%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU236+3 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n015.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 22.03s 5.88s % Output : Proof 30.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU236+3 : TPTP v8.1.0. Released v3.2.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n015.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sun Jun 19 10:47:44 EDT 2022 % 0.12/0.34 % CPUTime : % 0.52/0.58 ____ _ % 0.52/0.58 ___ / __ \_____(_)___ ________ __________ % 0.52/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.52/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.52/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.52/0.58 % 0.52/0.58 A Theorem Prover for First-Order Logic % 0.52/0.58 (ePrincess v.1.0) % 0.52/0.58 % 0.52/0.58 (c) Philipp Rümmer, 2009-2015 % 0.52/0.58 (c) Peter Backeman, 2014-2015 % 0.52/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.52/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.52/0.58 Bug reports to peter@backeman.se % 0.52/0.58 % 0.52/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.52/0.58 % 0.52/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.73/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.68/0.97 Prover 0: Preprocessing ... % 2.33/1.22 Prover 0: Warning: ignoring some quantifiers % 2.49/1.25 Prover 0: Constructing countermodel ... % 5.62/2.03 Prover 0: gave up % 5.62/2.03 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 6.05/2.08 Prover 1: Preprocessing ... % 6.45/2.19 Prover 1: Warning: ignoring some quantifiers % 6.45/2.19 Prover 1: Constructing countermodel ... % 7.52/2.44 Prover 1: gave up % 7.52/2.44 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 7.70/2.48 Prover 2: Preprocessing ... % 8.39/2.60 Prover 2: Warning: ignoring some quantifiers % 8.39/2.61 Prover 2: Constructing countermodel ... % 16.43/4.55 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 16.55/4.61 Prover 3: Preprocessing ... % 16.82/4.65 Prover 3: Warning: ignoring some quantifiers % 16.96/4.66 Prover 3: Constructing countermodel ... % 19.81/5.37 Prover 3: gave up % 19.81/5.37 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 20.06/5.39 Prover 4: Preprocessing ... % 20.44/5.47 Prover 4: Warning: ignoring some quantifiers % 20.44/5.47 Prover 4: Constructing countermodel ... % 22.03/5.87 Prover 4: proved (507ms) % 22.03/5.88 Prover 2: stopped % 22.03/5.88 % 22.03/5.88 No countermodel exists, formula is valid % 22.03/5.88 % SZS status Theorem for theBenchmark % 22.03/5.88 % 22.03/5.88 Generating proof ... Warning: ignoring some quantifiers % 29.63/7.68 found it (size 163) % 29.63/7.68 % 29.63/7.68 % SZS output start Proof for theBenchmark % 29.63/7.68 Assumed formulas after preprocessing and simplification: % 29.63/7.68 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ( ~ (v14 = 0) & ~ (v12 = 0) & ~ (v9 = 0) & relation_non_empty(v5) = 0 & relation_empty_yielding(v7) = 0 & relation_empty_yielding(v6) = 0 & relation_empty_yielding(empty_set) = 0 & succ(v0) = v1 & ordinal_subset(v1, v2) = v4 & one_to_one(v15) = 0 & one_to_one(v10) = 0 & one_to_one(empty_set) = 0 & relation(v20) = 0 & relation(v18) = 0 & relation(v16) = 0 & relation(v15) = 0 & relation(v13) = 0 & relation(v10) = 0 & relation(v7) = 0 & relation(v6) = 0 & relation(v5) = 0 & relation(empty_set) = 0 & ordinal(v19) = 0 & ordinal(v15) = 0 & ordinal(v8) = 0 & ordinal(v2) = 0 & ordinal(v0) = 0 & ordinal(empty_set) = 0 & epsilon_transitive(v19) = 0 & epsilon_transitive(v15) = 0 & epsilon_transitive(v8) = 0 & epsilon_transitive(empty_set) = 0 & epsilon_connected(v19) = 0 & epsilon_connected(v15) = 0 & epsilon_connected(v8) = 0 & epsilon_connected(empty_set) = 0 & empty(v18) = 0 & empty(v17) = 0 & empty(v16) = 0 & empty(v15) = 0 & empty(v13) = v14 & empty(v11) = v12 & empty(v8) = v9 & empty(empty_set) = 0 & function(v20) = 0 & function(v16) = 0 & function(v15) = 0 & function(v10) = 0 & function(v6) = 0 & function(v5) = 0 & function(empty_set) = 0 & in(v0, v2) = v3 & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (powerset(v23) = v24) | ~ (element(v22, v24) = 0) | ~ (element(v21, v23) = v25) | ? [v26] : ( ~ (v26 = 0) & in(v21, v22) = v26)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (subset(v24, v22) = v25) | ~ (set_union2(v21, v23) = v24) | ? [v26] : ? [v27] : (subset(v23, v22) = v27 & subset(v21, v22) = v26 & ( ~ (v27 = 0) | ~ (v26 = 0)))) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (powerset(v22) = v23) | ~ (element(v21, v23) = v24) | ? [v25] : ( ~ (v25 = 0) & subset(v21, v22) = v25)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (element(v21, v23) = v24) | ~ (in(v21, v22) = 0) | ? [v25] : ? [v26] : ( ~ (v26 = 0) & powerset(v23) = v25 & element(v22, v25) = v26)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (subset(v21, v22) = 0) | ~ (in(v23, v22) = v24) | ? [v25] : ( ~ (v25 = 0) & in(v23, v21) = v25)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v22 = v21 | ~ (element(v24, v23) = v22) | ~ (element(v24, v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v22 = v21 | ~ (subset(v24, v23) = v22) | ~ (subset(v24, v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v22 = v21 | ~ (ordinal_subset(v24, v23) = v22) | ~ (ordinal_subset(v24, v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v22 = v21 | ~ (set_union2(v24, v23) = v22) | ~ (set_union2(v24, v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v22 = v21 | ~ (in(v24, v23) = v22) | ~ (in(v24, v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (powerset(v23) = v24) | ~ (element(v22, v24) = 0) | ~ (in(v21, v22) = 0) | element(v21, v23) = 0) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (powerset(v23) = v24) | ~ (element(v22, v24) = 0) | ~ (in(v21, v22) = 0) | ? [v25] : ( ~ (v25 = 0) & empty(v23) = v25)) & ! [v21] : ! [v22] : ! [v23] : (v23 = v21 | ~ (singleton(v21) = v22) | ~ (in(v23, v22) = 0)) & ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (element(v21, v22) = v23) | ? [v24] : ( ~ (v24 = 0) & in(v21, v22) = v24)) & ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (subset(v22, v21) = v23) | ~ (epsilon_transitive(v21) = 0) | ? [v24] : ( ~ (v24 = 0) & in(v22, v21) = v24)) & ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (subset(v21, v22) = v23) | ? [v24] : ? [v25] : ( ~ (v25 = 0) & powerset(v22) = v24 & element(v21, v24) = v25)) & ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (subset(v21, v22) = v23) | ? [v24] : ? [v25] : ( ~ (v25 = 0) & in(v24, v22) = v25 & in(v24, v21) = 0)) & ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (singleton(v21) = v22) | ~ (in(v21, v22) = v23)) & ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (ordinal_subset(v22, v21) = v23) | ? [v24] : ? [v25] : ? [v26] : (ordinal_subset(v21, v22) = v26 & ordinal(v22) = v25 & ordinal(v21) = v24 & ( ~ (v25 = 0) | ~ (v24 = 0) | v26 = 0))) & ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (ordinal_subset(v21, v22) = v23) | ? [v24] : ? [v25] : ? [v26] : (ordinal_subset(v22, v21) = v26 & ordinal(v22) = v25 & ordinal(v21) = v24 & ( ~ (v25 = 0) | ~ (v24 = 0) | v26 = 0))) & ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (ordinal_subset(v21, v21) = v23) | ~ (ordinal(v22) = 0) | ? [v24] : ( ~ (v24 = 0) & ordinal(v21) = v24)) & ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (in(v21, v22) = v23) | ? [v24] : ? [v25] : (element(v21, v22) = v24 & empty(v22) = v25 & ( ~ (v24 = 0) | v25 = 0))) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (powerset(v23) = v22) | ~ (powerset(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (relation_non_empty(v23) = v22) | ~ (relation_non_empty(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (relation_empty_yielding(v23) = v22) | ~ (relation_empty_yielding(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (succ(v23) = v22) | ~ (succ(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (singleton(v23) = v22) | ~ (singleton(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (one_to_one(v23) = v22) | ~ (one_to_one(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (relation(v23) = v22) | ~ (relation(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (ordinal(v23) = v22) | ~ (ordinal(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (epsilon_transitive(v23) = v22) | ~ (epsilon_transitive(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (epsilon_connected(v23) = v22) | ~ (epsilon_connected(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (empty(v23) = v22) | ~ (empty(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (function(v23) = v22) | ~ (function(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ( ~ (powerset(v22) = v23) | ~ (element(v21, v23) = 0) | subset(v21, v22) = 0) & ! [v21] : ! [v22] : ! [v23] : ( ~ (subset(v21, v22) = v23) | ? [v24] : ? [v25] : ? [v26] : (ordinal_subset(v21, v22) = v26 & ordinal(v22) = v25 & ordinal(v21) = v24 & ( ~ (v25 = 0) | ~ (v24 = 0) | (( ~ (v26 = 0) | v23 = 0) & ( ~ (v23 = 0) | v26 = 0))))) & ! [v21] : ! [v22] : ! [v23] : ( ~ (subset(v21, v22) = 0) | ~ (in(v23, v21) = 0) | in(v23, v22) = 0) & ! [v21] : ! [v22] : ! [v23] : ( ~ (ordinal_subset(v21, v22) = v23) | ? [v24] : ? [v25] : ? [v26] : (subset(v21, v22) = v26 & ordinal(v22) = v25 & ordinal(v21) = v24 & ( ~ (v25 = 0) | ~ (v24 = 0) | (( ~ (v26 = 0) | v23 = 0) & ( ~ (v23 = 0) | v26 = 0))))) & ! [v21] : ! [v22] : ! [v23] : ( ~ (set_union2(v22, v21) = v23) | set_union2(v21, v22) = v23) & ! [v21] : ! [v22] : ! [v23] : ( ~ (set_union2(v22, v21) = v23) | ? [v24] : ? [v25] : (empty(v23) = v25 & empty(v21) = v24 & ( ~ (v25 = 0) | v24 = 0))) & ! [v21] : ! [v22] : ! [v23] : ( ~ (set_union2(v21, v22) = v23) | set_union2(v22, v21) = v23) & ! [v21] : ! [v22] : ! [v23] : ( ~ (set_union2(v21, v22) = v23) | ? [v24] : ? [v25] : ? [v26] : (relation(v23) = v26 & relation(v22) = v25 & relation(v21) = v24 & ( ~ (v25 = 0) | ~ (v24 = 0) | v26 = 0))) & ! [v21] : ! [v22] : ! [v23] : ( ~ (set_union2(v21, v22) = v23) | ? [v24] : ? [v25] : (empty(v23) = v25 & empty(v21) = v24 & ( ~ (v25 = 0) | v24 = 0))) & ! [v21] : ! [v22] : ! [v23] : ( ~ (empty(v23) = 0) | ~ (in(v21, v22) = 0) | ? [v24] : ? [v25] : ( ~ (v25 = 0) & powerset(v23) = v24 & element(v22, v24) = v25)) & ? [v21] : ! [v22] : ! [v23] : (v23 = v21 | ~ (singleton(v22) = v23) | ? [v24] : ? [v25] : (in(v24, v21) = v25 & ( ~ (v25 = 0) | ~ (v24 = v22)) & (v25 = 0 | v24 = v22))) & ! [v21] : ! [v22] : (v22 = v21 | ~ (set_union2(v21, v21) = v22)) & ! [v21] : ! [v22] : (v22 = v21 | ~ (set_union2(v21, empty_set) = v22)) & ! [v21] : ! [v22] : (v22 = v21 | ~ (empty(v22) = 0) | ~ (empty(v21) = 0)) & ! [v21] : ! [v22] : (v22 = 0 | ~ (subset(v21, v21) = v22)) & ! [v21] : ! [v22] : (v22 = 0 | ~ (relation(v21) = v22) | ? [v23] : ( ~ (v23 = 0) & empty(v21) = v23)) & ! [v21] : ! [v22] : (v22 = 0 | ~ (ordinal(v21) = v22) | ? [v23] : ? [v24] : (epsilon_transitive(v21) = v23 & epsilon_connected(v21) = v24 & ( ~ (v24 = 0) | ~ (v23 = 0)))) & ! [v21] : ! [v22] : (v22 = 0 | ~ (epsilon_transitive(v21) = v22) | ? [v23] : ? [v24] : ( ~ (v24 = 0) & subset(v23, v21) = v24 & in(v23, v21) = 0)) & ! [v21] : ! [v22] : (v22 = 0 | ~ (function(v21) = v22) | ? [v23] : ( ~ (v23 = 0) & empty(v21) = v23)) & ! [v21] : ! [v22] : ( ~ (element(v21, v22) = 0) | ? [v23] : ? [v24] : (empty(v22) = v23 & in(v21, v22) = v24 & (v24 = 0 | v23 = 0))) & ! [v21] : ! [v22] : ( ~ (subset(v21, v22) = 0) | ? [v23] : (powerset(v22) = v23 & element(v21, v23) = 0)) & ! [v21] : ! [v22] : ( ~ (succ(v21) = v22) | in(v21, v22) = 0) & ! [v21] : ! [v22] : ( ~ (succ(v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (ordinal(v22) = v27 & ordinal(v21) = v23 & epsilon_transitive(v22) = v25 & epsilon_connected(v22) = v26 & empty(v22) = v24 & ( ~ (v23 = 0) | (v27 = 0 & v26 = 0 & v25 = 0 & ~ (v24 = 0))))) & ! [v21] : ! [v22] : ( ~ (succ(v21) = v22) | ? [v23] : ( ~ (v23 = 0) & empty(v22) = v23)) & ! [v21] : ! [v22] : ( ~ (succ(v21) = v22) | ? [v23] : (singleton(v21) = v23 & set_union2(v21, v23) = v22)) & ! [v21] : ! [v22] : ( ~ (singleton(v21) = v22) | ? [v23] : (succ(v21) = v23 & set_union2(v21, v22) = v23)) & ! [v21] : ! [v22] : ( ~ (one_to_one(v21) = v22) | ? [v23] : ? [v24] : ? [v25] : (relation(v21) = v23 & empty(v21) = v24 & function(v21) = v25 & ( ~ (v25 = 0) | ~ (v24 = 0) | ~ (v23 = 0) | v22 = 0))) & ! [v21] : ! [v22] : ( ~ (ordinal(v22) = 0) | ~ (ordinal(v21) = 0) | ordinal_subset(v21, v21) = 0) & ! [v21] : ! [v22] : ( ~ (ordinal(v21) = v22) | ? [v23] : ? [v24] : ? [v25] : (epsilon_transitive(v21) = v24 & epsilon_connected(v21) = v25 & empty(v21) = v23 & ( ~ (v23 = 0) | (v25 = 0 & v24 = 0 & v22 = 0)))) & ! [v21] : ! [v22] : ( ~ (epsilon_transitive(v21) = v22) | ? [v23] : ? [v24] : ? [v25] : (ordinal(v21) = v25 & epsilon_connected(v21) = v24 & empty(v21) = v23 & ( ~ (v23 = 0) | (v25 = 0 & v24 = 0 & v22 = 0)))) & ! [v21] : ! [v22] : ( ~ (epsilon_transitive(v21) = v22) | ? [v23] : ? [v24] : (ordinal(v21) = v23 & epsilon_connected(v21) = v24 & ( ~ (v23 = 0) | (v24 = 0 & v22 = 0)))) & ! [v21] : ! [v22] : ( ~ (epsilon_transitive(v21) = 0) | ~ (in(v22, v21) = 0) | subset(v22, v21) = 0) & ! [v21] : ! [v22] : ( ~ (epsilon_connected(v21) = v22) | ? [v23] : ? [v24] : ? [v25] : (ordinal(v21) = v25 & epsilon_transitive(v21) = v24 & empty(v21) = v23 & ( ~ (v23 = 0) | (v25 = 0 & v24 = 0 & v22 = 0)))) & ! [v21] : ! [v22] : ( ~ (epsilon_connected(v21) = v22) | ? [v23] : ? [v24] : (ordinal(v21) = v23 & epsilon_transitive(v21) = v24 & ( ~ (v23 = 0) | (v24 = 0 & v22 = 0)))) & ! [v21] : ! [v22] : ( ~ (in(v22, v21) = 0) | ? [v23] : ( ~ (v23 = 0) & in(v21, v22) = v23)) & ! [v21] : ! [v22] : ( ~ (in(v21, v22) = 0) | element(v21, v22) = 0) & ! [v21] : ! [v22] : ( ~ (in(v21, v22) = 0) | ? [v23] : ( ~ (v23 = 0) & empty(v22) = v23)) & ! [v21] : ! [v22] : ( ~ (in(v21, v22) = 0) | ? [v23] : ( ~ (v23 = 0) & in(v22, v21) = v23)) & ! [v21] : (v21 = empty_set | ~ (empty(v21) = 0)) & ! [v21] : ( ~ (relation(v21) = 0) | ? [v22] : ? [v23] : ? [v24] : (one_to_one(v21) = v24 & empty(v21) = v22 & function(v21) = v23 & ( ~ (v23 = 0) | ~ (v22 = 0) | v24 = 0))) & ! [v21] : ( ~ (ordinal(v21) = 0) | ? [v22] : ? [v23] : ( ~ (v23 = 0) & succ(v21) = v22 & ordinal(v22) = 0 & epsilon_transitive(v22) = 0 & epsilon_connected(v22) = 0 & empty(v22) = v23)) & ! [v21] : ( ~ (ordinal(v21) = 0) | (epsilon_transitive(v21) = 0 & epsilon_connected(v21) = 0)) & ! [v21] : ( ~ (epsilon_transitive(v21) = 0) | ? [v22] : ? [v23] : (ordinal(v21) = v23 & epsilon_connected(v21) = v22 & ( ~ (v22 = 0) | v23 = 0))) & ! [v21] : ( ~ (epsilon_connected(v21) = 0) | ? [v22] : ? [v23] : (ordinal(v21) = v23 & epsilon_transitive(v21) = v22 & ( ~ (v22 = 0) | v23 = 0))) & ! [v21] : ( ~ (empty(v21) = 0) | relation(v21) = 0) & ! [v21] : ( ~ (empty(v21) = 0) | function(v21) = 0) & ! [v21] : ( ~ (empty(v21) = 0) | ? [v22] : ? [v23] : ? [v24] : (one_to_one(v21) = v24 & relation(v21) = v22 & function(v21) = v23 & ( ~ (v23 = 0) | ~ (v22 = 0) | v24 = 0))) & ! [v21] : ( ~ (empty(v21) = 0) | (ordinal(v21) = 0 & epsilon_transitive(v21) = 0 & epsilon_connected(v21) = 0)) & ! [v21] : ( ~ (function(v21) = 0) | ? [v22] : ? [v23] : ? [v24] : (one_to_one(v21) = v24 & relation(v21) = v22 & empty(v21) = v23 & ( ~ (v23 = 0) | ~ (v22 = 0) | v24 = 0))) & ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (powerset(v23) = v25 & element(v22, v25) = v26 & element(v21, v23) = v27 & in(v21, v22) = v24 & ( ~ (v26 = 0) | ~ (v24 = 0) | v27 = 0)) & ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (subset(v26, v22) = v27 & subset(v23, v22) = v25 & subset(v21, v22) = v24 & set_union2(v21, v23) = v26 & ( ~ (v25 = 0) | ~ (v24 = 0) | v27 = 0)) & ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (subset(v21, v22) = v26 & ordinal_subset(v21, v22) = v25 & ordinal(v22) = v24 & ordinal(v21) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | (( ~ (v26 = 0) | v25 = 0) & ( ~ (v25 = 0) | v26 = 0)))) & ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (one_to_one(v21) = v25 & relation(v21) = v22 & empty(v21) = v23 & function(v21) = v24 & ( ~ (v24 = 0) | ~ (v23 = 0) | ~ (v22 = 0) | v25 = 0)) & ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (ordinal(v21) = v25 & epsilon_transitive(v21) = v23 & epsilon_connected(v21) = v24 & empty(v21) = v22 & ( ~ (v22 = 0) | (v25 = 0 & v24 = 0 & v23 = 0))) & ? [v21] : ? [v22] : ? [v23] : (succ(v21) = v22 & singleton(v21) = v23 & set_union2(v21, v23) = v22) & ? [v21] : ? [v22] : element(v22, v21) = 0 & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0)))) % 29.98/7.75 | 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, all_0_20_20 yields: % 29.98/7.75 | (1) ~ (all_0_6_6 = 0) & ~ (all_0_8_8 = 0) & ~ (all_0_11_11 = 0) & relation_non_empty(all_0_15_15) = 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_20_20) = all_0_19_19 & ordinal_subset(all_0_19_19, all_0_18_18) = all_0_16_16 & 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(all_0_15_15) = 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_18_18) = 0 & ordinal(all_0_20_20) = 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(all_0_15_15) = 0 & function(empty_set) = 0 & in(all_0_20_20, all_0_18_18) = all_0_17_17 & ! [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_non_empty(v2) = v1) | ~ (relation_non_empty(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_16_16 = 0 & ~ (all_0_17_17 = 0)) | (all_0_17_17 = 0 & ~ (all_0_16_16 = 0))) % 29.98/7.77 | % 29.98/7.77 | Applying alpha-rule on (1) yields: % 29.98/7.77 | (2) relation(empty_set) = 0 % 29.98/7.77 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 29.98/7.77 | (4) function(all_0_0_0) = 0 % 29.98/7.77 | (5) relation(all_0_13_13) = 0 % 29.98/7.77 | (6) ! [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)) % 29.98/7.77 | (7) ! [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))) % 29.98/7.77 | (8) function(all_0_5_5) = 0 % 29.98/7.77 | (9) relation(all_0_14_14) = 0 % 29.98/7.77 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 29.98/7.77 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) % 29.98/7.77 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) % 29.98/7.77 | (13) ! [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)) % 29.98/7.77 | (14) ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ? [v3] : (ordinal(v0) = v2 & epsilon_transitive(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) % 29.98/7.77 | (15) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : (ordinal(v0) = v2 & epsilon_connected(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) % 30.21/7.77 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (ordinal_subset(v0, v0) = v2) | ~ (ordinal(v1) = 0) | ? [v3] : ( ~ (v3 = 0) & ordinal(v0) = v3)) % 30.21/7.77 | (17) ordinal(all_0_12_12) = 0 % 30.21/7.77 | (18) ! [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)))) % 30.21/7.78 | (19) ordinal(all_0_20_20) = 0 % 30.21/7.78 | (20) ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) % 30.21/7.78 | (21) ordinal(all_0_18_18) = 0 % 30.21/7.78 | (22) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : (succ(v0) = v2 & set_union2(v0, v1) = v2)) % 30.21/7.78 | (23) epsilon_transitive(all_0_12_12) = 0 % 30.21/7.78 | (24) ? [v0] : ? [v1] : ? [v2] : (succ(v0) = v1 & singleton(v0) = v2 & set_union2(v0, v2) = v1) % 30.21/7.78 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 30.21/7.78 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) % 30.21/7.78 | (27) ! [v0] : ! [v1] : (v1 = 0 | ~ (ordinal(v0) = v1) | ? [v2] : ? [v3] : (epsilon_transitive(v0) = v2 & epsilon_connected(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 30.21/7.78 | (28) (all_0_16_16 = 0 & ~ (all_0_17_17 = 0)) | (all_0_17_17 = 0 & ~ (all_0_16_16 = 0)) % 30.21/7.78 | (29) empty(all_0_4_4) = 0 % 30.21/7.78 | (30) ! [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))))) % 30.21/7.78 | (31) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) % 30.21/7.78 | (32) relation(all_0_2_2) = 0 % 30.21/7.78 | (33) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : (singleton(v0) = v2 & set_union2(v0, v2) = v1)) % 30.21/7.78 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) % 30.21/7.78 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) % 30.21/7.78 | (36) ! [v0] : ( ~ (empty(v0) = 0) | (ordinal(v0) = 0 & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)) % 30.21/7.78 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4)) % 30.21/7.78 | (38) ordinal(empty_set) = 0 % 30.21/7.78 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 30.21/7.78 | (40) epsilon_connected(all_0_1_1) = 0 % 30.21/7.78 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 30.21/7.78 | (42) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) % 30.21/7.78 | (43) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 30.21/7.78 | (44) relation(all_0_7_7) = 0 % 30.21/7.78 | (45) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = 0) | ~ (in(v1, v0) = 0) | subset(v1, v0) = 0) % 30.21/7.78 | (46) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) % 30.21/7.78 | (47) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 30.21/7.78 | (48) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 30.21/7.78 | (49) one_to_one(all_0_10_10) = 0 % 30.21/7.78 | (50) epsilon_transitive(all_0_1_1) = 0 % 30.21/7.78 | (51) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 30.21/7.78 | (52) ! [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)))) % 30.21/7.78 | (53) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 30.21/7.78 | (54) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 30.21/7.78 | (55) empty(all_0_5_5) = 0 % 30.21/7.78 | (56) ! [v0] : ( ~ (epsilon_connected(v0) = 0) | ? [v1] : ? [v2] : (ordinal(v0) = v2 & epsilon_transitive(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))) % 30.21/7.79 | (57) ! [v0] : ( ~ (epsilon_transitive(v0) = 0) | ? [v1] : ? [v2] : (ordinal(v0) = v2 & epsilon_connected(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))) % 30.21/7.79 | (58) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) % 30.21/7.79 | (59) ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)) % 30.21/7.79 | (60) ? [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))) % 30.21/7.79 | (61) ordinal(all_0_5_5) = 0 % 30.21/7.79 | (62) empty(empty_set) = 0 % 30.21/7.79 | (63) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) % 30.21/7.79 | (64) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) % 30.21/7.79 | (65) relation(all_0_5_5) = 0 % 30.21/7.79 | (66) empty(all_0_3_3) = 0 % 30.21/7.79 | (67) relation(all_0_0_0) = 0 % 30.21/7.79 | (68) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 30.21/7.79 | (69) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) % 30.21/7.79 | (70) ! [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)))) % 30.21/7.79 | (71) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 30.21/7.79 | (72) relation(all_0_4_4) = 0 % 30.21/7.79 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) % 30.21/7.79 | (74) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 30.21/7.79 | (75) ! [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))) % 30.21/7.79 | (76) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) % 30.21/7.79 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 30.21/7.79 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) % 30.21/7.79 | (79) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | in(v0, v1) = 0) % 30.21/7.79 | (80) ordinal(all_0_1_1) = 0 % 30.21/7.79 | (81) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 30.21/7.79 | (82) one_to_one(all_0_5_5) = 0 % 30.21/7.79 | (83) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) % 30.21/7.79 | (84) ! [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))) % 30.21/7.79 | (85) ? [v0] : ? [v1] : element(v1, v0) = 0 % 30.21/7.79 | (86) relation_empty_yielding(empty_set) = 0 % 30.21/7.79 | (87) ? [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)) % 30.21/7.79 | (88) ~ (all_0_11_11 = 0) % 30.21/7.79 | (89) function(all_0_10_10) = 0 % 30.21/7.79 | (90) ! [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))) % 30.21/7.79 | (91) function(all_0_15_15) = 0 % 30.21/7.79 | (92) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) % 30.21/7.79 | (93) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 30.21/7.80 | (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)))) % 30.21/7.80 | (95) empty(all_0_2_2) = 0 % 30.21/7.80 | (96) relation_empty_yielding(all_0_13_13) = 0 % 30.21/7.80 | (97) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_non_empty(v2) = v1) | ~ (relation_non_empty(v2) = v0)) % 30.21/7.80 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 30.21/7.80 | (99) empty(all_0_7_7) = all_0_6_6 % 30.21/7.80 | (100) ordinal_subset(all_0_19_19, all_0_18_18) = all_0_16_16 % 30.21/7.80 | (101) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) % 30.21/7.80 | (102) relation_empty_yielding(all_0_14_14) = 0 % 30.21/7.80 | (103) relation(all_0_10_10) = 0 % 30.21/7.80 | (104) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 30.21/7.80 | (105) relation_non_empty(all_0_15_15) = 0 % 30.21/7.80 | (106) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & empty(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 30.21/7.80 | (107) ~ (all_0_8_8 = 0) % 30.21/7.80 | (108) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 30.21/7.80 | (109) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) % 30.21/7.80 | (110) empty(all_0_9_9) = all_0_8_8 % 30.21/7.80 | (111) epsilon_connected(empty_set) = 0 % 30.21/7.80 | (112) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v1, v0) = v2) | ~ (epsilon_transitive(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3)) % 30.21/7.80 | (113) in(all_0_20_20, all_0_18_18) = all_0_17_17 % 30.21/7.80 | (114) relation(all_0_15_15) = 0 % 30.21/7.80 | (115) empty(all_0_12_12) = all_0_11_11 % 30.21/7.80 | (116) function(all_0_14_14) = 0 % 30.21/7.80 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 30.21/7.80 | (118) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) % 30.21/7.80 | (119) function(empty_set) = 0 % 30.21/7.80 | (120) ~ (all_0_6_6 = 0) % 30.21/7.80 | (121) ! [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)))) % 30.21/7.80 | (122) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 30.21/7.80 | (123) epsilon_connected(all_0_5_5) = 0 % 30.21/7.80 | (124) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 30.21/7.80 | (125) function(all_0_4_4) = 0 % 30.21/7.80 | (126) epsilon_connected(all_0_12_12) = 0 % 30.21/7.80 | (127) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 30.21/7.80 | (128) epsilon_transitive(all_0_5_5) = 0 % 30.21/7.80 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 30.21/7.80 | (130) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordinal_subset(v3, v2) = v1) | ~ (ordinal_subset(v3, v2) = v0)) % 30.21/7.80 | (131) ! [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))))) % 30.21/7.80 | (132) succ(all_0_20_20) = all_0_19_19 % 30.21/7.80 | (133) ! [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))))) % 30.21/7.80 | (134) ! [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)) % 30.21/7.80 | (135) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) % 30.21/7.81 | (136) epsilon_transitive(empty_set) = 0 % 30.21/7.81 | (137) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 30.21/7.81 | (138) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 30.21/7.81 | (139) one_to_one(empty_set) = 0 % 30.21/7.81 | (140) ? [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)) % 30.21/7.81 | (141) ! [v0] : ! [v1] : ( ~ (ordinal(v1) = 0) | ~ (ordinal(v0) = 0) | ordinal_subset(v0, v0) = 0) % 30.21/7.81 | (142) ! [v0] : ! [v1] : (v1 = 0 | ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & subset(v2, v0) = v3 & in(v2, v0) = 0)) % 30.21/7.81 | (143) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 30.21/7.81 | (144) ? [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)) % 30.21/7.81 | % 30.21/7.81 | Instantiating formula (108) 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: % 30.21/7.81 | (145) all_0_2_2 = all_0_3_3 % 30.21/7.81 | % 30.21/7.81 | Instantiating formula (108) 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: % 30.21/7.81 | (146) all_0_3_3 = all_0_4_4 % 30.21/7.81 | % 30.21/7.81 | Instantiating formula (108) 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: % 30.21/7.81 | (147) all_0_2_2 = all_0_5_5 % 30.21/7.81 | % 30.21/7.81 | Instantiating formula (108) with empty_set, all_0_3_3 and discharging atoms empty(all_0_3_3) = 0, empty(empty_set) = 0, yields: % 30.21/7.81 | (148) all_0_3_3 = empty_set % 30.21/7.81 | % 30.21/7.81 | Combining equations (145,147) yields a new equation: % 30.21/7.81 | (149) all_0_3_3 = all_0_5_5 % 30.21/7.81 | % 30.21/7.81 | Simplifying 149 yields: % 30.21/7.81 | (150) all_0_3_3 = all_0_5_5 % 30.21/7.81 | % 30.21/7.81 | Combining equations (148,146) yields a new equation: % 30.21/7.81 | (151) all_0_4_4 = empty_set % 30.21/7.81 | % 30.21/7.81 | Combining equations (150,146) yields a new equation: % 30.21/7.81 | (152) all_0_4_4 = all_0_5_5 % 30.21/7.81 | % 30.21/7.81 | Combining equations (152,151) yields a new equation: % 30.21/7.81 | (153) all_0_5_5 = empty_set % 30.21/7.81 | % 30.21/7.81 | Simplifying 153 yields: % 30.21/7.81 | (154) all_0_5_5 = empty_set % 30.21/7.81 | % 30.21/7.81 | From (154) and (61) follows: % 30.21/7.81 | (38) ordinal(empty_set) = 0 % 30.21/7.81 | % 30.21/7.81 | Instantiating formula (79) with all_0_19_19, all_0_20_20 and discharging atoms succ(all_0_20_20) = all_0_19_19, yields: % 30.21/7.81 | (156) in(all_0_20_20, all_0_19_19) = 0 % 30.21/7.81 | % 30.21/7.81 | Instantiating formula (133) with all_0_19_19, all_0_20_20 and discharging atoms succ(all_0_20_20) = all_0_19_19, yields: % 30.21/7.81 | (157) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordinal(all_0_19_19) = v4 & ordinal(all_0_20_20) = v0 & epsilon_transitive(all_0_19_19) = v2 & epsilon_connected(all_0_19_19) = v3 & empty(all_0_19_19) = v1 & ( ~ (v0 = 0) | (v4 = 0 & v3 = 0 & v2 = 0 & ~ (v1 = 0)))) % 30.21/7.81 | % 30.21/7.81 | Instantiating formula (33) with all_0_19_19, all_0_20_20 and discharging atoms succ(all_0_20_20) = all_0_19_19, yields: % 30.21/7.81 | (158) ? [v0] : (singleton(all_0_20_20) = v0 & set_union2(all_0_20_20, v0) = all_0_19_19) % 30.21/7.81 | % 30.21/7.81 | Instantiating formula (84) with all_0_16_16, all_0_18_18, all_0_19_19 and discharging atoms ordinal_subset(all_0_19_19, all_0_18_18) = all_0_16_16, yields: % 30.21/7.81 | (159) all_0_16_16 = 0 | ? [v0] : ? [v1] : ? [v2] : (ordinal_subset(all_0_18_18, all_0_19_19) = v2 & ordinal(all_0_18_18) = v1 & ordinal(all_0_19_19) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 30.21/7.81 | % 30.21/7.81 | Instantiating formula (131) with all_0_16_16, all_0_18_18, all_0_19_19 and discharging atoms ordinal_subset(all_0_19_19, all_0_18_18) = all_0_16_16, yields: % 30.21/7.81 | (160) ? [v0] : ? [v1] : ? [v2] : (subset(all_0_19_19, all_0_18_18) = v2 & ordinal(all_0_18_18) = v1 & ordinal(all_0_19_19) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (v2 = 0) | all_0_16_16 = 0) & ( ~ (all_0_16_16 = 0) | v2 = 0)))) % 30.21/7.81 | % 30.21/7.81 | Instantiating formula (59) with all_0_18_18 and discharging atoms ordinal(all_0_18_18) = 0, yields: % 30.21/7.81 | (161) epsilon_transitive(all_0_18_18) = 0 & epsilon_connected(all_0_18_18) = 0 % 30.21/7.81 | % 30.21/7.81 | Applying alpha-rule on (161) yields: % 30.21/7.81 | (162) epsilon_transitive(all_0_18_18) = 0 % 30.21/7.81 | (163) epsilon_connected(all_0_18_18) = 0 % 30.21/7.81 | % 30.21/7.81 | Instantiating formula (70) with 0, all_0_18_18 and discharging atoms ordinal(all_0_18_18) = 0, yields: % 30.21/7.81 | (164) ? [v0] : ? [v1] : ? [v2] : (epsilon_transitive(all_0_18_18) = v1 & epsilon_connected(all_0_18_18) = v2 & empty(all_0_18_18) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 30.21/7.81 | % 30.21/7.81 | Instantiating formula (141) with empty_set, all_0_18_18 and discharging atoms ordinal(all_0_18_18) = 0, ordinal(empty_set) = 0, yields: % 30.21/7.82 | (165) ordinal_subset(all_0_18_18, all_0_18_18) = 0 % 30.21/7.82 | % 30.21/7.82 | Instantiating formula (26) with all_0_17_17, all_0_18_18, all_0_20_20 and discharging atoms in(all_0_20_20, all_0_18_18) = all_0_17_17, yields: % 30.21/7.82 | (166) all_0_17_17 = 0 | ? [v0] : ? [v1] : (element(all_0_20_20, all_0_18_18) = v0 & empty(all_0_18_18) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 30.21/7.82 | % 30.21/7.82 | Instantiating (164) with all_45_0_80, all_45_1_81, all_45_2_82 yields: % 30.21/7.82 | (167) epsilon_transitive(all_0_18_18) = all_45_1_81 & epsilon_connected(all_0_18_18) = all_45_0_80 & empty(all_0_18_18) = all_45_2_82 & ( ~ (all_45_2_82 = 0) | (all_45_0_80 = 0 & all_45_1_81 = 0)) % 30.21/7.82 | % 30.21/7.82 | Applying alpha-rule on (167) yields: % 30.21/7.82 | (168) epsilon_transitive(all_0_18_18) = all_45_1_81 % 30.21/7.82 | (169) epsilon_connected(all_0_18_18) = all_45_0_80 % 30.21/7.82 | (170) empty(all_0_18_18) = all_45_2_82 % 30.21/7.82 | (171) ~ (all_45_2_82 = 0) | (all_45_0_80 = 0 & all_45_1_81 = 0) % 30.21/7.82 | % 30.21/7.82 | Instantiating (160) with all_69_0_112, all_69_1_113, all_69_2_114 yields: % 30.21/7.82 | (172) subset(all_0_19_19, all_0_18_18) = all_69_0_112 & ordinal(all_0_18_18) = all_69_1_113 & ordinal(all_0_19_19) = all_69_2_114 & ( ~ (all_69_1_113 = 0) | ~ (all_69_2_114 = 0) | (( ~ (all_69_0_112 = 0) | all_0_16_16 = 0) & ( ~ (all_0_16_16 = 0) | all_69_0_112 = 0))) % 30.21/7.82 | % 30.21/7.82 | Applying alpha-rule on (172) yields: % 30.21/7.82 | (173) subset(all_0_19_19, all_0_18_18) = all_69_0_112 % 30.21/7.82 | (174) ordinal(all_0_18_18) = all_69_1_113 % 30.21/7.82 | (175) ordinal(all_0_19_19) = all_69_2_114 % 30.21/7.82 | (176) ~ (all_69_1_113 = 0) | ~ (all_69_2_114 = 0) | (( ~ (all_69_0_112 = 0) | all_0_16_16 = 0) & ( ~ (all_0_16_16 = 0) | all_69_0_112 = 0)) % 30.21/7.82 | % 30.21/7.82 | Instantiating (158) with all_109_0_169 yields: % 30.21/7.82 | (177) singleton(all_0_20_20) = all_109_0_169 & set_union2(all_0_20_20, all_109_0_169) = all_0_19_19 % 30.21/7.82 | % 30.21/7.82 | Applying alpha-rule on (177) yields: % 30.21/7.82 | (178) singleton(all_0_20_20) = all_109_0_169 % 30.21/7.82 | (179) set_union2(all_0_20_20, all_109_0_169) = all_0_19_19 % 30.21/7.82 | % 30.21/7.82 | Instantiating (157) with all_113_0_171, all_113_1_172, all_113_2_173, all_113_3_174, all_113_4_175 yields: % 30.21/7.82 | (180) ordinal(all_0_19_19) = all_113_0_171 & ordinal(all_0_20_20) = all_113_4_175 & epsilon_transitive(all_0_19_19) = all_113_2_173 & epsilon_connected(all_0_19_19) = all_113_1_172 & empty(all_0_19_19) = all_113_3_174 & ( ~ (all_113_4_175 = 0) | (all_113_0_171 = 0 & all_113_1_172 = 0 & all_113_2_173 = 0 & ~ (all_113_3_174 = 0))) % 30.21/7.82 | % 30.21/7.82 | Applying alpha-rule on (180) yields: % 30.21/7.82 | (181) ordinal(all_0_20_20) = all_113_4_175 % 30.21/7.82 | (182) epsilon_transitive(all_0_19_19) = all_113_2_173 % 30.21/7.82 | (183) empty(all_0_19_19) = all_113_3_174 % 30.21/7.82 | (184) epsilon_connected(all_0_19_19) = all_113_1_172 % 30.21/7.82 | (185) ordinal(all_0_19_19) = all_113_0_171 % 30.21/7.82 | (186) ~ (all_113_4_175 = 0) | (all_113_0_171 = 0 & all_113_1_172 = 0 & all_113_2_173 = 0 & ~ (all_113_3_174 = 0)) % 30.21/7.82 | % 30.21/7.82 | Instantiating formula (11) with all_0_18_18, all_69_1_113, 0 and discharging atoms ordinal(all_0_18_18) = all_69_1_113, ordinal(all_0_18_18) = 0, yields: % 30.21/7.82 | (187) all_69_1_113 = 0 % 30.21/7.82 | % 30.21/7.82 | Instantiating formula (11) with all_0_19_19, all_69_2_114, all_113_0_171 and discharging atoms ordinal(all_0_19_19) = all_113_0_171, ordinal(all_0_19_19) = all_69_2_114, yields: % 30.21/7.82 | (188) all_113_0_171 = all_69_2_114 % 30.21/7.82 | % 30.21/7.82 | Instantiating formula (11) with all_0_20_20, all_113_4_175, 0 and discharging atoms ordinal(all_0_20_20) = all_113_4_175, ordinal(all_0_20_20) = 0, yields: % 30.21/7.82 | (189) all_113_4_175 = 0 % 30.21/7.82 | % 30.21/7.82 | Instantiating formula (58) with all_0_18_18, 0, all_45_1_81 and discharging atoms epsilon_transitive(all_0_18_18) = all_45_1_81, epsilon_transitive(all_0_18_18) = 0, yields: % 30.21/7.82 | (190) all_45_1_81 = 0 % 30.21/7.82 | % 30.21/7.82 | Instantiating formula (76) with all_0_18_18, 0, all_45_0_80 and discharging atoms epsilon_connected(all_0_18_18) = all_45_0_80, epsilon_connected(all_0_18_18) = 0, yields: % 30.21/7.82 | (191) all_45_0_80 = 0 % 30.21/7.82 | % 30.21/7.82 | From (187) and (174) follows: % 30.21/7.82 | (21) ordinal(all_0_18_18) = 0 % 30.21/7.82 | % 30.21/7.82 | From (188) and (185) follows: % 30.21/7.82 | (175) ordinal(all_0_19_19) = all_69_2_114 % 30.21/7.82 | % 30.21/7.82 | From (190) and (168) follows: % 30.21/7.82 | (162) epsilon_transitive(all_0_18_18) = 0 % 30.21/7.82 | % 30.21/7.82 | From (191) and (169) follows: % 30.21/7.82 | (163) epsilon_connected(all_0_18_18) = 0 % 30.21/7.82 | % 30.21/7.82 +-Applying beta-rule and splitting (186), into two cases. % 30.21/7.82 |-Branch one: % 30.21/7.82 | (196) ~ (all_113_4_175 = 0) % 30.21/7.82 | % 30.21/7.82 | Equations (189) can reduce 196 to: % 30.21/7.82 | (197) $false % 30.21/7.82 | % 30.21/7.82 |-The branch is then unsatisfiable % 30.21/7.82 |-Branch two: % 30.21/7.82 | (189) all_113_4_175 = 0 % 30.21/7.82 | (199) all_113_0_171 = 0 & all_113_1_172 = 0 & all_113_2_173 = 0 & ~ (all_113_3_174 = 0) % 30.21/7.82 | % 30.21/7.82 | Applying alpha-rule on (199) yields: % 30.21/7.82 | (200) all_113_0_171 = 0 % 30.21/7.82 | (201) all_113_1_172 = 0 % 30.21/7.82 | (202) all_113_2_173 = 0 % 30.21/7.82 | (203) ~ (all_113_3_174 = 0) % 30.21/7.82 | % 30.21/7.82 | Combining equations (188,200) yields a new equation: % 30.21/7.82 | (204) all_69_2_114 = 0 % 30.21/7.82 | % 30.21/7.82 | Simplifying 204 yields: % 30.21/7.82 | (205) all_69_2_114 = 0 % 30.21/7.82 | % 30.21/7.82 | From (205) and (175) follows: % 30.21/7.82 | (206) ordinal(all_0_19_19) = 0 % 30.21/7.82 | % 30.21/7.82 | Instantiating formula (12) with all_69_0_112, all_0_18_18, all_0_19_19 and discharging atoms subset(all_0_19_19, all_0_18_18) = all_69_0_112, yields: % 30.21/7.82 | (207) all_69_0_112 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_0_18_18) = v0 & element(all_0_19_19, v0) = v1) % 30.21/7.83 | % 30.21/7.83 | Instantiating formula (71) with all_69_0_112, all_0_18_18, all_0_19_19 and discharging atoms subset(all_0_19_19, all_0_18_18) = all_69_0_112, yields: % 30.21/7.83 | (208) all_69_0_112 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_18_18) = v1 & in(v0, all_0_19_19) = 0) % 30.21/7.83 | % 30.21/7.83 | Instantiating formula (30) with all_69_0_112, all_0_18_18, all_0_19_19 and discharging atoms subset(all_0_19_19, all_0_18_18) = all_69_0_112, yields: % 30.21/7.83 | (209) ? [v0] : ? [v1] : ? [v2] : (ordinal_subset(all_0_19_19, all_0_18_18) = v2 & ordinal(all_0_18_18) = v1 & ordinal(all_0_19_19) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (v2 = 0) | all_69_0_112 = 0) & ( ~ (all_69_0_112 = 0) | v2 = 0)))) % 30.21/7.83 | % 30.21/7.83 | Instantiating formula (131) with 0, all_0_18_18, all_0_18_18 and discharging atoms ordinal_subset(all_0_18_18, all_0_18_18) = 0, yields: % 30.21/7.83 | (210) ? [v0] : ? [v1] : ? [v2] : (subset(all_0_18_18, all_0_18_18) = v2 & ordinal(all_0_18_18) = v1 & ordinal(all_0_18_18) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 30.21/7.83 | % 30.21/7.83 | Instantiating formula (18) with all_69_0_112, all_0_19_19, all_109_0_169, all_0_18_18, all_0_20_20 and discharging atoms subset(all_0_19_19, all_0_18_18) = all_69_0_112, set_union2(all_0_20_20, all_109_0_169) = all_0_19_19, yields: % 30.21/7.83 | (211) all_69_0_112 = 0 | ? [v0] : ? [v1] : (subset(all_109_0_169, all_0_18_18) = v1 & subset(all_0_20_20, all_0_18_18) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 30.21/7.83 | % 30.21/7.83 | Instantiating formula (112) with all_69_0_112, all_0_19_19, all_0_18_18 and discharging atoms subset(all_0_19_19, all_0_18_18) = all_69_0_112, epsilon_transitive(all_0_18_18) = 0, yields: % 30.21/7.83 | (212) all_69_0_112 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_0_19_19, all_0_18_18) = v0) % 30.21/7.83 | % 30.21/7.83 | Instantiating formula (121) with 0, all_0_18_18 and discharging atoms epsilon_transitive(all_0_18_18) = 0, yields: % 30.21/7.83 | (213) ? [v0] : ? [v1] : ? [v2] : (ordinal(all_0_18_18) = v2 & epsilon_connected(all_0_18_18) = v1 & empty(all_0_18_18) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 30.21/7.83 | % 30.21/7.83 | Instantiating formula (52) with 0, all_0_18_18 and discharging atoms epsilon_connected(all_0_18_18) = 0, yields: % 30.21/7.83 | (214) ? [v0] : ? [v1] : ? [v2] : (ordinal(all_0_18_18) = v2 & epsilon_transitive(all_0_18_18) = v1 & empty(all_0_18_18) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0))) % 30.21/7.83 | % 30.21/7.83 | Instantiating (209) with all_153_0_197, all_153_1_198, all_153_2_199 yields: % 30.21/7.83 | (215) ordinal_subset(all_0_19_19, all_0_18_18) = all_153_0_197 & ordinal(all_0_18_18) = all_153_1_198 & ordinal(all_0_19_19) = all_153_2_199 & ( ~ (all_153_1_198 = 0) | ~ (all_153_2_199 = 0) | (( ~ (all_153_0_197 = 0) | all_69_0_112 = 0) & ( ~ (all_69_0_112 = 0) | all_153_0_197 = 0))) % 30.21/7.83 | % 30.21/7.83 | Applying alpha-rule on (215) yields: % 30.21/7.83 | (216) ordinal_subset(all_0_19_19, all_0_18_18) = all_153_0_197 % 30.21/7.83 | (217) ordinal(all_0_18_18) = all_153_1_198 % 30.21/7.83 | (218) ordinal(all_0_19_19) = all_153_2_199 % 30.21/7.83 | (219) ~ (all_153_1_198 = 0) | ~ (all_153_2_199 = 0) | (( ~ (all_153_0_197 = 0) | all_69_0_112 = 0) & ( ~ (all_69_0_112 = 0) | all_153_0_197 = 0)) % 30.21/7.83 | % 30.21/7.83 | Instantiating (214) with all_175_0_223, all_175_1_224, all_175_2_225 yields: % 30.21/7.83 | (220) ordinal(all_0_18_18) = all_175_0_223 & epsilon_transitive(all_0_18_18) = all_175_1_224 & empty(all_0_18_18) = all_175_2_225 & ( ~ (all_175_2_225 = 0) | (all_175_0_223 = 0 & all_175_1_224 = 0)) % 30.21/7.83 | % 30.21/7.83 | Applying alpha-rule on (220) yields: % 30.21/7.83 | (221) ordinal(all_0_18_18) = all_175_0_223 % 30.21/7.83 | (222) epsilon_transitive(all_0_18_18) = all_175_1_224 % 30.21/7.83 | (223) empty(all_0_18_18) = all_175_2_225 % 30.21/7.83 | (224) ~ (all_175_2_225 = 0) | (all_175_0_223 = 0 & all_175_1_224 = 0) % 30.21/7.83 | % 30.21/7.83 | Instantiating (213) with all_227_0_284, all_227_1_285, all_227_2_286 yields: % 30.21/7.83 | (225) ordinal(all_0_18_18) = all_227_0_284 & epsilon_connected(all_0_18_18) = all_227_1_285 & empty(all_0_18_18) = all_227_2_286 & ( ~ (all_227_2_286 = 0) | (all_227_0_284 = 0 & all_227_1_285 = 0)) % 30.21/7.83 | % 30.21/7.83 | Applying alpha-rule on (225) yields: % 30.21/7.83 | (226) ordinal(all_0_18_18) = all_227_0_284 % 30.21/7.83 | (227) epsilon_connected(all_0_18_18) = all_227_1_285 % 30.21/7.83 | (228) empty(all_0_18_18) = all_227_2_286 % 30.21/7.83 | (229) ~ (all_227_2_286 = 0) | (all_227_0_284 = 0 & all_227_1_285 = 0) % 30.21/7.83 | % 30.21/7.83 | Instantiating (210) with all_239_0_300, all_239_1_301, all_239_2_302 yields: % 30.21/7.83 | (230) subset(all_0_18_18, all_0_18_18) = all_239_0_300 & ordinal(all_0_18_18) = all_239_1_301 & ordinal(all_0_18_18) = all_239_2_302 & ( ~ (all_239_1_301 = 0) | ~ (all_239_2_302 = 0) | all_239_0_300 = 0) % 30.21/7.83 | % 30.21/7.83 | Applying alpha-rule on (230) yields: % 30.21/7.83 | (231) subset(all_0_18_18, all_0_18_18) = all_239_0_300 % 30.21/7.83 | (232) ordinal(all_0_18_18) = all_239_1_301 % 30.21/7.83 | (233) ordinal(all_0_18_18) = all_239_2_302 % 30.21/7.83 | (234) ~ (all_239_1_301 = 0) | ~ (all_239_2_302 = 0) | all_239_0_300 = 0 % 30.21/7.83 | % 30.21/7.83 | Instantiating formula (130) with all_0_19_19, all_0_18_18, all_153_0_197, all_0_16_16 and discharging atoms ordinal_subset(all_0_19_19, all_0_18_18) = all_153_0_197, ordinal_subset(all_0_19_19, all_0_18_18) = all_0_16_16, yields: % 30.21/7.83 | (235) all_153_0_197 = all_0_16_16 % 30.21/7.83 | % 30.21/7.83 | Instantiating formula (11) with all_0_18_18, all_239_2_302, all_239_1_301 and discharging atoms ordinal(all_0_18_18) = all_239_1_301, ordinal(all_0_18_18) = all_239_2_302, yields: % 30.21/7.84 | (236) all_239_1_301 = all_239_2_302 % 30.21/7.84 | % 30.21/7.84 | Instantiating formula (11) with all_0_18_18, all_227_0_284, all_239_1_301 and discharging atoms ordinal(all_0_18_18) = all_239_1_301, ordinal(all_0_18_18) = all_227_0_284, yields: % 30.21/7.84 | (237) all_239_1_301 = all_227_0_284 % 30.21/7.84 | % 30.21/7.84 | Instantiating formula (11) with all_0_18_18, all_175_0_223, 0 and discharging atoms ordinal(all_0_18_18) = all_175_0_223, ordinal(all_0_18_18) = 0, yields: % 30.21/7.84 | (238) all_175_0_223 = 0 % 30.21/7.84 | % 30.21/7.84 | Instantiating formula (11) with all_0_18_18, all_175_0_223, all_239_2_302 and discharging atoms ordinal(all_0_18_18) = all_239_2_302, ordinal(all_0_18_18) = all_175_0_223, yields: % 30.21/7.84 | (239) all_239_2_302 = all_175_0_223 % 30.21/7.84 | % 30.21/7.84 | Instantiating formula (11) with all_0_18_18, all_153_1_198, all_239_2_302 and discharging atoms ordinal(all_0_18_18) = all_239_2_302, ordinal(all_0_18_18) = all_153_1_198, yields: % 30.21/7.84 | (240) all_239_2_302 = all_153_1_198 % 30.21/7.84 | % 30.21/7.84 | Instantiating formula (11) with all_0_19_19, all_153_2_199, 0 and discharging atoms ordinal(all_0_19_19) = all_153_2_199, ordinal(all_0_19_19) = 0, yields: % 30.21/7.84 | (241) all_153_2_199 = 0 % 30.21/7.84 | % 30.21/7.84 | Instantiating formula (58) with all_0_18_18, all_175_1_224, 0 and discharging atoms epsilon_transitive(all_0_18_18) = all_175_1_224, epsilon_transitive(all_0_18_18) = 0, yields: % 30.21/7.84 | (242) all_175_1_224 = 0 % 30.21/7.84 | % 30.21/7.84 | Combining equations (236,237) yields a new equation: % 30.21/7.84 | (243) all_239_2_302 = all_227_0_284 % 30.21/7.84 | % 30.21/7.84 | Simplifying 243 yields: % 30.21/7.84 | (244) all_239_2_302 = all_227_0_284 % 30.21/7.84 | % 30.21/7.84 | Combining equations (239,244) yields a new equation: % 30.21/7.84 | (245) all_227_0_284 = all_175_0_223 % 30.21/7.84 | % 30.21/7.84 | Combining equations (240,244) yields a new equation: % 30.21/7.84 | (246) all_227_0_284 = all_153_1_198 % 30.21/7.84 | % 30.21/7.84 | Combining equations (245,246) yields a new equation: % 30.21/7.84 | (247) all_175_0_223 = all_153_1_198 % 30.21/7.84 | % 30.21/7.84 | Simplifying 247 yields: % 30.21/7.84 | (248) all_175_0_223 = all_153_1_198 % 30.21/7.84 | % 30.21/7.84 | Combining equations (238,248) yields a new equation: % 30.21/7.84 | (249) all_153_1_198 = 0 % 30.21/7.84 | % 30.21/7.84 | From (242) and (222) follows: % 30.21/7.84 | (162) epsilon_transitive(all_0_18_18) = 0 % 30.21/7.84 | % 30.21/7.84 +-Applying beta-rule and splitting (28), into two cases. % 30.21/7.84 |-Branch one: % 30.21/7.84 | (251) all_0_16_16 = 0 & ~ (all_0_17_17 = 0) % 30.21/7.84 | % 30.21/7.84 | Applying alpha-rule on (251) yields: % 30.21/7.84 | (252) all_0_16_16 = 0 % 30.21/7.84 | (253) ~ (all_0_17_17 = 0) % 30.21/7.84 | % 30.21/7.84 | Combining equations (252,235) yields a new equation: % 30.21/7.84 | (254) all_153_0_197 = 0 % 30.21/7.84 | % 30.21/7.84 +-Applying beta-rule and splitting (219), into two cases. % 30.21/7.84 |-Branch one: % 30.21/7.84 | (255) ~ (all_153_1_198 = 0) % 30.21/7.84 | % 30.21/7.84 | Equations (249) can reduce 255 to: % 30.21/7.84 | (197) $false % 30.21/7.84 | % 30.21/7.84 |-The branch is then unsatisfiable % 30.21/7.84 |-Branch two: % 30.21/7.84 | (249) all_153_1_198 = 0 % 30.21/7.84 | (258) ~ (all_153_2_199 = 0) | (( ~ (all_153_0_197 = 0) | all_69_0_112 = 0) & ( ~ (all_69_0_112 = 0) | all_153_0_197 = 0)) % 30.21/7.84 | % 30.21/7.84 +-Applying beta-rule and splitting (166), into two cases. % 30.21/7.84 |-Branch one: % 30.21/7.84 | (259) all_0_17_17 = 0 % 30.21/7.84 | % 30.21/7.84 | Equations (259) can reduce 253 to: % 30.21/7.84 | (197) $false % 30.21/7.84 | % 30.21/7.84 |-The branch is then unsatisfiable % 30.21/7.84 |-Branch two: % 30.21/7.84 | (253) ~ (all_0_17_17 = 0) % 30.21/7.84 | (262) ? [v0] : ? [v1] : (element(all_0_20_20, all_0_18_18) = v0 & empty(all_0_18_18) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 30.21/7.84 | % 30.21/7.84 +-Applying beta-rule and splitting (258), into two cases. % 30.21/7.84 |-Branch one: % 30.21/7.84 | (263) ~ (all_153_2_199 = 0) % 30.21/7.84 | % 30.21/7.84 | Equations (241) can reduce 263 to: % 30.21/7.84 | (197) $false % 30.21/7.84 | % 30.21/7.84 |-The branch is then unsatisfiable % 30.21/7.84 |-Branch two: % 30.21/7.84 | (241) all_153_2_199 = 0 % 30.21/7.84 | (266) ( ~ (all_153_0_197 = 0) | all_69_0_112 = 0) & ( ~ (all_69_0_112 = 0) | all_153_0_197 = 0) % 30.21/7.84 | % 30.21/7.84 | Applying alpha-rule on (266) yields: % 30.21/7.84 | (267) ~ (all_153_0_197 = 0) | all_69_0_112 = 0 % 30.21/7.84 | (268) ~ (all_69_0_112 = 0) | all_153_0_197 = 0 % 30.21/7.84 | % 30.21/7.84 +-Applying beta-rule and splitting (267), into two cases. % 30.21/7.84 |-Branch one: % 30.21/7.84 | (269) ~ (all_153_0_197 = 0) % 30.21/7.84 | % 30.21/7.84 | Equations (254) can reduce 269 to: % 30.21/7.84 | (197) $false % 30.21/7.84 | % 30.21/7.84 |-The branch is then unsatisfiable % 30.21/7.84 |-Branch two: % 30.21/7.84 | (254) all_153_0_197 = 0 % 30.21/7.84 | (272) all_69_0_112 = 0 % 30.21/7.84 | % 30.21/7.84 | From (272) and (173) follows: % 30.21/7.84 | (273) subset(all_0_19_19, all_0_18_18) = 0 % 30.21/7.84 | % 30.21/7.84 | Instantiating formula (73) with all_0_17_17, all_0_20_20, all_0_18_18, all_0_19_19 and discharging atoms subset(all_0_19_19, all_0_18_18) = 0, in(all_0_20_20, all_0_18_18) = all_0_17_17, yields: % 30.21/7.84 | (274) all_0_17_17 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_0_20_20, all_0_19_19) = v0) % 30.21/7.84 | % 30.21/7.84 | Instantiating formula (25) with all_0_20_20, all_0_18_18, all_0_19_19 and discharging atoms subset(all_0_19_19, all_0_18_18) = 0, in(all_0_20_20, all_0_19_19) = 0, yields: % 30.21/7.84 | (275) in(all_0_20_20, all_0_18_18) = 0 % 30.21/7.84 | % 30.21/7.84 +-Applying beta-rule and splitting (274), into two cases. % 30.21/7.84 |-Branch one: % 30.21/7.84 | (259) all_0_17_17 = 0 % 30.21/7.84 | % 30.21/7.84 | Equations (259) can reduce 253 to: % 30.21/7.84 | (197) $false % 30.21/7.84 | % 30.21/7.84 |-The branch is then unsatisfiable % 30.21/7.84 |-Branch two: % 30.21/7.84 | (253) ~ (all_0_17_17 = 0) % 30.21/7.84 | (279) ? [v0] : ( ~ (v0 = 0) & in(all_0_20_20, all_0_19_19) = v0) % 30.57/7.84 | % 30.57/7.84 | Instantiating formula (77) with all_0_20_20, all_0_18_18, 0, all_0_17_17 and discharging atoms in(all_0_20_20, all_0_18_18) = all_0_17_17, in(all_0_20_20, all_0_18_18) = 0, yields: % 30.57/7.84 | (259) all_0_17_17 = 0 % 30.57/7.84 | % 30.57/7.84 | Equations (259) can reduce 253 to: % 30.57/7.84 | (197) $false % 30.57/7.84 | % 30.57/7.84 |-The branch is then unsatisfiable % 30.57/7.85 |-Branch two: % 30.57/7.85 | (282) all_0_17_17 = 0 & ~ (all_0_16_16 = 0) % 30.57/7.85 | % 30.57/7.85 | Applying alpha-rule on (282) yields: % 30.57/7.85 | (259) all_0_17_17 = 0 % 30.57/7.85 | (284) ~ (all_0_16_16 = 0) % 30.57/7.85 | % 30.57/7.85 | From (259) and (113) follows: % 30.57/7.85 | (275) in(all_0_20_20, all_0_18_18) = 0 % 30.57/7.85 | % 30.57/7.85 +-Applying beta-rule and splitting (159), into two cases. % 30.57/7.85 |-Branch one: % 30.57/7.85 | (252) all_0_16_16 = 0 % 30.57/7.85 | % 30.57/7.85 | Equations (252) can reduce 284 to: % 30.57/7.85 | (197) $false % 30.57/7.85 | % 30.57/7.85 |-The branch is then unsatisfiable % 30.57/7.85 |-Branch two: % 30.57/7.85 | (284) ~ (all_0_16_16 = 0) % 30.57/7.85 | (289) ? [v0] : ? [v1] : ? [v2] : (ordinal_subset(all_0_18_18, all_0_19_19) = v2 & ordinal(all_0_18_18) = v1 & ordinal(all_0_19_19) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 30.57/7.85 | % 30.57/7.85 +-Applying beta-rule and splitting (219), into two cases. % 30.57/7.85 |-Branch one: % 30.57/7.85 | (255) ~ (all_153_1_198 = 0) % 30.57/7.85 | % 30.57/7.85 | Equations (249) can reduce 255 to: % 30.57/7.85 | (197) $false % 30.57/7.85 | % 30.57/7.85 |-The branch is then unsatisfiable % 30.57/7.85 |-Branch two: % 30.57/7.85 | (249) all_153_1_198 = 0 % 30.57/7.85 | (258) ~ (all_153_2_199 = 0) | (( ~ (all_153_0_197 = 0) | all_69_0_112 = 0) & ( ~ (all_69_0_112 = 0) | all_153_0_197 = 0)) % 30.57/7.85 | % 30.57/7.85 +-Applying beta-rule and splitting (258), into two cases. % 30.57/7.85 |-Branch one: % 30.57/7.85 | (263) ~ (all_153_2_199 = 0) % 30.57/7.85 | % 30.57/7.85 | Equations (241) can reduce 263 to: % 30.57/7.85 | (197) $false % 30.57/7.85 | % 30.57/7.85 |-The branch is then unsatisfiable % 30.57/7.85 |-Branch two: % 30.57/7.85 | (241) all_153_2_199 = 0 % 30.57/7.85 | (266) ( ~ (all_153_0_197 = 0) | all_69_0_112 = 0) & ( ~ (all_69_0_112 = 0) | all_153_0_197 = 0) % 30.57/7.85 | % 30.57/7.85 | Applying alpha-rule on (266) yields: % 30.57/7.85 | (267) ~ (all_153_0_197 = 0) | all_69_0_112 = 0 % 30.57/7.85 | (268) ~ (all_69_0_112 = 0) | all_153_0_197 = 0 % 30.57/7.85 | % 30.57/7.85 +-Applying beta-rule and splitting (268), into two cases. % 30.57/7.85 |-Branch one: % 30.57/7.85 | (300) ~ (all_69_0_112 = 0) % 30.57/7.85 | % 30.57/7.85 +-Applying beta-rule and splitting (212), into two cases. % 30.57/7.85 |-Branch one: % 30.57/7.85 | (272) all_69_0_112 = 0 % 30.57/7.85 | % 30.57/7.85 | Equations (272) can reduce 300 to: % 30.57/7.85 | (197) $false % 30.57/7.85 | % 30.57/7.85 |-The branch is then unsatisfiable % 30.57/7.85 |-Branch two: % 30.57/7.85 | (300) ~ (all_69_0_112 = 0) % 30.57/7.85 | (304) ? [v0] : ( ~ (v0 = 0) & in(all_0_19_19, all_0_18_18) = v0) % 30.57/7.85 | % 30.57/7.85 +-Applying beta-rule and splitting (208), into two cases. % 30.57/7.85 |-Branch one: % 30.57/7.85 | (272) all_69_0_112 = 0 % 30.57/7.85 | % 30.57/7.85 | Equations (272) can reduce 300 to: % 30.57/7.85 | (197) $false % 30.57/7.85 | % 30.57/7.85 |-The branch is then unsatisfiable % 30.57/7.85 |-Branch two: % 30.57/7.85 | (300) ~ (all_69_0_112 = 0) % 30.57/7.85 | (308) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_18_18) = v1 & in(v0, all_0_19_19) = 0) % 30.57/7.85 | % 30.57/7.85 +-Applying beta-rule and splitting (207), into two cases. % 30.57/7.85 |-Branch one: % 30.57/7.85 | (272) all_69_0_112 = 0 % 30.57/7.85 | % 30.57/7.85 | Equations (272) can reduce 300 to: % 30.57/7.85 | (197) $false % 30.57/7.85 | % 30.57/7.85 |-The branch is then unsatisfiable % 30.57/7.85 |-Branch two: % 30.57/7.85 | (300) ~ (all_69_0_112 = 0) % 30.57/7.85 | (312) ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_0_18_18) = v0 & element(all_0_19_19, v0) = v1) % 30.57/7.85 | % 30.57/7.85 +-Applying beta-rule and splitting (211), into two cases. % 30.57/7.85 |-Branch one: % 30.57/7.85 | (272) all_69_0_112 = 0 % 30.57/7.85 | % 30.57/7.85 | Equations (272) can reduce 300 to: % 30.57/7.85 | (197) $false % 30.57/7.85 | % 30.57/7.85 |-The branch is then unsatisfiable % 30.57/7.85 |-Branch two: % 30.57/7.85 | (300) ~ (all_69_0_112 = 0) % 30.57/7.85 | (316) ? [v0] : ? [v1] : (subset(all_109_0_169, all_0_18_18) = v1 & subset(all_0_20_20, all_0_18_18) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 30.57/7.85 | % 30.57/7.85 | Instantiating (316) with all_304_0_512, all_304_1_513 yields: % 30.57/7.85 | (317) subset(all_109_0_169, all_0_18_18) = all_304_0_512 & subset(all_0_20_20, all_0_18_18) = all_304_1_513 & ( ~ (all_304_0_512 = 0) | ~ (all_304_1_513 = 0)) % 30.57/7.85 | % 30.57/7.85 | Applying alpha-rule on (317) yields: % 30.57/7.85 | (318) subset(all_109_0_169, all_0_18_18) = all_304_0_512 % 30.57/7.85 | (319) subset(all_0_20_20, all_0_18_18) = all_304_1_513 % 30.57/7.85 | (320) ~ (all_304_0_512 = 0) | ~ (all_304_1_513 = 0) % 30.57/7.85 | % 30.57/7.85 | Instantiating formula (71) with all_304_0_512, all_0_18_18, all_109_0_169 and discharging atoms subset(all_109_0_169, all_0_18_18) = all_304_0_512, yields: % 30.57/7.85 | (321) all_304_0_512 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_109_0_169) = 0 & in(v0, all_0_18_18) = v1) % 30.57/7.85 | % 30.57/7.85 | Instantiating formula (112) with all_304_1_513, all_0_20_20, all_0_18_18 and discharging atoms subset(all_0_20_20, all_0_18_18) = all_304_1_513, epsilon_transitive(all_0_18_18) = 0, yields: % 30.57/7.85 | (322) all_304_1_513 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_0_20_20, all_0_18_18) = v0) % 30.57/7.85 | % 30.57/7.85 | Instantiating formula (12) with all_304_1_513, all_0_18_18, all_0_20_20 and discharging atoms subset(all_0_20_20, all_0_18_18) = all_304_1_513, yields: % 30.57/7.85 | (323) all_304_1_513 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_0_18_18) = v0 & element(all_0_20_20, v0) = v1) % 30.57/7.85 | % 30.57/7.85 | Instantiating formula (71) with all_304_1_513, all_0_18_18, all_0_20_20 and discharging atoms subset(all_0_20_20, all_0_18_18) = all_304_1_513, yields: % 30.57/7.85 | (324) all_304_1_513 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_18_18) = v1 & in(v0, all_0_20_20) = 0) % 30.57/7.85 | % 30.57/7.85 | Instantiating formula (45) with all_0_20_20, all_0_18_18 and discharging atoms epsilon_transitive(all_0_18_18) = 0, in(all_0_20_20, all_0_18_18) = 0, yields: % 30.57/7.85 | (325) subset(all_0_20_20, all_0_18_18) = 0 % 30.57/7.85 | % 30.57/7.85 +-Applying beta-rule and splitting (322), into two cases. % 30.57/7.85 |-Branch one: % 30.57/7.85 | (326) all_304_1_513 = 0 % 30.57/7.85 | % 30.57/7.85 +-Applying beta-rule and splitting (320), into two cases. % 30.57/7.85 |-Branch one: % 30.57/7.85 | (327) ~ (all_304_0_512 = 0) % 30.57/7.85 | % 30.57/7.85 +-Applying beta-rule and splitting (321), into two cases. % 30.57/7.85 |-Branch one: % 30.57/7.85 | (328) all_304_0_512 = 0 % 30.57/7.85 | % 30.57/7.85 | Equations (328) can reduce 327 to: % 30.57/7.85 | (197) $false % 30.57/7.85 | % 30.57/7.85 |-The branch is then unsatisfiable % 30.57/7.85 |-Branch two: % 30.57/7.85 | (327) ~ (all_304_0_512 = 0) % 30.57/7.85 | (331) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_109_0_169) = 0 & in(v0, all_0_18_18) = v1) % 30.57/7.85 | % 30.57/7.85 | Instantiating (331) with all_728_0_723, all_728_1_724 yields: % 30.57/7.85 | (332) ~ (all_728_0_723 = 0) & in(all_728_1_724, all_109_0_169) = 0 & in(all_728_1_724, all_0_18_18) = all_728_0_723 % 30.57/7.85 | % 30.57/7.85 | Applying alpha-rule on (332) yields: % 30.57/7.85 | (333) ~ (all_728_0_723 = 0) % 30.57/7.85 | (334) in(all_728_1_724, all_109_0_169) = 0 % 30.57/7.85 | (335) in(all_728_1_724, all_0_18_18) = all_728_0_723 % 30.57/7.85 | % 30.57/7.85 | Instantiating formula (92) with all_728_1_724, all_109_0_169, all_0_20_20 and discharging atoms singleton(all_0_20_20) = all_109_0_169, in(all_728_1_724, all_109_0_169) = 0, yields: % 30.57/7.85 | (336) all_728_1_724 = all_0_20_20 % 30.57/7.85 | % 30.57/7.85 | From (336) and (335) follows: % 30.57/7.85 | (337) in(all_0_20_20, all_0_18_18) = all_728_0_723 % 30.57/7.85 | % 30.57/7.85 | Instantiating formula (77) with all_0_20_20, all_0_18_18, all_728_0_723, 0 and discharging atoms in(all_0_20_20, all_0_18_18) = all_728_0_723, in(all_0_20_20, all_0_18_18) = 0, yields: % 30.57/7.85 | (338) all_728_0_723 = 0 % 30.57/7.85 | % 30.57/7.85 | Equations (338) can reduce 333 to: % 30.57/7.85 | (197) $false % 30.57/7.85 | % 30.57/7.85 |-The branch is then unsatisfiable % 30.57/7.85 |-Branch two: % 30.57/7.85 | (328) all_304_0_512 = 0 % 30.57/7.85 | (341) ~ (all_304_1_513 = 0) % 30.57/7.85 | % 30.57/7.85 | Equations (326) can reduce 341 to: % 30.57/7.85 | (197) $false % 30.57/7.85 | % 30.57/7.85 |-The branch is then unsatisfiable % 30.57/7.85 |-Branch two: % 30.57/7.85 | (341) ~ (all_304_1_513 = 0) % 30.57/7.85 | (344) ? [v0] : ( ~ (v0 = 0) & in(all_0_20_20, all_0_18_18) = v0) % 30.57/7.85 | % 30.57/7.85 +-Applying beta-rule and splitting (324), into two cases. % 30.57/7.85 |-Branch one: % 30.57/7.85 | (326) all_304_1_513 = 0 % 30.57/7.85 | % 30.57/7.85 | Equations (326) can reduce 341 to: % 30.57/7.85 | (197) $false % 30.57/7.85 | % 30.57/7.85 |-The branch is then unsatisfiable % 30.57/7.85 |-Branch two: % 30.57/7.85 | (341) ~ (all_304_1_513 = 0) % 30.57/7.85 | (348) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_18_18) = v1 & in(v0, all_0_20_20) = 0) % 30.57/7.85 | % 30.57/7.85 +-Applying beta-rule and splitting (323), into two cases. % 30.57/7.85 |-Branch one: % 30.57/7.85 | (326) all_304_1_513 = 0 % 30.57/7.85 | % 30.57/7.85 | Equations (326) can reduce 341 to: % 30.57/7.85 | (197) $false % 30.57/7.85 | % 30.57/7.85 |-The branch is then unsatisfiable % 30.57/7.85 |-Branch two: % 30.57/7.85 | (341) ~ (all_304_1_513 = 0) % 30.57/7.86 | (352) ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_0_18_18) = v0 & element(all_0_20_20, v0) = v1) % 30.57/7.86 | % 30.57/7.86 | Instantiating formula (98) with all_0_20_20, all_0_18_18, 0, all_304_1_513 and discharging atoms subset(all_0_20_20, all_0_18_18) = all_304_1_513, subset(all_0_20_20, all_0_18_18) = 0, yields: % 30.57/7.86 | (326) all_304_1_513 = 0 % 30.57/7.86 | % 30.57/7.86 | Equations (326) can reduce 341 to: % 30.57/7.86 | (197) $false % 30.57/7.86 | % 30.57/7.86 |-The branch is then unsatisfiable % 30.57/7.86 |-Branch two: % 30.57/7.86 | (272) all_69_0_112 = 0 % 30.57/7.86 | (254) all_153_0_197 = 0 % 30.57/7.86 | % 30.57/7.86 | Combining equations (235,254) yields a new equation: % 30.57/7.86 | (357) all_0_16_16 = 0 % 30.57/7.86 | % 30.57/7.86 | Simplifying 357 yields: % 30.57/7.86 | (252) all_0_16_16 = 0 % 30.57/7.86 | % 30.57/7.86 | Equations (252) can reduce 284 to: % 30.57/7.86 | (197) $false % 30.57/7.86 | % 30.57/7.86 |-The branch is then unsatisfiable % 30.57/7.86 % SZS output end Proof for theBenchmark % 30.57/7.86 % 30.57/7.86 7262ms %------------------------------------------------------------------------------