%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU215+3 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n007.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 08:47:44 EDT 2022 % Result : Theorem 4.10s 1.62s % Output : Proof 7.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SEU215+3 : TPTP v8.1.0. Released v3.2.0. % 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n007.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 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sun Jun 19 10:22:59 EDT 2022 % 0.12/0.34 % CPUTime : % 0.58/0.58 ____ _ % 0.58/0.58 ___ / __ \_____(_)___ ________ __________ % 0.58/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.58 % 0.58/0.58 A Theorem Prover for First-Order Logic % 0.58/0.59 (ePrincess v.1.0) % 0.58/0.59 % 0.58/0.59 (c) Philipp Rümmer, 2009-2015 % 0.58/0.59 (c) Peter Backeman, 2014-2015 % 0.58/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.59 Bug reports to peter@backeman.se % 0.58/0.59 % 0.58/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.59 % 0.58/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.76/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.40/0.96 Prover 0: Preprocessing ... % 2.44/1.26 Prover 0: Warning: ignoring some quantifiers % 2.74/1.29 Prover 0: Constructing countermodel ... % 4.10/1.62 Prover 0: proved (983ms) % 4.10/1.62 % 4.10/1.62 No countermodel exists, formula is valid % 4.10/1.62 % SZS status Theorem for theBenchmark % 4.10/1.62 % 4.10/1.62 Generating proof ... Warning: ignoring some quantifiers % 6.86/2.21 found it (size 211) % 6.86/2.21 % 6.86/2.21 % SZS output start Proof for theBenchmark % 6.86/2.21 Assumed formulas after preprocessing and simplification: % 6.86/2.21 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ( ~ (v7 = v6) & relation_composition(v1, v4) = v5 & relation_dom(v1) = v2 & apply(v5, v0) = v6 & apply(v4, v3) = v7 & apply(v1, v0) = v3 & relation_empty_yielding(v8) & relation_empty_yielding(empty_set) & relation(v13) & relation(v12) & relation(v10) & relation(v8) & relation(v4) & relation(v1) & relation(empty_set) & function(v13) & function(v4) & function(v1) & empty(v12) & empty(v11) & empty(empty_set) & in(v0, v2) & ~ empty(v10) & ~ empty(v9) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v16, v15) = v17) | ~ (apply(v17, v14) = v18) | ~ relation(v16) | ~ relation(v15) | ~ function(v16) | ~ function(v15) | ? [v19] : ? [v20] : ? [v21] : (relation_dom(v17) = v19 & apply(v16, v14) = v20 & apply(v15, v20) = v21 & (v21 = v18 | ~ in(v14, v19)))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (singleton(v14) = v17) | ~ (unordered_pair(v16, v17) = v18) | ~ (unordered_pair(v14, v15) = v16) | ordered_pair(v14, v15) = v18) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom(v15) = v16) | ~ (apply(v17, v14) = v18) | ~ relation(v17) | ~ relation(v15) | ~ function(v17) | ~ function(v15) | ? [v19] : ? [v20] : ? [v21] : (relation_composition(v17, v15) = v19 & relation_dom(v19) = v20 & relation_dom(v17) = v21 & ( ~ in(v18, v16) | ~ in(v14, v21) | in(v14, v20)) & ( ~ in(v14, v20) | (in(v18, v16) & in(v14, v21))))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom(v14) = v15) | ~ (ordered_pair(v16, v17) = v18) | ~ relation(v14) | ~ function(v14) | ~ in(v16, v15) | ? [v19] : (apply(v14, v16) = v19 & ( ~ (v19 = v17) | in(v18, v14)) & (v19 = v17 | ~ in(v18, v14)))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (apply(v16, v14) = v17) | ~ (apply(v15, v17) = v18) | ~ relation(v16) | ~ relation(v15) | ~ function(v16) | ~ function(v15) | ? [v19] : ? [v20] : ? [v21] : (relation_composition(v16, v15) = v19 & relation_dom(v19) = v20 & apply(v19, v14) = v21 & (v21 = v18 | ~ in(v14, v20)))) & ? [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v17, v15) = v18) | ~ (relation_dom(v15) = v16) | ~ relation(v17) | ~ relation(v15) | ~ function(v17) | ~ function(v15) | ? [v19] : ? [v20] : ? [v21] : (relation_dom(v18) = v19 & relation_dom(v17) = v20 & apply(v17, v14) = v21 & ( ~ in(v21, v16) | ~ in(v14, v20) | in(v14, v19)) & ( ~ in(v14, v19) | (in(v21, v16) & in(v14, v20))))) & ? [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ~ (relation_dom(v15) = v16) | ~ relation(v17) | ~ relation(v15) | ~ function(v17) | ~ function(v15) | ? [v19] : ? [v20] : ? [v21] : (relation_composition(v17, v15) = v19 & relation_dom(v19) = v20 & apply(v17, v14) = v21 & ( ~ in(v21, v16) | ~ in(v14, v18) | in(v14, v20)) & ( ~ in(v14, v20) | (in(v21, v16) & in(v14, v18))))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = empty_set | ~ (relation_dom(v14) = v15) | ~ (apply(v14, v16) = v17) | ~ relation(v14) | ~ function(v14) | in(v16, v15)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (relation_composition(v17, v16) = v15) | ~ (relation_composition(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 | ~ (apply(v17, v16) = v15) | ~ (apply(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (unordered_pair(v17, v16) = v15) | ~ (unordered_pair(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ element(v15, v17) | ~ empty(v16) | ~ in(v14, v15)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ element(v15, v17) | ~ in(v14, v15) | element(v14, v16)) & ? [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v16, v15) = v17) | ~ relation(v16) | ~ relation(v15) | ~ function(v16) | ~ function(v15) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (relation_dom(v17) = v18 & apply(v17, v14) = v19 & apply(v16, v14) = v20 & apply(v15, v20) = v21 & (v21 = v19 | ~ in(v14, v18)))) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (powerset(v16) = v15) | ~ (powerset(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (singleton(v16) = v15) | ~ (singleton(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_dom(v16) = v15) | ~ (relation_dom(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ subset(v14, v15) | element(v14, v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ element(v14, v16) | subset(v14, v15)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v15, v14) = v16) | ~ relation(v15) | ~ empty(v14) | relation(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v15, v14) = v16) | ~ relation(v15) | ~ empty(v14) | empty(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v14, v15) = v16) | ~ relation(v15) | ~ relation(v14) | ~ function(v15) | ~ function(v14) | relation(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v14, v15) = v16) | ~ relation(v15) | ~ relation(v14) | ~ function(v15) | ~ function(v14) | function(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v14, v15) = v16) | ~ relation(v15) | ~ relation(v14) | relation(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v14, v15) = v16) | ~ relation(v15) | ~ empty(v14) | relation(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v14, v15) = v16) | ~ relation(v15) | ~ empty(v14) | empty(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (ordered_pair(v14, v15) = v16) | ~ empty(v16)) & ! [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] : ( ~ (unordered_pair(v15, v14) = v16) | unordered_pair(v14, v15) = v16) & ! [v14] : ! [v15] : ! [v16] : ( ~ (unordered_pair(v14, v15) = v16) | ~ empty(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (unordered_pair(v14, v15) = v16) | unordered_pair(v15, v14) = v16) & ! [v14] : ! [v15] : (v15 = v14 | ~ empty(v15) | ~ empty(v14)) & ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ empty(v15)) & ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | empty(v14) | ? [v16] : (element(v16, v15) & ~ empty(v16))) & ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ? [v16] : (element(v16, v15) & empty(v16))) & ! [v14] : ! [v15] : ( ~ (singleton(v14) = v15) | ~ empty(v15)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ relation(v14) | ~ empty(v15) | empty(v14)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ empty(v14) | relation(v15)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ empty(v14) | empty(v15)) & ! [v14] : ! [v15] : ( ~ element(v14, v15) | empty(v15) | in(v14, v15)) & ! [v14] : ! [v15] : ( ~ empty(v15) | ~ in(v14, v15)) & ! [v14] : ! [v15] : ( ~ in(v15, v14) | ~ in(v14, v15)) & ! [v14] : ! [v15] : ( ~ in(v14, v15) | element(v14, v15)) & ! [v14] : (v14 = empty_set | ~ empty(v14)) & ! [v14] : ( ~ empty(v14) | relation(v14)) & ! [v14] : ( ~ empty(v14) | function(v14)) & ? [v14] : ? [v15] : element(v15, v14) & ? [v14] : subset(v14, v14)) % 6.86/2.25 | 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: % 6.86/2.25 | (1) ~ (all_0_6_6 = all_0_7_7) & relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8 & relation_dom(all_0_12_12) = all_0_11_11 & apply(all_0_8_8, all_0_13_13) = all_0_7_7 & apply(all_0_9_9, all_0_10_10) = all_0_6_6 & apply(all_0_12_12, all_0_13_13) = all_0_10_10 & relation_empty_yielding(all_0_5_5) & relation_empty_yielding(empty_set) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_3_3) & relation(all_0_5_5) & relation(all_0_9_9) & relation(all_0_12_12) & relation(empty_set) & function(all_0_0_0) & function(all_0_9_9) & function(all_0_12_12) & empty(all_0_1_1) & empty(all_0_2_2) & empty(empty_set) & in(all_0_13_13, all_0_11_11) & ~ empty(all_0_3_3) & ~ empty(all_0_4_4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v4 | ~ in(v0, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (apply(v3, v0) = v4) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & relation_dom(v3) = v7 & ( ~ in(v4, v2) | ~ in(v0, v7) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v4, v2) & in(v0, v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ function(v0) | ~ in(v2, v1) | ? [v5] : (apply(v0, v2) = v5 & ( ~ (v5 = v3) | in(v4, v0)) & (v5 = v3 | ~ in(v4, v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v0) = v3) | ~ (apply(v1, v3) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, v1) = v5 & relation_dom(v5) = v6 & apply(v5, v0) = v7 & (v7 = v4 | ~ in(v0, v6)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v1) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_dom(v4) = v5 & relation_dom(v3) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) | ~ in(v0, v6) | in(v0, v5)) & ( ~ in(v0, v5) | (in(v7, v2) & in(v0, v6))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) | ~ in(v0, v4) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v7, v2) & in(v0, v4))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(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 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v4 & apply(v3, v0) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v5 | ~ in(v0, v4)))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [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] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) % 6.86/2.27 | % 6.86/2.27 | Applying alpha-rule on (1) yields: % 6.86/2.27 | (2) ~ empty(all_0_4_4) % 6.86/2.27 | (3) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 6.86/2.27 | (4) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 6.86/2.27 | (5) function(all_0_9_9) % 6.86/2.27 | (6) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v4 & apply(v3, v0) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v5 | ~ in(v0, v4)))) % 6.86/2.27 | (7) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) % 6.86/2.27 | (8) relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8 % 6.86/2.27 | (9) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v1) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_dom(v4) = v5 & relation_dom(v3) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) | ~ in(v0, v6) | in(v0, v5)) & ( ~ in(v0, v5) | (in(v7, v2) & in(v0, v6))))) % 6.86/2.27 | (10) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) % 6.86/2.27 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 6.86/2.27 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (apply(v3, v0) = v4) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & relation_dom(v3) = v7 & ( ~ in(v4, v2) | ~ in(v0, v7) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v4, v2) & in(v0, v7))))) % 7.30/2.27 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 7.30/2.27 | (14) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) % 7.30/2.27 | (15) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 7.30/2.27 | (16) relation_dom(all_0_12_12) = all_0_11_11 % 7.30/2.27 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 7.30/2.27 | (18) relation(empty_set) % 7.30/2.27 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 7.30/2.27 | (20) relation(all_0_12_12) % 7.30/2.27 | (21) ? [v0] : subset(v0, v0) % 7.30/2.27 | (22) ~ (all_0_6_6 = all_0_7_7) % 7.30/2.27 | (23) empty(empty_set) % 7.30/2.27 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 7.30/2.27 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 7.30/2.28 | (26) function(all_0_12_12) % 7.30/2.28 | (27) apply(all_0_12_12, all_0_13_13) = all_0_10_10 % 7.30/2.28 | (28) ~ empty(all_0_3_3) % 7.30/2.28 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ function(v0) | ~ in(v2, v1) | ? [v5] : (apply(v0, v2) = v5 & ( ~ (v5 = v3) | in(v4, v0)) & (v5 = v3 | ~ in(v4, v0)))) % 7.30/2.28 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 7.30/2.28 | (31) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 7.30/2.28 | (32) function(all_0_0_0) % 7.30/2.28 | (33) in(all_0_13_13, all_0_11_11) % 7.30/2.28 | (34) ? [v0] : ? [v1] : element(v1, v0) % 7.30/2.28 | (35) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 7.30/2.28 | (36) relation(all_0_5_5) % 7.30/2.28 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) % 7.30/2.28 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 7.30/2.28 | (39) apply(all_0_8_8, all_0_13_13) = all_0_7_7 % 7.30/2.28 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2)) % 7.30/2.28 | (41) empty(all_0_1_1) % 7.30/2.28 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 7.30/2.28 | (43) ! [v0] : ( ~ empty(v0) | function(v0)) % 7.30/2.28 | (44) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 7.30/2.28 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 7.30/2.28 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 7.30/2.28 | (47) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) % 7.30/2.28 | (48) relation_empty_yielding(empty_set) % 7.30/2.28 | (49) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 7.30/2.28 | (50) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 7.30/2.28 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v0) = v3) | ~ (apply(v1, v3) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, v1) = v5 & relation_dom(v5) = v6 & apply(v5, v0) = v7 & (v7 = v4 | ~ in(v0, v6)))) % 7.30/2.28 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v4 | ~ in(v0, v5)))) % 7.30/2.28 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | in(v2, v1)) % 7.30/2.28 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) % 7.30/2.28 | (55) ! [v0] : ( ~ empty(v0) | relation(v0)) % 7.30/2.29 | (56) apply(all_0_9_9, all_0_10_10) = all_0_6_6 % 7.30/2.29 | (57) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) | ~ in(v0, v4) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v7, v2) & in(v0, v4))))) % 7.30/2.29 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 7.30/2.29 | (59) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 7.30/2.29 | (60) relation(all_0_9_9) % 7.30/2.29 | (61) relation(all_0_1_1) % 7.30/2.29 | (62) empty(all_0_2_2) % 7.30/2.29 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 7.30/2.29 | (64) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 7.30/2.29 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 7.30/2.29 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) % 7.30/2.29 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 7.30/2.29 | (68) relation(all_0_0_0) % 7.30/2.29 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 7.30/2.29 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 7.30/2.29 | (71) relation(all_0_3_3) % 7.30/2.29 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 7.30/2.29 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2)) % 7.30/2.29 | (74) relation_empty_yielding(all_0_5_5) % 7.30/2.29 | % 7.30/2.29 | Instantiating (6) with all_5_0_16 yields: % 7.30/2.29 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v2) = v3 & apply(v2, all_5_0_16) = v4 & apply(v1, all_5_0_16) = v5 & apply(v0, v5) = v6 & (v6 = v4 | ~ in(all_5_0_16, v3)))) % 7.40/2.29 | % 7.40/2.29 | Instantiating (57) with all_7_0_17 yields: % 7.40/2.29 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ~ (relation_dom(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ~ function(v2) | ~ function(v0) | ? [v4] : ? [v5] : ? [v6] : (relation_composition(v2, v0) = v4 & relation_dom(v4) = v5 & apply(v2, all_7_0_17) = v6 & ( ~ in(v6, v1) | ~ in(all_7_0_17, v3) | in(all_7_0_17, v5)) & ( ~ in(all_7_0_17, v5) | (in(v6, v1) & in(all_7_0_17, v3))))) % 7.40/2.29 | % 7.40/2.29 | Instantiating (9) with all_11_0_19 yields: % 7.40/2.29 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v0) = v3) | ~ (relation_dom(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ~ function(v2) | ~ function(v0) | ? [v4] : ? [v5] : ? [v6] : (relation_dom(v3) = v4 & relation_dom(v2) = v5 & apply(v2, all_11_0_19) = v6 & ( ~ in(v6, v1) | ~ in(all_11_0_19, v5) | in(all_11_0_19, v4)) & ( ~ in(all_11_0_19, v4) | (in(v6, v1) & in(all_11_0_19, v5))))) % 7.40/2.29 | % 7.40/2.29 | Instantiating formula (52) with all_0_7_7, all_0_8_8, all_0_12_12, all_0_9_9, all_0_13_13 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, apply(all_0_8_8, all_0_13_13) = all_0_7_7, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 7.40/2.29 | (78) ? [v0] : ? [v1] : ? [v2] : (relation_dom(all_0_8_8) = v0 & apply(all_0_9_9, v1) = v2 & apply(all_0_12_12, all_0_13_13) = v1 & (v2 = all_0_7_7 | ~ in(all_0_13_13, v0))) % 7.40/2.29 | % 7.40/2.29 | Instantiating formula (73) with all_0_8_8, all_0_9_9, all_0_12_12 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 7.40/2.29 | (79) relation(all_0_8_8) % 7.40/2.29 | % 7.40/2.29 | Instantiating formula (40) with all_0_8_8, all_0_9_9, all_0_12_12 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 7.40/2.30 | (80) function(all_0_8_8) % 7.40/2.30 | % 7.40/2.30 | Instantiating formula (75) with all_0_8_8, all_0_12_12, all_0_9_9 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 7.40/2.30 | (81) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_dom(all_0_8_8) = v0 & apply(all_0_8_8, all_5_0_16) = v1 & apply(all_0_9_9, v2) = v3 & apply(all_0_12_12, all_5_0_16) = v2 & (v3 = v1 | ~ in(all_5_0_16, v0))) % 7.40/2.30 | % 7.40/2.30 | Instantiating formula (12) with all_0_10_10, all_0_12_12, all_0_11_11, all_0_12_12, all_0_13_13 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, apply(all_0_12_12, all_0_13_13) = all_0_10_10, relation(all_0_12_12), function(all_0_12_12), yields: % 7.40/2.30 | (82) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_12_12) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_0_10_10, all_0_11_11) | ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_10_10, all_0_11_11) & in(all_0_13_13, v2)))) % 7.40/2.30 | % 7.40/2.30 | Instantiating formula (76) with all_0_11_11, all_0_12_12, all_0_11_11, all_0_12_12 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, relation(all_0_12_12), function(all_0_12_12), yields: % 7.40/2.30 | (83) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_12_12) = v0 & relation_dom(v0) = v1 & apply(all_0_12_12, all_7_0_17) = v2 & ( ~ in(v2, all_0_11_11) | ~ in(all_7_0_17, all_0_11_11) | in(all_7_0_17, v1)) & ( ~ in(all_7_0_17, v1) | (in(v2, all_0_11_11) & in(all_7_0_17, all_0_11_11)))) % 7.40/2.30 | % 7.40/2.30 | Instantiating formula (12) with all_0_6_6, all_0_9_9, all_0_11_11, all_0_12_12, all_0_10_10 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, apply(all_0_9_9, all_0_10_10) = all_0_6_6, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 7.40/2.30 | (84) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_9_9, all_0_12_12) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_9_9) = v2 & ( ~ in(all_0_6_6, all_0_11_11) | ~ in(all_0_10_10, v2) | in(all_0_10_10, v1)) & ( ~ in(all_0_10_10, v1) | (in(all_0_6_6, all_0_11_11) & in(all_0_10_10, v2)))) % 7.40/2.30 | % 7.40/2.30 | Instantiating formula (51) with all_0_6_6, all_0_10_10, all_0_12_12, all_0_9_9, all_0_13_13 and discharging atoms apply(all_0_9_9, all_0_10_10) = all_0_6_6, apply(all_0_12_12, all_0_13_13) = all_0_10_10, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 7.40/2.30 | (85) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_9_9) = v0 & relation_dom(v0) = v1 & apply(v0, all_0_13_13) = v2 & (v2 = all_0_6_6 | ~ in(all_0_13_13, v1))) % 7.40/2.30 | % 7.40/2.30 | Instantiating (84) with all_23_0_20, all_23_1_21, all_23_2_22 yields: % 7.40/2.30 | (86) relation_composition(all_0_9_9, all_0_12_12) = all_23_2_22 & relation_dom(all_23_2_22) = all_23_1_21 & relation_dom(all_0_9_9) = all_23_0_20 & ( ~ in(all_0_6_6, all_0_11_11) | ~ in(all_0_10_10, all_23_0_20) | in(all_0_10_10, all_23_1_21)) & ( ~ in(all_0_10_10, all_23_1_21) | (in(all_0_6_6, all_0_11_11) & in(all_0_10_10, all_23_0_20))) % 7.40/2.30 | % 7.40/2.30 | Applying alpha-rule on (86) yields: % 7.40/2.30 | (87) relation_dom(all_0_9_9) = all_23_0_20 % 7.40/2.30 | (88) ~ in(all_0_10_10, all_23_1_21) | (in(all_0_6_6, all_0_11_11) & in(all_0_10_10, all_23_0_20)) % 7.40/2.30 | (89) relation_dom(all_23_2_22) = all_23_1_21 % 7.40/2.30 | (90) relation_composition(all_0_9_9, all_0_12_12) = all_23_2_22 % 7.40/2.30 | (91) ~ in(all_0_6_6, all_0_11_11) | ~ in(all_0_10_10, all_23_0_20) | in(all_0_10_10, all_23_1_21) % 7.40/2.30 | % 7.40/2.30 | Instantiating (82) with all_25_0_23, all_25_1_24, all_25_2_25 yields: % 7.40/2.30 | (92) relation_composition(all_0_12_12, all_0_12_12) = all_25_2_25 & relation_dom(all_25_2_25) = all_25_1_24 & relation_dom(all_0_12_12) = all_25_0_23 & ( ~ in(all_0_10_10, all_0_11_11) | ~ in(all_0_13_13, all_25_0_23) | in(all_0_13_13, all_25_1_24)) & ( ~ in(all_0_13_13, all_25_1_24) | (in(all_0_10_10, all_0_11_11) & in(all_0_13_13, all_25_0_23))) % 7.40/2.30 | % 7.40/2.30 | Applying alpha-rule on (92) yields: % 7.40/2.30 | (93) relation_dom(all_25_2_25) = all_25_1_24 % 7.40/2.30 | (94) ~ in(all_0_10_10, all_0_11_11) | ~ in(all_0_13_13, all_25_0_23) | in(all_0_13_13, all_25_1_24) % 7.40/2.30 | (95) relation_dom(all_0_12_12) = all_25_0_23 % 7.40/2.30 | (96) relation_composition(all_0_12_12, all_0_12_12) = all_25_2_25 % 7.40/2.30 | (97) ~ in(all_0_13_13, all_25_1_24) | (in(all_0_10_10, all_0_11_11) & in(all_0_13_13, all_25_0_23)) % 7.40/2.30 | % 7.40/2.30 | Instantiating (81) with all_27_0_26, all_27_1_27, all_27_2_28, all_27_3_29 yields: % 7.40/2.30 | (98) relation_dom(all_0_8_8) = all_27_3_29 & apply(all_0_8_8, all_5_0_16) = all_27_2_28 & apply(all_0_9_9, all_27_1_27) = all_27_0_26 & apply(all_0_12_12, all_5_0_16) = all_27_1_27 & (all_27_0_26 = all_27_2_28 | ~ in(all_5_0_16, all_27_3_29)) % 7.40/2.30 | % 7.40/2.30 | Applying alpha-rule on (98) yields: % 7.40/2.30 | (99) all_27_0_26 = all_27_2_28 | ~ in(all_5_0_16, all_27_3_29) % 7.40/2.30 | (100) apply(all_0_8_8, all_5_0_16) = all_27_2_28 % 7.40/2.30 | (101) apply(all_0_12_12, all_5_0_16) = all_27_1_27 % 7.40/2.30 | (102) apply(all_0_9_9, all_27_1_27) = all_27_0_26 % 7.40/2.30 | (103) relation_dom(all_0_8_8) = all_27_3_29 % 7.40/2.30 | % 7.40/2.30 | Instantiating (83) with all_29_0_30, all_29_1_31, all_29_2_32 yields: % 7.40/2.30 | (104) relation_composition(all_0_12_12, all_0_12_12) = all_29_2_32 & relation_dom(all_29_2_32) = all_29_1_31 & apply(all_0_12_12, all_7_0_17) = all_29_0_30 & ( ~ in(all_29_0_30, all_0_11_11) | ~ in(all_7_0_17, all_0_11_11) | in(all_7_0_17, all_29_1_31)) & ( ~ in(all_7_0_17, all_29_1_31) | (in(all_29_0_30, all_0_11_11) & in(all_7_0_17, all_0_11_11))) % 7.40/2.30 | % 7.40/2.30 | Applying alpha-rule on (104) yields: % 7.40/2.30 | (105) relation_dom(all_29_2_32) = all_29_1_31 % 7.40/2.30 | (106) relation_composition(all_0_12_12, all_0_12_12) = all_29_2_32 % 7.40/2.30 | (107) apply(all_0_12_12, all_7_0_17) = all_29_0_30 % 7.40/2.30 | (108) ~ in(all_29_0_30, all_0_11_11) | ~ in(all_7_0_17, all_0_11_11) | in(all_7_0_17, all_29_1_31) % 7.40/2.30 | (109) ~ in(all_7_0_17, all_29_1_31) | (in(all_29_0_30, all_0_11_11) & in(all_7_0_17, all_0_11_11)) % 7.40/2.30 | % 7.40/2.30 | Instantiating (85) with all_31_0_33, all_31_1_34, all_31_2_35 yields: % 7.40/2.30 | (110) relation_composition(all_0_12_12, all_0_9_9) = all_31_2_35 & relation_dom(all_31_2_35) = all_31_1_34 & apply(all_31_2_35, all_0_13_13) = all_31_0_33 & (all_31_0_33 = all_0_6_6 | ~ in(all_0_13_13, all_31_1_34)) % 7.40/2.30 | % 7.40/2.30 | Applying alpha-rule on (110) yields: % 7.40/2.30 | (111) relation_composition(all_0_12_12, all_0_9_9) = all_31_2_35 % 7.40/2.30 | (112) relation_dom(all_31_2_35) = all_31_1_34 % 7.40/2.30 | (113) apply(all_31_2_35, all_0_13_13) = all_31_0_33 % 7.40/2.30 | (114) all_31_0_33 = all_0_6_6 | ~ in(all_0_13_13, all_31_1_34) % 7.40/2.30 | % 7.40/2.30 | Instantiating (78) with all_33_0_36, all_33_1_37, all_33_2_38 yields: % 7.40/2.30 | (115) relation_dom(all_0_8_8) = all_33_2_38 & apply(all_0_9_9, all_33_1_37) = all_33_0_36 & apply(all_0_12_12, all_0_13_13) = all_33_1_37 & (all_33_0_36 = all_0_7_7 | ~ in(all_0_13_13, all_33_2_38)) % 7.40/2.30 | % 7.40/2.30 | Applying alpha-rule on (115) yields: % 7.40/2.30 | (116) relation_dom(all_0_8_8) = all_33_2_38 % 7.40/2.30 | (117) apply(all_0_9_9, all_33_1_37) = all_33_0_36 % 7.40/2.30 | (118) apply(all_0_12_12, all_0_13_13) = all_33_1_37 % 7.40/2.30 | (119) all_33_0_36 = all_0_7_7 | ~ in(all_0_13_13, all_33_2_38) % 7.40/2.30 | % 7.40/2.30 | Instantiating formula (54) with all_0_12_12, all_0_9_9, all_31_2_35, all_0_8_8 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_31_2_35, relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, yields: % 7.40/2.30 | (120) all_31_2_35 = all_0_8_8 % 7.40/2.30 | % 7.40/2.30 | Instantiating formula (54) with all_0_12_12, all_0_12_12, all_25_2_25, all_29_2_32 and discharging atoms relation_composition(all_0_12_12, all_0_12_12) = all_29_2_32, relation_composition(all_0_12_12, all_0_12_12) = all_25_2_25, yields: % 7.40/2.30 | (121) all_29_2_32 = all_25_2_25 % 7.40/2.30 | % 7.40/2.30 | Instantiating formula (38) with all_0_8_8, all_27_3_29, all_33_2_38 and discharging atoms relation_dom(all_0_8_8) = all_33_2_38, relation_dom(all_0_8_8) = all_27_3_29, yields: % 7.40/2.30 | (122) all_33_2_38 = all_27_3_29 % 7.40/2.30 | % 7.40/2.30 | Instantiating formula (38) with all_0_12_12, all_25_0_23, all_0_11_11 and discharging atoms relation_dom(all_0_12_12) = all_25_0_23, relation_dom(all_0_12_12) = all_0_11_11, yields: % 7.40/2.30 | (123) all_25_0_23 = all_0_11_11 % 7.40/2.30 | % 7.40/2.30 | Instantiating formula (13) with all_0_12_12, all_0_13_13, all_33_1_37, all_0_10_10 and discharging atoms apply(all_0_12_12, all_0_13_13) = all_33_1_37, apply(all_0_12_12, all_0_13_13) = all_0_10_10, yields: % 7.40/2.31 | (124) all_33_1_37 = all_0_10_10 % 7.40/2.31 | % 7.40/2.31 | From (120) and (111) follows: % 7.40/2.31 | (8) relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8 % 7.40/2.31 | % 7.40/2.31 | From (121) and (106) follows: % 7.40/2.31 | (96) relation_composition(all_0_12_12, all_0_12_12) = all_25_2_25 % 7.40/2.31 | % 7.40/2.31 | From (120) and (112) follows: % 7.40/2.31 | (127) relation_dom(all_0_8_8) = all_31_1_34 % 7.40/2.31 | % 7.40/2.31 | From (122) and (116) follows: % 7.40/2.31 | (103) relation_dom(all_0_8_8) = all_27_3_29 % 7.40/2.31 | % 7.40/2.31 | From (123) and (95) follows: % 7.40/2.31 | (16) relation_dom(all_0_12_12) = all_0_11_11 % 7.40/2.31 | % 7.40/2.31 | From (120) and (113) follows: % 7.40/2.31 | (130) apply(all_0_8_8, all_0_13_13) = all_31_0_33 % 7.40/2.31 | % 7.40/2.31 | From (124) and (117) follows: % 7.40/2.31 | (131) apply(all_0_9_9, all_0_10_10) = all_33_0_36 % 7.40/2.31 | % 7.40/2.31 | From (124) and (118) follows: % 7.40/2.31 | (27) apply(all_0_12_12, all_0_13_13) = all_0_10_10 % 7.40/2.31 | % 7.40/2.31 | Instantiating formula (38) with all_0_8_8, all_31_1_34, all_27_3_29 and discharging atoms relation_dom(all_0_8_8) = all_31_1_34, relation_dom(all_0_8_8) = all_27_3_29, yields: % 7.40/2.31 | (133) all_31_1_34 = all_27_3_29 % 7.40/2.31 | % 7.40/2.31 | Instantiating formula (13) with all_0_8_8, all_0_13_13, all_31_0_33, all_0_7_7 and discharging atoms apply(all_0_8_8, all_0_13_13) = all_31_0_33, apply(all_0_8_8, all_0_13_13) = all_0_7_7, yields: % 7.40/2.31 | (134) all_31_0_33 = all_0_7_7 % 7.40/2.31 | % 7.40/2.31 | Instantiating formula (13) with all_0_9_9, all_0_10_10, all_33_0_36, all_0_6_6 and discharging atoms apply(all_0_9_9, all_0_10_10) = all_33_0_36, apply(all_0_9_9, all_0_10_10) = all_0_6_6, yields: % 7.40/2.31 | (135) all_33_0_36 = all_0_6_6 % 7.40/2.31 | % 7.40/2.31 | From (133) and (127) follows: % 7.40/2.31 | (103) relation_dom(all_0_8_8) = all_27_3_29 % 7.40/2.31 | % 7.40/2.31 | From (134) and (130) follows: % 7.40/2.31 | (39) apply(all_0_8_8, all_0_13_13) = all_0_7_7 % 7.40/2.31 | % 7.40/2.31 | From (135) and (131) follows: % 7.40/2.31 | (56) apply(all_0_9_9, all_0_10_10) = all_0_6_6 % 7.40/2.31 | % 7.40/2.31 +-Applying beta-rule and splitting (114), into two cases. % 7.40/2.31 |-Branch one: % 7.40/2.31 | (139) ~ in(all_0_13_13, all_31_1_34) % 7.40/2.31 | % 7.40/2.31 | From (133) and (139) follows: % 7.40/2.31 | (140) ~ in(all_0_13_13, all_27_3_29) % 7.40/2.31 | % 7.40/2.31 | Instantiating formula (77) with all_25_2_25, all_0_12_12, all_0_11_11, all_0_12_12 and discharging atoms relation_composition(all_0_12_12, all_0_12_12) = all_25_2_25, relation_dom(all_0_12_12) = all_0_11_11, relation(all_0_12_12), function(all_0_12_12), yields: % 7.40/2.31 | (141) ? [v0] : ? [v1] : ? [v2] : (relation_dom(all_25_2_25) = v0 & relation_dom(all_0_12_12) = v1 & apply(all_0_12_12, all_11_0_19) = v2 & ( ~ in(v2, all_0_11_11) | ~ in(all_11_0_19, v1) | in(all_11_0_19, v0)) & ( ~ in(all_11_0_19, v0) | (in(v2, all_0_11_11) & in(all_11_0_19, v1)))) % 7.40/2.31 | % 7.40/2.31 | Instantiating formula (53) with all_0_6_6, all_0_10_10, all_23_0_20, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_23_0_20, apply(all_0_9_9, all_0_10_10) = all_0_6_6, relation(all_0_9_9), function(all_0_9_9), yields: % 7.40/2.31 | (142) all_0_6_6 = empty_set | in(all_0_10_10, all_23_0_20) % 7.40/2.31 | % 7.40/2.31 | Instantiating formula (12) with all_0_10_10, all_0_12_12, all_23_0_20, all_0_9_9, all_0_13_13 and discharging atoms relation_dom(all_0_9_9) = all_23_0_20, apply(all_0_12_12, all_0_13_13) = all_0_10_10, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 7.40/2.31 | (143) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_9_9) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_0_10_10, all_23_0_20) | ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_10_10, all_23_0_20) & in(all_0_13_13, v2)))) % 7.40/2.31 | % 7.40/2.31 | Instantiating formula (77) with all_0_8_8, all_0_12_12, all_23_0_20, all_0_9_9 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, relation_dom(all_0_9_9) = all_23_0_20, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 7.40/2.31 | (144) ? [v0] : ? [v1] : ? [v2] : (relation_dom(all_0_8_8) = v0 & relation_dom(all_0_12_12) = v1 & apply(all_0_12_12, all_11_0_19) = v2 & ( ~ in(v2, all_23_0_20) | ~ in(all_11_0_19, v1) | in(all_11_0_19, v0)) & ( ~ in(all_11_0_19, v0) | (in(v2, all_23_0_20) & in(all_11_0_19, v1)))) % 7.40/2.31 | % 7.40/2.31 | Instantiating formula (76) with all_0_11_11, all_0_12_12, all_23_0_20, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_23_0_20, relation_dom(all_0_12_12) = all_0_11_11, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 7.40/2.31 | (145) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_9_9) = v0 & relation_dom(v0) = v1 & apply(all_0_12_12, all_7_0_17) = v2 & ( ~ in(v2, all_23_0_20) | ~ in(all_7_0_17, all_0_11_11) | in(all_7_0_17, v1)) & ( ~ in(all_7_0_17, v1) | (in(v2, all_23_0_20) & in(all_7_0_17, all_0_11_11)))) % 7.40/2.31 | % 7.40/2.31 | Instantiating formula (52) with all_27_2_28, all_0_8_8, all_0_12_12, all_0_9_9, all_5_0_16 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, apply(all_0_8_8, all_5_0_16) = all_27_2_28, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 7.40/2.31 | (146) ? [v0] : ? [v1] : ? [v2] : (relation_dom(all_0_8_8) = v0 & apply(all_0_9_9, v1) = v2 & apply(all_0_12_12, all_5_0_16) = v1 & (v2 = all_27_2_28 | ~ in(all_5_0_16, v0))) % 7.40/2.31 | % 7.40/2.31 | Instantiating formula (12) with all_29_0_30, all_0_12_12, all_0_11_11, all_0_12_12, all_7_0_17 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, apply(all_0_12_12, all_7_0_17) = all_29_0_30, relation(all_0_12_12), function(all_0_12_12), yields: % 7.40/2.31 | (147) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_12_12) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_29_0_30, all_0_11_11) | ~ in(all_7_0_17, v2) | in(all_7_0_17, v1)) & ( ~ in(all_7_0_17, v1) | (in(all_29_0_30, all_0_11_11) & in(all_7_0_17, v2)))) % 7.40/2.31 | % 7.40/2.31 | Instantiating formula (12) with all_29_0_30, all_0_12_12, all_23_0_20, all_0_9_9, all_7_0_17 and discharging atoms relation_dom(all_0_9_9) = all_23_0_20, apply(all_0_12_12, all_7_0_17) = all_29_0_30, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 7.40/2.31 | (148) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_9_9) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_29_0_30, all_23_0_20) | ~ in(all_7_0_17, v2) | in(all_7_0_17, v1)) & ( ~ in(all_7_0_17, v1) | (in(all_29_0_30, all_23_0_20) & in(all_7_0_17, v2)))) % 7.40/2.31 | % 7.40/2.31 | Instantiating formula (12) with all_27_1_27, all_0_12_12, all_0_11_11, all_0_12_12, all_5_0_16 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, apply(all_0_12_12, all_5_0_16) = all_27_1_27, relation(all_0_12_12), function(all_0_12_12), yields: % 7.40/2.31 | (149) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_12_12) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_27_1_27, all_0_11_11) | ~ in(all_5_0_16, v2) | in(all_5_0_16, v1)) & ( ~ in(all_5_0_16, v1) | (in(all_27_1_27, all_0_11_11) & in(all_5_0_16, v2)))) % 7.40/2.31 | % 7.40/2.31 | Instantiating formula (12) with all_27_1_27, all_0_12_12, all_23_0_20, all_0_9_9, all_5_0_16 and discharging atoms relation_dom(all_0_9_9) = all_23_0_20, apply(all_0_12_12, all_5_0_16) = all_27_1_27, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 7.40/2.31 | (150) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_9_9) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_27_1_27, all_23_0_20) | ~ in(all_5_0_16, v2) | in(all_5_0_16, v1)) & ( ~ in(all_5_0_16, v1) | (in(all_27_1_27, all_23_0_20) & in(all_5_0_16, v2)))) % 7.40/2.31 | % 7.40/2.31 | Instantiating formula (51) with all_27_0_26, all_27_1_27, all_0_12_12, all_0_9_9, all_5_0_16 and discharging atoms apply(all_0_9_9, all_27_1_27) = all_27_0_26, apply(all_0_12_12, all_5_0_16) = all_27_1_27, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 7.40/2.32 | (151) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_9_9) = v0 & relation_dom(v0) = v1 & apply(v0, all_5_0_16) = v2 & (v2 = all_27_0_26 | ~ in(all_5_0_16, v1))) % 7.40/2.32 | % 7.40/2.32 | Instantiating formula (12) with all_0_7_7, all_0_8_8, all_0_11_11, all_0_12_12, all_0_13_13 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, apply(all_0_8_8, all_0_13_13) = all_0_7_7, relation(all_0_8_8), relation(all_0_12_12), function(all_0_8_8), function(all_0_12_12), yields: % 7.40/2.32 | (152) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_8_8, all_0_12_12) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_8_8) = v2 & ( ~ in(all_0_7_7, all_0_11_11) | ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_7_7, all_0_11_11) & in(all_0_13_13, v2)))) % 7.52/2.32 | % 7.52/2.32 | Instantiating formula (12) with all_27_2_28, all_0_8_8, all_0_11_11, all_0_12_12, all_5_0_16 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, apply(all_0_8_8, all_5_0_16) = all_27_2_28, relation(all_0_8_8), relation(all_0_12_12), function(all_0_8_8), function(all_0_12_12), yields: % 7.52/2.32 | (153) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_8_8, all_0_12_12) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_8_8) = v2 & ( ~ in(all_27_2_28, all_0_11_11) | ~ in(all_5_0_16, v2) | in(all_5_0_16, v1)) & ( ~ in(all_5_0_16, v1) | (in(all_27_2_28, all_0_11_11) & in(all_5_0_16, v2)))) % 7.52/2.32 | % 7.52/2.32 | Instantiating formula (12) with all_0_7_7, all_0_8_8, all_27_3_29, all_0_8_8, all_0_13_13 and discharging atoms relation_dom(all_0_8_8) = all_27_3_29, apply(all_0_8_8, all_0_13_13) = all_0_7_7, relation(all_0_8_8), function(all_0_8_8), yields: % 7.52/2.32 | (154) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_8_8, all_0_8_8) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_8_8) = v2 & ( ~ in(all_0_7_7, all_27_3_29) | ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_7_7, all_27_3_29) & in(all_0_13_13, v2)))) % 7.52/2.32 | % 7.52/2.32 | Instantiating formula (12) with all_27_2_28, all_0_8_8, all_27_3_29, all_0_8_8, all_5_0_16 and discharging atoms relation_dom(all_0_8_8) = all_27_3_29, apply(all_0_8_8, all_5_0_16) = all_27_2_28, relation(all_0_8_8), function(all_0_8_8), yields: % 7.52/2.32 | (155) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_8_8, all_0_8_8) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_8_8) = v2 & ( ~ in(all_27_2_28, all_27_3_29) | ~ in(all_5_0_16, v2) | in(all_5_0_16, v1)) & ( ~ in(all_5_0_16, v1) | (in(all_27_2_28, all_27_3_29) & in(all_5_0_16, v2)))) % 7.52/2.32 | % 7.52/2.32 | Instantiating formula (53) with all_0_7_7, all_0_13_13, all_27_3_29, all_0_8_8 and discharging atoms relation_dom(all_0_8_8) = all_27_3_29, apply(all_0_8_8, all_0_13_13) = all_0_7_7, relation(all_0_8_8), function(all_0_8_8), ~ in(all_0_13_13, all_27_3_29), yields: % 7.52/2.32 | (156) all_0_7_7 = empty_set % 7.52/2.32 | % 7.52/2.32 | Instantiating formula (12) with all_0_10_10, all_0_12_12, all_27_3_29, all_0_8_8, all_0_13_13 and discharging atoms relation_dom(all_0_8_8) = all_27_3_29, apply(all_0_12_12, all_0_13_13) = all_0_10_10, relation(all_0_8_8), relation(all_0_12_12), function(all_0_8_8), function(all_0_12_12), yields: % 7.52/2.32 | (157) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_8_8) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_0_10_10, all_27_3_29) | ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_10_10, all_27_3_29) & in(all_0_13_13, v2)))) % 7.52/2.32 | % 7.52/2.32 | Instantiating formula (12) with all_29_0_30, all_0_12_12, all_27_3_29, all_0_8_8, all_7_0_17 and discharging atoms relation_dom(all_0_8_8) = all_27_3_29, apply(all_0_12_12, all_7_0_17) = all_29_0_30, relation(all_0_8_8), relation(all_0_12_12), function(all_0_8_8), function(all_0_12_12), yields: % 7.52/2.32 | (158) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_8_8) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_29_0_30, all_27_3_29) | ~ in(all_7_0_17, v2) | in(all_7_0_17, v1)) & ( ~ in(all_7_0_17, v1) | (in(all_29_0_30, all_27_3_29) & in(all_7_0_17, v2)))) % 7.52/2.32 | % 7.52/2.32 | Instantiating formula (12) with all_27_1_27, all_0_12_12, all_27_3_29, all_0_8_8, all_5_0_16 and discharging atoms relation_dom(all_0_8_8) = all_27_3_29, apply(all_0_12_12, all_5_0_16) = all_27_1_27, relation(all_0_8_8), relation(all_0_12_12), function(all_0_8_8), function(all_0_12_12), yields: % 7.52/2.32 | (159) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_8_8) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_27_1_27, all_27_3_29) | ~ in(all_5_0_16, v2) | in(all_5_0_16, v1)) & ( ~ in(all_5_0_16, v1) | (in(all_27_1_27, all_27_3_29) & in(all_5_0_16, v2)))) % 7.52/2.32 | % 7.52/2.32 | Instantiating formula (12) with all_0_7_7, all_0_8_8, all_23_0_20, all_0_9_9, all_0_13_13 and discharging atoms relation_dom(all_0_9_9) = all_23_0_20, apply(all_0_8_8, all_0_13_13) = all_0_7_7, relation(all_0_8_8), relation(all_0_9_9), function(all_0_8_8), function(all_0_9_9), yields: % 7.52/2.32 | (160) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_8_8, all_0_9_9) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_8_8) = v2 & ( ~ in(all_0_7_7, all_23_0_20) | ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_7_7, all_23_0_20) & in(all_0_13_13, v2)))) % 7.52/2.32 | % 7.52/2.32 | Instantiating formula (12) with all_27_2_28, all_0_8_8, all_23_0_20, all_0_9_9, all_5_0_16 and discharging atoms relation_dom(all_0_9_9) = all_23_0_20, apply(all_0_8_8, all_5_0_16) = all_27_2_28, relation(all_0_8_8), relation(all_0_9_9), function(all_0_8_8), function(all_0_9_9), yields: % 7.52/2.32 | (161) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_8_8, all_0_9_9) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_8_8) = v2 & ( ~ in(all_27_2_28, all_23_0_20) | ~ in(all_5_0_16, v2) | in(all_5_0_16, v1)) & ( ~ in(all_5_0_16, v1) | (in(all_27_2_28, all_23_0_20) & in(all_5_0_16, v2)))) % 7.52/2.32 | % 7.52/2.32 | Instantiating (161) with all_55_0_42, all_55_1_43, all_55_2_44 yields: % 7.52/2.32 | (162) relation_composition(all_0_8_8, all_0_9_9) = all_55_2_44 & relation_dom(all_55_2_44) = all_55_1_43 & relation_dom(all_0_8_8) = all_55_0_42 & ( ~ in(all_27_2_28, all_23_0_20) | ~ in(all_5_0_16, all_55_0_42) | in(all_5_0_16, all_55_1_43)) & ( ~ in(all_5_0_16, all_55_1_43) | (in(all_27_2_28, all_23_0_20) & in(all_5_0_16, all_55_0_42))) % 7.52/2.32 | % 7.52/2.32 | Applying alpha-rule on (162) yields: % 7.52/2.32 | (163) ~ in(all_5_0_16, all_55_1_43) | (in(all_27_2_28, all_23_0_20) & in(all_5_0_16, all_55_0_42)) % 7.52/2.32 | (164) relation_dom(all_55_2_44) = all_55_1_43 % 7.52/2.32 | (165) relation_dom(all_0_8_8) = all_55_0_42 % 7.52/2.32 | (166) relation_composition(all_0_8_8, all_0_9_9) = all_55_2_44 % 7.52/2.32 | (167) ~ in(all_27_2_28, all_23_0_20) | ~ in(all_5_0_16, all_55_0_42) | in(all_5_0_16, all_55_1_43) % 7.52/2.32 | % 7.52/2.32 | Instantiating (159) with all_61_0_52, all_61_1_53, all_61_2_54 yields: % 7.52/2.32 | (168) relation_composition(all_0_12_12, all_0_8_8) = all_61_2_54 & relation_dom(all_61_2_54) = all_61_1_53 & relation_dom(all_0_12_12) = all_61_0_52 & ( ~ in(all_27_1_27, all_27_3_29) | ~ in(all_5_0_16, all_61_0_52) | in(all_5_0_16, all_61_1_53)) & ( ~ in(all_5_0_16, all_61_1_53) | (in(all_27_1_27, all_27_3_29) & in(all_5_0_16, all_61_0_52))) % 7.55/2.32 | % 7.55/2.32 | Applying alpha-rule on (168) yields: % 7.55/2.32 | (169) ~ in(all_5_0_16, all_61_1_53) | (in(all_27_1_27, all_27_3_29) & in(all_5_0_16, all_61_0_52)) % 7.55/2.32 | (170) ~ in(all_27_1_27, all_27_3_29) | ~ in(all_5_0_16, all_61_0_52) | in(all_5_0_16, all_61_1_53) % 7.55/2.32 | (171) relation_dom(all_0_12_12) = all_61_0_52 % 7.55/2.32 | (172) relation_composition(all_0_12_12, all_0_8_8) = all_61_2_54 % 7.55/2.32 | (173) relation_dom(all_61_2_54) = all_61_1_53 % 7.55/2.32 | % 7.55/2.32 | Instantiating (158) with all_63_0_55, all_63_1_56, all_63_2_57 yields: % 7.55/2.32 | (174) relation_composition(all_0_12_12, all_0_8_8) = all_63_2_57 & relation_dom(all_63_2_57) = all_63_1_56 & relation_dom(all_0_12_12) = all_63_0_55 & ( ~ in(all_29_0_30, all_27_3_29) | ~ in(all_7_0_17, all_63_0_55) | in(all_7_0_17, all_63_1_56)) & ( ~ in(all_7_0_17, all_63_1_56) | (in(all_29_0_30, all_27_3_29) & in(all_7_0_17, all_63_0_55))) % 7.55/2.32 | % 7.55/2.32 | Applying alpha-rule on (174) yields: % 7.55/2.32 | (175) ~ in(all_7_0_17, all_63_1_56) | (in(all_29_0_30, all_27_3_29) & in(all_7_0_17, all_63_0_55)) % 7.55/2.32 | (176) ~ in(all_29_0_30, all_27_3_29) | ~ in(all_7_0_17, all_63_0_55) | in(all_7_0_17, all_63_1_56) % 7.55/2.32 | (177) relation_dom(all_0_12_12) = all_63_0_55 % 7.55/2.32 | (178) relation_dom(all_63_2_57) = all_63_1_56 % 7.55/2.32 | (179) relation_composition(all_0_12_12, all_0_8_8) = all_63_2_57 % 7.55/2.32 | % 7.55/2.32 | Instantiating (160) with all_65_0_58, all_65_1_59, all_65_2_60 yields: % 7.55/2.32 | (180) relation_composition(all_0_8_8, all_0_9_9) = all_65_2_60 & relation_dom(all_65_2_60) = all_65_1_59 & relation_dom(all_0_8_8) = all_65_0_58 & ( ~ in(all_0_7_7, all_23_0_20) | ~ in(all_0_13_13, all_65_0_58) | in(all_0_13_13, all_65_1_59)) & ( ~ in(all_0_13_13, all_65_1_59) | (in(all_0_7_7, all_23_0_20) & in(all_0_13_13, all_65_0_58))) % 7.55/2.32 | % 7.55/2.32 | Applying alpha-rule on (180) yields: % 7.55/2.32 | (181) relation_composition(all_0_8_8, all_0_9_9) = all_65_2_60 % 7.55/2.32 | (182) ~ in(all_0_13_13, all_65_1_59) | (in(all_0_7_7, all_23_0_20) & in(all_0_13_13, all_65_0_58)) % 7.55/2.32 | (183) ~ in(all_0_7_7, all_23_0_20) | ~ in(all_0_13_13, all_65_0_58) | in(all_0_13_13, all_65_1_59) % 7.55/2.32 | (184) relation_dom(all_65_2_60) = all_65_1_59 % 7.55/2.32 | (185) relation_dom(all_0_8_8) = all_65_0_58 % 7.55/2.32 | % 7.55/2.32 | Instantiating (149) with all_71_0_67, all_71_1_68, all_71_2_69 yields: % 7.55/2.32 | (186) relation_composition(all_0_12_12, all_0_12_12) = all_71_2_69 & relation_dom(all_71_2_69) = all_71_1_68 & relation_dom(all_0_12_12) = all_71_0_67 & ( ~ in(all_27_1_27, all_0_11_11) | ~ in(all_5_0_16, all_71_0_67) | in(all_5_0_16, all_71_1_68)) & ( ~ in(all_5_0_16, all_71_1_68) | (in(all_27_1_27, all_0_11_11) & in(all_5_0_16, all_71_0_67))) % 7.55/2.32 | % 7.55/2.32 | Applying alpha-rule on (186) yields: % 7.55/2.32 | (187) ~ in(all_27_1_27, all_0_11_11) | ~ in(all_5_0_16, all_71_0_67) | in(all_5_0_16, all_71_1_68) % 7.55/2.32 | (188) relation_dom(all_71_2_69) = all_71_1_68 % 7.55/2.32 | (189) relation_dom(all_0_12_12) = all_71_0_67 % 7.55/2.32 | (190) ~ in(all_5_0_16, all_71_1_68) | (in(all_27_1_27, all_0_11_11) & in(all_5_0_16, all_71_0_67)) % 7.55/2.33 | (191) relation_composition(all_0_12_12, all_0_12_12) = all_71_2_69 % 7.55/2.33 | % 7.55/2.33 | Instantiating (147) with all_73_0_70, all_73_1_71, all_73_2_72 yields: % 7.55/2.33 | (192) relation_composition(all_0_12_12, all_0_12_12) = all_73_2_72 & relation_dom(all_73_2_72) = all_73_1_71 & relation_dom(all_0_12_12) = all_73_0_70 & ( ~ in(all_29_0_30, all_0_11_11) | ~ in(all_7_0_17, all_73_0_70) | in(all_7_0_17, all_73_1_71)) & ( ~ in(all_7_0_17, all_73_1_71) | (in(all_29_0_30, all_0_11_11) & in(all_7_0_17, all_73_0_70))) % 7.55/2.33 | % 7.55/2.33 | Applying alpha-rule on (192) yields: % 7.55/2.33 | (193) relation_dom(all_73_2_72) = all_73_1_71 % 7.55/2.33 | (194) ~ in(all_7_0_17, all_73_1_71) | (in(all_29_0_30, all_0_11_11) & in(all_7_0_17, all_73_0_70)) % 7.55/2.33 | (195) relation_dom(all_0_12_12) = all_73_0_70 % 7.55/2.33 | (196) ~ in(all_29_0_30, all_0_11_11) | ~ in(all_7_0_17, all_73_0_70) | in(all_7_0_17, all_73_1_71) % 7.55/2.33 | (197) relation_composition(all_0_12_12, all_0_12_12) = all_73_2_72 % 7.55/2.33 | % 7.55/2.33 | Instantiating (148) with all_75_0_73, all_75_1_74, all_75_2_75 yields: % 7.55/2.33 | (198) relation_composition(all_0_12_12, all_0_9_9) = all_75_2_75 & relation_dom(all_75_2_75) = all_75_1_74 & relation_dom(all_0_12_12) = all_75_0_73 & ( ~ in(all_29_0_30, all_23_0_20) | ~ in(all_7_0_17, all_75_0_73) | in(all_7_0_17, all_75_1_74)) & ( ~ in(all_7_0_17, all_75_1_74) | (in(all_29_0_30, all_23_0_20) & in(all_7_0_17, all_75_0_73))) % 7.55/2.33 | % 7.55/2.33 | Applying alpha-rule on (198) yields: % 7.55/2.33 | (199) relation_dom(all_0_12_12) = all_75_0_73 % 7.55/2.33 | (200) ~ in(all_29_0_30, all_23_0_20) | ~ in(all_7_0_17, all_75_0_73) | in(all_7_0_17, all_75_1_74) % 7.55/2.33 | (201) ~ in(all_7_0_17, all_75_1_74) | (in(all_29_0_30, all_23_0_20) & in(all_7_0_17, all_75_0_73)) % 7.55/2.33 | (202) relation_dom(all_75_2_75) = all_75_1_74 % 7.55/2.33 | (203) relation_composition(all_0_12_12, all_0_9_9) = all_75_2_75 % 7.55/2.33 | % 7.55/2.33 | Instantiating (146) with all_79_0_79, all_79_1_80, all_79_2_81 yields: % 7.55/2.33 | (204) relation_dom(all_0_8_8) = all_79_2_81 & apply(all_0_9_9, all_79_1_80) = all_79_0_79 & apply(all_0_12_12, all_5_0_16) = all_79_1_80 & (all_79_0_79 = all_27_2_28 | ~ in(all_5_0_16, all_79_2_81)) % 7.55/2.33 | % 7.55/2.33 | Applying alpha-rule on (204) yields: % 7.55/2.33 | (205) relation_dom(all_0_8_8) = all_79_2_81 % 7.55/2.33 | (206) apply(all_0_9_9, all_79_1_80) = all_79_0_79 % 7.55/2.33 | (207) apply(all_0_12_12, all_5_0_16) = all_79_1_80 % 7.55/2.33 | (208) all_79_0_79 = all_27_2_28 | ~ in(all_5_0_16, all_79_2_81) % 7.55/2.33 | % 7.55/2.33 | Instantiating (145) with all_81_0_82, all_81_1_83, all_81_2_84 yields: % 7.55/2.33 | (209) relation_composition(all_0_12_12, all_0_9_9) = all_81_2_84 & relation_dom(all_81_2_84) = all_81_1_83 & apply(all_0_12_12, all_7_0_17) = all_81_0_82 & ( ~ in(all_81_0_82, all_23_0_20) | ~ in(all_7_0_17, all_0_11_11) | in(all_7_0_17, all_81_1_83)) & ( ~ in(all_7_0_17, all_81_1_83) | (in(all_81_0_82, all_23_0_20) & in(all_7_0_17, all_0_11_11))) % 7.55/2.33 | % 7.55/2.33 | Applying alpha-rule on (209) yields: % 7.55/2.33 | (210) ~ in(all_81_0_82, all_23_0_20) | ~ in(all_7_0_17, all_0_11_11) | in(all_7_0_17, all_81_1_83) % 7.55/2.33 | (211) apply(all_0_12_12, all_7_0_17) = all_81_0_82 % 7.55/2.33 | (212) relation_composition(all_0_12_12, all_0_9_9) = all_81_2_84 % 7.55/2.33 | (213) relation_dom(all_81_2_84) = all_81_1_83 % 7.55/2.33 | (214) ~ in(all_7_0_17, all_81_1_83) | (in(all_81_0_82, all_23_0_20) & in(all_7_0_17, all_0_11_11)) % 7.55/2.33 | % 7.55/2.33 | Instantiating (157) with all_85_0_88, all_85_1_89, all_85_2_90 yields: % 7.55/2.33 | (215) relation_composition(all_0_12_12, all_0_8_8) = all_85_2_90 & relation_dom(all_85_2_90) = all_85_1_89 & relation_dom(all_0_12_12) = all_85_0_88 & ( ~ in(all_0_10_10, all_27_3_29) | ~ in(all_0_13_13, all_85_0_88) | in(all_0_13_13, all_85_1_89)) & ( ~ in(all_0_13_13, all_85_1_89) | (in(all_0_10_10, all_27_3_29) & in(all_0_13_13, all_85_0_88))) % 7.55/2.33 | % 7.55/2.33 | Applying alpha-rule on (215) yields: % 7.55/2.33 | (216) ~ in(all_0_13_13, all_85_1_89) | (in(all_0_10_10, all_27_3_29) & in(all_0_13_13, all_85_0_88)) % 7.55/2.33 | (217) relation_composition(all_0_12_12, all_0_8_8) = all_85_2_90 % 7.55/2.33 | (218) ~ in(all_0_10_10, all_27_3_29) | ~ in(all_0_13_13, all_85_0_88) | in(all_0_13_13, all_85_1_89) % 7.55/2.33 | (219) relation_dom(all_0_12_12) = all_85_0_88 % 7.55/2.33 | (220) relation_dom(all_85_2_90) = all_85_1_89 % 7.55/2.33 | % 7.55/2.33 | Instantiating (155) with all_89_0_94, all_89_1_95, all_89_2_96 yields: % 7.55/2.33 | (221) relation_composition(all_0_8_8, all_0_8_8) = all_89_2_96 & relation_dom(all_89_2_96) = all_89_1_95 & relation_dom(all_0_8_8) = all_89_0_94 & ( ~ in(all_27_2_28, all_27_3_29) | ~ in(all_5_0_16, all_89_0_94) | in(all_5_0_16, all_89_1_95)) & ( ~ in(all_5_0_16, all_89_1_95) | (in(all_27_2_28, all_27_3_29) & in(all_5_0_16, all_89_0_94))) % 7.55/2.33 | % 7.55/2.33 | Applying alpha-rule on (221) yields: % 7.55/2.33 | (222) relation_dom(all_89_2_96) = all_89_1_95 % 7.55/2.33 | (223) relation_dom(all_0_8_8) = all_89_0_94 % 7.55/2.33 | (224) ~ in(all_27_2_28, all_27_3_29) | ~ in(all_5_0_16, all_89_0_94) | in(all_5_0_16, all_89_1_95) % 7.55/2.33 | (225) relation_composition(all_0_8_8, all_0_8_8) = all_89_2_96 % 7.55/2.33 | (226) ~ in(all_5_0_16, all_89_1_95) | (in(all_27_2_28, all_27_3_29) & in(all_5_0_16, all_89_0_94)) % 7.55/2.33 | % 7.55/2.33 | Instantiating (153) with all_91_0_97, all_91_1_98, all_91_2_99 yields: % 7.55/2.33 | (227) relation_composition(all_0_8_8, all_0_12_12) = all_91_2_99 & relation_dom(all_91_2_99) = all_91_1_98 & relation_dom(all_0_8_8) = all_91_0_97 & ( ~ in(all_27_2_28, all_0_11_11) | ~ in(all_5_0_16, all_91_0_97) | in(all_5_0_16, all_91_1_98)) & ( ~ in(all_5_0_16, all_91_1_98) | (in(all_27_2_28, all_0_11_11) & in(all_5_0_16, all_91_0_97))) % 7.55/2.33 | % 7.55/2.33 | Applying alpha-rule on (227) yields: % 7.55/2.33 | (228) relation_dom(all_0_8_8) = all_91_0_97 % 7.55/2.33 | (229) ~ in(all_5_0_16, all_91_1_98) | (in(all_27_2_28, all_0_11_11) & in(all_5_0_16, all_91_0_97)) % 7.55/2.33 | (230) ~ in(all_27_2_28, all_0_11_11) | ~ in(all_5_0_16, all_91_0_97) | in(all_5_0_16, all_91_1_98) % 7.55/2.33 | (231) relation_dom(all_91_2_99) = all_91_1_98 % 7.55/2.33 | (232) relation_composition(all_0_8_8, all_0_12_12) = all_91_2_99 % 7.55/2.33 | % 7.55/2.33 | Instantiating (152) with all_93_0_100, all_93_1_101, all_93_2_102 yields: % 7.55/2.33 | (233) relation_composition(all_0_8_8, all_0_12_12) = all_93_2_102 & relation_dom(all_93_2_102) = all_93_1_101 & relation_dom(all_0_8_8) = all_93_0_100 & ( ~ in(all_0_7_7, all_0_11_11) | ~ in(all_0_13_13, all_93_0_100) | in(all_0_13_13, all_93_1_101)) & ( ~ in(all_0_13_13, all_93_1_101) | (in(all_0_7_7, all_0_11_11) & in(all_0_13_13, all_93_0_100))) % 7.55/2.33 | % 7.55/2.33 | Applying alpha-rule on (233) yields: % 7.55/2.33 | (234) ~ in(all_0_13_13, all_93_1_101) | (in(all_0_7_7, all_0_11_11) & in(all_0_13_13, all_93_0_100)) % 7.55/2.33 | (235) relation_dom(all_93_2_102) = all_93_1_101 % 7.55/2.33 | (236) ~ in(all_0_7_7, all_0_11_11) | ~ in(all_0_13_13, all_93_0_100) | in(all_0_13_13, all_93_1_101) % 7.55/2.33 | (237) relation_dom(all_0_8_8) = all_93_0_100 % 7.55/2.33 | (238) relation_composition(all_0_8_8, all_0_12_12) = all_93_2_102 % 7.55/2.33 | % 7.55/2.33 | Instantiating (151) with all_95_0_103, all_95_1_104, all_95_2_105 yields: % 7.55/2.33 | (239) relation_composition(all_0_12_12, all_0_9_9) = all_95_2_105 & relation_dom(all_95_2_105) = all_95_1_104 & apply(all_95_2_105, all_5_0_16) = all_95_0_103 & (all_95_0_103 = all_27_0_26 | ~ in(all_5_0_16, all_95_1_104)) % 7.55/2.33 | % 7.55/2.33 | Applying alpha-rule on (239) yields: % 7.55/2.33 | (240) relation_composition(all_0_12_12, all_0_9_9) = all_95_2_105 % 7.55/2.33 | (241) relation_dom(all_95_2_105) = all_95_1_104 % 7.55/2.33 | (242) apply(all_95_2_105, all_5_0_16) = all_95_0_103 % 7.55/2.33 | (243) all_95_0_103 = all_27_0_26 | ~ in(all_5_0_16, all_95_1_104) % 7.55/2.33 | % 7.55/2.33 | Instantiating (154) with all_97_0_106, all_97_1_107, all_97_2_108 yields: % 7.55/2.33 | (244) relation_composition(all_0_8_8, all_0_8_8) = all_97_2_108 & relation_dom(all_97_2_108) = all_97_1_107 & relation_dom(all_0_8_8) = all_97_0_106 & ( ~ in(all_0_7_7, all_27_3_29) | ~ in(all_0_13_13, all_97_0_106) | in(all_0_13_13, all_97_1_107)) & ( ~ in(all_0_13_13, all_97_1_107) | (in(all_0_7_7, all_27_3_29) & in(all_0_13_13, all_97_0_106))) % 7.55/2.33 | % 7.55/2.33 | Applying alpha-rule on (244) yields: % 7.55/2.33 | (245) ~ in(all_0_7_7, all_27_3_29) | ~ in(all_0_13_13, all_97_0_106) | in(all_0_13_13, all_97_1_107) % 7.55/2.33 | (246) relation_dom(all_97_2_108) = all_97_1_107 % 7.55/2.33 | (247) relation_composition(all_0_8_8, all_0_8_8) = all_97_2_108 % 7.55/2.33 | (248) ~ in(all_0_13_13, all_97_1_107) | (in(all_0_7_7, all_27_3_29) & in(all_0_13_13, all_97_0_106)) % 7.55/2.33 | (249) relation_dom(all_0_8_8) = all_97_0_106 % 7.55/2.33 | % 7.55/2.33 | Instantiating (141) with all_101_0_112, all_101_1_113, all_101_2_114 yields: % 7.55/2.33 | (250) relation_dom(all_25_2_25) = all_101_2_114 & relation_dom(all_0_12_12) = all_101_1_113 & apply(all_0_12_12, all_11_0_19) = all_101_0_112 & ( ~ in(all_101_0_112, all_0_11_11) | ~ in(all_11_0_19, all_101_1_113) | in(all_11_0_19, all_101_2_114)) & ( ~ in(all_11_0_19, all_101_2_114) | (in(all_101_0_112, all_0_11_11) & in(all_11_0_19, all_101_1_113))) % 7.55/2.33 | % 7.55/2.33 | Applying alpha-rule on (250) yields: % 7.55/2.33 | (251) ~ in(all_101_0_112, all_0_11_11) | ~ in(all_11_0_19, all_101_1_113) | in(all_11_0_19, all_101_2_114) % 7.55/2.33 | (252) ~ in(all_11_0_19, all_101_2_114) | (in(all_101_0_112, all_0_11_11) & in(all_11_0_19, all_101_1_113)) % 7.55/2.33 | (253) relation_dom(all_0_12_12) = all_101_1_113 % 7.55/2.33 | (254) apply(all_0_12_12, all_11_0_19) = all_101_0_112 % 7.55/2.33 | (255) relation_dom(all_25_2_25) = all_101_2_114 % 7.55/2.33 | % 7.55/2.33 | Instantiating (150) with all_103_0_115, all_103_1_116, all_103_2_117 yields: % 7.55/2.33 | (256) relation_composition(all_0_12_12, all_0_9_9) = all_103_2_117 & relation_dom(all_103_2_117) = all_103_1_116 & relation_dom(all_0_12_12) = all_103_0_115 & ( ~ in(all_27_1_27, all_23_0_20) | ~ in(all_5_0_16, all_103_0_115) | in(all_5_0_16, all_103_1_116)) & ( ~ in(all_5_0_16, all_103_1_116) | (in(all_27_1_27, all_23_0_20) & in(all_5_0_16, all_103_0_115))) % 7.55/2.33 | % 7.55/2.33 | Applying alpha-rule on (256) yields: % 7.55/2.33 | (257) ~ in(all_5_0_16, all_103_1_116) | (in(all_27_1_27, all_23_0_20) & in(all_5_0_16, all_103_0_115)) % 7.55/2.33 | (258) relation_dom(all_103_2_117) = all_103_1_116 % 7.55/2.33 | (259) relation_dom(all_0_12_12) = all_103_0_115 % 7.55/2.33 | (260) ~ in(all_27_1_27, all_23_0_20) | ~ in(all_5_0_16, all_103_0_115) | in(all_5_0_16, all_103_1_116) % 7.55/2.33 | (261) relation_composition(all_0_12_12, all_0_9_9) = all_103_2_117 % 7.55/2.33 | % 7.55/2.33 | Instantiating (144) with all_107_0_121, all_107_1_122, all_107_2_123 yields: % 7.55/2.33 | (262) relation_dom(all_0_8_8) = all_107_2_123 & relation_dom(all_0_12_12) = all_107_1_122 & apply(all_0_12_12, all_11_0_19) = all_107_0_121 & ( ~ in(all_107_0_121, all_23_0_20) | ~ in(all_11_0_19, all_107_1_122) | in(all_11_0_19, all_107_2_123)) & ( ~ in(all_11_0_19, all_107_2_123) | (in(all_107_0_121, all_23_0_20) & in(all_11_0_19, all_107_1_122))) % 7.55/2.33 | % 7.55/2.33 | Applying alpha-rule on (262) yields: % 7.55/2.33 | (263) ~ in(all_107_0_121, all_23_0_20) | ~ in(all_11_0_19, all_107_1_122) | in(all_11_0_19, all_107_2_123) % 7.55/2.33 | (264) relation_dom(all_0_8_8) = all_107_2_123 % 7.55/2.33 | (265) apply(all_0_12_12, all_11_0_19) = all_107_0_121 % 7.55/2.33 | (266) ~ in(all_11_0_19, all_107_2_123) | (in(all_107_0_121, all_23_0_20) & in(all_11_0_19, all_107_1_122)) % 7.55/2.33 | (267) relation_dom(all_0_12_12) = all_107_1_122 % 7.55/2.33 | % 7.55/2.33 | Instantiating (143) with all_109_0_124, all_109_1_125, all_109_2_126 yields: % 7.55/2.33 | (268) relation_composition(all_0_12_12, all_0_9_9) = all_109_2_126 & relation_dom(all_109_2_126) = all_109_1_125 & relation_dom(all_0_12_12) = all_109_0_124 & ( ~ in(all_0_10_10, all_23_0_20) | ~ in(all_0_13_13, all_109_0_124) | in(all_0_13_13, all_109_1_125)) & ( ~ in(all_0_13_13, all_109_1_125) | (in(all_0_10_10, all_23_0_20) & in(all_0_13_13, all_109_0_124))) % 7.55/2.33 | % 7.55/2.33 | Applying alpha-rule on (268) yields: % 7.55/2.33 | (269) ~ in(all_0_13_13, all_109_1_125) | (in(all_0_10_10, all_23_0_20) & in(all_0_13_13, all_109_0_124)) % 7.55/2.34 | (270) relation_dom(all_109_2_126) = all_109_1_125 % 7.55/2.34 | (271) ~ in(all_0_10_10, all_23_0_20) | ~ in(all_0_13_13, all_109_0_124) | in(all_0_13_13, all_109_1_125) % 7.55/2.34 | (272) relation_dom(all_0_12_12) = all_109_0_124 % 7.55/2.34 | (273) relation_composition(all_0_12_12, all_0_9_9) = all_109_2_126 % 7.55/2.34 | % 7.55/2.34 | Equations (156) can reduce 22 to: % 7.55/2.34 | (274) ~ (all_0_6_6 = empty_set) % 7.55/2.34 | % 7.55/2.34 +-Applying beta-rule and splitting (142), into two cases. % 7.55/2.34 |-Branch one: % 7.55/2.34 | (275) in(all_0_10_10, all_23_0_20) % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (54) with all_0_12_12, all_0_9_9, all_109_2_126, all_0_8_8 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_109_2_126, relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, yields: % 7.55/2.34 | (276) all_109_2_126 = all_0_8_8 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (54) with all_0_12_12, all_0_9_9, all_103_2_117, all_109_2_126 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_109_2_126, relation_composition(all_0_12_12, all_0_9_9) = all_103_2_117, yields: % 7.55/2.34 | (277) all_109_2_126 = all_103_2_117 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (54) with all_0_12_12, all_0_9_9, all_95_2_105, all_103_2_117 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_103_2_117, relation_composition(all_0_12_12, all_0_9_9) = all_95_2_105, yields: % 7.55/2.34 | (278) all_103_2_117 = all_95_2_105 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (54) with all_0_12_12, all_0_9_9, all_81_2_84, all_95_2_105 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_95_2_105, relation_composition(all_0_12_12, all_0_9_9) = all_81_2_84, yields: % 7.55/2.34 | (279) all_95_2_105 = all_81_2_84 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (54) with all_0_12_12, all_0_9_9, all_75_2_75, all_81_2_84 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_81_2_84, relation_composition(all_0_12_12, all_0_9_9) = all_75_2_75, yields: % 7.55/2.34 | (280) all_81_2_84 = all_75_2_75 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (38) with all_0_8_8, all_97_0_106, all_107_2_123 and discharging atoms relation_dom(all_0_8_8) = all_107_2_123, relation_dom(all_0_8_8) = all_97_0_106, yields: % 7.55/2.34 | (281) all_107_2_123 = all_97_0_106 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (38) with all_0_8_8, all_93_0_100, all_107_2_123 and discharging atoms relation_dom(all_0_8_8) = all_107_2_123, relation_dom(all_0_8_8) = all_93_0_100, yields: % 7.55/2.34 | (282) all_107_2_123 = all_93_0_100 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (38) with all_0_8_8, all_91_0_97, all_27_3_29 and discharging atoms relation_dom(all_0_8_8) = all_91_0_97, relation_dom(all_0_8_8) = all_27_3_29, yields: % 7.55/2.34 | (283) all_91_0_97 = all_27_3_29 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (38) with all_0_8_8, all_89_0_94, all_91_0_97 and discharging atoms relation_dom(all_0_8_8) = all_91_0_97, relation_dom(all_0_8_8) = all_89_0_94, yields: % 7.55/2.34 | (284) all_91_0_97 = all_89_0_94 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (38) with all_0_8_8, all_79_2_81, all_97_0_106 and discharging atoms relation_dom(all_0_8_8) = all_97_0_106, relation_dom(all_0_8_8) = all_79_2_81, yields: % 7.55/2.34 | (285) all_97_0_106 = all_79_2_81 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (38) with all_0_8_8, all_79_2_81, all_91_0_97 and discharging atoms relation_dom(all_0_8_8) = all_91_0_97, relation_dom(all_0_8_8) = all_79_2_81, yields: % 7.55/2.34 | (286) all_91_0_97 = all_79_2_81 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (38) with all_0_8_8, all_65_0_58, all_97_0_106 and discharging atoms relation_dom(all_0_8_8) = all_97_0_106, relation_dom(all_0_8_8) = all_65_0_58, yields: % 7.55/2.34 | (287) all_97_0_106 = all_65_0_58 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (38) with all_0_8_8, all_55_0_42, all_79_2_81 and discharging atoms relation_dom(all_0_8_8) = all_79_2_81, relation_dom(all_0_8_8) = all_55_0_42, yields: % 7.55/2.34 | (288) all_79_2_81 = all_55_0_42 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (38) with all_0_12_12, all_101_1_113, all_109_0_124 and discharging atoms relation_dom(all_0_12_12) = all_109_0_124, relation_dom(all_0_12_12) = all_101_1_113, yields: % 7.55/2.34 | (289) all_109_0_124 = all_101_1_113 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (38) with all_0_12_12, all_85_0_88, all_109_0_124 and discharging atoms relation_dom(all_0_12_12) = all_109_0_124, relation_dom(all_0_12_12) = all_85_0_88, yields: % 7.55/2.34 | (290) all_109_0_124 = all_85_0_88 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (38) with all_0_12_12, all_85_0_88, all_103_0_115 and discharging atoms relation_dom(all_0_12_12) = all_103_0_115, relation_dom(all_0_12_12) = all_85_0_88, yields: % 7.55/2.34 | (291) all_103_0_115 = all_85_0_88 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (38) with all_0_12_12, all_75_0_73, all_109_0_124 and discharging atoms relation_dom(all_0_12_12) = all_109_0_124, relation_dom(all_0_12_12) = all_75_0_73, yields: % 7.55/2.34 | (292) all_109_0_124 = all_75_0_73 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (38) with all_0_12_12, all_73_0_70, all_0_11_11 and discharging atoms relation_dom(all_0_12_12) = all_73_0_70, relation_dom(all_0_12_12) = all_0_11_11, yields: % 7.55/2.34 | (293) all_73_0_70 = all_0_11_11 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (38) with all_0_12_12, all_73_0_70, all_107_1_122 and discharging atoms relation_dom(all_0_12_12) = all_107_1_122, relation_dom(all_0_12_12) = all_73_0_70, yields: % 7.55/2.34 | (294) all_107_1_122 = all_73_0_70 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (38) with all_0_12_12, all_73_0_70, all_101_1_113 and discharging atoms relation_dom(all_0_12_12) = all_101_1_113, relation_dom(all_0_12_12) = all_73_0_70, yields: % 7.55/2.34 | (295) all_101_1_113 = all_73_0_70 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (38) with all_0_12_12, all_71_0_67, all_101_1_113 and discharging atoms relation_dom(all_0_12_12) = all_101_1_113, relation_dom(all_0_12_12) = all_71_0_67, yields: % 7.55/2.34 | (296) all_101_1_113 = all_71_0_67 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (38) with all_0_12_12, all_63_0_55, all_107_1_122 and discharging atoms relation_dom(all_0_12_12) = all_107_1_122, relation_dom(all_0_12_12) = all_63_0_55, yields: % 7.55/2.34 | (297) all_107_1_122 = all_63_0_55 % 7.55/2.34 | % 7.55/2.34 | Instantiating formula (38) with all_0_12_12, all_61_0_52, all_103_0_115 and discharging atoms relation_dom(all_0_12_12) = all_103_0_115, relation_dom(all_0_12_12) = all_61_0_52, yields: % 7.55/2.34 | (298) all_103_0_115 = all_61_0_52 % 7.55/2.34 | % 7.55/2.34 | Combining equations (289,292) yields a new equation: % 7.55/2.34 | (299) all_101_1_113 = all_75_0_73 % 7.55/2.34 | % 7.55/2.34 | Simplifying 299 yields: % 7.55/2.34 | (300) all_101_1_113 = all_75_0_73 % 7.55/2.34 | % 7.55/2.34 | Combining equations (290,292) yields a new equation: % 7.55/2.34 | (301) all_85_0_88 = all_75_0_73 % 7.55/2.34 | % 7.55/2.34 | Simplifying 301 yields: % 7.55/2.34 | (302) all_85_0_88 = all_75_0_73 % 7.55/2.34 | % 7.55/2.34 | Combining equations (277,276) yields a new equation: % 7.55/2.34 | (303) all_103_2_117 = all_0_8_8 % 7.55/2.34 | % 7.55/2.34 | Simplifying 303 yields: % 7.55/2.34 | (304) all_103_2_117 = all_0_8_8 % 7.55/2.34 | % 7.55/2.34 | Combining equations (294,297) yields a new equation: % 7.55/2.34 | (305) all_73_0_70 = all_63_0_55 % 7.55/2.34 | % 7.55/2.34 | Simplifying 305 yields: % 7.55/2.34 | (306) all_73_0_70 = all_63_0_55 % 7.55/2.34 | % 7.55/2.34 | Combining equations (281,282) yields a new equation: % 7.55/2.34 | (307) all_97_0_106 = all_93_0_100 % 7.55/2.34 | % 7.55/2.34 | Simplifying 307 yields: % 7.55/2.34 | (308) all_97_0_106 = all_93_0_100 % 7.55/2.34 | % 7.55/2.34 | Combining equations (291,298) yields a new equation: % 7.55/2.34 | (309) all_85_0_88 = all_61_0_52 % 7.55/2.34 | % 7.55/2.34 | Simplifying 309 yields: % 7.55/2.34 | (310) all_85_0_88 = all_61_0_52 % 7.55/2.34 | % 7.55/2.34 | Combining equations (278,304) yields a new equation: % 7.55/2.34 | (311) all_95_2_105 = all_0_8_8 % 7.55/2.34 | % 7.55/2.34 | Simplifying 311 yields: % 7.55/2.34 | (312) all_95_2_105 = all_0_8_8 % 7.55/2.34 | % 7.55/2.34 | Combining equations (300,296) yields a new equation: % 7.55/2.34 | (313) all_75_0_73 = all_71_0_67 % 7.55/2.34 | % 7.55/2.34 | Simplifying 313 yields: % 7.55/2.34 | (314) all_75_0_73 = all_71_0_67 % 7.55/2.34 | % 7.55/2.34 | Combining equations (295,296) yields a new equation: % 7.55/2.34 | (315) all_73_0_70 = all_71_0_67 % 7.55/2.34 | % 7.55/2.34 | Simplifying 315 yields: % 7.55/2.34 | (316) all_73_0_70 = all_71_0_67 % 7.55/2.34 | % 7.55/2.34 | Combining equations (287,308) yields a new equation: % 7.55/2.34 | (317) all_93_0_100 = all_65_0_58 % 7.55/2.34 | % 7.55/2.34 | Combining equations (285,308) yields a new equation: % 7.55/2.34 | (318) all_93_0_100 = all_79_2_81 % 7.55/2.34 | % 7.55/2.34 | Combining equations (279,312) yields a new equation: % 7.55/2.34 | (319) all_81_2_84 = all_0_8_8 % 7.55/2.34 | % 7.55/2.34 | Simplifying 319 yields: % 7.55/2.34 | (320) all_81_2_84 = all_0_8_8 % 7.55/2.34 | % 7.55/2.34 | Combining equations (318,317) yields a new equation: % 7.55/2.34 | (321) all_79_2_81 = all_65_0_58 % 7.55/2.34 | % 7.55/2.34 | Simplifying 321 yields: % 7.55/2.34 | (322) all_79_2_81 = all_65_0_58 % 7.55/2.34 | % 7.55/2.34 | Combining equations (286,284) yields a new equation: % 7.55/2.34 | (323) all_89_0_94 = all_79_2_81 % 7.55/2.34 | % 7.55/2.34 | Combining equations (283,284) yields a new equation: % 7.55/2.34 | (324) all_89_0_94 = all_27_3_29 % 7.55/2.34 | % 7.55/2.34 | Combining equations (323,324) yields a new equation: % 7.55/2.34 | (325) all_79_2_81 = all_27_3_29 % 7.55/2.34 | % 7.55/2.34 | Simplifying 325 yields: % 7.55/2.34 | (326) all_79_2_81 = all_27_3_29 % 7.55/2.34 | % 7.55/2.34 | Combining equations (302,310) yields a new equation: % 7.55/2.34 | (327) all_75_0_73 = all_61_0_52 % 7.55/2.34 | % 7.55/2.34 | Simplifying 327 yields: % 7.55/2.34 | (328) all_75_0_73 = all_61_0_52 % 7.55/2.34 | % 7.55/2.34 | Combining equations (280,320) yields a new equation: % 7.55/2.34 | (329) all_75_2_75 = all_0_8_8 % 7.55/2.34 | % 7.55/2.34 | Simplifying 329 yields: % 7.55/2.34 | (330) all_75_2_75 = all_0_8_8 % 7.55/2.34 | % 7.55/2.34 | Combining equations (288,322) yields a new equation: % 7.55/2.34 | (331) all_65_0_58 = all_55_0_42 % 7.55/2.34 | % 7.55/2.34 | Combining equations (326,322) yields a new equation: % 7.55/2.34 | (332) all_65_0_58 = all_27_3_29 % 7.55/2.34 | % 7.55/2.34 | Combining equations (314,328) yields a new equation: % 7.55/2.34 | (333) all_71_0_67 = all_61_0_52 % 7.55/2.34 | % 7.55/2.34 | Simplifying 333 yields: % 7.55/2.34 | (334) all_71_0_67 = all_61_0_52 % 7.55/2.34 | % 7.55/2.34 | Combining equations (316,306) yields a new equation: % 7.55/2.34 | (335) all_71_0_67 = all_63_0_55 % 7.55/2.34 | % 7.55/2.34 | Simplifying 335 yields: % 7.55/2.34 | (336) all_71_0_67 = all_63_0_55 % 7.55/2.34 | % 7.55/2.34 | Combining equations (293,306) yields a new equation: % 7.55/2.34 | (337) all_63_0_55 = all_0_11_11 % 7.55/2.34 | % 7.55/2.34 | Combining equations (336,334) yields a new equation: % 7.55/2.34 | (338) all_63_0_55 = all_61_0_52 % 7.55/2.34 | % 7.55/2.34 | Simplifying 338 yields: % 7.55/2.34 | (339) all_63_0_55 = all_61_0_52 % 7.55/2.34 | % 7.55/2.34 | Combining equations (331,332) yields a new equation: % 7.55/2.34 | (340) all_55_0_42 = all_27_3_29 % 7.55/2.34 | % 7.55/2.34 | Simplifying 340 yields: % 7.55/2.34 | (341) all_55_0_42 = all_27_3_29 % 7.55/2.34 | % 7.55/2.35 | Combining equations (337,339) yields a new equation: % 7.55/2.35 | (342) all_61_0_52 = all_0_11_11 % 7.55/2.35 | % 7.55/2.35 | Combining equations (342,328) yields a new equation: % 7.55/2.35 | (343) all_75_0_73 = all_0_11_11 % 7.55/2.35 | % 7.55/2.35 | Combining equations (343,292) yields a new equation: % 7.55/2.35 | (344) all_109_0_124 = all_0_11_11 % 7.55/2.35 | % 7.55/2.35 | From (276) and (270) follows: % 7.55/2.35 | (345) relation_dom(all_0_8_8) = all_109_1_125 % 7.55/2.35 | % 7.55/2.35 | From (304) and (258) follows: % 7.55/2.35 | (346) relation_dom(all_0_8_8) = all_103_1_116 % 7.55/2.35 | % 7.55/2.35 | From (312) and (241) follows: % 7.55/2.35 | (347) relation_dom(all_0_8_8) = all_95_1_104 % 7.55/2.35 | % 7.55/2.35 | From (320) and (213) follows: % 7.55/2.35 | (348) relation_dom(all_0_8_8) = all_81_1_83 % 7.55/2.35 | % 7.55/2.35 | From (330) and (202) follows: % 7.55/2.35 | (349) relation_dom(all_0_8_8) = all_75_1_74 % 7.55/2.35 | % 7.55/2.35 | From (341) and (165) follows: % 7.55/2.35 | (103) relation_dom(all_0_8_8) = all_27_3_29 % 7.55/2.35 | % 7.55/2.35 +-Applying beta-rule and splitting (271), into two cases. % 7.55/2.35 |-Branch one: % 7.55/2.35 | (351) ~ in(all_0_10_10, all_23_0_20) % 7.55/2.35 | % 7.55/2.35 | Using (275) and (351) yields: % 7.55/2.35 | (352) $false % 7.55/2.35 | % 7.55/2.35 |-The branch is then unsatisfiable % 7.55/2.35 |-Branch two: % 7.55/2.35 | (275) in(all_0_10_10, all_23_0_20) % 7.55/2.35 | (354) ~ in(all_0_13_13, all_109_0_124) | in(all_0_13_13, all_109_1_125) % 7.55/2.35 | % 7.55/2.35 +-Applying beta-rule and splitting (354), into two cases. % 7.55/2.35 |-Branch one: % 7.55/2.35 | (355) ~ in(all_0_13_13, all_109_0_124) % 7.55/2.35 | % 7.55/2.35 | From (344) and (355) follows: % 7.55/2.35 | (356) ~ in(all_0_13_13, all_0_11_11) % 7.55/2.35 | % 7.55/2.35 | Using (33) and (356) yields: % 7.55/2.35 | (352) $false % 7.55/2.35 | % 7.55/2.35 |-The branch is then unsatisfiable % 7.55/2.35 |-Branch two: % 7.55/2.35 | (358) in(all_0_13_13, all_109_0_124) % 7.55/2.35 | (359) in(all_0_13_13, all_109_1_125) % 7.55/2.35 | % 7.55/2.35 | Instantiating formula (38) with all_0_8_8, all_103_1_116, all_109_1_125 and discharging atoms relation_dom(all_0_8_8) = all_109_1_125, relation_dom(all_0_8_8) = all_103_1_116, yields: % 7.55/2.35 | (360) all_109_1_125 = all_103_1_116 % 7.55/2.35 | % 7.55/2.35 | Instantiating formula (38) with all_0_8_8, all_95_1_104, all_27_3_29 and discharging atoms relation_dom(all_0_8_8) = all_95_1_104, relation_dom(all_0_8_8) = all_27_3_29, yields: % 7.55/2.35 | (361) all_95_1_104 = all_27_3_29 % 7.55/2.35 | % 7.55/2.35 | Instantiating formula (38) with all_0_8_8, all_81_1_83, all_103_1_116 and discharging atoms relation_dom(all_0_8_8) = all_103_1_116, relation_dom(all_0_8_8) = all_81_1_83, yields: % 7.55/2.35 | (362) all_103_1_116 = all_81_1_83 % 7.55/2.35 | % 7.55/2.35 | Instantiating formula (38) with all_0_8_8, all_81_1_83, all_95_1_104 and discharging atoms relation_dom(all_0_8_8) = all_95_1_104, relation_dom(all_0_8_8) = all_81_1_83, yields: % 7.55/2.35 | (363) all_95_1_104 = all_81_1_83 % 7.55/2.35 | % 7.55/2.35 | Instantiating formula (38) with all_0_8_8, all_75_1_74, all_109_1_125 and discharging atoms relation_dom(all_0_8_8) = all_109_1_125, relation_dom(all_0_8_8) = all_75_1_74, yields: % 7.55/2.35 | (364) all_109_1_125 = all_75_1_74 % 7.55/2.35 | % 7.55/2.35 | Combining equations (360,364) yields a new equation: % 7.55/2.35 | (365) all_103_1_116 = all_75_1_74 % 7.55/2.35 | % 7.55/2.35 | Simplifying 365 yields: % 7.55/2.35 | (366) all_103_1_116 = all_75_1_74 % 7.55/2.35 | % 7.55/2.35 | Combining equations (362,366) yields a new equation: % 7.55/2.35 | (367) all_81_1_83 = all_75_1_74 % 7.55/2.35 | % 7.55/2.35 | Simplifying 367 yields: % 7.55/2.35 | (368) all_81_1_83 = all_75_1_74 % 7.55/2.35 | % 7.55/2.35 | Combining equations (363,361) yields a new equation: % 7.55/2.35 | (369) all_81_1_83 = all_27_3_29 % 7.55/2.35 | % 7.55/2.35 | Simplifying 369 yields: % 7.55/2.35 | (370) all_81_1_83 = all_27_3_29 % 7.55/2.35 | % 7.55/2.35 | Combining equations (370,368) yields a new equation: % 7.55/2.35 | (371) all_75_1_74 = all_27_3_29 % 7.55/2.35 | % 7.55/2.35 | Combining equations (371,364) yields a new equation: % 7.55/2.35 | (372) all_109_1_125 = all_27_3_29 % 7.55/2.35 | % 7.55/2.35 | From (372) and (359) follows: % 7.55/2.35 | (373) in(all_0_13_13, all_27_3_29) % 7.55/2.35 | % 7.55/2.35 | Using (373) and (140) yields: % 7.55/2.35 | (352) $false % 7.55/2.35 | % 7.55/2.35 |-The branch is then unsatisfiable % 7.55/2.35 |-Branch two: % 7.55/2.35 | (351) ~ in(all_0_10_10, all_23_0_20) % 7.55/2.35 | (376) all_0_6_6 = empty_set % 7.55/2.35 | % 7.55/2.35 | Equations (376) can reduce 274 to: % 7.55/2.35 | (377) $false % 7.55/2.35 | % 7.55/2.35 |-The branch is then unsatisfiable % 7.55/2.35 |-Branch two: % 7.55/2.35 | (378) in(all_0_13_13, all_31_1_34) % 7.55/2.35 | (379) all_31_0_33 = all_0_6_6 % 7.55/2.35 | % 7.55/2.35 | Combining equations (379,134) yields a new equation: % 7.55/2.35 | (380) all_0_6_6 = all_0_7_7 % 7.55/2.35 | % 7.55/2.35 | Simplifying 380 yields: % 7.55/2.35 | (381) all_0_6_6 = all_0_7_7 % 7.55/2.35 | % 7.55/2.35 | Equations (381) can reduce 22 to: % 7.55/2.35 | (377) $false % 7.55/2.35 | % 7.55/2.35 |-The branch is then unsatisfiable % 7.55/2.35 % SZS output end Proof for theBenchmark % 7.55/2.35 % 7.55/2.35 1755ms %------------------------------------------------------------------------------