%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET773+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n021.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 00:21:58 EDT 2022 % Result : Theorem 6.74s 2.21s % Output : Proof 23.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET773+4 : TPTP v8.1.0. Released v2.2.0. % 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n021.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sun Jul 10 16:23:22 EDT 2022 % 0.13/0.34 % CPUTime : % 0.58/0.60 ____ _ % 0.58/0.60 ___ / __ \_____(_)___ ________ __________ % 0.58/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.60 % 0.58/0.60 A Theorem Prover for First-Order Logic % 0.58/0.60 (ePrincess v.1.0) % 0.58/0.60 % 0.58/0.60 (c) Philipp Rümmer, 2009-2015 % 0.58/0.60 (c) Peter Backeman, 2014-2015 % 0.58/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.60 Bug reports to peter@backeman.se % 0.58/0.60 % 0.58/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.60 % 0.58/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.77/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.79/0.99 Prover 0: Preprocessing ... % 2.74/1.25 Prover 0: Warning: ignoring some quantifiers % 2.74/1.28 Prover 0: Constructing countermodel ... % 3.37/1.43 Prover 0: gave up % 3.37/1.43 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.71/1.47 Prover 1: Preprocessing ... % 4.49/1.66 Prover 1: Constructing countermodel ... % 4.87/1.76 Prover 1: gave up % 4.87/1.76 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 5.22/1.79 Prover 2: Preprocessing ... % 5.80/1.94 Prover 2: Warning: ignoring some quantifiers % 5.80/1.95 Prover 2: Constructing countermodel ... % 6.74/2.21 Prover 2: proved (451ms) % 6.74/2.21 % 6.74/2.21 No countermodel exists, formula is valid % 6.74/2.21 % SZS status Theorem for theBenchmark % 6.74/2.21 % 6.74/2.21 Generating proof ... Warning: ignoring some quantifiers % 22.49/6.35 found it (size 745) % 22.49/6.35 % 22.49/6.35 % SZS output start Proof for theBenchmark % 22.49/6.35 Assumed formulas after preprocessing and simplification: % 22.49/6.35 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & equivalence(v3, v0) = v4 & equivalence(v2, v0) = 0 & equivalence(v1, v0) = 0 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (pre_order(v5, v6) = 0) | ~ (apply(v5, v8, v9) = 0) | ~ (apply(v5, v7, v9) = v10) | ? [v11] : (( ~ (v11 = 0) & apply(v5, v7, v8) = v11) | ( ~ (v11 = 0) & member(v9, v6) = v11) | ( ~ (v11 = 0) & member(v8, v6) = v11) | ( ~ (v11 = 0) & member(v7, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (pre_order(v5, v6) = 0) | ~ (apply(v5, v7, v9) = v10) | ~ (apply(v5, v7, v8) = 0) | ? [v11] : (( ~ (v11 = 0) & apply(v5, v8, v9) = v11) | ( ~ (v11 = 0) & member(v9, v6) = v11) | ( ~ (v11 = 0) & member(v8, v6) = v11) | ( ~ (v11 = 0) & member(v7, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (pre_order(v5, v6) = 0) | ~ (apply(v5, v7, v9) = v10) | ~ (member(v8, v6) = 0) | ? [v11] : (( ~ (v11 = 0) & apply(v5, v8, v9) = v11) | ( ~ (v11 = 0) & apply(v5, v7, v8) = v11) | ( ~ (v11 = 0) & member(v9, v6) = v11) | ( ~ (v11 = 0) & member(v7, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equivalence_class(v7, v6, v5) = v9) | ~ (member(v8, v9) = v10) | ? [v11] : (( ~ (v11 = 0) & apply(v5, v7, v8) = v11) | ( ~ (v11 = 0) & member(v8, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equivalence(v6, v5) = 0) | ~ (apply(v6, v8, v9) = 0) | ~ (apply(v6, v7, v9) = v10) | ? [v11] : (( ~ (v11 = 0) & apply(v6, v7, v8) = v11) | ( ~ (v11 = 0) & member(v9, v5) = v11) | ( ~ (v11 = 0) & member(v8, v5) = v11) | ( ~ (v11 = 0) & member(v7, v5) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equivalence(v6, v5) = 0) | ~ (apply(v6, v7, v9) = v10) | ~ (apply(v6, v7, v8) = 0) | ? [v11] : (( ~ (v11 = 0) & apply(v6, v8, v9) = v11) | ( ~ (v11 = 0) & member(v9, v5) = v11) | ( ~ (v11 = 0) & member(v8, v5) = v11) | ( ~ (v11 = 0) & member(v7, v5) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equivalence(v6, v5) = 0) | ~ (apply(v6, v7, v9) = v10) | ~ (member(v8, v5) = 0) | ? [v11] : (( ~ (v11 = 0) & apply(v6, v8, v9) = v11) | ( ~ (v11 = 0) & apply(v6, v7, v8) = v11) | ( ~ (v11 = 0) & member(v9, v5) = v11) | ( ~ (v11 = 0) & member(v7, v5) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (equivalence(v6, v5) = 0) | ~ (apply(v6, v8, v7) = v9) | ? [v10] : (( ~ (v10 = 0) & apply(v6, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v5) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (product(v6) = v7) | ~ (member(v5, v8) = v9) | ~ (member(v5, v7) = 0) | ? [v10] : ( ~ (v10 = 0) & member(v8, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (difference(v7, v6) = v8) | ~ (member(v5, v8) = v9) | ? [v10] : ((v10 = 0 & member(v5, v6) = 0) | ( ~ (v10 = 0) & member(v5, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (union(v6, v7) = v8) | ~ (member(v5, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & ~ (v10 = 0) & member(v5, v7) = v11 & member(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (intersection(v6, v7) = v8) | ~ (member(v5, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & member(v5, v7) = v10) | ( ~ (v10 = 0) & member(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (partition(v5, v6) = 0) | ~ (member(v9, v8) = 0) | ~ (member(v8, v5) = 0) | ~ (member(v7, v5) = 0) | ? [v10] : ( ~ (v10 = 0) & member(v9, v7) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (partition(v5, v6) = 0) | ~ (member(v9, v7) = 0) | ~ (member(v8, v5) = 0) | ~ (member(v7, v5) = 0) | ? [v10] : ( ~ (v10 = 0) & member(v9, v8) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (sum(v6) = v7) | ~ (member(v9, v6) = 0) | ~ (member(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & member(v5, v9) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (sum(v6) = v7) | ~ (member(v5, v9) = 0) | ~ (member(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & member(v9, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (equivalence_class(v9, v8, v7) = v6) | ~ (equivalence_class(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (apply(v9, v8, v7) = v6) | ~ (apply(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (pre_order(v5, v6) = 0) | ~ (apply(v5, v8, v9) = 0) | ~ (apply(v5, v7, v8) = 0) | ? [v10] : ((v10 = 0 & apply(v5, v7, v9) = 0) | ( ~ (v10 = 0) & member(v9, v6) = v10) | ( ~ (v10 = 0) & member(v8, v6) = v10) | ( ~ (v10 = 0) & member(v7, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (pre_order(v5, v6) = 0) | ~ (apply(v5, v8, v9) = 0) | ~ (member(v7, v6) = 0) | ? [v10] : ((v10 = 0 & apply(v5, v7, v9) = 0) | ( ~ (v10 = 0) & apply(v5, v7, v8) = v10) | ( ~ (v10 = 0) & member(v9, v6) = v10) | ( ~ (v10 = 0) & member(v8, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (pre_order(v5, v6) = 0) | ~ (apply(v5, v7, v8) = 0) | ~ (member(v9, v6) = 0) | ? [v10] : ((v10 = 0 & apply(v5, v7, v9) = 0) | ( ~ (v10 = 0) & apply(v5, v8, v9) = v10) | ( ~ (v10 = 0) & member(v8, v6) = v10) | ( ~ (v10 = 0) & member(v7, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (pre_order(v5, v6) = 0) | ~ (member(v9, v6) = 0) | ~ (member(v8, v6) = 0) | ~ (member(v7, v6) = 0) | ? [v10] : ((v10 = 0 & apply(v5, v7, v9) = 0) | ( ~ (v10 = 0) & apply(v5, v8, v9) = v10) | ( ~ (v10 = 0) & apply(v5, v7, v8) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (equivalence_class(v7, v6, v5) = v9) | ~ (member(v8, v9) = 0) | (apply(v5, v7, v8) = 0 & member(v8, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (equivalence(v6, v5) = 0) | ~ (apply(v6, v8, v9) = 0) | ~ (apply(v6, v7, v8) = 0) | ? [v10] : ((v10 = 0 & apply(v6, v7, v9) = 0) | ( ~ (v10 = 0) & member(v9, v5) = v10) | ( ~ (v10 = 0) & member(v8, v5) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (equivalence(v6, v5) = 0) | ~ (apply(v6, v8, v9) = 0) | ~ (member(v7, v5) = 0) | ? [v10] : ((v10 = 0 & apply(v6, v7, v9) = 0) | ( ~ (v10 = 0) & apply(v6, v7, v8) = v10) | ( ~ (v10 = 0) & member(v9, v5) = v10) | ( ~ (v10 = 0) & member(v8, v5) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (equivalence(v6, v5) = 0) | ~ (apply(v6, v7, v8) = 0) | ~ (member(v9, v5) = 0) | ? [v10] : ((v10 = 0 & apply(v6, v7, v9) = 0) | ( ~ (v10 = 0) & apply(v6, v8, v9) = v10) | ( ~ (v10 = 0) & member(v8, v5) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (equivalence(v6, v5) = 0) | ~ (member(v9, v5) = 0) | ~ (member(v8, v5) = 0) | ~ (member(v7, v5) = 0) | ? [v10] : ((v10 = 0 & apply(v6, v7, v9) = 0) | ( ~ (v10 = 0) & apply(v6, v8, v9) = v10) | ( ~ (v10 = 0) & apply(v6, v7, v8) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (pre_order(v5, v6) = 0) | ~ (apply(v5, v7, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equivalence(v6, v5) = 0) | ~ (apply(v6, v7, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (partition(v5, v6) = 0) | ~ (subset(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (product(v6) = v7) | ~ (member(v5, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & member(v9, v6) = 0 & member(v5, v9) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unordered_pair(v6, v5) = v7) | ~ (member(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unordered_pair(v5, v6) = v7) | ~ (member(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (power_set(v6) = v7) | ~ (member(v5, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & subset(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v5, v6) = 0) | ~ (member(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v5 | v6 = v5 | ~ (unordered_pair(v6, v7) = v8) | ~ (member(v5, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (pre_order(v8, v7) = v6) | ~ (pre_order(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (equivalence(v8, v7) = v6) | ~ (equivalence(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (partition(v8, v7) = v6) | ~ (partition(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (disjoint(v8, v7) = v6) | ~ (disjoint(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (unordered_pair(v8, v7) = v6) | ~ (unordered_pair(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (difference(v8, v7) = v6) | ~ (difference(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (union(v8, v7) = v6) | ~ (union(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection(v8, v7) = v6) | ~ (intersection(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (equal_set(v8, v7) = v6) | ~ (equal_set(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (subset(v8, v7) = v6) | ~ (subset(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (member(v8, v7) = v6) | ~ (member(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (equivalence(v6, v5) = 0) | ~ (apply(v6, v7, v8) = 0) | ? [v9] : ((v9 = 0 & apply(v6, v8, v7) = 0) | ( ~ (v9 = 0) & member(v8, v5) = v9) | ( ~ (v9 = 0) & member(v7, v5) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (product(v6) = v7) | ~ (member(v8, v6) = 0) | ~ (member(v5, v7) = 0) | member(v5, v8) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (difference(v7, v6) = v8) | ~ (member(v5, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v5, v7) = 0 & member(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v6, v7) = v8) | ~ (member(v5, v8) = 0) | ? [v9] : ((v9 = 0 & member(v5, v7) = 0) | (v9 = 0 & member(v5, v6) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection(v6, v7) = v8) | ~ (member(v5, v8) = 0) | (member(v5, v7) = 0 & member(v5, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (pre_order(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & ~ (v16 = 0) & apply(v5, v9, v10) = 0 & apply(v5, v8, v10) = v16 & apply(v5, v8, v9) = 0 & member(v10, v6) = 0 & member(v9, v6) = 0 & member(v8, v6) = 0) | (v9 = 0 & ~ (v10 = 0) & apply(v5, v8, v8) = v10 & member(v8, v6) = 0))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (equivalence(v6, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & ~ (v16 = 0) & apply(v6, v9, v10) = 0 & apply(v6, v8, v10) = v16 & apply(v6, v8, v9) = 0 & member(v10, v5) = 0 & member(v9, v5) = 0 & member(v8, v5) = 0) | (v12 = 0 & v11 = 0 & v10 = 0 & ~ (v13 = 0) & apply(v6, v9, v8) = v13 & apply(v6, v8, v9) = 0 & member(v9, v5) = 0 & member(v8, v5) = 0) | (v9 = 0 & ~ (v10 = 0) & apply(v6, v8, v8) = v10 & member(v8, v5) = 0))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (partition(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = 0 & v13 = 0 & v11 = 0 & v10 = 0 & ~ (v9 = v8) & member(v12, v9) = 0 & member(v12, v8) = 0 & member(v9, v5) = 0 & member(v8, v5) = 0) | (v9 = 0 & ~ (v10 = 0) & subset(v8, v6) = v10 & member(v8, v5) = 0) | (v9 = 0 & member(v8, v6) = 0 & ! [v15] : ( ~ (member(v15, v5) = 0) | ? [v16] : ( ~ (v16 = 0) & member(v8, v15) = v16)) & ! [v15] : ( ~ (member(v8, v15) = 0) | ? [v16] : ( ~ (v16 = 0) & member(v15, v5) = v16))))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (disjoint(v5, v6) = v7) | ? [v8] : (member(v8, v6) = 0 & member(v8, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (singleton(v5) = v6) | ~ (member(v5, v6) = v7)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (equal_set(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & subset(v6, v5) = v8) | ( ~ (v8 = 0) & subset(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & power_set(v6) = v8 & member(v5, v8) = v9)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & member(v8, v6) = v9 & member(v8, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (product(v7) = v6) | ~ (product(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (sum(v7) = v6) | ~ (sum(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (singleton(v7) = v6) | ~ (singleton(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (singleton(v6) = v7) | ~ (member(v5, v7) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (power_set(v7) = v6) | ~ (power_set(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (pre_order(v5, v6) = 0) | ~ (member(v7, v6) = 0) | apply(v5, v7, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (equivalence(v6, v5) = 0) | ~ (member(v7, v5) = 0) | apply(v6, v7, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (apply(v3, v5, v6) = v7) | ? [v8] : ? [v9] : (( ~ (v8 = 0) & member(v6, v0) = v8) | ( ~ (v8 = 0) & member(v5, v0) = v8) | (( ~ (v7 = 0) | (v9 = 0 & v8 = 0 & apply(v2, v5, v6) = 0 & apply(v1, v5, v6) = 0)) & (v7 = 0 | ( ~ (v9 = 0) & apply(v2, v5, v6) = v9) | ( ~ (v8 = 0) & apply(v1, v5, v6) = v8))))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (apply(v2, v5, v6) = v7) | ? [v8] : ? [v9] : (( ~ (v8 = 0) & member(v6, v0) = v8) | ( ~ (v8 = 0) & member(v5, v0) = v8) | (( ~ (v7 = 0) | (v8 = 0 & apply(v3, v5, v6) = 0) | ( ~ (v9 = 0) & apply(v1, v5, v6) = v9)) & ((v9 = 0 & v7 = 0 & apply(v1, v5, v6) = 0) | ( ~ (v8 = 0) & apply(v3, v5, v6) = v8))))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (apply(v1, v5, v6) = v7) | ? [v8] : ? [v9] : (( ~ (v8 = 0) & member(v6, v0) = v8) | ( ~ (v8 = 0) & member(v5, v0) = v8) | (( ~ (v7 = 0) | (v8 = 0 & apply(v3, v5, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v6) = v9)) & ((v9 = 0 & v7 = 0 & apply(v2, v5, v6) = 0) | ( ~ (v8 = 0) & apply(v3, v5, v6) = v8))))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (partition(v5, v6) = 0) | ~ (member(v7, v6) = 0) | ? [v8] : (member(v8, v5) = 0 & member(v7, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (partition(v5, v6) = 0) | ~ (member(v7, v5) = 0) | subset(v7, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (disjoint(v5, v6) = 0) | ~ (member(v7, v6) = 0) | ? [v8] : ( ~ (v8 = 0) & member(v7, v5) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (disjoint(v5, v6) = 0) | ~ (member(v7, v5) = 0) | ? [v8] : ( ~ (v8 = 0) & member(v7, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sum(v6) = v7) | ~ (member(v5, v7) = 0) | ? [v8] : (member(v8, v6) = 0 & member(v5, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (power_set(v6) = v7) | ~ (member(v5, v7) = 0) | subset(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (subset(v6, v5) = v7) | ? [v8] : ((v8 = 0 & v7 = 0 & subset(v5, v6) = 0) | ( ~ (v8 = 0) & equal_set(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (subset(v5, v6) = v7) | ? [v8] : ((v8 = 0 & v7 = 0 & subset(v6, v5) = 0) | ( ~ (v8 = 0) & equal_set(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (subset(v5, v6) = 0) | ~ (member(v7, v5) = 0) | member(v7, v6) = 0) & ! [v5] : ! [v6] : ( ~ (equal_set(v5, v6) = 0) | (subset(v6, v5) = 0 & subset(v5, v6) = 0)) & ! [v5] : ! [v6] : ( ~ (subset(v6, v5) = 0) | ? [v7] : ((v7 = 0 & equal_set(v5, v6) = 0) | ( ~ (v7 = 0) & subset(v5, v6) = v7))) & ! [v5] : ! [v6] : ( ~ (subset(v5, v6) = 0) | ? [v7] : (power_set(v6) = v7 & member(v5, v7) = 0)) & ! [v5] : ! [v6] : ( ~ (subset(v5, v6) = 0) | ? [v7] : ((v7 = 0 & equal_set(v5, v6) = 0) | ( ~ (v7 = 0) & subset(v6, v5) = v7))) & ! [v5] : ~ (member(v5, empty_set) = 0) & ? [v5] : ? [v6] : ? [v7] : ? [v8] : equivalence_class(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : apply(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : pre_order(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : equivalence(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : partition(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : disjoint(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : unordered_pair(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : difference(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : union(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : intersection(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : equal_set(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : subset(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : member(v6, v5) = v7 & ? [v5] : ? [v6] : product(v5) = v6 & ? [v5] : ? [v6] : sum(v5) = v6 & ? [v5] : ? [v6] : singleton(v5) = v6 & ? [v5] : ? [v6] : power_set(v5) = v6) % 22.81/6.43 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 22.81/6.43 | (1) ~ (all_0_0_0 = 0) & equivalence(all_0_1_1, all_0_4_4) = all_0_0_0 & equivalence(all_0_2_2, all_0_4_4) = 0 & equivalence(all_0_3_3, all_0_4_4) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v3, v4) = 0) | ~ (apply(v0, v2, v4) = v5) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v2, v3) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6) | ( ~ (v6 = 0) & member(v2, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v4) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6) | ( ~ (v6 = 0) & member(v2, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v4) = v5) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v4) = v6) | ( ~ (v6 = 0) & apply(v0, v2, v3) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v2, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = v5) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v2, v3) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v3, v4) = 0) | ~ (apply(v1, v2, v4) = v5) | ? [v6] : (( ~ (v6 = 0) & apply(v1, v2, v3) = v6) | ( ~ (v6 = 0) & member(v4, v0) = v6) | ( ~ (v6 = 0) & member(v3, v0) = v6) | ( ~ (v6 = 0) & member(v2, v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v4) = v5) | ~ (apply(v1, v2, v3) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v1, v3, v4) = v6) | ( ~ (v6 = 0) & member(v4, v0) = v6) | ( ~ (v6 = 0) & member(v3, v0) = v6) | ( ~ (v6 = 0) & member(v2, v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v4) = v5) | ~ (member(v3, v0) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v1, v3, v4) = v6) | ( ~ (v6 = 0) & apply(v1, v2, v3) = v6) | ( ~ (v6 = 0) & member(v4, v0) = v6) | ( ~ (v6 = 0) & member(v2, v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v3, v2) = v4) | ? [v5] : (( ~ (v5 = 0) & apply(v1, v2, v3) = v5) | ( ~ (v5 = 0) & member(v3, v0) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ((v5 = 0 & member(v0, v1) = 0) | ( ~ (v5 = 0) & member(v0, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & member(v0, v2) = v5) | ( ~ (v5 = 0) & member(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (partition(v0, v1) = 0) | ~ (member(v4, v3) = 0) | ~ (member(v3, v0) = 0) | ~ (member(v2, v0) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v4, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (partition(v0, v1) = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v0) = 0) | ~ (member(v2, v0) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v4, v3) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v4, v1) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ (equivalence_class(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v3, v4) = 0) | ~ (apply(v0, v2, v3) = 0) | ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & member(v4, v1) = v5) | ( ~ (v5 = 0) & member(v3, v1) = v5) | ( ~ (v5 = 0) & member(v2, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v3, v4) = 0) | ~ (member(v2, v1) = 0) | ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v0, v2, v3) = v5) | ( ~ (v5 = 0) & member(v4, v1) = v5) | ( ~ (v5 = 0) & member(v3, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v3) = 0) | ~ (member(v4, v1) = 0) | ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v0, v3, v4) = v5) | ( ~ (v5 = 0) & member(v3, v1) = v5) | ( ~ (v5 = 0) & member(v2, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pre_order(v0, v1) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v0, v3, v4) = v5) | ( ~ (v5 = 0) & apply(v0, v2, v3) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = 0) | (apply(v0, v2, v3) = 0 & member(v3, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v3, v4) = 0) | ~ (apply(v1, v2, v3) = 0) | ? [v5] : ((v5 = 0 & apply(v1, v2, v4) = 0) | ( ~ (v5 = 0) & member(v4, v0) = v5) | ( ~ (v5 = 0) & member(v3, v0) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v3, v4) = 0) | ~ (member(v2, v0) = 0) | ? [v5] : ((v5 = 0 & apply(v1, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v1, v2, v3) = v5) | ( ~ (v5 = 0) & member(v4, v0) = v5) | ( ~ (v5 = 0) & member(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v3) = 0) | ~ (member(v4, v0) = 0) | ? [v5] : ((v5 = 0 & apply(v1, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v1, v3, v4) = v5) | ( ~ (v5 = 0) & member(v3, v0) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equivalence(v1, v0) = 0) | ~ (member(v4, v0) = 0) | ~ (member(v3, v0) = 0) | ~ (member(v2, v0) = 0) | ? [v5] : ((v5 = 0 & apply(v1, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v1, v3, v4) = v5) | ( ~ (v5 = 0) & apply(v1, v2, v3) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (partition(v0, v1) = 0) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ (partition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(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 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v3) = 0) | ? [v4] : ((v4 = 0 & apply(v1, v3, v2) = 0) | ( ~ (v4 = 0) & member(v3, v0) = v4) | ( ~ (v4 = 0) & member(v2, v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ((v4 = 0 & member(v0, v2) = 0) | (v4 = 0 & member(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pre_order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v11 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v0, v3, v3) = v5 & member(v3, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equivalence(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v1, v4, v5) = 0 & apply(v1, v3, v5) = v11 & apply(v1, v3, v4) = 0 & member(v5, v0) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v7 = 0 & v6 = 0 & v5 = 0 & ~ (v8 = 0) & apply(v1, v4, v3) = v8 & apply(v1, v3, v4) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v1, v3, v3) = v5 & member(v3, v0) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (partition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & v6 = 0 & v5 = 0 & ~ (v4 = v3) & member(v7, v4) = 0 & member(v7, v3) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v4 = 0 & ~ (v5 = 0) & subset(v3, v1) = v5 & member(v3, v0) = 0) | (v4 = 0 & member(v3, v1) = 0 & ! [v10] : ( ~ (member(v10, v0) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v3, v10) = v11)) & ! [v10] : ( ~ (member(v3, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v10, v0) = v11))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (member(v3, v1) = 0 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (pre_order(v0, v1) = 0) | ~ (member(v2, v1) = 0) | apply(v0, v2, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (equivalence(v1, v0) = 0) | ~ (member(v2, v0) = 0) | apply(v1, v2, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(all_0_1_1, v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & member(v1, all_0_4_4) = v3) | ( ~ (v3 = 0) & member(v0, all_0_4_4) = v3) | (( ~ (v2 = 0) | (v4 = 0 & v3 = 0 & apply(all_0_2_2, v0, v1) = 0 & apply(all_0_3_3, v0, v1) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & apply(all_0_2_2, v0, v1) = v4) | ( ~ (v3 = 0) & apply(all_0_3_3, v0, v1) = v3))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(all_0_2_2, v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & member(v1, all_0_4_4) = v3) | ( ~ (v3 = 0) & member(v0, all_0_4_4) = v3) | (( ~ (v2 = 0) | (v3 = 0 & apply(all_0_1_1, v0, v1) = 0) | ( ~ (v4 = 0) & apply(all_0_3_3, v0, v1) = v4)) & ((v4 = 0 & v2 = 0 & apply(all_0_3_3, v0, v1) = 0) | ( ~ (v3 = 0) & apply(all_0_1_1, v0, v1) = v3))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(all_0_3_3, v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & member(v1, all_0_4_4) = v3) | ( ~ (v3 = 0) & member(v0, all_0_4_4) = v3) | (( ~ (v2 = 0) | (v3 = 0 & apply(all_0_1_1, v0, v1) = 0) | ( ~ (v4 = 0) & apply(all_0_2_2, v0, v1) = v4)) & ((v4 = 0 & v2 = 0 & apply(all_0_2_2, v0, v1) = 0) | ( ~ (v3 = 0) & apply(all_0_1_1, v0, v1) = v3))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (partition(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v3] : (member(v3, v0) = 0 & member(v2, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (partition(v0, v1) = 0) | ~ (member(v2, v0) = 0) | subset(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2))) & ! [v0] : ~ (member(v0, empty_set) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : equivalence_class(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : pre_order(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equivalence(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : partition(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2 & ? [v0] : ? [v1] : product(v0) = v1 & ? [v0] : ? [v1] : sum(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : power_set(v0) = v1 % 22.81/6.46 | % 22.81/6.46 | Applying alpha-rule on (1) yields: % 22.81/6.46 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(all_0_2_2, v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & member(v1, all_0_4_4) = v3) | ( ~ (v3 = 0) & member(v0, all_0_4_4) = v3) | (( ~ (v2 = 0) | (v3 = 0 & apply(all_0_1_1, v0, v1) = 0) | ( ~ (v4 = 0) & apply(all_0_3_3, v0, v1) = v4)) & ((v4 = 0 & v2 = 0 & apply(all_0_3_3, v0, v1) = 0) | ( ~ (v3 = 0) & apply(all_0_1_1, v0, v1) = v3))))) % 22.81/6.47 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 22.81/6.47 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 22.81/6.47 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v0) = v3)) % 22.81/6.47 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v3, v4) = 0) | ~ (apply(v1, v2, v3) = 0) | ? [v5] : ((v5 = 0 & apply(v1, v2, v4) = 0) | ( ~ (v5 = 0) & member(v4, v0) = v5) | ( ~ (v5 = 0) & member(v3, v0) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5))) % 22.81/6.47 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3))) % 22.81/6.47 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ((v4 = 0 & member(v0, v2) = 0) | (v4 = 0 & member(v0, v1) = 0))) % 22.81/6.47 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(all_0_3_3, v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & member(v1, all_0_4_4) = v3) | ( ~ (v3 = 0) & member(v0, all_0_4_4) = v3) | (( ~ (v2 = 0) | (v3 = 0 & apply(all_0_1_1, v0, v1) = 0) | ( ~ (v4 = 0) & apply(all_0_2_2, v0, v1) = v4)) & ((v4 = 0 & v2 = 0 & apply(all_0_2_2, v0, v1) = 0) | ( ~ (v3 = 0) & apply(all_0_1_1, v0, v1) = v3))))) % 22.81/6.47 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v3, v4) = 0) | ~ (apply(v0, v2, v3) = 0) | ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & member(v4, v1) = v5) | ( ~ (v5 = 0) & member(v3, v1) = v5) | ( ~ (v5 = 0) & member(v2, v1) = v5))) % 22.81/6.47 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0)) % 22.81/6.47 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v3) = 0) | ~ (member(v4, v0) = 0) | ? [v5] : ((v5 = 0 & apply(v1, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v1, v3, v4) = v5) | ( ~ (v5 = 0) & member(v3, v0) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5))) % 22.81/6.47 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 22.81/6.47 | (14) ? [v0] : ? [v1] : ? [v2] : partition(v1, v0) = v2 % 22.81/6.47 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 22.81/6.47 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (partition(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v3] : (member(v3, v0) = 0 & member(v2, v3) = 0)) % 22.81/6.47 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 22.81/6.47 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v3, v4) = 0) | ~ (member(v2, v0) = 0) | ? [v5] : ((v5 = 0 & apply(v1, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v1, v2, v3) = v5) | ( ~ (v5 = 0) & member(v4, v0) = v5) | ( ~ (v5 = 0) & member(v3, v0) = v5))) % 22.81/6.47 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = v5) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v2, v3) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) % 22.81/6.47 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v3) = 0) | ~ (member(v4, v1) = 0) | ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v0, v3, v4) = v5) | ( ~ (v5 = 0) & member(v3, v1) = v5) | ( ~ (v5 = 0) & member(v2, v1) = v5))) % 22.81/6.47 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v1) = v3)) % 22.81/6.47 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ (equivalence_class(v4, v3, v2) = v0)) % 22.81/6.47 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v3) = 0) | ? [v4] : ((v4 = 0 & apply(v1, v3, v2) = 0) | ( ~ (v4 = 0) & member(v3, v0) = v4) | ( ~ (v4 = 0) & member(v2, v0) = v4))) % 22.81/6.48 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ (partition(v3, v2) = v0)) % 22.81/6.48 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) % 22.81/6.48 | (26) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 22.81/6.48 | (27) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 22.81/6.48 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v4) = v5) | ~ (member(v3, v0) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v1, v3, v4) = v6) | ( ~ (v6 = 0) & apply(v1, v2, v3) = v6) | ( ~ (v6 = 0) & member(v4, v0) = v6) | ( ~ (v6 = 0) & member(v2, v0) = v6))) % 22.81/6.48 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 22.81/6.48 | (30) ? [v0] : ? [v1] : sum(v0) = v1 % 22.81/6.48 | (31) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equivalence(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v1, v4, v5) = 0 & apply(v1, v3, v5) = v11 & apply(v1, v3, v4) = 0 & member(v5, v0) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v7 = 0 & v6 = 0 & v5 = 0 & ~ (v8 = 0) & apply(v1, v4, v3) = v8 & apply(v1, v3, v4) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v1, v3, v3) = v5 & member(v3, v0) = 0))) % 22.81/6.48 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 22.81/6.48 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 22.81/6.48 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v4) = v5) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v4) = v6) | ( ~ (v6 = 0) & apply(v0, v2, v3) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v2, v1) = v6))) % 22.81/6.48 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v4) = v5) | ~ (apply(v1, v2, v3) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v1, v3, v4) = v6) | ( ~ (v6 = 0) & member(v4, v0) = v6) | ( ~ (v6 = 0) & member(v3, v0) = v6) | ( ~ (v6 = 0) & member(v2, v0) = v6))) % 22.81/6.48 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 22.81/6.48 | (37) ? [v0] : ? [v1] : power_set(v0) = v1 % 22.81/6.48 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) % 22.81/6.48 | (39) equivalence(all_0_1_1, all_0_4_4) = all_0_0_0 % 22.81/6.48 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) % 22.81/6.48 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) % 22.81/6.48 | (42) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0)) % 22.81/6.48 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & member(v0, v2) = v5) | ( ~ (v5 = 0) & member(v0, v1) = v5))) % 22.81/6.48 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0) % 22.81/6.48 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) % 22.81/6.48 | (46) ? [v0] : ? [v1] : ? [v2] : ? [v3] : equivalence_class(v2, v1, v0) = v3 % 22.81/6.48 | (47) ? [v0] : ? [v1] : ? [v2] : pre_order(v1, v0) = v2 % 22.81/6.48 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pre_order(v0, v1) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v0, v3, v4) = v5) | ( ~ (v5 = 0) & apply(v0, v2, v3) = v5))) % 22.81/6.49 | (49) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 22.81/6.49 | (50) ? [v0] : ? [v1] : ? [v2] : equivalence(v1, v0) = v2 % 22.81/6.49 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) % 22.81/6.49 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 22.81/6.49 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 22.81/6.49 | (54) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4)) % 22.81/6.49 | (55) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pre_order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v11 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v0, v3, v3) = v5 & member(v3, v1) = 0))) % 22.81/6.49 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = 0) | (apply(v0, v2, v3) = 0 & member(v3, v1) = 0)) % 22.81/6.49 | (57) ~ (all_0_0_0 = 0) % 22.81/6.49 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 22.81/6.49 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (equivalence(v1, v0) = 0) | ~ (member(v2, v0) = 0) | apply(v1, v2, v2) = 0) % 22.81/6.49 | (60) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (member(v3, v1) = 0 & member(v3, v0) = 0)) % 22.81/6.49 | (61) ? [v0] : ? [v1] : product(v0) = v1 % 22.81/6.49 | (62) equivalence(all_0_2_2, all_0_4_4) = 0 % 22.81/6.49 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 22.81/6.49 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) % 22.81/6.49 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v3, v4) = 0) | ~ (apply(v1, v2, v4) = v5) | ? [v6] : (( ~ (v6 = 0) & apply(v1, v2, v3) = v6) | ( ~ (v6 = 0) & member(v4, v0) = v6) | ( ~ (v6 = 0) & member(v3, v0) = v6) | ( ~ (v6 = 0) & member(v2, v0) = v6))) % 22.81/6.49 | (66) ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2))) % 22.81/6.49 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ((v5 = 0 & member(v0, v1) = 0) | ( ~ (v5 = 0) & member(v0, v2) = v5))) % 22.81/6.49 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) % 22.81/6.49 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (partition(v0, v1) = 0) | ~ (member(v2, v0) = 0) | subset(v2, v1) = 0) % 22.81/6.49 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) % 22.81/6.49 | (71) ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2 % 22.81/6.49 | (72) ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply(v2, v1, v0) = v3 % 22.81/6.49 | (73) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2))) % 22.81/6.49 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v3, v4) = 0) | ~ (apply(v0, v2, v4) = v5) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v2, v3) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6) | ( ~ (v6 = 0) & member(v2, v1) = v6))) % 22.81/6.49 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (pre_order(v0, v1) = 0) | ~ (member(v2, v1) = 0) | apply(v0, v2, v2) = 0) % 22.81/6.49 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equivalence(v1, v0) = 0) | ~ (member(v4, v0) = 0) | ~ (member(v3, v0) = 0) | ~ (member(v2, v0) = 0) | ? [v5] : ((v5 = 0 & apply(v1, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v1, v3, v4) = v5) | ( ~ (v5 = 0) & apply(v1, v2, v3) = v5))) % 22.81/6.49 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v3, v2) = v4) | ? [v5] : (( ~ (v5 = 0) & apply(v1, v2, v3) = v5) | ( ~ (v5 = 0) & member(v3, v0) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5))) % 22.81/6.50 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v3, v4) = 0) | ~ (member(v2, v1) = 0) | ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v0, v2, v3) = v5) | ( ~ (v5 = 0) & member(v4, v1) = v5) | ( ~ (v5 = 0) & member(v3, v1) = v5))) % 22.81/6.50 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v4, v1) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v0, v4) = v5)) % 22.81/6.50 | (80) ! [v0] : ~ (member(v0, empty_set) = 0) % 22.81/6.50 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (partition(v0, v1) = 0) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) % 22.81/6.50 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 22.81/6.50 | (83) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 22.81/6.50 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (partition(v0, v1) = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v0) = 0) | ~ (member(v2, v0) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v4, v3) = v5)) % 22.81/6.50 | (85) ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2 % 22.81/6.50 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 22.81/6.50 | (87) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2 % 22.81/6.50 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 22.81/6.50 | (89) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 22.81/6.50 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = v0)) % 22.81/6.50 | (91) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2 % 22.81/6.50 | (92) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (partition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & v6 = 0 & v5 = 0 & ~ (v4 = v3) & member(v7, v4) = 0 & member(v7, v3) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v4 = 0 & ~ (v5 = 0) & subset(v3, v1) = v5 & member(v3, v0) = 0) | (v4 = 0 & member(v3, v1) = 0 & ! [v10] : ( ~ (member(v10, v0) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v3, v10) = v11)) & ! [v10] : ( ~ (member(v3, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v10, v0) = v11))))) % 22.81/6.50 | (93) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(all_0_1_1, v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & member(v1, all_0_4_4) = v3) | ( ~ (v3 = 0) & member(v0, all_0_4_4) = v3) | (( ~ (v2 = 0) | (v4 = 0 & v3 = 0 & apply(all_0_2_2, v0, v1) = 0 & apply(all_0_3_3, v0, v1) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & apply(all_0_2_2, v0, v1) = v4) | ( ~ (v3 = 0) & apply(all_0_3_3, v0, v1) = v3))))) % 22.81/6.50 | (94) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2 % 22.81/6.50 | (95) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 % 22.81/6.50 | (96) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) % 22.81/6.50 | (97) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 22.81/6.50 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 22.81/6.50 | (99) equivalence(all_0_3_3, all_0_4_4) = 0 % 22.81/6.50 | (100) ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2 % 22.81/6.50 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 22.81/6.50 | (102) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 % 22.81/6.50 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v4) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6) | ( ~ (v6 = 0) & member(v2, v1) = v6))) % 22.81/6.50 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 22.81/6.50 | (105) ? [v0] : ? [v1] : singleton(v0) = v1 % 22.81/6.50 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (partition(v0, v1) = 0) | ~ (member(v4, v3) = 0) | ~ (member(v3, v0) = 0) | ~ (member(v2, v0) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v4, v2) = v5)) % 22.81/6.50 | % 23.24/6.50 | Instantiating formula (31) with all_0_0_0, all_0_1_1, all_0_4_4 and discharging atoms equivalence(all_0_1_1, all_0_4_4) = all_0_0_0, yields: % 23.24/6.50 | (107) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v8 = 0) & apply(all_0_1_1, v1, v2) = 0 & apply(all_0_1_1, v0, v2) = v8 & apply(all_0_1_1, v0, v1) = 0 & member(v2, all_0_4_4) = 0 & member(v1, all_0_4_4) = 0 & member(v0, all_0_4_4) = 0) | (v4 = 0 & v3 = 0 & v2 = 0 & ~ (v5 = 0) & apply(all_0_1_1, v1, v0) = v5 & apply(all_0_1_1, v0, v1) = 0 & member(v1, all_0_4_4) = 0 & member(v0, all_0_4_4) = 0) | (v1 = 0 & ~ (v2 = 0) & apply(all_0_1_1, v0, v0) = v2 & member(v0, all_0_4_4) = 0)) % 23.24/6.50 | % 23.24/6.50 +-Applying beta-rule and splitting (107), into two cases. % 23.24/6.50 |-Branch one: % 23.24/6.50 | (108) all_0_0_0 = 0 % 23.24/6.50 | % 23.24/6.51 | Equations (108) can reduce 57 to: % 23.24/6.51 | (109) $false % 23.24/6.51 | % 23.24/6.51 |-The branch is then unsatisfiable % 23.24/6.51 |-Branch two: % 23.24/6.51 | (57) ~ (all_0_0_0 = 0) % 23.24/6.51 | (111) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v8 = 0) & apply(all_0_1_1, v1, v2) = 0 & apply(all_0_1_1, v0, v2) = v8 & apply(all_0_1_1, v0, v1) = 0 & member(v2, all_0_4_4) = 0 & member(v1, all_0_4_4) = 0 & member(v0, all_0_4_4) = 0) | (v4 = 0 & v3 = 0 & v2 = 0 & ~ (v5 = 0) & apply(all_0_1_1, v1, v0) = v5 & apply(all_0_1_1, v0, v1) = 0 & member(v1, all_0_4_4) = 0 & member(v0, all_0_4_4) = 0) | (v1 = 0 & ~ (v2 = 0) & apply(all_0_1_1, v0, v0) = v2 & member(v0, all_0_4_4) = 0)) % 23.24/6.51 | % 23.24/6.51 | Instantiating (111) with all_44_0_54, all_44_1_55, all_44_2_56, all_44_3_57, all_44_4_58, all_44_5_59, all_44_6_60, all_44_7_61, all_44_8_62 yields: % 23.24/6.51 | (112) (all_44_1_55 = 0 & all_44_2_56 = 0 & all_44_3_57 = 0 & all_44_4_58 = 0 & all_44_5_59 = 0 & ~ (all_44_0_54 = 0) & apply(all_0_1_1, all_44_7_61, all_44_6_60) = 0 & apply(all_0_1_1, all_44_8_62, all_44_6_60) = all_44_0_54 & apply(all_0_1_1, all_44_8_62, all_44_7_61) = 0 & member(all_44_6_60, all_0_4_4) = 0 & member(all_44_7_61, all_0_4_4) = 0 & member(all_44_8_62, all_0_4_4) = 0) | (all_44_4_58 = 0 & all_44_5_59 = 0 & all_44_6_60 = 0 & ~ (all_44_3_57 = 0) & apply(all_0_1_1, all_44_7_61, all_44_8_62) = all_44_3_57 & apply(all_0_1_1, all_44_8_62, all_44_7_61) = 0 & member(all_44_7_61, all_0_4_4) = 0 & member(all_44_8_62, all_0_4_4) = 0) | (all_44_7_61 = 0 & ~ (all_44_6_60 = 0) & apply(all_0_1_1, all_44_8_62, all_44_8_62) = all_44_6_60 & member(all_44_8_62, all_0_4_4) = 0) % 23.24/6.51 | % 23.24/6.51 +-Applying beta-rule and splitting (112), into two cases. % 23.24/6.51 |-Branch one: % 23.24/6.51 | (113) (all_44_1_55 = 0 & all_44_2_56 = 0 & all_44_3_57 = 0 & all_44_4_58 = 0 & all_44_5_59 = 0 & ~ (all_44_0_54 = 0) & apply(all_0_1_1, all_44_7_61, all_44_6_60) = 0 & apply(all_0_1_1, all_44_8_62, all_44_6_60) = all_44_0_54 & apply(all_0_1_1, all_44_8_62, all_44_7_61) = 0 & member(all_44_6_60, all_0_4_4) = 0 & member(all_44_7_61, all_0_4_4) = 0 & member(all_44_8_62, all_0_4_4) = 0) | (all_44_4_58 = 0 & all_44_5_59 = 0 & all_44_6_60 = 0 & ~ (all_44_3_57 = 0) & apply(all_0_1_1, all_44_7_61, all_44_8_62) = all_44_3_57 & apply(all_0_1_1, all_44_8_62, all_44_7_61) = 0 & member(all_44_7_61, all_0_4_4) = 0 & member(all_44_8_62, all_0_4_4) = 0) % 23.24/6.51 | % 23.24/6.51 +-Applying beta-rule and splitting (113), into two cases. % 23.24/6.51 |-Branch one: % 23.24/6.51 | (114) all_44_1_55 = 0 & all_44_2_56 = 0 & all_44_3_57 = 0 & all_44_4_58 = 0 & all_44_5_59 = 0 & ~ (all_44_0_54 = 0) & apply(all_0_1_1, all_44_7_61, all_44_6_60) = 0 & apply(all_0_1_1, all_44_8_62, all_44_6_60) = all_44_0_54 & apply(all_0_1_1, all_44_8_62, all_44_7_61) = 0 & member(all_44_6_60, all_0_4_4) = 0 & member(all_44_7_61, all_0_4_4) = 0 & member(all_44_8_62, all_0_4_4) = 0 % 23.24/6.51 | % 23.24/6.51 | Applying alpha-rule on (114) yields: % 23.24/6.51 | (115) member(all_44_6_60, all_0_4_4) = 0 % 23.24/6.51 | (116) apply(all_0_1_1, all_44_8_62, all_44_7_61) = 0 % 23.24/6.51 | (117) all_44_2_56 = 0 % 23.24/6.51 | (118) all_44_5_59 = 0 % 23.24/6.51 | (119) apply(all_0_1_1, all_44_8_62, all_44_6_60) = all_44_0_54 % 23.24/6.51 | (120) all_44_1_55 = 0 % 23.24/6.51 | (121) member(all_44_8_62, all_0_4_4) = 0 % 23.24/6.51 | (122) all_44_3_57 = 0 % 23.24/6.51 | (123) member(all_44_7_61, all_0_4_4) = 0 % 23.24/6.51 | (124) apply(all_0_1_1, all_44_7_61, all_44_6_60) = 0 % 23.24/6.51 | (125) all_44_4_58 = 0 % 23.24/6.51 | (126) ~ (all_44_0_54 = 0) % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (93) with 0, all_44_6_60, all_44_7_61 and discharging atoms apply(all_0_1_1, all_44_7_61, all_44_6_60) = 0, yields: % 23.24/6.51 | (127) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & apply(all_0_2_2, all_44_7_61, all_44_6_60) = 0 & apply(all_0_3_3, all_44_7_61, all_44_6_60) = 0) | ( ~ (v0 = 0) & member(all_44_6_60, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_44_7_61, all_0_4_4) = v0)) % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (93) with all_44_0_54, all_44_6_60, all_44_8_62 and discharging atoms apply(all_0_1_1, all_44_8_62, all_44_6_60) = all_44_0_54, yields: % 23.24/6.51 | (128) ? [v0] : ? [v1] : (( ~ (v0 = 0) & member(all_44_6_60, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_44_8_62, all_0_4_4) = v0) | (( ~ (all_44_0_54 = 0) | (v1 = 0 & v0 = 0 & apply(all_0_2_2, all_44_8_62, all_44_6_60) = 0 & apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0)) & (all_44_0_54 = 0 | ( ~ (v1 = 0) & apply(all_0_2_2, all_44_8_62, all_44_6_60) = v1) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_8_62, all_44_6_60) = v0)))) % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (93) with 0, all_44_7_61, all_44_8_62 and discharging atoms apply(all_0_1_1, all_44_8_62, all_44_7_61) = 0, yields: % 23.24/6.51 | (129) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0) | ( ~ (v0 = 0) & member(all_44_7_61, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_44_8_62, all_0_4_4) = v0)) % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (59) with all_44_6_60, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_6_60, all_0_4_4) = 0, yields: % 23.24/6.51 | (130) apply(all_0_2_2, all_44_6_60, all_44_6_60) = 0 % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (76) with all_44_6_60, all_44_6_60, all_44_6_60, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_6_60, all_0_4_4) = 0, yields: % 23.24/6.51 | (131) ? [v0] : ((v0 = 0 & apply(all_0_3_3, all_44_6_60, all_44_6_60) = 0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_6_60, all_44_6_60) = v0)) % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (59) with all_44_6_60, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_6_60, all_0_4_4) = 0, yields: % 23.24/6.51 | (132) apply(all_0_3_3, all_44_6_60, all_44_6_60) = 0 % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (76) with all_44_6_60, all_44_6_60, all_44_7_61, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_6_60, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.24/6.51 | (133) ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_7_61, all_44_6_60) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_6_60, all_44_6_60) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_61, all_44_6_60) = v0)) % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (76) with all_44_6_60, all_44_7_61, all_44_7_61, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_6_60, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.24/6.51 | (134) ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_7_61, all_44_6_60) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_61, all_44_6_60) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_61, all_44_7_61) = v0)) % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (76) with all_44_7_61, all_44_7_61, all_44_7_61, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.24/6.51 | (135) ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_7_61, all_44_7_61) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_61, all_44_7_61) = v0)) % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (59) with all_44_7_61, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.24/6.51 | (136) apply(all_0_2_2, all_44_7_61, all_44_7_61) = 0 % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (76) with all_44_6_60, all_44_6_60, all_44_7_61, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_6_60, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.24/6.51 | (137) ? [v0] : ((v0 = 0 & apply(all_0_3_3, all_44_7_61, all_44_6_60) = 0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_6_60, all_44_6_60) = v0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_7_61, all_44_6_60) = v0)) % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (76) with all_44_6_60, all_44_7_61, all_44_7_61, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_6_60, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.24/6.52 | (138) ? [v0] : ((v0 = 0 & apply(all_0_3_3, all_44_7_61, all_44_6_60) = 0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_7_61, all_44_6_60) = v0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = v0)) % 23.24/6.52 | % 23.24/6.52 | Instantiating formula (76) with all_44_7_61, all_44_7_61, all_44_7_61, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.24/6.52 | (139) ? [v0] : ((v0 = 0 & apply(all_0_3_3, all_44_7_61, all_44_7_61) = 0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = v0)) % 23.24/6.52 | % 23.24/6.52 | Instantiating formula (59) with all_44_7_61, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.24/6.52 | (140) apply(all_0_3_3, all_44_7_61, all_44_7_61) = 0 % 23.24/6.52 | % 23.24/6.52 | Instantiating formula (76) with all_44_6_60, all_44_7_61, all_44_8_62, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_6_60, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.52 | (141) ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_8_62, all_44_6_60) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_61, all_44_6_60) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_62, all_44_7_61) = v0)) % 23.24/6.52 | % 23.24/6.52 | Instantiating formula (76) with all_44_6_60, all_44_8_62, all_44_8_62, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_6_60, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.52 | (142) ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_8_62, all_44_6_60) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_62, all_44_6_60) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = v0)) % 23.24/6.52 | % 23.24/6.52 | Instantiating formula (76) with all_44_7_61, all_44_7_61, all_44_8_62, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.52 | (143) ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_61, all_44_7_61) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_62, all_44_7_61) = v0)) % 23.24/6.52 | % 23.24/6.52 | Instantiating formula (76) with all_44_7_61, all_44_8_62, all_44_8_62, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.52 | (144) ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_62, all_44_7_61) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = v0)) % 23.24/6.52 | % 23.24/6.52 | Instantiating formula (76) with all_44_8_62, all_44_8_62, all_44_8_62, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.52 | (145) ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = v0)) % 23.24/6.52 | % 23.24/6.52 | Instantiating formula (59) with all_44_8_62, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.52 | (146) apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0 % 23.24/6.52 | % 23.24/6.52 | Instantiating formula (76) with all_44_6_60, all_44_6_60, all_44_8_62, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_6_60, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.52 | (147) ? [v0] : ((v0 = 0 & apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_6_60, all_44_6_60) = v0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_8_62, all_44_6_60) = v0)) % 23.24/6.52 | % 23.24/6.52 | Instantiating formula (76) with all_44_6_60, all_44_7_61, all_44_8_62, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_6_60, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.52 | (148) ? [v0] : ((v0 = 0 & apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_7_61, all_44_6_60) = v0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_8_62, all_44_7_61) = v0)) % 23.24/6.52 | % 23.24/6.52 | Instantiating formula (76) with all_44_6_60, all_44_8_62, all_44_8_62, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_6_60, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.52 | (149) ? [v0] : ((v0 = 0 & apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_8_62, all_44_6_60) = v0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = v0)) % 23.24/6.52 | % 23.24/6.52 | Instantiating formula (76) with all_44_7_61, all_44_7_61, all_44_8_62, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.52 | (150) ? [v0] : ((v0 = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = v0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_8_62, all_44_7_61) = v0)) % 23.24/6.52 | % 23.24/6.52 | Instantiating formula (76) with all_44_7_61, all_44_8_62, all_44_8_62, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.52 | (151) ? [v0] : ((v0 = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_8_62, all_44_7_61) = v0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = v0)) % 23.24/6.52 | % 23.24/6.52 | Instantiating formula (76) with all_44_8_62, all_44_8_62, all_44_8_62, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.52 | (152) ? [v0] : ((v0 = 0 & apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = v0)) % 23.24/6.52 | % 23.24/6.52 | Instantiating formula (59) with all_44_8_62, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.52 | (153) apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0 % 23.24/6.52 | % 23.24/6.52 | Instantiating (138) with all_59_0_64 yields: % 23.24/6.52 | (154) (all_59_0_64 = 0 & apply(all_0_3_3, all_44_7_61, all_44_6_60) = 0) | ( ~ (all_59_0_64 = 0) & apply(all_0_3_3, all_44_7_61, all_44_6_60) = all_59_0_64) | ( ~ (all_59_0_64 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_59_0_64) % 23.24/6.52 | % 23.24/6.52 | Instantiating (137) with all_61_0_66 yields: % 23.24/6.52 | (155) (all_61_0_66 = 0 & apply(all_0_3_3, all_44_7_61, all_44_6_60) = 0) | ( ~ (all_61_0_66 = 0) & apply(all_0_3_3, all_44_6_60, all_44_6_60) = all_61_0_66) | ( ~ (all_61_0_66 = 0) & apply(all_0_3_3, all_44_7_61, all_44_6_60) = all_61_0_66) % 23.24/6.52 | % 23.24/6.52 | Instantiating (134) with all_64_0_69 yields: % 23.24/6.52 | (156) (all_64_0_69 = 0 & apply(all_0_2_2, all_44_7_61, all_44_6_60) = 0) | ( ~ (all_64_0_69 = 0) & apply(all_0_2_2, all_44_7_61, all_44_6_60) = all_64_0_69) | ( ~ (all_64_0_69 = 0) & apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_64_0_69) % 23.24/6.52 | % 23.24/6.52 | Instantiating (133) with all_66_0_71 yields: % 23.24/6.52 | (157) (all_66_0_71 = 0 & apply(all_0_2_2, all_44_7_61, all_44_6_60) = 0) | ( ~ (all_66_0_71 = 0) & apply(all_0_2_2, all_44_6_60, all_44_6_60) = all_66_0_71) | ( ~ (all_66_0_71 = 0) & apply(all_0_2_2, all_44_7_61, all_44_6_60) = all_66_0_71) % 23.24/6.52 | % 23.24/6.52 | Instantiating (135) with all_67_0_72 yields: % 23.24/6.52 | (158) (all_67_0_72 = 0 & apply(all_0_2_2, all_44_7_61, all_44_7_61) = 0) | ( ~ (all_67_0_72 = 0) & apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_67_0_72) % 23.24/6.52 | % 23.24/6.52 | Instantiating (151) with all_69_0_74 yields: % 23.24/6.52 | (159) (all_69_0_74 = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0) | ( ~ (all_69_0_74 = 0) & apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_69_0_74) | ( ~ (all_69_0_74 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_69_0_74) % 23.24/6.52 | % 23.24/6.52 | Instantiating (147) with all_72_0_77 yields: % 23.24/6.52 | (160) (all_72_0_77 = 0 & apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0) | ( ~ (all_72_0_77 = 0) & apply(all_0_3_3, all_44_6_60, all_44_6_60) = all_72_0_77) | ( ~ (all_72_0_77 = 0) & apply(all_0_3_3, all_44_8_62, all_44_6_60) = all_72_0_77) % 23.24/6.52 | % 23.24/6.52 | Instantiating (129) with all_77_0_82, all_77_1_83 yields: % 23.24/6.52 | (161) (all_77_0_82 = 0 & all_77_1_83 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0) | ( ~ (all_77_1_83 = 0) & member(all_44_7_61, all_0_4_4) = all_77_1_83) | ( ~ (all_77_1_83 = 0) & member(all_44_8_62, all_0_4_4) = all_77_1_83) % 23.24/6.52 | % 23.24/6.52 | Instantiating (150) with all_78_0_84 yields: % 23.24/6.52 | (162) (all_78_0_84 = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0) | ( ~ (all_78_0_84 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_78_0_84) | ( ~ (all_78_0_84 = 0) & apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_78_0_84) % 23.24/6.52 | % 23.24/6.52 | Instantiating (128) with all_80_0_86, all_80_1_87 yields: % 23.24/6.52 | (163) ( ~ (all_80_1_87 = 0) & member(all_44_6_60, all_0_4_4) = all_80_1_87) | ( ~ (all_80_1_87 = 0) & member(all_44_8_62, all_0_4_4) = all_80_1_87) | (( ~ (all_44_0_54 = 0) | (all_80_0_86 = 0 & all_80_1_87 = 0 & apply(all_0_2_2, all_44_8_62, all_44_6_60) = 0 & apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0)) & (all_44_0_54 = 0 | ( ~ (all_80_0_86 = 0) & apply(all_0_2_2, all_44_8_62, all_44_6_60) = all_80_0_86) | ( ~ (all_80_1_87 = 0) & apply(all_0_3_3, all_44_8_62, all_44_6_60) = all_80_1_87))) % 23.24/6.52 | % 23.24/6.52 | Instantiating (127) with all_81_0_88, all_81_1_89 yields: % 23.24/6.52 | (164) (all_81_0_88 = 0 & all_81_1_89 = 0 & apply(all_0_2_2, all_44_7_61, all_44_6_60) = 0 & apply(all_0_3_3, all_44_7_61, all_44_6_60) = 0) | ( ~ (all_81_1_89 = 0) & member(all_44_6_60, all_0_4_4) = all_81_1_89) | ( ~ (all_81_1_89 = 0) & member(all_44_7_61, all_0_4_4) = all_81_1_89) % 23.24/6.52 | % 23.24/6.52 | Instantiating (131) with all_83_0_91 yields: % 23.24/6.52 | (165) (all_83_0_91 = 0 & apply(all_0_3_3, all_44_6_60, all_44_6_60) = 0) | ( ~ (all_83_0_91 = 0) & apply(all_0_3_3, all_44_6_60, all_44_6_60) = all_83_0_91) % 23.24/6.52 | % 23.24/6.52 | Instantiating (152) with all_85_0_93 yields: % 23.24/6.52 | (166) (all_85_0_93 = 0 & apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0) | ( ~ (all_85_0_93 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_85_0_93) % 23.24/6.53 | % 23.24/6.53 | Instantiating (145) with all_87_0_95 yields: % 23.24/6.53 | (167) (all_87_0_95 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0) | ( ~ (all_87_0_95 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_87_0_95) % 23.24/6.53 | % 23.24/6.53 | Instantiating (149) with all_92_0_100 yields: % 23.24/6.53 | (168) (all_92_0_100 = 0 & apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0) | ( ~ (all_92_0_100 = 0) & apply(all_0_3_3, all_44_8_62, all_44_6_60) = all_92_0_100) | ( ~ (all_92_0_100 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_92_0_100) % 23.24/6.53 | % 23.24/6.53 | Instantiating (148) with all_96_0_104 yields: % 23.24/6.53 | (169) (all_96_0_104 = 0 & apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0) | ( ~ (all_96_0_104 = 0) & apply(all_0_3_3, all_44_7_61, all_44_6_60) = all_96_0_104) | ( ~ (all_96_0_104 = 0) & apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_96_0_104) % 23.24/6.53 | % 23.24/6.53 | Instantiating (144) with all_98_0_106 yields: % 23.24/6.53 | (170) (all_98_0_106 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0) | ( ~ (all_98_0_106 = 0) & apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_98_0_106) | ( ~ (all_98_0_106 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_98_0_106) % 23.24/6.53 | % 23.24/6.53 | Instantiating (143) with all_103_0_111 yields: % 23.24/6.53 | (171) (all_103_0_111 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0) | ( ~ (all_103_0_111 = 0) & apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_103_0_111) | ( ~ (all_103_0_111 = 0) & apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_103_0_111) % 23.24/6.53 | % 23.24/6.53 | Instantiating (142) with all_106_0_114 yields: % 23.24/6.53 | (172) (all_106_0_114 = 0 & apply(all_0_2_2, all_44_8_62, all_44_6_60) = 0) | ( ~ (all_106_0_114 = 0) & apply(all_0_2_2, all_44_8_62, all_44_6_60) = all_106_0_114) | ( ~ (all_106_0_114 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_106_0_114) % 23.24/6.53 | % 23.24/6.53 | Instantiating (139) with all_111_0_119 yields: % 23.24/6.53 | (173) (all_111_0_119 = 0 & apply(all_0_3_3, all_44_7_61, all_44_7_61) = 0) | ( ~ (all_111_0_119 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_111_0_119) % 23.24/6.53 | % 23.24/6.53 | Instantiating (141) with all_112_0_120 yields: % 23.24/6.53 | (174) (all_112_0_120 = 0 & apply(all_0_2_2, all_44_8_62, all_44_6_60) = 0) | ( ~ (all_112_0_120 = 0) & apply(all_0_2_2, all_44_7_61, all_44_6_60) = all_112_0_120) | ( ~ (all_112_0_120 = 0) & apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_112_0_120) % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (166), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (175) all_85_0_93 = 0 & apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0 % 23.24/6.53 | % 23.24/6.53 | Applying alpha-rule on (175) yields: % 23.24/6.53 | (176) all_85_0_93 = 0 % 23.24/6.53 | (153) apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0 % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (165), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (178) all_83_0_91 = 0 & apply(all_0_3_3, all_44_6_60, all_44_6_60) = 0 % 23.24/6.53 | % 23.24/6.53 | Applying alpha-rule on (178) yields: % 23.24/6.53 | (179) all_83_0_91 = 0 % 23.24/6.53 | (132) apply(all_0_3_3, all_44_6_60, all_44_6_60) = 0 % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (161), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (181) (all_77_0_82 = 0 & all_77_1_83 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0) | ( ~ (all_77_1_83 = 0) & member(all_44_7_61, all_0_4_4) = all_77_1_83) % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (181), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (182) all_77_0_82 = 0 & all_77_1_83 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0 % 23.24/6.53 | % 23.24/6.53 | Applying alpha-rule on (182) yields: % 23.24/6.53 | (183) all_77_0_82 = 0 % 23.24/6.53 | (184) all_77_1_83 = 0 % 23.24/6.53 | (185) apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0 % 23.24/6.53 | (186) apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0 % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (170), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (187) (all_98_0_106 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0) | ( ~ (all_98_0_106 = 0) & apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_98_0_106) % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (187), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (188) all_98_0_106 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0 % 23.24/6.53 | % 23.24/6.53 | Applying alpha-rule on (188) yields: % 23.24/6.53 | (189) all_98_0_106 = 0 % 23.24/6.53 | (185) apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0 % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (158), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (191) all_67_0_72 = 0 & apply(all_0_2_2, all_44_7_61, all_44_7_61) = 0 % 23.24/6.53 | % 23.24/6.53 | Applying alpha-rule on (191) yields: % 23.24/6.53 | (192) all_67_0_72 = 0 % 23.24/6.53 | (136) apply(all_0_2_2, all_44_7_61, all_44_7_61) = 0 % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (159), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (194) (all_69_0_74 = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0) | ( ~ (all_69_0_74 = 0) & apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_69_0_74) % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (194), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (195) all_69_0_74 = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0 % 23.24/6.53 | % 23.24/6.53 | Applying alpha-rule on (195) yields: % 23.24/6.53 | (196) all_69_0_74 = 0 % 23.24/6.53 | (186) apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0 % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (164), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (198) (all_81_0_88 = 0 & all_81_1_89 = 0 & apply(all_0_2_2, all_44_7_61, all_44_6_60) = 0 & apply(all_0_3_3, all_44_7_61, all_44_6_60) = 0) | ( ~ (all_81_1_89 = 0) & member(all_44_6_60, all_0_4_4) = all_81_1_89) % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (198), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (199) all_81_0_88 = 0 & all_81_1_89 = 0 & apply(all_0_2_2, all_44_7_61, all_44_6_60) = 0 & apply(all_0_3_3, all_44_7_61, all_44_6_60) = 0 % 23.24/6.53 | % 23.24/6.53 | Applying alpha-rule on (199) yields: % 23.24/6.53 | (200) all_81_0_88 = 0 % 23.24/6.53 | (201) all_81_1_89 = 0 % 23.24/6.53 | (202) apply(all_0_2_2, all_44_7_61, all_44_6_60) = 0 % 23.24/6.53 | (203) apply(all_0_3_3, all_44_7_61, all_44_6_60) = 0 % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (154), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (204) (all_59_0_64 = 0 & apply(all_0_3_3, all_44_7_61, all_44_6_60) = 0) | ( ~ (all_59_0_64 = 0) & apply(all_0_3_3, all_44_7_61, all_44_6_60) = all_59_0_64) % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (204), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (205) all_59_0_64 = 0 & apply(all_0_3_3, all_44_7_61, all_44_6_60) = 0 % 23.24/6.53 | % 23.24/6.53 | Applying alpha-rule on (205) yields: % 23.24/6.53 | (206) all_59_0_64 = 0 % 23.24/6.53 | (203) apply(all_0_3_3, all_44_7_61, all_44_6_60) = 0 % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (173), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (208) all_111_0_119 = 0 & apply(all_0_3_3, all_44_7_61, all_44_7_61) = 0 % 23.24/6.53 | % 23.24/6.53 | Applying alpha-rule on (208) yields: % 23.24/6.53 | (209) all_111_0_119 = 0 % 23.24/6.53 | (140) apply(all_0_3_3, all_44_7_61, all_44_7_61) = 0 % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (167), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (211) all_87_0_95 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0 % 23.24/6.53 | % 23.24/6.53 | Applying alpha-rule on (211) yields: % 23.24/6.53 | (212) all_87_0_95 = 0 % 23.24/6.53 | (146) apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0 % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (155), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (214) (all_61_0_66 = 0 & apply(all_0_3_3, all_44_7_61, all_44_6_60) = 0) | ( ~ (all_61_0_66 = 0) & apply(all_0_3_3, all_44_6_60, all_44_6_60) = all_61_0_66) % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (214), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (215) all_61_0_66 = 0 & apply(all_0_3_3, all_44_7_61, all_44_6_60) = 0 % 23.24/6.53 | % 23.24/6.53 | Applying alpha-rule on (215) yields: % 23.24/6.53 | (216) all_61_0_66 = 0 % 23.24/6.53 | (203) apply(all_0_3_3, all_44_7_61, all_44_6_60) = 0 % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (157), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (218) (all_66_0_71 = 0 & apply(all_0_2_2, all_44_7_61, all_44_6_60) = 0) | ( ~ (all_66_0_71 = 0) & apply(all_0_2_2, all_44_6_60, all_44_6_60) = all_66_0_71) % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (218), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (219) all_66_0_71 = 0 & apply(all_0_2_2, all_44_7_61, all_44_6_60) = 0 % 23.24/6.53 | % 23.24/6.53 | Applying alpha-rule on (219) yields: % 23.24/6.53 | (220) all_66_0_71 = 0 % 23.24/6.53 | (202) apply(all_0_2_2, all_44_7_61, all_44_6_60) = 0 % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (156), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (222) (all_64_0_69 = 0 & apply(all_0_2_2, all_44_7_61, all_44_6_60) = 0) | ( ~ (all_64_0_69 = 0) & apply(all_0_2_2, all_44_7_61, all_44_6_60) = all_64_0_69) % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (222), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (223) all_64_0_69 = 0 & apply(all_0_2_2, all_44_7_61, all_44_6_60) = 0 % 23.24/6.53 | % 23.24/6.53 | Applying alpha-rule on (223) yields: % 23.24/6.53 | (224) all_64_0_69 = 0 % 23.24/6.53 | (202) apply(all_0_2_2, all_44_7_61, all_44_6_60) = 0 % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (171), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (226) (all_103_0_111 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0) | ( ~ (all_103_0_111 = 0) & apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_103_0_111) % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (226), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (227) all_103_0_111 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0 % 23.24/6.53 | % 23.24/6.53 | Applying alpha-rule on (227) yields: % 23.24/6.53 | (228) all_103_0_111 = 0 % 23.24/6.53 | (185) apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0 % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (162), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (230) (all_78_0_84 = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0) | ( ~ (all_78_0_84 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_78_0_84) % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (230), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (231) all_78_0_84 = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0 % 23.24/6.53 | % 23.24/6.53 | Applying alpha-rule on (231) yields: % 23.24/6.53 | (232) all_78_0_84 = 0 % 23.24/6.53 | (186) apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0 % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (169), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (234) (all_96_0_104 = 0 & apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0) | ( ~ (all_96_0_104 = 0) & apply(all_0_3_3, all_44_7_61, all_44_6_60) = all_96_0_104) % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (234), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (235) all_96_0_104 = 0 & apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0 % 23.24/6.53 | % 23.24/6.53 | Applying alpha-rule on (235) yields: % 23.24/6.53 | (236) all_96_0_104 = 0 % 23.24/6.53 | (237) apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0 % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (168), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (238) (all_92_0_100 = 0 & apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0) | ( ~ (all_92_0_100 = 0) & apply(all_0_3_3, all_44_8_62, all_44_6_60) = all_92_0_100) % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (238), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (239) all_92_0_100 = 0 & apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0 % 23.24/6.53 | % 23.24/6.53 | Applying alpha-rule on (239) yields: % 23.24/6.53 | (240) all_92_0_100 = 0 % 23.24/6.53 | (237) apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0 % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (160), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (242) (all_72_0_77 = 0 & apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0) | ( ~ (all_72_0_77 = 0) & apply(all_0_3_3, all_44_6_60, all_44_6_60) = all_72_0_77) % 23.24/6.53 | % 23.24/6.53 +-Applying beta-rule and splitting (242), into two cases. % 23.24/6.53 |-Branch one: % 23.24/6.53 | (243) all_72_0_77 = 0 & apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0 % 23.24/6.53 | % 23.24/6.53 | Applying alpha-rule on (243) yields: % 23.24/6.53 | (244) all_72_0_77 = 0 % 23.24/6.54 | (237) apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0 % 23.24/6.54 | % 23.24/6.54 +-Applying beta-rule and splitting (163), into two cases. % 23.24/6.54 |-Branch one: % 23.24/6.54 | (246) ( ~ (all_80_1_87 = 0) & member(all_44_6_60, all_0_4_4) = all_80_1_87) | ( ~ (all_80_1_87 = 0) & member(all_44_8_62, all_0_4_4) = all_80_1_87) % 23.24/6.54 | % 23.24/6.54 +-Applying beta-rule and splitting (246), into two cases. % 23.24/6.54 |-Branch one: % 23.24/6.54 | (247) ~ (all_80_1_87 = 0) & member(all_44_6_60, all_0_4_4) = all_80_1_87 % 23.24/6.54 | % 23.24/6.54 | Applying alpha-rule on (247) yields: % 23.24/6.54 | (248) ~ (all_80_1_87 = 0) % 23.24/6.54 | (249) member(all_44_6_60, all_0_4_4) = all_80_1_87 % 23.24/6.54 | % 23.24/6.54 | Instantiating formula (88) with all_44_6_60, all_0_4_4, all_80_1_87, 0 and discharging atoms member(all_44_6_60, all_0_4_4) = all_80_1_87, member(all_44_6_60, all_0_4_4) = 0, yields: % 23.24/6.54 | (250) all_80_1_87 = 0 % 23.24/6.54 | % 23.24/6.54 | Equations (250) can reduce 248 to: % 23.24/6.54 | (109) $false % 23.24/6.54 | % 23.24/6.54 |-The branch is then unsatisfiable % 23.24/6.54 |-Branch two: % 23.24/6.54 | (252) ~ (all_80_1_87 = 0) & member(all_44_8_62, all_0_4_4) = all_80_1_87 % 23.24/6.54 | % 23.24/6.54 | Applying alpha-rule on (252) yields: % 23.24/6.54 | (248) ~ (all_80_1_87 = 0) % 23.24/6.54 | (254) member(all_44_8_62, all_0_4_4) = all_80_1_87 % 23.24/6.54 | % 23.24/6.54 | Instantiating formula (88) with all_44_8_62, all_0_4_4, all_80_1_87, 0 and discharging atoms member(all_44_8_62, all_0_4_4) = all_80_1_87, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.54 | (250) all_80_1_87 = 0 % 23.24/6.54 | % 23.24/6.54 | Equations (250) can reduce 248 to: % 23.24/6.54 | (109) $false % 23.24/6.54 | % 23.24/6.54 |-The branch is then unsatisfiable % 23.24/6.54 |-Branch two: % 23.24/6.54 | (257) ( ~ (all_44_0_54 = 0) | (all_80_0_86 = 0 & all_80_1_87 = 0 & apply(all_0_2_2, all_44_8_62, all_44_6_60) = 0 & apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0)) & (all_44_0_54 = 0 | ( ~ (all_80_0_86 = 0) & apply(all_0_2_2, all_44_8_62, all_44_6_60) = all_80_0_86) | ( ~ (all_80_1_87 = 0) & apply(all_0_3_3, all_44_8_62, all_44_6_60) = all_80_1_87)) % 23.24/6.54 | % 23.24/6.54 | Applying alpha-rule on (257) yields: % 23.24/6.54 | (258) ~ (all_44_0_54 = 0) | (all_80_0_86 = 0 & all_80_1_87 = 0 & apply(all_0_2_2, all_44_8_62, all_44_6_60) = 0 & apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0) % 23.24/6.54 | (259) all_44_0_54 = 0 | ( ~ (all_80_0_86 = 0) & apply(all_0_2_2, all_44_8_62, all_44_6_60) = all_80_0_86) | ( ~ (all_80_1_87 = 0) & apply(all_0_3_3, all_44_8_62, all_44_6_60) = all_80_1_87) % 23.24/6.54 | % 23.24/6.54 +-Applying beta-rule and splitting (259), into two cases. % 23.24/6.54 |-Branch one: % 23.24/6.54 | (260) all_44_0_54 = 0 % 23.24/6.54 | % 23.24/6.54 | Equations (260) can reduce 126 to: % 23.24/6.54 | (109) $false % 23.24/6.54 | % 23.24/6.54 |-The branch is then unsatisfiable % 23.24/6.54 |-Branch two: % 23.24/6.54 | (126) ~ (all_44_0_54 = 0) % 23.24/6.54 | (263) ( ~ (all_80_0_86 = 0) & apply(all_0_2_2, all_44_8_62, all_44_6_60) = all_80_0_86) | ( ~ (all_80_1_87 = 0) & apply(all_0_3_3, all_44_8_62, all_44_6_60) = all_80_1_87) % 23.24/6.54 | % 23.24/6.54 +-Applying beta-rule and splitting (263), into two cases. % 23.24/6.54 |-Branch one: % 23.24/6.54 | (264) ~ (all_80_0_86 = 0) & apply(all_0_2_2, all_44_8_62, all_44_6_60) = all_80_0_86 % 23.24/6.54 | % 23.24/6.54 | Applying alpha-rule on (264) yields: % 23.24/6.54 | (265) ~ (all_80_0_86 = 0) % 23.24/6.54 | (266) apply(all_0_2_2, all_44_8_62, all_44_6_60) = all_80_0_86 % 23.24/6.54 | % 23.24/6.54 +-Applying beta-rule and splitting (172), into two cases. % 23.24/6.54 |-Branch one: % 23.24/6.54 | (267) (all_106_0_114 = 0 & apply(all_0_2_2, all_44_8_62, all_44_6_60) = 0) | ( ~ (all_106_0_114 = 0) & apply(all_0_2_2, all_44_8_62, all_44_6_60) = all_106_0_114) % 23.24/6.54 | % 23.24/6.54 +-Applying beta-rule and splitting (267), into two cases. % 23.24/6.54 |-Branch one: % 23.24/6.54 | (268) all_106_0_114 = 0 & apply(all_0_2_2, all_44_8_62, all_44_6_60) = 0 % 23.24/6.54 | % 23.24/6.54 | Applying alpha-rule on (268) yields: % 23.24/6.54 | (269) all_106_0_114 = 0 % 23.24/6.54 | (270) apply(all_0_2_2, all_44_8_62, all_44_6_60) = 0 % 23.24/6.54 | % 23.24/6.54 | Instantiating formula (70) with all_0_2_2, all_44_8_62, all_44_6_60, 0, all_80_0_86 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_6_60) = all_80_0_86, apply(all_0_2_2, all_44_8_62, all_44_6_60) = 0, yields: % 23.24/6.54 | (271) all_80_0_86 = 0 % 23.24/6.54 | % 23.24/6.54 | Equations (271) can reduce 265 to: % 23.24/6.54 | (109) $false % 23.24/6.54 | % 23.24/6.54 |-The branch is then unsatisfiable % 23.24/6.54 |-Branch two: % 23.24/6.54 | (273) ~ (all_106_0_114 = 0) & apply(all_0_2_2, all_44_8_62, all_44_6_60) = all_106_0_114 % 23.24/6.54 | % 23.24/6.54 | Applying alpha-rule on (273) yields: % 23.24/6.54 | (274) ~ (all_106_0_114 = 0) % 23.24/6.54 | (275) apply(all_0_2_2, all_44_8_62, all_44_6_60) = all_106_0_114 % 23.24/6.54 | % 23.24/6.54 +-Applying beta-rule and splitting (174), into two cases. % 23.24/6.54 |-Branch one: % 23.24/6.54 | (276) (all_112_0_120 = 0 & apply(all_0_2_2, all_44_8_62, all_44_6_60) = 0) | ( ~ (all_112_0_120 = 0) & apply(all_0_2_2, all_44_7_61, all_44_6_60) = all_112_0_120) % 23.24/6.54 | % 23.24/6.54 +-Applying beta-rule and splitting (276), into two cases. % 23.24/6.54 |-Branch one: % 23.24/6.54 | (277) all_112_0_120 = 0 & apply(all_0_2_2, all_44_8_62, all_44_6_60) = 0 % 23.24/6.54 | % 23.24/6.54 | Applying alpha-rule on (277) yields: % 23.24/6.54 | (278) all_112_0_120 = 0 % 23.24/6.54 | (270) apply(all_0_2_2, all_44_8_62, all_44_6_60) = 0 % 23.24/6.54 | % 23.24/6.54 | Instantiating formula (70) with all_0_2_2, all_44_8_62, all_44_6_60, all_80_0_86, all_106_0_114 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_6_60) = all_106_0_114, apply(all_0_2_2, all_44_8_62, all_44_6_60) = all_80_0_86, yields: % 23.24/6.54 | (280) all_106_0_114 = all_80_0_86 % 23.24/6.54 | % 23.24/6.54 | Instantiating formula (70) with all_0_2_2, all_44_8_62, all_44_6_60, 0, all_106_0_114 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_6_60) = all_106_0_114, apply(all_0_2_2, all_44_8_62, all_44_6_60) = 0, yields: % 23.24/6.54 | (269) all_106_0_114 = 0 % 23.24/6.54 | % 23.24/6.54 | Combining equations (280,269) yields a new equation: % 23.24/6.54 | (282) all_80_0_86 = 0 % 23.24/6.54 | % 23.24/6.54 | Simplifying 282 yields: % 23.24/6.54 | (271) all_80_0_86 = 0 % 23.24/6.54 | % 23.24/6.54 | Equations (271) can reduce 265 to: % 23.24/6.54 | (109) $false % 23.24/6.54 | % 23.24/6.54 |-The branch is then unsatisfiable % 23.24/6.54 |-Branch two: % 23.24/6.54 | (285) ~ (all_112_0_120 = 0) & apply(all_0_2_2, all_44_7_61, all_44_6_60) = all_112_0_120 % 23.24/6.54 | % 23.24/6.54 | Applying alpha-rule on (285) yields: % 23.24/6.54 | (286) ~ (all_112_0_120 = 0) % 23.24/6.54 | (287) apply(all_0_2_2, all_44_7_61, all_44_6_60) = all_112_0_120 % 23.24/6.54 | % 23.24/6.54 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_6_60, 0, all_112_0_120 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_6_60) = all_112_0_120, apply(all_0_2_2, all_44_7_61, all_44_6_60) = 0, yields: % 23.24/6.54 | (278) all_112_0_120 = 0 % 23.24/6.54 | % 23.24/6.54 | Equations (278) can reduce 286 to: % 23.24/6.54 | (109) $false % 23.24/6.54 | % 23.24/6.54 |-The branch is then unsatisfiable % 23.24/6.54 |-Branch two: % 23.24/6.54 | (290) ~ (all_112_0_120 = 0) & apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_112_0_120 % 23.24/6.54 | % 23.24/6.54 | Applying alpha-rule on (290) yields: % 23.24/6.54 | (286) ~ (all_112_0_120 = 0) % 23.24/6.54 | (292) apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_112_0_120 % 23.24/6.54 | % 23.24/6.54 | Instantiating formula (70) with all_0_2_2, all_44_8_62, all_44_7_61, 0, all_112_0_120 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_112_0_120, apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0, yields: % 23.24/6.54 | (278) all_112_0_120 = 0 % 23.24/6.54 | % 23.24/6.54 | Equations (278) can reduce 286 to: % 23.24/6.54 | (109) $false % 23.24/6.54 | % 23.24/6.54 |-The branch is then unsatisfiable % 23.24/6.54 |-Branch two: % 23.24/6.54 | (295) ~ (all_106_0_114 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_106_0_114 % 23.24/6.54 | % 23.24/6.54 | Applying alpha-rule on (295) yields: % 23.24/6.54 | (274) ~ (all_106_0_114 = 0) % 23.24/6.54 | (297) apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_106_0_114 % 23.24/6.54 | % 23.24/6.54 | Instantiating formula (70) with all_0_2_2, all_44_8_62, all_44_8_62, 0, all_106_0_114 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_106_0_114, apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0, yields: % 23.24/6.54 | (269) all_106_0_114 = 0 % 23.24/6.54 | % 23.24/6.54 | Equations (269) can reduce 274 to: % 23.24/6.54 | (109) $false % 23.24/6.54 | % 23.24/6.54 |-The branch is then unsatisfiable % 23.24/6.54 |-Branch two: % 23.24/6.54 | (300) ~ (all_80_1_87 = 0) & apply(all_0_3_3, all_44_8_62, all_44_6_60) = all_80_1_87 % 23.24/6.54 | % 23.24/6.54 | Applying alpha-rule on (300) yields: % 23.24/6.54 | (248) ~ (all_80_1_87 = 0) % 23.24/6.54 | (302) apply(all_0_3_3, all_44_8_62, all_44_6_60) = all_80_1_87 % 23.24/6.54 | % 23.24/6.54 | Instantiating formula (70) with all_0_3_3, all_44_8_62, all_44_6_60, 0, all_80_1_87 and discharging atoms apply(all_0_3_3, all_44_8_62, all_44_6_60) = all_80_1_87, apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0, yields: % 23.24/6.54 | (250) all_80_1_87 = 0 % 23.24/6.54 | % 23.24/6.54 | Equations (250) can reduce 248 to: % 23.24/6.54 | (109) $false % 23.24/6.54 | % 23.24/6.54 |-The branch is then unsatisfiable % 23.24/6.54 |-Branch two: % 23.24/6.54 | (305) ~ (all_72_0_77 = 0) & apply(all_0_3_3, all_44_6_60, all_44_6_60) = all_72_0_77 % 23.24/6.54 | % 23.24/6.54 | Applying alpha-rule on (305) yields: % 23.24/6.54 | (306) ~ (all_72_0_77 = 0) % 23.24/6.54 | (307) apply(all_0_3_3, all_44_6_60, all_44_6_60) = all_72_0_77 % 23.24/6.54 | % 23.24/6.54 | Instantiating formula (70) with all_0_3_3, all_44_6_60, all_44_6_60, 0, all_72_0_77 and discharging atoms apply(all_0_3_3, all_44_6_60, all_44_6_60) = all_72_0_77, apply(all_0_3_3, all_44_6_60, all_44_6_60) = 0, yields: % 23.24/6.54 | (244) all_72_0_77 = 0 % 23.24/6.54 | % 23.24/6.54 | Equations (244) can reduce 306 to: % 23.24/6.54 | (109) $false % 23.24/6.54 | % 23.24/6.54 |-The branch is then unsatisfiable % 23.24/6.54 |-Branch two: % 23.24/6.54 | (310) ~ (all_72_0_77 = 0) & apply(all_0_3_3, all_44_8_62, all_44_6_60) = all_72_0_77 % 23.24/6.54 | % 23.24/6.54 | Applying alpha-rule on (310) yields: % 23.24/6.54 | (306) ~ (all_72_0_77 = 0) % 23.24/6.54 | (312) apply(all_0_3_3, all_44_8_62, all_44_6_60) = all_72_0_77 % 23.24/6.54 | % 23.24/6.54 | Instantiating formula (70) with all_0_3_3, all_44_8_62, all_44_6_60, 0, all_72_0_77 and discharging atoms apply(all_0_3_3, all_44_8_62, all_44_6_60) = all_72_0_77, apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0, yields: % 23.24/6.54 | (244) all_72_0_77 = 0 % 23.24/6.54 | % 23.24/6.54 | Equations (244) can reduce 306 to: % 23.24/6.54 | (109) $false % 23.24/6.54 | % 23.24/6.54 |-The branch is then unsatisfiable % 23.24/6.54 |-Branch two: % 23.24/6.54 | (315) ~ (all_92_0_100 = 0) & apply(all_0_3_3, all_44_8_62, all_44_6_60) = all_92_0_100 % 23.24/6.54 | % 23.24/6.54 | Applying alpha-rule on (315) yields: % 23.24/6.54 | (316) ~ (all_92_0_100 = 0) % 23.24/6.54 | (317) apply(all_0_3_3, all_44_8_62, all_44_6_60) = all_92_0_100 % 23.24/6.54 | % 23.24/6.54 | Instantiating formula (70) with all_0_3_3, all_44_8_62, all_44_6_60, 0, all_92_0_100 and discharging atoms apply(all_0_3_3, all_44_8_62, all_44_6_60) = all_92_0_100, apply(all_0_3_3, all_44_8_62, all_44_6_60) = 0, yields: % 23.24/6.55 | (240) all_92_0_100 = 0 % 23.24/6.55 | % 23.24/6.55 | Equations (240) can reduce 316 to: % 23.24/6.55 | (109) $false % 23.24/6.55 | % 23.24/6.55 |-The branch is then unsatisfiable % 23.24/6.55 |-Branch two: % 23.24/6.55 | (320) ~ (all_92_0_100 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_92_0_100 % 23.24/6.55 | % 23.24/6.55 | Applying alpha-rule on (320) yields: % 23.24/6.55 | (316) ~ (all_92_0_100 = 0) % 23.24/6.55 | (322) apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_92_0_100 % 23.24/6.55 | % 23.24/6.55 | Instantiating formula (70) with all_0_3_3, all_44_8_62, all_44_8_62, 0, all_92_0_100 and discharging atoms apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_92_0_100, apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0, yields: % 23.24/6.55 | (240) all_92_0_100 = 0 % 23.24/6.55 | % 23.24/6.55 | Equations (240) can reduce 316 to: % 23.24/6.55 | (109) $false % 23.24/6.55 | % 23.24/6.55 |-The branch is then unsatisfiable % 23.24/6.55 |-Branch two: % 23.24/6.55 | (325) ~ (all_96_0_104 = 0) & apply(all_0_3_3, all_44_7_61, all_44_6_60) = all_96_0_104 % 23.24/6.55 | % 23.24/6.55 | Applying alpha-rule on (325) yields: % 23.24/6.55 | (326) ~ (all_96_0_104 = 0) % 23.24/6.55 | (327) apply(all_0_3_3, all_44_7_61, all_44_6_60) = all_96_0_104 % 23.24/6.55 | % 23.24/6.55 | Instantiating formula (70) with all_0_3_3, all_44_7_61, all_44_6_60, 0, all_96_0_104 and discharging atoms apply(all_0_3_3, all_44_7_61, all_44_6_60) = all_96_0_104, apply(all_0_3_3, all_44_7_61, all_44_6_60) = 0, yields: % 23.24/6.55 | (236) all_96_0_104 = 0 % 23.24/6.55 | % 23.24/6.55 | Equations (236) can reduce 326 to: % 23.24/6.55 | (109) $false % 23.24/6.55 | % 23.24/6.55 |-The branch is then unsatisfiable % 23.24/6.55 |-Branch two: % 23.24/6.55 | (330) ~ (all_96_0_104 = 0) & apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_96_0_104 % 23.24/6.55 | % 23.24/6.55 | Applying alpha-rule on (330) yields: % 23.24/6.55 | (326) ~ (all_96_0_104 = 0) % 23.24/6.55 | (332) apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_96_0_104 % 23.24/6.55 | % 23.24/6.55 | Instantiating formula (70) with all_0_3_3, all_44_8_62, all_44_7_61, 0, all_96_0_104 and discharging atoms apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_96_0_104, apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0, yields: % 23.24/6.55 | (236) all_96_0_104 = 0 % 23.24/6.55 | % 23.24/6.55 | Equations (236) can reduce 326 to: % 23.24/6.55 | (109) $false % 23.24/6.55 | % 23.24/6.55 |-The branch is then unsatisfiable % 23.24/6.55 |-Branch two: % 23.24/6.55 | (335) ~ (all_78_0_84 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_78_0_84 % 23.24/6.55 | % 23.24/6.55 | Applying alpha-rule on (335) yields: % 23.24/6.55 | (336) ~ (all_78_0_84 = 0) % 23.24/6.55 | (337) apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_78_0_84 % 23.24/6.55 | % 23.24/6.55 | Instantiating formula (70) with all_0_3_3, all_44_7_61, all_44_7_61, 0, all_78_0_84 and discharging atoms apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_78_0_84, apply(all_0_3_3, all_44_7_61, all_44_7_61) = 0, yields: % 23.24/6.55 | (232) all_78_0_84 = 0 % 23.24/6.55 | % 23.24/6.55 | Equations (232) can reduce 336 to: % 23.24/6.55 | (109) $false % 23.24/6.55 | % 23.24/6.55 |-The branch is then unsatisfiable % 23.24/6.55 |-Branch two: % 23.24/6.55 | (340) ~ (all_78_0_84 = 0) & apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_78_0_84 % 23.24/6.55 | % 23.24/6.55 | Applying alpha-rule on (340) yields: % 23.24/6.55 | (336) ~ (all_78_0_84 = 0) % 23.24/6.55 | (342) apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_78_0_84 % 23.24/6.55 | % 23.24/6.55 | Instantiating formula (70) with all_0_3_3, all_44_8_62, all_44_7_61, 0, all_78_0_84 and discharging atoms apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_78_0_84, apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0, yields: % 23.24/6.55 | (232) all_78_0_84 = 0 % 23.24/6.55 | % 23.24/6.55 | Equations (232) can reduce 336 to: % 23.24/6.55 | (109) $false % 23.24/6.55 | % 23.24/6.55 |-The branch is then unsatisfiable % 23.24/6.55 |-Branch two: % 23.24/6.55 | (345) ~ (all_103_0_111 = 0) & apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_103_0_111 % 23.24/6.55 | % 23.24/6.55 | Applying alpha-rule on (345) yields: % 23.24/6.55 | (346) ~ (all_103_0_111 = 0) % 23.24/6.55 | (347) apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_103_0_111 % 23.24/6.55 | % 23.24/6.55 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_7_61, 0, all_103_0_111 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_103_0_111, apply(all_0_2_2, all_44_7_61, all_44_7_61) = 0, yields: % 23.24/6.55 | (228) all_103_0_111 = 0 % 23.24/6.55 | % 23.24/6.55 | Equations (228) can reduce 346 to: % 23.24/6.55 | (109) $false % 23.24/6.55 | % 23.24/6.55 |-The branch is then unsatisfiable % 23.24/6.55 |-Branch two: % 23.24/6.55 | (350) ~ (all_103_0_111 = 0) & apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_103_0_111 % 23.24/6.55 | % 23.24/6.55 | Applying alpha-rule on (350) yields: % 23.24/6.55 | (346) ~ (all_103_0_111 = 0) % 23.24/6.55 | (352) apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_103_0_111 % 23.24/6.55 | % 23.24/6.55 | Instantiating formula (70) with all_0_2_2, all_44_8_62, all_44_7_61, 0, all_103_0_111 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_103_0_111, apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0, yields: % 23.24/6.55 | (228) all_103_0_111 = 0 % 23.24/6.55 | % 23.24/6.55 | Equations (228) can reduce 346 to: % 23.24/6.55 | (109) $false % 23.24/6.55 | % 23.24/6.55 |-The branch is then unsatisfiable % 23.24/6.55 |-Branch two: % 23.24/6.55 | (355) ~ (all_64_0_69 = 0) & apply(all_0_2_2, all_44_7_61, all_44_6_60) = all_64_0_69 % 23.24/6.55 | % 23.24/6.55 | Applying alpha-rule on (355) yields: % 23.24/6.55 | (356) ~ (all_64_0_69 = 0) % 23.24/6.55 | (357) apply(all_0_2_2, all_44_7_61, all_44_6_60) = all_64_0_69 % 23.24/6.55 | % 23.24/6.55 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_6_60, 0, all_64_0_69 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_6_60) = all_64_0_69, apply(all_0_2_2, all_44_7_61, all_44_6_60) = 0, yields: % 23.24/6.55 | (224) all_64_0_69 = 0 % 23.24/6.55 | % 23.24/6.55 | Equations (224) can reduce 356 to: % 23.24/6.55 | (109) $false % 23.24/6.55 | % 23.24/6.55 |-The branch is then unsatisfiable % 23.24/6.55 |-Branch two: % 23.24/6.55 | (360) ~ (all_64_0_69 = 0) & apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_64_0_69 % 23.24/6.55 | % 23.24/6.55 | Applying alpha-rule on (360) yields: % 23.24/6.55 | (356) ~ (all_64_0_69 = 0) % 23.24/6.55 | (362) apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_64_0_69 % 23.24/6.55 | % 23.24/6.55 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_7_61, 0, all_64_0_69 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_64_0_69, apply(all_0_2_2, all_44_7_61, all_44_7_61) = 0, yields: % 23.24/6.55 | (224) all_64_0_69 = 0 % 23.24/6.55 | % 23.24/6.55 | Equations (224) can reduce 356 to: % 23.24/6.55 | (109) $false % 23.24/6.55 | % 23.24/6.55 |-The branch is then unsatisfiable % 23.24/6.55 |-Branch two: % 23.24/6.55 | (365) ~ (all_66_0_71 = 0) & apply(all_0_2_2, all_44_6_60, all_44_6_60) = all_66_0_71 % 23.24/6.55 | % 23.24/6.55 | Applying alpha-rule on (365) yields: % 23.24/6.55 | (366) ~ (all_66_0_71 = 0) % 23.24/6.55 | (367) apply(all_0_2_2, all_44_6_60, all_44_6_60) = all_66_0_71 % 23.24/6.55 | % 23.24/6.55 | Instantiating formula (70) with all_0_2_2, all_44_6_60, all_44_6_60, 0, all_66_0_71 and discharging atoms apply(all_0_2_2, all_44_6_60, all_44_6_60) = all_66_0_71, apply(all_0_2_2, all_44_6_60, all_44_6_60) = 0, yields: % 23.24/6.55 | (220) all_66_0_71 = 0 % 23.24/6.55 | % 23.24/6.55 | Equations (220) can reduce 366 to: % 23.24/6.55 | (109) $false % 23.24/6.55 | % 23.24/6.55 |-The branch is then unsatisfiable % 23.24/6.55 |-Branch two: % 23.24/6.55 | (370) ~ (all_66_0_71 = 0) & apply(all_0_2_2, all_44_7_61, all_44_6_60) = all_66_0_71 % 23.24/6.55 | % 23.24/6.55 | Applying alpha-rule on (370) yields: % 23.24/6.55 | (366) ~ (all_66_0_71 = 0) % 23.24/6.55 | (372) apply(all_0_2_2, all_44_7_61, all_44_6_60) = all_66_0_71 % 23.24/6.55 | % 23.24/6.55 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_6_60, 0, all_66_0_71 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_6_60) = all_66_0_71, apply(all_0_2_2, all_44_7_61, all_44_6_60) = 0, yields: % 23.24/6.55 | (220) all_66_0_71 = 0 % 23.24/6.55 | % 23.24/6.55 | Equations (220) can reduce 366 to: % 23.24/6.55 | (109) $false % 23.24/6.55 | % 23.24/6.55 |-The branch is then unsatisfiable % 23.24/6.55 |-Branch two: % 23.24/6.55 | (375) ~ (all_61_0_66 = 0) & apply(all_0_3_3, all_44_6_60, all_44_6_60) = all_61_0_66 % 23.24/6.55 | % 23.24/6.55 | Applying alpha-rule on (375) yields: % 23.24/6.55 | (376) ~ (all_61_0_66 = 0) % 23.24/6.55 | (377) apply(all_0_3_3, all_44_6_60, all_44_6_60) = all_61_0_66 % 23.24/6.55 | % 23.24/6.55 | Instantiating formula (70) with all_0_3_3, all_44_6_60, all_44_6_60, 0, all_61_0_66 and discharging atoms apply(all_0_3_3, all_44_6_60, all_44_6_60) = all_61_0_66, apply(all_0_3_3, all_44_6_60, all_44_6_60) = 0, yields: % 23.24/6.55 | (216) all_61_0_66 = 0 % 23.24/6.55 | % 23.24/6.55 | Equations (216) can reduce 376 to: % 23.24/6.55 | (109) $false % 23.24/6.55 | % 23.24/6.55 |-The branch is then unsatisfiable % 23.24/6.55 |-Branch two: % 23.24/6.55 | (380) ~ (all_61_0_66 = 0) & apply(all_0_3_3, all_44_7_61, all_44_6_60) = all_61_0_66 % 23.24/6.55 | % 23.24/6.55 | Applying alpha-rule on (380) yields: % 23.24/6.55 | (376) ~ (all_61_0_66 = 0) % 23.24/6.55 | (382) apply(all_0_3_3, all_44_7_61, all_44_6_60) = all_61_0_66 % 23.24/6.55 | % 23.24/6.55 | Instantiating formula (70) with all_0_3_3, all_44_7_61, all_44_6_60, 0, all_61_0_66 and discharging atoms apply(all_0_3_3, all_44_7_61, all_44_6_60) = all_61_0_66, apply(all_0_3_3, all_44_7_61, all_44_6_60) = 0, yields: % 23.24/6.55 | (216) all_61_0_66 = 0 % 23.24/6.55 | % 23.24/6.55 | Equations (216) can reduce 376 to: % 23.24/6.55 | (109) $false % 23.24/6.55 | % 23.24/6.55 |-The branch is then unsatisfiable % 23.24/6.55 |-Branch two: % 23.24/6.55 | (385) ~ (all_87_0_95 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_87_0_95 % 23.24/6.55 | % 23.24/6.55 | Applying alpha-rule on (385) yields: % 23.24/6.55 | (386) ~ (all_87_0_95 = 0) % 23.24/6.55 | (387) apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_87_0_95 % 23.24/6.55 | % 23.24/6.55 | Instantiating formula (70) with all_0_2_2, all_44_8_62, all_44_8_62, 0, all_87_0_95 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_87_0_95, apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0, yields: % 23.24/6.55 | (212) all_87_0_95 = 0 % 23.24/6.55 | % 23.24/6.55 | Equations (212) can reduce 386 to: % 23.24/6.55 | (109) $false % 23.24/6.55 | % 23.24/6.55 |-The branch is then unsatisfiable % 23.24/6.55 |-Branch two: % 23.24/6.55 | (390) ~ (all_111_0_119 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_111_0_119 % 23.24/6.55 | % 23.24/6.55 | Applying alpha-rule on (390) yields: % 23.24/6.55 | (391) ~ (all_111_0_119 = 0) % 23.24/6.55 | (392) apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_111_0_119 % 23.24/6.55 | % 23.24/6.55 | Instantiating formula (70) with all_0_3_3, all_44_7_61, all_44_7_61, 0, all_111_0_119 and discharging atoms apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_111_0_119, apply(all_0_3_3, all_44_7_61, all_44_7_61) = 0, yields: % 23.24/6.55 | (209) all_111_0_119 = 0 % 23.24/6.55 | % 23.24/6.55 | Equations (209) can reduce 391 to: % 23.24/6.55 | (109) $false % 23.24/6.55 | % 23.24/6.55 |-The branch is then unsatisfiable % 23.24/6.55 |-Branch two: % 23.24/6.55 | (395) ~ (all_59_0_64 = 0) & apply(all_0_3_3, all_44_7_61, all_44_6_60) = all_59_0_64 % 23.24/6.55 | % 23.24/6.55 | Applying alpha-rule on (395) yields: % 23.24/6.55 | (396) ~ (all_59_0_64 = 0) % 23.24/6.55 | (397) apply(all_0_3_3, all_44_7_61, all_44_6_60) = all_59_0_64 % 23.24/6.55 | % 23.24/6.55 | Instantiating formula (70) with all_0_3_3, all_44_7_61, all_44_6_60, 0, all_59_0_64 and discharging atoms apply(all_0_3_3, all_44_7_61, all_44_6_60) = all_59_0_64, apply(all_0_3_3, all_44_7_61, all_44_6_60) = 0, yields: % 23.24/6.55 | (206) all_59_0_64 = 0 % 23.24/6.55 | % 23.24/6.55 | Equations (206) can reduce 396 to: % 23.24/6.55 | (109) $false % 23.24/6.55 | % 23.24/6.55 |-The branch is then unsatisfiable % 23.24/6.56 |-Branch two: % 23.24/6.56 | (400) ~ (all_59_0_64 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_59_0_64 % 23.24/6.56 | % 23.24/6.56 | Applying alpha-rule on (400) yields: % 23.24/6.56 | (396) ~ (all_59_0_64 = 0) % 23.24/6.56 | (402) apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_59_0_64 % 23.24/6.56 | % 23.24/6.56 | Instantiating formula (70) with all_0_3_3, all_44_7_61, all_44_7_61, 0, all_59_0_64 and discharging atoms apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_59_0_64, apply(all_0_3_3, all_44_7_61, all_44_7_61) = 0, yields: % 23.24/6.56 | (206) all_59_0_64 = 0 % 23.24/6.56 | % 23.24/6.56 | Equations (206) can reduce 396 to: % 23.24/6.56 | (109) $false % 23.24/6.56 | % 23.24/6.56 |-The branch is then unsatisfiable % 23.24/6.56 |-Branch two: % 23.24/6.56 | (405) ~ (all_81_1_89 = 0) & member(all_44_6_60, all_0_4_4) = all_81_1_89 % 23.24/6.56 | % 23.24/6.56 | Applying alpha-rule on (405) yields: % 23.24/6.56 | (406) ~ (all_81_1_89 = 0) % 23.24/6.56 | (407) member(all_44_6_60, all_0_4_4) = all_81_1_89 % 23.24/6.56 | % 23.24/6.56 | Instantiating formula (88) with all_44_6_60, all_0_4_4, all_81_1_89, 0 and discharging atoms member(all_44_6_60, all_0_4_4) = all_81_1_89, member(all_44_6_60, all_0_4_4) = 0, yields: % 23.24/6.56 | (201) all_81_1_89 = 0 % 23.24/6.56 | % 23.24/6.56 | Equations (201) can reduce 406 to: % 23.24/6.56 | (109) $false % 23.24/6.56 | % 23.24/6.56 |-The branch is then unsatisfiable % 23.24/6.56 |-Branch two: % 23.24/6.56 | (410) ~ (all_81_1_89 = 0) & member(all_44_7_61, all_0_4_4) = all_81_1_89 % 23.24/6.56 | % 23.24/6.56 | Applying alpha-rule on (410) yields: % 23.24/6.56 | (406) ~ (all_81_1_89 = 0) % 23.24/6.56 | (412) member(all_44_7_61, all_0_4_4) = all_81_1_89 % 23.24/6.56 | % 23.24/6.56 | Instantiating formula (88) with all_44_7_61, all_0_4_4, all_81_1_89, 0 and discharging atoms member(all_44_7_61, all_0_4_4) = all_81_1_89, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.24/6.56 | (201) all_81_1_89 = 0 % 23.24/6.56 | % 23.24/6.56 | Equations (201) can reduce 406 to: % 23.24/6.56 | (109) $false % 23.24/6.56 | % 23.24/6.56 |-The branch is then unsatisfiable % 23.24/6.56 |-Branch two: % 23.24/6.56 | (415) ~ (all_69_0_74 = 0) & apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_69_0_74 % 23.24/6.56 | % 23.24/6.56 | Applying alpha-rule on (415) yields: % 23.24/6.56 | (416) ~ (all_69_0_74 = 0) % 23.24/6.56 | (417) apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_69_0_74 % 23.24/6.56 | % 23.24/6.56 | Instantiating formula (70) with all_0_3_3, all_44_8_62, all_44_7_61, 0, all_69_0_74 and discharging atoms apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_69_0_74, apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0, yields: % 23.24/6.56 | (196) all_69_0_74 = 0 % 23.24/6.56 | % 23.24/6.56 | Equations (196) can reduce 416 to: % 23.24/6.56 | (109) $false % 23.24/6.56 | % 23.24/6.56 |-The branch is then unsatisfiable % 23.24/6.56 |-Branch two: % 23.24/6.56 | (420) ~ (all_69_0_74 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_69_0_74 % 23.24/6.56 | % 23.24/6.56 | Applying alpha-rule on (420) yields: % 23.24/6.56 | (416) ~ (all_69_0_74 = 0) % 23.24/6.56 | (422) apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_69_0_74 % 23.24/6.56 | % 23.24/6.56 | Instantiating formula (70) with all_0_3_3, all_44_8_62, all_44_8_62, 0, all_69_0_74 and discharging atoms apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_69_0_74, apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0, yields: % 23.24/6.56 | (196) all_69_0_74 = 0 % 23.24/6.56 | % 23.24/6.56 | Equations (196) can reduce 416 to: % 23.24/6.56 | (109) $false % 23.24/6.56 | % 23.24/6.56 |-The branch is then unsatisfiable % 23.24/6.56 |-Branch two: % 23.24/6.56 | (425) ~ (all_67_0_72 = 0) & apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_67_0_72 % 23.24/6.56 | % 23.24/6.56 | Applying alpha-rule on (425) yields: % 23.24/6.56 | (426) ~ (all_67_0_72 = 0) % 23.24/6.56 | (427) apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_67_0_72 % 23.24/6.56 | % 23.24/6.56 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_7_61, 0, all_67_0_72 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_67_0_72, apply(all_0_2_2, all_44_7_61, all_44_7_61) = 0, yields: % 23.24/6.56 | (192) all_67_0_72 = 0 % 23.24/6.56 | % 23.24/6.56 | Equations (192) can reduce 426 to: % 23.24/6.56 | (109) $false % 23.24/6.56 | % 23.24/6.56 |-The branch is then unsatisfiable % 23.24/6.56 |-Branch two: % 23.24/6.56 | (430) ~ (all_98_0_106 = 0) & apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_98_0_106 % 23.24/6.56 | % 23.24/6.56 | Applying alpha-rule on (430) yields: % 23.24/6.56 | (431) ~ (all_98_0_106 = 0) % 23.24/6.56 | (432) apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_98_0_106 % 23.24/6.56 | % 23.24/6.56 | Instantiating formula (70) with all_0_2_2, all_44_8_62, all_44_7_61, 0, all_98_0_106 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_98_0_106, apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0, yields: % 23.24/6.56 | (189) all_98_0_106 = 0 % 23.24/6.56 | % 23.24/6.56 | Equations (189) can reduce 431 to: % 23.24/6.56 | (109) $false % 23.24/6.56 | % 23.24/6.56 |-The branch is then unsatisfiable % 23.24/6.56 |-Branch two: % 23.24/6.56 | (435) ~ (all_98_0_106 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_98_0_106 % 23.24/6.56 | % 23.24/6.56 | Applying alpha-rule on (435) yields: % 23.24/6.56 | (431) ~ (all_98_0_106 = 0) % 23.24/6.56 | (437) apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_98_0_106 % 23.24/6.56 | % 23.24/6.56 | Instantiating formula (70) with all_0_2_2, all_44_8_62, all_44_8_62, 0, all_98_0_106 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_98_0_106, apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0, yields: % 23.24/6.56 | (189) all_98_0_106 = 0 % 23.24/6.56 | % 23.24/6.56 | Equations (189) can reduce 431 to: % 23.24/6.56 | (109) $false % 23.24/6.56 | % 23.24/6.56 |-The branch is then unsatisfiable % 23.24/6.56 |-Branch two: % 23.24/6.56 | (440) ~ (all_77_1_83 = 0) & member(all_44_7_61, all_0_4_4) = all_77_1_83 % 23.24/6.56 | % 23.24/6.56 | Applying alpha-rule on (440) yields: % 23.24/6.56 | (441) ~ (all_77_1_83 = 0) % 23.24/6.56 | (442) member(all_44_7_61, all_0_4_4) = all_77_1_83 % 23.24/6.56 | % 23.24/6.56 | Instantiating formula (88) with all_44_7_61, all_0_4_4, all_77_1_83, 0 and discharging atoms member(all_44_7_61, all_0_4_4) = all_77_1_83, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.24/6.56 | (184) all_77_1_83 = 0 % 23.24/6.56 | % 23.24/6.56 | Equations (184) can reduce 441 to: % 23.24/6.56 | (109) $false % 23.24/6.56 | % 23.24/6.56 |-The branch is then unsatisfiable % 23.24/6.56 |-Branch two: % 23.24/6.56 | (445) ~ (all_77_1_83 = 0) & member(all_44_8_62, all_0_4_4) = all_77_1_83 % 23.24/6.56 | % 23.24/6.56 | Applying alpha-rule on (445) yields: % 23.24/6.56 | (441) ~ (all_77_1_83 = 0) % 23.24/6.56 | (447) member(all_44_8_62, all_0_4_4) = all_77_1_83 % 23.24/6.56 | % 23.24/6.56 | Instantiating formula (88) with all_44_8_62, all_0_4_4, all_77_1_83, 0 and discharging atoms member(all_44_8_62, all_0_4_4) = all_77_1_83, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.56 | (184) all_77_1_83 = 0 % 23.24/6.56 | % 23.24/6.56 | Equations (184) can reduce 441 to: % 23.24/6.56 | (109) $false % 23.24/6.56 | % 23.24/6.56 |-The branch is then unsatisfiable % 23.24/6.56 |-Branch two: % 23.24/6.56 | (450) ~ (all_83_0_91 = 0) & apply(all_0_3_3, all_44_6_60, all_44_6_60) = all_83_0_91 % 23.24/6.56 | % 23.24/6.56 | Applying alpha-rule on (450) yields: % 23.24/6.56 | (451) ~ (all_83_0_91 = 0) % 23.24/6.56 | (452) apply(all_0_3_3, all_44_6_60, all_44_6_60) = all_83_0_91 % 23.24/6.56 | % 23.24/6.56 | Instantiating formula (70) with all_0_3_3, all_44_6_60, all_44_6_60, 0, all_83_0_91 and discharging atoms apply(all_0_3_3, all_44_6_60, all_44_6_60) = all_83_0_91, apply(all_0_3_3, all_44_6_60, all_44_6_60) = 0, yields: % 23.24/6.56 | (179) all_83_0_91 = 0 % 23.24/6.56 | % 23.24/6.56 | Equations (179) can reduce 451 to: % 23.24/6.56 | (109) $false % 23.24/6.56 | % 23.24/6.56 |-The branch is then unsatisfiable % 23.24/6.56 |-Branch two: % 23.24/6.56 | (455) ~ (all_85_0_93 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_85_0_93 % 23.24/6.56 | % 23.24/6.56 | Applying alpha-rule on (455) yields: % 23.24/6.56 | (456) ~ (all_85_0_93 = 0) % 23.24/6.56 | (457) apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_85_0_93 % 23.24/6.56 | % 23.24/6.56 | Instantiating formula (70) with all_0_3_3, all_44_8_62, all_44_8_62, 0, all_85_0_93 and discharging atoms apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_85_0_93, apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0, yields: % 23.24/6.56 | (176) all_85_0_93 = 0 % 23.24/6.56 | % 23.24/6.56 | Equations (176) can reduce 456 to: % 23.24/6.56 | (109) $false % 23.24/6.56 | % 23.24/6.56 |-The branch is then unsatisfiable % 23.24/6.56 |-Branch two: % 23.24/6.56 | (460) all_44_4_58 = 0 & all_44_5_59 = 0 & all_44_6_60 = 0 & ~ (all_44_3_57 = 0) & apply(all_0_1_1, all_44_7_61, all_44_8_62) = all_44_3_57 & apply(all_0_1_1, all_44_8_62, all_44_7_61) = 0 & member(all_44_7_61, all_0_4_4) = 0 & member(all_44_8_62, all_0_4_4) = 0 % 23.24/6.56 | % 23.24/6.56 | Applying alpha-rule on (460) yields: % 23.24/6.56 | (116) apply(all_0_1_1, all_44_8_62, all_44_7_61) = 0 % 23.24/6.56 | (118) all_44_5_59 = 0 % 23.24/6.56 | (463) all_44_6_60 = 0 % 23.24/6.56 | (121) member(all_44_8_62, all_0_4_4) = 0 % 23.24/6.56 | (465) ~ (all_44_3_57 = 0) % 23.24/6.56 | (123) member(all_44_7_61, all_0_4_4) = 0 % 23.24/6.56 | (467) apply(all_0_1_1, all_44_7_61, all_44_8_62) = all_44_3_57 % 23.24/6.56 | (125) all_44_4_58 = 0 % 23.24/6.56 | % 23.24/6.56 | Instantiating formula (93) with all_44_3_57, all_44_8_62, all_44_7_61 and discharging atoms apply(all_0_1_1, all_44_7_61, all_44_8_62) = all_44_3_57, yields: % 23.24/6.56 | (469) ? [v0] : ? [v1] : (( ~ (v0 = 0) & member(all_44_7_61, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_44_8_62, all_0_4_4) = v0) | (( ~ (all_44_3_57 = 0) | (v1 = 0 & v0 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 & apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0)) & (all_44_3_57 = 0 | ( ~ (v1 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = v1) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_7_61, all_44_8_62) = v0)))) % 23.24/6.56 | % 23.24/6.56 | Instantiating formula (93) with 0, all_44_7_61, all_44_8_62 and discharging atoms apply(all_0_1_1, all_44_8_62, all_44_7_61) = 0, yields: % 23.24/6.56 | (129) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0) | ( ~ (v0 = 0) & member(all_44_7_61, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_44_8_62, all_0_4_4) = v0)) % 23.24/6.56 | % 23.24/6.56 | Instantiating formula (76) with all_44_7_61, all_44_7_61, all_44_7_61, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.24/6.56 | (135) ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_7_61, all_44_7_61) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_61, all_44_7_61) = v0)) % 23.24/6.56 | % 23.24/6.56 | Instantiating formula (59) with all_44_7_61, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.24/6.56 | (136) apply(all_0_2_2, all_44_7_61, all_44_7_61) = 0 % 23.24/6.56 | % 23.24/6.56 | Instantiating formula (76) with all_44_7_61, all_44_7_61, all_44_7_61, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.24/6.56 | (139) ? [v0] : ((v0 = 0 & apply(all_0_3_3, all_44_7_61, all_44_7_61) = 0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = v0)) % 23.24/6.56 | % 23.24/6.56 | Instantiating formula (59) with all_44_7_61, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.24/6.56 | (140) apply(all_0_3_3, all_44_7_61, all_44_7_61) = 0 % 23.24/6.56 | % 23.24/6.56 | Instantiating formula (76) with all_44_7_61, all_44_7_61, all_44_8_62, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.57 | (143) ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_61, all_44_7_61) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_62, all_44_7_61) = v0)) % 23.24/6.57 | % 23.24/6.57 | Instantiating formula (76) with all_44_8_62, all_44_7_61, all_44_8_62, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.57 | (476) ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_62, all_44_7_61) = v0)) % 23.24/6.57 | % 23.24/6.57 | Instantiating formula (76) with all_44_7_61, all_44_8_62, all_44_8_62, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.57 | (144) ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_62, all_44_7_61) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = v0)) % 23.24/6.57 | % 23.24/6.57 | Instantiating formula (76) with all_44_8_62, all_44_8_62, all_44_7_61, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.57 | (478) ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = v0)) % 23.24/6.57 | % 23.24/6.57 | Instantiating formula (76) with all_44_8_62, all_44_8_62, all_44_8_62, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.57 | (145) ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = v0)) % 23.24/6.57 | % 23.24/6.57 | Instantiating formula (59) with all_44_8_62, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.57 | (146) apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0 % 23.24/6.57 | % 23.24/6.57 | Instantiating formula (76) with all_44_8_62, all_44_7_61, all_44_7_61, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.57 | (481) ? [v0] : ((v0 = 0 & apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = v0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_7_61, all_44_8_62) = v0)) % 23.24/6.57 | % 23.24/6.57 | Instantiating formula (76) with all_44_7_61, all_44_7_61, all_44_8_62, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.57 | (150) ? [v0] : ((v0 = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = v0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_8_62, all_44_7_61) = v0)) % 23.24/6.57 | % 23.24/6.57 | Instantiating formula (76) with all_44_7_61, all_44_8_62, all_44_8_62, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.57 | (151) ? [v0] : ((v0 = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_8_62, all_44_7_61) = v0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = v0)) % 23.24/6.57 | % 23.24/6.57 | Instantiating formula (76) with all_44_8_62, all_44_8_62, all_44_7_61, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_7_61, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.57 | (484) ? [v0] : ((v0 = 0 & apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_7_61, all_44_8_62) = v0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = v0)) % 23.24/6.57 | % 23.24/6.57 | Instantiating formula (76) with all_44_8_62, all_44_8_62, all_44_8_62, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.57 | (152) ? [v0] : ((v0 = 0 & apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = v0)) % 23.24/6.57 | % 23.24/6.57 | Instantiating formula (59) with all_44_8_62, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.57 | (153) apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0 % 23.24/6.57 | % 23.24/6.57 | Instantiating (139) with all_58_0_123 yields: % 23.24/6.57 | (487) (all_58_0_123 = 0 & apply(all_0_3_3, all_44_7_61, all_44_7_61) = 0) | ( ~ (all_58_0_123 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_58_0_123) % 23.24/6.57 | % 23.24/6.57 | Instantiating (135) with all_59_0_124 yields: % 23.24/6.57 | (488) (all_59_0_124 = 0 & apply(all_0_2_2, all_44_7_61, all_44_7_61) = 0) | ( ~ (all_59_0_124 = 0) & apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_59_0_124) % 23.24/6.57 | % 23.24/6.57 | Instantiating (129) with all_60_0_125, all_60_1_126 yields: % 23.24/6.57 | (489) (all_60_0_125 = 0 & all_60_1_126 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0) | ( ~ (all_60_1_126 = 0) & member(all_44_7_61, all_0_4_4) = all_60_1_126) | ( ~ (all_60_1_126 = 0) & member(all_44_8_62, all_0_4_4) = all_60_1_126) % 23.24/6.57 | % 23.24/6.57 | Instantiating (152) with all_61_0_127 yields: % 23.24/6.57 | (490) (all_61_0_127 = 0 & apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0) | ( ~ (all_61_0_127 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_61_0_127) % 23.24/6.57 | % 23.24/6.57 | Instantiating (145) with all_62_0_128 yields: % 23.24/6.57 | (491) (all_62_0_128 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0) | ( ~ (all_62_0_128 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_62_0_128) % 23.24/6.57 | % 23.24/6.57 | Instantiating (478) with all_63_0_129 yields: % 23.24/6.57 | (492) (all_63_0_129 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_63_0_129 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_63_0_129) | ( ~ (all_63_0_129 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_63_0_129) % 23.24/6.57 | % 23.24/6.57 | Instantiating (144) with all_64_0_130 yields: % 23.24/6.57 | (493) (all_64_0_130 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0) | ( ~ (all_64_0_130 = 0) & apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_64_0_130) | ( ~ (all_64_0_130 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_64_0_130) % 23.24/6.57 | % 23.24/6.57 | Instantiating (476) with all_65_0_131 yields: % 23.24/6.57 | (494) (all_65_0_131 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0) | ( ~ (all_65_0_131 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_65_0_131) | ( ~ (all_65_0_131 = 0) & apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_65_0_131) % 23.24/6.57 | % 23.24/6.57 | Instantiating (484) with all_66_0_132 yields: % 23.24/6.57 | (495) (all_66_0_132 = 0 & apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_66_0_132 = 0) & apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_66_0_132) | ( ~ (all_66_0_132 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_66_0_132) % 23.24/6.57 | % 23.24/6.57 | Instantiating (151) with all_67_0_133 yields: % 23.24/6.57 | (496) (all_67_0_133 = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0) | ( ~ (all_67_0_133 = 0) & apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_67_0_133) | ( ~ (all_67_0_133 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_67_0_133) % 23.24/6.57 | % 23.24/6.57 | Instantiating (469) with all_68_0_134, all_68_1_135 yields: % 23.24/6.57 | (497) ( ~ (all_68_1_135 = 0) & member(all_44_7_61, all_0_4_4) = all_68_1_135) | ( ~ (all_68_1_135 = 0) & member(all_44_8_62, all_0_4_4) = all_68_1_135) | (( ~ (all_44_3_57 = 0) | (all_68_0_134 = 0 & all_68_1_135 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 & apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0)) & (all_44_3_57 = 0 | ( ~ (all_68_0_134 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_68_0_134) | ( ~ (all_68_1_135 = 0) & apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_68_1_135))) % 23.24/6.57 | % 23.24/6.57 | Instantiating (150) with all_70_0_137 yields: % 23.24/6.57 | (498) (all_70_0_137 = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0) | ( ~ (all_70_0_137 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_70_0_137) | ( ~ (all_70_0_137 = 0) & apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_70_0_137) % 23.24/6.57 | % 23.24/6.57 | Instantiating (143) with all_71_0_138 yields: % 23.24/6.57 | (499) (all_71_0_138 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0) | ( ~ (all_71_0_138 = 0) & apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_71_0_138) | ( ~ (all_71_0_138 = 0) & apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_71_0_138) % 23.24/6.57 | % 23.24/6.57 | Instantiating (481) with all_75_0_142 yields: % 23.24/6.57 | (500) (all_75_0_142 = 0 & apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_75_0_142 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_75_0_142) | ( ~ (all_75_0_142 = 0) & apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_75_0_142) % 23.24/6.57 | % 23.24/6.57 +-Applying beta-rule and splitting (487), into two cases. % 23.24/6.57 |-Branch one: % 23.24/6.57 | (501) all_58_0_123 = 0 & apply(all_0_3_3, all_44_7_61, all_44_7_61) = 0 % 23.24/6.57 | % 23.24/6.57 | Applying alpha-rule on (501) yields: % 23.24/6.57 | (502) all_58_0_123 = 0 % 23.24/6.57 | (140) apply(all_0_3_3, all_44_7_61, all_44_7_61) = 0 % 23.24/6.57 | % 23.24/6.57 +-Applying beta-rule and splitting (491), into two cases. % 23.24/6.57 |-Branch one: % 23.24/6.57 | (504) all_62_0_128 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0 % 23.24/6.57 | % 23.24/6.57 | Applying alpha-rule on (504) yields: % 23.24/6.57 | (505) all_62_0_128 = 0 % 23.24/6.57 | (146) apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0 % 23.24/6.57 | % 23.24/6.57 +-Applying beta-rule and splitting (488), into two cases. % 23.24/6.57 |-Branch one: % 23.24/6.57 | (507) all_59_0_124 = 0 & apply(all_0_2_2, all_44_7_61, all_44_7_61) = 0 % 23.24/6.57 | % 23.24/6.57 | Applying alpha-rule on (507) yields: % 23.24/6.57 | (508) all_59_0_124 = 0 % 23.24/6.57 | (136) apply(all_0_2_2, all_44_7_61, all_44_7_61) = 0 % 23.24/6.57 | % 23.24/6.57 +-Applying beta-rule and splitting (489), into two cases. % 23.24/6.57 |-Branch one: % 23.24/6.57 | (510) (all_60_0_125 = 0 & all_60_1_126 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0) | ( ~ (all_60_1_126 = 0) & member(all_44_7_61, all_0_4_4) = all_60_1_126) % 23.24/6.57 | % 23.24/6.57 +-Applying beta-rule and splitting (510), into two cases. % 23.24/6.57 |-Branch one: % 23.24/6.57 | (511) all_60_0_125 = 0 & all_60_1_126 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0 % 23.24/6.57 | % 23.24/6.57 | Applying alpha-rule on (511) yields: % 23.24/6.57 | (512) all_60_0_125 = 0 % 23.24/6.57 | (513) all_60_1_126 = 0 % 23.24/6.57 | (185) apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0 % 23.24/6.57 | (186) apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0 % 23.24/6.57 | % 23.24/6.57 +-Applying beta-rule and splitting (498), into two cases. % 23.24/6.57 |-Branch one: % 23.24/6.57 | (516) (all_70_0_137 = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0) | ( ~ (all_70_0_137 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_70_0_137) % 23.24/6.57 | % 23.24/6.57 +-Applying beta-rule and splitting (516), into two cases. % 23.24/6.57 |-Branch one: % 23.24/6.57 | (517) all_70_0_137 = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0 % 23.24/6.58 | % 23.24/6.58 | Applying alpha-rule on (517) yields: % 23.24/6.58 | (518) all_70_0_137 = 0 % 23.24/6.58 | (186) apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0 % 23.24/6.58 | % 23.24/6.58 +-Applying beta-rule and splitting (490), into two cases. % 23.24/6.58 |-Branch one: % 23.24/6.58 | (520) all_61_0_127 = 0 & apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0 % 23.24/6.58 | % 23.24/6.58 | Applying alpha-rule on (520) yields: % 23.24/6.58 | (521) all_61_0_127 = 0 % 23.24/6.58 | (153) apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0 % 23.24/6.58 | % 23.24/6.58 +-Applying beta-rule and splitting (493), into two cases. % 23.24/6.58 |-Branch one: % 23.24/6.58 | (523) (all_64_0_130 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0) | ( ~ (all_64_0_130 = 0) & apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_64_0_130) % 23.24/6.58 | % 23.24/6.58 +-Applying beta-rule and splitting (523), into two cases. % 23.24/6.58 |-Branch one: % 23.24/6.58 | (524) all_64_0_130 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0 % 23.24/6.58 | % 23.24/6.58 | Applying alpha-rule on (524) yields: % 23.24/6.58 | (525) all_64_0_130 = 0 % 23.24/6.58 | (185) apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0 % 23.24/6.58 | % 23.24/6.58 +-Applying beta-rule and splitting (496), into two cases. % 23.24/6.58 |-Branch one: % 23.24/6.58 | (527) (all_67_0_133 = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0) | ( ~ (all_67_0_133 = 0) & apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_67_0_133) % 23.24/6.58 | % 23.24/6.58 +-Applying beta-rule and splitting (527), into two cases. % 23.24/6.58 |-Branch one: % 23.24/6.58 | (528) all_67_0_133 = 0 & apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0 % 23.24/6.58 | % 23.24/6.58 | Applying alpha-rule on (528) yields: % 23.24/6.58 | (529) all_67_0_133 = 0 % 23.24/6.58 | (186) apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0 % 23.24/6.58 | % 23.24/6.58 +-Applying beta-rule and splitting (499), into two cases. % 23.24/6.58 |-Branch one: % 23.24/6.58 | (531) (all_71_0_138 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0) | ( ~ (all_71_0_138 = 0) & apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_71_0_138) % 23.24/6.58 | % 23.24/6.58 +-Applying beta-rule and splitting (531), into two cases. % 23.24/6.58 |-Branch one: % 23.24/6.58 | (532) all_71_0_138 = 0 & apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0 % 23.24/6.58 | % 23.24/6.58 | Applying alpha-rule on (532) yields: % 23.24/6.58 | (533) all_71_0_138 = 0 % 23.24/6.58 | (185) apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0 % 23.24/6.58 | % 23.24/6.58 | Instantiating formula (12) with all_44_8_62, all_44_7_61, all_44_7_61, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, apply(all_0_2_2, all_44_7_61, all_44_7_61) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.58 | (535) ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = v0) | ( ~ (v0 = 0) & member(all_44_7_61, all_0_4_4) = v0)) % 23.24/6.58 | % 23.24/6.58 | Instantiating formula (23) with all_44_7_61, all_44_8_62, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0, yields: % 23.24/6.58 | (536) ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0) | ( ~ (v0 = 0) & member(all_44_7_61, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_44_8_62, all_0_4_4) = v0)) % 23.24/6.58 | % 23.24/6.58 | Instantiating formula (18) with all_44_8_62, all_44_8_62, all_44_7_61, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.24/6.58 | (537) ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = v0) | ( ~ (v0 = 0) & member(all_44_8_62, all_0_4_4) = v0)) % 23.24/6.58 | % 23.24/6.58 | Instantiating formula (2) with 0, all_44_8_62, all_44_8_62 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0, yields: % 23.24/6.58 | (538) ? [v0] : ? [v1] : (( ~ (v0 = 0) & member(all_44_8_62, all_0_4_4) = v0) | (((v1 = 0 & apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0) | ( ~ (v0 = 0) & apply(all_0_1_1, all_44_8_62, all_44_8_62) = v0)) & ((v0 = 0 & apply(all_0_1_1, all_44_8_62, all_44_8_62) = 0) | ( ~ (v1 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = v1)))) % 23.24/6.58 | % 23.24/6.58 | Instantiating formula (23) with all_44_7_61, all_44_8_62, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0, yields: % 23.24/6.58 | (539) ? [v0] : ((v0 = 0 & apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0) | ( ~ (v0 = 0) & member(all_44_7_61, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_44_8_62, all_0_4_4) = v0)) % 23.24/6.58 | % 23.24/6.58 | Instantiating formula (18) with all_44_8_62, all_44_8_62, all_44_7_61, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.24/6.58 | (540) ? [v0] : ((v0 = 0 & apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_7_61, all_44_8_62) = v0) | ( ~ (v0 = 0) & member(all_44_8_62, all_0_4_4) = v0)) % 23.24/6.58 | % 23.24/6.58 | Instantiating formula (9) with 0, all_44_8_62, all_44_8_62 and discharging atoms apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0, yields: % 23.24/6.58 | (541) ? [v0] : ? [v1] : (( ~ (v0 = 0) & member(all_44_8_62, all_0_4_4) = v0) | (((v1 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0) | ( ~ (v0 = 0) & apply(all_0_1_1, all_44_8_62, all_44_8_62) = v0)) & ((v0 = 0 & apply(all_0_1_1, all_44_8_62, all_44_8_62) = 0) | ( ~ (v1 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = v1)))) % 23.24/6.58 | % 23.24/6.58 | Instantiating (541) with all_117_0_143, all_117_1_144 yields: % 23.24/6.58 | (542) ( ~ (all_117_1_144 = 0) & member(all_44_8_62, all_0_4_4) = all_117_1_144) | (((all_117_0_143 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0) | ( ~ (all_117_1_144 = 0) & apply(all_0_1_1, all_44_8_62, all_44_8_62) = all_117_1_144)) & ((all_117_1_144 = 0 & apply(all_0_1_1, all_44_8_62, all_44_8_62) = 0) | ( ~ (all_117_0_143 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_117_0_143))) % 23.24/6.58 | % 23.24/6.58 | Instantiating (540) with all_118_0_145 yields: % 23.24/6.58 | (543) (all_118_0_145 = 0 & apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_118_0_145 = 0) & apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_118_0_145) | ( ~ (all_118_0_145 = 0) & member(all_44_8_62, all_0_4_4) = all_118_0_145) % 23.24/6.58 | % 23.24/6.58 | Instantiating (538) with all_120_0_147, all_120_1_148 yields: % 23.24/6.58 | (544) ( ~ (all_120_1_148 = 0) & member(all_44_8_62, all_0_4_4) = all_120_1_148) | (((all_120_0_147 = 0 & apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0) | ( ~ (all_120_1_148 = 0) & apply(all_0_1_1, all_44_8_62, all_44_8_62) = all_120_1_148)) & ((all_120_1_148 = 0 & apply(all_0_1_1, all_44_8_62, all_44_8_62) = 0) | ( ~ (all_120_0_147 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_120_0_147))) % 23.24/6.58 | % 23.24/6.58 | Instantiating (537) with all_123_0_151 yields: % 23.24/6.58 | (545) (all_123_0_151 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_123_0_151 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151) | ( ~ (all_123_0_151 = 0) & member(all_44_8_62, all_0_4_4) = all_123_0_151) % 23.24/6.58 | % 23.24/6.58 | Instantiating (536) with all_124_0_152 yields: % 23.24/6.58 | (546) (all_124_0_152 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_124_0_152 = 0) & member(all_44_7_61, all_0_4_4) = all_124_0_152) | ( ~ (all_124_0_152 = 0) & member(all_44_8_62, all_0_4_4) = all_124_0_152) % 23.24/6.58 | % 23.24/6.58 | Instantiating (535) with all_126_0_155 yields: % 23.24/6.58 | (547) (all_126_0_155 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_126_0_155 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_126_0_155) | ( ~ (all_126_0_155 = 0) & member(all_44_7_61, all_0_4_4) = all_126_0_155) % 23.24/6.58 | % 23.24/6.58 | Instantiating (539) with all_127_0_156 yields: % 23.24/6.58 | (548) (all_127_0_156 = 0 & apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_127_0_156 = 0) & member(all_44_7_61, all_0_4_4) = all_127_0_156) | ( ~ (all_127_0_156 = 0) & member(all_44_8_62, all_0_4_4) = all_127_0_156) % 23.24/6.58 | % 23.24/6.58 +-Applying beta-rule and splitting (494), into two cases. % 23.24/6.58 |-Branch one: % 23.24/6.58 | (549) (all_65_0_131 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0) | ( ~ (all_65_0_131 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_65_0_131) % 23.24/6.58 | % 23.24/6.58 +-Applying beta-rule and splitting (549), into two cases. % 23.24/6.58 |-Branch one: % 23.24/6.58 | (550) all_65_0_131 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0 % 23.24/6.58 | % 23.24/6.58 | Applying alpha-rule on (550) yields: % 23.24/6.58 | (551) all_65_0_131 = 0 % 23.24/6.58 | (146) apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0 % 23.24/6.58 | % 23.24/6.58 +-Applying beta-rule and splitting (542), into two cases. % 23.24/6.58 |-Branch one: % 23.24/6.58 | (553) ~ (all_117_1_144 = 0) & member(all_44_8_62, all_0_4_4) = all_117_1_144 % 23.24/6.58 | % 23.24/6.58 | Applying alpha-rule on (553) yields: % 23.24/6.58 | (554) ~ (all_117_1_144 = 0) % 23.24/6.58 | (555) member(all_44_8_62, all_0_4_4) = all_117_1_144 % 23.24/6.58 | % 23.24/6.58 | Instantiating formula (88) with all_44_8_62, all_0_4_4, all_117_1_144, 0 and discharging atoms member(all_44_8_62, all_0_4_4) = all_117_1_144, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.58 | (556) all_117_1_144 = 0 % 23.24/6.58 | % 23.24/6.58 | Equations (556) can reduce 554 to: % 23.24/6.58 | (109) $false % 23.24/6.58 | % 23.24/6.58 |-The branch is then unsatisfiable % 23.24/6.58 |-Branch two: % 23.24/6.58 | (558) ((all_117_0_143 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0) | ( ~ (all_117_1_144 = 0) & apply(all_0_1_1, all_44_8_62, all_44_8_62) = all_117_1_144)) & ((all_117_1_144 = 0 & apply(all_0_1_1, all_44_8_62, all_44_8_62) = 0) | ( ~ (all_117_0_143 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_117_0_143)) % 23.24/6.58 | % 23.24/6.58 | Applying alpha-rule on (558) yields: % 23.24/6.58 | (559) (all_117_0_143 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0) | ( ~ (all_117_1_144 = 0) & apply(all_0_1_1, all_44_8_62, all_44_8_62) = all_117_1_144) % 23.24/6.58 | (560) (all_117_1_144 = 0 & apply(all_0_1_1, all_44_8_62, all_44_8_62) = 0) | ( ~ (all_117_0_143 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_117_0_143) % 23.24/6.58 | % 23.24/6.58 +-Applying beta-rule and splitting (560), into two cases. % 23.24/6.58 |-Branch one: % 23.24/6.58 | (561) all_117_1_144 = 0 & apply(all_0_1_1, all_44_8_62, all_44_8_62) = 0 % 23.24/6.59 | % 23.24/6.59 | Applying alpha-rule on (561) yields: % 23.24/6.59 | (556) all_117_1_144 = 0 % 23.24/6.59 | (563) apply(all_0_1_1, all_44_8_62, all_44_8_62) = 0 % 23.24/6.59 | % 23.24/6.59 +-Applying beta-rule and splitting (544), into two cases. % 23.24/6.59 |-Branch one: % 23.24/6.59 | (564) ~ (all_120_1_148 = 0) & member(all_44_8_62, all_0_4_4) = all_120_1_148 % 23.24/6.59 | % 23.24/6.59 | Applying alpha-rule on (564) yields: % 23.24/6.59 | (565) ~ (all_120_1_148 = 0) % 23.24/6.59 | (566) member(all_44_8_62, all_0_4_4) = all_120_1_148 % 23.24/6.59 | % 23.24/6.59 | Instantiating formula (88) with all_44_8_62, all_0_4_4, all_120_1_148, 0 and discharging atoms member(all_44_8_62, all_0_4_4) = all_120_1_148, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.24/6.59 | (567) all_120_1_148 = 0 % 23.24/6.59 | % 23.24/6.59 | Equations (567) can reduce 565 to: % 23.24/6.59 | (109) $false % 23.24/6.59 | % 23.24/6.59 |-The branch is then unsatisfiable % 23.24/6.59 |-Branch two: % 23.24/6.59 | (569) ((all_120_0_147 = 0 & apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0) | ( ~ (all_120_1_148 = 0) & apply(all_0_1_1, all_44_8_62, all_44_8_62) = all_120_1_148)) & ((all_120_1_148 = 0 & apply(all_0_1_1, all_44_8_62, all_44_8_62) = 0) | ( ~ (all_120_0_147 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_120_0_147)) % 23.24/6.59 | % 23.24/6.59 | Applying alpha-rule on (569) yields: % 23.24/6.59 | (570) (all_120_0_147 = 0 & apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0) | ( ~ (all_120_1_148 = 0) & apply(all_0_1_1, all_44_8_62, all_44_8_62) = all_120_1_148) % 23.24/6.59 | (571) (all_120_1_148 = 0 & apply(all_0_1_1, all_44_8_62, all_44_8_62) = 0) | ( ~ (all_120_0_147 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_120_0_147) % 23.24/6.59 | % 23.24/6.59 +-Applying beta-rule and splitting (559), into two cases. % 23.24/6.59 |-Branch one: % 23.24/6.59 | (572) all_117_0_143 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0 % 23.24/6.59 | % 23.24/6.59 | Applying alpha-rule on (572) yields: % 23.24/6.59 | (573) all_117_0_143 = 0 % 23.24/6.59 | (146) apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0 % 23.24/6.59 | % 23.24/6.59 +-Applying beta-rule and splitting (548), into two cases. % 23.24/6.59 |-Branch one: % 23.24/6.59 | (575) (all_127_0_156 = 0 & apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_127_0_156 = 0) & member(all_44_7_61, all_0_4_4) = all_127_0_156) % 23.62/6.59 | % 23.62/6.59 +-Applying beta-rule and splitting (575), into two cases. % 23.62/6.59 |-Branch one: % 23.62/6.59 | (576) all_127_0_156 = 0 & apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0 % 23.62/6.59 | % 23.62/6.59 | Applying alpha-rule on (576) yields: % 23.62/6.59 | (577) all_127_0_156 = 0 % 23.62/6.59 | (578) apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0 % 23.62/6.59 | % 23.62/6.59 +-Applying beta-rule and splitting (495), into two cases. % 23.62/6.59 |-Branch one: % 23.62/6.59 | (579) (all_66_0_132 = 0 & apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_66_0_132 = 0) & apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_66_0_132) % 23.62/6.59 | % 23.62/6.59 +-Applying beta-rule and splitting (579), into two cases. % 23.62/6.59 |-Branch one: % 23.62/6.59 | (580) all_66_0_132 = 0 & apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0 % 23.62/6.59 | % 23.62/6.59 | Applying alpha-rule on (580) yields: % 23.62/6.59 | (581) all_66_0_132 = 0 % 23.62/6.59 | (578) apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0 % 23.62/6.59 | % 23.62/6.59 +-Applying beta-rule and splitting (500), into two cases. % 23.62/6.59 |-Branch one: % 23.62/6.59 | (583) (all_75_0_142 = 0 & apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_75_0_142 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_75_0_142) % 23.62/6.59 | % 23.62/6.59 +-Applying beta-rule and splitting (583), into two cases. % 23.62/6.59 |-Branch one: % 23.62/6.59 | (584) all_75_0_142 = 0 & apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0 % 23.62/6.59 | % 23.62/6.59 | Applying alpha-rule on (584) yields: % 23.62/6.59 | (585) all_75_0_142 = 0 % 23.62/6.59 | (578) apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0 % 23.62/6.59 | % 23.62/6.59 +-Applying beta-rule and splitting (543), into two cases. % 23.62/6.59 |-Branch one: % 23.62/6.59 | (587) (all_118_0_145 = 0 & apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_118_0_145 = 0) & apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_118_0_145) % 23.62/6.59 | % 23.62/6.59 +-Applying beta-rule and splitting (587), into two cases. % 23.62/6.59 |-Branch one: % 23.62/6.59 | (588) all_118_0_145 = 0 & apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0 % 23.62/6.59 | % 23.62/6.59 | Applying alpha-rule on (588) yields: % 23.62/6.59 | (589) all_118_0_145 = 0 % 23.62/6.59 | (578) apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0 % 23.62/6.59 | % 23.62/6.59 +-Applying beta-rule and splitting (497), into two cases. % 23.62/6.59 |-Branch one: % 23.62/6.59 | (591) ( ~ (all_68_1_135 = 0) & member(all_44_7_61, all_0_4_4) = all_68_1_135) | ( ~ (all_68_1_135 = 0) & member(all_44_8_62, all_0_4_4) = all_68_1_135) % 23.62/6.59 | % 23.62/6.59 +-Applying beta-rule and splitting (591), into two cases. % 23.62/6.59 |-Branch one: % 23.62/6.59 | (592) ~ (all_68_1_135 = 0) & member(all_44_7_61, all_0_4_4) = all_68_1_135 % 23.62/6.59 | % 23.62/6.59 | Applying alpha-rule on (592) yields: % 23.62/6.59 | (593) ~ (all_68_1_135 = 0) % 23.62/6.59 | (594) member(all_44_7_61, all_0_4_4) = all_68_1_135 % 23.62/6.59 | % 23.62/6.59 | Instantiating formula (88) with all_44_7_61, all_0_4_4, all_68_1_135, 0 and discharging atoms member(all_44_7_61, all_0_4_4) = all_68_1_135, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.62/6.59 | (595) all_68_1_135 = 0 % 23.62/6.59 | % 23.62/6.59 | Equations (595) can reduce 593 to: % 23.62/6.59 | (109) $false % 23.62/6.59 | % 23.62/6.59 |-The branch is then unsatisfiable % 23.62/6.59 |-Branch two: % 23.62/6.59 | (597) ~ (all_68_1_135 = 0) & member(all_44_8_62, all_0_4_4) = all_68_1_135 % 23.62/6.59 | % 23.62/6.59 | Applying alpha-rule on (597) yields: % 23.62/6.59 | (593) ~ (all_68_1_135 = 0) % 23.62/6.59 | (599) member(all_44_8_62, all_0_4_4) = all_68_1_135 % 23.62/6.59 | % 23.62/6.59 | Instantiating formula (88) with all_44_8_62, all_0_4_4, all_68_1_135, 0 and discharging atoms member(all_44_8_62, all_0_4_4) = all_68_1_135, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.62/6.59 | (595) all_68_1_135 = 0 % 23.62/6.59 | % 23.62/6.59 | Equations (595) can reduce 593 to: % 23.62/6.59 | (109) $false % 23.62/6.59 | % 23.62/6.59 |-The branch is then unsatisfiable % 23.62/6.59 |-Branch two: % 23.62/6.59 | (602) ( ~ (all_44_3_57 = 0) | (all_68_0_134 = 0 & all_68_1_135 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 & apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0)) & (all_44_3_57 = 0 | ( ~ (all_68_0_134 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_68_0_134) | ( ~ (all_68_1_135 = 0) & apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_68_1_135)) % 23.62/6.59 | % 23.62/6.59 | Applying alpha-rule on (602) yields: % 23.62/6.59 | (603) ~ (all_44_3_57 = 0) | (all_68_0_134 = 0 & all_68_1_135 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 & apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0) % 23.62/6.59 | (604) all_44_3_57 = 0 | ( ~ (all_68_0_134 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_68_0_134) | ( ~ (all_68_1_135 = 0) & apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_68_1_135) % 23.62/6.59 | % 23.62/6.59 +-Applying beta-rule and splitting (604), into two cases. % 23.62/6.59 |-Branch one: % 23.62/6.59 | (122) all_44_3_57 = 0 % 23.62/6.59 | % 23.62/6.59 | Equations (122) can reduce 465 to: % 23.62/6.59 | (109) $false % 23.62/6.59 | % 23.62/6.59 |-The branch is then unsatisfiable % 23.62/6.59 |-Branch two: % 23.62/6.59 | (465) ~ (all_44_3_57 = 0) % 23.62/6.59 | (608) ( ~ (all_68_0_134 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_68_0_134) | ( ~ (all_68_1_135 = 0) & apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_68_1_135) % 23.62/6.59 | % 23.62/6.59 +-Applying beta-rule and splitting (608), into two cases. % 23.62/6.59 |-Branch one: % 23.62/6.59 | (609) ~ (all_68_0_134 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_68_0_134 % 23.62/6.59 | % 23.62/6.59 | Applying alpha-rule on (609) yields: % 23.62/6.59 | (610) ~ (all_68_0_134 = 0) % 23.62/6.59 | (611) apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_68_0_134 % 23.62/6.59 | % 23.62/6.59 +-Applying beta-rule and splitting (492), into two cases. % 23.62/6.59 |-Branch one: % 23.62/6.59 | (612) (all_63_0_129 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_63_0_129 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_63_0_129) % 23.62/6.59 | % 23.62/6.59 +-Applying beta-rule and splitting (612), into two cases. % 23.62/6.59 |-Branch one: % 23.62/6.59 | (613) all_63_0_129 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.59 | % 23.62/6.59 | Applying alpha-rule on (613) yields: % 23.62/6.59 | (614) all_63_0_129 = 0 % 23.62/6.59 | (615) apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.59 | % 23.62/6.59 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, 0, all_68_0_134 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_68_0_134, apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0, yields: % 23.62/6.59 | (616) all_68_0_134 = 0 % 23.62/6.59 | % 23.62/6.59 | Equations (616) can reduce 610 to: % 23.62/6.59 | (109) $false % 23.62/6.59 | % 23.62/6.59 |-The branch is then unsatisfiable % 23.62/6.59 |-Branch two: % 23.62/6.59 | (618) ~ (all_63_0_129 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_63_0_129 % 23.62/6.59 | % 23.62/6.59 | Applying alpha-rule on (618) yields: % 23.62/6.59 | (619) ~ (all_63_0_129 = 0) % 23.62/6.59 | (620) apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_63_0_129 % 23.62/6.59 | % 23.62/6.59 +-Applying beta-rule and splitting (545), into two cases. % 23.62/6.59 |-Branch one: % 23.62/6.59 | (621) (all_123_0_151 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_123_0_151 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151) % 23.62/6.59 | % 23.62/6.59 +-Applying beta-rule and splitting (621), into two cases. % 23.62/6.59 |-Branch one: % 23.62/6.59 | (622) all_123_0_151 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.59 | % 23.62/6.59 | Applying alpha-rule on (622) yields: % 23.62/6.59 | (623) all_123_0_151 = 0 % 23.62/6.59 | (615) apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.59 | % 23.62/6.59 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, all_63_0_129, all_68_0_134 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_68_0_134, apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_63_0_129, yields: % 23.62/6.59 | (625) all_68_0_134 = all_63_0_129 % 23.62/6.59 | % 23.62/6.59 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, 0, all_68_0_134 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_68_0_134, apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0, yields: % 23.62/6.59 | (616) all_68_0_134 = 0 % 23.62/6.59 | % 23.62/6.59 | Combining equations (625,616) yields a new equation: % 23.62/6.59 | (627) all_63_0_129 = 0 % 23.62/6.59 | % 23.62/6.59 | Simplifying 627 yields: % 23.62/6.60 | (614) all_63_0_129 = 0 % 23.62/6.60 | % 23.62/6.60 | Equations (614) can reduce 619 to: % 23.62/6.60 | (109) $false % 23.62/6.60 | % 23.62/6.60 |-The branch is then unsatisfiable % 23.62/6.60 |-Branch two: % 23.62/6.60 | (630) ~ (all_123_0_151 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151 % 23.62/6.60 | % 23.62/6.60 | Applying alpha-rule on (630) yields: % 23.62/6.60 | (631) ~ (all_123_0_151 = 0) % 23.62/6.60 | (632) apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151 % 23.62/6.60 | % 23.62/6.60 +-Applying beta-rule and splitting (547), into two cases. % 23.62/6.60 |-Branch one: % 23.62/6.60 | (633) (all_126_0_155 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_126_0_155 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_126_0_155) % 23.62/6.60 | % 23.62/6.60 +-Applying beta-rule and splitting (633), into two cases. % 23.62/6.60 |-Branch one: % 23.62/6.60 | (634) all_126_0_155 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.60 | % 23.62/6.60 | Applying alpha-rule on (634) yields: % 23.62/6.60 | (635) all_126_0_155 = 0 % 23.62/6.60 | (615) apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.60 | % 23.62/6.60 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, all_68_0_134, all_123_0_151 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151, apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_68_0_134, yields: % 23.62/6.60 | (637) all_123_0_151 = all_68_0_134 % 23.62/6.60 | % 23.62/6.60 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, all_63_0_129, all_123_0_151 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151, apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_63_0_129, yields: % 23.62/6.60 | (638) all_123_0_151 = all_63_0_129 % 23.62/6.60 | % 23.62/6.60 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, 0, all_123_0_151 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151, apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0, yields: % 23.62/6.60 | (623) all_123_0_151 = 0 % 23.62/6.60 | % 23.62/6.60 | Combining equations (623,637) yields a new equation: % 23.62/6.60 | (616) all_68_0_134 = 0 % 23.62/6.60 | % 23.62/6.60 | Combining equations (638,637) yields a new equation: % 23.62/6.60 | (625) all_68_0_134 = all_63_0_129 % 23.62/6.60 | % 23.62/6.60 | Combining equations (625,616) yields a new equation: % 23.62/6.60 | (627) all_63_0_129 = 0 % 23.62/6.60 | % 23.62/6.60 | Simplifying 627 yields: % 23.62/6.60 | (614) all_63_0_129 = 0 % 23.62/6.60 | % 23.62/6.60 | Equations (614) can reduce 619 to: % 23.62/6.60 | (109) $false % 23.62/6.60 | % 23.62/6.60 |-The branch is then unsatisfiable % 23.62/6.60 |-Branch two: % 23.62/6.60 | (645) ~ (all_126_0_155 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_126_0_155 % 23.62/6.60 | % 23.62/6.60 | Applying alpha-rule on (645) yields: % 23.62/6.60 | (646) ~ (all_126_0_155 = 0) % 23.62/6.60 | (647) apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_126_0_155 % 23.62/6.60 | % 23.62/6.60 +-Applying beta-rule and splitting (546), into two cases. % 23.62/6.60 |-Branch one: % 23.62/6.60 | (648) (all_124_0_152 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_124_0_152 = 0) & member(all_44_7_61, all_0_4_4) = all_124_0_152) % 23.62/6.60 | % 23.62/6.60 +-Applying beta-rule and splitting (648), into two cases. % 23.62/6.60 |-Branch one: % 23.62/6.60 | (649) all_124_0_152 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.60 | % 23.62/6.60 | Applying alpha-rule on (649) yields: % 23.62/6.60 | (650) all_124_0_152 = 0 % 23.62/6.60 | (615) apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.60 | % 23.62/6.60 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, all_123_0_151, all_126_0_155 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_126_0_155, apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151, yields: % 23.62/6.60 | (652) all_126_0_155 = all_123_0_151 % 23.62/6.60 | % 23.62/6.60 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, all_68_0_134, all_126_0_155 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_126_0_155, apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_68_0_134, yields: % 23.62/6.60 | (653) all_126_0_155 = all_68_0_134 % 23.62/6.60 | % 23.62/6.60 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, all_63_0_129, all_126_0_155 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_126_0_155, apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_63_0_129, yields: % 23.62/6.60 | (654) all_126_0_155 = all_63_0_129 % 23.62/6.60 | % 23.62/6.60 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, 0, all_126_0_155 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_126_0_155, apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0, yields: % 23.62/6.60 | (635) all_126_0_155 = 0 % 23.62/6.60 | % 23.62/6.60 | Combining equations (654,652) yields a new equation: % 23.62/6.60 | (638) all_123_0_151 = all_63_0_129 % 23.62/6.60 | % 23.62/6.60 | Combining equations (635,652) yields a new equation: % 23.62/6.60 | (623) all_123_0_151 = 0 % 23.62/6.60 | % 23.62/6.60 | Combining equations (653,652) yields a new equation: % 23.62/6.60 | (637) all_123_0_151 = all_68_0_134 % 23.62/6.60 | % 23.62/6.60 | Combining equations (638,637) yields a new equation: % 23.62/6.60 | (625) all_68_0_134 = all_63_0_129 % 23.62/6.60 | % 23.62/6.60 | Combining equations (623,637) yields a new equation: % 23.62/6.60 | (616) all_68_0_134 = 0 % 23.62/6.60 | % 23.62/6.60 | Combining equations (625,616) yields a new equation: % 23.62/6.60 | (627) all_63_0_129 = 0 % 23.62/6.60 | % 23.62/6.60 | Simplifying 627 yields: % 23.62/6.60 | (614) all_63_0_129 = 0 % 23.62/6.60 | % 23.62/6.60 | Equations (614) can reduce 619 to: % 23.62/6.60 | (109) $false % 23.62/6.60 | % 23.62/6.60 |-The branch is then unsatisfiable % 23.62/6.60 |-Branch two: % 23.62/6.60 | (664) ~ (all_124_0_152 = 0) & member(all_44_7_61, all_0_4_4) = all_124_0_152 % 23.62/6.60 | % 23.62/6.60 | Applying alpha-rule on (664) yields: % 23.62/6.60 | (665) ~ (all_124_0_152 = 0) % 23.62/6.60 | (666) member(all_44_7_61, all_0_4_4) = all_124_0_152 % 23.62/6.60 | % 23.62/6.60 | Instantiating formula (88) with all_44_7_61, all_0_4_4, all_124_0_152, 0 and discharging atoms member(all_44_7_61, all_0_4_4) = all_124_0_152, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.62/6.60 | (650) all_124_0_152 = 0 % 23.62/6.60 | % 23.62/6.60 | Equations (650) can reduce 665 to: % 23.62/6.60 | (109) $false % 23.62/6.60 | % 23.62/6.60 |-The branch is then unsatisfiable % 23.62/6.60 |-Branch two: % 23.62/6.60 | (669) ~ (all_124_0_152 = 0) & member(all_44_8_62, all_0_4_4) = all_124_0_152 % 23.62/6.60 | % 23.62/6.60 | Applying alpha-rule on (669) yields: % 23.62/6.60 | (665) ~ (all_124_0_152 = 0) % 23.62/6.60 | (671) member(all_44_8_62, all_0_4_4) = all_124_0_152 % 23.62/6.60 | % 23.62/6.60 | Instantiating formula (88) with all_44_8_62, all_0_4_4, all_124_0_152, 0 and discharging atoms member(all_44_8_62, all_0_4_4) = all_124_0_152, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.62/6.60 | (650) all_124_0_152 = 0 % 23.62/6.60 | % 23.62/6.60 | Equations (650) can reduce 665 to: % 23.62/6.60 | (109) $false % 23.62/6.60 | % 23.62/6.60 |-The branch is then unsatisfiable % 23.62/6.60 |-Branch two: % 23.62/6.60 | (674) ~ (all_126_0_155 = 0) & member(all_44_7_61, all_0_4_4) = all_126_0_155 % 23.62/6.60 | % 23.62/6.60 | Applying alpha-rule on (674) yields: % 23.62/6.60 | (646) ~ (all_126_0_155 = 0) % 23.62/6.60 | (676) member(all_44_7_61, all_0_4_4) = all_126_0_155 % 23.62/6.60 | % 23.62/6.60 +-Applying beta-rule and splitting (546), into two cases. % 23.62/6.60 |-Branch one: % 23.62/6.60 | (648) (all_124_0_152 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_124_0_152 = 0) & member(all_44_7_61, all_0_4_4) = all_124_0_152) % 23.62/6.60 | % 23.62/6.60 +-Applying beta-rule and splitting (648), into two cases. % 23.62/6.60 |-Branch one: % 23.62/6.60 | (649) all_124_0_152 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.60 | % 23.62/6.60 | Applying alpha-rule on (649) yields: % 23.62/6.60 | (650) all_124_0_152 = 0 % 23.62/6.60 | (615) apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.60 | % 23.62/6.60 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, all_68_0_134, all_123_0_151 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151, apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_68_0_134, yields: % 23.62/6.60 | (637) all_123_0_151 = all_68_0_134 % 23.62/6.60 | % 23.62/6.60 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, all_63_0_129, all_123_0_151 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151, apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_63_0_129, yields: % 23.62/6.60 | (638) all_123_0_151 = all_63_0_129 % 23.62/6.60 | % 23.62/6.60 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, 0, all_123_0_151 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151, apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0, yields: % 23.62/6.60 | (623) all_123_0_151 = 0 % 23.62/6.60 | % 23.62/6.60 | Combining equations (623,637) yields a new equation: % 23.62/6.60 | (616) all_68_0_134 = 0 % 23.62/6.60 | % 23.62/6.60 | Combining equations (638,637) yields a new equation: % 23.62/6.60 | (625) all_68_0_134 = all_63_0_129 % 23.62/6.60 | % 23.62/6.60 | Combining equations (625,616) yields a new equation: % 23.62/6.60 | (627) all_63_0_129 = 0 % 23.62/6.60 | % 23.62/6.60 | Simplifying 627 yields: % 23.62/6.60 | (614) all_63_0_129 = 0 % 23.62/6.60 | % 23.62/6.60 | Equations (614) can reduce 619 to: % 23.62/6.60 | (109) $false % 23.62/6.60 | % 23.62/6.60 |-The branch is then unsatisfiable % 23.62/6.60 |-Branch two: % 23.62/6.60 | (664) ~ (all_124_0_152 = 0) & member(all_44_7_61, all_0_4_4) = all_124_0_152 % 23.62/6.60 | % 23.62/6.60 | Applying alpha-rule on (664) yields: % 23.62/6.60 | (665) ~ (all_124_0_152 = 0) % 23.62/6.60 | (666) member(all_44_7_61, all_0_4_4) = all_124_0_152 % 23.62/6.60 | % 23.62/6.60 | Instantiating formula (88) with all_44_7_61, all_0_4_4, all_126_0_155, 0 and discharging atoms member(all_44_7_61, all_0_4_4) = all_126_0_155, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.62/6.60 | (635) all_126_0_155 = 0 % 23.62/6.60 | % 23.62/6.60 | Instantiating formula (88) with all_44_7_61, all_0_4_4, all_124_0_152, all_126_0_155 and discharging atoms member(all_44_7_61, all_0_4_4) = all_126_0_155, member(all_44_7_61, all_0_4_4) = all_124_0_152, yields: % 23.62/6.60 | (693) all_126_0_155 = all_124_0_152 % 23.62/6.60 | % 23.62/6.60 | Combining equations (635,693) yields a new equation: % 23.62/6.60 | (650) all_124_0_152 = 0 % 23.62/6.60 | % 23.62/6.60 | Equations (650) can reduce 665 to: % 23.62/6.60 | (109) $false % 23.62/6.60 | % 23.62/6.60 |-The branch is then unsatisfiable % 23.62/6.60 |-Branch two: % 23.62/6.60 | (669) ~ (all_124_0_152 = 0) & member(all_44_8_62, all_0_4_4) = all_124_0_152 % 23.62/6.60 | % 23.62/6.60 | Applying alpha-rule on (669) yields: % 23.62/6.60 | (665) ~ (all_124_0_152 = 0) % 23.62/6.60 | (671) member(all_44_8_62, all_0_4_4) = all_124_0_152 % 23.62/6.61 | % 23.62/6.61 | Instantiating formula (88) with all_44_8_62, all_0_4_4, all_124_0_152, 0 and discharging atoms member(all_44_8_62, all_0_4_4) = all_124_0_152, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.62/6.61 | (650) all_124_0_152 = 0 % 23.62/6.61 | % 23.62/6.61 | Equations (650) can reduce 665 to: % 23.62/6.61 | (109) $false % 23.62/6.61 | % 23.62/6.61 |-The branch is then unsatisfiable % 23.62/6.61 |-Branch two: % 23.62/6.61 | (701) ~ (all_123_0_151 = 0) & member(all_44_8_62, all_0_4_4) = all_123_0_151 % 23.62/6.61 | % 23.62/6.61 | Applying alpha-rule on (701) yields: % 23.62/6.61 | (631) ~ (all_123_0_151 = 0) % 23.62/6.61 | (703) member(all_44_8_62, all_0_4_4) = all_123_0_151 % 23.62/6.61 | % 23.62/6.61 | Instantiating formula (88) with all_44_8_62, all_0_4_4, all_123_0_151, 0 and discharging atoms member(all_44_8_62, all_0_4_4) = all_123_0_151, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.62/6.61 | (623) all_123_0_151 = 0 % 23.62/6.61 | % 23.62/6.61 | Equations (623) can reduce 631 to: % 23.62/6.61 | (109) $false % 23.62/6.61 | % 23.62/6.61 |-The branch is then unsatisfiable % 23.62/6.61 |-Branch two: % 23.62/6.61 | (706) ~ (all_63_0_129 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_63_0_129 % 23.62/6.61 | % 23.62/6.61 | Applying alpha-rule on (706) yields: % 23.62/6.61 | (619) ~ (all_63_0_129 = 0) % 23.62/6.61 | (708) apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_63_0_129 % 23.62/6.61 | % 23.62/6.61 | Instantiating formula (70) with all_0_2_2, all_44_8_62, all_44_8_62, all_63_0_129, 0 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_63_0_129, apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0, yields: % 23.62/6.61 | (614) all_63_0_129 = 0 % 23.62/6.61 | % 23.62/6.61 | Equations (614) can reduce 619 to: % 23.62/6.61 | (109) $false % 23.62/6.61 | % 23.62/6.61 |-The branch is then unsatisfiable % 23.62/6.61 |-Branch two: % 23.62/6.61 | (711) ~ (all_68_1_135 = 0) & apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_68_1_135 % 23.62/6.61 | % 23.62/6.61 | Applying alpha-rule on (711) yields: % 23.62/6.61 | (593) ~ (all_68_1_135 = 0) % 23.62/6.61 | (713) apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_68_1_135 % 23.62/6.61 | % 23.62/6.61 | Instantiating formula (70) with all_0_3_3, all_44_7_61, all_44_8_62, 0, all_68_1_135 and discharging atoms apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_68_1_135, apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0, yields: % 23.62/6.61 | (595) all_68_1_135 = 0 % 23.62/6.61 | % 23.62/6.61 | Equations (595) can reduce 593 to: % 23.62/6.61 | (109) $false % 23.62/6.61 | % 23.62/6.61 |-The branch is then unsatisfiable % 23.62/6.61 |-Branch two: % 23.62/6.61 | (716) ~ (all_118_0_145 = 0) & apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_118_0_145 % 23.62/6.61 | % 23.62/6.61 | Applying alpha-rule on (716) yields: % 23.62/6.61 | (717) ~ (all_118_0_145 = 0) % 23.62/6.61 | (718) apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_118_0_145 % 23.62/6.61 | % 23.62/6.61 | Instantiating formula (70) with all_0_3_3, all_44_7_61, all_44_8_62, 0, all_118_0_145 and discharging atoms apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_118_0_145, apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0, yields: % 23.62/6.61 | (589) all_118_0_145 = 0 % 23.62/6.61 | % 23.62/6.61 | Equations (589) can reduce 717 to: % 23.62/6.61 | (109) $false % 23.62/6.61 | % 23.62/6.61 |-The branch is then unsatisfiable % 23.62/6.61 |-Branch two: % 23.62/6.61 | (721) ~ (all_118_0_145 = 0) & member(all_44_8_62, all_0_4_4) = all_118_0_145 % 23.62/6.61 | % 23.62/6.61 | Applying alpha-rule on (721) yields: % 23.62/6.61 | (717) ~ (all_118_0_145 = 0) % 23.62/6.61 | (723) member(all_44_8_62, all_0_4_4) = all_118_0_145 % 23.62/6.61 | % 23.62/6.61 | Instantiating formula (88) with all_44_8_62, all_0_4_4, all_118_0_145, 0 and discharging atoms member(all_44_8_62, all_0_4_4) = all_118_0_145, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.62/6.61 | (589) all_118_0_145 = 0 % 23.62/6.61 | % 23.62/6.61 | Equations (589) can reduce 717 to: % 23.62/6.61 | (109) $false % 23.62/6.61 | % 23.62/6.61 |-The branch is then unsatisfiable % 23.62/6.61 |-Branch two: % 23.62/6.61 | (726) ~ (all_75_0_142 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_75_0_142 % 23.62/6.61 | % 23.62/6.61 | Applying alpha-rule on (726) yields: % 23.62/6.61 | (727) ~ (all_75_0_142 = 0) % 23.62/6.61 | (728) apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_75_0_142 % 23.62/6.61 | % 23.62/6.61 | Instantiating formula (70) with all_0_3_3, all_44_7_61, all_44_7_61, all_75_0_142, 0 and discharging atoms apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_75_0_142, apply(all_0_3_3, all_44_7_61, all_44_7_61) = 0, yields: % 23.62/6.61 | (585) all_75_0_142 = 0 % 23.62/6.61 | % 23.62/6.61 | Equations (585) can reduce 727 to: % 23.62/6.61 | (109) $false % 23.62/6.61 | % 23.62/6.61 |-The branch is then unsatisfiable % 23.62/6.61 |-Branch two: % 23.62/6.61 | (731) ~ (all_75_0_142 = 0) & apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_75_0_142 % 23.62/6.61 | % 23.62/6.61 | Applying alpha-rule on (731) yields: % 23.62/6.61 | (727) ~ (all_75_0_142 = 0) % 23.62/6.61 | (733) apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_75_0_142 % 23.62/6.61 | % 23.62/6.61 | Instantiating formula (70) with all_0_3_3, all_44_7_61, all_44_8_62, 0, all_75_0_142 and discharging atoms apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_75_0_142, apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0, yields: % 23.62/6.61 | (585) all_75_0_142 = 0 % 23.62/6.61 | % 23.62/6.61 | Equations (585) can reduce 727 to: % 23.62/6.61 | (109) $false % 23.62/6.61 | % 23.62/6.61 |-The branch is then unsatisfiable % 23.62/6.61 |-Branch two: % 23.62/6.61 | (736) ~ (all_66_0_132 = 0) & apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_66_0_132 % 23.62/6.61 | % 23.62/6.61 | Applying alpha-rule on (736) yields: % 23.62/6.61 | (737) ~ (all_66_0_132 = 0) % 23.62/6.61 | (738) apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_66_0_132 % 23.62/6.61 | % 23.62/6.61 | Instantiating formula (70) with all_0_3_3, all_44_7_61, all_44_8_62, 0, all_66_0_132 and discharging atoms apply(all_0_3_3, all_44_7_61, all_44_8_62) = all_66_0_132, apply(all_0_3_3, all_44_7_61, all_44_8_62) = 0, yields: % 23.62/6.61 | (581) all_66_0_132 = 0 % 23.62/6.61 | % 23.62/6.61 | Equations (581) can reduce 737 to: % 23.62/6.61 | (109) $false % 23.62/6.61 | % 23.62/6.61 |-The branch is then unsatisfiable % 23.62/6.61 |-Branch two: % 23.62/6.61 | (741) ~ (all_66_0_132 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_66_0_132 % 23.62/6.61 | % 23.62/6.61 | Applying alpha-rule on (741) yields: % 23.62/6.61 | (737) ~ (all_66_0_132 = 0) % 23.62/6.61 | (743) apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_66_0_132 % 23.62/6.61 | % 23.62/6.61 +-Applying beta-rule and splitting (570), into two cases. % 23.62/6.61 |-Branch one: % 23.62/6.61 | (744) all_120_0_147 = 0 & apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0 % 23.62/6.61 | % 23.62/6.61 | Applying alpha-rule on (744) yields: % 23.62/6.61 | (745) all_120_0_147 = 0 % 23.62/6.61 | (153) apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0 % 23.62/6.61 | % 23.62/6.61 | Instantiating formula (70) with all_0_3_3, all_44_8_62, all_44_8_62, all_66_0_132, 0 and discharging atoms apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_66_0_132, apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0, yields: % 23.62/6.61 | (581) all_66_0_132 = 0 % 23.62/6.61 | % 23.62/6.61 | Equations (581) can reduce 737 to: % 23.62/6.61 | (109) $false % 23.62/6.61 | % 23.62/6.61 |-The branch is then unsatisfiable % 23.62/6.61 |-Branch two: % 23.62/6.61 | (749) ~ (all_120_1_148 = 0) & apply(all_0_1_1, all_44_8_62, all_44_8_62) = all_120_1_148 % 23.62/6.61 | % 23.62/6.61 | Applying alpha-rule on (749) yields: % 23.62/6.61 | (565) ~ (all_120_1_148 = 0) % 23.62/6.61 | (751) apply(all_0_1_1, all_44_8_62, all_44_8_62) = all_120_1_148 % 23.62/6.61 | % 23.62/6.61 +-Applying beta-rule and splitting (571), into two cases. % 23.62/6.61 |-Branch one: % 23.62/6.61 | (752) all_120_1_148 = 0 & apply(all_0_1_1, all_44_8_62, all_44_8_62) = 0 % 23.62/6.61 | % 23.62/6.61 | Applying alpha-rule on (752) yields: % 23.62/6.61 | (567) all_120_1_148 = 0 % 23.62/6.61 | (563) apply(all_0_1_1, all_44_8_62, all_44_8_62) = 0 % 23.62/6.61 | % 23.62/6.61 | Equations (567) can reduce 565 to: % 23.62/6.61 | (109) $false % 23.62/6.61 | % 23.62/6.61 |-The branch is then unsatisfiable % 23.62/6.61 |-Branch two: % 23.62/6.61 | (756) ~ (all_120_0_147 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_120_0_147 % 23.62/6.61 | % 23.62/6.61 | Applying alpha-rule on (756) yields: % 23.62/6.61 | (757) ~ (all_120_0_147 = 0) % 23.62/6.61 | (758) apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_120_0_147 % 23.62/6.61 | % 23.62/6.61 | Instantiating formula (70) with all_0_3_3, all_44_8_62, all_44_8_62, all_120_0_147, 0 and discharging atoms apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_120_0_147, apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0, yields: % 23.62/6.61 | (745) all_120_0_147 = 0 % 23.62/6.61 | % 23.62/6.61 | Instantiating formula (70) with all_0_3_3, all_44_8_62, all_44_8_62, all_66_0_132, all_120_0_147 and discharging atoms apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_120_0_147, apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_66_0_132, yields: % 23.62/6.61 | (760) all_120_0_147 = all_66_0_132 % 23.62/6.61 | % 23.62/6.61 | Combining equations (760,745) yields a new equation: % 23.62/6.61 | (761) all_66_0_132 = 0 % 23.62/6.61 | % 23.62/6.61 | Simplifying 761 yields: % 23.62/6.61 | (581) all_66_0_132 = 0 % 23.62/6.61 | % 23.62/6.61 | Equations (581) can reduce 737 to: % 23.62/6.61 | (109) $false % 23.62/6.61 | % 23.62/6.61 |-The branch is then unsatisfiable % 23.62/6.61 |-Branch two: % 23.62/6.61 | (764) ~ (all_127_0_156 = 0) & member(all_44_7_61, all_0_4_4) = all_127_0_156 % 23.62/6.61 | % 23.62/6.61 | Applying alpha-rule on (764) yields: % 23.62/6.61 | (765) ~ (all_127_0_156 = 0) % 23.62/6.61 | (766) member(all_44_7_61, all_0_4_4) = all_127_0_156 % 23.62/6.61 | % 23.62/6.61 | Instantiating formula (88) with all_44_7_61, all_0_4_4, all_127_0_156, 0 and discharging atoms member(all_44_7_61, all_0_4_4) = all_127_0_156, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.62/6.61 | (577) all_127_0_156 = 0 % 23.62/6.61 | % 23.62/6.61 | Equations (577) can reduce 765 to: % 23.62/6.61 | (109) $false % 23.62/6.61 | % 23.62/6.61 |-The branch is then unsatisfiable % 23.62/6.61 |-Branch two: % 23.62/6.61 | (769) ~ (all_127_0_156 = 0) & member(all_44_8_62, all_0_4_4) = all_127_0_156 % 23.62/6.61 | % 23.62/6.61 | Applying alpha-rule on (769) yields: % 23.62/6.61 | (765) ~ (all_127_0_156 = 0) % 23.62/6.61 | (771) member(all_44_8_62, all_0_4_4) = all_127_0_156 % 23.62/6.61 | % 23.62/6.61 | Instantiating formula (88) with all_44_8_62, all_0_4_4, all_127_0_156, 0 and discharging atoms member(all_44_8_62, all_0_4_4) = all_127_0_156, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.62/6.61 | (577) all_127_0_156 = 0 % 23.62/6.61 | % 23.62/6.61 | Equations (577) can reduce 765 to: % 23.62/6.61 | (109) $false % 23.62/6.61 | % 23.62/6.61 |-The branch is then unsatisfiable % 23.62/6.61 |-Branch two: % 23.62/6.61 | (774) ~ (all_117_1_144 = 0) & apply(all_0_1_1, all_44_8_62, all_44_8_62) = all_117_1_144 % 23.62/6.61 | % 23.62/6.61 | Applying alpha-rule on (774) yields: % 23.62/6.61 | (554) ~ (all_117_1_144 = 0) % 23.62/6.61 | (776) apply(all_0_1_1, all_44_8_62, all_44_8_62) = all_117_1_144 % 23.62/6.61 | % 23.62/6.61 | Equations (556) can reduce 554 to: % 23.62/6.61 | (109) $false % 23.62/6.61 | % 23.62/6.61 |-The branch is then unsatisfiable % 23.62/6.61 |-Branch two: % 23.62/6.61 | (778) ~ (all_117_0_143 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_117_0_143 % 23.62/6.61 | % 23.62/6.61 | Applying alpha-rule on (778) yields: % 23.62/6.61 | (779) ~ (all_117_0_143 = 0) % 23.62/6.61 | (780) apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_117_0_143 % 23.62/6.61 | % 23.62/6.61 | Instantiating formula (70) with all_0_2_2, all_44_8_62, all_44_8_62, all_117_0_143, 0 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_117_0_143, apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0, yields: % 23.62/6.61 | (573) all_117_0_143 = 0 % 23.62/6.61 | % 23.62/6.61 | Equations (573) can reduce 779 to: % 23.62/6.61 | (109) $false % 23.62/6.61 | % 23.62/6.61 |-The branch is then unsatisfiable % 23.62/6.61 |-Branch two: % 23.62/6.61 | (783) ~ (all_65_0_131 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_65_0_131 % 23.62/6.61 | % 23.62/6.61 | Applying alpha-rule on (783) yields: % 23.62/6.61 | (784) ~ (all_65_0_131 = 0) % 23.62/6.61 | (785) apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_65_0_131 % 23.62/6.61 | % 23.62/6.61 +-Applying beta-rule and splitting (492), into two cases. % 23.62/6.61 |-Branch one: % 23.62/6.61 | (612) (all_63_0_129 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_63_0_129 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_63_0_129) % 23.62/6.61 | % 23.62/6.61 +-Applying beta-rule and splitting (612), into two cases. % 23.62/6.61 |-Branch one: % 23.62/6.61 | (613) all_63_0_129 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.61 | % 23.62/6.61 | Applying alpha-rule on (613) yields: % 23.62/6.61 | (614) all_63_0_129 = 0 % 23.62/6.61 | (615) apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.61 | % 23.62/6.61 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, 0, all_65_0_131 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_65_0_131, apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0, yields: % 23.62/6.61 | (551) all_65_0_131 = 0 % 23.62/6.61 | % 23.62/6.61 | Equations (551) can reduce 784 to: % 23.62/6.61 | (109) $false % 23.62/6.61 | % 23.62/6.61 |-The branch is then unsatisfiable % 23.62/6.61 |-Branch two: % 23.62/6.61 | (618) ~ (all_63_0_129 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_63_0_129 % 23.62/6.61 | % 23.62/6.61 | Applying alpha-rule on (618) yields: % 23.62/6.61 | (619) ~ (all_63_0_129 = 0) % 23.62/6.62 | (620) apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_63_0_129 % 23.62/6.62 | % 23.62/6.62 +-Applying beta-rule and splitting (547), into two cases. % 23.62/6.62 |-Branch one: % 23.62/6.62 | (633) (all_126_0_155 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_126_0_155 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_126_0_155) % 23.62/6.62 | % 23.62/6.62 +-Applying beta-rule and splitting (633), into two cases. % 23.62/6.62 |-Branch one: % 23.62/6.62 | (634) all_126_0_155 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.62 | % 23.62/6.62 | Applying alpha-rule on (634) yields: % 23.62/6.62 | (635) all_126_0_155 = 0 % 23.62/6.62 | (615) apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, all_63_0_129, all_65_0_131 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_65_0_131, apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_63_0_129, yields: % 23.62/6.62 | (799) all_65_0_131 = all_63_0_129 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, 0, all_65_0_131 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_65_0_131, apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0, yields: % 23.62/6.62 | (551) all_65_0_131 = 0 % 23.62/6.62 | % 23.62/6.62 | Combining equations (799,551) yields a new equation: % 23.62/6.62 | (627) all_63_0_129 = 0 % 23.62/6.62 | % 23.62/6.62 | Simplifying 627 yields: % 23.62/6.62 | (614) all_63_0_129 = 0 % 23.62/6.62 | % 23.62/6.62 | Equations (614) can reduce 619 to: % 23.62/6.62 | (109) $false % 23.62/6.62 | % 23.62/6.62 |-The branch is then unsatisfiable % 23.62/6.62 |-Branch two: % 23.62/6.62 | (645) ~ (all_126_0_155 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_126_0_155 % 23.62/6.62 | % 23.62/6.62 | Applying alpha-rule on (645) yields: % 23.62/6.62 | (646) ~ (all_126_0_155 = 0) % 23.62/6.62 | (647) apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_126_0_155 % 23.62/6.62 | % 23.62/6.62 +-Applying beta-rule and splitting (545), into two cases. % 23.62/6.62 |-Branch one: % 23.62/6.62 | (621) (all_123_0_151 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_123_0_151 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151) % 23.62/6.62 | % 23.62/6.62 +-Applying beta-rule and splitting (621), into two cases. % 23.62/6.62 |-Branch one: % 23.62/6.62 | (622) all_123_0_151 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.62 | % 23.62/6.62 | Applying alpha-rule on (622) yields: % 23.62/6.62 | (623) all_123_0_151 = 0 % 23.62/6.62 | (615) apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, all_65_0_131, all_126_0_155 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_126_0_155, apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_65_0_131, yields: % 23.62/6.62 | (811) all_126_0_155 = all_65_0_131 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, all_63_0_129, all_126_0_155 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_126_0_155, apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_63_0_129, yields: % 23.62/6.62 | (654) all_126_0_155 = all_63_0_129 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, 0, all_126_0_155 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_126_0_155, apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0, yields: % 23.62/6.62 | (635) all_126_0_155 = 0 % 23.62/6.62 | % 23.62/6.62 | Combining equations (635,811) yields a new equation: % 23.62/6.62 | (551) all_65_0_131 = 0 % 23.62/6.62 | % 23.62/6.62 | Combining equations (654,811) yields a new equation: % 23.62/6.62 | (799) all_65_0_131 = all_63_0_129 % 23.62/6.62 | % 23.62/6.62 | Combining equations (799,551) yields a new equation: % 23.62/6.62 | (627) all_63_0_129 = 0 % 23.62/6.62 | % 23.62/6.62 | Simplifying 627 yields: % 23.62/6.62 | (614) all_63_0_129 = 0 % 23.62/6.62 | % 23.62/6.62 | Equations (614) can reduce 619 to: % 23.62/6.62 | (109) $false % 23.62/6.62 | % 23.62/6.62 |-The branch is then unsatisfiable % 23.62/6.62 |-Branch two: % 23.62/6.62 | (630) ~ (all_123_0_151 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151 % 23.62/6.62 | % 23.62/6.62 | Applying alpha-rule on (630) yields: % 23.62/6.62 | (631) ~ (all_123_0_151 = 0) % 23.62/6.62 | (632) apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151 % 23.62/6.62 | % 23.62/6.62 +-Applying beta-rule and splitting (546), into two cases. % 23.62/6.62 |-Branch one: % 23.62/6.62 | (648) (all_124_0_152 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_124_0_152 = 0) & member(all_44_7_61, all_0_4_4) = all_124_0_152) % 23.62/6.62 | % 23.62/6.62 +-Applying beta-rule and splitting (648), into two cases. % 23.62/6.62 |-Branch one: % 23.62/6.62 | (649) all_124_0_152 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.62 | % 23.62/6.62 | Applying alpha-rule on (649) yields: % 23.62/6.62 | (650) all_124_0_152 = 0 % 23.62/6.62 | (615) apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, all_123_0_151, all_126_0_155 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_126_0_155, apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151, yields: % 23.62/6.62 | (652) all_126_0_155 = all_123_0_151 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, all_65_0_131, all_126_0_155 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_126_0_155, apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_65_0_131, yields: % 23.62/6.62 | (811) all_126_0_155 = all_65_0_131 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, all_63_0_129, all_123_0_151 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151, apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_63_0_129, yields: % 23.62/6.62 | (638) all_123_0_151 = all_63_0_129 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, 0, all_123_0_151 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151, apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0, yields: % 23.62/6.62 | (623) all_123_0_151 = 0 % 23.62/6.62 | % 23.62/6.62 | Combining equations (652,811) yields a new equation: % 23.62/6.62 | (830) all_123_0_151 = all_65_0_131 % 23.62/6.62 | % 23.62/6.62 | Simplifying 830 yields: % 23.62/6.62 | (831) all_123_0_151 = all_65_0_131 % 23.62/6.62 | % 23.62/6.62 | Combining equations (638,831) yields a new equation: % 23.62/6.62 | (799) all_65_0_131 = all_63_0_129 % 23.62/6.62 | % 23.62/6.62 | Combining equations (623,831) yields a new equation: % 23.62/6.62 | (551) all_65_0_131 = 0 % 23.62/6.62 | % 23.62/6.62 | Combining equations (799,551) yields a new equation: % 23.62/6.62 | (627) all_63_0_129 = 0 % 23.62/6.62 | % 23.62/6.62 | Simplifying 627 yields: % 23.62/6.62 | (614) all_63_0_129 = 0 % 23.62/6.62 | % 23.62/6.62 | Equations (614) can reduce 619 to: % 23.62/6.62 | (109) $false % 23.62/6.62 | % 23.62/6.62 |-The branch is then unsatisfiable % 23.62/6.62 |-Branch two: % 23.62/6.62 | (664) ~ (all_124_0_152 = 0) & member(all_44_7_61, all_0_4_4) = all_124_0_152 % 23.62/6.62 | % 23.62/6.62 | Applying alpha-rule on (664) yields: % 23.62/6.62 | (665) ~ (all_124_0_152 = 0) % 23.62/6.62 | (666) member(all_44_7_61, all_0_4_4) = all_124_0_152 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (88) with all_44_7_61, all_0_4_4, all_124_0_152, 0 and discharging atoms member(all_44_7_61, all_0_4_4) = all_124_0_152, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.62/6.62 | (650) all_124_0_152 = 0 % 23.62/6.62 | % 23.62/6.62 | Equations (650) can reduce 665 to: % 23.62/6.62 | (109) $false % 23.62/6.62 | % 23.62/6.62 |-The branch is then unsatisfiable % 23.62/6.62 |-Branch two: % 23.62/6.62 | (669) ~ (all_124_0_152 = 0) & member(all_44_8_62, all_0_4_4) = all_124_0_152 % 23.62/6.62 | % 23.62/6.62 | Applying alpha-rule on (669) yields: % 23.62/6.62 | (665) ~ (all_124_0_152 = 0) % 23.62/6.62 | (671) member(all_44_8_62, all_0_4_4) = all_124_0_152 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (88) with all_44_8_62, all_0_4_4, all_124_0_152, 0 and discharging atoms member(all_44_8_62, all_0_4_4) = all_124_0_152, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.62/6.62 | (650) all_124_0_152 = 0 % 23.62/6.62 | % 23.62/6.62 | Equations (650) can reduce 665 to: % 23.62/6.62 | (109) $false % 23.62/6.62 | % 23.62/6.62 |-The branch is then unsatisfiable % 23.62/6.62 |-Branch two: % 23.62/6.62 | (701) ~ (all_123_0_151 = 0) & member(all_44_8_62, all_0_4_4) = all_123_0_151 % 23.62/6.62 | % 23.62/6.62 | Applying alpha-rule on (701) yields: % 23.62/6.62 | (631) ~ (all_123_0_151 = 0) % 23.62/6.62 | (703) member(all_44_8_62, all_0_4_4) = all_123_0_151 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (88) with all_44_8_62, all_0_4_4, all_123_0_151, 0 and discharging atoms member(all_44_8_62, all_0_4_4) = all_123_0_151, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.62/6.62 | (623) all_123_0_151 = 0 % 23.62/6.62 | % 23.62/6.62 | Equations (623) can reduce 631 to: % 23.62/6.62 | (109) $false % 23.62/6.62 | % 23.62/6.62 |-The branch is then unsatisfiable % 23.62/6.62 |-Branch two: % 23.62/6.62 | (674) ~ (all_126_0_155 = 0) & member(all_44_7_61, all_0_4_4) = all_126_0_155 % 23.62/6.62 | % 23.62/6.62 | Applying alpha-rule on (674) yields: % 23.62/6.62 | (646) ~ (all_126_0_155 = 0) % 23.62/6.62 | (676) member(all_44_7_61, all_0_4_4) = all_126_0_155 % 23.62/6.62 | % 23.62/6.62 +-Applying beta-rule and splitting (545), into two cases. % 23.62/6.62 |-Branch one: % 23.62/6.62 | (621) (all_123_0_151 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_123_0_151 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151) % 23.62/6.62 | % 23.62/6.62 +-Applying beta-rule and splitting (621), into two cases. % 23.62/6.62 |-Branch one: % 23.62/6.62 | (622) all_123_0_151 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.62 | % 23.62/6.62 | Applying alpha-rule on (622) yields: % 23.62/6.62 | (623) all_123_0_151 = 0 % 23.62/6.62 | (615) apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, all_63_0_129, all_65_0_131 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_65_0_131, apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_63_0_129, yields: % 23.62/6.62 | (799) all_65_0_131 = all_63_0_129 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, 0, all_65_0_131 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_65_0_131, apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0, yields: % 23.62/6.62 | (551) all_65_0_131 = 0 % 23.62/6.62 | % 23.62/6.62 | Combining equations (799,551) yields a new equation: % 23.62/6.62 | (627) all_63_0_129 = 0 % 23.62/6.62 | % 23.62/6.62 | Simplifying 627 yields: % 23.62/6.62 | (614) all_63_0_129 = 0 % 23.62/6.62 | % 23.62/6.62 | Equations (614) can reduce 619 to: % 23.62/6.62 | (109) $false % 23.62/6.62 | % 23.62/6.62 |-The branch is then unsatisfiable % 23.62/6.62 |-Branch two: % 23.62/6.62 | (630) ~ (all_123_0_151 = 0) & apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151 % 23.62/6.62 | % 23.62/6.62 | Applying alpha-rule on (630) yields: % 23.62/6.62 | (631) ~ (all_123_0_151 = 0) % 23.62/6.62 | (632) apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151 % 23.62/6.62 | % 23.62/6.62 +-Applying beta-rule and splitting (546), into two cases. % 23.62/6.62 |-Branch one: % 23.62/6.62 | (648) (all_124_0_152 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0) | ( ~ (all_124_0_152 = 0) & member(all_44_7_61, all_0_4_4) = all_124_0_152) % 23.62/6.62 | % 23.62/6.62 +-Applying beta-rule and splitting (648), into two cases. % 23.62/6.62 |-Branch one: % 23.62/6.62 | (649) all_124_0_152 = 0 & apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.62 | % 23.62/6.62 | Applying alpha-rule on (649) yields: % 23.62/6.62 | (650) all_124_0_152 = 0 % 23.62/6.62 | (615) apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, all_65_0_131, all_123_0_151 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151, apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_65_0_131, yields: % 23.62/6.62 | (831) all_123_0_151 = all_65_0_131 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, all_63_0_129, all_65_0_131 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_65_0_131, apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_63_0_129, yields: % 23.62/6.62 | (799) all_65_0_131 = all_63_0_129 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_8_62, 0, all_123_0_151 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_8_62) = all_123_0_151, apply(all_0_2_2, all_44_7_61, all_44_8_62) = 0, yields: % 23.62/6.62 | (623) all_123_0_151 = 0 % 23.62/6.62 | % 23.62/6.62 | Combining equations (831,623) yields a new equation: % 23.62/6.62 | (874) all_65_0_131 = 0 % 23.62/6.62 | % 23.62/6.62 | Simplifying 874 yields: % 23.62/6.62 | (551) all_65_0_131 = 0 % 23.62/6.62 | % 23.62/6.62 | Combining equations (799,551) yields a new equation: % 23.62/6.62 | (627) all_63_0_129 = 0 % 23.62/6.62 | % 23.62/6.62 | Simplifying 627 yields: % 23.62/6.62 | (614) all_63_0_129 = 0 % 23.62/6.62 | % 23.62/6.62 | Equations (614) can reduce 619 to: % 23.62/6.62 | (109) $false % 23.62/6.62 | % 23.62/6.62 |-The branch is then unsatisfiable % 23.62/6.62 |-Branch two: % 23.62/6.62 | (664) ~ (all_124_0_152 = 0) & member(all_44_7_61, all_0_4_4) = all_124_0_152 % 23.62/6.62 | % 23.62/6.62 | Applying alpha-rule on (664) yields: % 23.62/6.62 | (665) ~ (all_124_0_152 = 0) % 23.62/6.62 | (666) member(all_44_7_61, all_0_4_4) = all_124_0_152 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (88) with all_44_7_61, all_0_4_4, all_126_0_155, 0 and discharging atoms member(all_44_7_61, all_0_4_4) = all_126_0_155, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.62/6.62 | (635) all_126_0_155 = 0 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (88) with all_44_7_61, all_0_4_4, all_124_0_152, all_126_0_155 and discharging atoms member(all_44_7_61, all_0_4_4) = all_126_0_155, member(all_44_7_61, all_0_4_4) = all_124_0_152, yields: % 23.62/6.62 | (693) all_126_0_155 = all_124_0_152 % 23.62/6.62 | % 23.62/6.62 | Combining equations (693,635) yields a new equation: % 23.62/6.62 | (884) all_124_0_152 = 0 % 23.62/6.62 | % 23.62/6.62 | Simplifying 884 yields: % 23.62/6.62 | (650) all_124_0_152 = 0 % 23.62/6.62 | % 23.62/6.62 | Equations (650) can reduce 665 to: % 23.62/6.62 | (109) $false % 23.62/6.62 | % 23.62/6.62 |-The branch is then unsatisfiable % 23.62/6.62 |-Branch two: % 23.62/6.62 | (669) ~ (all_124_0_152 = 0) & member(all_44_8_62, all_0_4_4) = all_124_0_152 % 23.62/6.62 | % 23.62/6.62 | Applying alpha-rule on (669) yields: % 23.62/6.62 | (665) ~ (all_124_0_152 = 0) % 23.62/6.62 | (671) member(all_44_8_62, all_0_4_4) = all_124_0_152 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (88) with all_44_8_62, all_0_4_4, all_124_0_152, 0 and discharging atoms member(all_44_8_62, all_0_4_4) = all_124_0_152, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.62/6.62 | (650) all_124_0_152 = 0 % 23.62/6.62 | % 23.62/6.62 | Equations (650) can reduce 665 to: % 23.62/6.62 | (109) $false % 23.62/6.62 | % 23.62/6.62 |-The branch is then unsatisfiable % 23.62/6.62 |-Branch two: % 23.62/6.62 | (701) ~ (all_123_0_151 = 0) & member(all_44_8_62, all_0_4_4) = all_123_0_151 % 23.62/6.62 | % 23.62/6.62 | Applying alpha-rule on (701) yields: % 23.62/6.62 | (631) ~ (all_123_0_151 = 0) % 23.62/6.62 | (703) member(all_44_8_62, all_0_4_4) = all_123_0_151 % 23.62/6.62 | % 23.62/6.62 | Instantiating formula (88) with all_44_8_62, all_0_4_4, all_123_0_151, 0 and discharging atoms member(all_44_8_62, all_0_4_4) = all_123_0_151, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.62/6.62 | (623) all_123_0_151 = 0 % 23.62/6.62 | % 23.62/6.62 | Equations (623) can reduce 631 to: % 23.62/6.62 | (109) $false % 23.62/6.62 | % 23.62/6.62 |-The branch is then unsatisfiable % 23.62/6.63 |-Branch two: % 23.62/6.63 | (706) ~ (all_63_0_129 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_63_0_129 % 23.62/6.63 | % 23.62/6.63 | Applying alpha-rule on (706) yields: % 23.62/6.63 | (619) ~ (all_63_0_129 = 0) % 23.62/6.63 | (708) apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_63_0_129 % 23.62/6.63 | % 23.62/6.63 | Instantiating formula (70) with all_0_2_2, all_44_8_62, all_44_8_62, all_63_0_129, 0 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_63_0_129, apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0, yields: % 23.62/6.63 | (614) all_63_0_129 = 0 % 23.62/6.63 | % 23.62/6.63 | Equations (614) can reduce 619 to: % 23.62/6.63 | (109) $false % 23.62/6.63 | % 23.62/6.63 |-The branch is then unsatisfiable % 23.62/6.63 |-Branch two: % 23.62/6.63 | (902) ~ (all_65_0_131 = 0) & apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_65_0_131 % 23.62/6.63 | % 23.62/6.63 | Applying alpha-rule on (902) yields: % 23.62/6.63 | (784) ~ (all_65_0_131 = 0) % 23.62/6.63 | (904) apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_65_0_131 % 23.62/6.63 | % 23.62/6.63 | Instantiating formula (70) with all_0_2_2, all_44_8_62, all_44_7_61, all_65_0_131, 0 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_65_0_131, apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0, yields: % 23.62/6.63 | (551) all_65_0_131 = 0 % 23.62/6.63 | % 23.62/6.63 | Equations (551) can reduce 784 to: % 23.62/6.63 | (109) $false % 23.62/6.63 | % 23.62/6.63 |-The branch is then unsatisfiable % 23.62/6.63 |-Branch two: % 23.62/6.63 | (907) ~ (all_71_0_138 = 0) & apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_71_0_138 % 23.62/6.63 | % 23.62/6.63 | Applying alpha-rule on (907) yields: % 23.62/6.63 | (908) ~ (all_71_0_138 = 0) % 23.62/6.63 | (909) apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_71_0_138 % 23.62/6.63 | % 23.62/6.63 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_7_61, 0, all_71_0_138 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_71_0_138, apply(all_0_2_2, all_44_7_61, all_44_7_61) = 0, yields: % 23.62/6.63 | (533) all_71_0_138 = 0 % 23.62/6.63 | % 23.62/6.63 | Equations (533) can reduce 908 to: % 23.62/6.63 | (109) $false % 23.62/6.63 | % 23.62/6.63 |-The branch is then unsatisfiable % 23.62/6.63 |-Branch two: % 23.62/6.63 | (912) ~ (all_71_0_138 = 0) & apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_71_0_138 % 23.62/6.63 | % 23.62/6.63 | Applying alpha-rule on (912) yields: % 23.62/6.63 | (908) ~ (all_71_0_138 = 0) % 23.62/6.63 | (914) apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_71_0_138 % 23.62/6.63 | % 23.62/6.63 | Instantiating formula (70) with all_0_2_2, all_44_8_62, all_44_7_61, 0, all_71_0_138 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_71_0_138, apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0, yields: % 23.62/6.63 | (533) all_71_0_138 = 0 % 23.62/6.63 | % 23.62/6.63 | Equations (533) can reduce 908 to: % 23.62/6.63 | (109) $false % 23.62/6.63 | % 23.62/6.63 |-The branch is then unsatisfiable % 23.62/6.63 |-Branch two: % 23.62/6.63 | (917) ~ (all_67_0_133 = 0) & apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_67_0_133 % 23.62/6.63 | % 23.62/6.63 | Applying alpha-rule on (917) yields: % 23.62/6.63 | (918) ~ (all_67_0_133 = 0) % 23.62/6.63 | (919) apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_67_0_133 % 23.62/6.63 | % 23.62/6.63 | Instantiating formula (70) with all_0_3_3, all_44_8_62, all_44_7_61, 0, all_67_0_133 and discharging atoms apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_67_0_133, apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0, yields: % 23.62/6.63 | (529) all_67_0_133 = 0 % 23.62/6.63 | % 23.62/6.63 | Equations (529) can reduce 918 to: % 23.62/6.63 | (109) $false % 23.62/6.63 | % 23.62/6.63 |-The branch is then unsatisfiable % 23.62/6.63 |-Branch two: % 23.62/6.63 | (922) ~ (all_67_0_133 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_67_0_133 % 23.62/6.63 | % 23.62/6.63 | Applying alpha-rule on (922) yields: % 23.62/6.63 | (918) ~ (all_67_0_133 = 0) % 23.62/6.63 | (924) apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_67_0_133 % 23.62/6.63 | % 23.62/6.63 | Instantiating formula (70) with all_0_3_3, all_44_8_62, all_44_8_62, 0, all_67_0_133 and discharging atoms apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_67_0_133, apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0, yields: % 23.62/6.63 | (529) all_67_0_133 = 0 % 23.62/6.63 | % 23.62/6.63 | Equations (529) can reduce 918 to: % 23.62/6.63 | (109) $false % 23.62/6.63 | % 23.62/6.63 |-The branch is then unsatisfiable % 23.62/6.63 |-Branch two: % 23.62/6.63 | (927) ~ (all_64_0_130 = 0) & apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_64_0_130 % 23.62/6.63 | % 23.62/6.63 | Applying alpha-rule on (927) yields: % 23.62/6.63 | (928) ~ (all_64_0_130 = 0) % 23.62/6.63 | (929) apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_64_0_130 % 23.62/6.63 | % 23.62/6.63 | Instantiating formula (70) with all_0_2_2, all_44_8_62, all_44_7_61, 0, all_64_0_130 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_7_61) = all_64_0_130, apply(all_0_2_2, all_44_8_62, all_44_7_61) = 0, yields: % 23.62/6.63 | (525) all_64_0_130 = 0 % 23.62/6.63 | % 23.62/6.63 | Equations (525) can reduce 928 to: % 23.62/6.63 | (109) $false % 23.62/6.63 | % 23.62/6.63 |-The branch is then unsatisfiable % 23.62/6.63 |-Branch two: % 23.62/6.63 | (932) ~ (all_64_0_130 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_64_0_130 % 23.62/6.63 | % 23.62/6.63 | Applying alpha-rule on (932) yields: % 23.62/6.63 | (928) ~ (all_64_0_130 = 0) % 23.62/6.63 | (934) apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_64_0_130 % 23.62/6.63 | % 23.62/6.63 | Instantiating formula (70) with all_0_2_2, all_44_8_62, all_44_8_62, 0, all_64_0_130 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_64_0_130, apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0, yields: % 23.62/6.63 | (525) all_64_0_130 = 0 % 23.62/6.63 | % 23.62/6.63 | Equations (525) can reduce 928 to: % 23.62/6.63 | (109) $false % 23.62/6.63 | % 23.62/6.63 |-The branch is then unsatisfiable % 23.62/6.63 |-Branch two: % 23.62/6.63 | (937) ~ (all_61_0_127 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_61_0_127 % 23.62/6.63 | % 23.62/6.63 | Applying alpha-rule on (937) yields: % 23.62/6.63 | (938) ~ (all_61_0_127 = 0) % 23.62/6.63 | (939) apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_61_0_127 % 23.62/6.63 | % 23.62/6.63 | Instantiating formula (70) with all_0_3_3, all_44_8_62, all_44_8_62, 0, all_61_0_127 and discharging atoms apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_61_0_127, apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0, yields: % 23.62/6.63 | (521) all_61_0_127 = 0 % 23.62/6.63 | % 23.62/6.63 | Equations (521) can reduce 938 to: % 23.62/6.63 | (109) $false % 23.62/6.63 | % 23.62/6.63 |-The branch is then unsatisfiable % 23.62/6.63 |-Branch two: % 23.62/6.63 | (942) ~ (all_70_0_137 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_70_0_137 % 23.62/6.63 | % 23.62/6.63 | Applying alpha-rule on (942) yields: % 23.62/6.63 | (943) ~ (all_70_0_137 = 0) % 23.62/6.63 | (944) apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_70_0_137 % 23.62/6.63 | % 23.62/6.63 | Instantiating formula (70) with all_0_3_3, all_44_7_61, all_44_7_61, 0, all_70_0_137 and discharging atoms apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_70_0_137, apply(all_0_3_3, all_44_7_61, all_44_7_61) = 0, yields: % 23.62/6.63 | (518) all_70_0_137 = 0 % 23.62/6.63 | % 23.62/6.63 | Equations (518) can reduce 943 to: % 23.62/6.63 | (109) $false % 23.62/6.63 | % 23.62/6.63 |-The branch is then unsatisfiable % 23.62/6.63 |-Branch two: % 23.62/6.63 | (947) ~ (all_70_0_137 = 0) & apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_70_0_137 % 23.62/6.63 | % 23.62/6.63 | Applying alpha-rule on (947) yields: % 23.62/6.63 | (943) ~ (all_70_0_137 = 0) % 23.62/6.63 | (949) apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_70_0_137 % 23.62/6.63 | % 23.62/6.63 | Instantiating formula (70) with all_0_3_3, all_44_8_62, all_44_7_61, 0, all_70_0_137 and discharging atoms apply(all_0_3_3, all_44_8_62, all_44_7_61) = all_70_0_137, apply(all_0_3_3, all_44_8_62, all_44_7_61) = 0, yields: % 23.62/6.63 | (518) all_70_0_137 = 0 % 23.62/6.63 | % 23.62/6.63 | Equations (518) can reduce 943 to: % 23.62/6.63 | (109) $false % 23.62/6.63 | % 23.62/6.63 |-The branch is then unsatisfiable % 23.62/6.63 |-Branch two: % 23.62/6.63 | (952) ~ (all_60_1_126 = 0) & member(all_44_7_61, all_0_4_4) = all_60_1_126 % 23.62/6.63 | % 23.62/6.63 | Applying alpha-rule on (952) yields: % 23.62/6.63 | (953) ~ (all_60_1_126 = 0) % 23.62/6.63 | (954) member(all_44_7_61, all_0_4_4) = all_60_1_126 % 23.62/6.63 | % 23.62/6.63 | Instantiating formula (88) with all_44_7_61, all_0_4_4, all_60_1_126, 0 and discharging atoms member(all_44_7_61, all_0_4_4) = all_60_1_126, member(all_44_7_61, all_0_4_4) = 0, yields: % 23.62/6.63 | (513) all_60_1_126 = 0 % 23.62/6.63 | % 23.62/6.63 | Equations (513) can reduce 953 to: % 23.62/6.63 | (109) $false % 23.62/6.63 | % 23.62/6.63 |-The branch is then unsatisfiable % 23.62/6.63 |-Branch two: % 23.62/6.63 | (957) ~ (all_60_1_126 = 0) & member(all_44_8_62, all_0_4_4) = all_60_1_126 % 23.62/6.63 | % 23.62/6.63 | Applying alpha-rule on (957) yields: % 23.62/6.63 | (953) ~ (all_60_1_126 = 0) % 23.62/6.63 | (959) member(all_44_8_62, all_0_4_4) = all_60_1_126 % 23.62/6.63 | % 23.62/6.63 | Instantiating formula (88) with all_44_8_62, all_0_4_4, all_60_1_126, 0 and discharging atoms member(all_44_8_62, all_0_4_4) = all_60_1_126, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.62/6.63 | (513) all_60_1_126 = 0 % 23.62/6.63 | % 23.62/6.63 | Equations (513) can reduce 953 to: % 23.62/6.63 | (109) $false % 23.62/6.63 | % 23.62/6.63 |-The branch is then unsatisfiable % 23.62/6.63 |-Branch two: % 23.62/6.63 | (962) ~ (all_59_0_124 = 0) & apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_59_0_124 % 23.62/6.63 | % 23.62/6.63 | Applying alpha-rule on (962) yields: % 23.62/6.63 | (963) ~ (all_59_0_124 = 0) % 23.62/6.63 | (964) apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_59_0_124 % 23.62/6.63 | % 23.62/6.63 | Instantiating formula (70) with all_0_2_2, all_44_7_61, all_44_7_61, 0, all_59_0_124 and discharging atoms apply(all_0_2_2, all_44_7_61, all_44_7_61) = all_59_0_124, apply(all_0_2_2, all_44_7_61, all_44_7_61) = 0, yields: % 23.62/6.63 | (508) all_59_0_124 = 0 % 23.62/6.63 | % 23.62/6.63 | Equations (508) can reduce 963 to: % 23.62/6.63 | (109) $false % 23.62/6.63 | % 23.62/6.63 |-The branch is then unsatisfiable % 23.62/6.63 |-Branch two: % 23.62/6.63 | (967) ~ (all_62_0_128 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_62_0_128 % 23.62/6.63 | % 23.62/6.63 | Applying alpha-rule on (967) yields: % 23.62/6.63 | (968) ~ (all_62_0_128 = 0) % 23.62/6.63 | (969) apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_62_0_128 % 23.62/6.63 | % 23.62/6.63 | Instantiating formula (70) with all_0_2_2, all_44_8_62, all_44_8_62, 0, all_62_0_128 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_62_0_128, apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0, yields: % 23.62/6.63 | (505) all_62_0_128 = 0 % 23.62/6.63 | % 23.62/6.63 | Equations (505) can reduce 968 to: % 23.62/6.63 | (109) $false % 23.62/6.63 | % 23.62/6.63 |-The branch is then unsatisfiable % 23.62/6.63 |-Branch two: % 23.62/6.63 | (972) ~ (all_58_0_123 = 0) & apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_58_0_123 % 23.62/6.63 | % 23.62/6.63 | Applying alpha-rule on (972) yields: % 23.62/6.63 | (973) ~ (all_58_0_123 = 0) % 23.62/6.63 | (974) apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_58_0_123 % 23.62/6.63 | % 23.62/6.63 | Instantiating formula (70) with all_0_3_3, all_44_7_61, all_44_7_61, 0, all_58_0_123 and discharging atoms apply(all_0_3_3, all_44_7_61, all_44_7_61) = all_58_0_123, apply(all_0_3_3, all_44_7_61, all_44_7_61) = 0, yields: % 23.62/6.63 | (502) all_58_0_123 = 0 % 23.62/6.63 | % 23.62/6.63 | Equations (502) can reduce 973 to: % 23.62/6.63 | (109) $false % 23.62/6.63 | % 23.62/6.63 |-The branch is then unsatisfiable % 23.62/6.63 |-Branch two: % 23.62/6.63 | (977) all_44_7_61 = 0 & ~ (all_44_6_60 = 0) & apply(all_0_1_1, all_44_8_62, all_44_8_62) = all_44_6_60 & member(all_44_8_62, all_0_4_4) = 0 % 23.62/6.63 | % 23.62/6.63 | Applying alpha-rule on (977) yields: % 23.62/6.63 | (978) all_44_7_61 = 0 % 23.62/6.63 | (979) ~ (all_44_6_60 = 0) % 23.62/6.63 | (980) apply(all_0_1_1, all_44_8_62, all_44_8_62) = all_44_6_60 % 23.62/6.63 | (121) member(all_44_8_62, all_0_4_4) = 0 % 23.62/6.63 | % 23.62/6.63 | Instantiating formula (93) with all_44_6_60, all_44_8_62, all_44_8_62 and discharging atoms apply(all_0_1_1, all_44_8_62, all_44_8_62) = all_44_6_60, yields: % 23.62/6.63 | (982) ? [v0] : ? [v1] : (( ~ (v0 = 0) & member(all_44_8_62, all_0_4_4) = v0) | (( ~ (all_44_6_60 = 0) | (v1 = 0 & v0 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0 & apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0)) & (all_44_6_60 = 0 | ( ~ (v1 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = v1) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = v0)))) % 23.62/6.64 | % 23.62/6.64 | Instantiating formula (76) with all_44_8_62, all_44_8_62, all_44_8_62, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.62/6.64 | (145) ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = v0)) % 23.62/6.64 | % 23.62/6.64 | Instantiating formula (59) with all_44_8_62, all_0_2_2, all_0_4_4 and discharging atoms equivalence(all_0_2_2, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.62/6.64 | (146) apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0 % 23.62/6.64 | % 23.62/6.64 | Instantiating formula (76) with all_44_8_62, all_44_8_62, all_44_8_62, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.62/6.64 | (152) ? [v0] : ((v0 = 0 & apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0) | ( ~ (v0 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = v0)) % 23.62/6.64 | % 23.62/6.64 | Instantiating formula (59) with all_44_8_62, all_0_3_3, all_0_4_4 and discharging atoms equivalence(all_0_3_3, all_0_4_4) = 0, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.62/6.64 | (153) apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0 % 23.62/6.64 | % 23.62/6.64 | Instantiating (145) with all_58_0_161 yields: % 23.62/6.64 | (987) (all_58_0_161 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0) | ( ~ (all_58_0_161 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_58_0_161) % 23.62/6.64 | % 23.62/6.64 | Instantiating (982) with all_59_0_162, all_59_1_163 yields: % 23.62/6.64 | (988) ( ~ (all_59_1_163 = 0) & member(all_44_8_62, all_0_4_4) = all_59_1_163) | (( ~ (all_44_6_60 = 0) | (all_59_0_162 = 0 & all_59_1_163 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0 & apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0)) & (all_44_6_60 = 0 | ( ~ (all_59_0_162 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_59_0_162) | ( ~ (all_59_1_163 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_59_1_163))) % 23.62/6.64 | % 23.62/6.64 | Instantiating (152) with all_60_0_164 yields: % 23.62/6.64 | (989) (all_60_0_164 = 0 & apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0) | ( ~ (all_60_0_164 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_60_0_164) % 23.62/6.64 | % 23.62/6.64 +-Applying beta-rule and splitting (988), into two cases. % 23.62/6.64 |-Branch one: % 23.62/6.64 | (990) ~ (all_59_1_163 = 0) & member(all_44_8_62, all_0_4_4) = all_59_1_163 % 23.62/6.64 | % 23.62/6.64 | Applying alpha-rule on (990) yields: % 23.62/6.64 | (991) ~ (all_59_1_163 = 0) % 23.62/6.64 | (992) member(all_44_8_62, all_0_4_4) = all_59_1_163 % 23.62/6.64 | % 23.62/6.64 | Instantiating formula (88) with all_44_8_62, all_0_4_4, all_59_1_163, 0 and discharging atoms member(all_44_8_62, all_0_4_4) = all_59_1_163, member(all_44_8_62, all_0_4_4) = 0, yields: % 23.62/6.64 | (993) all_59_1_163 = 0 % 23.62/6.64 | % 23.62/6.64 | Equations (993) can reduce 991 to: % 23.62/6.64 | (109) $false % 23.62/6.64 | % 23.62/6.64 |-The branch is then unsatisfiable % 23.62/6.64 |-Branch two: % 23.62/6.64 | (995) ( ~ (all_44_6_60 = 0) | (all_59_0_162 = 0 & all_59_1_163 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0 & apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0)) & (all_44_6_60 = 0 | ( ~ (all_59_0_162 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_59_0_162) | ( ~ (all_59_1_163 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_59_1_163)) % 23.62/6.64 | % 23.62/6.64 | Applying alpha-rule on (995) yields: % 23.62/6.64 | (996) ~ (all_44_6_60 = 0) | (all_59_0_162 = 0 & all_59_1_163 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0 & apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0) % 23.62/6.64 | (997) all_44_6_60 = 0 | ( ~ (all_59_0_162 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_59_0_162) | ( ~ (all_59_1_163 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_59_1_163) % 23.62/6.64 | % 23.62/6.64 +-Applying beta-rule and splitting (987), into two cases. % 23.62/6.64 |-Branch one: % 23.62/6.64 | (998) all_58_0_161 = 0 & apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0 % 23.62/6.64 | % 23.62/6.64 | Applying alpha-rule on (998) yields: % 23.62/6.64 | (999) all_58_0_161 = 0 % 23.62/6.64 | (146) apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0 % 23.62/6.64 | % 23.62/6.64 +-Applying beta-rule and splitting (997), into two cases. % 23.62/6.64 |-Branch one: % 23.62/6.64 | (463) all_44_6_60 = 0 % 23.62/6.64 | % 23.62/6.64 | Equations (463) can reduce 979 to: % 23.62/6.64 | (109) $false % 23.62/6.64 | % 23.62/6.64 |-The branch is then unsatisfiable % 23.62/6.64 |-Branch two: % 23.62/6.64 | (979) ~ (all_44_6_60 = 0) % 23.62/6.64 | (1004) ( ~ (all_59_0_162 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_59_0_162) | ( ~ (all_59_1_163 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_59_1_163) % 23.62/6.64 | % 23.62/6.64 +-Applying beta-rule and splitting (989), into two cases. % 23.62/6.64 |-Branch one: % 23.62/6.64 | (1005) all_60_0_164 = 0 & apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0 % 23.62/6.64 | % 23.62/6.64 | Applying alpha-rule on (1005) yields: % 23.62/6.64 | (1006) all_60_0_164 = 0 % 23.62/6.64 | (153) apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0 % 23.62/6.64 | % 23.62/6.64 +-Applying beta-rule and splitting (1004), into two cases. % 23.62/6.64 |-Branch one: % 23.62/6.64 | (1008) ~ (all_59_0_162 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_59_0_162 % 23.62/6.64 | % 23.62/6.64 | Applying alpha-rule on (1008) yields: % 23.62/6.64 | (1009) ~ (all_59_0_162 = 0) % 23.62/6.64 | (1010) apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_59_0_162 % 23.62/6.64 | % 23.62/6.64 | Instantiating formula (70) with all_0_2_2, all_44_8_62, all_44_8_62, 0, all_59_0_162 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_59_0_162, apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0, yields: % 23.62/6.64 | (1011) all_59_0_162 = 0 % 23.62/6.64 | % 23.62/6.64 | Equations (1011) can reduce 1009 to: % 23.62/6.64 | (109) $false % 23.62/6.64 | % 23.62/6.64 |-The branch is then unsatisfiable % 23.62/6.64 |-Branch two: % 23.62/6.64 | (1013) ~ (all_59_1_163 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_59_1_163 % 23.62/6.64 | % 23.62/6.64 | Applying alpha-rule on (1013) yields: % 23.62/6.64 | (991) ~ (all_59_1_163 = 0) % 23.62/6.64 | (1015) apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_59_1_163 % 23.62/6.64 | % 23.62/6.64 | Instantiating formula (70) with all_0_3_3, all_44_8_62, all_44_8_62, 0, all_59_1_163 and discharging atoms apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_59_1_163, apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0, yields: % 23.62/6.64 | (993) all_59_1_163 = 0 % 23.62/6.64 | % 23.62/6.64 | Equations (993) can reduce 991 to: % 23.62/6.64 | (109) $false % 23.62/6.64 | % 23.62/6.64 |-The branch is then unsatisfiable % 23.62/6.64 |-Branch two: % 23.62/6.64 | (1018) ~ (all_60_0_164 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_60_0_164 % 23.62/6.64 | % 23.62/6.64 | Applying alpha-rule on (1018) yields: % 23.62/6.64 | (1019) ~ (all_60_0_164 = 0) % 23.62/6.64 | (1020) apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_60_0_164 % 23.62/6.64 | % 23.62/6.64 +-Applying beta-rule and splitting (1004), into two cases. % 23.62/6.64 |-Branch one: % 23.62/6.64 | (1008) ~ (all_59_0_162 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_59_0_162 % 23.62/6.64 | % 23.62/6.64 | Applying alpha-rule on (1008) yields: % 23.62/6.64 | (1009) ~ (all_59_0_162 = 0) % 23.62/6.64 | (1010) apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_59_0_162 % 23.62/6.64 | % 23.62/6.64 | Instantiating formula (70) with all_0_2_2, all_44_8_62, all_44_8_62, 0, all_59_0_162 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_59_0_162, apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0, yields: % 23.62/6.64 | (1011) all_59_0_162 = 0 % 23.62/6.64 | % 23.62/6.64 | Equations (1011) can reduce 1009 to: % 23.62/6.64 | (109) $false % 23.62/6.64 | % 23.62/6.64 |-The branch is then unsatisfiable % 23.62/6.64 |-Branch two: % 23.62/6.64 | (1013) ~ (all_59_1_163 = 0) & apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_59_1_163 % 23.62/6.64 | % 23.62/6.64 | Applying alpha-rule on (1013) yields: % 23.62/6.64 | (991) ~ (all_59_1_163 = 0) % 23.62/6.64 | (1015) apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_59_1_163 % 23.62/6.64 | % 23.62/6.64 | Instantiating formula (70) with all_0_3_3, all_44_8_62, all_44_8_62, all_59_1_163, all_60_0_164 and discharging atoms apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_60_0_164, apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_59_1_163, yields: % 23.62/6.64 | (1029) all_60_0_164 = all_59_1_163 % 23.62/6.64 | % 23.62/6.64 | Instantiating formula (70) with all_0_3_3, all_44_8_62, all_44_8_62, 0, all_60_0_164 and discharging atoms apply(all_0_3_3, all_44_8_62, all_44_8_62) = all_60_0_164, apply(all_0_3_3, all_44_8_62, all_44_8_62) = 0, yields: % 23.62/6.64 | (1006) all_60_0_164 = 0 % 23.62/6.64 | % 23.62/6.64 | Combining equations (1006,1029) yields a new equation: % 23.62/6.64 | (993) all_59_1_163 = 0 % 23.62/6.64 | % 23.62/6.64 | Equations (993) can reduce 991 to: % 23.62/6.64 | (109) $false % 23.62/6.64 | % 23.62/6.64 |-The branch is then unsatisfiable % 23.62/6.64 |-Branch two: % 23.62/6.64 | (1033) ~ (all_58_0_161 = 0) & apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_58_0_161 % 23.62/6.64 | % 23.62/6.64 | Applying alpha-rule on (1033) yields: % 23.62/6.64 | (1034) ~ (all_58_0_161 = 0) % 23.62/6.64 | (1035) apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_58_0_161 % 23.62/6.64 | % 23.62/6.64 | Instantiating formula (70) with all_0_2_2, all_44_8_62, all_44_8_62, 0, all_58_0_161 and discharging atoms apply(all_0_2_2, all_44_8_62, all_44_8_62) = all_58_0_161, apply(all_0_2_2, all_44_8_62, all_44_8_62) = 0, yields: % 23.62/6.64 | (999) all_58_0_161 = 0 % 23.62/6.64 | % 23.62/6.64 | Equations (999) can reduce 1034 to: % 23.62/6.64 | (109) $false % 23.62/6.64 | % 23.62/6.64 |-The branch is then unsatisfiable % 23.62/6.64 % SZS output end Proof for theBenchmark % 23.62/6.64 % 23.62/6.64 6033ms %------------------------------------------------------------------------------