%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : NUM411+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n016.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Mon Jul 18 08:44:13 EDT 2022 % Result : Theorem 6.69s 2.26s % Output : Proof 10.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : NUM411+1 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.35 % Computer : n016.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Tue Jul 5 05:51:03 EDT 2022 % 0.13/0.35 % CPUTime : % 0.20/0.60 ____ _ % 0.20/0.60 ___ / __ \_____(_)___ ________ __________ % 0.20/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.20/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.20/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic % 0.20/0.60 (ePrincess v.1.0) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2015 % 0.20/0.60 (c) Peter Backeman, 2014-2015 % 0.20/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.20/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.20/0.60 Bug reports to peter@backeman.se % 0.20/0.60 % 0.20/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.74/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.66/1.00 Prover 0: Preprocessing ... % 2.18/1.18 Prover 0: Warning: ignoring some quantifiers % 2.26/1.21 Prover 0: Constructing countermodel ... % 3.15/1.45 Prover 0: gave up % 3.15/1.45 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.32/1.49 Prover 1: Preprocessing ... % 3.85/1.63 Prover 1: Warning: ignoring some quantifiers % 3.85/1.64 Prover 1: Constructing countermodel ... % 5.37/1.94 Prover 1: gave up % 5.37/1.94 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 5.37/1.97 Prover 2: Preprocessing ... % 5.92/2.08 Prover 2: Warning: ignoring some quantifiers % 5.92/2.09 Prover 2: Constructing countermodel ... % 6.69/2.25 Prover 2: proved (316ms) % 6.69/2.26 % 6.69/2.26 No countermodel exists, formula is valid % 6.69/2.26 % SZS status Theorem for theBenchmark % 6.69/2.26 % 6.69/2.26 Generating proof ... Warning: ignoring some quantifiers % 9.89/3.01 found it (size 62) % 9.89/3.01 % 9.89/3.01 % SZS output start Proof for theBenchmark % 9.89/3.01 Assumed formulas after preprocessing and simplification: % 9.89/3.02 | (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) & ~ (v3 = 0) & relation_empty_yielding(v7) = 0 & relation_empty_yielding(v6) = 0 & relation_empty_yielding(empty_set) = 0 & relation_non_empty(v4) = 0 & subset(v0, v1) = 0 & transfinite_sequence(v5) = 0 & transfinite_sequence_of(v2, v1) = v3 & transfinite_sequence_of(v2, v0) = 0 & 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(v4) = 0 & relation(empty_set) = 0 & epsilon_transitive(v19) = 0 & epsilon_transitive(v15) = 0 & epsilon_transitive(v8) = 0 & epsilon_transitive(empty_set) = 0 & ordinal(v19) = 0 & ordinal(v15) = 0 & ordinal(v8) = 0 & ordinal(empty_set) = 0 & epsilon_connected(v19) = 0 & epsilon_connected(v15) = 0 & epsilon_connected(v8) = 0 & epsilon_connected(empty_set) = 0 & function(v20) = 0 & function(v16) = 0 & function(v15) = 0 & function(v10) = 0 & function(v6) = 0 & function(v5) = 0 & function(v4) = 0 & function(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 & ! [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] : (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(v22, v23) = 0) | ~ (subset(v21, v23) = v24) | ? [v25] : ( ~ (v25 = 0) & subset(v21, v22) = v25)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (subset(v21, v23) = v24) | ~ (subset(v21, v22) = 0) | ? [v25] : ( ~ (v25 = 0) & subset(v22, v23) = 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 | ~ (transfinite_sequence_of(v24, v23) = v22) | ~ (transfinite_sequence_of(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] : ! [v24] : ( ~ (relation_rng(v22) = v23) | ~ (subset(v23, v21) = v24) | ? [v25] : (( ~ (v25 = 0) & transfinite_sequence(v22) = v25) | ( ~ (v25 = 0) & relation(v22) = v25) | ( ~ (v25 = 0) & function(v22) = v25) | (( ~ (v24 = 0) | (v25 = 0 & transfinite_sequence_of(v22, v21) = 0)) & (v24 = 0 | ( ~ (v25 = 0) & transfinite_sequence_of(v22, v21) = v25))))) & ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (element(v21, v22) = v23) | ? [v24] : ( ~ (v24 = 0) & in(v21, v22) = 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 | ~ (in(v21, v22) = v23) | ? [v24] : ((v24 = 0 & empty(v22) = 0) | ( ~ (v24 = 0) & element(v21, v22) = v24))) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (powerset(v23) = v22) | ~ (powerset(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (relation_empty_yielding(v23) = v22) | ~ (relation_empty_yielding(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (relation_non_empty(v23) = v22) | ~ (relation_non_empty(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (with_non_empty_elements(v23) = v22) | ~ (with_non_empty_elements(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (relation_rng(v23) = v22) | ~ (relation_rng(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (transfinite_sequence(v23) = v22) | ~ (transfinite_sequence(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 | ~ (epsilon_transitive(v23) = v22) | ~ (epsilon_transitive(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (ordinal(v23) = v22) | ~ (ordinal(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (epsilon_connected(v23) = v22) | ~ (epsilon_connected(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (function(v23) = v22) | ~ (function(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (empty(v23) = v22) | ~ (empty(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ( ~ (powerset(v22) = v23) | ~ (element(v21, v23) = 0) | subset(v21, v22) = 0) & ! [v21] : ! [v22] : ! [v23] : ( ~ (subset(v22, v23) = 0) | ~ (subset(v21, v22) = 0) | subset(v21, v23) = 0) & ! [v21] : ! [v22] : ! [v23] : ( ~ (transfinite_sequence_of(v22, v21) = v23) | ? [v24] : ? [v25] : (( ~ (v24 = 0) & transfinite_sequence(v22) = v24) | ( ~ (v24 = 0) & relation(v22) = v24) | ( ~ (v24 = 0) & function(v22) = v24) | (( ~ (v23 = 0) | (v25 = 0 & relation_rng(v22) = v24 & subset(v24, v21) = 0)) & (v23 = 0 | ( ~ (v25 = 0) & relation_rng(v22) = v24 & subset(v24, v21) = v25))))) & ! [v21] : ! [v22] : ! [v23] : ( ~ (empty(v23) = 0) | ~ (in(v21, v22) = 0) | ? [v24] : ? [v25] : ( ~ (v25 = 0) & powerset(v23) = v24 & element(v22, v24) = v25)) & ! [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] : (( ~ (v23 = 0) & epsilon_transitive(v21) = v23) | ( ~ (v23 = 0) & epsilon_connected(v21) = v23))) & ! [v21] : ! [v22] : (v22 = 0 | ~ (function(v21) = v22) | ? [v23] : ( ~ (v23 = 0) & empty(v21) = v23)) & ! [v21] : ! [v22] : (v22 = 0 | ~ (empty(v21) = v22) | ? [v23] : ? [v24] : (( ~ (v24 = 0) & relation_rng(v21) = v23 & empty(v23) = v24) | ( ~ (v23 = 0) & relation(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (element(v21, v22) = 0) | ? [v23] : ((v23 = 0 & empty(v22) = 0) | (v23 = 0 & in(v21, v22) = 0))) & ! [v21] : ! [v22] : ( ~ (relation_rng(v21) = v22) | ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & relation(v22) = 0 & empty(v22) = 0) | ( ~ (v23 = 0) & empty(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (relation_rng(v21) = v22) | ? [v23] : ((v23 = 0 & with_non_empty_elements(v22) = 0) | ( ~ (v23 = 0) & relation_non_empty(v21) = v23) | ( ~ (v23 = 0) & relation(v21) = v23) | ( ~ (v23 = 0) & function(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (relation_rng(v21) = v22) | ? [v23] : ((v23 = 0 & empty(v21) = 0) | ( ~ (v23 = 0) & relation(v21) = v23) | ( ~ (v23 = 0) & empty(v22) = v23))) & ! [v21] : ! [v22] : ( ~ (subset(v21, v22) = 0) | ? [v23] : (powerset(v22) = v23 & element(v21, v23) = 0)) & ! [v21] : ! [v22] : ( ~ (transfinite_sequence_of(v22, v21) = 0) | (transfinite_sequence(v22) = 0 & relation(v22) = 0 & function(v22) = 0)) & ! [v21] : ! [v22] : ( ~ (one_to_one(v21) = v22) | ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & v22 = 0 & relation(v21) = 0 & function(v21) = 0) | ( ~ (v23 = 0) & relation(v21) = v23) | ( ~ (v23 = 0) & function(v21) = v23) | ( ~ (v23 = 0) & empty(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (epsilon_transitive(v21) = v22) | ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & v22 = 0 & ordinal(v21) = 0 & epsilon_connected(v21) = 0) | ( ~ (v23 = 0) & empty(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (epsilon_transitive(v21) = v22) | ? [v23] : ((v23 = 0 & v22 = 0 & epsilon_connected(v21) = 0) | ( ~ (v23 = 0) & ordinal(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (ordinal(v21) = v22) | ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & v22 = 0 & epsilon_transitive(v21) = 0 & epsilon_connected(v21) = 0) | ( ~ (v23 = 0) & empty(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (epsilon_connected(v21) = v22) | ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & v22 = 0 & epsilon_transitive(v21) = 0 & ordinal(v21) = 0) | ( ~ (v23 = 0) & empty(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (epsilon_connected(v21) = v22) | ? [v23] : ((v23 = 0 & v22 = 0 & epsilon_transitive(v21) = 0) | ( ~ (v23 = 0) & ordinal(v21) = v23))) & ! [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_non_empty(v21) = 0) | ? [v22] : ? [v23] : ((v23 = 0 & with_non_empty_elements(v22) = 0 & relation_rng(v21) = v22) | ( ~ (v22 = 0) & relation(v21) = v22) | ( ~ (v22 = 0) & function(v21) = v22))) & ! [v21] : ( ~ (relation(v21) = 0) | ? [v22] : ? [v23] : ((v23 = 0 & v22 = 0 & one_to_one(v21) = 0 & function(v21) = 0) | ( ~ (v22 = 0) & function(v21) = v22) | ( ~ (v22 = 0) & empty(v21) = v22))) & ! [v21] : ( ~ (relation(v21) = 0) | ? [v22] : ? [v23] : ((v23 = 0 & with_non_empty_elements(v22) = 0 & relation_rng(v21) = v22) | ( ~ (v22 = 0) & relation_non_empty(v21) = v22) | ( ~ (v22 = 0) & function(v21) = v22))) & ! [v21] : ( ~ (relation(v21) = 0) | ? [v22] : ? [v23] : ((v22 = 0 & empty(v21) = 0) | ( ~ (v23 = 0) & relation_rng(v21) = v22 & empty(v22) = v23))) & ! [v21] : ( ~ (epsilon_transitive(v21) = 0) | ? [v22] : ((v22 = 0 & ordinal(v21) = 0) | ( ~ (v22 = 0) & epsilon_connected(v21) = v22))) & ! [v21] : ( ~ (ordinal(v21) = 0) | (epsilon_transitive(v21) = 0 & epsilon_connected(v21) = 0)) & ! [v21] : ( ~ (epsilon_connected(v21) = 0) | ? [v22] : ((v22 = 0 & ordinal(v21) = 0) | ( ~ (v22 = 0) & epsilon_transitive(v21) = v22))) & ! [v21] : ( ~ (function(v21) = 0) | ? [v22] : ? [v23] : ((v23 = 0 & v22 = 0 & one_to_one(v21) = 0 & relation(v21) = 0) | ( ~ (v22 = 0) & relation(v21) = v22) | ( ~ (v22 = 0) & empty(v21) = v22))) & ! [v21] : ( ~ (function(v21) = 0) | ? [v22] : ? [v23] : ((v23 = 0 & with_non_empty_elements(v22) = 0 & relation_rng(v21) = v22) | ( ~ (v22 = 0) & relation_non_empty(v21) = v22) | ( ~ (v22 = 0) & relation(v21) = v22))) & ! [v21] : ( ~ (empty(v21) = 0) | relation(v21) = 0) & ! [v21] : ( ~ (empty(v21) = 0) | function(v21) = 0) & ! [v21] : ( ~ (empty(v21) = 0) | ? [v22] : ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & v22 = 0 & one_to_one(v21) = 0 & relation(v21) = 0 & function(v21) = 0) | ( ~ (v22 = 0) & relation(v21) = v22) | ( ~ (v22 = 0) & function(v21) = v22))) & ! [v21] : ( ~ (empty(v21) = 0) | ? [v22] : (relation_rng(v21) = v22 & relation(v22) = 0 & empty(v22) = 0)) & ! [v21] : ( ~ (empty(v21) = 0) | (epsilon_transitive(v21) = 0 & ordinal(v21) = 0 & epsilon_connected(v21) = 0)) & ? [v21] : ? [v22] : ? [v23] : element(v22, v21) = v23 & ? [v21] : ? [v22] : ? [v23] : subset(v22, v21) = v23 & ? [v21] : ? [v22] : ? [v23] : transfinite_sequence_of(v22, v21) = v23 & ? [v21] : ? [v22] : ? [v23] : in(v22, v21) = v23 & ? [v21] : ? [v22] : powerset(v21) = v22 & ? [v21] : ? [v22] : relation_empty_yielding(v21) = v22 & ? [v21] : ? [v22] : relation_non_empty(v21) = v22 & ? [v21] : ? [v22] : with_non_empty_elements(v21) = v22 & ? [v21] : ? [v22] : element(v22, v21) = 0 & ? [v21] : ? [v22] : relation_rng(v21) = v22 & ? [v21] : ? [v22] : transfinite_sequence(v21) = v22 & ? [v21] : ? [v22] : transfinite_sequence_of(v22, v21) = 0 & ? [v21] : ? [v22] : one_to_one(v21) = v22 & ? [v21] : ? [v22] : relation(v21) = v22 & ? [v21] : ? [v22] : epsilon_transitive(v21) = v22 & ? [v21] : ? [v22] : ordinal(v21) = v22 & ? [v21] : ? [v22] : epsilon_connected(v21) = v22 & ? [v21] : ? [v22] : function(v21) = v22 & ? [v21] : ? [v22] : empty(v21) = v22) % 10.30/3.09 | 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: % 10.30/3.09 | (1) ~ (all_0_6_6 = 0) & ~ (all_0_8_8 = 0) & ~ (all_0_11_11 = 0) & ~ (all_0_17_17 = 0) & relation_empty_yielding(all_0_13_13) = 0 & relation_empty_yielding(all_0_14_14) = 0 & relation_empty_yielding(empty_set) = 0 & relation_non_empty(all_0_16_16) = 0 & subset(all_0_20_20, all_0_19_19) = 0 & transfinite_sequence(all_0_15_15) = 0 & transfinite_sequence_of(all_0_18_18, all_0_19_19) = all_0_17_17 & transfinite_sequence_of(all_0_18_18, all_0_20_20) = 0 & 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(all_0_16_16) = 0 & relation(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 & ordinal(all_0_1_1) = 0 & ordinal(all_0_5_5) = 0 & ordinal(all_0_12_12) = 0 & ordinal(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 & 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(all_0_16_16) = 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_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 & ! [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] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = 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 | ~ (transfinite_sequence_of(v3, v2) = v1) | ~ (transfinite_sequence_of(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] : ( ~ (relation_rng(v1) = v2) | ~ (subset(v2, v0) = v3) | ? [v4] : (( ~ (v4 = 0) & transfinite_sequence(v1) = v4) | ( ~ (v4 = 0) & relation(v1) = v4) | ( ~ (v4 = 0) & function(v1) = v4) | (( ~ (v3 = 0) | (v4 = 0 & transfinite_sequence_of(v1, v0) = 0)) & (v3 = 0 | ( ~ (v4 = 0) & transfinite_sequence_of(v1, v0) = v4))))) & ! [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 | ~ (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 | ~ (relation_non_empty(v2) = v1) | ~ (relation_non_empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (with_non_empty_elements(v2) = v1) | ~ (with_non_empty_elements(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (transfinite_sequence(v2) = v1) | ~ (transfinite_sequence(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] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (transfinite_sequence_of(v1, v0) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & transfinite_sequence(v1) = v3) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & function(v1) = v3) | (( ~ (v2 = 0) | (v4 = 0 & relation_rng(v1) = v3 & subset(v3, v0) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & relation_rng(v1) = v3 & subset(v3, v0) = v4))))) & ! [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 | ~ (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] : (( ~ (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] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v3 = 0) & relation_rng(v0) = v2 & empty(v2) = v3) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & relation(v1) = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0) | ( ~ (v2 = 0) & relation_non_empty(v0) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ((v2 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (transfinite_sequence_of(v1, v0) = 0) | (transfinite_sequence(v1) = 0 & relation(v1) = 0 & function(v1) = 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_non_empty(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0 & relation_rng(v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) & ! [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] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0 & relation_rng(v0) = v1) | ( ~ (v1 = 0) & relation_non_empty(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation_rng(v0) = v1 & empty(v1) = v2))) & ! [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] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0 & relation_rng(v0) = v1) | ( ~ (v1 = 0) & relation_non_empty(v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1))) & ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) & ! [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) | ? [v1] : (relation_rng(v0) = v1 & relation(v1) = 0 & empty(v1) = 0)) & ! [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] : transfinite_sequence_of(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : powerset(v0) = v1 & ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1 & ? [v0] : ? [v1] : relation_non_empty(v0) = v1 & ? [v0] : ? [v1] : with_non_empty_elements(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : relation_rng(v0) = v1 & ? [v0] : ? [v1] : transfinite_sequence(v0) = v1 & ? [v0] : ? [v1] : transfinite_sequence_of(v1, v0) = 0 & ? [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 % 10.56/3.13 | % 10.56/3.13 | Applying alpha-rule on (1) yields: % 10.56/3.13 | (2) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation_rng(v0) = v1 & empty(v1) = v2))) % 10.56/3.13 | (3) ! [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))) % 10.56/3.14 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) % 10.56/3.14 | (5) ! [v0] : ! [v1] : ( ~ (transfinite_sequence_of(v1, v0) = 0) | (transfinite_sequence(v1) = 0 & relation(v1) = 0 & function(v1) = 0)) % 10.56/3.14 | (6) transfinite_sequence_of(all_0_18_18, all_0_19_19) = all_0_17_17 % 10.56/3.14 | (7) relation(all_0_7_7) = 0 % 10.56/3.14 | (8) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0 & relation_rng(v0) = v1) | ( ~ (v1 = 0) & relation_non_empty(v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1))) % 10.56/3.14 | (9) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0 & relation_rng(v0) = v1) | ( ~ (v1 = 0) & relation_non_empty(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) % 10.56/3.14 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) % 10.56/3.14 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 10.56/3.14 | (12) empty(all_0_5_5) = 0 % 10.56/3.14 | (13) function(all_0_15_15) = 0 % 10.56/3.14 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) % 10.56/3.14 | (15) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) % 10.56/3.14 | (16) epsilon_transitive(all_0_1_1) = 0 % 10.56/3.14 | (17) ordinal(empty_set) = 0 % 10.56/3.14 | (18) relation(all_0_5_5) = 0 % 10.56/3.14 | (19) relation_empty_yielding(empty_set) = 0 % 10.56/3.14 | (20) empty(all_0_3_3) = 0 % 10.56/3.14 | (21) epsilon_transitive(empty_set) = 0 % 10.56/3.14 | (22) function(all_0_10_10) = 0 % 10.56/3.14 | (23) epsilon_connected(all_0_5_5) = 0 % 10.56/3.14 | (24) ? [v0] : ? [v1] : with_non_empty_elements(v0) = v1 % 10.56/3.14 | (25) ~ (all_0_8_8 = 0) % 10.56/3.14 | (26) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 10.56/3.14 | (27) function(empty_set) = 0 % 10.56/3.14 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3))) % 10.56/3.14 | (29) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 10.56/3.14 | (30) ? [v0] : ? [v1] : relation_non_empty(v0) = v1 % 10.56/3.14 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v1) = v2) | ~ (subset(v2, v0) = v3) | ? [v4] : (( ~ (v4 = 0) & transfinite_sequence(v1) = v4) | ( ~ (v4 = 0) & relation(v1) = v4) | ( ~ (v4 = 0) & function(v1) = v4) | (( ~ (v3 = 0) | (v4 = 0 & transfinite_sequence_of(v1, v0) = 0)) & (v3 = 0 | ( ~ (v4 = 0) & transfinite_sequence_of(v1, v0) = v4))))) % 10.56/3.15 | (32) empty(empty_set) = 0 % 10.56/3.15 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (transfinite_sequence_of(v3, v2) = v1) | ~ (transfinite_sequence_of(v3, v2) = v0)) % 10.56/3.15 | (34) transfinite_sequence_of(all_0_18_18, all_0_20_20) = 0 % 10.56/3.15 | (35) ! [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))) % 10.56/3.15 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 10.56/3.15 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) % 10.56/3.15 | (38) ? [v0] : ? [v1] : function(v0) = v1 % 10.56/3.15 | (39) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 10.56/3.15 | (40) ! [v0] : ( ~ (relation_non_empty(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0 & relation_rng(v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) % 10.56/3.15 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (with_non_empty_elements(v2) = v1) | ~ (with_non_empty_elements(v2) = v0)) % 10.56/3.15 | (42) relation(all_0_0_0) = 0 % 10.56/3.15 | (43) ! [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))) % 10.56/3.15 | (44) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 % 10.56/3.15 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0) % 10.56/3.15 | (46) ? [v0] : ? [v1] : epsilon_connected(v0) = v1 % 10.56/3.15 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 10.56/3.15 | (48) relation_non_empty(all_0_16_16) = 0 % 10.56/3.15 | (49) ! [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))) % 10.56/3.15 | (50) empty(all_0_4_4) = 0 % 10.56/3.15 | (51) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v3 = 0) & relation_rng(v0) = v2 & empty(v2) = v3) | ( ~ (v2 = 0) & relation(v0) = v2))) % 10.56/3.15 | (52) relation(all_0_2_2) = 0 % 10.56/3.15 | (53) one_to_one(all_0_10_10) = 0 % 10.56/3.15 | (54) ordinal(all_0_5_5) = 0 % 10.56/3.15 | (55) one_to_one(all_0_5_5) = 0 % 10.56/3.15 | (56) ! [v0] : ( ~ (epsilon_connected(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0) = v1))) % 10.56/3.15 | (57) ! [v0] : ( ~ (epsilon_transitive(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_connected(v0) = v1))) % 10.56/3.15 | (58) ! [v0] : ! [v1] : (v1 = 0 | ~ (ordinal(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & epsilon_transitive(v0) = v2) | ( ~ (v2 = 0) & epsilon_connected(v0) = v2))) % 10.56/3.15 | (59) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 10.56/3.15 | (60) relation(all_0_14_14) = 0 % 10.56/3.15 | (61) ? [v0] : ? [v1] : ? [v2] : transfinite_sequence_of(v1, v0) = v2 % 10.56/3.15 | (62) ordinal(all_0_1_1) = 0 % 10.56/3.15 | (63) ! [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)) % 10.56/3.15 | (64) ? [v0] : ? [v1] : transfinite_sequence_of(v1, v0) = 0 % 10.56/3.15 | (65) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) % 10.56/3.15 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) % 10.56/3.15 | (67) ~ (all_0_11_11 = 0) % 10.56/3.16 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4)) % 10.56/3.16 | (69) ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) % 10.56/3.16 | (70) relation(all_0_4_4) = 0 % 10.56/3.16 | (71) function(all_0_0_0) = 0 % 10.56/3.16 | (72) relation_empty_yielding(all_0_13_13) = 0 % 10.56/3.16 | (73) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 % 10.56/3.16 | (74) relation(all_0_15_15) = 0 % 10.56/3.16 | (75) function(all_0_14_14) = 0 % 10.56/3.16 | (76) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 % 10.56/3.16 | (77) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ((v2 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2))) % 10.56/3.16 | (78) function(all_0_5_5) = 0 % 10.56/3.16 | (79) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (transfinite_sequence(v2) = v1) | ~ (transfinite_sequence(v2) = v0)) % 10.56/3.16 | (80) ? [v0] : ? [v1] : element(v1, v0) = 0 % 10.56/3.16 | (81) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) % 10.56/3.16 | (82) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) % 10.56/3.16 | (83) epsilon_connected(empty_set) = 0 % 10.56/3.16 | (84) ~ (all_0_17_17 = 0) % 10.56/3.16 | (85) epsilon_transitive(all_0_5_5) = 0 % 10.56/3.16 | (86) ? [v0] : ? [v1] : transfinite_sequence(v0) = v1 % 10.56/3.16 | (87) ordinal(all_0_12_12) = 0 % 10.56/3.16 | (88) relation_empty_yielding(all_0_14_14) = 0 % 10.56/3.16 | (89) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 10.56/3.16 | (90) ? [v0] : ? [v1] : relation_rng(v0) = v1 % 10.56/3.16 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 10.56/3.16 | (92) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) % 10.56/3.16 | (93) ? [v0] : ? [v1] : one_to_one(v0) = v1 % 10.56/3.16 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 10.56/3.16 | (95) empty(all_0_12_12) = all_0_11_11 % 10.56/3.16 | (96) ? [v0] : ? [v1] : empty(v0) = v1 % 10.56/3.16 | (97) ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2))) % 10.56/3.16 | (98) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 10.56/3.16 | (99) epsilon_connected(all_0_12_12) = 0 % 10.56/3.16 | (100) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) % 10.56/3.16 | (101) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & relation(v1) = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) % 10.56/3.16 | (102) relation(all_0_16_16) = 0 % 10.56/3.16 | (103) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 10.56/3.16 | (104) ? [v0] : ? [v1] : powerset(v0) = v1 % 10.56/3.16 | (105) relation(all_0_10_10) = 0 % 10.56/3.16 | (106) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 10.56/3.16 | (107) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_rng(v0) = v1 & relation(v1) = 0 & empty(v1) = 0)) % 10.56/3.16 | (108) ! [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)) % 10.56/3.16 | (109) empty(all_0_2_2) = 0 % 10.56/3.16 | (110) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 10.56/3.16 | (111) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) % 10.56/3.16 | (112) ~ (all_0_6_6 = 0) % 10.56/3.16 | (113) function(all_0_4_4) = 0 % 10.56/3.16 | (114) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 10.56/3.16 | (115) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0) | ( ~ (v2 = 0) & relation_non_empty(v0) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2))) % 10.56/3.16 | (116) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) % 10.56/3.16 | (117) one_to_one(empty_set) = 0 % 10.56/3.16 | (118) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 10.56/3.16 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) % 10.56/3.16 | (120) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_non_empty(v2) = v1) | ~ (relation_non_empty(v2) = v0)) % 10.56/3.17 | (121) relation(all_0_13_13) = 0 % 10.56/3.17 | (122) ? [v0] : ? [v1] : ordinal(v0) = v1 % 10.56/3.17 | (123) relation(empty_set) = 0 % 10.56/3.17 | (124) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2))) % 10.56/3.17 | (125) empty(all_0_9_9) = all_0_8_8 % 10.56/3.17 | (126) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 10.56/3.17 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 10.56/3.17 | (128) subset(all_0_20_20, all_0_19_19) = 0 % 10.56/3.17 | (129) transfinite_sequence(all_0_15_15) = 0 % 10.56/3.17 | (130) ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)) % 10.56/3.17 | (131) epsilon_transitive(all_0_12_12) = 0 % 10.56/3.17 | (132) ! [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))) % 10.56/3.17 | (133) ! [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))) % 10.56/3.17 | (134) empty(all_0_7_7) = all_0_6_6 % 10.56/3.17 | (135) epsilon_connected(all_0_1_1) = 0 % 10.56/3.17 | (136) ? [v0] : ? [v1] : relation(v0) = v1 % 10.56/3.17 | (137) ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1 % 10.56/3.17 | (138) ? [v0] : ? [v1] : epsilon_transitive(v0) = v1 % 10.56/3.17 | (139) ! [v0] : ! [v1] : ! [v2] : ( ~ (transfinite_sequence_of(v1, v0) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & transfinite_sequence(v1) = v3) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & function(v1) = v3) | (( ~ (v2 = 0) | (v4 = 0 & relation_rng(v1) = v3 & subset(v3, v0) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & relation_rng(v1) = v3 & subset(v3, v0) = v4))))) % 10.56/3.17 | (140) ! [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))) % 10.56/3.17 | (141) function(all_0_16_16) = 0 % 10.56/3.17 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 10.56/3.17 | (143) ! [v0] : ( ~ (empty(v0) = 0) | (epsilon_transitive(v0) = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0)) % 10.56/3.17 | % 10.56/3.17 | Instantiating formula (139) with all_0_17_17, all_0_18_18, all_0_19_19 and discharging atoms transfinite_sequence_of(all_0_18_18, all_0_19_19) = all_0_17_17, yields: % 10.56/3.17 | (144) ? [v0] : ? [v1] : (( ~ (v0 = 0) & transfinite_sequence(all_0_18_18) = v0) | ( ~ (v0 = 0) & relation(all_0_18_18) = v0) | ( ~ (v0 = 0) & function(all_0_18_18) = v0) | (( ~ (all_0_17_17 = 0) | (v1 = 0 & relation_rng(all_0_18_18) = v0 & subset(v0, all_0_19_19) = 0)) & (all_0_17_17 = 0 | ( ~ (v1 = 0) & relation_rng(all_0_18_18) = v0 & subset(v0, all_0_19_19) = v1)))) % 10.56/3.17 | % 10.56/3.17 | Instantiating formula (5) with all_0_18_18, all_0_20_20 and discharging atoms transfinite_sequence_of(all_0_18_18, all_0_20_20) = 0, yields: % 10.56/3.17 | (145) transfinite_sequence(all_0_18_18) = 0 & relation(all_0_18_18) = 0 & function(all_0_18_18) = 0 % 10.56/3.17 | % 10.56/3.17 | Applying alpha-rule on (145) yields: % 10.56/3.17 | (146) transfinite_sequence(all_0_18_18) = 0 % 10.56/3.17 | (147) relation(all_0_18_18) = 0 % 10.56/3.17 | (148) function(all_0_18_18) = 0 % 10.56/3.17 | % 10.56/3.17 | Instantiating formula (139) with 0, all_0_18_18, all_0_20_20 and discharging atoms transfinite_sequence_of(all_0_18_18, all_0_20_20) = 0, yields: % 10.56/3.17 | (149) ? [v0] : ? [v1] : ((v1 = 0 & relation_rng(all_0_18_18) = v0 & subset(v0, all_0_20_20) = 0) | ( ~ (v0 = 0) & transfinite_sequence(all_0_18_18) = v0) | ( ~ (v0 = 0) & relation(all_0_18_18) = v0) | ( ~ (v0 = 0) & function(all_0_18_18) = v0)) % 10.56/3.17 | % 10.56/3.17 | Instantiating (144) with all_73_0_103, all_73_1_104 yields: % 10.56/3.17 | (150) ( ~ (all_73_1_104 = 0) & transfinite_sequence(all_0_18_18) = all_73_1_104) | ( ~ (all_73_1_104 = 0) & relation(all_0_18_18) = all_73_1_104) | ( ~ (all_73_1_104 = 0) & function(all_0_18_18) = all_73_1_104) | (( ~ (all_0_17_17 = 0) | (all_73_0_103 = 0 & relation_rng(all_0_18_18) = all_73_1_104 & subset(all_73_1_104, all_0_19_19) = 0)) & (all_0_17_17 = 0 | ( ~ (all_73_0_103 = 0) & relation_rng(all_0_18_18) = all_73_1_104 & subset(all_73_1_104, all_0_19_19) = all_73_0_103))) % 10.56/3.17 | % 10.56/3.17 | Instantiating (149) with all_96_0_149, all_96_1_150 yields: % 10.56/3.17 | (151) (all_96_0_149 = 0 & relation_rng(all_0_18_18) = all_96_1_150 & subset(all_96_1_150, all_0_20_20) = 0) | ( ~ (all_96_1_150 = 0) & transfinite_sequence(all_0_18_18) = all_96_1_150) | ( ~ (all_96_1_150 = 0) & relation(all_0_18_18) = all_96_1_150) | ( ~ (all_96_1_150 = 0) & function(all_0_18_18) = all_96_1_150) % 10.56/3.17 | % 10.56/3.17 +-Applying beta-rule and splitting (150), into two cases. % 10.56/3.17 |-Branch one: % 10.56/3.17 | (152) ( ~ (all_73_1_104 = 0) & transfinite_sequence(all_0_18_18) = all_73_1_104) | ( ~ (all_73_1_104 = 0) & relation(all_0_18_18) = all_73_1_104) | ( ~ (all_73_1_104 = 0) & function(all_0_18_18) = all_73_1_104) % 10.56/3.17 | % 10.56/3.17 +-Applying beta-rule and splitting (152), into two cases. % 10.56/3.17 |-Branch one: % 10.56/3.17 | (153) ( ~ (all_73_1_104 = 0) & transfinite_sequence(all_0_18_18) = all_73_1_104) | ( ~ (all_73_1_104 = 0) & relation(all_0_18_18) = all_73_1_104) % 10.56/3.17 | % 10.56/3.17 +-Applying beta-rule and splitting (153), into two cases. % 10.56/3.17 |-Branch one: % 10.56/3.17 | (154) ~ (all_73_1_104 = 0) & transfinite_sequence(all_0_18_18) = all_73_1_104 % 10.56/3.17 | % 10.56/3.17 | Applying alpha-rule on (154) yields: % 10.56/3.17 | (155) ~ (all_73_1_104 = 0) % 10.56/3.17 | (156) transfinite_sequence(all_0_18_18) = all_73_1_104 % 10.56/3.17 | % 10.56/3.17 | Instantiating formula (79) with all_0_18_18, 0, all_73_1_104 and discharging atoms transfinite_sequence(all_0_18_18) = all_73_1_104, transfinite_sequence(all_0_18_18) = 0, yields: % 10.56/3.18 | (157) all_73_1_104 = 0 % 10.56/3.18 | % 10.56/3.18 | Equations (157) can reduce 155 to: % 10.56/3.18 | (158) $false % 10.56/3.18 | % 10.56/3.18 |-The branch is then unsatisfiable % 10.56/3.18 |-Branch two: % 10.56/3.18 | (159) ~ (all_73_1_104 = 0) & relation(all_0_18_18) = all_73_1_104 % 10.56/3.18 | % 10.56/3.18 | Applying alpha-rule on (159) yields: % 10.56/3.18 | (155) ~ (all_73_1_104 = 0) % 10.56/3.18 | (161) relation(all_0_18_18) = all_73_1_104 % 10.56/3.18 | % 10.56/3.18 | Instantiating formula (126) with all_0_18_18, 0, all_73_1_104 and discharging atoms relation(all_0_18_18) = all_73_1_104, relation(all_0_18_18) = 0, yields: % 10.56/3.18 | (157) all_73_1_104 = 0 % 10.56/3.18 | % 10.56/3.18 | Equations (157) can reduce 155 to: % 10.56/3.18 | (158) $false % 10.56/3.18 | % 10.56/3.18 |-The branch is then unsatisfiable % 10.56/3.18 |-Branch two: % 10.56/3.18 | (164) ~ (all_73_1_104 = 0) & function(all_0_18_18) = all_73_1_104 % 10.56/3.18 | % 10.56/3.18 | Applying alpha-rule on (164) yields: % 10.56/3.18 | (155) ~ (all_73_1_104 = 0) % 10.56/3.18 | (166) function(all_0_18_18) = all_73_1_104 % 10.56/3.18 | % 10.56/3.18 | Instantiating formula (47) with all_0_18_18, 0, all_73_1_104 and discharging atoms function(all_0_18_18) = all_73_1_104, function(all_0_18_18) = 0, yields: % 10.56/3.18 | (157) all_73_1_104 = 0 % 10.56/3.18 | % 10.56/3.18 | Equations (157) can reduce 155 to: % 10.56/3.18 | (158) $false % 10.56/3.18 | % 10.56/3.18 |-The branch is then unsatisfiable % 10.56/3.18 |-Branch two: % 10.56/3.18 | (169) ( ~ (all_0_17_17 = 0) | (all_73_0_103 = 0 & relation_rng(all_0_18_18) = all_73_1_104 & subset(all_73_1_104, all_0_19_19) = 0)) & (all_0_17_17 = 0 | ( ~ (all_73_0_103 = 0) & relation_rng(all_0_18_18) = all_73_1_104 & subset(all_73_1_104, all_0_19_19) = all_73_0_103)) % 10.56/3.18 | % 10.56/3.18 | Applying alpha-rule on (169) yields: % 10.56/3.18 | (170) ~ (all_0_17_17 = 0) | (all_73_0_103 = 0 & relation_rng(all_0_18_18) = all_73_1_104 & subset(all_73_1_104, all_0_19_19) = 0) % 10.56/3.18 | (171) all_0_17_17 = 0 | ( ~ (all_73_0_103 = 0) & relation_rng(all_0_18_18) = all_73_1_104 & subset(all_73_1_104, all_0_19_19) = all_73_0_103) % 10.56/3.18 | % 10.56/3.18 +-Applying beta-rule and splitting (171), into two cases. % 10.56/3.18 |-Branch one: % 10.56/3.18 | (172) all_0_17_17 = 0 % 10.56/3.18 | % 10.56/3.18 | Equations (172) can reduce 84 to: % 10.56/3.18 | (158) $false % 10.56/3.18 | % 10.56/3.18 |-The branch is then unsatisfiable % 10.56/3.18 |-Branch two: % 10.56/3.18 | (84) ~ (all_0_17_17 = 0) % 10.56/3.18 | (175) ~ (all_73_0_103 = 0) & relation_rng(all_0_18_18) = all_73_1_104 & subset(all_73_1_104, all_0_19_19) = all_73_0_103 % 10.56/3.18 | % 10.56/3.18 | Applying alpha-rule on (175) yields: % 10.56/3.18 | (176) ~ (all_73_0_103 = 0) % 10.56/3.18 | (177) relation_rng(all_0_18_18) = all_73_1_104 % 10.56/3.18 | (178) subset(all_73_1_104, all_0_19_19) = all_73_0_103 % 10.56/3.18 | % 10.56/3.18 +-Applying beta-rule and splitting (151), into two cases. % 10.56/3.18 |-Branch one: % 10.56/3.18 | (179) (all_96_0_149 = 0 & relation_rng(all_0_18_18) = all_96_1_150 & subset(all_96_1_150, all_0_20_20) = 0) | ( ~ (all_96_1_150 = 0) & transfinite_sequence(all_0_18_18) = all_96_1_150) | ( ~ (all_96_1_150 = 0) & relation(all_0_18_18) = all_96_1_150) % 10.56/3.18 | % 10.56/3.18 +-Applying beta-rule and splitting (179), into two cases. % 10.56/3.18 |-Branch one: % 10.56/3.18 | (180) (all_96_0_149 = 0 & relation_rng(all_0_18_18) = all_96_1_150 & subset(all_96_1_150, all_0_20_20) = 0) | ( ~ (all_96_1_150 = 0) & transfinite_sequence(all_0_18_18) = all_96_1_150) % 10.56/3.18 | % 10.56/3.18 +-Applying beta-rule and splitting (180), into two cases. % 10.56/3.18 |-Branch one: % 10.56/3.18 | (181) all_96_0_149 = 0 & relation_rng(all_0_18_18) = all_96_1_150 & subset(all_96_1_150, all_0_20_20) = 0 % 10.56/3.18 | % 10.56/3.18 | Applying alpha-rule on (181) yields: % 10.56/3.18 | (182) all_96_0_149 = 0 % 10.56/3.18 | (183) relation_rng(all_0_18_18) = all_96_1_150 % 10.56/3.18 | (184) subset(all_96_1_150, all_0_20_20) = 0 % 10.56/3.18 | % 10.56/3.18 | Instantiating formula (89) with all_0_18_18, all_73_1_104, all_96_1_150 and discharging atoms relation_rng(all_0_18_18) = all_96_1_150, relation_rng(all_0_18_18) = all_73_1_104, yields: % 10.56/3.18 | (185) all_96_1_150 = all_73_1_104 % 10.56/3.18 | % 10.56/3.18 | From (185) and (184) follows: % 10.56/3.18 | (186) subset(all_73_1_104, all_0_20_20) = 0 % 10.56/3.18 | % 10.56/3.18 | Instantiating formula (94) with all_73_0_103, all_0_19_19, all_0_20_20, all_73_1_104 and discharging atoms subset(all_73_1_104, all_0_19_19) = all_73_0_103, subset(all_0_20_20, all_0_19_19) = 0, yields: % 10.56/3.18 | (187) all_73_0_103 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_73_1_104, all_0_20_20) = v0) % 10.56/3.18 | % 10.56/3.18 | Instantiating formula (4) with all_73_0_103, all_0_19_19, all_73_1_104 and discharging atoms subset(all_73_1_104, all_0_19_19) = all_73_0_103, yields: % 10.56/3.18 | (188) all_73_0_103 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_0_19_19) = v0 & element(all_73_1_104, v0) = v1) % 10.56/3.18 | % 10.56/3.18 | Instantiating formula (45) with all_0_19_19, all_0_20_20, all_73_1_104 and discharging atoms subset(all_73_1_104, all_0_20_20) = 0, subset(all_0_20_20, all_0_19_19) = 0, yields: % 10.56/3.18 | (189) subset(all_73_1_104, all_0_19_19) = 0 % 10.56/3.18 | % 10.56/3.18 | Instantiating formula (119) with all_73_0_103, all_0_19_19, all_0_20_20, all_73_1_104 and discharging atoms subset(all_73_1_104, all_0_19_19) = all_73_0_103, subset(all_73_1_104, all_0_20_20) = 0, yields: % 10.56/3.18 | (190) all_73_0_103 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_0_20_20, all_0_19_19) = v0) % 10.56/3.18 | % 10.56/3.18 +-Applying beta-rule and splitting (190), into two cases. % 10.56/3.18 |-Branch one: % 10.56/3.18 | (191) all_73_0_103 = 0 % 10.56/3.18 | % 10.56/3.18 | Equations (191) can reduce 176 to: % 10.56/3.18 | (158) $false % 10.56/3.18 | % 10.56/3.18 |-The branch is then unsatisfiable % 10.56/3.18 |-Branch two: % 10.56/3.18 | (176) ~ (all_73_0_103 = 0) % 10.56/3.18 | (194) ? [v0] : ( ~ (v0 = 0) & subset(all_0_20_20, all_0_19_19) = v0) % 10.56/3.18 | % 10.56/3.18 +-Applying beta-rule and splitting (187), into two cases. % 10.56/3.18 |-Branch one: % 10.56/3.18 | (191) all_73_0_103 = 0 % 10.56/3.18 | % 10.56/3.18 | Equations (191) can reduce 176 to: % 10.56/3.19 | (158) $false % 10.56/3.19 | % 10.56/3.19 |-The branch is then unsatisfiable % 10.56/3.19 |-Branch two: % 10.56/3.19 | (176) ~ (all_73_0_103 = 0) % 10.56/3.19 | (198) ? [v0] : ( ~ (v0 = 0) & subset(all_73_1_104, all_0_20_20) = v0) % 10.56/3.19 | % 10.56/3.19 +-Applying beta-rule and splitting (188), into two cases. % 10.56/3.19 |-Branch one: % 10.56/3.19 | (191) all_73_0_103 = 0 % 10.56/3.19 | % 10.56/3.19 | Equations (191) can reduce 176 to: % 10.56/3.19 | (158) $false % 10.56/3.19 | % 10.56/3.19 |-The branch is then unsatisfiable % 10.56/3.19 |-Branch two: % 10.56/3.19 | (176) ~ (all_73_0_103 = 0) % 10.56/3.19 | (202) ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_0_19_19) = v0 & element(all_73_1_104, v0) = v1) % 10.56/3.19 | % 10.56/3.19 | Instantiating formula (91) with all_73_1_104, all_0_19_19, 0, all_73_0_103 and discharging atoms subset(all_73_1_104, all_0_19_19) = all_73_0_103, subset(all_73_1_104, all_0_19_19) = 0, yields: % 10.56/3.19 | (191) all_73_0_103 = 0 % 10.56/3.19 | % 10.56/3.19 | Equations (191) can reduce 176 to: % 10.56/3.19 | (158) $false % 10.56/3.19 | % 10.56/3.19 |-The branch is then unsatisfiable % 10.56/3.19 |-Branch two: % 10.56/3.19 | (205) ~ (all_96_1_150 = 0) & transfinite_sequence(all_0_18_18) = all_96_1_150 % 10.56/3.19 | % 10.56/3.19 | Applying alpha-rule on (205) yields: % 10.56/3.19 | (206) ~ (all_96_1_150 = 0) % 10.56/3.19 | (207) transfinite_sequence(all_0_18_18) = all_96_1_150 % 10.56/3.19 | % 10.56/3.19 | Instantiating formula (79) with all_0_18_18, 0, all_96_1_150 and discharging atoms transfinite_sequence(all_0_18_18) = all_96_1_150, transfinite_sequence(all_0_18_18) = 0, yields: % 10.56/3.19 | (208) all_96_1_150 = 0 % 10.56/3.19 | % 10.56/3.19 | Equations (208) can reduce 206 to: % 10.56/3.19 | (158) $false % 10.56/3.19 | % 10.56/3.19 |-The branch is then unsatisfiable % 10.56/3.19 |-Branch two: % 10.56/3.19 | (210) ~ (all_96_1_150 = 0) & relation(all_0_18_18) = all_96_1_150 % 10.56/3.19 | % 10.56/3.19 | Applying alpha-rule on (210) yields: % 10.56/3.19 | (206) ~ (all_96_1_150 = 0) % 10.56/3.19 | (212) relation(all_0_18_18) = all_96_1_150 % 10.56/3.19 | % 10.56/3.19 | Instantiating formula (126) with all_0_18_18, 0, all_96_1_150 and discharging atoms relation(all_0_18_18) = all_96_1_150, relation(all_0_18_18) = 0, yields: % 10.56/3.19 | (208) all_96_1_150 = 0 % 10.56/3.19 | % 10.56/3.19 | Equations (208) can reduce 206 to: % 10.56/3.19 | (158) $false % 10.56/3.19 | % 10.56/3.19 |-The branch is then unsatisfiable % 10.56/3.19 |-Branch two: % 10.56/3.19 | (215) ~ (all_96_1_150 = 0) & function(all_0_18_18) = all_96_1_150 % 10.56/3.19 | % 10.56/3.19 | Applying alpha-rule on (215) yields: % 10.56/3.19 | (206) ~ (all_96_1_150 = 0) % 10.56/3.19 | (217) function(all_0_18_18) = all_96_1_150 % 10.56/3.19 | % 10.56/3.19 | Instantiating formula (47) with all_0_18_18, 0, all_96_1_150 and discharging atoms function(all_0_18_18) = all_96_1_150, function(all_0_18_18) = 0, yields: % 10.56/3.19 | (208) all_96_1_150 = 0 % 10.56/3.19 | % 10.56/3.19 | Equations (208) can reduce 206 to: % 10.56/3.19 | (158) $false % 10.56/3.19 | % 10.56/3.19 |-The branch is then unsatisfiable % 10.56/3.19 % SZS output end Proof for theBenchmark % 10.56/3.19 % 10.56/3.19 2579ms %------------------------------------------------------------------------------