%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU236+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n017.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Tue Jul 19 08:48:00 EDT 2022 % Result : Theorem 28.42s 7.50s % Output : Proof 36.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU236+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n017.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 : Sat Jun 18 20:08:12 EDT 2022 % 0.13/0.34 % CPUTime : % 0.20/0.59 ____ _ % 0.20/0.59 ___ / __ \_____(_)___ ________ __________ % 0.20/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.20/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.20/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic % 0.20/0.59 (ePrincess v.1.0) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2015 % 0.20/0.59 (c) Peter Backeman, 2014-2015 % 0.20/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.20/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.20/0.59 Bug reports to peter@backeman.se % 0.20/0.59 % 0.20/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.62/0.98 Prover 0: Preprocessing ... % 2.40/1.24 Prover 0: Warning: ignoring some quantifiers % 2.50/1.29 Prover 0: Constructing countermodel ... % 12.98/3.82 Prover 0: gave up % 12.98/3.82 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 12.98/3.87 Prover 1: Preprocessing ... % 13.87/3.99 Prover 1: Warning: ignoring some quantifiers % 13.87/3.99 Prover 1: Constructing countermodel ... % 14.71/4.26 Prover 1: gave up % 14.71/4.26 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 15.28/4.30 Prover 2: Preprocessing ... % 15.74/4.42 Prover 2: Warning: ignoring some quantifiers % 15.74/4.42 Prover 2: Constructing countermodel ... % 22.91/6.15 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 22.91/6.21 Prover 3: Preprocessing ... % 23.32/6.26 Prover 3: Warning: ignoring some quantifiers % 23.32/6.27 Prover 3: Constructing countermodel ... % 26.17/6.95 Prover 3: gave up % 26.17/6.95 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 26.17/6.98 Prover 4: Preprocessing ... % 26.56/7.07 Prover 4: Warning: ignoring some quantifiers % 26.56/7.07 Prover 4: Constructing countermodel ... % 28.42/7.49 Prover 4: proved (542ms) % 28.42/7.50 Prover 2: stopped % 28.42/7.50 % 28.42/7.50 No countermodel exists, formula is valid % 28.42/7.50 % SZS status Theorem for theBenchmark % 28.42/7.50 % 28.42/7.50 Generating proof ... Warning: ignoring some quantifiers % 35.37/9.16 found it (size 164) % 35.37/9.16 % 35.37/9.16 % SZS output start Proof for theBenchmark % 35.37/9.16 Assumed formulas after preprocessing and simplification: % 35.37/9.16 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ( ~ (v13 = 0) & ~ (v11 = 0) & ~ (v8 = 0) & relation_empty_yielding(v6) = 0 & relation_empty_yielding(v5) = 0 & relation_empty_yielding(empty_set) = 0 & succ(v0) = v1 & ordinal_subset(v1, v2) = v4 & one_to_one(v14) = 0 & one_to_one(v9) = 0 & one_to_one(empty_set) = 0 & relation(v19) = 0 & relation(v17) = 0 & relation(v15) = 0 & relation(v14) = 0 & relation(v12) = 0 & relation(v9) = 0 & relation(v6) = 0 & relation(v5) = 0 & relation(empty_set) = 0 & ordinal(v18) = 0 & ordinal(v14) = 0 & ordinal(v7) = 0 & ordinal(v2) = 0 & ordinal(v0) = 0 & ordinal(empty_set) = 0 & epsilon_transitive(v18) = 0 & epsilon_transitive(v14) = 0 & epsilon_transitive(v7) = 0 & epsilon_transitive(empty_set) = 0 & epsilon_connected(v18) = 0 & epsilon_connected(v14) = 0 & epsilon_connected(v7) = 0 & epsilon_connected(empty_set) = 0 & empty(v17) = 0 & empty(v16) = 0 & empty(v15) = 0 & empty(v14) = 0 & empty(v12) = v13 & empty(v10) = v11 & empty(v7) = v8 & empty(empty_set) = 0 & function(v19) = 0 & function(v15) = 0 & function(v14) = 0 & function(v9) = 0 & function(v5) = 0 & function(empty_set) = 0 & in(v0, v2) = v3 & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (powerset(v22) = v23) | ~ (element(v21, v23) = 0) | ~ (element(v20, v22) = v24) | ? [v25] : ( ~ (v25 = 0) & in(v20, v21) = v25)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (subset(v23, v21) = v24) | ~ (set_union2(v20, v22) = v23) | ? [v25] : ? [v26] : (subset(v22, v21) = v26 & subset(v20, v21) = v25 & ( ~ (v26 = 0) | ~ (v25 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (powerset(v21) = v22) | ~ (element(v20, v22) = v23) | ? [v24] : ( ~ (v24 = 0) & subset(v20, v21) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (element(v20, v22) = v23) | ~ (in(v20, v21) = 0) | ? [v24] : ? [v25] : ( ~ (v25 = 0) & powerset(v22) = v24 & element(v21, v24) = v25)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (subset(v20, v21) = 0) | ~ (in(v22, v21) = v23) | ? [v24] : ( ~ (v24 = 0) & in(v22, v20) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (element(v23, v22) = v21) | ~ (element(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (subset(v23, v22) = v21) | ~ (subset(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (ordinal_subset(v23, v22) = v21) | ~ (ordinal_subset(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (set_union2(v23, v22) = v21) | ~ (set_union2(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (in(v23, v22) = v21) | ~ (in(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (powerset(v22) = v23) | ~ (element(v21, v23) = 0) | ~ (in(v20, v21) = 0) | element(v20, v22) = 0) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (powerset(v22) = v23) | ~ (element(v21, v23) = 0) | ~ (in(v20, v21) = 0) | ? [v24] : ( ~ (v24 = 0) & empty(v22) = v24)) & ! [v20] : ! [v21] : ! [v22] : (v22 = v20 | ~ (singleton(v20) = v21) | ~ (in(v22, v21) = 0)) & ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (element(v20, v21) = v22) | ? [v23] : ( ~ (v23 = 0) & in(v20, v21) = v23)) & ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (subset(v21, v20) = v22) | ~ (epsilon_transitive(v20) = 0) | ? [v23] : ( ~ (v23 = 0) & in(v21, v20) = v23)) & ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (subset(v20, v21) = v22) | ? [v23] : ? [v24] : ( ~ (v24 = 0) & powerset(v21) = v23 & element(v20, v23) = v24)) & ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (subset(v20, v21) = v22) | ? [v23] : ? [v24] : ( ~ (v24 = 0) & in(v23, v21) = v24 & in(v23, v20) = 0)) & ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (singleton(v20) = v21) | ~ (in(v20, v21) = v22)) & ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (ordinal_subset(v21, v20) = v22) | ? [v23] : ? [v24] : ? [v25] : (ordinal_subset(v20, v21) = v25 & ordinal(v21) = v24 & ordinal(v20) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | v25 = 0))) & ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (ordinal_subset(v20, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : (ordinal_subset(v21, v20) = v25 & ordinal(v21) = v24 & ordinal(v20) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | v25 = 0))) & ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (ordinal_subset(v20, v20) = v22) | ~ (ordinal(v21) = 0) | ? [v23] : ( ~ (v23 = 0) & ordinal(v20) = v23)) & ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (in(v20, v21) = v22) | ? [v23] : ? [v24] : (element(v20, v21) = v23 & empty(v21) = v24 & ( ~ (v23 = 0) | v24 = 0))) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (powerset(v22) = v21) | ~ (powerset(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (relation_empty_yielding(v22) = v21) | ~ (relation_empty_yielding(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (succ(v22) = v21) | ~ (succ(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (singleton(v22) = v21) | ~ (singleton(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (one_to_one(v22) = v21) | ~ (one_to_one(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (relation(v22) = v21) | ~ (relation(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (ordinal(v22) = v21) | ~ (ordinal(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (epsilon_transitive(v22) = v21) | ~ (epsilon_transitive(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (epsilon_connected(v22) = v21) | ~ (epsilon_connected(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (empty(v22) = v21) | ~ (empty(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (function(v22) = v21) | ~ (function(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ( ~ (powerset(v21) = v22) | ~ (element(v20, v22) = 0) | subset(v20, v21) = 0) & ! [v20] : ! [v21] : ! [v22] : ( ~ (subset(v20, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : (ordinal_subset(v20, v21) = v25 & ordinal(v21) = v24 & ordinal(v20) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | (( ~ (v25 = 0) | v22 = 0) & ( ~ (v22 = 0) | v25 = 0))))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (subset(v20, v21) = 0) | ~ (in(v22, v20) = 0) | in(v22, v21) = 0) & ! [v20] : ! [v21] : ! [v22] : ( ~ (ordinal_subset(v20, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : (subset(v20, v21) = v25 & ordinal(v21) = v24 & ordinal(v20) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | (( ~ (v25 = 0) | v22 = 0) & ( ~ (v22 = 0) | v25 = 0))))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (set_union2(v21, v20) = v22) | set_union2(v20, v21) = v22) & ! [v20] : ! [v21] : ! [v22] : ( ~ (set_union2(v21, v20) = v22) | ? [v23] : ? [v24] : (empty(v22) = v24 & empty(v20) = v23 & ( ~ (v24 = 0) | v23 = 0))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (set_union2(v20, v21) = v22) | set_union2(v21, v20) = v22) & ! [v20] : ! [v21] : ! [v22] : ( ~ (set_union2(v20, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : (relation(v22) = v25 & relation(v21) = v24 & relation(v20) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | v25 = 0))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (set_union2(v20, v21) = v22) | ? [v23] : ? [v24] : (empty(v22) = v24 & empty(v20) = v23 & ( ~ (v24 = 0) | v23 = 0))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (empty(v22) = 0) | ~ (in(v20, v21) = 0) | ? [v23] : ? [v24] : ( ~ (v24 = 0) & powerset(v22) = v23 & element(v21, v23) = v24)) & ? [v20] : ! [v21] : ! [v22] : (v22 = v20 | ~ (singleton(v21) = v22) | ? [v23] : ? [v24] : (in(v23, v20) = v24 & ( ~ (v24 = 0) | ~ (v23 = v21)) & (v24 = 0 | v23 = v21))) & ! [v20] : ! [v21] : (v21 = v20 | ~ (set_union2(v20, v20) = v21)) & ! [v20] : ! [v21] : (v21 = v20 | ~ (set_union2(v20, empty_set) = v21)) & ! [v20] : ! [v21] : (v21 = v20 | ~ (empty(v21) = 0) | ~ (empty(v20) = 0)) & ! [v20] : ! [v21] : (v21 = 0 | ~ (subset(v20, v20) = v21)) & ! [v20] : ! [v21] : (v21 = 0 | ~ (relation(v20) = v21) | ? [v22] : ( ~ (v22 = 0) & empty(v20) = v22)) & ! [v20] : ! [v21] : (v21 = 0 | ~ (ordinal(v20) = v21) | ? [v22] : ? [v23] : (epsilon_transitive(v20) = v22 & epsilon_connected(v20) = v23 & ( ~ (v23 = 0) | ~ (v22 = 0)))) & ! [v20] : ! [v21] : (v21 = 0 | ~ (epsilon_transitive(v20) = v21) | ? [v22] : ? [v23] : ( ~ (v23 = 0) & subset(v22, v20) = v23 & in(v22, v20) = 0)) & ! [v20] : ! [v21] : (v21 = 0 | ~ (function(v20) = v21) | ? [v22] : ( ~ (v22 = 0) & empty(v20) = v22)) & ! [v20] : ! [v21] : ( ~ (element(v20, v21) = 0) | ? [v22] : ? [v23] : (empty(v21) = v22 & in(v20, v21) = v23 & (v23 = 0 | v22 = 0))) & ! [v20] : ! [v21] : ( ~ (subset(v20, v21) = 0) | ? [v22] : (powerset(v21) = v22 & element(v20, v22) = 0)) & ! [v20] : ! [v21] : ( ~ (succ(v20) = v21) | in(v20, v21) = 0) & ! [v20] : ! [v21] : ( ~ (succ(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (ordinal(v21) = v26 & ordinal(v20) = v22 & epsilon_transitive(v21) = v24 & epsilon_connected(v21) = v25 & empty(v21) = v23 & ( ~ (v22 = 0) | (v26 = 0 & v25 = 0 & v24 = 0 & ~ (v23 = 0))))) & ! [v20] : ! [v21] : ( ~ (succ(v20) = v21) | ? [v22] : ( ~ (v22 = 0) & empty(v21) = v22)) & ! [v20] : ! [v21] : ( ~ (succ(v20) = v21) | ? [v22] : (singleton(v20) = v22 & set_union2(v20, v22) = v21)) & ! [v20] : ! [v21] : ( ~ (singleton(v20) = v21) | ? [v22] : (succ(v20) = v22 & set_union2(v20, v21) = v22)) & ! [v20] : ! [v21] : ( ~ (one_to_one(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : (relation(v20) = v22 & empty(v20) = v23 & function(v20) = v24 & ( ~ (v24 = 0) | ~ (v23 = 0) | ~ (v22 = 0) | v21 = 0))) & ! [v20] : ! [v21] : ( ~ (ordinal(v21) = 0) | ~ (ordinal(v20) = 0) | ordinal_subset(v20, v20) = 0) & ! [v20] : ! [v21] : ( ~ (ordinal(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : (epsilon_transitive(v20) = v23 & epsilon_connected(v20) = v24 & empty(v20) = v22 & ( ~ (v22 = 0) | (v24 = 0 & v23 = 0 & v21 = 0)))) & ! [v20] : ! [v21] : ( ~ (epsilon_transitive(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : (ordinal(v20) = v24 & epsilon_connected(v20) = v23 & empty(v20) = v22 & ( ~ (v22 = 0) | (v24 = 0 & v23 = 0 & v21 = 0)))) & ! [v20] : ! [v21] : ( ~ (epsilon_transitive(v20) = v21) | ? [v22] : ? [v23] : (ordinal(v20) = v22 & epsilon_connected(v20) = v23 & ( ~ (v22 = 0) | (v23 = 0 & v21 = 0)))) & ! [v20] : ! [v21] : ( ~ (epsilon_transitive(v20) = 0) | ~ (in(v21, v20) = 0) | subset(v21, v20) = 0) & ! [v20] : ! [v21] : ( ~ (epsilon_connected(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : (ordinal(v20) = v24 & epsilon_transitive(v20) = v23 & empty(v20) = v22 & ( ~ (v22 = 0) | (v24 = 0 & v23 = 0 & v21 = 0)))) & ! [v20] : ! [v21] : ( ~ (epsilon_connected(v20) = v21) | ? [v22] : ? [v23] : (ordinal(v20) = v22 & epsilon_transitive(v20) = v23 & ( ~ (v22 = 0) | (v23 = 0 & v21 = 0)))) & ! [v20] : ! [v21] : ( ~ (in(v21, v20) = 0) | ? [v22] : ( ~ (v22 = 0) & in(v20, v21) = v22)) & ! [v20] : ! [v21] : ( ~ (in(v20, v21) = 0) | element(v20, v21) = 0) & ! [v20] : ! [v21] : ( ~ (in(v20, v21) = 0) | ? [v22] : ( ~ (v22 = 0) & empty(v21) = v22)) & ! [v20] : ! [v21] : ( ~ (in(v20, v21) = 0) | ? [v22] : ( ~ (v22 = 0) & in(v21, v20) = v22)) & ! [v20] : (v20 = empty_set | ~ (empty(v20) = 0)) & ! [v20] : ( ~ (relation(v20) = 0) | ? [v21] : ? [v22] : ? [v23] : (one_to_one(v20) = v23 & empty(v20) = v21 & function(v20) = v22 & ( ~ (v22 = 0) | ~ (v21 = 0) | v23 = 0))) & ! [v20] : ( ~ (ordinal(v20) = 0) | ? [v21] : ? [v22] : ( ~ (v22 = 0) & succ(v20) = v21 & ordinal(v21) = 0 & epsilon_transitive(v21) = 0 & epsilon_connected(v21) = 0 & empty(v21) = v22)) & ! [v20] : ( ~ (ordinal(v20) = 0) | (epsilon_transitive(v20) = 0 & epsilon_connected(v20) = 0)) & ! [v20] : ( ~ (epsilon_transitive(v20) = 0) | ? [v21] : ? [v22] : (ordinal(v20) = v22 & epsilon_connected(v20) = v21 & ( ~ (v21 = 0) | v22 = 0))) & ! [v20] : ( ~ (epsilon_connected(v20) = 0) | ? [v21] : ? [v22] : (ordinal(v20) = v22 & epsilon_transitive(v20) = v21 & ( ~ (v21 = 0) | v22 = 0))) & ! [v20] : ( ~ (empty(v20) = 0) | relation(v20) = 0) & ! [v20] : ( ~ (empty(v20) = 0) | function(v20) = 0) & ! [v20] : ( ~ (empty(v20) = 0) | ? [v21] : ? [v22] : ? [v23] : (one_to_one(v20) = v23 & relation(v20) = v21 & function(v20) = v22 & ( ~ (v22 = 0) | ~ (v21 = 0) | v23 = 0))) & ! [v20] : ( ~ (empty(v20) = 0) | (ordinal(v20) = 0 & epsilon_transitive(v20) = 0 & epsilon_connected(v20) = 0)) & ! [v20] : ( ~ (function(v20) = 0) | ? [v21] : ? [v22] : ? [v23] : (one_to_one(v20) = v23 & relation(v20) = v21 & empty(v20) = v22 & ( ~ (v22 = 0) | ~ (v21 = 0) | v23 = 0))) & ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (powerset(v22) = v24 & element(v21, v24) = v25 & element(v20, v22) = v26 & in(v20, v21) = v23 & ( ~ (v25 = 0) | ~ (v23 = 0) | v26 = 0)) & ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (subset(v25, v21) = v26 & subset(v22, v21) = v24 & subset(v20, v21) = v23 & set_union2(v20, v22) = v25 & ( ~ (v24 = 0) | ~ (v23 = 0) | v26 = 0)) & ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (subset(v20, v21) = v25 & ordinal_subset(v20, v21) = v24 & ordinal(v21) = v23 & ordinal(v20) = v22 & ( ~ (v23 = 0) | ~ (v22 = 0) | (( ~ (v25 = 0) | v24 = 0) & ( ~ (v24 = 0) | v25 = 0)))) & ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (one_to_one(v20) = v24 & relation(v20) = v21 & empty(v20) = v22 & function(v20) = v23 & ( ~ (v23 = 0) | ~ (v22 = 0) | ~ (v21 = 0) | v24 = 0)) & ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (ordinal(v20) = v24 & epsilon_transitive(v20) = v22 & epsilon_connected(v20) = v23 & empty(v20) = v21 & ( ~ (v21 = 0) | (v24 = 0 & v23 = 0 & v22 = 0))) & ? [v20] : ? [v21] : ? [v22] : (succ(v20) = v21 & singleton(v20) = v22 & set_union2(v20, v22) = v21) & ? [v20] : ? [v21] : element(v21, v20) = 0 & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0)))) % 35.93/9.22 | 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, all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18, all_0_19_19 yields: % 35.93/9.22 | (1) ~ (all_0_6_6 = 0) & ~ (all_0_8_8 = 0) & ~ (all_0_11_11 = 0) & relation_empty_yielding(all_0_13_13) = 0 & relation_empty_yielding(all_0_14_14) = 0 & relation_empty_yielding(empty_set) = 0 & succ(all_0_19_19) = all_0_18_18 & ordinal_subset(all_0_18_18, all_0_17_17) = all_0_15_15 & one_to_one(all_0_5_5) = 0 & one_to_one(all_0_10_10) = 0 & one_to_one(empty_set) = 0 & relation(all_0_0_0) = 0 & relation(all_0_2_2) = 0 & relation(all_0_4_4) = 0 & relation(all_0_5_5) = 0 & relation(all_0_7_7) = 0 & relation(all_0_10_10) = 0 & relation(all_0_13_13) = 0 & relation(all_0_14_14) = 0 & relation(empty_set) = 0 & ordinal(all_0_1_1) = 0 & ordinal(all_0_5_5) = 0 & ordinal(all_0_12_12) = 0 & ordinal(all_0_17_17) = 0 & ordinal(all_0_19_19) = 0 & ordinal(empty_set) = 0 & epsilon_transitive(all_0_1_1) = 0 & epsilon_transitive(all_0_5_5) = 0 & epsilon_transitive(all_0_12_12) = 0 & epsilon_transitive(empty_set) = 0 & epsilon_connected(all_0_1_1) = 0 & epsilon_connected(all_0_5_5) = 0 & epsilon_connected(all_0_12_12) = 0 & epsilon_connected(empty_set) = 0 & empty(all_0_2_2) = 0 & empty(all_0_3_3) = 0 & empty(all_0_4_4) = 0 & empty(all_0_5_5) = 0 & empty(all_0_7_7) = all_0_6_6 & empty(all_0_9_9) = all_0_8_8 & empty(all_0_12_12) = all_0_11_11 & empty(empty_set) = 0 & function(all_0_0_0) = 0 & function(all_0_4_4) = 0 & function(all_0_5_5) = 0 & function(all_0_10_10) = 0 & function(all_0_14_14) = 0 & function(empty_set) = 0 & in(all_0_19_19, all_0_17_17) = all_0_16_16 & ! [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] : ! [v4] : (v4 = 0 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ? [v5] : ? [v6] : (subset(v2, v1) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 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] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordinal_subset(v3, v2) = v1) | ~ (ordinal_subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (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 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v1, v0) = v2) | ~ (epsilon_transitive(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3)) & ! [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 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (ordinal_subset(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : (ordinal_subset(v0, v1) = v5 & ordinal(v1) = v4 & ordinal(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (ordinal_subset(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (ordinal_subset(v1, v0) = v5 & ordinal(v1) = v4 & ordinal(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (ordinal_subset(v0, v0) = v2) | ~ (ordinal(v1) = 0) | ? [v3] : ( ~ (v3 = 0) & ordinal(v0) = v3)) & ! [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 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(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 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (ordinal_subset(v0, v1) = v5 & ordinal(v1) = v4 & ordinal(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordinal_subset(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset(v0, v1) = v5 & ordinal(v1) = v4 & ordinal(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 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] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [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 | ~ (ordinal(v0) = v1) | ? [v2] : ? [v3] : (epsilon_transitive(v0) = v2 & epsilon_connected(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & subset(v2, v0) = v3 & in(v2, v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | in(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (ordinal(v1) = v6 & ordinal(v0) = v2 & epsilon_transitive(v1) = v4 & epsilon_connected(v1) = v5 & empty(v1) = v3 & ( ~ (v2 = 0) | (v6 = 0 & v5 = 0 & v4 = 0 & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : (singleton(v0) = v2 & set_union2(v0, v2) = v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : (succ(v0) = v2 & set_union2(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v2 & empty(v0) = v3 & function(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0))) & ! [v0] : ! [v1] : ( ~ (ordinal(v1) = 0) | ~ (ordinal(v0) = 0) | ordinal_subset(v0, v0) = 0) & ! [v0] : ! [v1] : ( ~ (ordinal(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (epsilon_transitive(v0) = v3 & epsilon_connected(v0) = v4 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0 & v1 = 0)))) & ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (ordinal(v0) = v4 & epsilon_connected(v0) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0 & v1 = 0)))) & ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : (ordinal(v0) = v2 & epsilon_connected(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = 0) | ~ (in(v1, v0) = 0) | subset(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (ordinal(v0) = v4 & epsilon_transitive(v0) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0 & v1 = 0)))) & ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ? [v3] : (ordinal(v0) = v2 & epsilon_transitive(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 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] : (one_to_one(v0) = v3 & empty(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0] : ( ~ (ordinal(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & succ(v0) = v1 & ordinal(v1) = 0 & epsilon_transitive(v1) = 0 & epsilon_connected(v1) = 0 & empty(v1) = v2)) & ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)) & ! [v0] : ( ~ (epsilon_transitive(v0) = 0) | ? [v1] : ? [v2] : (ordinal(v0) = v2 & epsilon_connected(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))) & ! [v0] : ( ~ (epsilon_connected(v0) = 0) | ? [v1] : ? [v2] : (ordinal(v0) = v2 & epsilon_transitive(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))) & ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0] : ( ~ (empty(v0) = 0) | (ordinal(v0) = 0 & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)) & ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (powerset(v2) = v4 & element(v1, v4) = v5 & element(v0, v2) = v6 & in(v0, v1) = v3 & ( ~ (v5 = 0) | ~ (v3 = 0) | v6 = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (subset(v5, v1) = v6 & subset(v2, v1) = v4 & subset(v0, v1) = v3 & set_union2(v0, v2) = v5 & ( ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (subset(v0, v1) = v5 & ordinal_subset(v0, v1) = v4 & ordinal(v1) = v3 & ordinal(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (( ~ (v5 = 0) | v4 = 0) & ( ~ (v4 = 0) | v5 = 0)))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (one_to_one(v0) = v4 & relation(v0) = v1 & empty(v0) = v2 & function(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | v4 = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordinal(v0) = v4 & epsilon_transitive(v0) = v2 & epsilon_connected(v0) = v3 & empty(v0) = v1 & ( ~ (v1 = 0) | (v4 = 0 & v3 = 0 & v2 = 0))) & ? [v0] : ? [v1] : ? [v2] : (succ(v0) = v1 & singleton(v0) = v2 & set_union2(v0, v2) = v1) & ? [v0] : ? [v1] : element(v1, v0) = 0 & ((all_0_15_15 = 0 & ~ (all_0_16_16 = 0)) | (all_0_16_16 = 0 & ~ (all_0_15_15 = 0))) % 36.08/9.24 | % 36.08/9.24 | Applying alpha-rule on (1) yields: % 36.08/9.24 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4)) % 36.08/9.24 | (3) ordinal(empty_set) = 0 % 36.08/9.24 | (4) epsilon_transitive(all_0_1_1) = 0 % 36.08/9.24 | (5) ! [v0] : ( ~ (ordinal(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & succ(v0) = v1 & ordinal(v1) = 0 & epsilon_transitive(v1) = 0 & epsilon_connected(v1) = 0 & empty(v1) = v2)) % 36.08/9.24 | (6) ~ (all_0_8_8 = 0) % 36.08/9.24 | (7) ~ (all_0_11_11 = 0) % 36.08/9.24 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) % 36.08/9.24 | (9) ~ (all_0_6_6 = 0) % 36.08/9.24 | (10) ordinal(all_0_12_12) = 0 % 36.08/9.24 | (11) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) % 36.08/9.24 | (12) ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (ordinal(v0) = v4 & epsilon_transitive(v0) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0 & v1 = 0)))) % 36.08/9.24 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 36.08/9.24 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) % 36.08/9.24 | (15) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 36.08/9.24 | (16) epsilon_connected(all_0_1_1) = 0 % 36.08/9.24 | (17) function(all_0_14_14) = 0 % 36.08/9.24 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 36.08/9.24 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 36.08/9.24 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) % 36.08/9.24 | (21) epsilon_connected(all_0_5_5) = 0 % 36.08/9.24 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 36.08/9.24 | (23) ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) % 36.08/9.24 | (24) (all_0_15_15 = 0 & ~ (all_0_16_16 = 0)) | (all_0_16_16 = 0 & ~ (all_0_15_15 = 0)) % 36.08/9.24 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) % 36.08/9.24 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (ordinal_subset(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : (ordinal_subset(v0, v1) = v5 & ordinal(v1) = v4 & ordinal(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 36.08/9.24 | (27) function(all_0_5_5) = 0 % 36.08/9.24 | (28) ordinal(all_0_1_1) = 0 % 36.08/9.24 | (29) ordinal(all_0_19_19) = 0 % 36.08/9.24 | (30) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 36.08/9.24 | (31) ! [v0] : ! [v1] : ( ~ (ordinal(v1) = 0) | ~ (ordinal(v0) = 0) | ordinal_subset(v0, v0) = 0) % 36.08/9.24 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) % 36.08/9.25 | (33) epsilon_transitive(empty_set) = 0 % 36.08/9.25 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) % 36.08/9.25 | (35) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (one_to_one(v0) = v4 & relation(v0) = v1 & empty(v0) = v2 & function(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | v4 = 0)) % 36.08/9.25 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) % 36.08/9.25 | (37) empty(all_0_5_5) = 0 % 36.08/9.25 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 36.08/9.25 | (39) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 36.08/9.25 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) % 36.08/9.25 | (41) ? [v0] : ? [v1] : element(v1, v0) = 0 % 36.08/9.25 | (42) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 36.08/9.25 | (43) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordinal(v0) = v4 & epsilon_transitive(v0) = v2 & epsilon_connected(v0) = v3 & empty(v0) = v1 & ( ~ (v1 = 0) | (v4 = 0 & v3 = 0 & v2 = 0))) % 36.08/9.25 | (44) relation_empty_yielding(empty_set) = 0 % 36.08/9.25 | (45) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 36.08/9.25 | (46) function(all_0_4_4) = 0 % 36.08/9.25 | (47) empty(all_0_9_9) = all_0_8_8 % 36.08/9.25 | (48) ? [v0] : ? [v1] : ? [v2] : (succ(v0) = v1 & singleton(v0) = v2 & set_union2(v0, v2) = v1) % 36.08/9.25 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 36.08/9.25 | (50) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) % 36.08/9.25 | (51) relation_empty_yielding(all_0_13_13) = 0 % 36.08/9.25 | (52) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = 0) | ~ (in(v1, v0) = 0) | subset(v1, v0) = 0) % 36.08/9.25 | (53) function(empty_set) = 0 % 36.08/9.25 | (54) succ(all_0_19_19) = all_0_18_18 % 36.08/9.25 | (55) ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ? [v3] : (ordinal(v0) = v2 & epsilon_transitive(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) % 36.08/9.25 | (56) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : (ordinal(v0) = v2 & epsilon_connected(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) % 36.08/9.25 | (57) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (ordinal_subset(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (ordinal_subset(v1, v0) = v5 & ordinal(v1) = v4 & ordinal(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 36.08/9.25 | (58) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 36.08/9.25 | (59) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (subset(v5, v1) = v6 & subset(v2, v1) = v4 & subset(v0, v1) = v3 & set_union2(v0, v2) = v5 & ( ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0)) % 36.08/9.25 | (60) ordinal(all_0_5_5) = 0 % 36.08/9.25 | (61) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 36.08/9.25 | (62) epsilon_connected(all_0_12_12) = 0 % 36.08/9.25 | (63) ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v2 & empty(v0) = v3 & function(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0))) % 36.08/9.25 | (64) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) % 36.08/9.25 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 36.08/9.25 | (66) in(all_0_19_19, all_0_17_17) = all_0_16_16 % 36.08/9.25 | (67) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (ordinal(v1) = v6 & ordinal(v0) = v2 & epsilon_transitive(v1) = v4 & epsilon_connected(v1) = v5 & empty(v1) = v3 & ( ~ (v2 = 0) | (v6 = 0 & v5 = 0 & v4 = 0 & ~ (v3 = 0))))) % 36.08/9.25 | (68) empty(all_0_12_12) = all_0_11_11 % 36.08/9.25 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ? [v5] : ? [v6] : (subset(v2, v1) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) % 36.08/9.26 | (70) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 36.08/9.26 | (71) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : (succ(v0) = v2 & set_union2(v0, v1) = v2)) % 36.08/9.26 | (72) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) % 36.08/9.26 | (73) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (ordinal(v0) = v4 & epsilon_connected(v0) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0 & v1 = 0)))) % 36.08/9.26 | (74) relation(all_0_4_4) = 0 % 36.08/9.26 | (75) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 36.08/9.26 | (76) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 36.08/9.26 | (77) function(all_0_10_10) = 0 % 36.08/9.26 | (78) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) % 36.08/9.26 | (79) ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)) % 36.08/9.26 | (80) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | in(v0, v1) = 0) % 36.08/9.26 | (81) ordinal_subset(all_0_18_18, all_0_17_17) = all_0_15_15 % 36.08/9.26 | (82) empty(all_0_7_7) = all_0_6_6 % 36.08/9.26 | (83) one_to_one(all_0_10_10) = 0 % 36.08/9.26 | (84) ! [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)) % 36.08/9.26 | (85) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) % 36.08/9.26 | (86) ! [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)) % 36.08/9.26 | (87) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) % 36.08/9.26 | (88) ordinal(all_0_17_17) = 0 % 36.08/9.26 | (89) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) % 36.08/9.26 | (90) relation(all_0_10_10) = 0 % 36.08/9.26 | (91) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : (singleton(v0) = v2 & set_union2(v0, v2) = v1)) % 36.08/9.26 | (92) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) % 36.08/9.26 | (93) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) % 36.08/9.26 | (94) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (subset(v0, v1) = v5 & ordinal_subset(v0, v1) = v4 & ordinal(v1) = v3 & ordinal(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (( ~ (v5 = 0) | v4 = 0) & ( ~ (v4 = 0) | v5 = 0)))) % 36.08/9.26 | (95) relation(all_0_7_7) = 0 % 36.08/9.26 | (96) relation(all_0_14_14) = 0 % 36.08/9.26 | (97) ! [v0] : ! [v1] : (v1 = 0 | ~ (ordinal(v0) = v1) | ? [v2] : ? [v3] : (epsilon_transitive(v0) = v2 & epsilon_connected(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 36.08/9.26 | (98) relation(all_0_2_2) = 0 % 36.08/9.26 | (99) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & empty(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 36.08/9.26 | (100) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) % 36.08/9.26 | (101) relation_empty_yielding(all_0_14_14) = 0 % 36.08/9.26 | (102) epsilon_transitive(all_0_12_12) = 0 % 36.08/9.26 | (103) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) % 36.08/9.26 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 36.08/9.26 | (105) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 36.08/9.26 | (106) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 36.08/9.26 | (107) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) % 36.08/9.27 | (108) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 36.08/9.27 | (109) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 36.08/9.27 | (110) empty(empty_set) = 0 % 36.08/9.27 | (111) empty(all_0_3_3) = 0 % 36.08/9.27 | (112) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordinal_subset(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset(v0, v1) = v5 & ordinal(v1) = v4 & ordinal(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) % 36.08/9.27 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 36.08/9.27 | (114) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 36.08/9.27 | (115) empty(all_0_4_4) = 0 % 36.08/9.27 | (116) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 36.08/9.27 | (117) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 36.08/9.27 | (118) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (powerset(v2) = v4 & element(v1, v4) = v5 & element(v0, v2) = v6 & in(v0, v1) = v3 & ( ~ (v5 = 0) | ~ (v3 = 0) | v6 = 0)) % 36.08/9.27 | (119) ! [v0] : ( ~ (empty(v0) = 0) | (ordinal(v0) = 0 & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)) % 36.08/9.27 | (120) relation(all_0_5_5) = 0 % 36.08/9.27 | (121) one_to_one(all_0_5_5) = 0 % 36.08/9.27 | (122) one_to_one(empty_set) = 0 % 36.08/9.27 | (123) ! [v0] : ! [v1] : ( ~ (ordinal(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (epsilon_transitive(v0) = v3 & epsilon_connected(v0) = v4 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0 & v1 = 0)))) % 36.08/9.27 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 36.08/9.27 | (125) ! [v0] : ! [v1] : (v1 = 0 | ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & subset(v2, v0) = v3 & in(v2, v0) = 0)) % 36.08/9.27 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordinal_subset(v3, v2) = v1) | ~ (ordinal_subset(v3, v2) = v0)) % 36.08/9.27 | (127) relation(all_0_0_0) = 0 % 36.08/9.27 | (128) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 36.08/9.27 | (129) empty(all_0_2_2) = 0 % 36.08/9.27 | (130) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (ordinal_subset(v0, v0) = v2) | ~ (ordinal(v1) = 0) | ? [v3] : ( ~ (v3 = 0) & ordinal(v0) = v3)) % 36.08/9.27 | (131) epsilon_connected(empty_set) = 0 % 36.08/9.27 | (132) relation(empty_set) = 0 % 36.08/9.27 | (133) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 36.08/9.27 | (134) relation(all_0_13_13) = 0 % 36.08/9.27 | (135) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v1, v0) = v2) | ~ (epsilon_transitive(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3)) % 36.08/9.27 | (136) ! [v0] : ( ~ (epsilon_connected(v0) = 0) | ? [v1] : ? [v2] : (ordinal(v0) = v2 & epsilon_transitive(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))) % 36.08/9.27 | (137) ! [v0] : ( ~ (epsilon_transitive(v0) = 0) | ? [v1] : ? [v2] : (ordinal(v0) = v2 & epsilon_connected(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))) % 36.08/9.27 | (138) function(all_0_0_0) = 0 % 36.08/9.27 | (139) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (ordinal_subset(v0, v1) = v5 & ordinal(v1) = v4 & ordinal(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) % 36.08/9.27 | (140) epsilon_transitive(all_0_5_5) = 0 % 36.08/9.27 | % 36.08/9.27 | Instantiating formula (117) with all_0_3_3, all_0_2_2 and discharging atoms empty(all_0_2_2) = 0, empty(all_0_3_3) = 0, yields: % 36.08/9.27 | (141) all_0_2_2 = all_0_3_3 % 36.08/9.27 | % 36.08/9.27 | Instantiating formula (117) with all_0_4_4, all_0_3_3 and discharging atoms empty(all_0_3_3) = 0, empty(all_0_4_4) = 0, yields: % 36.08/9.27 | (142) all_0_3_3 = all_0_4_4 % 36.08/9.27 | % 36.08/9.28 | Instantiating formula (117) with all_0_5_5, all_0_2_2 and discharging atoms empty(all_0_2_2) = 0, empty(all_0_5_5) = 0, yields: % 36.08/9.28 | (143) all_0_2_2 = all_0_5_5 % 36.08/9.28 | % 36.08/9.28 | Instantiating formula (117) with empty_set, all_0_3_3 and discharging atoms empty(all_0_3_3) = 0, empty(empty_set) = 0, yields: % 36.08/9.28 | (144) all_0_3_3 = empty_set % 36.08/9.28 | % 36.08/9.28 | Combining equations (141,143) yields a new equation: % 36.08/9.28 | (145) all_0_3_3 = all_0_5_5 % 36.08/9.28 | % 36.08/9.28 | Simplifying 145 yields: % 36.08/9.28 | (146) all_0_3_3 = all_0_5_5 % 36.08/9.28 | % 36.08/9.28 | Combining equations (144,142) yields a new equation: % 36.08/9.28 | (147) all_0_4_4 = empty_set % 36.08/9.28 | % 36.08/9.28 | Combining equations (146,142) yields a new equation: % 36.08/9.28 | (148) all_0_4_4 = all_0_5_5 % 36.08/9.28 | % 36.08/9.28 | Combining equations (148,147) yields a new equation: % 36.08/9.28 | (149) all_0_5_5 = empty_set % 36.08/9.28 | % 36.08/9.28 | Simplifying 149 yields: % 36.08/9.28 | (150) all_0_5_5 = empty_set % 36.08/9.28 | % 36.08/9.28 | From (150) and (60) follows: % 36.08/9.28 | (3) ordinal(empty_set) = 0 % 36.08/9.28 | % 36.08/9.28 | Instantiating formula (80) with all_0_18_18, all_0_19_19 and discharging atoms succ(all_0_19_19) = all_0_18_18, yields: % 36.08/9.28 | (152) in(all_0_19_19, all_0_18_18) = 0 % 36.08/9.28 | % 36.08/9.28 | Instantiating formula (67) with all_0_18_18, all_0_19_19 and discharging atoms succ(all_0_19_19) = all_0_18_18, yields: % 36.08/9.28 | (153) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordinal(all_0_18_18) = v4 & ordinal(all_0_19_19) = v0 & epsilon_transitive(all_0_18_18) = v2 & epsilon_connected(all_0_18_18) = v3 & empty(all_0_18_18) = v1 & ( ~ (v0 = 0) | (v4 = 0 & v3 = 0 & v2 = 0 & ~ (v1 = 0)))) % 36.08/9.28 | % 36.08/9.28 | Instantiating formula (91) with all_0_18_18, all_0_19_19 and discharging atoms succ(all_0_19_19) = all_0_18_18, yields: % 36.08/9.28 | (154) ? [v0] : (singleton(all_0_19_19) = v0 & set_union2(all_0_19_19, v0) = all_0_18_18) % 36.08/9.28 | % 36.08/9.28 | Instantiating formula (26) with all_0_15_15, all_0_18_18, all_0_17_17 and discharging atoms ordinal_subset(all_0_18_18, all_0_17_17) = all_0_15_15, yields: % 36.08/9.28 | (155) all_0_15_15 = 0 | ? [v0] : ? [v1] : ? [v2] : (ordinal_subset(all_0_17_17, all_0_18_18) = v2 & ordinal(all_0_17_17) = v0 & ordinal(all_0_18_18) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 36.08/9.28 | % 36.08/9.28 | Instantiating formula (112) with all_0_15_15, all_0_17_17, all_0_18_18 and discharging atoms ordinal_subset(all_0_18_18, all_0_17_17) = all_0_15_15, yields: % 36.08/9.28 | (156) ? [v0] : ? [v1] : ? [v2] : (subset(all_0_18_18, all_0_17_17) = v2 & ordinal(all_0_17_17) = v1 & ordinal(all_0_18_18) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (v2 = 0) | all_0_15_15 = 0) & ( ~ (all_0_15_15 = 0) | v2 = 0)))) % 36.08/9.28 | % 36.08/9.28 | Instantiating formula (79) with all_0_17_17 and discharging atoms ordinal(all_0_17_17) = 0, yields: % 36.08/9.28 | (157) epsilon_transitive(all_0_17_17) = 0 & epsilon_connected(all_0_17_17) = 0 % 36.08/9.28 | % 36.08/9.28 | Applying alpha-rule on (157) yields: % 36.08/9.28 | (158) epsilon_transitive(all_0_17_17) = 0 % 36.08/9.28 | (159) epsilon_connected(all_0_17_17) = 0 % 36.08/9.28 | % 36.08/9.28 | Instantiating formula (123) with 0, all_0_17_17 and discharging atoms ordinal(all_0_17_17) = 0, yields: % 36.08/9.28 | (160) ? [v0] : ? [v1] : ? [v2] : (epsilon_transitive(all_0_17_17) = v1 & epsilon_connected(all_0_17_17) = v2 & empty(all_0_17_17) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 36.08/9.28 | % 36.08/9.28 | Instantiating formula (31) with empty_set, all_0_17_17 and discharging atoms ordinal(all_0_17_17) = 0, ordinal(empty_set) = 0, yields: % 36.08/9.28 | (161) ordinal_subset(all_0_17_17, all_0_17_17) = 0 % 36.08/9.28 | % 36.08/9.28 | Instantiating formula (92) with all_0_16_16, all_0_17_17, all_0_19_19 and discharging atoms in(all_0_19_19, all_0_17_17) = all_0_16_16, yields: % 36.08/9.28 | (162) all_0_16_16 = 0 | ? [v0] : ? [v1] : (element(all_0_19_19, all_0_17_17) = v0 & empty(all_0_17_17) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 36.08/9.28 | % 36.08/9.28 | Instantiating (156) with all_43_0_74, all_43_1_75, all_43_2_76 yields: % 36.08/9.28 | (163) subset(all_0_18_18, all_0_17_17) = all_43_0_74 & ordinal(all_0_17_17) = all_43_1_75 & ordinal(all_0_18_18) = all_43_2_76 & ( ~ (all_43_1_75 = 0) | ~ (all_43_2_76 = 0) | (( ~ (all_43_0_74 = 0) | all_0_15_15 = 0) & ( ~ (all_0_15_15 = 0) | all_43_0_74 = 0))) % 36.08/9.28 | % 36.08/9.28 | Applying alpha-rule on (163) yields: % 36.08/9.28 | (164) subset(all_0_18_18, all_0_17_17) = all_43_0_74 % 36.08/9.28 | (165) ordinal(all_0_17_17) = all_43_1_75 % 36.08/9.28 | (166) ordinal(all_0_18_18) = all_43_2_76 % 36.08/9.28 | (167) ~ (all_43_1_75 = 0) | ~ (all_43_2_76 = 0) | (( ~ (all_43_0_74 = 0) | all_0_15_15 = 0) & ( ~ (all_0_15_15 = 0) | all_43_0_74 = 0)) % 36.08/9.28 | % 36.08/9.28 | Instantiating (154) with all_63_0_104 yields: % 36.08/9.28 | (168) singleton(all_0_19_19) = all_63_0_104 & set_union2(all_0_19_19, all_63_0_104) = all_0_18_18 % 36.08/9.28 | % 36.08/9.28 | Applying alpha-rule on (168) yields: % 36.08/9.28 | (169) singleton(all_0_19_19) = all_63_0_104 % 36.08/9.28 | (170) set_union2(all_0_19_19, all_63_0_104) = all_0_18_18 % 36.08/9.28 | % 36.08/9.28 | Instantiating (160) with all_83_0_129, all_83_1_130, all_83_2_131 yields: % 36.08/9.28 | (171) epsilon_transitive(all_0_17_17) = all_83_1_130 & epsilon_connected(all_0_17_17) = all_83_0_129 & empty(all_0_17_17) = all_83_2_131 & ( ~ (all_83_2_131 = 0) | (all_83_0_129 = 0 & all_83_1_130 = 0)) % 36.08/9.28 | % 36.08/9.28 | Applying alpha-rule on (171) yields: % 36.08/9.28 | (172) epsilon_transitive(all_0_17_17) = all_83_1_130 % 36.08/9.28 | (173) epsilon_connected(all_0_17_17) = all_83_0_129 % 36.08/9.28 | (174) empty(all_0_17_17) = all_83_2_131 % 36.08/9.28 | (175) ~ (all_83_2_131 = 0) | (all_83_0_129 = 0 & all_83_1_130 = 0) % 36.08/9.28 | % 36.08/9.28 | Instantiating (153) with all_111_0_164, all_111_1_165, all_111_2_166, all_111_3_167, all_111_4_168 yields: % 36.08/9.28 | (176) ordinal(all_0_18_18) = all_111_0_164 & ordinal(all_0_19_19) = all_111_4_168 & epsilon_transitive(all_0_18_18) = all_111_2_166 & epsilon_connected(all_0_18_18) = all_111_1_165 & empty(all_0_18_18) = all_111_3_167 & ( ~ (all_111_4_168 = 0) | (all_111_0_164 = 0 & all_111_1_165 = 0 & all_111_2_166 = 0 & ~ (all_111_3_167 = 0))) % 36.08/9.28 | % 36.08/9.28 | Applying alpha-rule on (176) yields: % 36.08/9.28 | (177) ordinal(all_0_19_19) = all_111_4_168 % 36.08/9.29 | (178) ordinal(all_0_18_18) = all_111_0_164 % 36.08/9.29 | (179) empty(all_0_18_18) = all_111_3_167 % 36.08/9.29 | (180) epsilon_transitive(all_0_18_18) = all_111_2_166 % 36.08/9.29 | (181) epsilon_connected(all_0_18_18) = all_111_1_165 % 36.08/9.29 | (182) ~ (all_111_4_168 = 0) | (all_111_0_164 = 0 & all_111_1_165 = 0 & all_111_2_166 = 0 & ~ (all_111_3_167 = 0)) % 36.08/9.29 | % 36.08/9.29 | Instantiating formula (36) with all_0_17_17, all_43_1_75, 0 and discharging atoms ordinal(all_0_17_17) = all_43_1_75, ordinal(all_0_17_17) = 0, yields: % 36.08/9.29 | (183) all_43_1_75 = 0 % 36.08/9.29 | % 36.08/9.29 | Instantiating formula (36) with all_0_18_18, all_43_2_76, all_111_0_164 and discharging atoms ordinal(all_0_18_18) = all_111_0_164, ordinal(all_0_18_18) = all_43_2_76, yields: % 36.08/9.29 | (184) all_111_0_164 = all_43_2_76 % 36.08/9.29 | % 36.08/9.29 | Instantiating formula (36) with all_0_19_19, all_111_4_168, 0 and discharging atoms ordinal(all_0_19_19) = all_111_4_168, ordinal(all_0_19_19) = 0, yields: % 36.08/9.29 | (185) all_111_4_168 = 0 % 36.08/9.29 | % 36.08/9.29 | Instantiating formula (14) with all_0_17_17, 0, all_83_1_130 and discharging atoms epsilon_transitive(all_0_17_17) = all_83_1_130, epsilon_transitive(all_0_17_17) = 0, yields: % 36.08/9.29 | (186) all_83_1_130 = 0 % 36.08/9.29 | % 36.08/9.29 | Instantiating formula (50) with all_0_17_17, 0, all_83_0_129 and discharging atoms epsilon_connected(all_0_17_17) = all_83_0_129, epsilon_connected(all_0_17_17) = 0, yields: % 36.08/9.29 | (187) all_83_0_129 = 0 % 36.08/9.29 | % 36.08/9.29 | From (183) and (165) follows: % 36.08/9.29 | (88) ordinal(all_0_17_17) = 0 % 36.08/9.29 | % 36.08/9.29 | From (184) and (178) follows: % 36.08/9.29 | (166) ordinal(all_0_18_18) = all_43_2_76 % 36.08/9.29 | % 36.08/9.29 | From (186) and (172) follows: % 36.08/9.29 | (158) epsilon_transitive(all_0_17_17) = 0 % 36.08/9.29 | % 36.08/9.29 | From (187) and (173) follows: % 36.08/9.29 | (159) epsilon_connected(all_0_17_17) = 0 % 36.08/9.29 | % 36.08/9.29 +-Applying beta-rule and splitting (182), into two cases. % 36.08/9.29 |-Branch one: % 36.08/9.29 | (192) ~ (all_111_4_168 = 0) % 36.08/9.29 | % 36.08/9.29 | Equations (185) can reduce 192 to: % 36.08/9.29 | (193) $false % 36.08/9.29 | % 36.08/9.29 |-The branch is then unsatisfiable % 36.08/9.29 |-Branch two: % 36.08/9.29 | (185) all_111_4_168 = 0 % 36.08/9.29 | (195) all_111_0_164 = 0 & all_111_1_165 = 0 & all_111_2_166 = 0 & ~ (all_111_3_167 = 0) % 36.08/9.29 | % 36.08/9.29 | Applying alpha-rule on (195) yields: % 36.08/9.29 | (196) all_111_0_164 = 0 % 36.08/9.29 | (197) all_111_1_165 = 0 % 36.08/9.29 | (198) all_111_2_166 = 0 % 36.08/9.29 | (199) ~ (all_111_3_167 = 0) % 36.08/9.29 | % 36.08/9.29 | Combining equations (184,196) yields a new equation: % 36.08/9.29 | (200) all_43_2_76 = 0 % 36.08/9.29 | % 36.08/9.29 | Simplifying 200 yields: % 36.08/9.29 | (201) all_43_2_76 = 0 % 36.08/9.29 | % 36.08/9.29 | From (201) and (166) follows: % 36.08/9.29 | (202) ordinal(all_0_18_18) = 0 % 36.08/9.29 | % 36.08/9.29 | Instantiating formula (109) with all_43_0_74, all_0_17_17, all_0_18_18 and discharging atoms subset(all_0_18_18, all_0_17_17) = all_43_0_74, yields: % 36.08/9.29 | (203) all_43_0_74 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_17_17) = v1 & in(v0, all_0_18_18) = 0) % 36.08/9.29 | % 36.08/9.29 | Instantiating formula (139) with all_43_0_74, all_0_17_17, all_0_18_18 and discharging atoms subset(all_0_18_18, all_0_17_17) = all_43_0_74, yields: % 36.08/9.29 | (204) ? [v0] : ? [v1] : ? [v2] : (ordinal_subset(all_0_18_18, all_0_17_17) = v2 & ordinal(all_0_17_17) = v1 & ordinal(all_0_18_18) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (v2 = 0) | all_43_0_74 = 0) & ( ~ (all_43_0_74 = 0) | v2 = 0)))) % 36.08/9.29 | % 36.08/9.29 | Instantiating formula (112) with 0, all_0_17_17, all_0_17_17 and discharging atoms ordinal_subset(all_0_17_17, all_0_17_17) = 0, yields: % 36.08/9.29 | (205) ? [v0] : ? [v1] : ? [v2] : (subset(all_0_17_17, all_0_17_17) = v2 & ordinal(all_0_17_17) = v1 & ordinal(all_0_17_17) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 36.08/9.30 | % 36.08/9.30 | Instantiating formula (69) with all_43_0_74, all_0_18_18, all_63_0_104, all_0_17_17, all_0_19_19 and discharging atoms subset(all_0_18_18, all_0_17_17) = all_43_0_74, set_union2(all_0_19_19, all_63_0_104) = all_0_18_18, yields: % 36.08/9.30 | (206) all_43_0_74 = 0 | ? [v0] : ? [v1] : (subset(all_63_0_104, all_0_17_17) = v1 & subset(all_0_19_19, all_0_17_17) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 36.08/9.30 | % 36.08/9.30 | Instantiating formula (135) with all_43_0_74, all_0_18_18, all_0_17_17 and discharging atoms subset(all_0_18_18, all_0_17_17) = all_43_0_74, epsilon_transitive(all_0_17_17) = 0, yields: % 36.08/9.30 | (207) all_43_0_74 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_0_18_18, all_0_17_17) = v0) % 36.08/9.30 | % 36.08/9.30 | Instantiating formula (73) with 0, all_0_17_17 and discharging atoms epsilon_transitive(all_0_17_17) = 0, yields: % 36.08/9.30 | (208) ? [v0] : ? [v1] : ? [v2] : (ordinal(all_0_17_17) = v2 & epsilon_connected(all_0_17_17) = v1 & empty(all_0_17_17) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 36.08/9.30 | % 36.08/9.30 | Instantiating formula (12) with 0, all_0_17_17 and discharging atoms epsilon_connected(all_0_17_17) = 0, yields: % 36.08/9.30 | (209) ? [v0] : ? [v1] : ? [v2] : (ordinal(all_0_17_17) = v2 & epsilon_transitive(all_0_17_17) = v1 & empty(all_0_17_17) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 36.08/9.30 | % 36.08/9.30 | Instantiating (204) with all_143_0_181, all_143_1_182, all_143_2_183 yields: % 36.08/9.30 | (210) ordinal_subset(all_0_18_18, all_0_17_17) = all_143_0_181 & ordinal(all_0_17_17) = all_143_1_182 & ordinal(all_0_18_18) = all_143_2_183 & ( ~ (all_143_1_182 = 0) | ~ (all_143_2_183 = 0) | (( ~ (all_143_0_181 = 0) | all_43_0_74 = 0) & ( ~ (all_43_0_74 = 0) | all_143_0_181 = 0))) % 36.08/9.30 | % 36.08/9.30 | Applying alpha-rule on (210) yields: % 36.08/9.30 | (211) ordinal_subset(all_0_18_18, all_0_17_17) = all_143_0_181 % 36.08/9.30 | (212) ordinal(all_0_17_17) = all_143_1_182 % 36.08/9.30 | (213) ordinal(all_0_18_18) = all_143_2_183 % 36.08/9.30 | (214) ~ (all_143_1_182 = 0) | ~ (all_143_2_183 = 0) | (( ~ (all_143_0_181 = 0) | all_43_0_74 = 0) & ( ~ (all_43_0_74 = 0) | all_143_0_181 = 0)) % 36.08/9.30 | % 36.08/9.30 | Instantiating (205) with all_169_0_210, all_169_1_211, all_169_2_212 yields: % 36.08/9.30 | (215) subset(all_0_17_17, all_0_17_17) = all_169_0_210 & ordinal(all_0_17_17) = all_169_1_211 & ordinal(all_0_17_17) = all_169_2_212 & ( ~ (all_169_1_211 = 0) | ~ (all_169_2_212 = 0) | all_169_0_210 = 0) % 36.08/9.30 | % 36.08/9.30 | Applying alpha-rule on (215) yields: % 36.08/9.30 | (216) subset(all_0_17_17, all_0_17_17) = all_169_0_210 % 36.08/9.30 | (217) ordinal(all_0_17_17) = all_169_1_211 % 36.08/9.30 | (218) ordinal(all_0_17_17) = all_169_2_212 % 36.08/9.30 | (219) ~ (all_169_1_211 = 0) | ~ (all_169_2_212 = 0) | all_169_0_210 = 0 % 36.08/9.30 | % 36.08/9.30 | Instantiating (209) with all_179_0_225, all_179_1_226, all_179_2_227 yields: % 36.08/9.30 | (220) ordinal(all_0_17_17) = all_179_0_225 & epsilon_transitive(all_0_17_17) = all_179_1_226 & empty(all_0_17_17) = all_179_2_227 & ( ~ (all_179_2_227 = 0) | (all_179_0_225 = 0 & all_179_1_226 = 0)) % 36.08/9.30 | % 36.08/9.30 | Applying alpha-rule on (220) yields: % 36.08/9.30 | (221) ordinal(all_0_17_17) = all_179_0_225 % 36.08/9.30 | (222) epsilon_transitive(all_0_17_17) = all_179_1_226 % 36.08/9.30 | (223) empty(all_0_17_17) = all_179_2_227 % 36.08/9.30 | (224) ~ (all_179_2_227 = 0) | (all_179_0_225 = 0 & all_179_1_226 = 0) % 36.08/9.30 | % 36.08/9.30 | Instantiating (208) with all_227_0_285, all_227_1_286, all_227_2_287 yields: % 36.08/9.30 | (225) ordinal(all_0_17_17) = all_227_0_285 & epsilon_connected(all_0_17_17) = all_227_1_286 & empty(all_0_17_17) = all_227_2_287 & ( ~ (all_227_2_287 = 0) | (all_227_0_285 = 0 & all_227_1_286 = 0)) % 36.08/9.30 | % 36.08/9.30 | Applying alpha-rule on (225) yields: % 36.08/9.30 | (226) ordinal(all_0_17_17) = all_227_0_285 % 36.08/9.30 | (227) epsilon_connected(all_0_17_17) = all_227_1_286 % 36.08/9.30 | (228) empty(all_0_17_17) = all_227_2_287 % 36.08/9.30 | (229) ~ (all_227_2_287 = 0) | (all_227_0_285 = 0 & all_227_1_286 = 0) % 36.08/9.30 | % 36.08/9.30 | Instantiating formula (126) with all_0_18_18, all_0_17_17, all_143_0_181, all_0_15_15 and discharging atoms ordinal_subset(all_0_18_18, all_0_17_17) = all_143_0_181, ordinal_subset(all_0_18_18, all_0_17_17) = all_0_15_15, yields: % 36.08/9.30 | (230) all_143_0_181 = all_0_15_15 % 36.08/9.30 | % 36.08/9.30 | Instantiating formula (36) with all_0_17_17, all_227_0_285, 0 and discharging atoms ordinal(all_0_17_17) = all_227_0_285, ordinal(all_0_17_17) = 0, yields: % 36.08/9.30 | (231) all_227_0_285 = 0 % 36.08/9.30 | % 36.08/9.30 | Instantiating formula (36) with all_0_17_17, all_179_0_225, all_227_0_285 and discharging atoms ordinal(all_0_17_17) = all_227_0_285, ordinal(all_0_17_17) = all_179_0_225, yields: % 36.08/9.30 | (232) all_227_0_285 = all_179_0_225 % 36.08/9.30 | % 36.08/9.30 | Instantiating formula (36) with all_0_17_17, all_169_1_211, all_227_0_285 and discharging atoms ordinal(all_0_17_17) = all_227_0_285, ordinal(all_0_17_17) = all_169_1_211, yields: % 36.08/9.30 | (233) all_227_0_285 = all_169_1_211 % 36.08/9.30 | % 36.08/9.30 | Instantiating formula (36) with all_0_17_17, all_169_2_212, all_169_1_211 and discharging atoms ordinal(all_0_17_17) = all_169_1_211, ordinal(all_0_17_17) = all_169_2_212, yields: % 36.08/9.30 | (234) all_169_1_211 = all_169_2_212 % 36.08/9.30 | % 36.08/9.30 | Instantiating formula (36) with all_0_17_17, all_143_1_182, all_169_1_211 and discharging atoms ordinal(all_0_17_17) = all_169_1_211, ordinal(all_0_17_17) = all_143_1_182, yields: % 36.08/9.30 | (235) all_169_1_211 = all_143_1_182 % 36.08/9.30 | % 36.08/9.30 | Instantiating formula (36) with all_0_18_18, all_143_2_183, 0 and discharging atoms ordinal(all_0_18_18) = all_143_2_183, ordinal(all_0_18_18) = 0, yields: % 36.08/9.30 | (236) all_143_2_183 = 0 % 36.08/9.30 | % 36.08/9.30 | Instantiating formula (14) with all_0_17_17, all_179_1_226, 0 and discharging atoms epsilon_transitive(all_0_17_17) = all_179_1_226, epsilon_transitive(all_0_17_17) = 0, yields: % 36.08/9.30 | (237) all_179_1_226 = 0 % 36.08/9.30 | % 36.08/9.30 | Combining equations (231,232) yields a new equation: % 36.08/9.30 | (238) all_179_0_225 = 0 % 36.08/9.30 | % 36.08/9.30 | Combining equations (233,232) yields a new equation: % 36.08/9.30 | (239) all_179_0_225 = all_169_1_211 % 36.08/9.30 | % 36.08/9.30 | Combining equations (239,238) yields a new equation: % 36.08/9.30 | (240) all_169_1_211 = 0 % 36.08/9.30 | % 36.08/9.30 | Simplifying 240 yields: % 36.08/9.30 | (241) all_169_1_211 = 0 % 36.08/9.30 | % 36.08/9.30 | Combining equations (241,234) yields a new equation: % 36.08/9.30 | (242) all_169_2_212 = 0 % 36.08/9.30 | % 36.08/9.30 | Combining equations (235,234) yields a new equation: % 36.08/9.31 | (243) all_169_2_212 = all_143_1_182 % 36.08/9.31 | % 36.08/9.31 | Combining equations (243,242) yields a new equation: % 36.08/9.31 | (244) all_143_1_182 = 0 % 36.08/9.31 | % 36.08/9.31 | Simplifying 244 yields: % 36.08/9.31 | (245) all_143_1_182 = 0 % 36.08/9.31 | % 36.08/9.31 | From (237) and (222) follows: % 36.08/9.31 | (158) epsilon_transitive(all_0_17_17) = 0 % 36.08/9.31 | % 36.08/9.31 +-Applying beta-rule and splitting (24), into two cases. % 36.08/9.31 |-Branch one: % 36.08/9.31 | (247) all_0_15_15 = 0 & ~ (all_0_16_16 = 0) % 36.08/9.31 | % 36.08/9.31 | Applying alpha-rule on (247) yields: % 36.08/9.31 | (248) all_0_15_15 = 0 % 36.08/9.31 | (249) ~ (all_0_16_16 = 0) % 36.08/9.31 | % 36.08/9.31 | Combining equations (248,230) yields a new equation: % 36.08/9.31 | (250) all_143_0_181 = 0 % 36.08/9.31 | % 36.08/9.31 +-Applying beta-rule and splitting (214), into two cases. % 36.08/9.31 |-Branch one: % 36.08/9.31 | (251) ~ (all_143_1_182 = 0) % 36.08/9.31 | % 36.08/9.31 | Equations (245) can reduce 251 to: % 36.08/9.31 | (193) $false % 36.08/9.31 | % 36.08/9.31 |-The branch is then unsatisfiable % 36.08/9.31 |-Branch two: % 36.08/9.31 | (245) all_143_1_182 = 0 % 36.08/9.31 | (254) ~ (all_143_2_183 = 0) | (( ~ (all_143_0_181 = 0) | all_43_0_74 = 0) & ( ~ (all_43_0_74 = 0) | all_143_0_181 = 0)) % 36.08/9.31 | % 36.08/9.31 +-Applying beta-rule and splitting (162), into two cases. % 36.08/9.31 |-Branch one: % 36.08/9.31 | (255) all_0_16_16 = 0 % 36.08/9.31 | % 36.08/9.31 | Equations (255) can reduce 249 to: % 36.08/9.31 | (193) $false % 36.08/9.31 | % 36.08/9.31 |-The branch is then unsatisfiable % 36.08/9.31 |-Branch two: % 36.08/9.31 | (249) ~ (all_0_16_16 = 0) % 36.08/9.31 | (258) ? [v0] : ? [v1] : (element(all_0_19_19, all_0_17_17) = v0 & empty(all_0_17_17) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 36.08/9.31 | % 36.08/9.31 +-Applying beta-rule and splitting (254), into two cases. % 36.08/9.31 |-Branch one: % 36.08/9.31 | (259) ~ (all_143_2_183 = 0) % 36.08/9.31 | % 36.08/9.31 | Equations (236) can reduce 259 to: % 36.08/9.31 | (193) $false % 36.08/9.31 | % 36.08/9.31 |-The branch is then unsatisfiable % 36.08/9.31 |-Branch two: % 36.08/9.31 | (236) all_143_2_183 = 0 % 36.08/9.31 | (262) ( ~ (all_143_0_181 = 0) | all_43_0_74 = 0) & ( ~ (all_43_0_74 = 0) | all_143_0_181 = 0) % 36.08/9.31 | % 36.08/9.31 | Applying alpha-rule on (262) yields: % 36.08/9.31 | (263) ~ (all_143_0_181 = 0) | all_43_0_74 = 0 % 36.08/9.31 | (264) ~ (all_43_0_74 = 0) | all_143_0_181 = 0 % 36.08/9.31 | % 36.08/9.31 +-Applying beta-rule and splitting (263), into two cases. % 36.08/9.31 |-Branch one: % 36.08/9.31 | (265) ~ (all_143_0_181 = 0) % 36.08/9.31 | % 36.08/9.31 | Equations (250) can reduce 265 to: % 36.08/9.31 | (193) $false % 36.08/9.31 | % 36.08/9.31 |-The branch is then unsatisfiable % 36.08/9.31 |-Branch two: % 36.08/9.31 | (250) all_143_0_181 = 0 % 36.08/9.31 | (268) all_43_0_74 = 0 % 36.08/9.31 | % 36.08/9.31 | From (268) and (164) follows: % 36.08/9.31 | (269) subset(all_0_18_18, all_0_17_17) = 0 % 36.08/9.31 | % 36.08/9.31 | Instantiating formula (20) with all_0_16_16, all_0_19_19, all_0_17_17, all_0_18_18 and discharging atoms subset(all_0_18_18, all_0_17_17) = 0, in(all_0_19_19, all_0_17_17) = all_0_16_16, yields: % 36.08/9.31 | (270) all_0_16_16 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_0_19_19, all_0_18_18) = v0) % 36.08/9.31 | % 36.08/9.31 | Instantiating formula (49) with all_0_19_19, all_0_17_17, all_0_18_18 and discharging atoms subset(all_0_18_18, all_0_17_17) = 0, in(all_0_19_19, all_0_18_18) = 0, yields: % 36.08/9.31 | (271) in(all_0_19_19, all_0_17_17) = 0 % 36.08/9.31 | % 36.08/9.31 +-Applying beta-rule and splitting (270), into two cases. % 36.08/9.31 |-Branch one: % 36.08/9.31 | (255) all_0_16_16 = 0 % 36.08/9.31 | % 36.08/9.31 | Equations (255) can reduce 249 to: % 36.08/9.31 | (193) $false % 36.08/9.31 | % 36.08/9.31 |-The branch is then unsatisfiable % 36.08/9.31 |-Branch two: % 36.08/9.31 | (249) ~ (all_0_16_16 = 0) % 36.08/9.31 | (275) ? [v0] : ( ~ (v0 = 0) & in(all_0_19_19, all_0_18_18) = v0) % 36.08/9.31 | % 36.08/9.31 | Instantiating formula (65) with all_0_19_19, all_0_17_17, 0, all_0_16_16 and discharging atoms in(all_0_19_19, all_0_17_17) = all_0_16_16, in(all_0_19_19, all_0_17_17) = 0, yields: % 36.08/9.31 | (255) all_0_16_16 = 0 % 36.08/9.31 | % 36.08/9.31 | Equations (255) can reduce 249 to: % 36.08/9.31 | (193) $false % 36.08/9.31 | % 36.08/9.31 |-The branch is then unsatisfiable % 36.08/9.31 |-Branch two: % 36.08/9.31 | (278) all_0_16_16 = 0 & ~ (all_0_15_15 = 0) % 36.08/9.31 | % 36.08/9.31 | Applying alpha-rule on (278) yields: % 36.08/9.31 | (255) all_0_16_16 = 0 % 36.08/9.31 | (280) ~ (all_0_15_15 = 0) % 36.08/9.31 | % 36.08/9.31 | From (255) and (66) follows: % 36.08/9.31 | (271) in(all_0_19_19, all_0_17_17) = 0 % 36.08/9.31 | % 36.08/9.31 +-Applying beta-rule and splitting (155), into two cases. % 36.08/9.31 |-Branch one: % 36.08/9.31 | (248) all_0_15_15 = 0 % 36.08/9.31 | % 36.08/9.31 | Equations (248) can reduce 280 to: % 36.08/9.31 | (193) $false % 36.08/9.31 | % 36.08/9.31 |-The branch is then unsatisfiable % 36.08/9.31 |-Branch two: % 36.08/9.31 | (280) ~ (all_0_15_15 = 0) % 36.08/9.31 | (285) ? [v0] : ? [v1] : ? [v2] : (ordinal_subset(all_0_17_17, all_0_18_18) = v2 & ordinal(all_0_17_17) = v0 & ordinal(all_0_18_18) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 36.08/9.31 | % 36.08/9.31 +-Applying beta-rule and splitting (214), into two cases. % 36.08/9.31 |-Branch one: % 36.08/9.31 | (251) ~ (all_143_1_182 = 0) % 36.08/9.31 | % 36.08/9.31 | Equations (245) can reduce 251 to: % 36.08/9.31 | (193) $false % 36.08/9.31 | % 36.08/9.31 |-The branch is then unsatisfiable % 36.08/9.31 |-Branch two: % 36.08/9.31 | (245) all_143_1_182 = 0 % 36.08/9.31 | (254) ~ (all_143_2_183 = 0) | (( ~ (all_143_0_181 = 0) | all_43_0_74 = 0) & ( ~ (all_43_0_74 = 0) | all_143_0_181 = 0)) % 36.08/9.31 | % 36.08/9.31 +-Applying beta-rule and splitting (254), into two cases. % 36.08/9.31 |-Branch one: % 36.08/9.31 | (259) ~ (all_143_2_183 = 0) % 36.08/9.31 | % 36.08/9.31 | Equations (236) can reduce 259 to: % 36.08/9.31 | (193) $false % 36.08/9.31 | % 36.08/9.31 |-The branch is then unsatisfiable % 36.08/9.31 |-Branch two: % 36.08/9.31 | (236) all_143_2_183 = 0 % 36.08/9.31 | (262) ( ~ (all_143_0_181 = 0) | all_43_0_74 = 0) & ( ~ (all_43_0_74 = 0) | all_143_0_181 = 0) % 36.08/9.31 | % 36.08/9.31 | Applying alpha-rule on (262) yields: % 36.08/9.31 | (263) ~ (all_143_0_181 = 0) | all_43_0_74 = 0 % 36.08/9.31 | (264) ~ (all_43_0_74 = 0) | all_143_0_181 = 0 % 36.08/9.31 | % 36.08/9.31 +-Applying beta-rule and splitting (264), into two cases. % 36.08/9.31 |-Branch one: % 36.08/9.31 | (296) ~ (all_43_0_74 = 0) % 36.08/9.31 | % 36.08/9.31 +-Applying beta-rule and splitting (207), into two cases. % 36.08/9.31 |-Branch one: % 36.08/9.31 | (268) all_43_0_74 = 0 % 36.08/9.31 | % 36.08/9.31 | Equations (268) can reduce 296 to: % 36.08/9.31 | (193) $false % 36.08/9.31 | % 36.08/9.31 |-The branch is then unsatisfiable % 36.08/9.31 |-Branch two: % 36.08/9.31 | (296) ~ (all_43_0_74 = 0) % 36.08/9.31 | (300) ? [v0] : ( ~ (v0 = 0) & in(all_0_18_18, all_0_17_17) = v0) % 36.08/9.31 | % 36.08/9.31 +-Applying beta-rule and splitting (203), into two cases. % 36.08/9.31 |-Branch one: % 36.08/9.31 | (268) all_43_0_74 = 0 % 36.08/9.31 | % 36.08/9.31 | Equations (268) can reduce 296 to: % 36.08/9.31 | (193) $false % 36.08/9.31 | % 36.08/9.31 |-The branch is then unsatisfiable % 36.08/9.31 |-Branch two: % 36.08/9.31 | (296) ~ (all_43_0_74 = 0) % 36.08/9.31 | (304) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_17_17) = v1 & in(v0, all_0_18_18) = 0) % 36.08/9.32 | % 36.08/9.32 +-Applying beta-rule and splitting (206), into two cases. % 36.08/9.32 |-Branch one: % 36.08/9.32 | (268) all_43_0_74 = 0 % 36.08/9.32 | % 36.08/9.32 | Equations (268) can reduce 296 to: % 36.08/9.32 | (193) $false % 36.08/9.32 | % 36.08/9.32 |-The branch is then unsatisfiable % 36.08/9.32 |-Branch two: % 36.08/9.32 | (296) ~ (all_43_0_74 = 0) % 36.08/9.32 | (308) ? [v0] : ? [v1] : (subset(all_63_0_104, all_0_17_17) = v1 & subset(all_0_19_19, all_0_17_17) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 36.08/9.32 | % 36.08/9.32 | Instantiating (308) with all_285_0_500, all_285_1_501 yields: % 36.08/9.32 | (309) subset(all_63_0_104, all_0_17_17) = all_285_0_500 & subset(all_0_19_19, all_0_17_17) = all_285_1_501 & ( ~ (all_285_0_500 = 0) | ~ (all_285_1_501 = 0)) % 36.08/9.32 | % 36.08/9.32 | Applying alpha-rule on (309) yields: % 36.08/9.32 | (310) subset(all_63_0_104, all_0_17_17) = all_285_0_500 % 36.08/9.32 | (311) subset(all_0_19_19, all_0_17_17) = all_285_1_501 % 36.08/9.32 | (312) ~ (all_285_0_500 = 0) | ~ (all_285_1_501 = 0) % 36.08/9.32 | % 36.08/9.32 | Instantiating formula (135) with all_285_0_500, all_63_0_104, all_0_17_17 and discharging atoms subset(all_63_0_104, all_0_17_17) = all_285_0_500, epsilon_transitive(all_0_17_17) = 0, yields: % 36.08/9.32 | (313) all_285_0_500 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_63_0_104, all_0_17_17) = v0) % 36.08/9.32 | % 36.08/9.32 | Instantiating formula (109) with all_285_0_500, all_0_17_17, all_63_0_104 and discharging atoms subset(all_63_0_104, all_0_17_17) = all_285_0_500, yields: % 36.08/9.32 | (314) all_285_0_500 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_63_0_104) = 0 & in(v0, all_0_17_17) = v1) % 36.08/9.32 | % 36.08/9.32 | Instantiating formula (135) with all_285_1_501, all_0_19_19, all_0_17_17 and discharging atoms subset(all_0_19_19, all_0_17_17) = all_285_1_501, epsilon_transitive(all_0_17_17) = 0, yields: % 36.08/9.32 | (315) all_285_1_501 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_0_19_19, all_0_17_17) = v0) % 36.08/9.32 | % 36.08/9.32 | Instantiating formula (103) with all_285_1_501, all_0_17_17, all_0_19_19 and discharging atoms subset(all_0_19_19, all_0_17_17) = all_285_1_501, yields: % 36.08/9.32 | (316) all_285_1_501 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_0_17_17) = v0 & element(all_0_19_19, v0) = v1) % 36.08/9.32 | % 36.08/9.32 | Instantiating formula (109) with all_285_1_501, all_0_17_17, all_0_19_19 and discharging atoms subset(all_0_19_19, all_0_17_17) = all_285_1_501, yields: % 36.08/9.32 | (317) all_285_1_501 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_17_17) = v1 & in(v0, all_0_19_19) = 0) % 36.08/9.32 | % 36.08/9.32 | Instantiating formula (52) with all_0_19_19, all_0_17_17 and discharging atoms epsilon_transitive(all_0_17_17) = 0, in(all_0_19_19, all_0_17_17) = 0, yields: % 36.08/9.32 | (318) subset(all_0_19_19, all_0_17_17) = 0 % 36.08/9.32 | % 36.08/9.32 +-Applying beta-rule and splitting (315), into two cases. % 36.08/9.32 |-Branch one: % 36.08/9.32 | (319) all_285_1_501 = 0 % 36.08/9.32 | % 36.08/9.32 +-Applying beta-rule and splitting (312), into two cases. % 36.08/9.32 |-Branch one: % 36.08/9.32 | (320) ~ (all_285_0_500 = 0) % 36.08/9.32 | % 36.08/9.32 +-Applying beta-rule and splitting (313), into two cases. % 36.08/9.32 |-Branch one: % 36.08/9.32 | (321) all_285_0_500 = 0 % 36.08/9.32 | % 36.08/9.32 | Equations (321) can reduce 320 to: % 36.08/9.32 | (193) $false % 36.08/9.32 | % 36.08/9.32 |-The branch is then unsatisfiable % 36.08/9.32 |-Branch two: % 36.08/9.32 | (320) ~ (all_285_0_500 = 0) % 36.08/9.32 | (324) ? [v0] : ( ~ (v0 = 0) & in(all_63_0_104, all_0_17_17) = v0) % 36.08/9.32 | % 36.08/9.32 +-Applying beta-rule and splitting (314), into two cases. % 36.08/9.32 |-Branch one: % 36.08/9.32 | (321) all_285_0_500 = 0 % 36.08/9.32 | % 36.08/9.32 | Equations (321) can reduce 320 to: % 36.08/9.32 | (193) $false % 36.08/9.32 | % 36.08/9.32 |-The branch is then unsatisfiable % 36.08/9.32 |-Branch two: % 36.08/9.32 | (320) ~ (all_285_0_500 = 0) % 36.08/9.32 | (328) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_63_0_104) = 0 & in(v0, all_0_17_17) = v1) % 36.08/9.32 | % 36.08/9.32 | Instantiating (328) with all_724_0_714, all_724_1_715 yields: % 36.08/9.32 | (329) ~ (all_724_0_714 = 0) & in(all_724_1_715, all_63_0_104) = 0 & in(all_724_1_715, all_0_17_17) = all_724_0_714 % 36.08/9.32 | % 36.08/9.32 | Applying alpha-rule on (329) yields: % 36.08/9.32 | (330) ~ (all_724_0_714 = 0) % 36.08/9.32 | (331) in(all_724_1_715, all_63_0_104) = 0 % 36.08/9.32 | (332) in(all_724_1_715, all_0_17_17) = all_724_0_714 % 36.08/9.32 | % 36.08/9.32 | Instantiating formula (100) with all_724_1_715, all_63_0_104, all_0_19_19 and discharging atoms singleton(all_0_19_19) = all_63_0_104, in(all_724_1_715, all_63_0_104) = 0, yields: % 36.08/9.32 | (333) all_724_1_715 = all_0_19_19 % 36.08/9.32 | % 36.08/9.32 | From (333) and (332) follows: % 36.08/9.32 | (334) in(all_0_19_19, all_0_17_17) = all_724_0_714 % 36.08/9.32 | % 36.08/9.32 | Instantiating formula (65) with all_0_19_19, all_0_17_17, all_724_0_714, 0 and discharging atoms in(all_0_19_19, all_0_17_17) = all_724_0_714, in(all_0_19_19, all_0_17_17) = 0, yields: % 36.08/9.32 | (335) all_724_0_714 = 0 % 36.08/9.32 | % 36.08/9.32 | Equations (335) can reduce 330 to: % 36.08/9.32 | (193) $false % 36.08/9.32 | % 36.08/9.32 |-The branch is then unsatisfiable % 36.08/9.32 |-Branch two: % 36.08/9.32 | (321) all_285_0_500 = 0 % 36.08/9.32 | (338) ~ (all_285_1_501 = 0) % 36.08/9.32 | % 36.08/9.32 | Equations (319) can reduce 338 to: % 36.08/9.32 | (193) $false % 36.08/9.32 | % 36.08/9.32 |-The branch is then unsatisfiable % 36.08/9.32 |-Branch two: % 36.08/9.32 | (338) ~ (all_285_1_501 = 0) % 36.08/9.32 | (341) ? [v0] : ( ~ (v0 = 0) & in(all_0_19_19, all_0_17_17) = v0) % 36.08/9.32 | % 36.08/9.32 +-Applying beta-rule and splitting (317), into two cases. % 36.08/9.32 |-Branch one: % 36.08/9.32 | (319) all_285_1_501 = 0 % 36.08/9.32 | % 36.08/9.32 | Equations (319) can reduce 338 to: % 36.08/9.32 | (193) $false % 36.08/9.32 | % 36.08/9.32 |-The branch is then unsatisfiable % 36.08/9.32 |-Branch two: % 36.08/9.32 | (338) ~ (all_285_1_501 = 0) % 36.08/9.32 | (345) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_17_17) = v1 & in(v0, all_0_19_19) = 0) % 36.08/9.32 | % 36.08/9.32 +-Applying beta-rule and splitting (316), into two cases. % 36.08/9.32 |-Branch one: % 36.08/9.32 | (319) all_285_1_501 = 0 % 36.08/9.32 | % 36.08/9.32 | Equations (319) can reduce 338 to: % 36.08/9.32 | (193) $false % 36.08/9.32 | % 36.08/9.32 |-The branch is then unsatisfiable % 36.08/9.32 |-Branch two: % 36.08/9.32 | (338) ~ (all_285_1_501 = 0) % 36.08/9.32 | (349) ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_0_17_17) = v0 & element(all_0_19_19, v0) = v1) % 36.08/9.32 | % 36.08/9.32 | Instantiating formula (113) with all_0_19_19, all_0_17_17, 0, all_285_1_501 and discharging atoms subset(all_0_19_19, all_0_17_17) = all_285_1_501, subset(all_0_19_19, all_0_17_17) = 0, yields: % 36.08/9.32 | (319) all_285_1_501 = 0 % 36.08/9.32 | % 36.08/9.32 | Equations (319) can reduce 338 to: % 36.08/9.32 | (193) $false % 36.08/9.32 | % 36.08/9.32 |-The branch is then unsatisfiable % 36.08/9.32 |-Branch two: % 36.08/9.32 | (268) all_43_0_74 = 0 % 36.08/9.32 | (250) all_143_0_181 = 0 % 36.08/9.32 | % 36.08/9.32 | Combining equations (230,250) yields a new equation: % 36.08/9.32 | (354) all_0_15_15 = 0 % 36.08/9.32 | % 36.08/9.32 | Simplifying 354 yields: % 36.08/9.32 | (248) all_0_15_15 = 0 % 36.08/9.32 | % 36.08/9.32 | Equations (248) can reduce 280 to: % 36.08/9.32 | (193) $false % 36.08/9.32 | % 36.08/9.32 |-The branch is then unsatisfiable % 36.08/9.32 % SZS output end Proof for theBenchmark % 36.08/9.32 % 36.08/9.32 8727ms %------------------------------------------------------------------------------