%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU268+1 : TPTP v8.1.0. Released v3.3.0. % 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 08:48:19 EDT 2022 % Result : Theorem 6.78s 2.19s % Output : Proof 10.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU268+1 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n015.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sun Jun 19 04:46:44 EDT 2022 % 0.12/0.34 % CPUTime : % 0.19/0.57 ____ _ % 0.19/0.57 ___ / __ \_____(_)___ ________ __________ % 0.19/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.57 % 0.19/0.57 A Theorem Prover for First-Order Logic % 0.19/0.58 (ePrincess v.1.0) % 0.19/0.58 % 0.19/0.58 (c) Philipp Rümmer, 2009-2015 % 0.19/0.58 (c) Peter Backeman, 2014-2015 % 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.58 Bug reports to peter@backeman.se % 0.19/0.58 % 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.58 % 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.61/0.94 Prover 0: Preprocessing ... % 2.43/1.21 Prover 0: Warning: ignoring some quantifiers % 2.43/1.23 Prover 0: Constructing countermodel ... % 3.29/1.43 Prover 0: gave up % 3.29/1.43 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.41/1.48 Prover 1: Preprocessing ... % 4.10/1.61 Prover 1: Warning: ignoring some quantifiers % 4.10/1.62 Prover 1: Constructing countermodel ... % 4.83/1.79 Prover 1: gave up % 4.83/1.79 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.83/1.82 Prover 2: Preprocessing ... % 5.89/1.97 Prover 2: Warning: ignoring some quantifiers % 5.89/1.98 Prover 2: Constructing countermodel ... % 6.78/2.19 Prover 2: proved (399ms) % 6.78/2.19 % 6.78/2.19 No countermodel exists, formula is valid % 6.78/2.19 % SZS status Theorem for theBenchmark % 6.78/2.19 % 6.78/2.19 Generating proof ... Warning: ignoring some quantifiers % 9.44/2.82 found it (size 55) % 9.44/2.82 % 9.44/2.82 % SZS output start Proof for theBenchmark % 9.44/2.82 Assumed formulas after preprocessing and simplification: % 9.44/2.82 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ( ~ (v8 = 0) & ~ (v5 = 0) & ~ (v2 = 0) & relation_empty_yielding(v3) = 0 & relation_empty_yielding(empty_set) = 0 & reflexive(v1) = v2 & inclusion_relation(v0) = v1 & one_to_one(v9) = 0 & one_to_one(v6) = 0 & one_to_one(empty_set) = 0 & relation(v13) = 0 & relation(v10) = 0 & relation(v9) = 0 & relation(v6) = 0 & relation(v3) = 0 & relation(empty_set) = 0 & epsilon_transitive(v12) = 0 & epsilon_transitive(v9) = 0 & epsilon_transitive(v4) = 0 & epsilon_transitive(empty_set) = 0 & ordinal(v12) = 0 & ordinal(v9) = 0 & ordinal(v4) = 0 & ordinal(empty_set) = 0 & epsilon_connected(v12) = 0 & epsilon_connected(v9) = 0 & epsilon_connected(v4) = 0 & epsilon_connected(empty_set) = 0 & function(v13) = 0 & function(v10) = 0 & function(v9) = 0 & function(v6) = 0 & function(v3) = 0 & function(empty_set) = 0 & empty(v11) = 0 & empty(v10) = 0 & empty(v9) = 0 & empty(v7) = v8 & empty(v4) = v5 & empty(empty_set) = 0 & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (inclusion_relation(v14) = v15) | ~ (relation_field(v15) = v16) | ~ (subset(v17, v18) = v19) | ? [v20] : ? [v21] : (( ~ (v20 = 0) & relation(v15) = v20) | ( ~ (v20 = 0) & in(v18, v14) = v20) | ( ~ (v20 = 0) & in(v17, v14) = v20) | (( ~ (v19 = 0) | (v21 = 0 & ordered_pair(v17, v18) = v20 & in(v20, v15) = 0)) & (v19 = 0 | ( ~ (v21 = 0) & ordered_pair(v17, v18) = v20 & in(v20, v15) = v21))))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (inclusion_relation(v14) = v15) | ~ (relation_field(v15) = v16) | ~ (ordered_pair(v17, v18) = v19) | ? [v20] : ? [v21] : (( ~ (v20 = 0) & relation(v15) = v20) | ( ~ (v20 = 0) & in(v18, v14) = v20) | ( ~ (v20 = 0) & in(v17, v14) = v20) | (((v21 = 0 & subset(v17, v18) = 0) | ( ~ (v20 = 0) & in(v19, v15) = v20)) & ((v20 = 0 & in(v19, v15) = 0) | ( ~ (v21 = 0) & subset(v17, v18) = v21))))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (powerset(v16) = v17) | ~ (element(v15, v17) = 0) | ~ (element(v14, v16) = v18) | ? [v19] : ( ~ (v19 = 0) & in(v14, v15) = v19)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (powerset(v15) = v16) | ~ (element(v14, v16) = v17) | ? [v18] : ( ~ (v18 = 0) & subset(v14, v15) = v18)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (element(v14, v16) = v17) | ~ (in(v14, v15) = 0) | ? [v18] : ? [v19] : ( ~ (v19 = 0) & powerset(v16) = v18 & element(v15, v18) = v19)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (element(v17, v16) = v15) | ~ (element(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (subset(v17, v16) = v15) | ~ (subset(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (is_reflexive_in(v17, v16) = v15) | ~ (is_reflexive_in(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (ordered_pair(v17, v16) = v15) | ~ (ordered_pair(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (set_union2(v17, v16) = v15) | ~ (set_union2(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (unordered_pair(v17, v16) = v15) | ~ (unordered_pair(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (in(v17, v16) = v15) | ~ (in(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ (element(v15, v17) = 0) | ~ (in(v14, v15) = 0) | element(v14, v16) = 0) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ (element(v15, v17) = 0) | ~ (in(v14, v15) = 0) | ? [v18] : ( ~ (v18 = 0) & empty(v16) = v18)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (is_reflexive_in(v14, v15) = 0) | ~ (ordered_pair(v16, v16) = v17) | ~ (relation(v14) = 0) | ? [v18] : ((v18 = 0 & in(v17, v14) = 0) | ( ~ (v18 = 0) & in(v16, v15) = v18))) & ! [v14] : ! [v15] : ! [v16] : (v16 = v15 | ~ (inclusion_relation(v14) = v16) | ~ (relation_field(v15) = v14) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ((v20 = 0 & v19 = 0 & in(v18, v14) = 0 & in(v17, v14) = 0 & ((v23 = 0 & subset(v17, v18) = 0) | (v22 = 0 & ordered_pair(v17, v18) = v21 & in(v21, v15) = 0)) & (( ~ (v23 = 0) & subset(v17, v18) = v23) | ( ~ (v22 = 0) & ordered_pair(v17, v18) = v21 & in(v21, v15) = v22))) | ( ~ (v17 = 0) & relation(v15) = v17))) & ! [v14] : ! [v15] : ! [v16] : (v16 = v14 | ~ (inclusion_relation(v14) = v15) | ~ (relation_field(v15) = v16) | ? [v17] : ( ~ (v17 = 0) & relation(v15) = v17)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (element(v14, v15) = v16) | ? [v17] : ( ~ (v17 = 0) & in(v14, v15) = v17)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (subset(v14, v15) = v16) | ? [v17] : ? [v18] : ( ~ (v18 = 0) & powerset(v15) = v17 & element(v14, v17) = v18)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (is_reflexive_in(v14, v15) = v16) | ~ (relation(v14) = 0) | ? [v17] : ? [v18] : ? [v19] : ( ~ (v19 = 0) & ordered_pair(v17, v17) = v18 & in(v18, v14) = v19 & in(v17, v15) = 0)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (in(v14, v15) = v16) | ? [v17] : ((v17 = 0 & empty(v15) = 0) | ( ~ (v17 = 0) & element(v14, v15) = v17))) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (powerset(v16) = v15) | ~ (powerset(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_empty_yielding(v16) = v15) | ~ (relation_empty_yielding(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (reflexive(v16) = v15) | ~ (reflexive(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_dom(v16) = v15) | ~ (relation_dom(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_rng(v16) = v15) | ~ (relation_rng(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (singleton(v16) = v15) | ~ (singleton(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (inclusion_relation(v16) = v15) | ~ (inclusion_relation(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_field(v16) = v15) | ~ (relation_field(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (one_to_one(v16) = v15) | ~ (one_to_one(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation(v16) = v15) | ~ (relation(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (epsilon_transitive(v16) = v15) | ~ (epsilon_transitive(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (ordinal(v16) = v15) | ~ (ordinal(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (epsilon_connected(v16) = v15) | ~ (epsilon_connected(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (function(v16) = v15) | ~ (function(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (empty(v16) = v15) | ~ (empty(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ (element(v14, v16) = 0) | subset(v14, v15) = 0) & ! [v14] : ! [v15] : ! [v16] : ( ~ (inclusion_relation(v14) = v16) | ~ (relation(v15) = 0) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (( ~ (v16 = v15) | (v17 = v14 & relation_field(v15) = v14 & ! [v25] : ! [v26] : ! [v27] : ( ~ (subset(v25, v26) = v27) | ? [v28] : ? [v29] : (( ~ (v28 = 0) & in(v26, v14) = v28) | ( ~ (v28 = 0) & in(v25, v14) = v28) | (( ~ (v27 = 0) | (v29 = 0 & ordered_pair(v25, v26) = v28 & in(v28, v15) = 0)) & (v27 = 0 | ( ~ (v29 = 0) & ordered_pair(v25, v26) = v28 & in(v28, v15) = v29))))) & ! [v25] : ! [v26] : ! [v27] : ( ~ (ordered_pair(v25, v26) = v27) | ? [v28] : ? [v29] : (( ~ (v28 = 0) & in(v26, v14) = v28) | ( ~ (v28 = 0) & in(v25, v14) = v28) | (((v29 = 0 & subset(v25, v26) = 0) | ( ~ (v28 = 0) & in(v27, v15) = v28)) & ((v28 = 0 & in(v27, v15) = 0) | ( ~ (v29 = 0) & subset(v25, v26) = v29))))))) & (v16 = v15 | (v21 = 0 & v20 = 0 & in(v19, v14) = 0 & in(v18, v14) = 0 & ((v24 = 0 & subset(v18, v19) = 0) | (v23 = 0 & ordered_pair(v18, v19) = v22 & in(v22, v15) = 0)) & (( ~ (v24 = 0) & subset(v18, v19) = v24) | ( ~ (v23 = 0) & ordered_pair(v18, v19) = v22 & in(v22, v15) = v23))) | ( ~ (v17 = v14) & relation_field(v15) = v17)))) & ! [v14] : ! [v15] : ! [v16] : ( ~ (is_reflexive_in(v14, v15) = 0) | ~ (relation(v14) = 0) | ~ (in(v16, v15) = 0) | ? [v17] : (ordered_pair(v16, v16) = v17 & in(v17, v14) = 0)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (ordered_pair(v14, v15) = v16) | ? [v17] : ? [v18] : (singleton(v14) = v18 & unordered_pair(v17, v18) = v16 & unordered_pair(v14, v15) = v17)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (ordered_pair(v14, v15) = v16) | ? [v17] : ( ~ (v17 = 0) & empty(v16) = v17)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (set_union2(v15, v14) = v16) | set_union2(v14, v15) = v16) & ! [v14] : ! [v15] : ! [v16] : ( ~ (set_union2(v15, v14) = v16) | ? [v17] : ((v17 = 0 & empty(v14) = 0) | ( ~ (v17 = 0) & empty(v16) = v17))) & ! [v14] : ! [v15] : ! [v16] : ( ~ (set_union2(v14, v15) = v16) | set_union2(v15, v14) = v16) & ! [v14] : ! [v15] : ! [v16] : ( ~ (set_union2(v14, v15) = v16) | ? [v17] : ((v17 = 0 & empty(v14) = 0) | ( ~ (v17 = 0) & empty(v16) = v17))) & ! [v14] : ! [v15] : ! [v16] : ( ~ (unordered_pair(v15, v14) = v16) | unordered_pair(v14, v15) = v16) & ! [v14] : ! [v15] : ! [v16] : ( ~ (unordered_pair(v14, v15) = v16) | unordered_pair(v15, v14) = v16) & ! [v14] : ! [v15] : ! [v16] : ( ~ (unordered_pair(v14, v15) = v16) | ? [v17] : ? [v18] : (singleton(v14) = v18 & ordered_pair(v14, v15) = v17 & unordered_pair(v16, v18) = v17)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (empty(v16) = 0) | ~ (in(v14, v15) = 0) | ? [v17] : ? [v18] : ( ~ (v18 = 0) & powerset(v16) = v17 & element(v15, v17) = v18)) & ! [v14] : ! [v15] : (v15 = v14 | ~ (set_union2(v14, v14) = v15)) & ! [v14] : ! [v15] : (v15 = v14 | ~ (set_union2(v14, empty_set) = v15)) & ! [v14] : ! [v15] : (v15 = v14 | ~ (empty(v15) = 0) | ~ (empty(v14) = 0)) & ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v14, v14) = v15)) & ! [v14] : ! [v15] : (v15 = 0 | ~ (ordinal(v14) = v15) | ? [v16] : (( ~ (v16 = 0) & epsilon_transitive(v14) = v16) | ( ~ (v16 = 0) & epsilon_connected(v14) = v16))) & ! [v14] : ! [v15] : (v15 = 0 | ~ (function(v14) = v15) | ? [v16] : ( ~ (v16 = 0) & empty(v14) = v16)) & ! [v14] : ! [v15] : ( ~ (element(v14, v15) = 0) | ? [v16] : ((v16 = 0 & empty(v15) = 0) | (v16 = 0 & in(v14, v15) = 0))) & ! [v14] : ! [v15] : ( ~ (reflexive(v14) = v15) | ? [v16] : ? [v17] : (( ~ (v16 = 0) & relation(v14) = v16) | (( ~ (v15 = 0) | (v17 = 0 & relation_field(v14) = v16 & is_reflexive_in(v14, v16) = 0)) & (v15 = 0 | ( ~ (v17 = 0) & relation_field(v14) = v16 & is_reflexive_in(v14, v16) = v17))))) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v18 = v16 & relation_rng(v14) = v17 & relation_field(v14) = v16 & set_union2(v15, v17) = v16) | ( ~ (v16 = 0) & relation(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v18 = v16 & relation_dom(v14) = v17 & relation_field(v14) = v16 & set_union2(v17, v15) = v16) | ( ~ (v16 = 0) & relation(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (inclusion_relation(v14) = v15) | relation(v15) = 0) & ! [v14] : ! [v15] : ( ~ (relation_field(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v18 = v15 & relation_dom(v14) = v16 & relation_rng(v14) = v17 & set_union2(v16, v17) = v15) | ( ~ (v16 = 0) & relation(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (relation_field(v14) = v15) | ? [v16] : ? [v17] : (( ~ (v16 = 0) & relation(v14) = v16) | (((v17 = 0 & is_reflexive_in(v14, v15) = 0) | ( ~ (v16 = 0) & reflexive(v14) = v16)) & ((v16 = 0 & reflexive(v14) = 0) | ( ~ (v17 = 0) & is_reflexive_in(v14, v15) = v17))))) & ! [v14] : ! [v15] : ( ~ (subset(v14, v15) = 0) | ? [v16] : (powerset(v15) = v16 & element(v14, v16) = 0)) & ! [v14] : ! [v15] : ( ~ (one_to_one(v14) = v15) | ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & relation(v14) = 0 & function(v14) = 0) | ( ~ (v16 = 0) & relation(v14) = v16) | ( ~ (v16 = 0) & function(v14) = v16) | ( ~ (v16 = 0) & empty(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (epsilon_transitive(v14) = v15) | ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & ordinal(v14) = 0 & epsilon_connected(v14) = 0) | ( ~ (v16 = 0) & empty(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (epsilon_transitive(v14) = v15) | ? [v16] : ((v16 = 0 & v15 = 0 & epsilon_connected(v14) = 0) | ( ~ (v16 = 0) & ordinal(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (ordinal(v14) = v15) | ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & epsilon_transitive(v14) = 0 & epsilon_connected(v14) = 0) | ( ~ (v16 = 0) & empty(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (epsilon_connected(v14) = v15) | ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & epsilon_transitive(v14) = 0 & ordinal(v14) = 0) | ( ~ (v16 = 0) & empty(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (epsilon_connected(v14) = v15) | ? [v16] : ((v16 = 0 & v15 = 0 & epsilon_transitive(v14) = 0) | ( ~ (v16 = 0) & ordinal(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (in(v15, v14) = 0) | ? [v16] : ( ~ (v16 = 0) & in(v14, v15) = v16)) & ! [v14] : ! [v15] : ( ~ (in(v14, v15) = 0) | element(v14, v15) = 0) & ! [v14] : ! [v15] : ( ~ (in(v14, v15) = 0) | ? [v16] : ( ~ (v16 = 0) & empty(v15) = v16)) & ! [v14] : ! [v15] : ( ~ (in(v14, v15) = 0) | ? [v16] : ( ~ (v16 = 0) & in(v15, v14) = v16)) & ! [v14] : (v14 = empty_set | ~ (empty(v14) = 0)) & ! [v14] : ( ~ (relation(v14) = 0) | ? [v15] : ? [v16] : ? [v17] : (relation_dom(v14) = v16 & relation_rng(v14) = v17 & relation_field(v14) = v15 & set_union2(v16, v17) = v15)) & ! [v14] : ( ~ (relation(v14) = 0) | ? [v15] : ? [v16] : ? [v17] : (((v17 = 0 & relation_field(v14) = v16 & is_reflexive_in(v14, v16) = 0) | ( ~ (v15 = 0) & reflexive(v14) = v15)) & ((v15 = 0 & reflexive(v14) = 0) | ( ~ (v17 = 0) & relation_field(v14) = v16 & is_reflexive_in(v14, v16) = v17)))) & ! [v14] : ( ~ (relation(v14) = 0) | ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & one_to_one(v14) = 0 & function(v14) = 0) | ( ~ (v15 = 0) & function(v14) = v15) | ( ~ (v15 = 0) & empty(v14) = v15))) & ! [v14] : ( ~ (epsilon_transitive(v14) = 0) | ? [v15] : ((v15 = 0 & ordinal(v14) = 0) | ( ~ (v15 = 0) & epsilon_connected(v14) = v15))) & ! [v14] : ( ~ (ordinal(v14) = 0) | (epsilon_transitive(v14) = 0 & epsilon_connected(v14) = 0)) & ! [v14] : ( ~ (epsilon_connected(v14) = 0) | ? [v15] : ((v15 = 0 & ordinal(v14) = 0) | ( ~ (v15 = 0) & epsilon_transitive(v14) = v15))) & ! [v14] : ( ~ (function(v14) = 0) | ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & one_to_one(v14) = 0 & relation(v14) = 0) | ( ~ (v15 = 0) & relation(v14) = v15) | ( ~ (v15 = 0) & empty(v14) = v15))) & ! [v14] : ( ~ (empty(v14) = 0) | function(v14) = 0) & ! [v14] : ( ~ (empty(v14) = 0) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & one_to_one(v14) = 0 & relation(v14) = 0 & function(v14) = 0) | ( ~ (v15 = 0) & relation(v14) = v15) | ( ~ (v15 = 0) & function(v14) = v15))) & ! [v14] : ( ~ (empty(v14) = 0) | (epsilon_transitive(v14) = 0 & ordinal(v14) = 0 & epsilon_connected(v14) = 0)) & ? [v14] : ? [v15] : ? [v16] : element(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : subset(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : is_reflexive_in(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : ordered_pair(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : set_union2(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : unordered_pair(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : in(v15, v14) = v16 & ? [v14] : ? [v15] : powerset(v14) = v15 & ? [v14] : ? [v15] : relation_empty_yielding(v14) = v15 & ? [v14] : ? [v15] : element(v15, v14) = 0 & ? [v14] : ? [v15] : reflexive(v14) = v15 & ? [v14] : ? [v15] : relation_dom(v14) = v15 & ? [v14] : ? [v15] : relation_rng(v14) = v15 & ? [v14] : ? [v15] : singleton(v14) = v15 & ? [v14] : ? [v15] : inclusion_relation(v14) = v15 & ? [v14] : ? [v15] : relation_field(v14) = v15 & ? [v14] : ? [v15] : one_to_one(v14) = v15 & ? [v14] : ? [v15] : relation(v14) = v15 & ? [v14] : ? [v15] : epsilon_transitive(v14) = v15 & ? [v14] : ? [v15] : ordinal(v14) = v15 & ? [v14] : ? [v15] : epsilon_connected(v14) = v15 & ? [v14] : ? [v15] : function(v14) = v15 & ? [v14] : ? [v15] : empty(v14) = v15) % 9.89/2.87 | 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 yields: % 9.89/2.87 | (1) ~ (all_0_5_5 = 0) & ~ (all_0_8_8 = 0) & ~ (all_0_11_11 = 0) & relation_empty_yielding(all_0_10_10) = 0 & relation_empty_yielding(empty_set) = 0 & reflexive(all_0_12_12) = all_0_11_11 & inclusion_relation(all_0_13_13) = all_0_12_12 & one_to_one(all_0_4_4) = 0 & one_to_one(all_0_7_7) = 0 & one_to_one(empty_set) = 0 & relation(all_0_0_0) = 0 & relation(all_0_3_3) = 0 & relation(all_0_4_4) = 0 & relation(all_0_7_7) = 0 & relation(all_0_10_10) = 0 & relation(empty_set) = 0 & epsilon_transitive(all_0_1_1) = 0 & epsilon_transitive(all_0_4_4) = 0 & epsilon_transitive(all_0_9_9) = 0 & epsilon_transitive(empty_set) = 0 & ordinal(all_0_1_1) = 0 & ordinal(all_0_4_4) = 0 & ordinal(all_0_9_9) = 0 & ordinal(empty_set) = 0 & epsilon_connected(all_0_1_1) = 0 & epsilon_connected(all_0_4_4) = 0 & epsilon_connected(all_0_9_9) = 0 & epsilon_connected(empty_set) = 0 & function(all_0_0_0) = 0 & function(all_0_3_3) = 0 & function(all_0_4_4) = 0 & function(all_0_7_7) = 0 & function(all_0_10_10) = 0 & function(empty_set) = 0 & empty(all_0_2_2) = 0 & empty(all_0_3_3) = 0 & empty(all_0_4_4) = 0 & empty(all_0_6_6) = all_0_5_5 & empty(all_0_9_9) = all_0_8_8 & empty(empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & in(v4, v0) = v6) | ( ~ (v6 = 0) & in(v3, v0) = v6) | (( ~ (v5 = 0) | (v7 = 0 & ordered_pair(v3, v4) = v6 & in(v6, v1) = 0)) & (v5 = 0 | ( ~ (v7 = 0) & ordered_pair(v3, v4) = v6 & in(v6, v1) = v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & in(v4, v0) = v6) | ( ~ (v6 = 0) & in(v3, v0) = v6) | (((v7 = 0 & subset(v3, v4) = 0) | ( ~ (v6 = 0) & in(v5, v1) = v6)) & ((v6 = 0 & in(v5, v1) = 0) | ( ~ (v7 = 0) & subset(v3, v4) = v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & powerset(v2) = v4 & element(v1, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (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 | ~ (is_reflexive_in(v3, v2) = v1) | ~ (is_reflexive_in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(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 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(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] : ! [v3] : ( ~ (is_reflexive_in(v0, v1) = 0) | ~ (ordered_pair(v2, v2) = v3) | ~ (relation(v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v0) = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (inclusion_relation(v0) = v2) | ~ (relation_field(v1) = v0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v6 = 0 & v5 = 0 & in(v4, v0) = 0 & in(v3, v0) = 0 & ((v9 = 0 & subset(v3, v4) = 0) | (v8 = 0 & ordered_pair(v3, v4) = v7 & in(v7, v1) = 0)) & (( ~ (v9 = 0) & subset(v3, v4) = v9) | ( ~ (v8 = 0) & ordered_pair(v3, v4) = v7 & in(v7, v1) = v8))) | ( ~ (v3 = 0) & relation(v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & relation(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = 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 | ~ (is_reflexive_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & ordered_pair(v3, v3) = v4 & in(v4, v0) = v5 & in(v3, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3))) & ! [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 | ~ (reflexive(v2) = v1) | ~ (reflexive(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inclusion_relation(v2) = v1) | ~ (inclusion_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(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 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (inclusion_relation(v0) = v2) | ~ (relation(v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (( ~ (v2 = v1) | (v3 = v0 & relation_field(v1) = v0 & ! [v11] : ! [v12] : ! [v13] : ( ~ (subset(v11, v12) = v13) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & in(v12, v0) = v14) | ( ~ (v14 = 0) & in(v11, v0) = v14) | (( ~ (v13 = 0) | (v15 = 0 & ordered_pair(v11, v12) = v14 & in(v14, v1) = 0)) & (v13 = 0 | ( ~ (v15 = 0) & ordered_pair(v11, v12) = v14 & in(v14, v1) = v15))))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (ordered_pair(v11, v12) = v13) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & in(v12, v0) = v14) | ( ~ (v14 = 0) & in(v11, v0) = v14) | (((v15 = 0 & subset(v11, v12) = 0) | ( ~ (v14 = 0) & in(v13, v1) = v14)) & ((v14 = 0 & in(v13, v1) = 0) | ( ~ (v15 = 0) & subset(v11, v12) = v15))))))) & (v2 = v1 | (v7 = 0 & v6 = 0 & in(v5, v0) = 0 & in(v4, v0) = 0 & ((v10 = 0 & subset(v4, v5) = 0) | (v9 = 0 & ordered_pair(v4, v5) = v8 & in(v8, v1) = 0)) & (( ~ (v10 = 0) & subset(v4, v5) = v10) | ( ~ (v9 = 0) & ordered_pair(v4, v5) = v8 & in(v8, v1) = v9))) | ( ~ (v3 = v0) & relation_field(v1) = v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (is_reflexive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v2, v1) = 0) | ? [v3] : (ordered_pair(v2, v2) = v3 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4)) & ! [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 | ~ (ordinal(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & epsilon_transitive(v0) = v2) | ( ~ (v2 = 0) & epsilon_connected(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) & ! [v0] : ! [v1] : ( ~ (reflexive(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & relation_field(v0) = v2 & is_reflexive_in(v0, v2) = 0)) & (v1 = 0 | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_reflexive_in(v0, v2) = v3))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & relation_rng(v0) = v3 & relation_field(v0) = v2 & set_union2(v1, v3) = v2) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & relation_dom(v0) = v3 & relation_field(v0) = v2 & set_union2(v3, v1) = v2) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | relation(v1) = 0) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & relation_dom(v0) = v2 & relation_rng(v0) = v3 & set_union2(v2, v3) = v1) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (((v3 = 0 & is_reflexive_in(v0, v1) = 0) | ( ~ (v2 = 0) & reflexive(v0) = v2)) & ((v2 = 0 & reflexive(v0) = 0) | ( ~ (v3 = 0) & is_reflexive_in(v0, v1) = v3))))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (ordinal(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_dom(v0) = v2 & relation_rng(v0) = v3 & relation_field(v0) = v1 & set_union2(v2, v3) = v1)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & relation_field(v0) = v2 & is_reflexive_in(v0, v2) = 0) | ( ~ (v1 = 0) & reflexive(v0) = v1)) & ((v1 = 0 & reflexive(v0) = 0) | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_reflexive_in(v0, v2) = v3)))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & function(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1))) & ! [v0] : ( ~ (epsilon_transitive(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_connected(v0) = v1))) & ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)) & ! [v0] : ( ~ (epsilon_connected(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0) = v1))) & ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1))) & ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) & ! [v0] : ( ~ (empty(v0) = 0) | (epsilon_transitive(v0) = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0)) & ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : is_reflexive_in(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : powerset(v0) = v1 & ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : reflexive(v0) = v1 & ? [v0] : ? [v1] : relation_dom(v0) = v1 & ? [v0] : ? [v1] : relation_rng(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : inclusion_relation(v0) = v1 & ? [v0] : ? [v1] : relation_field(v0) = v1 & ? [v0] : ? [v1] : one_to_one(v0) = v1 & ? [v0] : ? [v1] : relation(v0) = v1 & ? [v0] : ? [v1] : epsilon_transitive(v0) = v1 & ? [v0] : ? [v1] : ordinal(v0) = v1 & ? [v0] : ? [v1] : epsilon_connected(v0) = v1 & ? [v0] : ? [v1] : function(v0) = v1 & ? [v0] : ? [v1] : empty(v0) = v1 % 10.03/2.90 | % 10.03/2.90 | Applying alpha-rule on (1) yields: % 10.03/2.90 | (2) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 10.03/2.90 | (3) relation(all_0_7_7) = 0 % 10.03/2.90 | (4) epsilon_connected(all_0_4_4) = 0 % 10.03/2.90 | (5) ? [v0] : ? [v1] : powerset(v0) = v1 % 10.03/2.90 | (6) ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1 % 10.03/2.90 | (7) ordinal(empty_set) = 0 % 10.03/2.90 | (8) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 % 10.03/2.90 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & in(v4, v0) = v6) | ( ~ (v6 = 0) & in(v3, v0) = v6) | (((v7 = 0 & subset(v3, v4) = 0) | ( ~ (v6 = 0) & in(v5, v1) = v6)) & ((v6 = 0 & in(v5, v1) = 0) | ( ~ (v7 = 0) & subset(v3, v4) = v7))))) % 10.03/2.90 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 10.03/2.90 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) % 10.03/2.90 | (12) ? [v0] : ? [v1] : relation_dom(v0) = v1 % 10.03/2.90 | (13) ? [v0] : ? [v1] : reflexive(v0) = v1 % 10.03/2.90 | (14) one_to_one(all_0_4_4) = 0 % 10.03/2.90 | (15) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) % 10.03/2.90 | (16) ordinal(all_0_1_1) = 0 % 10.03/2.90 | (17) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & relation_dom(v0) = v3 & relation_field(v0) = v2 & set_union2(v3, v1) = v2) | ( ~ (v2 = 0) & relation(v0) = v2))) % 10.03/2.90 | (18) inclusion_relation(all_0_13_13) = all_0_12_12 % 10.03/2.90 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & in(v4, v0) = v6) | ( ~ (v6 = 0) & in(v3, v0) = v6) | (( ~ (v5 = 0) | (v7 = 0 & ordered_pair(v3, v4) = v6 & in(v6, v1) = 0)) & (v5 = 0 | ( ~ (v7 = 0) & ordered_pair(v3, v4) = v6 & in(v6, v1) = v7))))) % 10.03/2.90 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 10.03/2.90 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (is_reflexive_in(v0, v1) = 0) | ~ (ordered_pair(v2, v2) = v3) | ~ (relation(v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v0) = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4))) % 10.03/2.90 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 10.03/2.90 | (23) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2))) % 10.03/2.90 | (24) ? [v0] : ? [v1] : one_to_one(v0) = v1 % 10.03/2.90 | (25) ~ (all_0_5_5 = 0) % 10.03/2.90 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (inclusion_relation(v0) = v2) | ~ (relation_field(v1) = v0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v6 = 0 & v5 = 0 & in(v4, v0) = 0 & in(v3, v0) = 0 & ((v9 = 0 & subset(v3, v4) = 0) | (v8 = 0 & ordered_pair(v3, v4) = v7 & in(v7, v1) = 0)) & (( ~ (v9 = 0) & subset(v3, v4) = v9) | ( ~ (v8 = 0) & ordered_pair(v3, v4) = v7 & in(v7, v1) = v8))) | ( ~ (v3 = 0) & relation(v1) = v3))) % 10.03/2.90 | (27) ? [v0] : ? [v1] : singleton(v0) = v1 % 10.03/2.90 | (28) ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)) % 10.03/2.90 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 10.03/2.90 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) % 10.03/2.91 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3)) % 10.03/2.91 | (32) function(all_0_10_10) = 0 % 10.03/2.91 | (33) empty(all_0_3_3) = 0 % 10.03/2.91 | (34) reflexive(all_0_12_12) = all_0_11_11 % 10.03/2.91 | (35) ? [v0] : ? [v1] : relation_rng(v0) = v1 % 10.03/2.91 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 10.03/2.91 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) % 10.03/2.91 | (38) ordinal(all_0_9_9) = 0 % 10.03/2.91 | (39) ? [v0] : ? [v1] : function(v0) = v1 % 10.03/2.91 | (40) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | relation(v1) = 0) % 10.03/2.91 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inclusion_relation(v2) = v1) | ~ (inclusion_relation(v2) = v0)) % 10.03/2.91 | (42) ? [v0] : ? [v1] : empty(v0) = v1 % 10.03/2.91 | (43) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1))) % 10.03/2.91 | (44) ! [v0] : ! [v1] : ( ~ (ordinal(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) % 10.03/2.91 | (45) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 10.03/2.91 | (46) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) % 10.03/2.91 | (47) function(all_0_3_3) = 0 % 10.03/2.91 | (48) ! [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)) % 10.03/2.91 | (49) ~ (all_0_8_8 = 0) % 10.03/2.91 | (50) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) % 10.03/2.91 | (51) ? [v0] : ? [v1] : relation(v0) = v1 % 10.03/2.91 | (52) function(all_0_7_7) = 0 % 10.03/2.91 | (53) ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) % 10.03/2.91 | (54) ! [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)) % 10.03/2.91 | (55) relation_empty_yielding(empty_set) = 0 % 10.03/2.91 | (56) function(empty_set) = 0 % 10.03/2.91 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 10.03/2.91 | (58) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 10.03/2.91 | (59) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reflexive(v2) = v1) | ~ (reflexive(v2) = v0)) % 10.03/2.91 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 10.03/2.91 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (is_reflexive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v2, v1) = 0) | ? [v3] : (ordered_pair(v2, v2) = v3 & in(v3, v0) = 0)) % 10.03/2.91 | (62) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & relation(v1) = v3)) % 10.03/2.91 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (inclusion_relation(v0) = v2) | ~ (relation(v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (( ~ (v2 = v1) | (v3 = v0 & relation_field(v1) = v0 & ! [v11] : ! [v12] : ! [v13] : ( ~ (subset(v11, v12) = v13) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & in(v12, v0) = v14) | ( ~ (v14 = 0) & in(v11, v0) = v14) | (( ~ (v13 = 0) | (v15 = 0 & ordered_pair(v11, v12) = v14 & in(v14, v1) = 0)) & (v13 = 0 | ( ~ (v15 = 0) & ordered_pair(v11, v12) = v14 & in(v14, v1) = v15))))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (ordered_pair(v11, v12) = v13) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & in(v12, v0) = v14) | ( ~ (v14 = 0) & in(v11, v0) = v14) | (((v15 = 0 & subset(v11, v12) = 0) | ( ~ (v14 = 0) & in(v13, v1) = v14)) & ((v14 = 0 & in(v13, v1) = 0) | ( ~ (v15 = 0) & subset(v11, v12) = v15))))))) & (v2 = v1 | (v7 = 0 & v6 = 0 & in(v5, v0) = 0 & in(v4, v0) = 0 & ((v10 = 0 & subset(v4, v5) = 0) | (v9 = 0 & ordered_pair(v4, v5) = v8 & in(v8, v1) = 0)) & (( ~ (v10 = 0) & subset(v4, v5) = v10) | ( ~ (v9 = 0) & ordered_pair(v4, v5) = v8 & in(v8, v1) = v9))) | ( ~ (v3 = v0) & relation_field(v1) = v3)))) % 10.03/2.91 | (64) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (is_reflexive_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & ordered_pair(v3, v3) = v4 & in(v4, v0) = v5 & in(v3, v1) = 0)) % 10.03/2.91 | (65) epsilon_transitive(all_0_1_1) = 0 % 10.03/2.91 | (66) empty(all_0_9_9) = all_0_8_8 % 10.03/2.91 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) % 10.03/2.91 | (68) ? [v0] : ? [v1] : relation_field(v0) = v1 % 10.03/2.91 | (69) ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2 % 10.03/2.91 | (70) function(all_0_4_4) = 0 % 10.03/2.91 | (71) epsilon_transitive(empty_set) = 0 % 10.03/2.91 | (72) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) % 10.03/2.91 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) % 10.03/2.91 | (74) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & relation_rng(v0) = v3 & relation_field(v0) = v2 & set_union2(v1, v3) = v2) | ( ~ (v2 = 0) & relation(v0) = v2))) % 10.03/2.91 | (75) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & relation_dom(v0) = v2 & relation_rng(v0) = v3 & set_union2(v2, v3) = v1) | ( ~ (v2 = 0) & relation(v0) = v2))) % 10.03/2.91 | (76) ! [v0] : ! [v1] : ( ~ (reflexive(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & relation_field(v0) = v2 & is_reflexive_in(v0, v2) = 0)) & (v1 = 0 | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_reflexive_in(v0, v2) = v3))))) % 10.03/2.91 | (77) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & function(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1))) % 10.03/2.91 | (78) one_to_one(all_0_7_7) = 0 % 10.03/2.91 | (79) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & relation_field(v0) = v2 & is_reflexive_in(v0, v2) = 0) | ( ~ (v1 = 0) & reflexive(v0) = v1)) & ((v1 = 0 & reflexive(v0) = 0) | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_reflexive_in(v0, v2) = v3)))) % 10.03/2.92 | (80) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 % 10.03/2.92 | (81) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 % 10.03/2.92 | (82) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 10.03/2.92 | (83) relation(all_0_0_0) = 0 % 10.03/2.92 | (84) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 10.03/2.92 | (85) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) % 10.03/2.92 | (86) ~ (all_0_11_11 = 0) % 10.03/2.92 | (87) ? [v0] : ? [v1] : epsilon_transitive(v0) = v1 % 10.03/2.92 | (88) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 10.03/2.92 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 10.03/2.92 | (90) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) % 10.03/2.92 | (91) relation_empty_yielding(all_0_10_10) = 0 % 10.03/2.92 | (92) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 10.03/2.92 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (is_reflexive_in(v3, v2) = v1) | ~ (is_reflexive_in(v3, v2) = v0)) % 10.03/2.92 | (94) empty(all_0_4_4) = 0 % 10.03/2.92 | (95) ? [v0] : ? [v1] : inclusion_relation(v0) = v1 % 10.03/2.92 | (96) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 10.03/2.92 | (97) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 % 10.03/2.92 | (98) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_dom(v0) = v2 & relation_rng(v0) = v3 & relation_field(v0) = v1 & set_union2(v2, v3) = v1)) % 10.03/2.92 | (99) empty(empty_set) = 0 % 10.03/2.92 | (100) ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2) | ( ~ (v2 = 0) & empty(v0) = v2))) % 10.03/2.92 | (101) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 10.03/2.92 | (102) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) % 10.03/2.92 | (103) ! [v0] : ( ~ (epsilon_connected(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0) = v1))) % 10.03/2.92 | (104) ! [v0] : ( ~ (epsilon_transitive(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_connected(v0) = v1))) % 10.03/2.92 | (105) epsilon_connected(all_0_1_1) = 0 % 10.03/2.92 | (106) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) % 10.03/2.92 | (107) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 10.03/2.92 | (108) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) % 10.03/2.92 | (109) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) % 10.03/2.92 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 10.03/2.92 | (111) relation(empty_set) = 0 % 10.03/2.92 | (112) ? [v0] : ? [v1] : element(v1, v0) = 0 % 10.03/2.92 | (113) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) % 10.03/2.92 | (114) ? [v0] : ? [v1] : ? [v2] : is_reflexive_in(v1, v0) = v2 % 10.03/2.92 | (115) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 10.03/2.92 | (116) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 10.03/2.92 | (117) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 10.03/2.92 | (118) ! [v0] : ( ~ (empty(v0) = 0) | (epsilon_transitive(v0) = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0)) % 10.03/2.92 | (119) epsilon_connected(all_0_9_9) = 0 % 10.03/2.92 | (120) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 10.03/2.92 | (121) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) % 10.03/2.92 | (122) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) % 10.03/2.92 | (123) empty(all_0_6_6) = all_0_5_5 % 10.03/2.92 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 10.03/2.92 | (125) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 10.03/2.92 | (126) ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2 % 10.03/2.92 | (127) relation(all_0_4_4) = 0 % 10.03/2.92 | (128) ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2))) % 10.03/2.92 | (129) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 10.03/2.92 | (130) function(all_0_0_0) = 0 % 10.03/2.92 | (131) relation(all_0_3_3) = 0 % 10.03/2.92 | (132) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 10.03/2.92 | (133) epsilon_transitive(all_0_4_4) = 0 % 10.03/2.92 | (134) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (((v3 = 0 & is_reflexive_in(v0, v1) = 0) | ( ~ (v2 = 0) & reflexive(v0) = v2)) & ((v2 = 0 & reflexive(v0) = 0) | ( ~ (v3 = 0) & is_reflexive_in(v0, v1) = v3))))) % 10.03/2.92 | (135) one_to_one(empty_set) = 0 % 10.03/2.92 | (136) empty(all_0_2_2) = 0 % 10.03/2.92 | (137) ! [v0] : ! [v1] : (v1 = 0 | ~ (ordinal(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & epsilon_transitive(v0) = v2) | ( ~ (v2 = 0) & epsilon_connected(v0) = v2))) % 10.03/2.92 | (138) epsilon_connected(empty_set) = 0 % 10.03/2.92 | (139) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3))) % 10.03/2.92 | (140) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) % 10.16/2.92 | (141) ? [v0] : ? [v1] : epsilon_connected(v0) = v1 % 10.16/2.92 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 10.16/2.92 | (143) relation(all_0_10_10) = 0 % 10.16/2.92 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 10.16/2.92 | (145) epsilon_transitive(all_0_9_9) = 0 % 10.16/2.93 | (146) ordinal(all_0_4_4) = 0 % 10.16/2.93 | (147) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4)) % 10.16/2.93 | (148) ? [v0] : ? [v1] : ordinal(v0) = v1 % 10.16/2.93 | % 10.16/2.93 | Instantiating formula (76) with all_0_11_11, all_0_12_12 and discharging atoms reflexive(all_0_12_12) = all_0_11_11, yields: % 10.16/2.93 | (149) ? [v0] : ? [v1] : (( ~ (v0 = 0) & relation(all_0_12_12) = v0) | (( ~ (all_0_11_11 = 0) | (v1 = 0 & relation_field(all_0_12_12) = v0 & is_reflexive_in(all_0_12_12, v0) = 0)) & (all_0_11_11 = 0 | ( ~ (v1 = 0) & relation_field(all_0_12_12) = v0 & is_reflexive_in(all_0_12_12, v0) = v1)))) % 10.16/2.93 | % 10.16/2.93 | Instantiating formula (40) with all_0_12_12, all_0_13_13 and discharging atoms inclusion_relation(all_0_13_13) = all_0_12_12, yields: % 10.16/2.93 | (150) relation(all_0_12_12) = 0 % 10.16/2.93 | % 10.16/2.93 | Instantiating (149) with all_69_0_87, all_69_1_88 yields: % 10.16/2.93 | (151) ( ~ (all_69_1_88 = 0) & relation(all_0_12_12) = all_69_1_88) | (( ~ (all_0_11_11 = 0) | (all_69_0_87 = 0 & relation_field(all_0_12_12) = all_69_1_88 & is_reflexive_in(all_0_12_12, all_69_1_88) = 0)) & (all_0_11_11 = 0 | ( ~ (all_69_0_87 = 0) & relation_field(all_0_12_12) = all_69_1_88 & is_reflexive_in(all_0_12_12, all_69_1_88) = all_69_0_87))) % 10.17/2.93 | % 10.17/2.93 +-Applying beta-rule and splitting (151), into two cases. % 10.17/2.93 |-Branch one: % 10.17/2.93 | (152) ~ (all_69_1_88 = 0) & relation(all_0_12_12) = all_69_1_88 % 10.17/2.93 | % 10.17/2.93 | Applying alpha-rule on (152) yields: % 10.17/2.93 | (153) ~ (all_69_1_88 = 0) % 10.17/2.93 | (154) relation(all_0_12_12) = all_69_1_88 % 10.17/2.93 | % 10.17/2.93 | Instantiating formula (132) with all_0_12_12, 0, all_69_1_88 and discharging atoms relation(all_0_12_12) = all_69_1_88, relation(all_0_12_12) = 0, yields: % 10.17/2.93 | (155) all_69_1_88 = 0 % 10.17/2.93 | % 10.17/2.93 | Equations (155) can reduce 153 to: % 10.17/2.93 | (156) $false % 10.17/2.93 | % 10.17/2.93 |-The branch is then unsatisfiable % 10.17/2.93 |-Branch two: % 10.17/2.93 | (157) ( ~ (all_0_11_11 = 0) | (all_69_0_87 = 0 & relation_field(all_0_12_12) = all_69_1_88 & is_reflexive_in(all_0_12_12, all_69_1_88) = 0)) & (all_0_11_11 = 0 | ( ~ (all_69_0_87 = 0) & relation_field(all_0_12_12) = all_69_1_88 & is_reflexive_in(all_0_12_12, all_69_1_88) = all_69_0_87)) % 10.17/2.93 | % 10.17/2.93 | Applying alpha-rule on (157) yields: % 10.17/2.93 | (158) ~ (all_0_11_11 = 0) | (all_69_0_87 = 0 & relation_field(all_0_12_12) = all_69_1_88 & is_reflexive_in(all_0_12_12, all_69_1_88) = 0) % 10.17/2.93 | (159) all_0_11_11 = 0 | ( ~ (all_69_0_87 = 0) & relation_field(all_0_12_12) = all_69_1_88 & is_reflexive_in(all_0_12_12, all_69_1_88) = all_69_0_87) % 10.17/2.93 | % 10.17/2.93 +-Applying beta-rule and splitting (159), into two cases. % 10.17/2.93 |-Branch one: % 10.17/2.93 | (160) all_0_11_11 = 0 % 10.17/2.93 | % 10.17/2.93 | Equations (160) can reduce 86 to: % 10.17/2.93 | (156) $false % 10.17/2.93 | % 10.17/2.93 |-The branch is then unsatisfiable % 10.17/2.93 |-Branch two: % 10.17/2.93 | (86) ~ (all_0_11_11 = 0) % 10.17/2.93 | (163) ~ (all_69_0_87 = 0) & relation_field(all_0_12_12) = all_69_1_88 & is_reflexive_in(all_0_12_12, all_69_1_88) = all_69_0_87 % 10.17/2.93 | % 10.17/2.93 | Applying alpha-rule on (163) yields: % 10.17/2.93 | (164) ~ (all_69_0_87 = 0) % 10.17/2.93 | (165) relation_field(all_0_12_12) = all_69_1_88 % 10.17/2.93 | (166) is_reflexive_in(all_0_12_12, all_69_1_88) = all_69_0_87 % 10.17/2.93 | % 10.17/2.93 | Instantiating formula (62) with all_69_1_88, all_0_12_12, all_0_13_13 and discharging atoms inclusion_relation(all_0_13_13) = all_0_12_12, relation_field(all_0_12_12) = all_69_1_88, yields: % 10.17/2.93 | (167) all_69_1_88 = all_0_13_13 | ? [v0] : ( ~ (v0 = 0) & relation(all_0_12_12) = v0) % 10.17/2.93 | % 10.17/2.93 | Instantiating formula (64) with all_69_0_87, all_69_1_88, all_0_12_12 and discharging atoms is_reflexive_in(all_0_12_12, all_69_1_88) = all_69_0_87, relation(all_0_12_12) = 0, yields: % 10.17/2.93 | (168) all_69_0_87 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & ordered_pair(v0, v0) = v1 & in(v1, all_0_12_12) = v2 & in(v0, all_69_1_88) = 0) % 10.17/2.93 | % 10.17/2.93 | Instantiating formula (63) with all_0_12_12, all_0_12_12, all_0_13_13 and discharging atoms inclusion_relation(all_0_13_13) = all_0_12_12, relation(all_0_12_12) = 0, yields: % 10.17/2.93 | (169) relation_field(all_0_12_12) = all_0_13_13 & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & in(v1, all_0_13_13) = v3) | ( ~ (v3 = 0) & in(v0, all_0_13_13) = v3) | (( ~ (v2 = 0) | (v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_0_12_12) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_0_12_12) = v4))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & in(v1, all_0_13_13) = v3) | ( ~ (v3 = 0) & in(v0, all_0_13_13) = v3) | (((v4 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & in(v2, all_0_12_12) = v3)) & ((v3 = 0 & in(v2, all_0_12_12) = 0) | ( ~ (v4 = 0) & subset(v0, v1) = v4))))) % 10.17/2.93 | % 10.17/2.93 | Applying alpha-rule on (169) yields: % 10.17/2.93 | (170) relation_field(all_0_12_12) = all_0_13_13 % 10.17/2.93 | (171) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & in(v1, all_0_13_13) = v3) | ( ~ (v3 = 0) & in(v0, all_0_13_13) = v3) | (( ~ (v2 = 0) | (v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_0_12_12) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_0_12_12) = v4))))) % 10.17/2.93 | (172) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & in(v1, all_0_13_13) = v3) | ( ~ (v3 = 0) & in(v0, all_0_13_13) = v3) | (((v4 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & in(v2, all_0_12_12) = v3)) & ((v3 = 0 & in(v2, all_0_12_12) = 0) | ( ~ (v4 = 0) & subset(v0, v1) = v4))))) % 10.17/2.93 | % 10.17/2.93 | Instantiating formula (98) with all_0_12_12 and discharging atoms relation(all_0_12_12) = 0, yields: % 10.17/2.93 | (173) ? [v0] : ? [v1] : ? [v2] : (relation_dom(all_0_12_12) = v1 & relation_rng(all_0_12_12) = v2 & relation_field(all_0_12_12) = v0 & set_union2(v1, v2) = v0) % 10.17/2.93 | % 10.17/2.93 | Instantiating (173) with all_108_0_158, all_108_1_159, all_108_2_160 yields: % 10.17/2.93 | (174) relation_dom(all_0_12_12) = all_108_1_159 & relation_rng(all_0_12_12) = all_108_0_158 & relation_field(all_0_12_12) = all_108_2_160 & set_union2(all_108_1_159, all_108_0_158) = all_108_2_160 % 10.17/2.93 | % 10.17/2.93 | Applying alpha-rule on (174) yields: % 10.17/2.93 | (175) relation_dom(all_0_12_12) = all_108_1_159 % 10.17/2.93 | (176) relation_rng(all_0_12_12) = all_108_0_158 % 10.17/2.93 | (177) relation_field(all_0_12_12) = all_108_2_160 % 10.17/2.93 | (178) set_union2(all_108_1_159, all_108_0_158) = all_108_2_160 % 10.17/2.93 | % 10.17/2.93 +-Applying beta-rule and splitting (167), into two cases. % 10.17/2.93 |-Branch one: % 10.17/2.93 | (179) all_69_1_88 = all_0_13_13 % 10.17/2.93 | % 10.17/2.93 +-Applying beta-rule and splitting (168), into two cases. % 10.17/2.93 |-Branch one: % 10.17/2.93 | (180) all_69_0_87 = 0 % 10.17/2.93 | % 10.17/2.93 | Equations (180) can reduce 164 to: % 10.17/2.93 | (156) $false % 10.17/2.93 | % 10.17/2.93 |-The branch is then unsatisfiable % 10.17/2.93 |-Branch two: % 10.17/2.93 | (164) ~ (all_69_0_87 = 0) % 10.17/2.93 | (183) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & ordered_pair(v0, v0) = v1 & in(v1, all_0_12_12) = v2 & in(v0, all_69_1_88) = 0) % 10.17/2.93 | % 10.17/2.93 | Instantiating (183) with all_126_0_176, all_126_1_177, all_126_2_178 yields: % 10.17/2.93 | (184) ~ (all_126_0_176 = 0) & ordered_pair(all_126_2_178, all_126_2_178) = all_126_1_177 & in(all_126_1_177, all_0_12_12) = all_126_0_176 & in(all_126_2_178, all_69_1_88) = 0 % 10.17/2.93 | % 10.17/2.93 | Applying alpha-rule on (184) yields: % 10.17/2.93 | (185) ~ (all_126_0_176 = 0) % 10.17/2.93 | (186) ordered_pair(all_126_2_178, all_126_2_178) = all_126_1_177 % 10.17/2.93 | (187) in(all_126_1_177, all_0_12_12) = all_126_0_176 % 10.17/2.93 | (188) in(all_126_2_178, all_69_1_88) = 0 % 10.17/2.93 | % 10.17/2.93 | From (179) and (188) follows: % 10.17/2.94 | (189) in(all_126_2_178, all_0_13_13) = 0 % 10.17/2.94 | % 10.17/2.94 | Instantiating formula (172) with all_126_1_177, all_126_2_178, all_126_2_178 and discharging atoms ordered_pair(all_126_2_178, all_126_2_178) = all_126_1_177, yields: % 10.17/2.94 | (190) ? [v0] : ? [v1] : (( ~ (v0 = 0) & in(all_126_2_178, all_0_13_13) = v0) | (((v1 = 0 & subset(all_126_2_178, all_126_2_178) = 0) | ( ~ (v0 = 0) & in(all_126_1_177, all_0_12_12) = v0)) & ((v0 = 0 & in(all_126_1_177, all_0_12_12) = 0) | ( ~ (v1 = 0) & subset(all_126_2_178, all_126_2_178) = v1)))) % 10.17/2.94 | % 10.17/2.94 | Instantiating formula (139) with all_126_0_176, all_0_12_12, all_126_1_177 and discharging atoms in(all_126_1_177, all_0_12_12) = all_126_0_176, yields: % 10.17/2.94 | (191) all_126_0_176 = 0 | ? [v0] : ((v0 = 0 & empty(all_0_12_12) = 0) | ( ~ (v0 = 0) & element(all_126_1_177, all_0_12_12) = v0)) % 10.17/2.94 | % 10.17/2.94 | Instantiating (190) with all_158_0_192, all_158_1_193 yields: % 10.17/2.94 | (192) ( ~ (all_158_1_193 = 0) & in(all_126_2_178, all_0_13_13) = all_158_1_193) | (((all_158_0_192 = 0 & subset(all_126_2_178, all_126_2_178) = 0) | ( ~ (all_158_1_193 = 0) & in(all_126_1_177, all_0_12_12) = all_158_1_193)) & ((all_158_1_193 = 0 & in(all_126_1_177, all_0_12_12) = 0) | ( ~ (all_158_0_192 = 0) & subset(all_126_2_178, all_126_2_178) = all_158_0_192))) % 10.17/2.94 | % 10.17/2.94 +-Applying beta-rule and splitting (191), into two cases. % 10.17/2.94 |-Branch one: % 10.17/2.94 | (193) all_126_0_176 = 0 % 10.17/2.94 | % 10.17/2.94 | Equations (193) can reduce 185 to: % 10.17/2.94 | (156) $false % 10.17/2.94 | % 10.17/2.94 |-The branch is then unsatisfiable % 10.17/2.94 |-Branch two: % 10.17/2.94 | (185) ~ (all_126_0_176 = 0) % 10.17/2.94 | (196) ? [v0] : ((v0 = 0 & empty(all_0_12_12) = 0) | ( ~ (v0 = 0) & element(all_126_1_177, all_0_12_12) = v0)) % 10.17/2.94 | % 10.17/2.94 +-Applying beta-rule and splitting (192), into two cases. % 10.17/2.94 |-Branch one: % 10.17/2.94 | (197) ~ (all_158_1_193 = 0) & in(all_126_2_178, all_0_13_13) = all_158_1_193 % 10.17/2.94 | % 10.17/2.94 | Applying alpha-rule on (197) yields: % 10.17/2.94 | (198) ~ (all_158_1_193 = 0) % 10.17/2.94 | (199) in(all_126_2_178, all_0_13_13) = all_158_1_193 % 10.17/2.94 | % 10.17/2.94 | Instantiating formula (29) with all_126_2_178, all_0_13_13, all_158_1_193, 0 and discharging atoms in(all_126_2_178, all_0_13_13) = all_158_1_193, in(all_126_2_178, all_0_13_13) = 0, yields: % 10.17/2.94 | (200) all_158_1_193 = 0 % 10.17/2.94 | % 10.17/2.94 | Equations (200) can reduce 198 to: % 10.17/2.94 | (156) $false % 10.17/2.94 | % 10.17/2.94 |-The branch is then unsatisfiable % 10.17/2.94 |-Branch two: % 10.17/2.94 | (202) ((all_158_0_192 = 0 & subset(all_126_2_178, all_126_2_178) = 0) | ( ~ (all_158_1_193 = 0) & in(all_126_1_177, all_0_12_12) = all_158_1_193)) & ((all_158_1_193 = 0 & in(all_126_1_177, all_0_12_12) = 0) | ( ~ (all_158_0_192 = 0) & subset(all_126_2_178, all_126_2_178) = all_158_0_192)) % 10.17/2.94 | % 10.17/2.94 | Applying alpha-rule on (202) yields: % 10.17/2.94 | (203) (all_158_0_192 = 0 & subset(all_126_2_178, all_126_2_178) = 0) | ( ~ (all_158_1_193 = 0) & in(all_126_1_177, all_0_12_12) = all_158_1_193) % 10.17/2.94 | (204) (all_158_1_193 = 0 & in(all_126_1_177, all_0_12_12) = 0) | ( ~ (all_158_0_192 = 0) & subset(all_126_2_178, all_126_2_178) = all_158_0_192) % 10.17/2.94 | % 10.17/2.94 +-Applying beta-rule and splitting (204), into two cases. % 10.17/2.94 |-Branch one: % 10.17/2.94 | (205) all_158_1_193 = 0 & in(all_126_1_177, all_0_12_12) = 0 % 10.17/2.94 | % 10.17/2.94 | Applying alpha-rule on (205) yields: % 10.17/2.94 | (200) all_158_1_193 = 0 % 10.17/2.94 | (207) in(all_126_1_177, all_0_12_12) = 0 % 10.17/2.94 | % 10.17/2.94 | Instantiating formula (29) with all_126_1_177, all_0_12_12, 0, all_126_0_176 and discharging atoms in(all_126_1_177, all_0_12_12) = all_126_0_176, in(all_126_1_177, all_0_12_12) = 0, yields: % 10.17/2.94 | (193) all_126_0_176 = 0 % 10.17/2.94 | % 10.17/2.94 | Equations (193) can reduce 185 to: % 10.17/2.94 | (156) $false % 10.17/2.94 | % 10.17/2.94 |-The branch is then unsatisfiable % 10.17/2.94 |-Branch two: % 10.17/2.94 | (210) ~ (all_158_0_192 = 0) & subset(all_126_2_178, all_126_2_178) = all_158_0_192 % 10.17/2.94 | % 10.17/2.94 | Applying alpha-rule on (210) yields: % 10.17/2.94 | (211) ~ (all_158_0_192 = 0) % 10.17/2.94 | (212) subset(all_126_2_178, all_126_2_178) = all_158_0_192 % 10.17/2.94 | % 10.17/2.94 | Instantiating formula (2) with all_158_0_192, all_126_2_178 and discharging atoms subset(all_126_2_178, all_126_2_178) = all_158_0_192, yields: % 10.17/2.94 | (213) all_158_0_192 = 0 % 10.17/2.94 | % 10.17/2.94 | Equations (213) can reduce 211 to: % 10.17/2.94 | (156) $false % 10.17/2.94 | % 10.17/2.94 |-The branch is then unsatisfiable % 10.17/2.94 |-Branch two: % 10.17/2.94 | (215) ~ (all_69_1_88 = all_0_13_13) % 10.17/2.94 | (216) ? [v0] : ( ~ (v0 = 0) & relation(all_0_12_12) = v0) % 10.17/2.94 | % 10.17/2.94 | Instantiating formula (46) with all_0_12_12, all_108_2_160, all_69_1_88 and discharging atoms relation_field(all_0_12_12) = all_108_2_160, relation_field(all_0_12_12) = all_69_1_88, yields: % 10.17/2.94 | (217) all_108_2_160 = all_69_1_88 % 10.17/2.94 | % 10.17/2.94 | Instantiating formula (46) with all_0_12_12, all_0_13_13, all_108_2_160 and discharging atoms relation_field(all_0_12_12) = all_108_2_160, relation_field(all_0_12_12) = all_0_13_13, yields: % 10.17/2.94 | (218) all_108_2_160 = all_0_13_13 % 10.17/2.94 | % 10.17/2.94 | Combining equations (218,217) yields a new equation: % 10.17/2.94 | (179) all_69_1_88 = all_0_13_13 % 10.17/2.94 | % 10.17/2.94 | Equations (179) can reduce 215 to: % 10.17/2.94 | (156) $false % 10.17/2.94 | % 10.17/2.94 |-The branch is then unsatisfiable % 10.17/2.94 % SZS output end Proof for theBenchmark % 10.17/2.94 % 10.17/2.94 2356ms %------------------------------------------------------------------------------