%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU255+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n019.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 08:48:12 EDT 2022 % Result : Theorem 6.67s 2.30s % Output : Proof 9.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SEU255+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.15/0.35 % Computer : n019.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 600 % 0.15/0.35 % DateTime : Sun Jun 19 06:01:39 EDT 2022 % 0.15/0.35 % CPUTime : % 0.61/0.61 ____ _ % 0.61/0.61 ___ / __ \_____(_)___ ________ __________ % 0.61/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.61/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.61/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.61/0.61 % 0.61/0.61 A Theorem Prover for First-Order Logic % 0.61/0.61 (ePrincess v.1.0) % 0.61/0.61 % 0.61/0.61 (c) Philipp Rümmer, 2009-2015 % 0.61/0.61 (c) Peter Backeman, 2014-2015 % 0.61/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.61/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.61/0.61 Bug reports to peter@backeman.se % 0.61/0.61 % 0.61/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.61/0.61 % 0.61/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.70/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.59/0.94 Prover 0: Preprocessing ... % 2.05/1.14 Prover 0: Warning: ignoring some quantifiers % 2.05/1.16 Prover 0: Constructing countermodel ... % 4.86/1.88 Prover 0: gave up % 4.86/1.88 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 4.86/1.91 Prover 1: Preprocessing ... % 5.31/1.98 Prover 1: Warning: ignoring some quantifiers % 5.31/1.98 Prover 1: Constructing countermodel ... % 6.11/2.10 Prover 1: gave up % 6.11/2.10 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 6.22/2.12 Prover 2: Preprocessing ... % 6.22/2.20 Prover 2: Warning: ignoring some quantifiers % 6.22/2.21 Prover 2: Constructing countermodel ... % 6.67/2.30 Prover 2: proved (198ms) % 6.67/2.30 % 6.67/2.30 No countermodel exists, formula is valid % 6.67/2.30 % SZS status Theorem for theBenchmark % 6.67/2.30 % 6.67/2.30 Generating proof ... Warning: ignoring some quantifiers % 8.80/2.79 found it (size 58) % 8.80/2.79 % 8.80/2.79 % SZS output start Proof for theBenchmark % 8.80/2.79 Assumed formulas after preprocessing and simplification: % 8.80/2.79 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v6 = 0) & ~ (v3 = 0) & antisymmetric(v2) = v3 & antisymmetric(v1) = 0 & relation_restriction(v1, v0) = v2 & one_to_one(v4) = 0 & relation(v9) = 0 & relation(v7) = 0 & relation(v4) = 0 & relation(v1) = 0 & function(v9) = 0 & function(v7) = 0 & function(v4) = 0 & empty(v8) = 0 & empty(v7) = 0 & empty(v5) = v6 & empty(empty_set) = 0 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_restriction(v12, v11) = v13) | ~ (in(v10, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (( ~ (v15 = 0) & relation(v12) = v15) | (( ~ (v14 = 0) | (v17 = 0 & v15 = 0 & cartesian_product2(v11, v11) = v16 & in(v10, v16) = 0 & in(v10, v12) = 0)) & (v14 = 0 | ( ~ (v17 = 0) & cartesian_product2(v11, v11) = v16 & in(v10, v16) = v17) | ( ~ (v15 = 0) & in(v10, v12) = v15))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (antisymmetric(v10) = 0) | ~ (ordered_pair(v12, v11) = v13) | ? [v14] : ? [v15] : (( ~ (v15 = 0) & ordered_pair(v11, v12) = v14 & in(v14, v10) = v15) | ( ~ (v14 = 0) & relation(v10) = v14) | ( ~ (v14 = 0) & in(v13, v10) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (antisymmetric(v10) = 0) | ~ (ordered_pair(v11, v12) = v13) | ? [v14] : ? [v15] : (( ~ (v15 = 0) & ordered_pair(v12, v11) = v14 & in(v14, v10) = v15) | ( ~ (v14 = 0) & relation(v10) = v14) | ( ~ (v14 = 0) & in(v13, v10) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (element(v13, v12) = v11) | ~ (element(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (cartesian_product2(v13, v12) = v11) | ~ (cartesian_product2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (relation_restriction(v13, v12) = v11) | ~ (relation_restriction(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (ordered_pair(v13, v12) = v11) | ~ (ordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_intersection2(v13, v12) = v11) | ~ (set_intersection2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (unordered_pair(v13, v12) = v11) | ~ (unordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (in(v13, v12) = v11) | ~ (in(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (element(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & in(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (in(v10, v11) = v12) | ? [v13] : ((v13 = 0 & empty(v11) = 0) | ( ~ (v13 = 0) & element(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (antisymmetric(v12) = v11) | ~ (antisymmetric(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v12) = v11) | ~ (singleton(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (one_to_one(v12) = v11) | ~ (one_to_one(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation(v12) = v11) | ~ (relation(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (function(v12) = v11) | ~ (function(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (empty(v12) = v11) | ~ (empty(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (cartesian_product2(v11, v11) = v12) | ~ (relation(v10) = 0) | ? [v13] : (relation_restriction(v10, v11) = v13 & set_intersection2(v10, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_restriction(v10, v11) = v12) | ~ (relation(v10) = 0) | ? [v13] : (cartesian_product2(v11, v11) = v13 & set_intersection2(v10, v13) = v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_restriction(v10, v11) = v12) | ? [v13] : ((v13 = 0 & relation(v12) = 0) | ( ~ (v13 = 0) & relation(v10) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v10, v11) = v12) | ? [v13] : ? [v14] : (singleton(v10) = v14 & unordered_pair(v13, v14) = v12 & unordered_pair(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v11, v10) = v12) | set_intersection2(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v10, v11) = v12) | set_intersection2(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v11, v10) = v12) | unordered_pair(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | unordered_pair(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | ? [v13] : ? [v14] : (ordered_pair(v10, v11) = v13 & singleton(v10) = v14 & unordered_pair(v12, v14) = v13)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_intersection2(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (empty(v11) = 0) | ~ (empty(v10) = 0)) & ! [v10] : ! [v11] : (v11 = empty_set | ~ (set_intersection2(v10, empty_set) = v11)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (antisymmetric(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v15 = 0 & ~ (v13 = v12) & ordered_pair(v13, v12) = v16 & ordered_pair(v12, v13) = v14 & in(v16, v10) = 0 & in(v14, v10) = 0) | ( ~ (v12 = 0) & relation(v10) = v12))) & ! [v10] : ! [v11] : (v11 = 0 | ~ (function(v10) = v11) | ? [v12] : ( ~ (v12 = 0) & empty(v10) = v12)) & ! [v10] : ! [v11] : ( ~ (element(v10, v11) = 0) | ? [v12] : ((v12 = 0 & empty(v11) = 0) | (v12 = 0 & in(v10, v11) = 0))) & ! [v10] : ! [v11] : ( ~ (one_to_one(v10) = v11) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v11 = 0 & relation(v10) = 0 & function(v10) = 0) | ( ~ (v12 = 0) & relation(v10) = v12) | ( ~ (v12 = 0) & function(v10) = v12) | ( ~ (v12 = 0) & empty(v10) = v12))) & ! [v10] : ! [v11] : ( ~ (in(v11, v10) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v11) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | element(v10, v11) = 0) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & empty(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v11, v10) = v12)) & ! [v10] : (v10 = empty_set | ~ (empty(v10) = 0)) & ! [v10] : ( ~ (relation(v10) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (((v17 = 0 & v15 = 0 & ~ (v13 = v12) & ordered_pair(v13, v12) = v16 & ordered_pair(v12, v13) = v14 & in(v16, v10) = 0 & in(v14, v10) = 0) | (v11 = 0 & antisymmetric(v10) = 0)) & (( ~ (v11 = 0) & antisymmetric(v10) = v11) | ( ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (ordered_pair(v19, v18) = v20) | ? [v21] : ? [v22] : (( ~ (v22 = 0) & ordered_pair(v18, v19) = v21 & in(v21, v10) = v22) | ( ~ (v21 = 0) & in(v20, v10) = v21))) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (ordered_pair(v18, v19) = v20) | ? [v21] : ? [v22] : (( ~ (v22 = 0) & ordered_pair(v19, v18) = v21 & in(v21, v10) = v22) | ( ~ (v21 = 0) & in(v20, v10) = v21))))))) & ! [v10] : ( ~ (relation(v10) = 0) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & one_to_one(v10) = 0 & function(v10) = 0) | ( ~ (v11 = 0) & function(v10) = v11) | ( ~ (v11 = 0) & empty(v10) = v11))) & ! [v10] : ( ~ (function(v10) = 0) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & one_to_one(v10) = 0 & relation(v10) = 0) | ( ~ (v11 = 0) & relation(v10) = v11) | ( ~ (v11 = 0) & empty(v10) = v11))) & ! [v10] : ( ~ (empty(v10) = 0) | function(v10) = 0) & ! [v10] : ( ~ (empty(v10) = 0) | ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v11 = 0 & one_to_one(v10) = 0 & relation(v10) = 0 & function(v10) = 0) | ( ~ (v11 = 0) & relation(v10) = v11) | ( ~ (v11 = 0) & function(v10) = v11))) & ? [v10] : ? [v11] : ? [v12] : element(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : cartesian_product2(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : relation_restriction(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : ordered_pair(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : set_intersection2(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : unordered_pair(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : in(v11, v10) = v12 & ? [v10] : ? [v11] : antisymmetric(v10) = v11 & ? [v10] : ? [v11] : element(v11, v10) = 0 & ? [v10] : ? [v11] : singleton(v10) = v11 & ? [v10] : ? [v11] : one_to_one(v10) = v11 & ? [v10] : ? [v11] : relation(v10) = v11 & ? [v10] : ? [v11] : function(v10) = v11 & ? [v10] : ? [v11] : empty(v10) = v11) % 9.31/2.84 | 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 yields: % 9.31/2.84 | (1) ~ (all_0_3_3 = 0) & ~ (all_0_6_6 = 0) & antisymmetric(all_0_7_7) = all_0_6_6 & antisymmetric(all_0_8_8) = 0 & relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7 & 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_8_8) = 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] : ( ~ (relation_restriction(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & relation(v2) = v5) | (( ~ (v4 = 0) | (v7 = 0 & v5 = 0 & cartesian_product2(v1, v1) = v6 & in(v0, v6) = 0 & in(v0, v2) = 0)) & (v4 = 0 | ( ~ (v7 = 0) & cartesian_product2(v1, v1) = v6 & in(v0, v6) = v7) | ( ~ (v5 = 0) & in(v0, v2) = v5))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (antisymmetric(v0) = 0) | ~ (ordered_pair(v2, v1) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & ordered_pair(v1, v2) = v4 & in(v4, v0) = v5) | ( ~ (v4 = 0) & relation(v0) = v4) | ( ~ (v4 = 0) & in(v3, v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (antisymmetric(v0) = 0) | ~ (ordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & ordered_pair(v2, v1) = v4 & in(v4, v0) = v5) | ( ~ (v4 = 0) & relation(v0) = v4) | ( ~ (v4 = 0) & in(v3, v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(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] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [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 | ~ (antisymmetric(v2) = v1) | ~ (antisymmetric(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v1, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : (relation_restriction(v0, v1) = v3 & set_intersection2(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : (cartesian_product2(v1, v1) = v3 & set_intersection2(v0, v3) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ? [v3] : ((v3 = 0 & relation(v2) = 0) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [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_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [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] : (ordered_pair(v0, v1) = v3 & singleton(v0) = v4 & unordered_pair(v2, v4) = v3)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (antisymmetric(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v5 = 0 & ~ (v3 = v2) & ordered_pair(v3, v2) = v6 & ordered_pair(v2, v3) = v4 & in(v6, v0) = 0 & in(v4, v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) & ! [v0] : ! [v1] : ( ~ (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] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v5 = 0 & ~ (v3 = v2) & ordered_pair(v3, v2) = v6 & ordered_pair(v2, v3) = v4 & in(v6, v0) = 0 & in(v4, v0) = 0) | (v1 = 0 & antisymmetric(v0) = 0)) & (( ~ (v1 = 0) & antisymmetric(v0) = v1) | ( ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (ordered_pair(v9, v8) = v10) | ? [v11] : ? [v12] : (( ~ (v12 = 0) & ordered_pair(v8, v9) = v11 & in(v11, v0) = v12) | ( ~ (v11 = 0) & in(v10, v0) = v11))) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (ordered_pair(v8, v9) = v10) | ? [v11] : ? [v12] : (( ~ (v12 = 0) & ordered_pair(v9, v8) = v11 & in(v11, v0) = v12) | ( ~ (v11 = 0) & in(v10, v0) = v11))))))) & ! [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] : cartesian_product2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : relation_restriction(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : antisymmetric(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : one_to_one(v0) = v1 & ? [v0] : ? [v1] : relation(v0) = v1 & ? [v0] : ? [v1] : function(v0) = v1 & ? [v0] : ? [v1] : empty(v0) = v1 % 9.31/2.85 | % 9.31/2.85 | Applying alpha-rule on (1) yields: % 9.31/2.85 | (2) ! [v0] : ! [v1] : (v1 = 0 | ~ (antisymmetric(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v5 = 0 & ~ (v3 = v2) & ordered_pair(v3, v2) = v6 & ordered_pair(v2, v3) = v4 & in(v6, v0) = 0 & in(v4, v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2))) % 9.31/2.85 | (3) ! [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))) % 9.31/2.85 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (antisymmetric(v0) = 0) | ~ (ordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & ordered_pair(v2, v1) = v4 & in(v4, v0) = v5) | ( ~ (v4 = 0) & relation(v0) = v4) | ( ~ (v4 = 0) & in(v3, v0) = v4))) % 9.31/2.85 | (5) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 9.31/2.85 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 9.31/2.85 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 9.31/2.85 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 9.31/2.85 | (9) ? [v0] : ? [v1] : antisymmetric(v0) = v1 % 9.31/2.85 | (10) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) % 9.31/2.85 | (11) ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2 % 9.31/2.85 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 9.31/2.85 | (13) empty(all_0_2_2) = 0 % 9.31/2.85 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 9.31/2.85 | (15) ? [v0] : ? [v1] : ? [v2] : relation_restriction(v1, v0) = v2 % 9.31/2.85 | (16) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) % 9.31/2.85 | (17) relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7 % 9.31/2.85 | (18) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v5 = 0 & ~ (v3 = v2) & ordered_pair(v3, v2) = v6 & ordered_pair(v2, v3) = v4 & in(v6, v0) = 0 & in(v4, v0) = 0) | (v1 = 0 & antisymmetric(v0) = 0)) & (( ~ (v1 = 0) & antisymmetric(v0) = v1) | ( ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (ordered_pair(v9, v8) = v10) | ? [v11] : ? [v12] : (( ~ (v12 = 0) & ordered_pair(v8, v9) = v11 & in(v11, v0) = v12) | ( ~ (v11 = 0) & in(v10, v0) = v11))) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (ordered_pair(v8, v9) = v10) | ? [v11] : ? [v12] : (( ~ (v12 = 0) & ordered_pair(v9, v8) = v11 & in(v11, v0) = v12) | ( ~ (v11 = 0) & in(v10, v0) = v11))))))) % 9.31/2.85 | (19) antisymmetric(all_0_7_7) = all_0_6_6 % 9.31/2.85 | (20) relation(all_0_5_5) = 0 % 9.31/2.85 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : (cartesian_product2(v1, v1) = v3 & set_intersection2(v0, v3) = v2)) % 9.31/2.85 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 9.31/2.85 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_restriction(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & relation(v2) = v5) | (( ~ (v4 = 0) | (v7 = 0 & v5 = 0 & cartesian_product2(v1, v1) = v6 & in(v0, v6) = 0 & in(v0, v2) = 0)) & (v4 = 0 | ( ~ (v7 = 0) & cartesian_product2(v1, v1) = v6 & in(v0, v6) = v7) | ( ~ (v5 = 0) & in(v0, v2) = v5))))) % 9.31/2.86 | (24) ~ (all_0_3_3 = 0) % 9.31/2.86 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) % 9.31/2.86 | (26) ? [v0] : ? [v1] : relation(v0) = v1 % 9.31/2.86 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 9.31/2.86 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3))) % 9.31/2.86 | (29) relation(all_0_0_0) = 0 % 9.31/2.86 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 9.31/2.86 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 9.31/2.86 | (32) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 % 9.31/2.86 | (33) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) % 9.31/2.86 | (34) ! [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))) % 9.31/2.86 | (35) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 % 9.31/2.86 | (36) ~ (all_0_6_6 = 0) % 9.31/2.86 | (37) relation(all_0_8_8) = 0 % 9.31/2.86 | (38) one_to_one(all_0_5_5) = 0 % 9.31/2.86 | (39) ? [v0] : ? [v1] : element(v1, v0) = 0 % 9.31/2.86 | (40) empty(all_0_4_4) = all_0_3_3 % 9.31/2.86 | (41) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 9.31/2.86 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 9.31/2.86 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 9.31/2.86 | (44) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 9.31/2.86 | (45) ? [v0] : ? [v1] : singleton(v0) = v1 % 9.31/2.86 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 9.31/2.86 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) % 9.31/2.86 | (48) empty(empty_set) = 0 % 9.31/2.86 | (49) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 9.31/2.86 | (50) function(all_0_0_0) = 0 % 9.31/2.86 | (51) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 9.31/2.86 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) = v0)) % 9.31/2.86 | (53) ? [v0] : ? [v1] : function(v0) = v1 % 9.31/2.86 | (54) antisymmetric(all_0_8_8) = 0 % 9.31/2.86 | (55) ? [v0] : ? [v1] : empty(v0) = v1 % 9.31/2.86 | (56) ? [v0] : ? [v1] : one_to_one(v0) = v1 % 9.31/2.86 | (57) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (antisymmetric(v2) = v1) | ~ (antisymmetric(v2) = v0)) % 9.31/2.86 | (58) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 9.31/2.86 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (antisymmetric(v0) = 0) | ~ (ordered_pair(v2, v1) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & ordered_pair(v1, v2) = v4 & in(v4, v0) = v5) | ( ~ (v4 = 0) & relation(v0) = v4) | ( ~ (v4 = 0) & in(v3, v0) = v4))) % 9.31/2.86 | (60) relation(all_0_2_2) = 0 % 9.31/2.86 | (61) ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2 % 9.31/2.86 | (62) ? [v0] : ? [v1] : ? [v2] : cartesian_product2(v1, v0) = v2 % 9.31/2.86 | (63) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 9.31/2.86 | (64) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 9.31/2.86 | (65) function(all_0_5_5) = 0 % 9.31/2.86 | (66) empty(all_0_1_1) = 0 % 9.31/2.86 | (67) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 9.31/2.87 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 9.31/2.87 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 9.31/2.87 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) % 9.31/2.87 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ? [v3] : ((v3 = 0 & relation(v2) = 0) | ( ~ (v3 = 0) & relation(v0) = v3))) % 9.31/2.87 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v1, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : (relation_restriction(v0, v1) = v3 & set_intersection2(v0, v2) = v3)) % 9.31/2.87 | (73) ! [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))) % 9.31/2.87 | (74) ! [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))) % 9.31/2.87 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (ordered_pair(v0, v1) = v3 & singleton(v0) = v4 & unordered_pair(v2, v4) = v3)) % 9.31/2.87 | (76) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 % 9.31/2.87 | (77) function(all_0_2_2) = 0 % 9.31/2.87 | % 9.31/2.87 | Instantiating formula (2) with all_0_6_6, all_0_7_7 and discharging atoms antisymmetric(all_0_7_7) = all_0_6_6, yields: % 9.31/2.87 | (78) all_0_6_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v3 = 0 & ~ (v1 = v0) & ordered_pair(v1, v0) = v4 & ordered_pair(v0, v1) = v2 & in(v4, all_0_7_7) = 0 & in(v2, all_0_7_7) = 0) | ( ~ (v0 = 0) & relation(all_0_7_7) = v0)) % 9.31/2.87 | % 9.31/2.87 | Instantiating formula (71) with all_0_7_7, all_0_9_9, all_0_8_8 and discharging atoms relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7, yields: % 9.31/2.87 | (79) ? [v0] : ((v0 = 0 & relation(all_0_7_7) = 0) | ( ~ (v0 = 0) & relation(all_0_8_8) = v0)) % 9.31/2.87 | % 9.31/2.87 | Instantiating (79) with all_55_0_93 yields: % 9.31/2.87 | (80) (all_55_0_93 = 0 & relation(all_0_7_7) = 0) | ( ~ (all_55_0_93 = 0) & relation(all_0_8_8) = all_55_0_93) % 9.31/2.87 | % 9.31/2.87 +-Applying beta-rule and splitting (80), into two cases. % 9.31/2.87 |-Branch one: % 9.31/2.87 | (81) all_55_0_93 = 0 & relation(all_0_7_7) = 0 % 9.31/2.87 | % 9.31/2.87 | Applying alpha-rule on (81) yields: % 9.31/2.87 | (82) all_55_0_93 = 0 % 9.31/2.87 | (83) relation(all_0_7_7) = 0 % 9.31/2.87 | % 9.31/2.87 +-Applying beta-rule and splitting (78), into two cases. % 9.31/2.87 |-Branch one: % 9.31/2.87 | (84) all_0_6_6 = 0 % 9.31/2.87 | % 9.31/2.87 | Equations (84) can reduce 36 to: % 9.31/2.87 | (85) $false % 9.31/2.87 | % 9.31/2.87 |-The branch is then unsatisfiable % 9.31/2.87 |-Branch two: % 9.31/2.87 | (36) ~ (all_0_6_6 = 0) % 9.31/2.87 | (87) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v3 = 0 & ~ (v1 = v0) & ordered_pair(v1, v0) = v4 & ordered_pair(v0, v1) = v2 & in(v4, all_0_7_7) = 0 & in(v2, all_0_7_7) = 0) | ( ~ (v0 = 0) & relation(all_0_7_7) = v0)) % 9.31/2.87 | % 9.31/2.87 | Instantiating (87) with all_68_0_95, all_68_1_96, all_68_2_97, all_68_3_98, all_68_4_99, all_68_5_100 yields: % 9.31/2.87 | (88) (all_68_0_95 = 0 & all_68_2_97 = 0 & ~ (all_68_4_99 = all_68_5_100) & ordered_pair(all_68_4_99, all_68_5_100) = all_68_1_96 & ordered_pair(all_68_5_100, all_68_4_99) = all_68_3_98 & in(all_68_1_96, all_0_7_7) = 0 & in(all_68_3_98, all_0_7_7) = 0) | ( ~ (all_68_5_100 = 0) & relation(all_0_7_7) = all_68_5_100) % 9.31/2.87 | % 9.31/2.87 +-Applying beta-rule and splitting (88), into two cases. % 9.31/2.87 |-Branch one: % 9.31/2.87 | (89) all_68_0_95 = 0 & all_68_2_97 = 0 & ~ (all_68_4_99 = all_68_5_100) & ordered_pair(all_68_4_99, all_68_5_100) = all_68_1_96 & ordered_pair(all_68_5_100, all_68_4_99) = all_68_3_98 & in(all_68_1_96, all_0_7_7) = 0 & in(all_68_3_98, all_0_7_7) = 0 % 9.31/2.88 | % 9.31/2.88 | Applying alpha-rule on (89) yields: % 9.31/2.88 | (90) all_68_2_97 = 0 % 9.31/2.88 | (91) ordered_pair(all_68_5_100, all_68_4_99) = all_68_3_98 % 9.31/2.88 | (92) ~ (all_68_4_99 = all_68_5_100) % 9.31/2.88 | (93) ordered_pair(all_68_4_99, all_68_5_100) = all_68_1_96 % 9.31/2.88 | (94) all_68_0_95 = 0 % 9.31/2.88 | (95) in(all_68_3_98, all_0_7_7) = 0 % 9.31/2.88 | (96) in(all_68_1_96, all_0_7_7) = 0 % 9.31/2.88 | % 9.31/2.88 | Instantiating formula (59) with all_68_1_96, all_68_4_99, all_68_5_100, all_0_8_8 and discharging atoms antisymmetric(all_0_8_8) = 0, ordered_pair(all_68_4_99, all_68_5_100) = all_68_1_96, yields: % 9.31/2.88 | (97) all_68_4_99 = all_68_5_100 | ? [v0] : ? [v1] : (( ~ (v1 = 0) & ordered_pair(all_68_5_100, all_68_4_99) = v0 & in(v0, all_0_8_8) = v1) | ( ~ (v0 = 0) & relation(all_0_8_8) = v0) | ( ~ (v0 = 0) & in(all_68_1_96, all_0_8_8) = v0)) % 9.31/2.88 | % 9.31/2.88 | Instantiating formula (23) with 0, all_0_7_7, all_0_8_8, all_0_9_9, all_68_1_96 and discharging atoms relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7, in(all_68_1_96, all_0_7_7) = 0, yields: % 9.31/2.88 | (98) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v0 = 0 & cartesian_product2(all_0_9_9, all_0_9_9) = v1 & in(all_68_1_96, v1) = 0 & in(all_68_1_96, all_0_8_8) = 0) | ( ~ (v0 = 0) & relation(all_0_8_8) = v0)) % 9.31/2.88 | % 9.31/2.88 | Instantiating formula (23) with 0, all_0_7_7, all_0_8_8, all_0_9_9, all_68_3_98 and discharging atoms relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7, in(all_68_3_98, all_0_7_7) = 0, yields: % 9.31/2.88 | (99) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v0 = 0 & cartesian_product2(all_0_9_9, all_0_9_9) = v1 & in(all_68_3_98, v1) = 0 & in(all_68_3_98, all_0_8_8) = 0) | ( ~ (v0 = 0) & relation(all_0_8_8) = v0)) % 9.31/2.88 | % 9.31/2.88 | Instantiating (99) with all_89_0_101, all_89_1_102, all_89_2_103 yields: % 9.31/2.88 | (100) (all_89_0_101 = 0 & all_89_2_103 = 0 & cartesian_product2(all_0_9_9, all_0_9_9) = all_89_1_102 & in(all_68_3_98, all_89_1_102) = 0 & in(all_68_3_98, all_0_8_8) = 0) | ( ~ (all_89_2_103 = 0) & relation(all_0_8_8) = all_89_2_103) % 9.31/2.88 | % 9.31/2.88 | Instantiating (98) with all_92_0_105, all_92_1_106, all_92_2_107 yields: % 9.31/2.88 | (101) (all_92_0_105 = 0 & all_92_2_107 = 0 & cartesian_product2(all_0_9_9, all_0_9_9) = all_92_1_106 & in(all_68_1_96, all_92_1_106) = 0 & in(all_68_1_96, all_0_8_8) = 0) | ( ~ (all_92_2_107 = 0) & relation(all_0_8_8) = all_92_2_107) % 9.31/2.88 | % 9.31/2.88 +-Applying beta-rule and splitting (97), into two cases. % 9.31/2.88 |-Branch one: % 9.31/2.88 | (102) all_68_4_99 = all_68_5_100 % 9.31/2.88 | % 9.31/2.88 | Equations (102) can reduce 92 to: % 9.31/2.88 | (85) $false % 9.31/2.88 | % 9.31/2.88 |-The branch is then unsatisfiable % 9.31/2.88 |-Branch two: % 9.31/2.88 | (92) ~ (all_68_4_99 = all_68_5_100) % 9.31/2.88 | (105) ? [v0] : ? [v1] : (( ~ (v1 = 0) & ordered_pair(all_68_5_100, all_68_4_99) = v0 & in(v0, all_0_8_8) = v1) | ( ~ (v0 = 0) & relation(all_0_8_8) = v0) | ( ~ (v0 = 0) & in(all_68_1_96, all_0_8_8) = v0)) % 9.31/2.88 | % 9.31/2.88 | Instantiating (105) with all_122_0_129, all_122_1_130 yields: % 9.31/2.88 | (106) ( ~ (all_122_0_129 = 0) & ordered_pair(all_68_5_100, all_68_4_99) = all_122_1_130 & in(all_122_1_130, all_0_8_8) = all_122_0_129) | ( ~ (all_122_1_130 = 0) & relation(all_0_8_8) = all_122_1_130) | ( ~ (all_122_1_130 = 0) & in(all_68_1_96, all_0_8_8) = all_122_1_130) % 9.31/2.88 | % 9.31/2.88 +-Applying beta-rule and splitting (101), into two cases. % 9.31/2.88 |-Branch one: % 9.31/2.88 | (107) all_92_0_105 = 0 & all_92_2_107 = 0 & cartesian_product2(all_0_9_9, all_0_9_9) = all_92_1_106 & in(all_68_1_96, all_92_1_106) = 0 & in(all_68_1_96, all_0_8_8) = 0 % 9.31/2.88 | % 9.31/2.88 | Applying alpha-rule on (107) yields: % 9.31/2.88 | (108) cartesian_product2(all_0_9_9, all_0_9_9) = all_92_1_106 % 9.31/2.88 | (109) all_92_0_105 = 0 % 9.31/2.88 | (110) in(all_68_1_96, all_92_1_106) = 0 % 9.31/2.88 | (111) all_92_2_107 = 0 % 9.31/2.88 | (112) in(all_68_1_96, all_0_8_8) = 0 % 9.31/2.88 | % 9.31/2.88 +-Applying beta-rule and splitting (106), into two cases. % 9.31/2.88 |-Branch one: % 9.31/2.88 | (113) ( ~ (all_122_0_129 = 0) & ordered_pair(all_68_5_100, all_68_4_99) = all_122_1_130 & in(all_122_1_130, all_0_8_8) = all_122_0_129) | ( ~ (all_122_1_130 = 0) & relation(all_0_8_8) = all_122_1_130) % 9.31/2.88 | % 9.31/2.88 +-Applying beta-rule and splitting (113), into two cases. % 9.31/2.88 |-Branch one: % 9.31/2.88 | (114) ~ (all_122_0_129 = 0) & ordered_pair(all_68_5_100, all_68_4_99) = all_122_1_130 & in(all_122_1_130, all_0_8_8) = all_122_0_129 % 9.31/2.88 | % 9.31/2.88 | Applying alpha-rule on (114) yields: % 9.31/2.88 | (115) ~ (all_122_0_129 = 0) % 9.31/2.88 | (116) ordered_pair(all_68_5_100, all_68_4_99) = all_122_1_130 % 9.31/2.88 | (117) in(all_122_1_130, all_0_8_8) = all_122_0_129 % 9.31/2.88 | % 9.31/2.88 +-Applying beta-rule and splitting (100), into two cases. % 9.31/2.88 |-Branch one: % 9.31/2.88 | (118) all_89_0_101 = 0 & all_89_2_103 = 0 & cartesian_product2(all_0_9_9, all_0_9_9) = all_89_1_102 & in(all_68_3_98, all_89_1_102) = 0 & in(all_68_3_98, all_0_8_8) = 0 % 9.31/2.88 | % 9.31/2.88 | Applying alpha-rule on (118) yields: % 9.31/2.88 | (119) all_89_2_103 = 0 % 9.31/2.88 | (120) in(all_68_3_98, all_89_1_102) = 0 % 9.31/2.88 | (121) cartesian_product2(all_0_9_9, all_0_9_9) = all_89_1_102 % 9.31/2.88 | (122) in(all_68_3_98, all_0_8_8) = 0 % 9.31/2.88 | (123) all_89_0_101 = 0 % 9.31/2.88 | % 9.31/2.88 | Instantiating formula (31) with all_68_5_100, all_68_4_99, all_122_1_130, all_68_3_98 and discharging atoms ordered_pair(all_68_5_100, all_68_4_99) = all_122_1_130, ordered_pair(all_68_5_100, all_68_4_99) = all_68_3_98, yields: % 9.31/2.88 | (124) all_122_1_130 = all_68_3_98 % 9.31/2.88 | % 9.31/2.88 | From (124) and (117) follows: % 9.31/2.88 | (125) in(all_68_3_98, all_0_8_8) = all_122_0_129 % 9.31/2.88 | % 9.31/2.88 | Instantiating formula (14) with all_68_3_98, all_0_8_8, all_122_0_129, 0 and discharging atoms in(all_68_3_98, all_0_8_8) = all_122_0_129, in(all_68_3_98, all_0_8_8) = 0, yields: % 9.31/2.88 | (126) all_122_0_129 = 0 % 9.31/2.88 | % 9.31/2.88 | Equations (126) can reduce 115 to: % 9.31/2.88 | (85) $false % 9.31/2.88 | % 9.31/2.88 |-The branch is then unsatisfiable % 9.31/2.88 |-Branch two: % 9.31/2.88 | (128) ~ (all_89_2_103 = 0) & relation(all_0_8_8) = all_89_2_103 % 9.31/2.88 | % 9.31/2.88 | Applying alpha-rule on (128) yields: % 9.31/2.88 | (129) ~ (all_89_2_103 = 0) % 9.31/2.88 | (130) relation(all_0_8_8) = all_89_2_103 % 9.31/2.88 | % 9.31/2.88 | Instantiating formula (64) with all_0_8_8, all_89_2_103, 0 and discharging atoms relation(all_0_8_8) = all_89_2_103, relation(all_0_8_8) = 0, yields: % 9.31/2.88 | (119) all_89_2_103 = 0 % 9.31/2.88 | % 9.31/2.88 | Equations (119) can reduce 129 to: % 9.31/2.89 | (85) $false % 9.31/2.89 | % 9.31/2.89 |-The branch is then unsatisfiable % 9.31/2.89 |-Branch two: % 9.31/2.89 | (133) ~ (all_122_1_130 = 0) & relation(all_0_8_8) = all_122_1_130 % 9.31/2.89 | % 9.31/2.89 | Applying alpha-rule on (133) yields: % 9.31/2.89 | (134) ~ (all_122_1_130 = 0) % 9.31/2.89 | (135) relation(all_0_8_8) = all_122_1_130 % 9.31/2.89 | % 9.31/2.89 | Instantiating formula (64) with all_0_8_8, all_122_1_130, 0 and discharging atoms relation(all_0_8_8) = all_122_1_130, relation(all_0_8_8) = 0, yields: % 9.31/2.89 | (136) all_122_1_130 = 0 % 9.31/2.89 | % 9.31/2.89 | Equations (136) can reduce 134 to: % 9.31/2.89 | (85) $false % 9.31/2.89 | % 9.31/2.89 |-The branch is then unsatisfiable % 9.31/2.89 |-Branch two: % 9.31/2.89 | (138) ~ (all_122_1_130 = 0) & in(all_68_1_96, all_0_8_8) = all_122_1_130 % 9.31/2.89 | % 9.31/2.89 | Applying alpha-rule on (138) yields: % 9.31/2.89 | (134) ~ (all_122_1_130 = 0) % 9.31/2.89 | (140) in(all_68_1_96, all_0_8_8) = all_122_1_130 % 9.31/2.89 | % 9.31/2.89 | Instantiating formula (14) with all_68_1_96, all_0_8_8, 0, all_122_1_130 and discharging atoms in(all_68_1_96, all_0_8_8) = all_122_1_130, in(all_68_1_96, all_0_8_8) = 0, yields: % 9.31/2.89 | (136) all_122_1_130 = 0 % 9.31/2.89 | % 9.31/2.89 | Equations (136) can reduce 134 to: % 9.31/2.89 | (85) $false % 9.31/2.89 | % 9.31/2.89 |-The branch is then unsatisfiable % 9.31/2.89 |-Branch two: % 9.31/2.89 | (143) ~ (all_92_2_107 = 0) & relation(all_0_8_8) = all_92_2_107 % 9.31/2.89 | % 9.31/2.89 | Applying alpha-rule on (143) yields: % 9.31/2.89 | (144) ~ (all_92_2_107 = 0) % 9.31/2.89 | (145) relation(all_0_8_8) = all_92_2_107 % 9.31/2.89 | % 9.31/2.89 | Instantiating formula (64) with all_0_8_8, all_92_2_107, 0 and discharging atoms relation(all_0_8_8) = all_92_2_107, relation(all_0_8_8) = 0, yields: % 9.31/2.89 | (111) all_92_2_107 = 0 % 9.31/2.89 | % 9.31/2.89 | Equations (111) can reduce 144 to: % 9.31/2.89 | (85) $false % 9.31/2.89 | % 9.31/2.89 |-The branch is then unsatisfiable % 9.31/2.89 |-Branch two: % 9.31/2.89 | (148) ~ (all_68_5_100 = 0) & relation(all_0_7_7) = all_68_5_100 % 9.31/2.89 | % 9.31/2.89 | Applying alpha-rule on (148) yields: % 9.31/2.89 | (149) ~ (all_68_5_100 = 0) % 9.31/2.89 | (150) relation(all_0_7_7) = all_68_5_100 % 9.31/2.89 | % 9.31/2.89 | Instantiating formula (64) with all_0_7_7, 0, all_68_5_100 and discharging atoms relation(all_0_7_7) = all_68_5_100, relation(all_0_7_7) = 0, yields: % 9.31/2.89 | (151) all_68_5_100 = 0 % 9.31/2.89 | % 9.31/2.89 | Equations (151) can reduce 149 to: % 9.31/2.89 | (85) $false % 9.31/2.89 | % 9.31/2.89 |-The branch is then unsatisfiable % 9.31/2.89 |-Branch two: % 9.31/2.89 | (153) ~ (all_55_0_93 = 0) & relation(all_0_8_8) = all_55_0_93 % 9.31/2.89 | % 9.31/2.89 | Applying alpha-rule on (153) yields: % 9.31/2.89 | (154) ~ (all_55_0_93 = 0) % 9.31/2.89 | (155) relation(all_0_8_8) = all_55_0_93 % 9.31/2.89 | % 9.31/2.89 | Instantiating formula (64) with all_0_8_8, all_55_0_93, 0 and discharging atoms relation(all_0_8_8) = all_55_0_93, relation(all_0_8_8) = 0, yields: % 9.31/2.89 | (82) all_55_0_93 = 0 % 9.31/2.89 | % 9.31/2.89 | Equations (82) can reduce 154 to: % 9.31/2.89 | (85) $false % 9.31/2.89 | % 9.31/2.89 |-The branch is then unsatisfiable % 9.31/2.89 % SZS output end Proof for theBenchmark % 9.31/2.89 % 9.31/2.89 2269ms %------------------------------------------------------------------------------