1 = 0))) & ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_rng(v0) = v1 & relation(v1) = 0 & empty(v1) = 0)) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation(v1) = 0 & relation_dom(v0) = v1 & empty(v1) = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_composition(v0, v1) = v6 & relation(v6) = v7 & relation(v1) = v4 & relation(v0) = v2 & function(v6) = v8 & function(v1) = v5 & function(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | (v8 = 0 & v7 = 0))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (identity_relation(v0) = v5 & subset(v3, v0) = v4 & relation_composition(v5, v1) = v6 & relation(v1) = v2 & relation_dom(v1) = v3 & ( ~ (v4 = 0) | ~ (v2 = 0) | v6 = v1)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (identity_relation(v0) = v5 & subset(v3, v0) = v4 & relation_composition(v1, v5) = v6 & relation_rng(v1) = v3 & relation(v1) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v6 = v1)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (subset(v0, v1) = v2 & powerset(v1) = v3 & element(v0, v3) = v4 & ( ~ (v2 = 0) | v4 = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (empty(v1) = v3 & element(v0, v1) = v2 & in(v0, v1) = v4 & ( ~ (v2 = 0) | v4 = 0 | v3 = 0)) & ? [v0] : ? [v1] : element(v1, v0) = 0 & ( ~ (all_0_8_8 = all_0_14_14) | ~ (all_0_11_11 = all_0_14_14)) % 40.85/11.72 | % 40.85/11.72 | Applying alpha-rule on (1) yields: % 40.85/11.72 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) % 40.85/11.72 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (identity_relation(v0) = v2) | ~ (relation_composition(v2, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : (subset(v5, v0) = v6 & relation(v1) = v4 & relation_dom(v1) = v5 & ( ~ (v6 = 0) | ~ (v4 = 0)))) % 40.85/11.72 | (4) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (identity_relation(v0) = v5 & subset(v3, v0) = v4 & relation_composition(v1, v5) = v6 & relation_rng(v1) = v3 & relation(v1) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v6 = v1)) % 40.85/11.72 | (5) relation_empty_yielding(all_0_4_4) = 0 % 40.85/11.72 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) % 40.85/11.72 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 40.85/11.72 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) % 40.85/11.72 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 40.85/11.72 | (10) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 40.85/11.72 | (11) empty(all_0_3_3) = all_0_2_2 % 40.85/11.72 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) % 40.85/11.72 | (13) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 40.85/11.72 | (14) relation(all_0_0_0) = 0 % 40.85/11.72 | (15) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v2 & relation_dom(v0) = v3 & empty(v3) = v4 & ( ~ (v4 = 0) | ~ (v2 = 0)))) % 40.85/11.72 | (16) relation(all_0_4_4) = 0 % 40.85/11.72 | (17) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation(v1) = 0 & relation_dom(v0) = v1 & empty(v1) = 0)) % 40.85/11.72 | (18) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 40.85/11.72 | (19) empty(all_0_5_5) = 0 % 40.85/11.72 | (20) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_dom(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 & ( ~ (v3 = 0) | v1 = 0))) % 40.85/11.72 | (21) ~ (all_0_2_2 = 0) % 40.85/11.72 | (22) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) % 40.85/11.72 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 40.85/11.72 | (24) identity_relation(all_0_13_13) = all_0_12_12 % 40.85/11.72 | (25) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (empty(v1) = v3 & element(v0, v1) = v2 & in(v0, v1) = v4 & ( ~ (v2 = 0) | v4 = 0 | v3 = 0)) % 40.85/11.72 | (26) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) % 40.85/11.72 | (27) ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) % 40.85/11.72 | (28) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_rng(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 & ( ~ (v3 = 0) | v1 = 0))) % 40.85/11.72 | (29) ~ (all_0_6_6 = 0) % 40.85/11.72 | (30) function(all_0_14_14) = 0 % 40.85/11.72 | (31) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v1) = v4 & element(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 40.85/11.72 | (32) relation(all_0_3_3) = 0 % 40.85/11.72 | (33) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) % 40.85/11.73 | (34) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 40.85/11.73 | (35) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1) = 0) % 40.85/11.73 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 40.85/11.73 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 40.85/11.73 | (38) empty(all_0_1_1) = 0 % 40.85/11.73 | (39) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & empty(v3) = v4 & powerset(v0) = v2 & element(v3, v2) = 0)) % 40.85/11.73 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) % 40.85/11.73 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation(v2) = v6 & relation(v1) = v4 & empty(v2) = v5 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0)))) % 40.85/11.73 | (42) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 40.85/11.73 | (43) relation(empty_set) = 0 % 40.85/11.73 | (44) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (identity_relation(v0) = v5 & subset(v3, v0) = v4 & relation_composition(v5, v1) = v6 & relation(v1) = v2 & relation_dom(v1) = v3 & ( ~ (v4 = 0) | ~ (v2 = 0) | v6 = v1)) % 40.85/11.73 | (45) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (subset(v0, v1) = v2 & powerset(v1) = v3 & element(v0, v3) = v4 & ( ~ (v2 = 0) | v4 = 0)) % 40.85/11.73 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 40.85/11.73 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation(v2) = v6 & relation(v1) = v4 & empty(v2) = v5 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0)))) % 40.85/11.73 | (48) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) % 40.85/11.73 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & powerset(v2) = v4 & element(v1, v4) = v5)) % 40.85/11.73 | (50) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) % 40.85/11.73 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v2, v0) = 0) | ~ (relation_rng(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (identity_relation(v0) = v4 & relation_composition(v1, v4) = v5 & relation(v1) = v3 & ( ~ (v3 = 0) | v5 = v1))) % 40.85/11.73 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 40.85/11.73 | (53) empty(empty_set) = 0 % 40.85/11.73 | (54) identity_relation(all_0_10_10) = all_0_9_9 % 40.85/11.73 | (55) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_composition(v0, v1) = v6 & relation(v6) = v7 & relation(v1) = v4 & relation(v0) = v2 & function(v6) = v8 & function(v1) = v5 & function(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | (v8 = 0 & v7 = 0))) % 40.85/11.73 | (56) relation_rng(all_0_14_14) = all_0_10_10 % 40.85/11.73 | (57) relation(all_0_1_1) = 0 % 40.85/11.73 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) % 40.85/11.73 | (59) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0))) % 40.85/11.73 | (60) relation_composition(all_0_14_14, all_0_9_9) = all_0_8_8 % 40.85/11.73 | (61) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) % 40.85/11.73 | (62) relation_empty_yielding(empty_set) = 0 % 40.85/11.73 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v2, v0) = 0) | ~ (relation_dom(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (identity_relation(v0) = v4 & relation_composition(v4, v1) = v5 & relation(v1) = v3 & ( ~ (v3 = 0) | v5 = v1))) % 40.85/11.73 | (64) function(all_0_0_0) = 0 % 40.85/11.73 | (65) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation_rng(v0) = v3 & relation(v0) = v2 & empty(v3) = v4 & ( ~ (v4 = 0) | ~ (v2 = 0)))) % 40.85/11.74 | (66) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) % 40.85/11.74 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation(v2) = v7 & relation(v1) = v5 & relation(v0) = v3 & function(v2) = v8 & function(v1) = v6 & function(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | (v8 = 0 & v7 = 0)))) % 40.85/11.74 | (68) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) % 40.85/11.74 | (69) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1) = 0) % 40.85/11.74 | (70) relation_dom(all_0_14_14) = all_0_13_13 % 40.85/11.74 | (71) empty(all_0_7_7) = all_0_6_6 % 40.85/11.74 | (72) ~ (all_0_8_8 = all_0_14_14) | ~ (all_0_11_11 = all_0_14_14) % 40.85/11.74 | (73) relation_composition(all_0_12_12, all_0_14_14) = all_0_11_11 % 40.85/11.74 | (74) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) % 40.85/11.74 | (75) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 40.85/11.74 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 40.85/11.74 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 40.85/11.74 | (78) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 40.85/11.74 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 40.85/11.74 | (80) ? [v0] : ? [v1] : element(v1, v0) = 0 % 40.85/11.74 | (81) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 40.85/11.74 | (82) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4)) % 40.85/11.74 | (83) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0)) % 40.85/11.74 | (84) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) % 40.85/11.74 | (85) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 40.85/11.74 | (86) relation(all_0_14_14) = 0 % 40.85/11.74 | (87) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 40.85/11.74 | (88) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_rng(v0) = v1 & relation(v1) = 0 & empty(v1) = 0)) % 40.85/11.74 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (identity_relation(v0) = v2) | ~ (relation_composition(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (subset(v5, v0) = v6 & relation_rng(v1) = v5 & relation(v1) = v4 & ( ~ (v6 = 0) | ~ (v4 = 0)))) % 40.85/11.74 | (90) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 40.85/11.74 | % 40.85/11.74 | Instantiating formula (35) with all_0_9_9, all_0_10_10 and discharging atoms identity_relation(all_0_10_10) = all_0_9_9, yields: % 40.85/11.74 | (91) relation(all_0_9_9) = 0 % 40.85/11.74 | % 40.85/11.74 | Instantiating formula (3) with all_0_11_11, all_0_12_12, all_0_14_14, all_0_13_13 and discharging atoms identity_relation(all_0_13_13) = all_0_12_12, relation_composition(all_0_12_12, all_0_14_14) = all_0_11_11, yields: % 40.85/11.74 | (92) all_0_11_11 = all_0_14_14 | ? [v0] : ? [v1] : ? [v2] : (subset(v1, all_0_13_13) = v2 & relation(all_0_14_14) = v0 & relation_dom(all_0_14_14) = v1 & ( ~ (v2 = 0) | ~ (v0 = 0))) % 40.85/11.74 | % 40.85/11.74 | Instantiating formula (67) with all_0_11_11, all_0_14_14, all_0_12_12 and discharging atoms relation_composition(all_0_12_12, all_0_14_14) = all_0_11_11, yields: % 40.85/11.74 | (93) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation(all_0_11_11) = v4 & relation(all_0_12_12) = v0 & relation(all_0_14_14) = v2 & function(all_0_11_11) = v5 & function(all_0_12_12) = v1 & function(all_0_14_14) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v5 = 0 & v4 = 0))) % 40.85/11.74 | % 40.85/11.74 | Instantiating formula (41) with all_0_11_11, all_0_14_14, all_0_12_12 and discharging atoms relation_composition(all_0_12_12, all_0_14_14) = all_0_11_11, yields: % 40.85/11.74 | (94) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation(all_0_11_11) = v3 & relation(all_0_14_14) = v1 & empty(all_0_11_11) = v2 & empty(all_0_12_12) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = 0 & v2 = 0))) % 40.85/11.74 | % 40.85/11.74 | Instantiating formula (37) with all_0_11_11, all_0_14_14, all_0_12_12 and discharging atoms relation_composition(all_0_12_12, all_0_14_14) = all_0_11_11, yields: % 40.85/11.75 | (95) ? [v0] : ? [v1] : ? [v2] : (relation(all_0_11_11) = v2 & relation(all_0_12_12) = v0 & relation(all_0_14_14) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 40.85/11.75 | % 40.85/11.75 | Instantiating formula (89) with all_0_8_8, all_0_9_9, all_0_14_14, all_0_10_10 and discharging atoms identity_relation(all_0_10_10) = all_0_9_9, relation_composition(all_0_14_14, all_0_9_9) = all_0_8_8, yields: % 40.85/11.75 | (96) all_0_8_8 = all_0_14_14 | ? [v0] : ? [v1] : ? [v2] : (subset(v1, all_0_10_10) = v2 & relation_rng(all_0_14_14) = v1 & relation(all_0_14_14) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0))) % 40.85/11.75 | % 40.85/11.75 | Instantiating formula (47) with all_0_8_8, all_0_14_14, all_0_9_9 and discharging atoms relation_composition(all_0_14_14, all_0_9_9) = all_0_8_8, yields: % 40.85/11.75 | (97) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation(all_0_8_8) = v3 & relation(all_0_14_14) = v1 & empty(all_0_8_8) = v2 & empty(all_0_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = 0 & v2 = 0))) % 40.85/11.75 | % 40.85/11.75 | Instantiating formula (67) with all_0_8_8, all_0_9_9, all_0_14_14 and discharging atoms relation_composition(all_0_14_14, all_0_9_9) = all_0_8_8, yields: % 40.85/11.75 | (98) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation(all_0_8_8) = v4 & relation(all_0_9_9) = v2 & relation(all_0_14_14) = v0 & function(all_0_8_8) = v5 & function(all_0_9_9) = v3 & function(all_0_14_14) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v5 = 0 & v4 = 0))) % 41.26/11.75 | % 41.26/11.75 | Instantiating formula (41) with all_0_8_8, all_0_9_9, all_0_14_14 and discharging atoms relation_composition(all_0_14_14, all_0_9_9) = all_0_8_8, yields: % 41.26/11.75 | (99) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation(all_0_8_8) = v3 & relation(all_0_9_9) = v1 & empty(all_0_8_8) = v2 & empty(all_0_14_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = 0 & v2 = 0))) % 41.26/11.75 | % 41.26/11.75 | Instantiating formula (37) with all_0_8_8, all_0_9_9, all_0_14_14 and discharging atoms relation_composition(all_0_14_14, all_0_9_9) = all_0_8_8, yields: % 41.26/11.75 | (100) ? [v0] : ? [v1] : ? [v2] : (relation(all_0_8_8) = v2 & relation(all_0_9_9) = v1 & relation(all_0_14_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 41.26/11.75 | % 41.26/11.75 | Instantiating formula (26) with all_0_10_10, all_0_14_14 and discharging atoms relation_rng(all_0_14_14) = all_0_10_10, yields: % 41.26/11.75 | (101) ? [v0] : ? [v1] : ? [v2] : (relation(all_0_14_14) = v1 & empty(all_0_10_10) = v2 & empty(all_0_14_14) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | v0 = 0)) % 41.26/11.75 | % 41.26/11.75 | Instantiating formula (28) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields: % 41.26/11.75 | (102) ? [v0] : ? [v1] : ? [v2] : (relation_rng(all_0_14_14) = v1 & empty(v1) = v2 & empty(all_0_14_14) = v0 & ( ~ (v2 = 0) | v0 = 0)) % 41.26/11.75 | % 41.26/11.75 | Instantiating formula (20) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields: % 41.26/11.75 | (103) ? [v0] : ? [v1] : ? [v2] : (relation_dom(all_0_14_14) = v1 & empty(v1) = v2 & empty(all_0_14_14) = v0 & ( ~ (v2 = 0) | v0 = 0)) % 41.26/11.75 | % 41.26/11.75 | Instantiating formula (61) with all_0_13_13, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_13_13, yields: % 41.26/11.75 | (104) ? [v0] : ? [v1] : ? [v2] : (relation(all_0_14_14) = v1 & empty(all_0_13_13) = v2 & empty(all_0_14_14) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | v0 = 0)) % 41.26/11.75 | % 41.26/11.75 | Instantiating (103) with all_29_0_56, all_29_1_57, all_29_2_58 yields: % 41.26/11.75 | (105) relation_dom(all_0_14_14) = all_29_1_57 & empty(all_29_1_57) = all_29_0_56 & empty(all_0_14_14) = all_29_2_58 & ( ~ (all_29_0_56 = 0) | all_29_2_58 = 0) % 41.26/11.75 | % 41.26/11.75 | Applying alpha-rule on (105) yields: % 41.26/11.75 | (106) relation_dom(all_0_14_14) = all_29_1_57 % 41.26/11.75 | (107) empty(all_29_1_57) = all_29_0_56 % 41.26/11.75 | (108) empty(all_0_14_14) = all_29_2_58 % 41.26/11.75 | (109) ~ (all_29_0_56 = 0) | all_29_2_58 = 0 % 41.26/11.75 | % 41.26/11.75 | Instantiating (102) with all_31_0_59, all_31_1_60, all_31_2_61 yields: % 41.26/11.75 | (110) relation_rng(all_0_14_14) = all_31_1_60 & empty(all_31_1_60) = all_31_0_59 & empty(all_0_14_14) = all_31_2_61 & ( ~ (all_31_0_59 = 0) | all_31_2_61 = 0) % 41.26/11.75 | % 41.26/11.75 | Applying alpha-rule on (110) yields: % 41.26/11.75 | (111) relation_rng(all_0_14_14) = all_31_1_60 % 41.26/11.75 | (112) empty(all_31_1_60) = all_31_0_59 % 41.26/11.75 | (113) empty(all_0_14_14) = all_31_2_61 % 41.26/11.75 | (114) ~ (all_31_0_59 = 0) | all_31_2_61 = 0 % 41.26/11.75 | % 41.26/11.75 | Instantiating (104) with all_39_0_71, all_39_1_72, all_39_2_73 yields: % 41.26/11.75 | (115) relation(all_0_14_14) = all_39_1_72 & empty(all_0_13_13) = all_39_0_71 & empty(all_0_14_14) = all_39_2_73 & ( ~ (all_39_0_71 = 0) | ~ (all_39_1_72 = 0) | all_39_2_73 = 0) % 41.26/11.75 | % 41.26/11.75 | Applying alpha-rule on (115) yields: % 41.26/11.75 | (116) relation(all_0_14_14) = all_39_1_72 % 41.26/11.75 | (117) empty(all_0_13_13) = all_39_0_71 % 41.26/11.75 | (118) empty(all_0_14_14) = all_39_2_73 % 41.26/11.75 | (119) ~ (all_39_0_71 = 0) | ~ (all_39_1_72 = 0) | all_39_2_73 = 0 % 41.26/11.75 | % 41.26/11.75 | Instantiating (101) with all_72_0_122, all_72_1_123, all_72_2_124 yields: % 41.26/11.75 | (120) relation(all_0_14_14) = all_72_1_123 & empty(all_0_10_10) = all_72_0_122 & empty(all_0_14_14) = all_72_2_124 & ( ~ (all_72_0_122 = 0) | ~ (all_72_1_123 = 0) | all_72_2_124 = 0) % 41.26/11.75 | % 41.26/11.75 | Applying alpha-rule on (120) yields: % 41.26/11.75 | (121) relation(all_0_14_14) = all_72_1_123 % 41.26/11.75 | (122) empty(all_0_10_10) = all_72_0_122 % 41.26/11.75 | (123) empty(all_0_14_14) = all_72_2_124 % 41.26/11.75 | (124) ~ (all_72_0_122 = 0) | ~ (all_72_1_123 = 0) | all_72_2_124 = 0 % 41.26/11.75 | % 41.26/11.75 | Instantiating (97) with all_76_0_128, all_76_1_129, all_76_2_130, all_76_3_131 yields: % 41.26/11.75 | (125) relation(all_0_8_8) = all_76_0_128 & relation(all_0_14_14) = all_76_2_130 & empty(all_0_8_8) = all_76_1_129 & empty(all_0_9_9) = all_76_3_131 & ( ~ (all_76_2_130 = 0) | ~ (all_76_3_131 = 0) | (all_76_0_128 = 0 & all_76_1_129 = 0)) % 41.26/11.75 | % 41.26/11.75 | Applying alpha-rule on (125) yields: % 41.26/11.75 | (126) empty(all_0_9_9) = all_76_3_131 % 41.26/11.75 | (127) relation(all_0_14_14) = all_76_2_130 % 41.26/11.75 | (128) empty(all_0_8_8) = all_76_1_129 % 41.26/11.75 | (129) ~ (all_76_2_130 = 0) | ~ (all_76_3_131 = 0) | (all_76_0_128 = 0 & all_76_1_129 = 0) % 41.26/11.75 | (130) relation(all_0_8_8) = all_76_0_128 % 41.26/11.75 | % 41.26/11.75 | Instantiating (95) with all_78_0_132, all_78_1_133, all_78_2_134 yields: % 41.26/11.75 | (131) relation(all_0_11_11) = all_78_0_132 & relation(all_0_12_12) = all_78_2_134 & relation(all_0_14_14) = all_78_1_133 & ( ~ (all_78_1_133 = 0) | ~ (all_78_2_134 = 0) | all_78_0_132 = 0) % 41.26/11.75 | % 41.26/11.75 | Applying alpha-rule on (131) yields: % 41.26/11.75 | (132) relation(all_0_11_11) = all_78_0_132 % 41.26/11.75 | (133) relation(all_0_12_12) = all_78_2_134 % 41.26/11.75 | (134) relation(all_0_14_14) = all_78_1_133 % 41.26/11.75 | (135) ~ (all_78_1_133 = 0) | ~ (all_78_2_134 = 0) | all_78_0_132 = 0 % 41.26/11.75 | % 41.26/11.75 | Instantiating (100) with all_82_0_138, all_82_1_139, all_82_2_140 yields: % 41.26/11.75 | (136) relation(all_0_8_8) = all_82_0_138 & relation(all_0_9_9) = all_82_1_139 & relation(all_0_14_14) = all_82_2_140 & ( ~ (all_82_1_139 = 0) | ~ (all_82_2_140 = 0) | all_82_0_138 = 0) % 41.26/11.75 | % 41.26/11.75 | Applying alpha-rule on (136) yields: % 41.26/11.75 | (137) relation(all_0_8_8) = all_82_0_138 % 41.26/11.76 | (138) relation(all_0_9_9) = all_82_1_139 % 41.26/11.76 | (139) relation(all_0_14_14) = all_82_2_140 % 41.26/11.76 | (140) ~ (all_82_1_139 = 0) | ~ (all_82_2_140 = 0) | all_82_0_138 = 0 % 41.26/11.76 | % 41.26/11.76 | Instantiating (99) with all_98_0_168, all_98_1_169, all_98_2_170, all_98_3_171 yields: % 41.26/11.76 | (141) relation(all_0_8_8) = all_98_0_168 & relation(all_0_9_9) = all_98_2_170 & empty(all_0_8_8) = all_98_1_169 & empty(all_0_14_14) = all_98_3_171 & ( ~ (all_98_2_170 = 0) | ~ (all_98_3_171 = 0) | (all_98_0_168 = 0 & all_98_1_169 = 0)) % 41.26/11.76 | % 41.26/11.76 | Applying alpha-rule on (141) yields: % 41.26/11.76 | (142) empty(all_0_14_14) = all_98_3_171 % 41.26/11.76 | (143) relation(all_0_9_9) = all_98_2_170 % 41.26/11.76 | (144) relation(all_0_8_8) = all_98_0_168 % 41.26/11.76 | (145) ~ (all_98_2_170 = 0) | ~ (all_98_3_171 = 0) | (all_98_0_168 = 0 & all_98_1_169 = 0) % 41.26/11.76 | (146) empty(all_0_8_8) = all_98_1_169 % 41.26/11.76 | % 41.26/11.76 | Instantiating (98) with all_100_0_172, all_100_1_173, all_100_2_174, all_100_3_175, all_100_4_176, all_100_5_177 yields: % 41.26/11.76 | (147) relation(all_0_8_8) = all_100_1_173 & relation(all_0_9_9) = all_100_3_175 & relation(all_0_14_14) = all_100_5_177 & function(all_0_8_8) = all_100_0_172 & function(all_0_9_9) = all_100_2_174 & function(all_0_14_14) = all_100_4_176 & ( ~ (all_100_2_174 = 0) | ~ (all_100_3_175 = 0) | ~ (all_100_4_176 = 0) | ~ (all_100_5_177 = 0) | (all_100_0_172 = 0 & all_100_1_173 = 0)) % 41.26/11.76 | % 41.26/11.76 | Applying alpha-rule on (147) yields: % 41.26/11.76 | (148) function(all_0_8_8) = all_100_0_172 % 41.26/11.76 | (149) ~ (all_100_2_174 = 0) | ~ (all_100_3_175 = 0) | ~ (all_100_4_176 = 0) | ~ (all_100_5_177 = 0) | (all_100_0_172 = 0 & all_100_1_173 = 0) % 41.26/11.76 | (150) function(all_0_9_9) = all_100_2_174 % 41.26/11.76 | (151) function(all_0_14_14) = all_100_4_176 % 41.26/11.76 | (152) relation(all_0_14_14) = all_100_5_177 % 41.26/11.76 | (153) relation(all_0_9_9) = all_100_3_175 % 41.26/11.76 | (154) relation(all_0_8_8) = all_100_1_173 % 41.26/11.76 | % 41.26/11.76 | Instantiating (94) with all_102_0_178, all_102_1_179, all_102_2_180, all_102_3_181 yields: % 41.26/11.76 | (155) relation(all_0_11_11) = all_102_0_178 & relation(all_0_14_14) = all_102_2_180 & empty(all_0_11_11) = all_102_1_179 & empty(all_0_12_12) = all_102_3_181 & ( ~ (all_102_2_180 = 0) | ~ (all_102_3_181 = 0) | (all_102_0_178 = 0 & all_102_1_179 = 0)) % 41.26/11.76 | % 41.26/11.76 | Applying alpha-rule on (155) yields: % 41.26/11.76 | (156) relation(all_0_14_14) = all_102_2_180 % 41.26/11.76 | (157) relation(all_0_11_11) = all_102_0_178 % 41.26/11.76 | (158) empty(all_0_12_12) = all_102_3_181 % 41.26/11.76 | (159) empty(all_0_11_11) = all_102_1_179 % 41.26/11.76 | (160) ~ (all_102_2_180 = 0) | ~ (all_102_3_181 = 0) | (all_102_0_178 = 0 & all_102_1_179 = 0) % 41.26/11.76 | % 41.26/11.76 | Instantiating (93) with all_104_0_182, all_104_1_183, all_104_2_184, all_104_3_185, all_104_4_186, all_104_5_187 yields: % 41.26/11.76 | (161) relation(all_0_11_11) = all_104_1_183 & relation(all_0_12_12) = all_104_5_187 & relation(all_0_14_14) = all_104_3_185 & function(all_0_11_11) = all_104_0_182 & function(all_0_12_12) = all_104_4_186 & function(all_0_14_14) = all_104_2_184 & ( ~ (all_104_2_184 = 0) | ~ (all_104_3_185 = 0) | ~ (all_104_4_186 = 0) | ~ (all_104_5_187 = 0) | (all_104_0_182 = 0 & all_104_1_183 = 0)) % 41.26/11.76 | % 41.26/11.76 | Applying alpha-rule on (161) yields: % 41.26/11.76 | (162) relation(all_0_14_14) = all_104_3_185 % 41.26/11.76 | (163) function(all_0_11_11) = all_104_0_182 % 41.26/11.76 | (164) function(all_0_14_14) = all_104_2_184 % 41.26/11.76 | (165) function(all_0_12_12) = all_104_4_186 % 41.26/11.76 | (166) ~ (all_104_2_184 = 0) | ~ (all_104_3_185 = 0) | ~ (all_104_4_186 = 0) | ~ (all_104_5_187 = 0) | (all_104_0_182 = 0 & all_104_1_183 = 0) % 41.26/11.76 | (167) relation(all_0_12_12) = all_104_5_187 % 41.26/11.76 | (168) relation(all_0_11_11) = all_104_1_183 % 41.26/11.76 | % 41.26/11.76 | Instantiating formula (36) with all_0_14_14, all_31_1_60, all_0_10_10 and discharging atoms relation_rng(all_0_14_14) = all_31_1_60, relation_rng(all_0_14_14) = all_0_10_10, yields: % 41.26/11.76 | (169) all_31_1_60 = all_0_10_10 % 41.26/11.76 | % 41.26/11.76 | Instantiating formula (9) with all_0_8_8, all_98_0_168, all_100_1_173 and discharging atoms relation(all_0_8_8) = all_100_1_173, relation(all_0_8_8) = all_98_0_168, yields: % 41.26/11.76 | (170) all_100_1_173 = all_98_0_168 % 41.26/11.76 | % 41.26/11.76 | Instantiating formula (9) with all_0_8_8, all_82_0_138, all_98_0_168 and discharging atoms relation(all_0_8_8) = all_98_0_168, relation(all_0_8_8) = all_82_0_138, yields: % 41.26/11.76 | (171) all_98_0_168 = all_82_0_138 % 41.26/11.76 | % 41.26/11.76 | Instantiating formula (9) with all_0_8_8, all_76_0_128, all_100_1_173 and discharging atoms relation(all_0_8_8) = all_100_1_173, relation(all_0_8_8) = all_76_0_128, yields: % 41.26/11.76 | (172) all_100_1_173 = all_76_0_128 % 41.26/11.76 | % 41.26/11.76 | Instantiating formula (9) with all_0_9_9, all_98_2_170, all_100_3_175 and discharging atoms relation(all_0_9_9) = all_100_3_175, relation(all_0_9_9) = all_98_2_170, yields: % 41.26/11.76 | (173) all_100_3_175 = all_98_2_170 % 41.26/11.76 | % 41.26/11.76 | Instantiating formula (9) with all_0_9_9, all_82_1_139, all_100_3_175 and discharging atoms relation(all_0_9_9) = all_100_3_175, relation(all_0_9_9) = all_82_1_139, yields: % 41.26/11.76 | (174) all_100_3_175 = all_82_1_139 % 41.26/11.76 | % 41.26/11.76 | Instantiating formula (9) with all_0_9_9, 0, all_100_3_175 and discharging atoms relation(all_0_9_9) = all_100_3_175, relation(all_0_9_9) = 0, yields: % 41.26/11.76 | (175) all_100_3_175 = 0 % 41.26/11.76 | % 41.26/11.76 | Instantiating formula (9) with all_0_14_14, all_100_5_177, all_104_3_185 and discharging atoms relation(all_0_14_14) = all_104_3_185, relation(all_0_14_14) = all_100_5_177, yields: % 41.26/11.76 | (176) all_104_3_185 = all_100_5_177 % 41.26/11.76 | % 41.26/11.76 | Instantiating formula (9) with all_0_14_14, all_100_5_177, all_102_2_180 and discharging atoms relation(all_0_14_14) = all_102_2_180, relation(all_0_14_14) = all_100_5_177, yields: % 41.26/11.76 | (177) all_102_2_180 = all_100_5_177 % 41.26/11.76 | % 41.26/11.76 | Instantiating formula (9) with all_0_14_14, all_82_2_140, all_102_2_180 and discharging atoms relation(all_0_14_14) = all_102_2_180, relation(all_0_14_14) = all_82_2_140, yields: % 41.26/11.76 | (178) all_102_2_180 = all_82_2_140 % 41.26/11.76 | % 41.26/11.76 | Instantiating formula (9) with all_0_14_14, all_78_1_133, all_102_2_180 and discharging atoms relation(all_0_14_14) = all_102_2_180, relation(all_0_14_14) = all_78_1_133, yields: % 41.26/11.76 | (179) all_102_2_180 = all_78_1_133 % 41.26/11.76 | % 41.26/11.76 | Instantiating formula (9) with all_0_14_14, all_76_2_130, 0 and discharging atoms relation(all_0_14_14) = all_76_2_130, relation(all_0_14_14) = 0, yields: % 41.26/11.76 | (180) all_76_2_130 = 0 % 41.26/11.76 | % 41.26/11.76 | Instantiating formula (9) with all_0_14_14, all_76_2_130, all_100_5_177 and discharging atoms relation(all_0_14_14) = all_100_5_177, relation(all_0_14_14) = all_76_2_130, yields: % 41.26/11.76 | (181) all_100_5_177 = all_76_2_130 % 41.26/11.76 | % 41.26/11.76 | Instantiating formula (9) with all_0_14_14, all_72_1_123, all_104_3_185 and discharging atoms relation(all_0_14_14) = all_104_3_185, relation(all_0_14_14) = all_72_1_123, yields: % 41.26/11.76 | (182) all_104_3_185 = all_72_1_123 % 41.26/11.76 | % 41.26/11.76 | Instantiating formula (9) with all_0_14_14, all_39_1_72, all_82_2_140 and discharging atoms relation(all_0_14_14) = all_82_2_140, relation(all_0_14_14) = all_39_1_72, yields: % 41.26/11.76 | (183) all_82_2_140 = all_39_1_72 % 41.26/11.76 | % 41.26/11.76 | Instantiating formula (52) with all_0_14_14, all_29_1_57, all_0_13_13 and discharging atoms relation_dom(all_0_14_14) = all_29_1_57, relation_dom(all_0_14_14) = all_0_13_13, yields: % 41.26/11.76 | (184) all_29_1_57 = all_0_13_13 % 41.26/11.76 | % 41.26/11.76 | Combining equations (176,182) yields a new equation: % 41.26/11.76 | (185) all_100_5_177 = all_72_1_123 % 41.26/11.76 | % 41.26/11.76 | Simplifying 185 yields: % 41.26/11.76 | (186) all_100_5_177 = all_72_1_123 % 41.26/11.76 | % 41.26/11.76 | Combining equations (178,179) yields a new equation: % 41.26/11.76 | (187) all_82_2_140 = all_78_1_133 % 41.26/11.76 | % 41.26/11.76 | Simplifying 187 yields: % 41.26/11.76 | (188) all_82_2_140 = all_78_1_133 % 41.26/11.76 | % 41.26/11.76 | Combining equations (177,179) yields a new equation: % 41.26/11.76 | (189) all_100_5_177 = all_78_1_133 % 41.26/11.76 | % 41.26/11.76 | Simplifying 189 yields: % 41.26/11.76 | (190) all_100_5_177 = all_78_1_133 % 41.26/11.76 | % 41.26/11.76 | Combining equations (170,172) yields a new equation: % 41.26/11.76 | (191) all_98_0_168 = all_76_0_128 % 41.26/11.76 | % 41.26/11.76 | Simplifying 191 yields: % 41.26/11.76 | (192) all_98_0_168 = all_76_0_128 % 41.26/11.76 | % 41.26/11.76 | Combining equations (175,173) yields a new equation: % 41.26/11.76 | (193) all_98_2_170 = 0 % 41.26/11.76 | % 41.26/11.76 | Combining equations (174,173) yields a new equation: % 41.26/11.76 | (194) all_98_2_170 = all_82_1_139 % 41.26/11.76 | % 41.26/11.76 | Combining equations (190,186) yields a new equation: % 41.26/11.76 | (195) all_78_1_133 = all_72_1_123 % 41.26/11.76 | % 41.26/11.76 | Simplifying 195 yields: % 41.26/11.76 | (196) all_78_1_133 = all_72_1_123 % 41.26/11.76 | % 41.26/11.76 | Combining equations (181,186) yields a new equation: % 41.26/11.76 | (197) all_76_2_130 = all_72_1_123 % 41.26/11.76 | % 41.26/11.76 | Simplifying 197 yields: % 41.26/11.76 | (198) all_76_2_130 = all_72_1_123 % 41.26/11.76 | % 41.26/11.76 | Combining equations (171,192) yields a new equation: % 41.26/11.76 | (199) all_82_0_138 = all_76_0_128 % 41.26/11.76 | % 41.26/11.76 | Simplifying 199 yields: % 41.26/11.76 | (200) all_82_0_138 = all_76_0_128 % 41.26/11.76 | % 41.26/11.76 | Combining equations (194,193) yields a new equation: % 41.26/11.76 | (201) all_82_1_139 = 0 % 41.26/11.76 | % 41.26/11.76 | Simplifying 201 yields: % 41.26/11.76 | (202) all_82_1_139 = 0 % 41.26/11.76 | % 41.26/11.77 | Combining equations (188,183) yields a new equation: % 41.26/11.77 | (203) all_78_1_133 = all_39_1_72 % 41.26/11.77 | % 41.26/11.77 | Simplifying 203 yields: % 41.26/11.77 | (204) all_78_1_133 = all_39_1_72 % 41.26/11.77 | % 41.26/11.77 | Combining equations (196,204) yields a new equation: % 41.26/11.77 | (205) all_72_1_123 = all_39_1_72 % 41.26/11.77 | % 41.26/11.77 | Simplifying 205 yields: % 41.26/11.77 | (206) all_72_1_123 = all_39_1_72 % 41.26/11.77 | % 41.26/11.77 | Combining equations (198,180) yields a new equation: % 41.26/11.77 | (207) all_72_1_123 = 0 % 41.26/11.77 | % 41.26/11.77 | Simplifying 207 yields: % 41.26/11.77 | (208) all_72_1_123 = 0 % 41.26/11.77 | % 41.26/11.77 | Combining equations (208,206) yields a new equation: % 41.26/11.77 | (209) all_39_1_72 = 0 % 41.26/11.77 | % 41.26/11.77 | Combining equations (209,183) yields a new equation: % 41.26/11.77 | (210) all_82_2_140 = 0 % 41.26/11.77 | % 41.26/11.77 | From (169) and (111) follows: % 41.26/11.77 | (56) relation_rng(all_0_14_14) = all_0_10_10 % 41.26/11.77 | % 41.26/11.77 | From (200) and (137) follows: % 41.26/11.77 | (130) relation(all_0_8_8) = all_76_0_128 % 41.26/11.77 | % 41.26/11.77 | From (209) and (116) follows: % 41.26/11.77 | (86) relation(all_0_14_14) = 0 % 41.26/11.77 | % 41.26/11.77 | From (184) and (106) follows: % 41.26/11.77 | (70) relation_dom(all_0_14_14) = all_0_13_13 % 41.26/11.77 | % 41.26/11.77 +-Applying beta-rule and splitting (140), into two cases. % 41.26/11.77 |-Branch one: % 41.26/11.77 | (215) ~ (all_82_1_139 = 0) % 41.26/11.77 | % 41.26/11.77 | Equations (202) can reduce 215 to: % 41.26/11.77 | (216) $false % 41.26/11.77 | % 41.26/11.77 |-The branch is then unsatisfiable % 41.26/11.77 |-Branch two: % 41.26/11.77 | (202) all_82_1_139 = 0 % 41.26/11.77 | (218) ~ (all_82_2_140 = 0) | all_82_0_138 = 0 % 41.26/11.77 | % 41.26/11.77 +-Applying beta-rule and splitting (218), into two cases. % 41.26/11.77 |-Branch one: % 41.26/11.77 | (219) ~ (all_82_2_140 = 0) % 41.26/11.77 | % 41.26/11.77 | Equations (210) can reduce 219 to: % 41.26/11.77 | (216) $false % 41.26/11.77 | % 41.26/11.77 |-The branch is then unsatisfiable % 41.26/11.77 |-Branch two: % 41.26/11.77 | (210) all_82_2_140 = 0 % 41.26/11.77 | (222) all_82_0_138 = 0 % 41.26/11.77 | % 41.26/11.77 | Combining equations (200,222) yields a new equation: % 41.26/11.77 | (223) all_76_0_128 = 0 % 41.26/11.77 | % 41.26/11.77 | Simplifying 223 yields: % 41.26/11.77 | (224) all_76_0_128 = 0 % 41.26/11.77 | % 41.26/11.77 | From (224) and (130) follows: % 41.26/11.77 | (225) relation(all_0_8_8) = 0 % 41.26/11.77 | % 41.26/11.77 +-Applying beta-rule and splitting (72), into two cases. % 41.26/11.77 |-Branch one: % 41.26/11.77 | (226) ~ (all_0_8_8 = all_0_14_14) % 41.26/11.77 | % 41.26/11.77 +-Applying beta-rule and splitting (96), into two cases. % 41.26/11.77 |-Branch one: % 41.26/11.77 | (227) all_0_8_8 = all_0_14_14 % 41.26/11.77 | % 41.26/11.77 | Equations (227) can reduce 226 to: % 41.26/11.77 | (216) $false % 41.26/11.77 | % 41.26/11.77 |-The branch is then unsatisfiable % 41.26/11.77 |-Branch two: % 41.26/11.77 | (226) ~ (all_0_8_8 = all_0_14_14) % 41.26/11.77 | (230) ? [v0] : ? [v1] : ? [v2] : (subset(v1, all_0_10_10) = v2 & relation_rng(all_0_14_14) = v1 & relation(all_0_14_14) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0))) % 41.26/11.77 | % 41.26/11.77 | Instantiating (230) with all_390_0_352, all_390_1_353, all_390_2_354 yields: % 41.26/11.77 | (231) subset(all_390_1_353, all_0_10_10) = all_390_0_352 & relation_rng(all_0_14_14) = all_390_1_353 & relation(all_0_14_14) = all_390_2_354 & ( ~ (all_390_0_352 = 0) | ~ (all_390_2_354 = 0)) % 41.26/11.77 | % 41.26/11.77 | Applying alpha-rule on (231) yields: % 41.26/11.77 | (232) subset(all_390_1_353, all_0_10_10) = all_390_0_352 % 41.26/11.77 | (233) relation_rng(all_0_14_14) = all_390_1_353 % 41.26/11.77 | (234) relation(all_0_14_14) = all_390_2_354 % 41.26/11.77 | (235) ~ (all_390_0_352 = 0) | ~ (all_390_2_354 = 0) % 41.26/11.77 | % 41.26/11.77 | Instantiating formula (36) with all_0_14_14, all_390_1_353, all_0_10_10 and discharging atoms relation_rng(all_0_14_14) = all_390_1_353, relation_rng(all_0_14_14) = all_0_10_10, yields: % 41.26/11.77 | (236) all_390_1_353 = all_0_10_10 % 41.26/11.77 | % 41.26/11.77 | Instantiating formula (9) with all_0_14_14, all_390_2_354, 0 and discharging atoms relation(all_0_14_14) = all_390_2_354, relation(all_0_14_14) = 0, yields: % 41.26/11.77 | (237) all_390_2_354 = 0 % 41.26/11.77 | % 41.26/11.77 | From (236) and (232) follows: % 41.26/11.77 | (238) subset(all_0_10_10, all_0_10_10) = all_390_0_352 % 41.26/11.77 | % 41.26/11.77 +-Applying beta-rule and splitting (235), into two cases. % 41.26/11.77 |-Branch one: % 41.26/11.77 | (239) ~ (all_390_0_352 = 0) % 41.26/11.77 | % 41.26/11.77 | Instantiating formula (13) with all_390_0_352, all_0_10_10 and discharging atoms subset(all_0_10_10, all_0_10_10) = all_390_0_352, yields: % 41.26/11.77 | (240) all_390_0_352 = 0 % 41.26/11.77 | % 41.26/11.77 | Equations (240) can reduce 239 to: % 41.26/11.77 | (216) $false % 41.26/11.77 | % 41.26/11.77 |-The branch is then unsatisfiable % 41.26/11.77 |-Branch two: % 41.26/11.77 | (240) all_390_0_352 = 0 % 41.26/11.77 | (243) ~ (all_390_2_354 = 0) % 41.26/11.77 | % 41.26/11.77 | Equations (237) can reduce 243 to: % 41.26/11.77 | (216) $false % 41.26/11.77 | % 41.26/11.77 |-The branch is then unsatisfiable % 41.26/11.77 |-Branch two: % 41.26/11.77 | (227) all_0_8_8 = all_0_14_14 % 41.26/11.77 | (246) ~ (all_0_11_11 = all_0_14_14) % 41.26/11.77 | % 41.26/11.77 | From (227) and (225) follows: % 41.26/11.77 | (86) relation(all_0_14_14) = 0 % 41.26/11.77 | % 41.26/11.77 +-Applying beta-rule and splitting (92), into two cases. % 41.26/11.77 |-Branch one: % 41.26/11.77 | (248) all_0_11_11 = all_0_14_14 % 41.26/11.77 | % 41.26/11.77 | Equations (248) can reduce 246 to: % 41.26/11.77 | (216) $false % 41.26/11.77 | % 41.26/11.77 |-The branch is then unsatisfiable % 41.26/11.77 |-Branch two: % 41.26/11.77 | (246) ~ (all_0_11_11 = all_0_14_14) % 41.26/11.77 | (251) ? [v0] : ? [v1] : ? [v2] : (subset(v1, all_0_13_13) = v2 & relation(all_0_14_14) = v0 & relation_dom(all_0_14_14) = v1 & ( ~ (v2 = 0) | ~ (v0 = 0))) % 41.26/11.77 | % 41.26/11.77 | Instantiating (251) with all_390_0_355, all_390_1_356, all_390_2_357 yields: % 41.26/11.77 | (252) subset(all_390_1_356, all_0_13_13) = all_390_0_355 & relation(all_0_14_14) = all_390_2_357 & relation_dom(all_0_14_14) = all_390_1_356 & ( ~ (all_390_0_355 = 0) | ~ (all_390_2_357 = 0)) % 41.26/11.77 | % 41.26/11.77 | Applying alpha-rule on (252) yields: % 41.26/11.77 | (253) subset(all_390_1_356, all_0_13_13) = all_390_0_355 % 41.26/11.77 | (254) relation(all_0_14_14) = all_390_2_357 % 41.26/11.77 | (255) relation_dom(all_0_14_14) = all_390_1_356 % 41.26/11.77 | (256) ~ (all_390_0_355 = 0) | ~ (all_390_2_357 = 0) % 41.26/11.77 | % 41.26/11.77 | Instantiating formula (9) with all_0_14_14, all_390_2_357, 0 and discharging atoms relation(all_0_14_14) = all_390_2_357, relation(all_0_14_14) = 0, yields: % 41.26/11.77 | (257) all_390_2_357 = 0 % 41.26/11.77 | % 41.26/11.77 | Instantiating formula (52) with all_0_14_14, all_390_1_356, all_0_13_13 and discharging atoms relation_dom(all_0_14_14) = all_390_1_356, relation_dom(all_0_14_14) = all_0_13_13, yields: % 41.26/11.77 | (258) all_390_1_356 = all_0_13_13 % 41.26/11.77 | % 41.26/11.77 | From (258) and (253) follows: % 41.26/11.77 | (259) subset(all_0_13_13, all_0_13_13) = all_390_0_355 % 41.26/11.77 | % 41.26/11.77 +-Applying beta-rule and splitting (256), into two cases. % 41.26/11.77 |-Branch one: % 41.26/11.77 | (260) ~ (all_390_0_355 = 0) % 41.26/11.77 | % 41.26/11.77 | Instantiating formula (13) with all_390_0_355, all_0_13_13 and discharging atoms subset(all_0_13_13, all_0_13_13) = all_390_0_355, yields: % 41.26/11.77 | (261) all_390_0_355 = 0 % 41.26/11.77 | % 41.26/11.77 | Equations (261) can reduce 260 to: % 41.26/11.77 | (216) $false % 41.26/11.77 | % 41.26/11.77 |-The branch is then unsatisfiable % 41.26/11.77 |-Branch two: % 41.26/11.77 | (261) all_390_0_355 = 0 % 41.26/11.77 | (264) ~ (all_390_2_357 = 0) % 41.26/11.77 | % 41.26/11.77 | Equations (257) can reduce 264 to: % 41.26/11.77 | (216) $false % 41.26/11.77 | % 41.26/11.77 |-The branch is then unsatisfiable % 41.26/11.77 % SZS output end Proof for theBenchmark % 41.26/11.77 % 41.26/11.77 11129ms %------------------------------------------------------------------------------