%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU241+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n027.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 08:48:03 EDT 2022 % Result : Theorem 10.60s 3.14s % Output : Proof 14.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU241+1 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n027.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 23:22:24 EDT 2022 % 0.12/0.33 % CPUTime : % 0.55/0.58 ____ _ % 0.55/0.58 ___ / __ \_____(_)___ ________ __________ % 0.55/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.55/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.55/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.55/0.58 % 0.55/0.58 A Theorem Prover for First-Order Logic % 0.55/0.58 (ePrincess v.1.0) % 0.55/0.58 % 0.55/0.58 (c) Philipp Rümmer, 2009-2015 % 0.55/0.58 (c) Peter Backeman, 2014-2015 % 0.55/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.55/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.55/0.58 Bug reports to peter@backeman.se % 0.55/0.58 % 0.55/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.55/0.58 % 0.55/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.73/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.56/0.95 Prover 0: Preprocessing ... % 2.15/1.18 Prover 0: Warning: ignoring some quantifiers % 2.24/1.21 Prover 0: Constructing countermodel ... % 8.10/2.64 Prover 0: gave up % 8.10/2.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 8.10/2.67 Prover 1: Preprocessing ... % 8.82/2.75 Prover 1: Warning: ignoring some quantifiers % 8.82/2.75 Prover 1: Constructing countermodel ... % 9.26/2.86 Prover 1: gave up % 9.26/2.86 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 9.26/2.89 Prover 2: Preprocessing ... % 9.80/2.99 Prover 2: Warning: ignoring some quantifiers % 9.80/2.99 Prover 2: Constructing countermodel ... % 10.60/3.14 Prover 2: proved (278ms) % 10.60/3.14 % 10.60/3.14 No countermodel exists, formula is valid % 10.60/3.14 % SZS status Theorem for theBenchmark % 10.60/3.14 % 10.60/3.14 Generating proof ... Warning: ignoring some quantifiers % 13.76/3.89 found it (size 164) % 13.76/3.89 % 13.76/3.89 % SZS output start Proof for theBenchmark % 13.76/3.89 Assumed formulas after preprocessing and simplification: % 13.76/3.89 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ( ~ (v10 = 0) & antisymmetric(v0) = v1 & one_to_one(v8) = 0 & relation(v13) = 0 & relation(v11) = 0 & relation(v8) = 0 & relation(v0) = 0 & function(v13) = 0 & function(v11) = 0 & function(v8) = 0 & empty(v12) = 0 & empty(v11) = 0 & empty(v9) = v10 & empty(empty_set) = 0 & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (ordered_pair(v17, v16) = v18) | ~ (is_antisymmetric_in(v14, v15) = 0) | ~ (relation(v14) = 0) | ? [v19] : ? [v20] : (( ~ (v20 = 0) & ordered_pair(v16, v17) = v19 & in(v19, v14) = v20) | ( ~ (v19 = 0) & in(v18, v14) = v19) | ( ~ (v19 = 0) & in(v17, v15) = v19) | ( ~ (v19 = 0) & in(v16, v15) = v19))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (ordered_pair(v16, v17) = v18) | ~ (is_antisymmetric_in(v14, v15) = 0) | ~ (relation(v14) = 0) | ? [v19] : ? [v20] : (( ~ (v20 = 0) & ordered_pair(v17, v16) = v19 & in(v19, v14) = v20) | ( ~ (v19 = 0) & in(v18, v14) = v19) | ( ~ (v19 = 0) & in(v17, v15) = v19) | ( ~ (v19 = 0) & in(v16, v15) = v19))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (element(v17, v16) = v15) | ~ (element(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 | ~ (is_antisymmetric_in(v17, v16) = v15) | ~ (is_antisymmetric_in(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] : ( ~ (ordered_pair(v14, v15) = v17) | ~ (in(v17, v16) = 0) | ? [v18] : ? [v19] : ? [v20] : ((v20 = 0 & v19 = 0 & relation_field(v16) = v18 & in(v15, v18) = 0 & in(v14, v18) = 0) | ( ~ (v18 = 0) & relation(v16) = v18))) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (element(v14, v15) = v16) | ? [v17] : ( ~ (v17 = 0) & in(v14, v15) = v17)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (is_antisymmetric_in(v14, v15) = v16) | ~ (relation(v14) = 0) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ( ~ (v18 = v17) & ordered_pair(v18, v17) = v20 & ordered_pair(v17, v18) = v19 & in(v20, v14) = 0 & in(v19, v14) = 0 & in(v18, v15) = 0 & 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 | ~ (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 | ~ (relation_field(v16) = v15) | ~ (relation_field(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (antisymmetric(v16) = v15) | ~ (antisymmetric(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 | ~ (function(v16) = v15) | ~ (function(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (empty(v16) = v15) | ~ (empty(v16) = v14)) & ! [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] : (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 | ~ (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] : ( ~ (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] : ( ~ (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_antisymmetric_in(v14, v15) = 0) | ( ~ (v16 = 0) & antisymmetric(v14) = v16)) & ((v16 = 0 & antisymmetric(v14) = 0) | ( ~ (v17 = 0) & is_antisymmetric_in(v14, v15) = v17))))) & ! [v14] : ! [v15] : ( ~ (antisymmetric(v14) = v15) | ? [v16] : ? [v17] : (( ~ (v16 = 0) & relation(v14) = v16) | (( ~ (v15 = 0) | (v17 = 0 & relation_field(v14) = v16 & is_antisymmetric_in(v14, v16) = 0)) & (v15 = 0 | ( ~ (v17 = 0) & relation_field(v14) = v16 & is_antisymmetric_in(v14, v16) = v17))))) & ! [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] : ( ~ (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_antisymmetric_in(v14, v16) = 0) | ( ~ (v15 = 0) & antisymmetric(v14) = v15)) & ((v15 = 0 & antisymmetric(v14) = 0) | ( ~ (v17 = 0) & relation_field(v14) = v16 & is_antisymmetric_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] : ( ~ (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] : ? [v15] : ? [v16] : element(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : ordered_pair(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : is_antisymmetric_in(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] : element(v15, v14) = 0 & ? [v14] : ? [v15] : relation_dom(v14) = v15 & ? [v14] : ? [v15] : relation_rng(v14) = v15 & ? [v14] : ? [v15] : singleton(v14) = v15 & ? [v14] : ? [v15] : relation_field(v14) = v15 & ? [v14] : ? [v15] : antisymmetric(v14) = v15 & ? [v14] : ? [v15] : one_to_one(v14) = v15 & ? [v14] : ? [v15] : relation(v14) = v15 & ? [v14] : ? [v15] : function(v14) = v15 & ? [v14] : ? [v15] : empty(v14) = v15 & ((v7 = 0 & v5 = 0 & v1 = 0 & ~ (v3 = v2) & ordered_pair(v3, v2) = v6 & ordered_pair(v2, v3) = v4 & in(v6, v0) = 0 & in(v4, v0) = 0) | ( ~ (v1 = 0) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (ordered_pair(v15, v14) = v16) | ? [v17] : ? [v18] : (( ~ (v18 = 0) & ordered_pair(v14, v15) = v17 & in(v17, v0) = v18) | ( ~ (v17 = 0) & in(v16, v0) = v17))) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (ordered_pair(v14, v15) = v16) | ? [v17] : ? [v18] : (( ~ (v18 = 0) & ordered_pair(v15, v14) = v17 & in(v17, v0) = v18) | ( ~ (v17 = 0) & in(v16, v0) = v17)))))) % 14.07/3.94 | 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: % 14.07/3.94 | (1) ~ (all_0_3_3 = 0) & antisymmetric(all_0_13_13) = all_0_12_12 & one_to_one(all_0_5_5) = 0 & relation(all_0_0_0) = 0 & relation(all_0_2_2) = 0 & relation(all_0_5_5) = 0 & relation(all_0_13_13) = 0 & function(all_0_0_0) = 0 & function(all_0_2_2) = 0 & function(all_0_5_5) = 0 & empty(all_0_1_1) = 0 & empty(all_0_2_2) = 0 & empty(all_0_4_4) = all_0_3_3 & empty(empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (ordered_pair(v3, v2) = v4) | ~ (is_antisymmetric_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = 0) & ordered_pair(v2, v3) = v5 & in(v5, v0) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5) | ( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v2, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (ordered_pair(v2, v3) = v4) | ~ (is_antisymmetric_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = 0) & ordered_pair(v3, v2) = v5 & in(v5, v0) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5) | ( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v2, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(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 | ~ (is_antisymmetric_in(v3, v2) = v1) | ~ (is_antisymmetric_in(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] : ( ~ (ordered_pair(v0, v1) = v3) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & relation_field(v2) = v4 & in(v1, v4) = 0 & in(v0, v4) = 0) | ( ~ (v4 = 0) & relation(v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (is_antisymmetric_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v4 = v3) & ordered_pair(v4, v3) = v6 & ordered_pair(v3, v4) = v5 & in(v6, v0) = 0 & in(v5, v0) = 0 & in(v4, v1) = 0 & 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 | ~ (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 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (antisymmetric(v2) = v1) | ~ (antisymmetric(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 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [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] : (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 | ~ (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] : ( ~ (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] : ( ~ (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_antisymmetric_in(v0, v1) = 0) | ( ~ (v2 = 0) & antisymmetric(v0) = v2)) & ((v2 = 0 & antisymmetric(v0) = 0) | ( ~ (v3 = 0) & is_antisymmetric_in(v0, v1) = v3))))) & ! [v0] : ! [v1] : ( ~ (antisymmetric(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & relation_field(v0) = v2 & is_antisymmetric_in(v0, v2) = 0)) & (v1 = 0 | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_antisymmetric_in(v0, v2) = v3))))) & ! [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] : ( ~ (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_antisymmetric_in(v0, v2) = 0) | ( ~ (v1 = 0) & antisymmetric(v0) = v1)) & ((v1 = 0 & antisymmetric(v0) = 0) | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_antisymmetric_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] : ( ~ (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] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : is_antisymmetric_in(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] : element(v1, v0) = 0 & ? [v0] : ? [v1] : relation_dom(v0) = v1 & ? [v0] : ? [v1] : relation_rng(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : relation_field(v0) = v1 & ? [v0] : ? [v1] : antisymmetric(v0) = v1 & ? [v0] : ? [v1] : one_to_one(v0) = v1 & ? [v0] : ? [v1] : relation(v0) = v1 & ? [v0] : ? [v1] : function(v0) = v1 & ? [v0] : ? [v1] : empty(v0) = v1 & ((all_0_6_6 = 0 & all_0_8_8 = 0 & all_0_12_12 = 0 & ~ (all_0_10_10 = all_0_11_11) & ordered_pair(all_0_10_10, all_0_11_11) = all_0_7_7 & ordered_pair(all_0_11_11, all_0_10_10) = all_0_9_9 & in(all_0_7_7, all_0_13_13) = 0 & in(all_0_9_9, all_0_13_13) = 0) | ( ~ (all_0_12_12 = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_0_13_13) = v4) | ( ~ (v3 = 0) & in(v2, all_0_13_13) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & ordered_pair(v1, v0) = v3 & in(v3, all_0_13_13) = v4) | ( ~ (v3 = 0) & in(v2, all_0_13_13) = v3))))) % 14.07/3.95 | % 14.07/3.95 | Applying alpha-rule on (1) yields: % 14.07/3.95 | (2) ! [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))) % 14.07/3.95 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (ordered_pair(v2, v3) = v4) | ~ (is_antisymmetric_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = 0) & ordered_pair(v3, v2) = v5 & in(v5, v0) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5) | ( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v2, v1) = v5))) % 14.07/3.95 | (4) ! [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))) % 14.07/3.95 | (5) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 14.07/3.96 | (6) function(all_0_5_5) = 0 % 14.07/3.96 | (7) ? [v0] : ? [v1] : function(v0) = v1 % 14.07/3.96 | (8) ! [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))) % 14.07/3.96 | (9) ? [v0] : ? [v1] : relation_field(v0) = v1 % 14.07/3.96 | (10) ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2 % 14.07/3.96 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 14.07/3.96 | (12) one_to_one(all_0_5_5) = 0 % 14.07/3.96 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3))) % 14.07/3.96 | (14) ! [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))) % 14.07/3.96 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) % 14.07/3.96 | (16) ~ (all_0_3_3 = 0) % 14.07/3.96 | (17) ? [v0] : ? [v1] : antisymmetric(v0) = v1 % 14.07/3.96 | (18) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 14.07/3.96 | (19) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (((v3 = 0 & is_antisymmetric_in(v0, v1) = 0) | ( ~ (v2 = 0) & antisymmetric(v0) = v2)) & ((v2 = 0 & antisymmetric(v0) = 0) | ( ~ (v3 = 0) & is_antisymmetric_in(v0, v1) = v3))))) % 14.07/3.96 | (20) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 % 14.07/3.96 | (21) (all_0_6_6 = 0 & all_0_8_8 = 0 & all_0_12_12 = 0 & ~ (all_0_10_10 = all_0_11_11) & ordered_pair(all_0_10_10, all_0_11_11) = all_0_7_7 & ordered_pair(all_0_11_11, all_0_10_10) = all_0_9_9 & in(all_0_7_7, all_0_13_13) = 0 & in(all_0_9_9, all_0_13_13) = 0) | ( ~ (all_0_12_12 = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_0_13_13) = v4) | ( ~ (v3 = 0) & in(v2, all_0_13_13) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & ordered_pair(v1, v0) = v3 & in(v3, all_0_13_13) = v4) | ( ~ (v3 = 0) & in(v2, all_0_13_13) = v3)))) % 14.07/3.96 | (22) ! [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))) % 14.07/3.96 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 14.07/3.96 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (is_antisymmetric_in(v3, v2) = v1) | ~ (is_antisymmetric_in(v3, v2) = v0)) % 14.07/3.96 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (ordered_pair(v3, v2) = v4) | ~ (is_antisymmetric_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = 0) & ordered_pair(v2, v3) = v5 & in(v5, v0) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5) | ( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v2, v1) = v5))) % 14.07/3.96 | (26) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_dom(v0) = v2 & relation_rng(v0) = v3 & relation_field(v0) = v1 & set_union2(v2, v3) = v1)) % 14.07/3.96 | (27) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 14.07/3.96 | (28) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 % 14.07/3.96 | (29) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 % 14.07/3.96 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 14.07/3.96 | (31) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) % 14.07/3.96 | (32) ! [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))) % 14.07/3.96 | (33) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 14.07/3.96 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 14.07/3.96 | (35) function(all_0_0_0) = 0 % 14.07/3.96 | (36) ? [v0] : ? [v1] : empty(v0) = v1 % 14.07/3.96 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 14.07/3.96 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 14.07/3.96 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) % 14.07/3.96 | (40) ! [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))) % 14.22/3.96 | (41) ? [v0] : ? [v1] : singleton(v0) = v1 % 14.22/3.96 | (42) ? [v0] : ? [v1] : relation(v0) = v1 % 14.22/3.96 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) % 14.22/3.96 | (44) empty(all_0_2_2) = 0 % 14.22/3.96 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ordered_pair(v0, v1) = v3) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & relation_field(v2) = v4 & in(v1, v4) = 0 & in(v0, v4) = 0) | ( ~ (v4 = 0) & relation(v2) = v4))) % 14.22/3.97 | (46) ? [v0] : ? [v1] : relation_dom(v0) = v1 % 14.22/3.97 | (47) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 14.22/3.97 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 14.22/3.97 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 14.22/3.97 | (50) function(all_0_2_2) = 0 % 14.22/3.97 | (51) ? [v0] : ? [v1] : ? [v2] : is_antisymmetric_in(v1, v0) = v2 % 14.22/3.97 | (52) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (is_antisymmetric_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v4 = v3) & ordered_pair(v4, v3) = v6 & ordered_pair(v3, v4) = v5 & in(v6, v0) = 0 & in(v5, v0) = 0 & in(v4, v1) = 0 & in(v3, v1) = 0)) % 14.22/3.97 | (53) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 14.22/3.97 | (54) relation(all_0_13_13) = 0 % 14.22/3.97 | (55) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 14.22/3.97 | (56) empty(all_0_4_4) = all_0_3_3 % 14.22/3.97 | (57) empty(empty_set) = 0 % 14.22/3.97 | (58) ? [v0] : ? [v1] : element(v1, v0) = 0 % 14.22/3.97 | (59) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) % 14.22/3.97 | (60) relation(all_0_2_2) = 0 % 14.22/3.97 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 14.22/3.97 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 14.22/3.97 | (63) ? [v0] : ? [v1] : relation_rng(v0) = v1 % 14.22/3.97 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 14.22/3.97 | (65) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 14.22/3.97 | (66) relation(all_0_5_5) = 0 % 14.22/3.97 | (67) relation(all_0_0_0) = 0 % 14.22/3.97 | (68) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 14.22/3.97 | (69) empty(all_0_1_1) = 0 % 14.22/3.97 | (70) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 14.22/3.97 | (71) antisymmetric(all_0_13_13) = all_0_12_12 % 14.22/3.97 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 14.22/3.97 | (73) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 14.22/3.97 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3)) % 14.22/3.97 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) % 14.22/3.97 | (76) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (antisymmetric(v2) = v1) | ~ (antisymmetric(v2) = v0)) % 14.22/3.97 | (77) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 14.22/3.97 | (78) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) % 14.22/3.97 | (79) ? [v0] : ? [v1] : one_to_one(v0) = v1 % 14.22/3.97 | (80) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & relation_field(v0) = v2 & is_antisymmetric_in(v0, v2) = 0) | ( ~ (v1 = 0) & antisymmetric(v0) = v1)) & ((v1 = 0 & antisymmetric(v0) = 0) | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_antisymmetric_in(v0, v2) = v3)))) % 14.22/3.97 | (81) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 14.22/3.97 | (82) ! [v0] : ! [v1] : ( ~ (antisymmetric(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & relation_field(v0) = v2 & is_antisymmetric_in(v0, v2) = 0)) & (v1 = 0 | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_antisymmetric_in(v0, v2) = v3))))) % 14.22/3.97 | (83) ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2 % 14.22/3.97 | (84) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) % 14.22/3.97 | % 14.22/3.97 | Instantiating formula (82) with all_0_12_12, all_0_13_13 and discharging atoms antisymmetric(all_0_13_13) = all_0_12_12, yields: % 14.22/3.97 | (85) ? [v0] : ? [v1] : (( ~ (v0 = 0) & relation(all_0_13_13) = v0) | (( ~ (all_0_12_12 = 0) | (v1 = 0 & relation_field(all_0_13_13) = v0 & is_antisymmetric_in(all_0_13_13, v0) = 0)) & (all_0_12_12 = 0 | ( ~ (v1 = 0) & relation_field(all_0_13_13) = v0 & is_antisymmetric_in(all_0_13_13, v0) = v1)))) % 14.22/3.97 | % 14.22/3.97 | Instantiating formula (26) with all_0_13_13 and discharging atoms relation(all_0_13_13) = 0, yields: % 14.22/3.97 | (86) ? [v0] : ? [v1] : ? [v2] : (relation_dom(all_0_13_13) = v1 & relation_rng(all_0_13_13) = v2 & relation_field(all_0_13_13) = v0 & set_union2(v1, v2) = v0) % 14.22/3.97 | % 14.22/3.97 | Instantiating formula (80) with all_0_13_13 and discharging atoms relation(all_0_13_13) = 0, yields: % 14.22/3.98 | (87) ? [v0] : ? [v1] : ? [v2] : (((v2 = 0 & relation_field(all_0_13_13) = v1 & is_antisymmetric_in(all_0_13_13, v1) = 0) | ( ~ (v0 = 0) & antisymmetric(all_0_13_13) = v0)) & ((v0 = 0 & antisymmetric(all_0_13_13) = 0) | ( ~ (v2 = 0) & relation_field(all_0_13_13) = v1 & is_antisymmetric_in(all_0_13_13, v1) = v2))) % 14.22/3.98 | % 14.22/3.98 | Instantiating (87) with all_50_0_66, all_50_1_67, all_50_2_68 yields: % 14.22/3.98 | (88) ((all_50_0_66 = 0 & relation_field(all_0_13_13) = all_50_1_67 & is_antisymmetric_in(all_0_13_13, all_50_1_67) = 0) | ( ~ (all_50_2_68 = 0) & antisymmetric(all_0_13_13) = all_50_2_68)) & ((all_50_2_68 = 0 & antisymmetric(all_0_13_13) = 0) | ( ~ (all_50_0_66 = 0) & relation_field(all_0_13_13) = all_50_1_67 & is_antisymmetric_in(all_0_13_13, all_50_1_67) = all_50_0_66)) % 14.22/3.98 | % 14.22/3.98 | Applying alpha-rule on (88) yields: % 14.22/3.98 | (89) (all_50_0_66 = 0 & relation_field(all_0_13_13) = all_50_1_67 & is_antisymmetric_in(all_0_13_13, all_50_1_67) = 0) | ( ~ (all_50_2_68 = 0) & antisymmetric(all_0_13_13) = all_50_2_68) % 14.22/3.98 | (90) (all_50_2_68 = 0 & antisymmetric(all_0_13_13) = 0) | ( ~ (all_50_0_66 = 0) & relation_field(all_0_13_13) = all_50_1_67 & is_antisymmetric_in(all_0_13_13, all_50_1_67) = all_50_0_66) % 14.22/3.98 | % 14.22/3.98 | Instantiating (86) with all_51_0_69, all_51_1_70, all_51_2_71 yields: % 14.22/3.98 | (91) relation_dom(all_0_13_13) = all_51_1_70 & relation_rng(all_0_13_13) = all_51_0_69 & relation_field(all_0_13_13) = all_51_2_71 & set_union2(all_51_1_70, all_51_0_69) = all_51_2_71 % 14.22/3.98 | % 14.22/3.98 | Applying alpha-rule on (91) yields: % 14.22/3.98 | (92) relation_dom(all_0_13_13) = all_51_1_70 % 14.22/3.98 | (93) relation_rng(all_0_13_13) = all_51_0_69 % 14.22/3.98 | (94) relation_field(all_0_13_13) = all_51_2_71 % 14.22/3.98 | (95) set_union2(all_51_1_70, all_51_0_69) = all_51_2_71 % 14.22/3.98 | % 14.22/3.98 | Instantiating (85) with all_60_0_84, all_60_1_85 yields: % 14.22/3.98 | (96) ( ~ (all_60_1_85 = 0) & relation(all_0_13_13) = all_60_1_85) | (( ~ (all_0_12_12 = 0) | (all_60_0_84 = 0 & relation_field(all_0_13_13) = all_60_1_85 & is_antisymmetric_in(all_0_13_13, all_60_1_85) = 0)) & (all_0_12_12 = 0 | ( ~ (all_60_0_84 = 0) & relation_field(all_0_13_13) = all_60_1_85 & is_antisymmetric_in(all_0_13_13, all_60_1_85) = all_60_0_84))) % 14.22/3.98 | % 14.22/3.98 | Instantiating formula (19) with all_51_2_71, all_0_13_13 and discharging atoms relation_field(all_0_13_13) = all_51_2_71, yields: % 14.22/3.98 | (97) ? [v0] : ? [v1] : (( ~ (v0 = 0) & relation(all_0_13_13) = v0) | (((v1 = 0 & is_antisymmetric_in(all_0_13_13, all_51_2_71) = 0) | ( ~ (v0 = 0) & antisymmetric(all_0_13_13) = v0)) & ((v0 = 0 & antisymmetric(all_0_13_13) = 0) | ( ~ (v1 = 0) & is_antisymmetric_in(all_0_13_13, all_51_2_71) = v1)))) % 14.22/3.98 | % 14.22/3.98 | Instantiating (97) with all_93_0_107, all_93_1_108 yields: % 14.22/3.98 | (98) ( ~ (all_93_1_108 = 0) & relation(all_0_13_13) = all_93_1_108) | (((all_93_0_107 = 0 & is_antisymmetric_in(all_0_13_13, all_51_2_71) = 0) | ( ~ (all_93_1_108 = 0) & antisymmetric(all_0_13_13) = all_93_1_108)) & ((all_93_1_108 = 0 & antisymmetric(all_0_13_13) = 0) | ( ~ (all_93_0_107 = 0) & is_antisymmetric_in(all_0_13_13, all_51_2_71) = all_93_0_107))) % 14.22/3.98 | % 14.22/3.98 +-Applying beta-rule and splitting (21), into two cases. % 14.22/3.98 |-Branch one: % 14.22/3.98 | (99) all_0_6_6 = 0 & all_0_8_8 = 0 & all_0_12_12 = 0 & ~ (all_0_10_10 = all_0_11_11) & ordered_pair(all_0_10_10, all_0_11_11) = all_0_7_7 & ordered_pair(all_0_11_11, all_0_10_10) = all_0_9_9 & in(all_0_7_7, all_0_13_13) = 0 & in(all_0_9_9, all_0_13_13) = 0 % 14.22/3.98 | % 14.22/3.98 | Applying alpha-rule on (99) yields: % 14.22/3.98 | (100) ~ (all_0_10_10 = all_0_11_11) % 14.22/3.98 | (101) all_0_8_8 = 0 % 14.22/3.98 | (102) in(all_0_9_9, all_0_13_13) = 0 % 14.22/3.98 | (103) all_0_6_6 = 0 % 14.22/3.98 | (104) in(all_0_7_7, all_0_13_13) = 0 % 14.22/3.98 | (105) ordered_pair(all_0_11_11, all_0_10_10) = all_0_9_9 % 14.22/3.98 | (106) all_0_12_12 = 0 % 14.22/3.98 | (107) ordered_pair(all_0_10_10, all_0_11_11) = all_0_7_7 % 14.22/3.98 | % 14.22/3.98 | From (106) and (71) follows: % 14.22/3.98 | (108) antisymmetric(all_0_13_13) = 0 % 14.22/3.98 | % 14.22/3.98 +-Applying beta-rule and splitting (89), into two cases. % 14.22/3.98 |-Branch one: % 14.22/3.98 | (109) all_50_0_66 = 0 & relation_field(all_0_13_13) = all_50_1_67 & is_antisymmetric_in(all_0_13_13, all_50_1_67) = 0 % 14.22/3.98 | % 14.22/3.98 | Applying alpha-rule on (109) yields: % 14.22/3.98 | (110) all_50_0_66 = 0 % 14.22/3.98 | (111) relation_field(all_0_13_13) = all_50_1_67 % 14.22/3.98 | (112) is_antisymmetric_in(all_0_13_13, all_50_1_67) = 0 % 14.22/3.98 | % 14.22/3.98 +-Applying beta-rule and splitting (98), into two cases. % 14.22/3.98 |-Branch one: % 14.22/3.98 | (113) ~ (all_93_1_108 = 0) & relation(all_0_13_13) = all_93_1_108 % 14.22/3.98 | % 14.22/3.98 | Applying alpha-rule on (113) yields: % 14.22/3.98 | (114) ~ (all_93_1_108 = 0) % 14.22/3.98 | (115) relation(all_0_13_13) = all_93_1_108 % 14.22/3.98 | % 14.22/3.98 | Instantiating formula (55) with all_0_13_13, all_93_1_108, 0 and discharging atoms relation(all_0_13_13) = all_93_1_108, relation(all_0_13_13) = 0, yields: % 14.22/3.98 | (116) all_93_1_108 = 0 % 14.22/3.98 | % 14.22/3.98 | Equations (116) can reduce 114 to: % 14.22/3.98 | (117) $false % 14.22/3.98 | % 14.22/3.98 |-The branch is then unsatisfiable % 14.22/3.98 |-Branch two: % 14.22/3.98 | (118) ((all_93_0_107 = 0 & is_antisymmetric_in(all_0_13_13, all_51_2_71) = 0) | ( ~ (all_93_1_108 = 0) & antisymmetric(all_0_13_13) = all_93_1_108)) & ((all_93_1_108 = 0 & antisymmetric(all_0_13_13) = 0) | ( ~ (all_93_0_107 = 0) & is_antisymmetric_in(all_0_13_13, all_51_2_71) = all_93_0_107)) % 14.22/3.98 | % 14.22/3.98 | Applying alpha-rule on (118) yields: % 14.22/3.98 | (119) (all_93_0_107 = 0 & is_antisymmetric_in(all_0_13_13, all_51_2_71) = 0) | ( ~ (all_93_1_108 = 0) & antisymmetric(all_0_13_13) = all_93_1_108) % 14.22/3.98 | (120) (all_93_1_108 = 0 & antisymmetric(all_0_13_13) = 0) | ( ~ (all_93_0_107 = 0) & is_antisymmetric_in(all_0_13_13, all_51_2_71) = all_93_0_107) % 14.22/3.98 | % 14.22/3.98 +-Applying beta-rule and splitting (90), into two cases. % 14.22/3.98 |-Branch one: % 14.22/3.98 | (121) all_50_2_68 = 0 & antisymmetric(all_0_13_13) = 0 % 14.22/3.98 | % 14.22/3.98 | Applying alpha-rule on (121) yields: % 14.22/3.98 | (122) all_50_2_68 = 0 % 14.22/3.98 | (108) antisymmetric(all_0_13_13) = 0 % 14.22/3.98 | % 14.22/3.98 +-Applying beta-rule and splitting (119), into two cases. % 14.22/3.98 |-Branch one: % 14.22/3.98 | (124) all_93_0_107 = 0 & is_antisymmetric_in(all_0_13_13, all_51_2_71) = 0 % 14.22/3.98 | % 14.22/3.98 | Applying alpha-rule on (124) yields: % 14.22/3.98 | (125) all_93_0_107 = 0 % 14.22/3.98 | (126) is_antisymmetric_in(all_0_13_13, all_51_2_71) = 0 % 14.22/3.99 | % 14.22/3.99 +-Applying beta-rule and splitting (96), into two cases. % 14.22/3.99 |-Branch one: % 14.22/3.99 | (127) ~ (all_60_1_85 = 0) & relation(all_0_13_13) = all_60_1_85 % 14.22/3.99 | % 14.22/3.99 | Applying alpha-rule on (127) yields: % 14.22/3.99 | (128) ~ (all_60_1_85 = 0) % 14.22/3.99 | (129) relation(all_0_13_13) = all_60_1_85 % 14.22/3.99 | % 14.22/3.99 | Instantiating formula (55) with all_0_13_13, all_60_1_85, 0 and discharging atoms relation(all_0_13_13) = all_60_1_85, relation(all_0_13_13) = 0, yields: % 14.22/3.99 | (130) all_60_1_85 = 0 % 14.22/3.99 | % 14.22/3.99 | Equations (130) can reduce 128 to: % 14.22/3.99 | (117) $false % 14.22/3.99 | % 14.22/3.99 |-The branch is then unsatisfiable % 14.22/3.99 |-Branch two: % 14.22/3.99 | (132) ( ~ (all_0_12_12 = 0) | (all_60_0_84 = 0 & relation_field(all_0_13_13) = all_60_1_85 & is_antisymmetric_in(all_0_13_13, all_60_1_85) = 0)) & (all_0_12_12 = 0 | ( ~ (all_60_0_84 = 0) & relation_field(all_0_13_13) = all_60_1_85 & is_antisymmetric_in(all_0_13_13, all_60_1_85) = all_60_0_84)) % 14.22/3.99 | % 14.22/3.99 | Applying alpha-rule on (132) yields: % 14.22/3.99 | (133) ~ (all_0_12_12 = 0) | (all_60_0_84 = 0 & relation_field(all_0_13_13) = all_60_1_85 & is_antisymmetric_in(all_0_13_13, all_60_1_85) = 0) % 14.22/3.99 | (134) all_0_12_12 = 0 | ( ~ (all_60_0_84 = 0) & relation_field(all_0_13_13) = all_60_1_85 & is_antisymmetric_in(all_0_13_13, all_60_1_85) = all_60_0_84) % 14.22/3.99 | % 14.22/3.99 +-Applying beta-rule and splitting (133), into two cases. % 14.22/3.99 |-Branch one: % 14.22/3.99 | (135) ~ (all_0_12_12 = 0) % 14.22/3.99 | % 14.22/3.99 | Equations (106) can reduce 135 to: % 14.22/3.99 | (117) $false % 14.22/3.99 | % 14.22/3.99 |-The branch is then unsatisfiable % 14.22/3.99 |-Branch two: % 14.22/3.99 | (106) all_0_12_12 = 0 % 14.22/3.99 | (138) all_60_0_84 = 0 & relation_field(all_0_13_13) = all_60_1_85 & is_antisymmetric_in(all_0_13_13, all_60_1_85) = 0 % 14.22/3.99 | % 14.22/3.99 | Applying alpha-rule on (138) yields: % 14.22/3.99 | (139) all_60_0_84 = 0 % 14.22/3.99 | (140) relation_field(all_0_13_13) = all_60_1_85 % 14.22/3.99 | (141) is_antisymmetric_in(all_0_13_13, all_60_1_85) = 0 % 14.22/3.99 | % 14.22/3.99 | Instantiating formula (43) with all_0_13_13, all_60_1_85, all_51_2_71 and discharging atoms relation_field(all_0_13_13) = all_60_1_85, relation_field(all_0_13_13) = all_51_2_71, yields: % 14.22/3.99 | (142) all_60_1_85 = all_51_2_71 % 14.22/3.99 | % 14.22/3.99 | Instantiating formula (43) with all_0_13_13, all_50_1_67, all_60_1_85 and discharging atoms relation_field(all_0_13_13) = all_60_1_85, relation_field(all_0_13_13) = all_50_1_67, yields: % 14.22/3.99 | (143) all_60_1_85 = all_50_1_67 % 14.22/3.99 | % 14.22/3.99 | Combining equations (142,143) yields a new equation: % 14.22/3.99 | (144) all_51_2_71 = all_50_1_67 % 14.22/3.99 | % 14.22/3.99 | Simplifying 144 yields: % 14.22/3.99 | (145) all_51_2_71 = all_50_1_67 % 14.22/3.99 | % 14.22/3.99 | From (145) and (94) follows: % 14.22/3.99 | (111) relation_field(all_0_13_13) = all_50_1_67 % 14.22/3.99 | % 14.22/3.99 | From (145) and (126) follows: % 14.22/3.99 | (112) is_antisymmetric_in(all_0_13_13, all_50_1_67) = 0 % 14.22/3.99 | % 14.22/3.99 | Instantiating formula (25) with all_0_7_7, all_0_10_10, all_0_11_11, all_50_1_67, all_0_13_13 and discharging atoms ordered_pair(all_0_10_10, all_0_11_11) = all_0_7_7, is_antisymmetric_in(all_0_13_13, all_50_1_67) = 0, relation(all_0_13_13) = 0, yields: % 14.22/3.99 | (148) all_0_10_10 = all_0_11_11 | ? [v0] : ? [v1] : (( ~ (v1 = 0) & ordered_pair(all_0_11_11, all_0_10_10) = v0 & in(v0, all_0_13_13) = v1) | ( ~ (v0 = 0) & in(all_0_7_7, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_0_10_10, all_50_1_67) = v0) | ( ~ (v0 = 0) & in(all_0_11_11, all_50_1_67) = v0)) % 14.22/3.99 | % 14.22/3.99 | Instantiating formula (45) with all_0_9_9, all_0_13_13, all_0_10_10, all_0_11_11 and discharging atoms ordered_pair(all_0_11_11, all_0_10_10) = all_0_9_9, in(all_0_9_9, all_0_13_13) = 0, yields: % 14.22/3.99 | (149) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & relation_field(all_0_13_13) = v0 & in(all_0_10_10, v0) = 0 & in(all_0_11_11, v0) = 0) | ( ~ (v0 = 0) & relation(all_0_13_13) = v0)) % 14.22/3.99 | % 14.22/3.99 | Instantiating (149) with all_152_0_125, all_152_1_126, all_152_2_127 yields: % 14.22/3.99 | (150) (all_152_0_125 = 0 & all_152_1_126 = 0 & relation_field(all_0_13_13) = all_152_2_127 & in(all_0_10_10, all_152_2_127) = 0 & in(all_0_11_11, all_152_2_127) = 0) | ( ~ (all_152_2_127 = 0) & relation(all_0_13_13) = all_152_2_127) % 14.22/3.99 | % 14.22/3.99 +-Applying beta-rule and splitting (150), into two cases. % 14.22/3.99 |-Branch one: % 14.22/3.99 | (151) all_152_0_125 = 0 & all_152_1_126 = 0 & relation_field(all_0_13_13) = all_152_2_127 & in(all_0_10_10, all_152_2_127) = 0 & in(all_0_11_11, all_152_2_127) = 0 % 14.22/3.99 | % 14.22/3.99 | Applying alpha-rule on (151) yields: % 14.22/3.99 | (152) all_152_1_126 = 0 % 14.22/3.99 | (153) all_152_0_125 = 0 % 14.22/3.99 | (154) relation_field(all_0_13_13) = all_152_2_127 % 14.22/3.99 | (155) in(all_0_11_11, all_152_2_127) = 0 % 14.22/3.99 | (156) in(all_0_10_10, all_152_2_127) = 0 % 14.22/3.99 | % 14.22/3.99 +-Applying beta-rule and splitting (148), into two cases. % 14.22/3.99 |-Branch one: % 14.22/3.99 | (157) all_0_10_10 = all_0_11_11 % 14.22/3.99 | % 14.22/3.99 | Equations (157) can reduce 100 to: % 14.22/3.99 | (117) $false % 14.22/3.99 | % 14.22/3.99 |-The branch is then unsatisfiable % 14.22/3.99 |-Branch two: % 14.22/3.99 | (100) ~ (all_0_10_10 = all_0_11_11) % 14.22/3.99 | (160) ? [v0] : ? [v1] : (( ~ (v1 = 0) & ordered_pair(all_0_11_11, all_0_10_10) = v0 & in(v0, all_0_13_13) = v1) | ( ~ (v0 = 0) & in(all_0_7_7, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_0_10_10, all_50_1_67) = v0) | ( ~ (v0 = 0) & in(all_0_11_11, all_50_1_67) = v0)) % 14.22/3.99 | % 14.22/3.99 | Instantiating (160) with all_168_0_134, all_168_1_135 yields: % 14.22/3.99 | (161) ( ~ (all_168_0_134 = 0) & ordered_pair(all_0_11_11, all_0_10_10) = all_168_1_135 & in(all_168_1_135, all_0_13_13) = all_168_0_134) | ( ~ (all_168_1_135 = 0) & in(all_0_7_7, all_0_13_13) = all_168_1_135) | ( ~ (all_168_1_135 = 0) & in(all_0_10_10, all_50_1_67) = all_168_1_135) | ( ~ (all_168_1_135 = 0) & in(all_0_11_11, all_50_1_67) = all_168_1_135) % 14.22/3.99 | % 14.22/3.99 | Instantiating formula (43) with all_0_13_13, all_152_2_127, all_50_1_67 and discharging atoms relation_field(all_0_13_13) = all_152_2_127, relation_field(all_0_13_13) = all_50_1_67, yields: % 14.22/3.99 | (162) all_152_2_127 = all_50_1_67 % 14.22/3.99 | % 14.22/3.99 | From (162) and (156) follows: % 14.22/3.99 | (163) in(all_0_10_10, all_50_1_67) = 0 % 14.22/3.99 | % 14.22/3.99 | From (162) and (155) follows: % 14.22/3.99 | (164) in(all_0_11_11, all_50_1_67) = 0 % 14.22/3.99 | % 14.22/3.99 +-Applying beta-rule and splitting (161), into two cases. % 14.22/3.99 |-Branch one: % 14.22/3.99 | (165) ( ~ (all_168_0_134 = 0) & ordered_pair(all_0_11_11, all_0_10_10) = all_168_1_135 & in(all_168_1_135, all_0_13_13) = all_168_0_134) | ( ~ (all_168_1_135 = 0) & in(all_0_7_7, all_0_13_13) = all_168_1_135) | ( ~ (all_168_1_135 = 0) & in(all_0_10_10, all_50_1_67) = all_168_1_135) % 14.22/3.99 | % 14.22/3.99 +-Applying beta-rule and splitting (165), into two cases. % 14.22/3.99 |-Branch one: % 14.22/3.99 | (166) ( ~ (all_168_0_134 = 0) & ordered_pair(all_0_11_11, all_0_10_10) = all_168_1_135 & in(all_168_1_135, all_0_13_13) = all_168_0_134) | ( ~ (all_168_1_135 = 0) & in(all_0_7_7, all_0_13_13) = all_168_1_135) % 14.22/3.99 | % 14.22/3.99 +-Applying beta-rule and splitting (166), into two cases. % 14.22/3.99 |-Branch one: % 14.22/3.99 | (167) ~ (all_168_0_134 = 0) & ordered_pair(all_0_11_11, all_0_10_10) = all_168_1_135 & in(all_168_1_135, all_0_13_13) = all_168_0_134 % 14.22/3.99 | % 14.22/3.99 | Applying alpha-rule on (167) yields: % 14.22/3.99 | (168) ~ (all_168_0_134 = 0) % 14.22/4.00 | (169) ordered_pair(all_0_11_11, all_0_10_10) = all_168_1_135 % 14.22/4.00 | (170) in(all_168_1_135, all_0_13_13) = all_168_0_134 % 14.22/4.00 | % 14.22/4.00 | Instantiating formula (64) with all_0_11_11, all_0_10_10, all_168_1_135, all_0_9_9 and discharging atoms ordered_pair(all_0_11_11, all_0_10_10) = all_168_1_135, ordered_pair(all_0_11_11, all_0_10_10) = all_0_9_9, yields: % 14.22/4.00 | (171) all_168_1_135 = all_0_9_9 % 14.22/4.00 | % 14.22/4.00 | From (171) and (170) follows: % 14.22/4.00 | (172) in(all_0_9_9, all_0_13_13) = all_168_0_134 % 14.22/4.00 | % 14.22/4.00 | Instantiating formula (30) with all_0_9_9, all_0_13_13, all_168_0_134, 0 and discharging atoms in(all_0_9_9, all_0_13_13) = all_168_0_134, in(all_0_9_9, all_0_13_13) = 0, yields: % 14.22/4.00 | (173) all_168_0_134 = 0 % 14.22/4.00 | % 14.22/4.00 | Equations (173) can reduce 168 to: % 14.22/4.00 | (117) $false % 14.22/4.00 | % 14.22/4.00 |-The branch is then unsatisfiable % 14.22/4.00 |-Branch two: % 14.22/4.00 | (175) ~ (all_168_1_135 = 0) & in(all_0_7_7, all_0_13_13) = all_168_1_135 % 14.22/4.00 | % 14.22/4.00 | Applying alpha-rule on (175) yields: % 14.22/4.00 | (176) ~ (all_168_1_135 = 0) % 14.22/4.00 | (177) in(all_0_7_7, all_0_13_13) = all_168_1_135 % 14.22/4.00 | % 14.22/4.00 | Instantiating formula (30) with all_0_7_7, all_0_13_13, all_168_1_135, 0 and discharging atoms in(all_0_7_7, all_0_13_13) = all_168_1_135, in(all_0_7_7, all_0_13_13) = 0, yields: % 14.22/4.00 | (178) all_168_1_135 = 0 % 14.22/4.00 | % 14.22/4.00 | Equations (178) can reduce 176 to: % 14.22/4.00 | (117) $false % 14.22/4.00 | % 14.22/4.00 |-The branch is then unsatisfiable % 14.22/4.00 |-Branch two: % 14.22/4.00 | (180) ~ (all_168_1_135 = 0) & in(all_0_10_10, all_50_1_67) = all_168_1_135 % 14.22/4.00 | % 14.22/4.00 | Applying alpha-rule on (180) yields: % 14.22/4.00 | (176) ~ (all_168_1_135 = 0) % 14.22/4.00 | (182) in(all_0_10_10, all_50_1_67) = all_168_1_135 % 14.22/4.00 | % 14.22/4.00 | Instantiating formula (30) with all_0_10_10, all_50_1_67, 0, all_168_1_135 and discharging atoms in(all_0_10_10, all_50_1_67) = all_168_1_135, in(all_0_10_10, all_50_1_67) = 0, yields: % 14.22/4.00 | (178) all_168_1_135 = 0 % 14.22/4.00 | % 14.22/4.00 | Equations (178) can reduce 176 to: % 14.22/4.00 | (117) $false % 14.22/4.00 | % 14.22/4.00 |-The branch is then unsatisfiable % 14.22/4.00 |-Branch two: % 14.22/4.00 | (185) ~ (all_168_1_135 = 0) & in(all_0_11_11, all_50_1_67) = all_168_1_135 % 14.22/4.00 | % 14.22/4.00 | Applying alpha-rule on (185) yields: % 14.22/4.00 | (176) ~ (all_168_1_135 = 0) % 14.22/4.00 | (187) in(all_0_11_11, all_50_1_67) = all_168_1_135 % 14.22/4.00 | % 14.22/4.00 | Instantiating formula (30) with all_0_11_11, all_50_1_67, 0, all_168_1_135 and discharging atoms in(all_0_11_11, all_50_1_67) = all_168_1_135, in(all_0_11_11, all_50_1_67) = 0, yields: % 14.22/4.00 | (178) all_168_1_135 = 0 % 14.22/4.00 | % 14.22/4.00 | Equations (178) can reduce 176 to: % 14.22/4.00 | (117) $false % 14.22/4.00 | % 14.22/4.00 |-The branch is then unsatisfiable % 14.22/4.00 |-Branch two: % 14.22/4.00 | (190) ~ (all_152_2_127 = 0) & relation(all_0_13_13) = all_152_2_127 % 14.22/4.00 | % 14.22/4.00 | Applying alpha-rule on (190) yields: % 14.22/4.00 | (191) ~ (all_152_2_127 = 0) % 14.22/4.00 | (192) relation(all_0_13_13) = all_152_2_127 % 14.22/4.00 | % 14.22/4.00 | Instantiating formula (55) with all_0_13_13, all_152_2_127, 0 and discharging atoms relation(all_0_13_13) = all_152_2_127, relation(all_0_13_13) = 0, yields: % 14.22/4.00 | (193) all_152_2_127 = 0 % 14.22/4.00 | % 14.22/4.00 | Equations (193) can reduce 191 to: % 14.22/4.00 | (117) $false % 14.22/4.00 | % 14.22/4.00 |-The branch is then unsatisfiable % 14.22/4.00 |-Branch two: % 14.22/4.00 | (195) ~ (all_93_1_108 = 0) & antisymmetric(all_0_13_13) = all_93_1_108 % 14.22/4.00 | % 14.22/4.00 | Applying alpha-rule on (195) yields: % 14.22/4.00 | (114) ~ (all_93_1_108 = 0) % 14.22/4.00 | (197) antisymmetric(all_0_13_13) = all_93_1_108 % 14.22/4.00 | % 14.22/4.00 | Instantiating formula (76) with all_0_13_13, 0, all_93_1_108 and discharging atoms antisymmetric(all_0_13_13) = all_93_1_108, antisymmetric(all_0_13_13) = 0, yields: % 14.22/4.00 | (116) all_93_1_108 = 0 % 14.22/4.00 | % 14.22/4.00 | Equations (116) can reduce 114 to: % 14.22/4.00 | (117) $false % 14.22/4.00 | % 14.22/4.00 |-The branch is then unsatisfiable % 14.22/4.00 |-Branch two: % 14.22/4.00 | (200) ~ (all_50_0_66 = 0) & relation_field(all_0_13_13) = all_50_1_67 & is_antisymmetric_in(all_0_13_13, all_50_1_67) = all_50_0_66 % 14.22/4.00 | % 14.22/4.00 | Applying alpha-rule on (200) yields: % 14.22/4.00 | (201) ~ (all_50_0_66 = 0) % 14.22/4.00 | (111) relation_field(all_0_13_13) = all_50_1_67 % 14.22/4.00 | (203) is_antisymmetric_in(all_0_13_13, all_50_1_67) = all_50_0_66 % 14.22/4.00 | % 14.22/4.00 | Equations (110) can reduce 201 to: % 14.22/4.00 | (117) $false % 14.22/4.00 | % 14.22/4.00 |-The branch is then unsatisfiable % 14.22/4.00 |-Branch two: % 14.22/4.00 | (205) ~ (all_50_2_68 = 0) & antisymmetric(all_0_13_13) = all_50_2_68 % 14.22/4.00 | % 14.22/4.00 | Applying alpha-rule on (205) yields: % 14.22/4.00 | (206) ~ (all_50_2_68 = 0) % 14.22/4.00 | (207) antisymmetric(all_0_13_13) = all_50_2_68 % 14.22/4.00 | % 14.22/4.00 | Instantiating formula (76) with all_0_13_13, 0, all_50_2_68 and discharging atoms antisymmetric(all_0_13_13) = all_50_2_68, antisymmetric(all_0_13_13) = 0, yields: % 14.22/4.00 | (122) all_50_2_68 = 0 % 14.22/4.00 | % 14.22/4.00 | Equations (122) can reduce 206 to: % 14.22/4.00 | (117) $false % 14.22/4.00 | % 14.22/4.00 |-The branch is then unsatisfiable % 14.22/4.00 |-Branch two: % 14.22/4.00 | (210) ~ (all_0_12_12 = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_0_13_13) = v4) | ( ~ (v3 = 0) & in(v2, all_0_13_13) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & ordered_pair(v1, v0) = v3 & in(v3, all_0_13_13) = v4) | ( ~ (v3 = 0) & in(v2, all_0_13_13) = v3))) % 14.22/4.00 | % 14.22/4.00 | Applying alpha-rule on (210) yields: % 14.22/4.00 | (135) ~ (all_0_12_12 = 0) % 14.22/4.00 | (212) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_0_13_13) = v4) | ( ~ (v3 = 0) & in(v2, all_0_13_13) = v3))) % 14.22/4.00 | (213) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & ordered_pair(v1, v0) = v3 & in(v3, all_0_13_13) = v4) | ( ~ (v3 = 0) & in(v2, all_0_13_13) = v3))) % 14.22/4.00 | % 14.22/4.00 +-Applying beta-rule and splitting (96), into two cases. % 14.22/4.00 |-Branch one: % 14.22/4.00 | (127) ~ (all_60_1_85 = 0) & relation(all_0_13_13) = all_60_1_85 % 14.22/4.00 | % 14.22/4.00 | Applying alpha-rule on (127) yields: % 14.22/4.00 | (128) ~ (all_60_1_85 = 0) % 14.22/4.00 | (129) relation(all_0_13_13) = all_60_1_85 % 14.22/4.00 | % 14.22/4.00 | Instantiating formula (55) with all_0_13_13, all_60_1_85, 0 and discharging atoms relation(all_0_13_13) = all_60_1_85, relation(all_0_13_13) = 0, yields: % 14.22/4.00 | (130) all_60_1_85 = 0 % 14.22/4.00 | % 14.22/4.00 | Equations (130) can reduce 128 to: % 14.22/4.00 | (117) $false % 14.22/4.00 | % 14.22/4.00 |-The branch is then unsatisfiable % 14.22/4.00 |-Branch two: % 14.22/4.00 | (132) ( ~ (all_0_12_12 = 0) | (all_60_0_84 = 0 & relation_field(all_0_13_13) = all_60_1_85 & is_antisymmetric_in(all_0_13_13, all_60_1_85) = 0)) & (all_0_12_12 = 0 | ( ~ (all_60_0_84 = 0) & relation_field(all_0_13_13) = all_60_1_85 & is_antisymmetric_in(all_0_13_13, all_60_1_85) = all_60_0_84)) % 14.22/4.00 | % 14.22/4.00 | Applying alpha-rule on (132) yields: % 14.22/4.00 | (133) ~ (all_0_12_12 = 0) | (all_60_0_84 = 0 & relation_field(all_0_13_13) = all_60_1_85 & is_antisymmetric_in(all_0_13_13, all_60_1_85) = 0) % 14.22/4.01 | (134) all_0_12_12 = 0 | ( ~ (all_60_0_84 = 0) & relation_field(all_0_13_13) = all_60_1_85 & is_antisymmetric_in(all_0_13_13, all_60_1_85) = all_60_0_84) % 14.22/4.01 | % 14.22/4.01 +-Applying beta-rule and splitting (98), into two cases. % 14.22/4.01 |-Branch one: % 14.22/4.01 | (113) ~ (all_93_1_108 = 0) & relation(all_0_13_13) = all_93_1_108 % 14.22/4.01 | % 14.22/4.01 | Applying alpha-rule on (113) yields: % 14.22/4.01 | (114) ~ (all_93_1_108 = 0) % 14.22/4.01 | (115) relation(all_0_13_13) = all_93_1_108 % 14.22/4.01 | % 14.22/4.01 | Instantiating formula (55) with all_0_13_13, all_93_1_108, 0 and discharging atoms relation(all_0_13_13) = all_93_1_108, relation(all_0_13_13) = 0, yields: % 14.22/4.01 | (116) all_93_1_108 = 0 % 14.22/4.01 | % 14.22/4.01 | Equations (116) can reduce 114 to: % 14.22/4.01 | (117) $false % 14.22/4.01 | % 14.22/4.01 |-The branch is then unsatisfiable % 14.22/4.01 |-Branch two: % 14.22/4.01 | (118) ((all_93_0_107 = 0 & is_antisymmetric_in(all_0_13_13, all_51_2_71) = 0) | ( ~ (all_93_1_108 = 0) & antisymmetric(all_0_13_13) = all_93_1_108)) & ((all_93_1_108 = 0 & antisymmetric(all_0_13_13) = 0) | ( ~ (all_93_0_107 = 0) & is_antisymmetric_in(all_0_13_13, all_51_2_71) = all_93_0_107)) % 14.22/4.01 | % 14.22/4.01 | Applying alpha-rule on (118) yields: % 14.22/4.01 | (119) (all_93_0_107 = 0 & is_antisymmetric_in(all_0_13_13, all_51_2_71) = 0) | ( ~ (all_93_1_108 = 0) & antisymmetric(all_0_13_13) = all_93_1_108) % 14.22/4.01 | (120) (all_93_1_108 = 0 & antisymmetric(all_0_13_13) = 0) | ( ~ (all_93_0_107 = 0) & is_antisymmetric_in(all_0_13_13, all_51_2_71) = all_93_0_107) % 14.22/4.01 | % 14.22/4.01 +-Applying beta-rule and splitting (120), into two cases. % 14.22/4.01 |-Branch one: % 14.22/4.01 | (230) all_93_1_108 = 0 & antisymmetric(all_0_13_13) = 0 % 14.22/4.01 | % 14.22/4.01 | Applying alpha-rule on (230) yields: % 14.22/4.01 | (116) all_93_1_108 = 0 % 14.22/4.01 | (108) antisymmetric(all_0_13_13) = 0 % 14.22/4.01 | % 14.22/4.01 +-Applying beta-rule and splitting (134), into two cases. % 14.22/4.01 |-Branch one: % 14.22/4.01 | (106) all_0_12_12 = 0 % 14.22/4.01 | % 14.22/4.01 | Equations (106) can reduce 135 to: % 14.22/4.01 | (117) $false % 14.22/4.01 | % 14.22/4.01 |-The branch is then unsatisfiable % 14.22/4.01 |-Branch two: % 14.22/4.01 | (135) ~ (all_0_12_12 = 0) % 14.22/4.01 | (236) ~ (all_60_0_84 = 0) & relation_field(all_0_13_13) = all_60_1_85 & is_antisymmetric_in(all_0_13_13, all_60_1_85) = all_60_0_84 % 14.22/4.01 | % 14.22/4.01 | Instantiating formula (76) with all_0_13_13, 0, all_0_12_12 and discharging atoms antisymmetric(all_0_13_13) = all_0_12_12, antisymmetric(all_0_13_13) = 0, yields: % 14.22/4.01 | (106) all_0_12_12 = 0 % 14.22/4.01 | % 14.22/4.01 | Equations (106) can reduce 135 to: % 14.22/4.01 | (117) $false % 14.22/4.01 | % 14.22/4.01 |-The branch is then unsatisfiable % 14.22/4.01 |-Branch two: % 14.22/4.01 | (239) ~ (all_93_0_107 = 0) & is_antisymmetric_in(all_0_13_13, all_51_2_71) = all_93_0_107 % 14.22/4.01 | % 14.22/4.01 | Applying alpha-rule on (239) yields: % 14.22/4.01 | (240) ~ (all_93_0_107 = 0) % 14.22/4.01 | (241) is_antisymmetric_in(all_0_13_13, all_51_2_71) = all_93_0_107 % 14.22/4.01 | % 14.22/4.01 +-Applying beta-rule and splitting (134), into two cases. % 14.22/4.01 |-Branch one: % 14.22/4.01 | (106) all_0_12_12 = 0 % 14.22/4.01 | % 14.22/4.01 | Equations (106) can reduce 135 to: % 14.22/4.01 | (117) $false % 14.22/4.01 | % 14.22/4.01 |-The branch is then unsatisfiable % 14.22/4.01 |-Branch two: % 14.22/4.01 | (135) ~ (all_0_12_12 = 0) % 14.22/4.01 | (236) ~ (all_60_0_84 = 0) & relation_field(all_0_13_13) = all_60_1_85 & is_antisymmetric_in(all_0_13_13, all_60_1_85) = all_60_0_84 % 14.22/4.01 | % 14.22/4.01 | Applying alpha-rule on (236) yields: % 14.22/4.01 | (246) ~ (all_60_0_84 = 0) % 14.22/4.01 | (140) relation_field(all_0_13_13) = all_60_1_85 % 14.22/4.01 | (248) is_antisymmetric_in(all_0_13_13, all_60_1_85) = all_60_0_84 % 14.22/4.01 | % 14.22/4.01 +-Applying beta-rule and splitting (90), into two cases. % 14.22/4.01 |-Branch one: % 14.22/4.01 | (121) all_50_2_68 = 0 & antisymmetric(all_0_13_13) = 0 % 14.22/4.01 | % 14.22/4.01 | Applying alpha-rule on (121) yields: % 14.22/4.01 | (122) all_50_2_68 = 0 % 14.22/4.01 | (108) antisymmetric(all_0_13_13) = 0 % 14.22/4.01 | % 14.22/4.01 +-Applying beta-rule and splitting (119), into two cases. % 14.22/4.01 |-Branch one: % 14.22/4.01 | (124) all_93_0_107 = 0 & is_antisymmetric_in(all_0_13_13, all_51_2_71) = 0 % 14.22/4.01 | % 14.22/4.01 | Applying alpha-rule on (124) yields: % 14.22/4.01 | (125) all_93_0_107 = 0 % 14.22/4.01 | (126) is_antisymmetric_in(all_0_13_13, all_51_2_71) = 0 % 14.22/4.01 | % 14.22/4.01 | Equations (125) can reduce 240 to: % 14.22/4.01 | (117) $false % 14.22/4.01 | % 14.22/4.01 |-The branch is then unsatisfiable % 14.22/4.01 |-Branch two: % 14.22/4.01 | (195) ~ (all_93_1_108 = 0) & antisymmetric(all_0_13_13) = all_93_1_108 % 14.22/4.01 | % 14.22/4.01 | Applying alpha-rule on (195) yields: % 14.22/4.01 | (114) ~ (all_93_1_108 = 0) % 14.22/4.01 | (197) antisymmetric(all_0_13_13) = all_93_1_108 % 14.22/4.01 | % 14.22/4.01 | Instantiating formula (76) with all_0_13_13, all_93_1_108, all_0_12_12 and discharging atoms antisymmetric(all_0_13_13) = all_93_1_108, antisymmetric(all_0_13_13) = all_0_12_12, yields: % 14.22/4.01 | (259) all_93_1_108 = all_0_12_12 % 14.22/4.01 | % 14.22/4.01 | Instantiating formula (76) with all_0_13_13, 0, all_93_1_108 and discharging atoms antisymmetric(all_0_13_13) = all_93_1_108, antisymmetric(all_0_13_13) = 0, yields: % 14.22/4.01 | (116) all_93_1_108 = 0 % 14.22/4.01 | % 14.22/4.01 | Combining equations (259,116) yields a new equation: % 14.22/4.01 | (261) all_0_12_12 = 0 % 14.22/4.01 | % 14.22/4.01 | Simplifying 261 yields: % 14.22/4.01 | (106) all_0_12_12 = 0 % 14.22/4.01 | % 14.22/4.01 | Equations (106) can reduce 135 to: % 14.22/4.01 | (117) $false % 14.22/4.01 | % 14.22/4.01 |-The branch is then unsatisfiable % 14.22/4.01 |-Branch two: % 14.22/4.01 | (200) ~ (all_50_0_66 = 0) & relation_field(all_0_13_13) = all_50_1_67 & is_antisymmetric_in(all_0_13_13, all_50_1_67) = all_50_0_66 % 14.22/4.01 | % 14.22/4.01 | Applying alpha-rule on (200) yields: % 14.22/4.01 | (201) ~ (all_50_0_66 = 0) % 14.22/4.01 | (111) relation_field(all_0_13_13) = all_50_1_67 % 14.22/4.01 | (203) is_antisymmetric_in(all_0_13_13, all_50_1_67) = all_50_0_66 % 14.22/4.01 | % 14.22/4.01 | Instantiating formula (43) with all_0_13_13, all_60_1_85, all_51_2_71 and discharging atoms relation_field(all_0_13_13) = all_60_1_85, relation_field(all_0_13_13) = all_51_2_71, yields: % 14.22/4.01 | (142) all_60_1_85 = all_51_2_71 % 14.22/4.01 | % 14.22/4.01 | Instantiating formula (43) with all_0_13_13, all_50_1_67, all_60_1_85 and discharging atoms relation_field(all_0_13_13) = all_60_1_85, relation_field(all_0_13_13) = all_50_1_67, yields: % 14.22/4.01 | (143) all_60_1_85 = all_50_1_67 % 14.22/4.01 | % 14.22/4.01 | Combining equations (143,142) yields a new equation: % 14.22/4.01 | (145) all_51_2_71 = all_50_1_67 % 14.22/4.01 | % 14.22/4.01 | Combining equations (145,142) yields a new equation: % 14.22/4.01 | (143) all_60_1_85 = all_50_1_67 % 14.22/4.01 | % 14.22/4.01 | From (143) and (248) follows: % 14.22/4.01 | (272) is_antisymmetric_in(all_0_13_13, all_50_1_67) = all_60_0_84 % 14.22/4.01 | % 14.22/4.01 | From (145) and (241) follows: % 14.22/4.01 | (273) is_antisymmetric_in(all_0_13_13, all_50_1_67) = all_93_0_107 % 14.22/4.01 | % 14.22/4.01 | Instantiating formula (24) with all_0_13_13, all_50_1_67, all_93_0_107, all_50_0_66 and discharging atoms is_antisymmetric_in(all_0_13_13, all_50_1_67) = all_93_0_107, is_antisymmetric_in(all_0_13_13, all_50_1_67) = all_50_0_66, yields: % 14.22/4.01 | (274) all_93_0_107 = all_50_0_66 % 14.22/4.01 | % 14.22/4.01 | Instantiating formula (24) with all_0_13_13, all_50_1_67, all_60_0_84, all_93_0_107 and discharging atoms is_antisymmetric_in(all_0_13_13, all_50_1_67) = all_93_0_107, is_antisymmetric_in(all_0_13_13, all_50_1_67) = all_60_0_84, yields: % 14.22/4.01 | (275) all_93_0_107 = all_60_0_84 % 14.22/4.01 | % 14.22/4.01 | Combining equations (274,275) yields a new equation: % 14.22/4.01 | (276) all_60_0_84 = all_50_0_66 % 14.22/4.01 | % 14.22/4.01 | Equations (276) can reduce 246 to: % 14.22/4.01 | (201) ~ (all_50_0_66 = 0) % 14.22/4.01 | % 14.22/4.01 | From (276) and (272) follows: % 14.22/4.01 | (203) is_antisymmetric_in(all_0_13_13, all_50_1_67) = all_50_0_66 % 14.22/4.01 | % 14.22/4.01 | Instantiating formula (52) with all_50_0_66, all_50_1_67, all_0_13_13 and discharging atoms is_antisymmetric_in(all_0_13_13, all_50_1_67) = all_50_0_66, relation(all_0_13_13) = 0, yields: % 14.22/4.01 | (279) all_50_0_66 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v1 = v0) & ordered_pair(v1, v0) = v3 & ordered_pair(v0, v1) = v2 & in(v3, all_0_13_13) = 0 & in(v2, all_0_13_13) = 0 & in(v1, all_50_1_67) = 0 & in(v0, all_50_1_67) = 0) % 14.22/4.01 | % 14.22/4.01 +-Applying beta-rule and splitting (279), into two cases. % 14.22/4.01 |-Branch one: % 14.22/4.01 | (110) all_50_0_66 = 0 % 14.22/4.01 | % 14.22/4.01 | Equations (110) can reduce 201 to: % 14.22/4.01 | (117) $false % 14.22/4.01 | % 14.22/4.01 |-The branch is then unsatisfiable % 14.22/4.01 |-Branch two: % 14.22/4.01 | (201) ~ (all_50_0_66 = 0) % 14.22/4.01 | (283) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v1 = v0) & ordered_pair(v1, v0) = v3 & ordered_pair(v0, v1) = v2 & in(v3, all_0_13_13) = 0 & in(v2, all_0_13_13) = 0 & in(v1, all_50_1_67) = 0 & in(v0, all_50_1_67) = 0) % 14.22/4.01 | % 14.22/4.01 | Instantiating (283) with all_161_0_146, all_161_1_147, all_161_2_148, all_161_3_149 yields: % 14.22/4.01 | (284) ~ (all_161_2_148 = all_161_3_149) & ordered_pair(all_161_2_148, all_161_3_149) = all_161_0_146 & ordered_pair(all_161_3_149, all_161_2_148) = all_161_1_147 & in(all_161_0_146, all_0_13_13) = 0 & in(all_161_1_147, all_0_13_13) = 0 & in(all_161_2_148, all_50_1_67) = 0 & in(all_161_3_149, all_50_1_67) = 0 % 14.22/4.01 | % 14.22/4.01 | Applying alpha-rule on (284) yields: % 14.22/4.01 | (285) ordered_pair(all_161_3_149, all_161_2_148) = all_161_1_147 % 14.22/4.01 | (286) ~ (all_161_2_148 = all_161_3_149) % 14.22/4.01 | (287) in(all_161_1_147, all_0_13_13) = 0 % 14.22/4.01 | (288) in(all_161_3_149, all_50_1_67) = 0 % 14.22/4.01 | (289) in(all_161_2_148, all_50_1_67) = 0 % 14.22/4.01 | (290) ordered_pair(all_161_2_148, all_161_3_149) = all_161_0_146 % 14.22/4.01 | (291) in(all_161_0_146, all_0_13_13) = 0 % 14.22/4.01 | % 14.22/4.01 | Instantiating formula (212) with all_161_1_147, all_161_3_149, all_161_2_148 and discharging atoms ordered_pair(all_161_3_149, all_161_2_148) = all_161_1_147, yields: % 14.22/4.01 | (292) all_161_2_148 = all_161_3_149 | ? [v0] : ? [v1] : (( ~ (v1 = 0) & ordered_pair(all_161_2_148, all_161_3_149) = v0 & in(v0, all_0_13_13) = v1) | ( ~ (v0 = 0) & in(all_161_1_147, all_0_13_13) = v0)) % 14.22/4.01 | % 14.22/4.01 +-Applying beta-rule and splitting (292), into two cases. % 14.22/4.01 |-Branch one: % 14.22/4.01 | (293) all_161_2_148 = all_161_3_149 % 14.22/4.01 | % 14.22/4.01 | Equations (293) can reduce 286 to: % 14.22/4.01 | (117) $false % 14.22/4.01 | % 14.22/4.01 |-The branch is then unsatisfiable % 14.22/4.01 |-Branch two: % 14.22/4.01 | (286) ~ (all_161_2_148 = all_161_3_149) % 14.22/4.01 | (296) ? [v0] : ? [v1] : (( ~ (v1 = 0) & ordered_pair(all_161_2_148, all_161_3_149) = v0 & in(v0, all_0_13_13) = v1) | ( ~ (v0 = 0) & in(all_161_1_147, all_0_13_13) = v0)) % 14.22/4.01 | % 14.22/4.01 | Instantiating (296) with all_205_0_162, all_205_1_163 yields: % 14.22/4.01 | (297) ( ~ (all_205_0_162 = 0) & ordered_pair(all_161_2_148, all_161_3_149) = all_205_1_163 & in(all_205_1_163, all_0_13_13) = all_205_0_162) | ( ~ (all_205_1_163 = 0) & in(all_161_1_147, all_0_13_13) = all_205_1_163) % 14.22/4.01 | % 14.22/4.01 +-Applying beta-rule and splitting (297), into two cases. % 14.22/4.01 |-Branch one: % 14.22/4.01 | (298) ~ (all_205_0_162 = 0) & ordered_pair(all_161_2_148, all_161_3_149) = all_205_1_163 & in(all_205_1_163, all_0_13_13) = all_205_0_162 % 14.22/4.01 | % 14.22/4.01 | Applying alpha-rule on (298) yields: % 14.22/4.01 | (299) ~ (all_205_0_162 = 0) % 14.22/4.01 | (300) ordered_pair(all_161_2_148, all_161_3_149) = all_205_1_163 % 14.22/4.01 | (301) in(all_205_1_163, all_0_13_13) = all_205_0_162 % 14.22/4.01 | % 14.22/4.01 | Instantiating formula (64) with all_161_2_148, all_161_3_149, all_205_1_163, all_161_0_146 and discharging atoms ordered_pair(all_161_2_148, all_161_3_149) = all_205_1_163, ordered_pair(all_161_2_148, all_161_3_149) = all_161_0_146, yields: % 14.22/4.01 | (302) all_205_1_163 = all_161_0_146 % 14.22/4.01 | % 14.22/4.01 | From (302) and (301) follows: % 14.22/4.01 | (303) in(all_161_0_146, all_0_13_13) = all_205_0_162 % 14.22/4.01 | % 14.22/4.01 | Instantiating formula (30) with all_161_0_146, all_0_13_13, all_205_0_162, 0 and discharging atoms in(all_161_0_146, all_0_13_13) = all_205_0_162, in(all_161_0_146, all_0_13_13) = 0, yields: % 14.22/4.01 | (304) all_205_0_162 = 0 % 14.22/4.01 | % 14.22/4.01 | Equations (304) can reduce 299 to: % 14.22/4.01 | (117) $false % 14.22/4.01 | % 14.22/4.01 |-The branch is then unsatisfiable % 14.22/4.01 |-Branch two: % 14.22/4.01 | (306) ~ (all_205_1_163 = 0) & in(all_161_1_147, all_0_13_13) = all_205_1_163 % 14.22/4.01 | % 14.22/4.01 | Applying alpha-rule on (306) yields: % 14.22/4.01 | (307) ~ (all_205_1_163 = 0) % 14.22/4.01 | (308) in(all_161_1_147, all_0_13_13) = all_205_1_163 % 14.22/4.01 | % 14.22/4.01 | Instantiating formula (30) with all_161_1_147, all_0_13_13, all_205_1_163, 0 and discharging atoms in(all_161_1_147, all_0_13_13) = all_205_1_163, in(all_161_1_147, all_0_13_13) = 0, yields: % 14.22/4.01 | (309) all_205_1_163 = 0 % 14.22/4.01 | % 14.22/4.01 | Equations (309) can reduce 307 to: % 14.22/4.01 | (117) $false % 14.22/4.01 | % 14.22/4.01 |-The branch is then unsatisfiable % 14.22/4.01 % SZS output end Proof for theBenchmark % 14.22/4.02 % 14.22/4.02 3424ms %------------------------------------------------------------------------------