%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET757+4 : TPTP v8.1.0. Bugfixed v2.2.1. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n023.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 00:21:52 EDT 2022 % Result : Theorem 7.13s 2.25s % Output : Proof 11.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SET757+4 : TPTP v8.1.0. Bugfixed v2.2.1. % 0.04/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n023.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sun Jul 10 08:31:55 EDT 2022 % 0.12/0.33 % CPUTime : % 0.52/0.62 ____ _ % 0.52/0.62 ___ / __ \_____(_)___ ________ __________ % 0.52/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.52/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.52/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.52/0.62 % 0.52/0.62 A Theorem Prover for First-Order Logic % 0.66/0.62 (ePrincess v.1.0) % 0.66/0.62 % 0.66/0.62 (c) Philipp Rümmer, 2009-2015 % 0.66/0.62 (c) Peter Backeman, 2014-2015 % 0.66/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.66/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.66/0.62 Bug reports to peter@backeman.se % 0.66/0.62 % 0.66/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.66/0.62 % 0.66/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.74/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.06/1.06 Prover 0: Preprocessing ... % 3.34/1.42 Prover 0: Warning: ignoring some quantifiers % 3.63/1.45 Prover 0: Constructing countermodel ... % 4.98/1.77 Prover 0: gave up % 4.98/1.77 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 5.16/1.82 Prover 1: Preprocessing ... % 6.01/2.06 Prover 1: Constructing countermodel ... % 7.13/2.25 Prover 1: proved (478ms) % 7.13/2.25 % 7.13/2.25 No countermodel exists, formula is valid % 7.13/2.25 % SZS status Theorem for theBenchmark % 7.13/2.25 % 7.13/2.25 Generating proof ... found it (size 178) % 10.91/3.10 % 10.91/3.10 % SZS output start Proof for theBenchmark % 10.91/3.10 Assumed formulas after preprocessing and simplification: % 10.91/3.10 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & inverse_image3(v0, v5, v1) = v6 & inverse_image3(v0, v4, v1) = v8 & inverse_image3(v0, v3, v1) = v7 & maps(v0, v1, v2) = 0 & intersection(v7, v8) = v9 & intersection(v3, v4) = v5 & equal_set(v6, v9) = v10 & subset(v4, v2) = 0 & subset(v3, v2) = 0 & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v19 = 0 | ~ (compose_function(v11, v12, v13, v14, v15) = v18) | ~ (apply(v18, v16, v17) = v19) | ~ (apply(v11, v20, v17) = 0) | ? [v21] : ? [v22] : ((apply(v12, v16, v20) = v22 & member(v20, v14) = v21 & ( ~ (v22 = 0) | ~ (v21 = 0))) | (member(v17, v15) = v22 & member(v16, v13) = v21 & ( ~ (v22 = 0) | ~ (v21 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v19 = 0 | ~ (compose_predicate(v11, v12, v13, v14, v15, v16) = 0) | ~ (apply(v12, v20, v18) = 0) | ~ (apply(v11, v17, v18) = v19) | ? [v21] : ? [v22] : ((apply(v13, v17, v20) = v22 & member(v20, v15) = v21 & ( ~ (v22 = 0) | ~ (v21 = 0))) | (member(v18, v16) = v22 & member(v17, v14) = v21 & ( ~ (v22 = 0) | ~ (v21 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (isomorphism(v11, v12, v13, v14, v15) = 0) | ~ (apply(v11, v18, v19) = 0) | ~ (apply(v11, v16, v17) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (apply(v15, v17, v19) = v25 & apply(v13, v16, v18) = v24 & member(v19, v14) = v23 & member(v18, v12) = v22 & member(v17, v14) = v21 & member(v16, v12) = v20 & ( ~ (v23 = 0) | ~ (v22 = 0) | ~ (v21 = 0) | ~ (v20 = 0) | (( ~ (v25 = 0) | v24 = 0) & ( ~ (v24 = 0) | v25 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (decreasing(v11, v12, v13, v14, v15) = 0) | ~ (apply(v11, v18, v19) = 0) | ~ (apply(v11, v16, v17) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (apply(v15, v19, v17) = v25 & apply(v13, v16, v18) = v24 & member(v19, v14) = v23 & member(v18, v12) = v22 & member(v17, v14) = v21 & member(v16, v12) = v20 & ( ~ (v24 = 0) | ~ (v23 = 0) | ~ (v22 = 0) | ~ (v21 = 0) | ~ (v20 = 0) | v25 = 0))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (increasing(v11, v12, v13, v14, v15) = 0) | ~ (apply(v11, v18, v19) = 0) | ~ (apply(v11, v16, v17) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (apply(v15, v17, v19) = v25 & apply(v13, v16, v18) = v24 & member(v19, v14) = v23 & member(v18, v12) = v22 & member(v17, v14) = v21 & member(v16, v12) = v20 & ( ~ (v24 = 0) | ~ (v23 = 0) | ~ (v22 = 0) | ~ (v21 = 0) | ~ (v20 = 0) | v25 = 0))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v12 = v11 | ~ (compose_predicate(v18, v17, v16, v15, v14, v13) = v12) | ~ (compose_predicate(v18, v17, v16, v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (compose_function(v11, v12, v13, v14, v15) = v18) | ~ (apply(v18, v16, v17) = 0) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ((v22 = 0 & v21 = 0 & v20 = 0 & apply(v12, v16, v19) = 0 & apply(v11, v19, v17) = 0 & member(v19, v14) = 0) | (member(v17, v15) = v20 & member(v16, v13) = v19 & ( ~ (v20 = 0) | ~ (v19 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (compose_predicate(v11, v12, v13, v14, v15, v16) = 0) | ~ (apply(v11, v17, v18) = 0) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ((v22 = 0 & v21 = 0 & v20 = 0 & apply(v13, v17, v19) = 0 & apply(v12, v19, v18) = 0 & member(v19, v15) = 0) | (member(v18, v16) = v20 & member(v17, v14) = v19 & ( ~ (v20 = 0) | ~ (v19 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ (equal_maps(v11, v12, v13, v14) = 0) | ~ (apply(v12, v15, v17) = 0) | ~ (apply(v11, v15, v16) = 0) | ? [v18] : ? [v19] : ? [v20] : (member(v17, v14) = v20 & member(v16, v14) = v19 & member(v15, v13) = v18 & ( ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (compose_predicate(v11, v12, v13, v14, v15, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (apply(v11, v18, v19) = v20 & member(v19, v16) = 0 & member(v18, v14) = 0 & ( ~ (v20 = 0) | ! [v25] : ( ~ (apply(v12, v25, v19) = 0) | ? [v26] : ? [v27] : (apply(v13, v18, v25) = v27 & member(v25, v15) = v26 & ( ~ (v27 = 0) | ~ (v26 = 0))))) & (v20 = 0 | (v24 = 0 & v23 = 0 & v22 = 0 & apply(v13, v18, v21) = 0 & apply(v12, v21, v19) = 0 & member(v21, v15) = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v16 = 0 | ~ (inverse_image3(v11, v12, v13) = v15) | ~ (apply(v11, v14, v17) = 0) | ~ (member(v14, v15) = v16) | ? [v18] : (( ~ (v18 = 0) & member(v17, v12) = v18) | ( ~ (v18 = 0) & member(v14, v13) = v18))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v16 = 0 | ~ (image3(v11, v12, v13) = v15) | ~ (apply(v11, v17, v14) = 0) | ~ (member(v14, v15) = v16) | ? [v18] : (( ~ (v18 = 0) & member(v17, v12) = v18) | ( ~ (v18 = 0) & member(v14, v13) = v18))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v12 = v11 | ~ (isomorphism(v17, v16, v15, v14, v13) = v12) | ~ (isomorphism(v17, v16, v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v12 = v11 | ~ (decreasing(v17, v16, v15, v14, v13) = v12) | ~ (decreasing(v17, v16, v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v12 = v11 | ~ (increasing(v17, v16, v15, v14, v13) = v12) | ~ (increasing(v17, v16, v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v12 = v11 | ~ (compose_function(v17, v16, v15, v14, v13) = v12) | ~ (compose_function(v17, v16, v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (inverse_function(v11, v12, v13) = v16) | ~ (apply(v16, v15, v14) = v17) | ? [v18] : ? [v19] : ? [v20] : (apply(v11, v14, v15) = v20 & member(v15, v13) = v19 & member(v14, v12) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0) | (( ~ (v20 = 0) | v17 = 0) & ( ~ (v17 = 0) | v20 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (inverse_predicate(v11, v12, v13, v14) = 0) | ~ (apply(v11, v16, v15) = v17) | ? [v18] : ? [v19] : ? [v20] : (apply(v12, v15, v16) = v20 & member(v16, v14) = v19 & member(v15, v13) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0) | (( ~ (v20 = 0) | v17 = 0) & ( ~ (v17 = 0) | v20 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v15 | ~ (maps(v11, v12, v13) = 0) | ~ (apply(v11, v14, v16) = 0) | ~ (apply(v11, v14, v15) = 0) | ? [v17] : ? [v18] : ? [v19] : (member(v16, v13) = v19 & member(v15, v13) = v18 & member(v14, v12) = v17 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (isomorphism(v11, v12, v13, v14, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ((v26 = 0 & v25 = 0 & v24 = 0 & v23 = 0 & v22 = 0 & v21 = 0 & apply(v15, v18, v20) = v28 & apply(v13, v17, v19) = v27 & apply(v11, v19, v20) = 0 & apply(v11, v17, v18) = 0 & member(v20, v14) = 0 & member(v19, v12) = 0 & member(v18, v14) = 0 & member(v17, v12) = 0 & ( ~ (v28 = 0) | ~ (v27 = 0)) & (v28 = 0 | v27 = 0)) | (one_to_one(v11, v12, v14) = v18 & maps(v11, v12, v14) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (decreasing(v11, v12, v13, v14, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ( ~ (v21 = 0) & apply(v15, v20, v18) = v21 & apply(v13, v17, v19) = 0 & apply(v11, v19, v20) = 0 & apply(v11, v17, v18) = 0 & member(v20, v14) = 0 & member(v19, v12) = 0 & member(v18, v14) = 0 & member(v17, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (increasing(v11, v12, v13, v14, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ( ~ (v21 = 0) & apply(v15, v18, v20) = v21 & apply(v13, v17, v19) = 0 & apply(v11, v19, v20) = 0 & apply(v11, v17, v18) = 0 & member(v20, v14) = 0 & member(v19, v12) = 0 & member(v18, v14) = 0 & member(v17, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (injective(v11, v12, v13) = 0) | ~ (apply(v11, v15, v16) = 0) | ~ (apply(v11, v14, v16) = 0) | ? [v17] : ? [v18] : ? [v19] : (member(v16, v13) = v19 & member(v15, v12) = v18 & member(v14, v12) = v17 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (inverse_image2(v11, v12) = v14) | ~ (apply(v11, v13, v16) = 0) | ~ (member(v13, v14) = v15) | ? [v17] : ( ~ (v17 = 0) & member(v16, v12) = v17)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (image2(v11, v12) = v14) | ~ (apply(v11, v16, v13) = 0) | ~ (member(v13, v14) = v15) | ? [v17] : ( ~ (v17 = 0) & member(v16, v12) = v17)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v12 = v11 | ~ (inverse_predicate(v16, v15, v14, v13) = v12) | ~ (inverse_predicate(v16, v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v12 = v11 | ~ (equal_maps(v16, v15, v14, v13) = v12) | ~ (equal_maps(v16, v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (inverse_predicate(v11, v12, v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (apply(v12, v16, v17) = v18 & apply(v11, v17, v16) = v19 & member(v17, v14) = 0 & member(v16, v13) = 0 & ( ~ (v19 = 0) | ~ (v18 = 0)) & (v19 = 0 | v18 = 0))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (equal_maps(v11, v12, v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = v17) & apply(v12, v16, v18) = 0 & apply(v11, v16, v17) = 0 & member(v18, v14) = 0 & member(v17, v14) = 0 & member(v16, v13) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (product(v12) = v13) | ~ (member(v11, v14) = v15) | ~ (member(v11, v13) = 0) | ? [v16] : ( ~ (v16 = 0) & member(v14, v12) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (difference(v13, v12) = v14) | ~ (member(v11, v14) = v15) | ? [v16] : ? [v17] : (member(v11, v13) = v16 & member(v11, v12) = v17 & ( ~ (v16 = 0) | v17 = 0))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (union(v12, v13) = v14) | ~ (member(v11, v14) = v15) | ? [v16] : ? [v17] : ( ~ (v17 = 0) & ~ (v16 = 0) & member(v11, v13) = v17 & member(v11, v12) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (intersection(v12, v13) = v14) | ~ (member(v11, v14) = v15) | ? [v16] : ? [v17] : (member(v11, v13) = v17 & member(v11, v12) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (sum(v12) = v13) | ~ (member(v11, v15) = 0) | ~ (member(v11, v13) = v14) | ? [v16] : ( ~ (v16 = 0) & member(v15, v12) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (inverse_image3(v15, v14, v13) = v12) | ~ (inverse_image3(v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (image3(v15, v14, v13) = v12) | ~ (image3(v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (inverse_function(v15, v14, v13) = v12) | ~ (inverse_function(v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (one_to_one(v15, v14, v13) = v12) | ~ (one_to_one(v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (surjective(v15, v14, v13) = v12) | ~ (surjective(v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (injective(v15, v14, v13) = v12) | ~ (injective(v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (maps(v15, v14, v13) = v12) | ~ (maps(v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (apply(v15, v14, v13) = v12) | ~ (apply(v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v11, v12, v13, v14, v15) = 0) | (one_to_one(v11, v12, v14) = 0 & maps(v11, v12, v14) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (inverse_image3(v11, v12, v13) = v15) | ~ (member(v14, v15) = 0) | member(v14, v13) = 0) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (inverse_image3(v11, v12, v13) = v15) | ~ (member(v14, v15) = 0) | ? [v16] : (apply(v11, v14, v16) = 0 & member(v16, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (image3(v11, v12, v13) = v15) | ~ (member(v14, v15) = 0) | member(v14, v13) = 0) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (image3(v11, v12, v13) = v15) | ~ (member(v14, v15) = 0) | ? [v16] : (apply(v11, v16, v14) = 0 & member(v16, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (surjective(v11, v12, v13) = v14) | ? [v15] : (member(v15, v13) = 0 & ! [v16] : ( ~ (apply(v11, v16, v15) = 0) | ? [v17] : ( ~ (v17 = 0) & member(v16, v12) = v17)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (injective(v11, v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ( ~ (v16 = v15) & apply(v11, v16, v17) = 0 & apply(v11, v15, v17) = 0 & member(v17, v13) = 0 & member(v16, v12) = 0 & member(v15, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (identity(v11, v12) = 0) | ~ (apply(v11, v13, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & member(v13, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (maps(v11, v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ((v22 = 0 & v21 = 0 & v20 = 0 & v19 = 0 & v18 = 0 & ~ (v17 = v16) & apply(v11, v15, v17) = 0 & apply(v11, v15, v16) = 0 & member(v17, v13) = 0 & member(v16, v13) = 0 & member(v15, v12) = 0) | (v16 = 0 & member(v15, v12) = 0 & ! [v23] : ( ~ (apply(v11, v15, v23) = 0) | ? [v24] : ( ~ (v24 = 0) & member(v23, v13) = v24))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (product(v12) = v13) | ~ (member(v11, v13) = v14) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & member(v15, v12) = 0 & member(v11, v15) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (unordered_pair(v12, v11) = v13) | ~ (member(v11, v13) = v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (unordered_pair(v11, v12) = v13) | ~ (member(v11, v13) = v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (power_set(v12) = v13) | ~ (member(v11, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & subset(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = v11 | v12 = v11 | ~ (unordered_pair(v12, v13) = v14) | ~ (member(v11, v14) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (inverse_image2(v14, v13) = v12) | ~ (inverse_image2(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (image2(v14, v13) = v12) | ~ (image2(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (identity(v14, v13) = v12) | ~ (identity(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (unordered_pair(v14, v13) = v12) | ~ (unordered_pair(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (difference(v14, v13) = v12) | ~ (difference(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (union(v14, v13) = v12) | ~ (union(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (intersection(v14, v13) = v12) | ~ (intersection(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (equal_set(v14, v13) = v12) | ~ (equal_set(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (subset(v14, v13) = v12) | ~ (subset(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (member(v14, v13) = v12) | ~ (member(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (inverse_image2(v11, v12) = v14) | ~ (member(v13, v14) = 0) | ? [v15] : (apply(v11, v13, v15) = 0 & member(v15, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (image2(v11, v12) = v14) | ~ (member(v13, v14) = 0) | ? [v15] : (apply(v11, v15, v13) = 0 & member(v15, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (surjective(v11, v12, v13) = v14) | ? [v15] : ? [v16] : (one_to_one(v11, v12, v13) = v15 & injective(v11, v12, v13) = v16 & ( ~ (v15 = 0) | (v16 = 0 & v14 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (surjective(v11, v12, v13) = 0) | ~ (member(v14, v13) = 0) | ? [v15] : (apply(v11, v15, v14) = 0 & member(v15, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (maps(v11, v12, v13) = 0) | ~ (member(v14, v12) = 0) | ? [v15] : (apply(v11, v14, v15) = 0 & member(v15, v13) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (difference(v13, v12) = v14) | ~ (member(v11, v14) = 0) | ? [v15] : ( ~ (v15 = 0) & member(v11, v13) = 0 & member(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (union(v12, v13) = v14) | ~ (member(v11, v14) = 0) | ? [v15] : ? [v16] : (member(v11, v13) = v16 & member(v11, v12) = v15 & (v16 = 0 | v15 = 0))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (intersection(v12, v13) = v14) | ~ (member(v11, v14) = 0) | (member(v11, v13) = 0 & member(v11, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (identity(v11, v12) = v13) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & apply(v11, v14, v14) = v15 & member(v14, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (singleton(v11) = v12) | ~ (member(v11, v12) = v13)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (equal_set(v11, v12) = v13) | ? [v14] : ? [v15] : (subset(v12, v11) = v15 & subset(v11, v12) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v11, v12) = v13) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & member(v14, v12) = v15 & member(v14, v11) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (product(v13) = v12) | ~ (product(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (sum(v13) = v12) | ~ (sum(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (singleton(v13) = v12) | ~ (singleton(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (singleton(v12) = v13) | ~ (member(v11, v13) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (power_set(v13) = v12) | ~ (power_set(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (surjective(v11, v12, v13) = 0) | ? [v14] : ? [v15] : (one_to_one(v11, v12, v13) = v15 & injective(v11, v12, v13) = v14 & ( ~ (v14 = 0) | v15 = 0))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (sum(v12) = v13) | ~ (member(v11, v13) = 0) | ? [v14] : (member(v14, v12) = 0 & member(v11, v14) = 0)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (power_set(v12) = v13) | ~ (member(v11, v13) = 0) | subset(v11, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (subset(v11, v12) = 0) | ~ (member(v13, v11) = 0) | member(v13, v12) = 0) & ! [v11] : ! [v12] : ( ~ (equal_set(v11, v12) = 0) | (subset(v12, v11) = 0 & subset(v11, v12) = 0)) & ! [v11] : ~ (member(v11, empty_set) = 0)) % 11.19/3.18 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10 yields: % 11.19/3.18 | (1) ~ (all_0_0_0 = 0) & inverse_image3(all_0_10_10, all_0_5_5, all_0_9_9) = all_0_4_4 & inverse_image3(all_0_10_10, all_0_6_6, all_0_9_9) = all_0_2_2 & inverse_image3(all_0_10_10, all_0_7_7, all_0_9_9) = all_0_3_3 & maps(all_0_10_10, all_0_9_9, all_0_8_8) = 0 & intersection(all_0_3_3, all_0_2_2) = all_0_1_1 & intersection(all_0_7_7, all_0_6_6) = all_0_5_5 & equal_set(all_0_4_4, all_0_1_1) = all_0_0_0 & subset(all_0_6_6, all_0_8_8) = 0 & subset(all_0_7_7, all_0_8_8) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ? [v10] : ? [v11] : ((apply(v1, v5, v9) = v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v1, v9, v7) = 0) | ~ (apply(v0, v6, v7) = v8) | ? [v10] : ? [v11] : ((apply(v2, v6, v9) = v11 & member(v9, v4) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v7, v5) = v11 & member(v6, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (apply(v0, v5, v6) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v4, v6, v8) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | (( ~ (v14 = 0) | v13 = 0) & ( ~ (v13 = 0) | v14 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (apply(v0, v5, v6) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v4, v8, v6) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | v14 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (apply(v0, v5, v6) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v4, v6, v8) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | v14 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v1 = v0 | ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & apply(v1, v5, v8) = 0 & apply(v0, v8, v6) = 0 & member(v8, v3) = 0) | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v0, v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & apply(v2, v6, v8) = 0 & apply(v1, v8, v7) = 0 & member(v8, v4) = 0) | (member(v7, v5) = v9 & member(v6, v3) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v1, v4, v6) = 0) | ~ (apply(v0, v4, v5) = 0) | ? [v7] : ? [v8] : ? [v9] : (member(v6, v3) = v9 & member(v5, v3) = v8 & member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (apply(v0, v7, v8) = v9 & member(v8, v5) = 0 & member(v7, v3) = 0 & ( ~ (v9 = 0) | ! [v14] : ( ~ (apply(v1, v14, v8) = 0) | ? [v15] : ? [v16] : (apply(v2, v7, v14) = v16 & member(v14, v4) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & (v9 = 0 | (v13 = 0 & v12 = 0 & v11 = 0 & apply(v2, v7, v10) = 0 & apply(v1, v10, v8) = 0 & member(v10, v4) = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (apply(v0, v3, v6) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & member(v6, v1) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (apply(v0, v6, v3) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & member(v6, v1) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_function(v0, v1, v2) = v5) | ~ (apply(v5, v4, v3) = v6) | ? [v7] : ? [v8] : ? [v9] : (apply(v0, v3, v4) = v9 & member(v4, v2) = v8 & member(v3, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0) | ~ (apply(v0, v5, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : (apply(v1, v4, v5) = v9 & member(v5, v3) = v8 & member(v4, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0, v3, v4) = 0) | ? [v6] : ? [v7] : ? [v8] : (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (isomorphism(v0, v1, v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & apply(v4, v7, v9) = v17 & apply(v2, v6, v8) = v16 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0 & ( ~ (v17 = 0) | ~ (v16 = 0)) & (v17 = 0 | v16 = 0)) | (one_to_one(v0, v1, v3) = v7 & maps(v0, v1, v3) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & apply(v4, v9, v7) = v10 & apply(v2, v6, v8) = 0 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & apply(v4, v7, v9) = v10 & apply(v2, v6, v8) = 0 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (apply(v0, v3, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (member(v5, v2) = v8 & member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (inverse_image2(v0, v1) = v3) | ~ (apply(v0, v2, v5) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (image2(v0, v1) = v3) | ~ (apply(v0, v5, v2) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (inverse_predicate(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v1, v5, v6) = v7 & apply(v0, v6, v5) = v8 & member(v6, v3) = 0 & member(v5, v2) = 0 & ( ~ (v8 = 0) | ~ (v7 = 0)) & (v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (equal_maps(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = v6) & apply(v1, v5, v7) = 0 & apply(v0, v5, v6) = 0 & member(v7, v3) = 0 & member(v6, v3) = 0 & member(v5, v2) = 0)) & ! [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] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [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] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [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 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(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] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v3, v5) = 0 & member(v5, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (surjective(v0, v1, v2) = v3) | ? [v4] : (member(v4, v2) = 0 & ! [v5] : ( ~ (apply(v0, v5, v4) = 0) | ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (injective(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = v4) & apply(v0, v5, v6) = 0 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (maps(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4, v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5, v2) = 0 & member(v4, v1) = 0) | (v5 = 0 & member(v4, v1) = 0 & ! [v12] : ( ~ (apply(v0, v4, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & member(v12, v2) = v13))))) & ! [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] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(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] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (one_to_one(v0, v1, v2) = v4 & injective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 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] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 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 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [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] : ( ~ (surjective(v0, v1, v2) = 0) | ? [v3] : ? [v4] : (one_to_one(v0, v1, v2) = v4 & injective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [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(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] : ~ (member(v0, empty_set) = 0) % 11.46/3.21 | % 11.46/3.21 | Applying alpha-rule on (1) yields: % 11.46/3.21 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (one_to_one(v0, v1, v2) = v4 & injective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) % 11.46/3.21 | (3) ! [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)) % 11.46/3.21 | (4) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 11.46/3.21 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 11.46/3.21 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0) % 11.46/3.21 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 11.46/3.21 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 11.46/3.21 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0)) % 11.46/3.21 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (surjective(v0, v1, v2) = v3) | ? [v4] : (member(v4, v2) = 0 & ! [v5] : ( ~ (apply(v0, v5, v4) = 0) | ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6)))) % 11.46/3.21 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 11.46/3.21 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) % 11.46/3.21 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 11.46/3.21 | (14) ! [v0] : ~ (member(v0, empty_set) = 0) % 11.46/3.21 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 11.46/3.21 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & apply(v1, v5, v8) = 0 & apply(v0, v8, v6) = 0 & member(v8, v3) = 0) | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))) % 11.46/3.21 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 11.46/3.21 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0)) % 11.46/3.21 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 11.46/3.21 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 11.46/3.21 | (21) ~ (all_0_0_0 = 0) % 11.46/3.21 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) % 11.46/3.21 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0)) % 11.46/3.21 | (24) subset(all_0_7_7, all_0_8_8) = 0 % 11.46/3.21 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0)) % 11.46/3.21 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 11.46/3.21 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v1 = v0 | ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) % 11.46/3.22 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (equal_maps(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = v6) & apply(v1, v5, v7) = 0 & apply(v0, v5, v6) = 0 & member(v7, v3) = 0 & member(v6, v3) = 0 & member(v5, v2) = 0)) % 11.46/3.22 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 11.46/3.22 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0)) % 11.46/3.22 | (31) intersection(all_0_7_7, all_0_6_6) = all_0_5_5 % 11.46/3.22 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0)) % 11.46/3.22 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0)) % 11.46/3.22 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ? [v10] : ? [v11] : ((apply(v1, v5, v9) = v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) % 11.46/3.22 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 11.46/3.22 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (image2(v0, v1) = v3) | ~ (apply(v0, v5, v2) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6)) % 11.46/3.22 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0)) % 11.46/3.22 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 11.46/3.22 | (39) equal_set(all_0_4_4, all_0_1_1) = all_0_0_0 % 11.46/3.22 | (40) inverse_image3(all_0_10_10, all_0_6_6, all_0_9_9) = all_0_2_2 % 11.46/3.22 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) % 11.46/3.22 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 11.46/3.22 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_function(v0, v1, v2) = v5) | ~ (apply(v5, v4, v3) = v6) | ? [v7] : ? [v8] : ? [v9] : (apply(v0, v3, v4) = v9 & member(v4, v2) = v8 & member(v3, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0))))) % 11.46/3.22 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (apply(v0, v6, v3) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & member(v6, v1) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7))) % 11.46/3.22 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (apply(v0, v3, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (member(v5, v2) = v8 & member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) % 11.46/3.22 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 11.46/3.22 | (47) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 11.46/3.22 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (maps(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4, v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5, v2) = 0 & member(v4, v1) = 0) | (v5 = 0 & member(v4, v1) = 0 & ! [v12] : ( ~ (apply(v0, v4, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & member(v12, v2) = v13))))) % 11.46/3.22 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (inverse_image2(v0, v1) = v3) | ~ (apply(v0, v2, v5) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6)) % 11.46/3.22 | (50) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 11.46/3.22 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (inverse_predicate(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v1, v5, v6) = v7 & apply(v0, v6, v5) = v8 & member(v6, v3) = 0 & member(v5, v2) = 0 & ( ~ (v8 = 0) | ~ (v7 = 0)) & (v8 = 0 | v7 = 0))) % 11.46/3.22 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0, v3, v4) = 0) | ? [v6] : ? [v7] : ? [v8] : (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) % 11.46/3.23 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 11.46/3.23 | (54) intersection(all_0_3_3, all_0_2_2) = all_0_1_1 % 11.46/3.23 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (isomorphism(v0, v1, v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & apply(v4, v7, v9) = v17 & apply(v2, v6, v8) = v16 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0 & ( ~ (v17 = 0) | ~ (v16 = 0)) & (v17 = 0 | v16 = 0)) | (one_to_one(v0, v1, v3) = v7 & maps(v0, v1, v3) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) % 11.46/3.23 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v3, v5) = 0 & member(v5, v1) = 0)) % 11.46/3.23 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0)) % 11.46/3.23 | (58) ! [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)) % 11.46/3.23 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 11.46/3.23 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & apply(v4, v9, v7) = v10 & apply(v2, v6, v8) = 0 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0)) % 11.46/3.23 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (apply(v0, v7, v8) = v9 & member(v8, v5) = 0 & member(v7, v3) = 0 & ( ~ (v9 = 0) | ! [v14] : ( ~ (apply(v1, v14, v8) = 0) | ? [v15] : ? [v16] : (apply(v2, v7, v14) = v16 & member(v14, v4) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & (v9 = 0 | (v13 = 0 & v12 = 0 & v11 = 0 & apply(v2, v7, v10) = 0 & apply(v1, v10, v8) = 0 & member(v10, v4) = 0)))) % 11.46/3.23 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0)) % 11.46/3.23 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 11.46/3.23 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 11.46/3.23 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) % 11.46/3.23 | (66) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 11.46/3.23 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0)) % 11.46/3.23 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0) % 11.46/3.23 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0)) % 11.46/3.23 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ (compose_function(v6, v5, v4, v3, v2) = v0)) % 11.46/3.23 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) % 11.46/3.23 | (72) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0)) % 11.46/3.23 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) % 11.46/3.23 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 11.46/3.23 | (75) inverse_image3(all_0_10_10, all_0_7_7, all_0_9_9) = all_0_3_3 % 11.46/3.23 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (surjective(v0, v1, v2) = 0) | ? [v3] : ? [v4] : (one_to_one(v0, v1, v2) = v4 & injective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 11.46/3.23 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) % 11.46/3.23 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (injective(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = v4) & apply(v0, v5, v6) = 0 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0)) % 11.46/3.23 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) % 11.46/3.23 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 11.46/3.23 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0)) % 11.46/3.23 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (apply(v0, v5, v6) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v4, v8, v6) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | v14 = 0))) % 11.46/3.24 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v1, v9, v7) = 0) | ~ (apply(v0, v6, v7) = v8) | ? [v10] : ? [v11] : ((apply(v2, v6, v9) = v11 & member(v9, v4) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v7, v5) = v11 & member(v6, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) % 11.46/3.24 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v1, v4, v6) = 0) | ~ (apply(v0, v4, v5) = 0) | ? [v7] : ? [v8] : ? [v9] : (member(v6, v3) = v9 & member(v5, v3) = v8 & member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) % 11.46/3.24 | (85) ! [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)) % 11.46/3.24 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & apply(v4, v7, v9) = v10 & apply(v2, v6, v8) = 0 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0)) % 11.46/3.24 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v0, v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & apply(v2, v6, v8) = 0 & apply(v1, v8, v7) = 0 & member(v8, v4) = 0) | (member(v7, v5) = v9 & member(v6, v3) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))) % 11.46/3.24 | (88) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 11.46/3.24 | (89) subset(all_0_6_6, all_0_8_8) = 0 % 11.46/3.24 | (90) ! [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)) % 11.46/3.24 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (apply(v0, v3, v6) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & member(v6, v1) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7))) % 11.46/3.24 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0) | ~ (apply(v0, v5, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : (apply(v1, v4, v5) = v9 & member(v5, v3) = v8 & member(v4, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0))))) % 11.46/3.24 | (93) maps(all_0_10_10, all_0_9_9, all_0_8_8) = 0 % 11.46/3.24 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0)) % 11.46/3.24 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (apply(v0, v5, v6) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v4, v6, v8) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | (( ~ (v14 = 0) | v13 = 0) & ( ~ (v13 = 0) | v14 = 0))))) % 11.46/3.24 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) % 11.46/3.24 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) % 11.46/3.24 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (apply(v0, v5, v6) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v4, v6, v8) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | v14 = 0))) % 11.46/3.24 | (99) inverse_image3(all_0_10_10, all_0_5_5, all_0_9_9) = all_0_4_4 % 11.46/3.24 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 11.46/3.24 | % 11.46/3.24 | Instantiating formula (47) with all_0_0_0, all_0_1_1, all_0_4_4 and discharging atoms equal_set(all_0_4_4, all_0_1_1) = all_0_0_0, yields: % 11.46/3.24 | (101) all_0_0_0 = 0 | ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_4_4) = v1 & subset(all_0_4_4, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 11.46/3.24 | % 11.46/3.24 +-Applying beta-rule and splitting (101), into two cases. % 11.46/3.24 |-Branch one: % 11.46/3.24 | (102) all_0_0_0 = 0 % 11.46/3.24 | % 11.46/3.24 | Equations (102) can reduce 21 to: % 11.46/3.24 | (103) $false % 11.46/3.24 | % 11.46/3.24 |-The branch is then unsatisfiable % 11.46/3.24 |-Branch two: % 11.46/3.24 | (21) ~ (all_0_0_0 = 0) % 11.46/3.24 | (105) ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_4_4) = v1 & subset(all_0_4_4, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 11.46/3.24 | % 11.46/3.24 | Instantiating (105) with all_14_0_11, all_14_1_12 yields: % 11.46/3.24 | (106) subset(all_0_1_1, all_0_4_4) = all_14_0_11 & subset(all_0_4_4, all_0_1_1) = all_14_1_12 & ( ~ (all_14_0_11 = 0) | ~ (all_14_1_12 = 0)) % 11.46/3.24 | % 11.46/3.24 | Applying alpha-rule on (106) yields: % 11.46/3.24 | (107) subset(all_0_1_1, all_0_4_4) = all_14_0_11 % 11.46/3.24 | (108) subset(all_0_4_4, all_0_1_1) = all_14_1_12 % 11.46/3.24 | (109) ~ (all_14_0_11 = 0) | ~ (all_14_1_12 = 0) % 11.46/3.24 | % 11.46/3.24 | Instantiating formula (19) with all_14_0_11, all_0_4_4, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_4_4) = all_14_0_11, yields: % 11.46/3.24 | (110) all_14_0_11 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_4_4) = v1) % 11.46/3.24 | % 11.46/3.24 | Instantiating formula (19) with all_14_1_12, all_0_1_1, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_1_1) = all_14_1_12, yields: % 11.46/3.24 | (111) all_14_1_12 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_4_4) = 0) % 11.46/3.24 | % 11.46/3.25 +-Applying beta-rule and splitting (109), into two cases. % 11.46/3.25 |-Branch one: % 11.46/3.25 | (112) ~ (all_14_0_11 = 0) % 11.46/3.25 | % 11.46/3.25 +-Applying beta-rule and splitting (110), into two cases. % 11.46/3.25 |-Branch one: % 11.46/3.25 | (113) all_14_0_11 = 0 % 11.46/3.25 | % 11.46/3.25 | Equations (113) can reduce 112 to: % 11.46/3.25 | (103) $false % 11.46/3.25 | % 11.46/3.25 |-The branch is then unsatisfiable % 11.46/3.25 |-Branch two: % 11.46/3.25 | (112) ~ (all_14_0_11 = 0) % 11.46/3.25 | (116) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_4_4) = v1) % 11.46/3.25 | % 11.46/3.25 | Instantiating (116) with all_53_0_13, all_53_1_14 yields: % 11.46/3.25 | (117) ~ (all_53_0_13 = 0) & member(all_53_1_14, all_0_1_1) = 0 & member(all_53_1_14, all_0_4_4) = all_53_0_13 % 11.46/3.25 | % 11.46/3.25 | Applying alpha-rule on (117) yields: % 11.46/3.25 | (118) ~ (all_53_0_13 = 0) % 11.46/3.25 | (119) member(all_53_1_14, all_0_1_1) = 0 % 11.46/3.25 | (120) member(all_53_1_14, all_0_4_4) = all_53_0_13 % 11.46/3.25 | % 11.46/3.25 | Instantiating formula (56) with all_0_2_2, all_53_1_14, all_0_9_9, all_0_6_6, all_0_10_10 and discharging atoms inverse_image3(all_0_10_10, all_0_6_6, all_0_9_9) = all_0_2_2, yields: % 11.46/3.25 | (121) ~ (member(all_53_1_14, all_0_2_2) = 0) | ? [v0] : (apply(all_0_10_10, all_53_1_14, v0) = 0 & member(v0, all_0_6_6) = 0) % 11.46/3.25 | % 11.46/3.25 | Instantiating formula (6) with all_0_3_3, all_53_1_14, all_0_9_9, all_0_7_7, all_0_10_10 and discharging atoms inverse_image3(all_0_10_10, all_0_7_7, all_0_9_9) = all_0_3_3, yields: % 11.46/3.25 | (122) ~ (member(all_53_1_14, all_0_3_3) = 0) | member(all_53_1_14, all_0_9_9) = 0 % 11.46/3.25 | % 11.46/3.25 | Instantiating formula (56) with all_0_3_3, all_53_1_14, all_0_9_9, all_0_7_7, all_0_10_10 and discharging atoms inverse_image3(all_0_10_10, all_0_7_7, all_0_9_9) = all_0_3_3, yields: % 11.46/3.25 | (123) ~ (member(all_53_1_14, all_0_3_3) = 0) | ? [v0] : (apply(all_0_10_10, all_53_1_14, v0) = 0 & member(v0, all_0_7_7) = 0) % 11.46/3.25 | % 11.46/3.25 | Instantiating formula (9) with all_53_1_14, all_0_8_8, all_0_9_9, all_0_10_10 and discharging atoms maps(all_0_10_10, all_0_9_9, all_0_8_8) = 0, yields: % 11.46/3.25 | (124) ~ (member(all_53_1_14, all_0_9_9) = 0) | ? [v0] : (apply(all_0_10_10, all_53_1_14, v0) = 0 & member(v0, all_0_8_8) = 0) % 11.46/3.25 | % 11.46/3.25 | Instantiating formula (15) with all_0_1_1, all_0_2_2, all_0_3_3, all_53_1_14 and discharging atoms intersection(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_53_1_14, all_0_1_1) = 0, yields: % 11.46/3.25 | (125) member(all_53_1_14, all_0_2_2) = 0 & member(all_53_1_14, all_0_3_3) = 0 % 11.46/3.25 | % 11.46/3.25 | Applying alpha-rule on (125) yields: % 11.46/3.25 | (126) member(all_53_1_14, all_0_2_2) = 0 % 11.46/3.25 | (127) member(all_53_1_14, all_0_3_3) = 0 % 11.46/3.25 | % 11.46/3.25 +-Applying beta-rule and splitting (122), into two cases. % 11.46/3.25 |-Branch one: % 11.46/3.25 | (128) ~ (member(all_53_1_14, all_0_3_3) = 0) % 11.46/3.25 | % 11.46/3.25 | Using (127) and (128) yields: % 11.46/3.25 | (129) $false % 11.46/3.25 | % 11.46/3.25 |-The branch is then unsatisfiable % 11.46/3.25 |-Branch two: % 11.46/3.25 | (127) member(all_53_1_14, all_0_3_3) = 0 % 11.46/3.25 | (131) member(all_53_1_14, all_0_9_9) = 0 % 11.46/3.25 | % 11.46/3.25 +-Applying beta-rule and splitting (124), into two cases. % 11.46/3.25 |-Branch one: % 11.46/3.25 | (132) ~ (member(all_53_1_14, all_0_9_9) = 0) % 11.46/3.25 | % 11.46/3.25 | Using (131) and (132) yields: % 11.46/3.25 | (129) $false % 11.46/3.25 | % 11.46/3.25 |-The branch is then unsatisfiable % 11.46/3.25 |-Branch two: % 11.46/3.25 | (131) member(all_53_1_14, all_0_9_9) = 0 % 11.46/3.25 | (135) ? [v0] : (apply(all_0_10_10, all_53_1_14, v0) = 0 & member(v0, all_0_8_8) = 0) % 11.46/3.25 | % 11.46/3.25 | Instantiating (135) with all_80_0_15 yields: % 11.46/3.25 | (136) apply(all_0_10_10, all_53_1_14, all_80_0_15) = 0 & member(all_80_0_15, all_0_8_8) = 0 % 11.46/3.25 | % 11.46/3.25 | Applying alpha-rule on (136) yields: % 11.46/3.25 | (137) apply(all_0_10_10, all_53_1_14, all_80_0_15) = 0 % 11.46/3.25 | (138) member(all_80_0_15, all_0_8_8) = 0 % 11.46/3.25 | % 11.46/3.25 +-Applying beta-rule and splitting (123), into two cases. % 11.46/3.25 |-Branch one: % 11.46/3.25 | (128) ~ (member(all_53_1_14, all_0_3_3) = 0) % 11.46/3.25 | % 11.46/3.25 | Using (127) and (128) yields: % 11.46/3.25 | (129) $false % 11.46/3.25 | % 11.46/3.25 |-The branch is then unsatisfiable % 11.46/3.25 |-Branch two: % 11.46/3.25 | (127) member(all_53_1_14, all_0_3_3) = 0 % 11.70/3.25 | (142) ? [v0] : (apply(all_0_10_10, all_53_1_14, v0) = 0 & member(v0, all_0_7_7) = 0) % 11.70/3.25 | % 11.70/3.25 | Instantiating (142) with all_86_0_16 yields: % 11.70/3.25 | (143) apply(all_0_10_10, all_53_1_14, all_86_0_16) = 0 & member(all_86_0_16, all_0_7_7) = 0 % 11.70/3.25 | % 11.70/3.25 | Applying alpha-rule on (143) yields: % 11.70/3.25 | (144) apply(all_0_10_10, all_53_1_14, all_86_0_16) = 0 % 11.70/3.25 | (145) member(all_86_0_16, all_0_7_7) = 0 % 11.70/3.25 | % 11.70/3.25 +-Applying beta-rule and splitting (121), into two cases. % 11.70/3.25 |-Branch one: % 11.70/3.25 | (146) ~ (member(all_53_1_14, all_0_2_2) = 0) % 11.70/3.25 | % 11.70/3.25 | Using (126) and (146) yields: % 11.70/3.25 | (129) $false % 11.70/3.25 | % 11.70/3.25 |-The branch is then unsatisfiable % 11.70/3.25 |-Branch two: % 11.70/3.25 | (126) member(all_53_1_14, all_0_2_2) = 0 % 11.70/3.25 | (149) ? [v0] : (apply(all_0_10_10, all_53_1_14, v0) = 0 & member(v0, all_0_6_6) = 0) % 11.70/3.25 | % 11.70/3.25 | Instantiating (149) with all_91_0_17 yields: % 11.70/3.25 | (150) apply(all_0_10_10, all_53_1_14, all_91_0_17) = 0 & member(all_91_0_17, all_0_6_6) = 0 % 11.70/3.25 | % 11.70/3.25 | Applying alpha-rule on (150) yields: % 11.70/3.25 | (151) apply(all_0_10_10, all_53_1_14, all_91_0_17) = 0 % 11.70/3.25 | (152) member(all_91_0_17, all_0_6_6) = 0 % 11.70/3.25 | % 11.70/3.25 | Instantiating formula (91) with all_91_0_17, all_53_0_13, all_0_4_4, all_53_1_14, all_0_9_9, all_0_5_5, all_0_10_10 and discharging atoms inverse_image3(all_0_10_10, all_0_5_5, all_0_9_9) = all_0_4_4, apply(all_0_10_10, all_53_1_14, all_91_0_17) = 0, member(all_53_1_14, all_0_4_4) = all_53_0_13, yields: % 11.70/3.25 | (153) all_53_0_13 = 0 | ? [v0] : (( ~ (v0 = 0) & member(all_91_0_17, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_53_1_14, all_0_9_9) = v0)) % 11.70/3.25 | % 11.70/3.25 | Instantiating formula (91) with all_86_0_16, all_53_0_13, all_0_4_4, all_53_1_14, all_0_9_9, all_0_5_5, all_0_10_10 and discharging atoms inverse_image3(all_0_10_10, all_0_5_5, all_0_9_9) = all_0_4_4, apply(all_0_10_10, all_53_1_14, all_86_0_16) = 0, member(all_53_1_14, all_0_4_4) = all_53_0_13, yields: % 11.70/3.25 | (154) all_53_0_13 = 0 | ? [v0] : (( ~ (v0 = 0) & member(all_86_0_16, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_53_1_14, all_0_9_9) = v0)) % 11.70/3.25 | % 11.70/3.25 | Instantiating formula (91) with all_80_0_15, all_53_0_13, all_0_4_4, all_53_1_14, all_0_9_9, all_0_5_5, all_0_10_10 and discharging atoms inverse_image3(all_0_10_10, all_0_5_5, all_0_9_9) = all_0_4_4, apply(all_0_10_10, all_53_1_14, all_80_0_15) = 0, member(all_53_1_14, all_0_4_4) = all_53_0_13, yields: % 11.70/3.25 | (155) all_53_0_13 = 0 | ? [v0] : (( ~ (v0 = 0) & member(all_80_0_15, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_53_1_14, all_0_9_9) = v0)) % 11.70/3.25 | % 11.70/3.25 | Instantiating formula (52) with all_80_0_15, all_91_0_17, all_53_1_14, all_0_8_8, all_0_9_9, all_0_10_10 and discharging atoms maps(all_0_10_10, all_0_9_9, all_0_8_8) = 0, apply(all_0_10_10, all_53_1_14, all_91_0_17) = 0, apply(all_0_10_10, all_53_1_14, all_80_0_15) = 0, yields: % 11.70/3.25 | (156) all_91_0_17 = all_80_0_15 | ? [v0] : ? [v1] : ? [v2] : (member(all_91_0_17, all_0_8_8) = v1 & member(all_80_0_15, all_0_8_8) = v2 & member(all_53_1_14, all_0_9_9) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 11.70/3.25 | % 11.70/3.25 | Instantiating formula (52) with all_80_0_15, all_86_0_16, all_53_1_14, all_0_8_8, all_0_9_9, all_0_10_10 and discharging atoms maps(all_0_10_10, all_0_9_9, all_0_8_8) = 0, apply(all_0_10_10, all_53_1_14, all_86_0_16) = 0, apply(all_0_10_10, all_53_1_14, all_80_0_15) = 0, yields: % 11.70/3.25 | (157) all_86_0_16 = all_80_0_15 | ? [v0] : ? [v1] : ? [v2] : (member(all_86_0_16, all_0_8_8) = v1 & member(all_80_0_15, all_0_8_8) = v2 & member(all_53_1_14, all_0_9_9) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 11.70/3.25 | % 11.70/3.25 | Instantiating formula (7) with all_91_0_17, all_0_8_8, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_8_8) = 0, member(all_91_0_17, all_0_6_6) = 0, yields: % 11.70/3.26 | (158) member(all_91_0_17, all_0_8_8) = 0 % 11.70/3.26 | % 11.70/3.26 | Instantiating formula (7) with all_86_0_16, all_0_8_8, all_0_7_7 and discharging atoms subset(all_0_7_7, all_0_8_8) = 0, member(all_86_0_16, all_0_7_7) = 0, yields: % 11.70/3.26 | (159) member(all_86_0_16, all_0_8_8) = 0 % 11.70/3.26 | % 11.70/3.26 +-Applying beta-rule and splitting (157), into two cases. % 11.70/3.26 |-Branch one: % 11.70/3.26 | (160) all_86_0_16 = all_80_0_15 % 11.70/3.26 | % 11.70/3.26 | From (160) and (145) follows: % 11.70/3.26 | (161) member(all_80_0_15, all_0_7_7) = 0 % 11.70/3.26 | % 11.70/3.26 | From (160) and (159) follows: % 11.70/3.26 | (138) member(all_80_0_15, all_0_8_8) = 0 % 11.70/3.26 | % 11.70/3.26 +-Applying beta-rule and splitting (156), into two cases. % 11.70/3.26 |-Branch one: % 11.70/3.26 | (163) all_91_0_17 = all_80_0_15 % 11.70/3.26 | % 11.70/3.26 | From (163) and (152) follows: % 11.70/3.26 | (164) member(all_80_0_15, all_0_6_6) = 0 % 11.70/3.26 | % 11.70/3.26 +-Applying beta-rule and splitting (153), into two cases. % 11.70/3.26 |-Branch one: % 11.70/3.26 | (165) all_53_0_13 = 0 % 11.70/3.26 | % 11.70/3.26 | Equations (165) can reduce 118 to: % 11.70/3.26 | (103) $false % 11.70/3.26 | % 11.70/3.26 |-The branch is then unsatisfiable % 11.70/3.26 |-Branch two: % 11.70/3.26 | (118) ~ (all_53_0_13 = 0) % 11.70/3.26 | (168) ? [v0] : (( ~ (v0 = 0) & member(all_91_0_17, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_53_1_14, all_0_9_9) = v0)) % 11.70/3.26 | % 11.70/3.26 | Instantiating (168) with all_119_0_18 yields: % 11.70/3.26 | (169) ( ~ (all_119_0_18 = 0) & member(all_91_0_17, all_0_5_5) = all_119_0_18) | ( ~ (all_119_0_18 = 0) & member(all_53_1_14, all_0_9_9) = all_119_0_18) % 11.70/3.26 | % 11.70/3.26 +-Applying beta-rule and splitting (154), into two cases. % 11.70/3.26 |-Branch one: % 11.70/3.26 | (165) all_53_0_13 = 0 % 11.70/3.26 | % 11.70/3.26 | Equations (165) can reduce 118 to: % 11.70/3.26 | (103) $false % 11.70/3.26 | % 11.70/3.26 |-The branch is then unsatisfiable % 11.70/3.26 |-Branch two: % 11.70/3.26 | (118) ~ (all_53_0_13 = 0) % 11.70/3.26 | (173) ? [v0] : (( ~ (v0 = 0) & member(all_86_0_16, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_53_1_14, all_0_9_9) = v0)) % 11.70/3.26 | % 11.70/3.26 | Instantiating (173) with all_123_0_19 yields: % 11.70/3.26 | (174) ( ~ (all_123_0_19 = 0) & member(all_86_0_16, all_0_5_5) = all_123_0_19) | ( ~ (all_123_0_19 = 0) & member(all_53_1_14, all_0_9_9) = all_123_0_19) % 11.70/3.26 | % 11.70/3.26 +-Applying beta-rule and splitting (155), into two cases. % 11.70/3.26 |-Branch one: % 11.70/3.26 | (165) all_53_0_13 = 0 % 11.70/3.26 | % 11.70/3.26 | Equations (165) can reduce 118 to: % 11.70/3.26 | (103) $false % 11.70/3.26 | % 11.70/3.26 |-The branch is then unsatisfiable % 11.70/3.26 |-Branch two: % 11.70/3.26 | (118) ~ (all_53_0_13 = 0) % 11.70/3.26 | (178) ? [v0] : (( ~ (v0 = 0) & member(all_80_0_15, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_53_1_14, all_0_9_9) = v0)) % 11.70/3.26 | % 11.70/3.26 | Instantiating (178) with all_127_0_20 yields: % 11.70/3.26 | (179) ( ~ (all_127_0_20 = 0) & member(all_80_0_15, all_0_5_5) = all_127_0_20) | ( ~ (all_127_0_20 = 0) & member(all_53_1_14, all_0_9_9) = all_127_0_20) % 11.70/3.26 | % 11.70/3.26 +-Applying beta-rule and splitting (169), into two cases. % 11.70/3.26 |-Branch one: % 11.70/3.26 | (180) ~ (all_119_0_18 = 0) & member(all_91_0_17, all_0_5_5) = all_119_0_18 % 11.70/3.26 | % 11.70/3.26 | Applying alpha-rule on (180) yields: % 11.70/3.26 | (181) ~ (all_119_0_18 = 0) % 11.70/3.26 | (182) member(all_91_0_17, all_0_5_5) = all_119_0_18 % 11.70/3.26 | % 11.70/3.26 | From (163) and (182) follows: % 11.70/3.26 | (183) member(all_80_0_15, all_0_5_5) = all_119_0_18 % 11.70/3.26 | % 11.70/3.26 +-Applying beta-rule and splitting (174), into two cases. % 11.70/3.26 |-Branch one: % 11.70/3.26 | (184) ~ (all_123_0_19 = 0) & member(all_86_0_16, all_0_5_5) = all_123_0_19 % 11.70/3.26 | % 11.70/3.26 | Applying alpha-rule on (184) yields: % 11.70/3.26 | (185) ~ (all_123_0_19 = 0) % 11.70/3.26 | (186) member(all_86_0_16, all_0_5_5) = all_123_0_19 % 11.70/3.26 | % 11.70/3.26 | From (160) and (186) follows: % 11.70/3.26 | (187) member(all_80_0_15, all_0_5_5) = all_123_0_19 % 11.70/3.26 | % 11.70/3.26 +-Applying beta-rule and splitting (179), into two cases. % 11.70/3.26 |-Branch one: % 11.70/3.26 | (188) ~ (all_127_0_20 = 0) & member(all_80_0_15, all_0_5_5) = all_127_0_20 % 11.70/3.26 | % 11.70/3.26 | Applying alpha-rule on (188) yields: % 11.70/3.26 | (189) ~ (all_127_0_20 = 0) % 11.70/3.26 | (190) member(all_80_0_15, all_0_5_5) = all_127_0_20 % 11.70/3.26 | % 11.70/3.26 | Instantiating formula (38) with all_80_0_15, all_0_5_5, all_123_0_19, all_127_0_20 and discharging atoms member(all_80_0_15, all_0_5_5) = all_127_0_20, member(all_80_0_15, all_0_5_5) = all_123_0_19, yields: % 11.70/3.26 | (191) all_127_0_20 = all_123_0_19 % 11.70/3.26 | % 11.70/3.26 | Instantiating formula (38) with all_80_0_15, all_0_5_5, all_119_0_18, all_127_0_20 and discharging atoms member(all_80_0_15, all_0_5_5) = all_127_0_20, member(all_80_0_15, all_0_5_5) = all_119_0_18, yields: % 11.70/3.26 | (192) all_127_0_20 = all_119_0_18 % 11.70/3.26 | % 11.70/3.26 | Combining equations (192,191) yields a new equation: % 11.70/3.26 | (193) all_123_0_19 = all_119_0_18 % 11.70/3.26 | % 11.70/3.26 | Equations (193) can reduce 185 to: % 11.70/3.26 | (181) ~ (all_119_0_18 = 0) % 11.70/3.26 | % 11.70/3.26 | From (193) and (187) follows: % 11.70/3.26 | (183) member(all_80_0_15, all_0_5_5) = all_119_0_18 % 11.70/3.26 | % 11.70/3.26 | Instantiating formula (96) with all_119_0_18, all_0_5_5, all_0_6_6, all_0_7_7, all_80_0_15 and discharging atoms intersection(all_0_7_7, all_0_6_6) = all_0_5_5, member(all_80_0_15, all_0_5_5) = all_119_0_18, yields: % 11.70/3.26 | (196) all_119_0_18 = 0 | ? [v0] : ? [v1] : (member(all_80_0_15, all_0_6_6) = v1 & member(all_80_0_15, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 11.70/3.26 | % 11.70/3.26 +-Applying beta-rule and splitting (196), into two cases. % 11.70/3.26 |-Branch one: % 11.70/3.26 | (197) all_119_0_18 = 0 % 11.70/3.26 | % 11.70/3.26 | Equations (197) can reduce 181 to: % 11.70/3.26 | (103) $false % 11.70/3.26 | % 11.70/3.26 |-The branch is then unsatisfiable % 11.70/3.26 |-Branch two: % 11.70/3.26 | (181) ~ (all_119_0_18 = 0) % 11.70/3.26 | (200) ? [v0] : ? [v1] : (member(all_80_0_15, all_0_6_6) = v1 & member(all_80_0_15, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 11.70/3.26 | % 11.70/3.26 | Instantiating (200) with all_155_0_21, all_155_1_22 yields: % 11.70/3.26 | (201) member(all_80_0_15, all_0_6_6) = all_155_0_21 & member(all_80_0_15, all_0_7_7) = all_155_1_22 & ( ~ (all_155_0_21 = 0) | ~ (all_155_1_22 = 0)) % 11.70/3.26 | % 11.70/3.26 | Applying alpha-rule on (201) yields: % 11.70/3.26 | (202) member(all_80_0_15, all_0_6_6) = all_155_0_21 % 11.70/3.26 | (203) member(all_80_0_15, all_0_7_7) = all_155_1_22 % 11.70/3.26 | (204) ~ (all_155_0_21 = 0) | ~ (all_155_1_22 = 0) % 11.70/3.26 | % 11.70/3.26 | Instantiating formula (38) with all_80_0_15, all_0_6_6, all_155_0_21, 0 and discharging atoms member(all_80_0_15, all_0_6_6) = all_155_0_21, member(all_80_0_15, all_0_6_6) = 0, yields: % 11.70/3.26 | (205) all_155_0_21 = 0 % 11.70/3.26 | % 11.70/3.26 | Instantiating formula (38) with all_80_0_15, all_0_7_7, all_155_1_22, 0 and discharging atoms member(all_80_0_15, all_0_7_7) = all_155_1_22, member(all_80_0_15, all_0_7_7) = 0, yields: % 11.70/3.26 | (206) all_155_1_22 = 0 % 11.70/3.26 | % 11.70/3.26 +-Applying beta-rule and splitting (204), into two cases. % 11.70/3.26 |-Branch one: % 11.70/3.26 | (207) ~ (all_155_0_21 = 0) % 11.70/3.26 | % 11.70/3.26 | Equations (205) can reduce 207 to: % 11.70/3.26 | (103) $false % 11.70/3.26 | % 11.70/3.26 |-The branch is then unsatisfiable % 11.70/3.26 |-Branch two: % 11.70/3.26 | (205) all_155_0_21 = 0 % 11.70/3.26 | (210) ~ (all_155_1_22 = 0) % 11.70/3.26 | % 11.70/3.26 | Equations (206) can reduce 210 to: % 11.70/3.26 | (103) $false % 11.70/3.26 | % 11.70/3.26 |-The branch is then unsatisfiable % 11.70/3.26 |-Branch two: % 11.70/3.26 | (212) ~ (all_127_0_20 = 0) & member(all_53_1_14, all_0_9_9) = all_127_0_20 % 11.70/3.26 | % 11.70/3.26 | Applying alpha-rule on (212) yields: % 11.70/3.26 | (189) ~ (all_127_0_20 = 0) % 11.70/3.26 | (214) member(all_53_1_14, all_0_9_9) = all_127_0_20 % 11.70/3.26 | % 11.70/3.26 | Instantiating formula (38) with all_53_1_14, all_0_9_9, all_127_0_20, 0 and discharging atoms member(all_53_1_14, all_0_9_9) = all_127_0_20, member(all_53_1_14, all_0_9_9) = 0, yields: % 11.70/3.26 | (215) all_127_0_20 = 0 % 11.70/3.26 | % 11.70/3.26 | Equations (215) can reduce 189 to: % 11.70/3.26 | (103) $false % 11.70/3.26 | % 11.70/3.26 |-The branch is then unsatisfiable % 11.70/3.26 |-Branch two: % 11.70/3.26 | (217) ~ (all_123_0_19 = 0) & member(all_53_1_14, all_0_9_9) = all_123_0_19 % 11.70/3.26 | % 11.70/3.26 | Applying alpha-rule on (217) yields: % 11.70/3.26 | (185) ~ (all_123_0_19 = 0) % 11.70/3.26 | (219) member(all_53_1_14, all_0_9_9) = all_123_0_19 % 11.70/3.26 | % 11.70/3.26 | Instantiating formula (38) with all_53_1_14, all_0_9_9, all_123_0_19, 0 and discharging atoms member(all_53_1_14, all_0_9_9) = all_123_0_19, member(all_53_1_14, all_0_9_9) = 0, yields: % 11.70/3.26 | (220) all_123_0_19 = 0 % 11.70/3.26 | % 11.70/3.26 | Equations (220) can reduce 185 to: % 11.70/3.26 | (103) $false % 11.70/3.26 | % 11.70/3.26 |-The branch is then unsatisfiable % 11.70/3.26 |-Branch two: % 11.70/3.26 | (222) ~ (all_119_0_18 = 0) & member(all_53_1_14, all_0_9_9) = all_119_0_18 % 11.70/3.26 | % 11.70/3.26 | Applying alpha-rule on (222) yields: % 11.70/3.26 | (181) ~ (all_119_0_18 = 0) % 11.70/3.26 | (224) member(all_53_1_14, all_0_9_9) = all_119_0_18 % 11.70/3.26 | % 11.70/3.26 | Instantiating formula (38) with all_53_1_14, all_0_9_9, all_119_0_18, 0 and discharging atoms member(all_53_1_14, all_0_9_9) = all_119_0_18, member(all_53_1_14, all_0_9_9) = 0, yields: % 11.70/3.26 | (197) all_119_0_18 = 0 % 11.70/3.26 | % 11.70/3.26 | Equations (197) can reduce 181 to: % 11.70/3.26 | (103) $false % 11.70/3.26 | % 11.70/3.26 |-The branch is then unsatisfiable % 11.70/3.27 |-Branch two: % 11.70/3.27 | (227) ~ (all_91_0_17 = all_80_0_15) % 11.70/3.27 | (228) ? [v0] : ? [v1] : ? [v2] : (member(all_91_0_17, all_0_8_8) = v1 & member(all_80_0_15, all_0_8_8) = v2 & member(all_53_1_14, all_0_9_9) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 11.70/3.27 | % 11.70/3.27 | Instantiating (228) with all_115_0_23, all_115_1_24, all_115_2_25 yields: % 11.70/3.27 | (229) member(all_91_0_17, all_0_8_8) = all_115_1_24 & member(all_80_0_15, all_0_8_8) = all_115_0_23 & member(all_53_1_14, all_0_9_9) = all_115_2_25 & ( ~ (all_115_0_23 = 0) | ~ (all_115_1_24 = 0) | ~ (all_115_2_25 = 0)) % 11.70/3.27 | % 11.70/3.27 | Applying alpha-rule on (229) yields: % 11.70/3.27 | (230) member(all_91_0_17, all_0_8_8) = all_115_1_24 % 11.70/3.27 | (231) member(all_80_0_15, all_0_8_8) = all_115_0_23 % 11.70/3.27 | (232) member(all_53_1_14, all_0_9_9) = all_115_2_25 % 11.70/3.27 | (233) ~ (all_115_0_23 = 0) | ~ (all_115_1_24 = 0) | ~ (all_115_2_25 = 0) % 11.70/3.27 | % 11.70/3.27 | Instantiating formula (38) with all_91_0_17, all_0_8_8, all_115_1_24, 0 and discharging atoms member(all_91_0_17, all_0_8_8) = all_115_1_24, member(all_91_0_17, all_0_8_8) = 0, yields: % 11.70/3.27 | (234) all_115_1_24 = 0 % 11.70/3.27 | % 11.70/3.27 | Instantiating formula (38) with all_80_0_15, all_0_8_8, all_115_0_23, 0 and discharging atoms member(all_80_0_15, all_0_8_8) = all_115_0_23, member(all_80_0_15, all_0_8_8) = 0, yields: % 11.70/3.27 | (235) all_115_0_23 = 0 % 11.70/3.27 | % 11.70/3.27 | Instantiating formula (38) with all_53_1_14, all_0_9_9, all_115_2_25, 0 and discharging atoms member(all_53_1_14, all_0_9_9) = all_115_2_25, member(all_53_1_14, all_0_9_9) = 0, yields: % 11.70/3.27 | (236) all_115_2_25 = 0 % 11.70/3.27 | % 11.70/3.27 +-Applying beta-rule and splitting (233), into two cases. % 11.70/3.27 |-Branch one: % 11.70/3.27 | (237) ~ (all_115_0_23 = 0) % 11.70/3.27 | % 11.70/3.27 | Equations (235) can reduce 237 to: % 11.70/3.27 | (103) $false % 11.70/3.27 | % 11.70/3.27 |-The branch is then unsatisfiable % 11.70/3.27 |-Branch two: % 11.70/3.27 | (235) all_115_0_23 = 0 % 11.70/3.27 | (240) ~ (all_115_1_24 = 0) | ~ (all_115_2_25 = 0) % 11.70/3.27 | % 11.70/3.27 +-Applying beta-rule and splitting (240), into two cases. % 11.70/3.27 |-Branch one: % 11.70/3.27 | (241) ~ (all_115_1_24 = 0) % 11.70/3.27 | % 11.70/3.27 | Equations (234) can reduce 241 to: % 11.70/3.27 | (103) $false % 11.70/3.27 | % 11.70/3.27 |-The branch is then unsatisfiable % 11.70/3.27 |-Branch two: % 11.70/3.27 | (234) all_115_1_24 = 0 % 11.70/3.27 | (244) ~ (all_115_2_25 = 0) % 11.70/3.27 | % 11.70/3.27 | Equations (236) can reduce 244 to: % 11.70/3.27 | (103) $false % 11.70/3.27 | % 11.70/3.27 |-The branch is then unsatisfiable % 11.70/3.27 |-Branch two: % 11.70/3.27 | (246) ~ (all_86_0_16 = all_80_0_15) % 11.70/3.27 | (247) ? [v0] : ? [v1] : ? [v2] : (member(all_86_0_16, all_0_8_8) = v1 & member(all_80_0_15, all_0_8_8) = v2 & member(all_53_1_14, all_0_9_9) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 11.70/3.27 | % 11.70/3.27 | Instantiating (247) with all_111_0_32, all_111_1_33, all_111_2_34 yields: % 11.70/3.27 | (248) member(all_86_0_16, all_0_8_8) = all_111_1_33 & member(all_80_0_15, all_0_8_8) = all_111_0_32 & member(all_53_1_14, all_0_9_9) = all_111_2_34 & ( ~ (all_111_0_32 = 0) | ~ (all_111_1_33 = 0) | ~ (all_111_2_34 = 0)) % 11.70/3.27 | % 11.70/3.27 | Applying alpha-rule on (248) yields: % 11.70/3.27 | (249) member(all_86_0_16, all_0_8_8) = all_111_1_33 % 11.70/3.27 | (250) member(all_80_0_15, all_0_8_8) = all_111_0_32 % 11.70/3.27 | (251) member(all_53_1_14, all_0_9_9) = all_111_2_34 % 11.70/3.27 | (252) ~ (all_111_0_32 = 0) | ~ (all_111_1_33 = 0) | ~ (all_111_2_34 = 0) % 11.70/3.27 | % 11.70/3.27 | Instantiating formula (38) with all_86_0_16, all_0_8_8, all_111_1_33, 0 and discharging atoms member(all_86_0_16, all_0_8_8) = all_111_1_33, member(all_86_0_16, all_0_8_8) = 0, yields: % 11.70/3.27 | (253) all_111_1_33 = 0 % 11.70/3.27 | % 11.70/3.27 | Instantiating formula (38) with all_80_0_15, all_0_8_8, all_111_0_32, 0 and discharging atoms member(all_80_0_15, all_0_8_8) = all_111_0_32, member(all_80_0_15, all_0_8_8) = 0, yields: % 11.70/3.27 | (254) all_111_0_32 = 0 % 11.70/3.27 | % 11.70/3.27 | Instantiating formula (38) with all_53_1_14, all_0_9_9, all_111_2_34, 0 and discharging atoms member(all_53_1_14, all_0_9_9) = all_111_2_34, member(all_53_1_14, all_0_9_9) = 0, yields: % 11.70/3.27 | (255) all_111_2_34 = 0 % 11.70/3.27 | % 11.70/3.27 +-Applying beta-rule and splitting (252), into two cases. % 11.70/3.27 |-Branch one: % 11.70/3.27 | (256) ~ (all_111_0_32 = 0) % 11.70/3.27 | % 11.70/3.27 | Equations (254) can reduce 256 to: % 11.70/3.27 | (103) $false % 11.70/3.27 | % 11.70/3.27 |-The branch is then unsatisfiable % 11.70/3.27 |-Branch two: % 11.70/3.27 | (254) all_111_0_32 = 0 % 11.70/3.27 | (259) ~ (all_111_1_33 = 0) | ~ (all_111_2_34 = 0) % 11.70/3.27 | % 11.70/3.27 +-Applying beta-rule and splitting (259), into two cases. % 11.70/3.27 |-Branch one: % 11.70/3.27 | (260) ~ (all_111_1_33 = 0) % 11.70/3.27 | % 11.70/3.27 | Equations (253) can reduce 260 to: % 11.70/3.27 | (103) $false % 11.70/3.27 | % 11.70/3.27 |-The branch is then unsatisfiable % 11.70/3.27 |-Branch two: % 11.70/3.27 | (253) all_111_1_33 = 0 % 11.70/3.27 | (263) ~ (all_111_2_34 = 0) % 11.70/3.27 | % 11.70/3.27 | Equations (255) can reduce 263 to: % 11.70/3.27 | (103) $false % 11.70/3.27 | % 11.70/3.27 |-The branch is then unsatisfiable % 11.70/3.27 |-Branch two: % 11.70/3.27 | (113) all_14_0_11 = 0 % 11.70/3.27 | (266) ~ (all_14_1_12 = 0) % 11.70/3.27 | % 11.70/3.27 +-Applying beta-rule and splitting (111), into two cases. % 11.70/3.27 |-Branch one: % 11.70/3.27 | (267) all_14_1_12 = 0 % 11.70/3.27 | % 11.70/3.27 | Equations (267) can reduce 266 to: % 11.70/3.27 | (103) $false % 11.70/3.27 | % 11.70/3.27 |-The branch is then unsatisfiable % 11.70/3.27 |-Branch two: % 11.70/3.27 | (266) ~ (all_14_1_12 = 0) % 11.70/3.27 | (270) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_4_4) = 0) % 11.70/3.27 | % 11.70/3.27 | Instantiating (270) with all_53_0_38, all_53_1_39 yields: % 11.70/3.27 | (271) ~ (all_53_0_38 = 0) & member(all_53_1_39, all_0_1_1) = all_53_0_38 & member(all_53_1_39, all_0_4_4) = 0 % 11.70/3.27 | % 11.70/3.27 | Applying alpha-rule on (271) yields: % 11.70/3.27 | (272) ~ (all_53_0_38 = 0) % 11.70/3.27 | (273) member(all_53_1_39, all_0_1_1) = all_53_0_38 % 11.70/3.27 | (274) member(all_53_1_39, all_0_4_4) = 0 % 11.70/3.27 | % 11.70/3.27 | Instantiating formula (96) with all_53_0_38, all_0_1_1, all_0_2_2, all_0_3_3, all_53_1_39 and discharging atoms intersection(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_53_1_39, all_0_1_1) = all_53_0_38, yields: % 11.70/3.27 | (275) all_53_0_38 = 0 | ? [v0] : ? [v1] : (member(all_53_1_39, all_0_2_2) = v1 & member(all_53_1_39, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 11.70/3.27 | % 11.70/3.27 | Instantiating formula (6) with all_0_4_4, all_53_1_39, all_0_9_9, all_0_5_5, all_0_10_10 and discharging atoms inverse_image3(all_0_10_10, all_0_5_5, all_0_9_9) = all_0_4_4, member(all_53_1_39, all_0_4_4) = 0, yields: % 11.70/3.27 | (276) member(all_53_1_39, all_0_9_9) = 0 % 11.70/3.27 | % 11.70/3.27 | Instantiating formula (56) with all_0_4_4, all_53_1_39, all_0_9_9, all_0_5_5, all_0_10_10 and discharging atoms inverse_image3(all_0_10_10, all_0_5_5, all_0_9_9) = all_0_4_4, member(all_53_1_39, all_0_4_4) = 0, yields: % 11.70/3.27 | (277) ? [v0] : (apply(all_0_10_10, all_53_1_39, v0) = 0 & member(v0, all_0_5_5) = 0) % 11.70/3.27 | % 11.70/3.27 | Instantiating formula (9) with all_53_1_39, all_0_8_8, all_0_9_9, all_0_10_10 and discharging atoms maps(all_0_10_10, all_0_9_9, all_0_8_8) = 0, yields: % 11.70/3.27 | (278) ~ (member(all_53_1_39, all_0_9_9) = 0) | ? [v0] : (apply(all_0_10_10, all_53_1_39, v0) = 0 & member(v0, all_0_8_8) = 0) % 11.70/3.27 | % 11.70/3.27 | Instantiating (277) with all_69_0_40 yields: % 11.70/3.27 | (279) apply(all_0_10_10, all_53_1_39, all_69_0_40) = 0 & member(all_69_0_40, all_0_5_5) = 0 % 11.70/3.27 | % 11.70/3.27 | Applying alpha-rule on (279) yields: % 11.70/3.27 | (280) apply(all_0_10_10, all_53_1_39, all_69_0_40) = 0 % 11.70/3.27 | (281) member(all_69_0_40, all_0_5_5) = 0 % 11.70/3.27 | % 11.70/3.27 +-Applying beta-rule and splitting (278), into two cases. % 11.70/3.27 |-Branch one: % 11.70/3.27 | (282) ~ (member(all_53_1_39, all_0_9_9) = 0) % 11.70/3.27 | % 11.70/3.27 | Using (276) and (282) yields: % 11.70/3.27 | (129) $false % 11.70/3.27 | % 11.70/3.27 |-The branch is then unsatisfiable % 11.70/3.27 |-Branch two: % 11.70/3.27 | (276) member(all_53_1_39, all_0_9_9) = 0 % 11.70/3.27 | (285) ? [v0] : (apply(all_0_10_10, all_53_1_39, v0) = 0 & member(v0, all_0_8_8) = 0) % 11.70/3.27 | % 11.70/3.27 +-Applying beta-rule and splitting (275), into two cases. % 11.70/3.27 |-Branch one: % 11.70/3.27 | (286) all_53_0_38 = 0 % 11.70/3.27 | % 11.70/3.27 | Equations (286) can reduce 272 to: % 11.70/3.27 | (103) $false % 11.70/3.27 | % 11.70/3.27 |-The branch is then unsatisfiable % 11.70/3.27 |-Branch two: % 11.70/3.27 | (272) ~ (all_53_0_38 = 0) % 11.70/3.27 | (289) ? [v0] : ? [v1] : (member(all_53_1_39, all_0_2_2) = v1 & member(all_53_1_39, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 11.70/3.27 | % 11.70/3.27 | Instantiating (289) with all_80_0_42, all_80_1_43 yields: % 11.70/3.27 | (290) member(all_53_1_39, all_0_2_2) = all_80_0_42 & member(all_53_1_39, all_0_3_3) = all_80_1_43 & ( ~ (all_80_0_42 = 0) | ~ (all_80_1_43 = 0)) % 11.70/3.27 | % 11.70/3.27 | Applying alpha-rule on (290) yields: % 11.70/3.27 | (291) member(all_53_1_39, all_0_2_2) = all_80_0_42 % 11.70/3.27 | (292) member(all_53_1_39, all_0_3_3) = all_80_1_43 % 11.70/3.27 | (293) ~ (all_80_0_42 = 0) | ~ (all_80_1_43 = 0) % 11.70/3.27 | % 11.70/3.27 | Instantiating formula (15) with all_0_5_5, all_0_6_6, all_0_7_7, all_69_0_40 and discharging atoms intersection(all_0_7_7, all_0_6_6) = all_0_5_5, member(all_69_0_40, all_0_5_5) = 0, yields: % 11.70/3.27 | (294) member(all_69_0_40, all_0_6_6) = 0 & member(all_69_0_40, all_0_7_7) = 0 % 11.70/3.27 | % 11.70/3.27 | Applying alpha-rule on (294) yields: % 11.70/3.27 | (295) member(all_69_0_40, all_0_6_6) = 0 % 11.70/3.27 | (296) member(all_69_0_40, all_0_7_7) = 0 % 11.70/3.27 | % 11.70/3.27 | Instantiating formula (91) with all_69_0_40, all_80_0_42, all_0_2_2, all_53_1_39, all_0_9_9, all_0_6_6, all_0_10_10 and discharging atoms inverse_image3(all_0_10_10, all_0_6_6, all_0_9_9) = all_0_2_2, apply(all_0_10_10, all_53_1_39, all_69_0_40) = 0, member(all_53_1_39, all_0_2_2) = all_80_0_42, yields: % 11.70/3.27 | (297) all_80_0_42 = 0 | ? [v0] : (( ~ (v0 = 0) & member(all_69_0_40, all_0_6_6) = v0) | ( ~ (v0 = 0) & member(all_53_1_39, all_0_9_9) = v0)) % 11.70/3.27 | % 11.70/3.27 | Instantiating formula (91) with all_69_0_40, all_80_1_43, all_0_3_3, all_53_1_39, all_0_9_9, all_0_7_7, all_0_10_10 and discharging atoms inverse_image3(all_0_10_10, all_0_7_7, all_0_9_9) = all_0_3_3, apply(all_0_10_10, all_53_1_39, all_69_0_40) = 0, member(all_53_1_39, all_0_3_3) = all_80_1_43, yields: % 11.70/3.27 | (298) all_80_1_43 = 0 | ? [v0] : (( ~ (v0 = 0) & member(all_69_0_40, all_0_7_7) = v0) | ( ~ (v0 = 0) & member(all_53_1_39, all_0_9_9) = v0)) % 11.70/3.27 | % 11.70/3.27 +-Applying beta-rule and splitting (297), into two cases. % 11.70/3.27 |-Branch one: % 11.70/3.27 | (299) all_80_0_42 = 0 % 11.70/3.27 | % 11.70/3.27 +-Applying beta-rule and splitting (293), into two cases. % 11.70/3.27 |-Branch one: % 11.70/3.27 | (300) ~ (all_80_0_42 = 0) % 11.70/3.27 | % 11.70/3.27 | Equations (299) can reduce 300 to: % 11.70/3.27 | (103) $false % 11.70/3.27 | % 11.70/3.27 |-The branch is then unsatisfiable % 11.70/3.27 |-Branch two: % 11.70/3.27 | (299) all_80_0_42 = 0 % 11.70/3.27 | (303) ~ (all_80_1_43 = 0) % 11.70/3.27 | % 11.70/3.27 +-Applying beta-rule and splitting (298), into two cases. % 11.70/3.27 |-Branch one: % 11.70/3.27 | (304) all_80_1_43 = 0 % 11.70/3.27 | % 11.70/3.27 | Equations (304) can reduce 303 to: % 11.70/3.27 | (103) $false % 11.70/3.27 | % 11.70/3.27 |-The branch is then unsatisfiable % 11.70/3.27 |-Branch two: % 11.70/3.27 | (303) ~ (all_80_1_43 = 0) % 11.70/3.27 | (307) ? [v0] : (( ~ (v0 = 0) & member(all_69_0_40, all_0_7_7) = v0) | ( ~ (v0 = 0) & member(all_53_1_39, all_0_9_9) = v0)) % 11.70/3.28 | % 11.70/3.28 | Instantiating (307) with all_125_0_45 yields: % 11.70/3.28 | (308) ( ~ (all_125_0_45 = 0) & member(all_69_0_40, all_0_7_7) = all_125_0_45) | ( ~ (all_125_0_45 = 0) & member(all_53_1_39, all_0_9_9) = all_125_0_45) % 11.70/3.28 | % 11.70/3.28 +-Applying beta-rule and splitting (308), into two cases. % 11.70/3.28 |-Branch one: % 11.70/3.28 | (309) ~ (all_125_0_45 = 0) & member(all_69_0_40, all_0_7_7) = all_125_0_45 % 11.70/3.28 | % 11.70/3.28 | Applying alpha-rule on (309) yields: % 11.70/3.28 | (310) ~ (all_125_0_45 = 0) % 11.70/3.28 | (311) member(all_69_0_40, all_0_7_7) = all_125_0_45 % 11.70/3.28 | % 11.70/3.28 | Instantiating formula (38) with all_69_0_40, all_0_7_7, 0, all_125_0_45 and discharging atoms member(all_69_0_40, all_0_7_7) = all_125_0_45, member(all_69_0_40, all_0_7_7) = 0, yields: % 11.70/3.28 | (312) all_125_0_45 = 0 % 11.70/3.28 | % 11.70/3.28 | Equations (312) can reduce 310 to: % 11.70/3.28 | (103) $false % 11.70/3.28 | % 11.70/3.28 |-The branch is then unsatisfiable % 11.70/3.28 |-Branch two: % 11.70/3.28 | (314) ~ (all_125_0_45 = 0) & member(all_53_1_39, all_0_9_9) = all_125_0_45 % 11.70/3.28 | % 11.70/3.28 | Applying alpha-rule on (314) yields: % 11.70/3.28 | (310) ~ (all_125_0_45 = 0) % 11.70/3.28 | (316) member(all_53_1_39, all_0_9_9) = all_125_0_45 % 11.70/3.28 | % 11.70/3.28 | Instantiating formula (38) with all_53_1_39, all_0_9_9, all_125_0_45, 0 and discharging atoms member(all_53_1_39, all_0_9_9) = all_125_0_45, member(all_53_1_39, all_0_9_9) = 0, yields: % 11.70/3.28 | (312) all_125_0_45 = 0 % 11.70/3.28 | % 11.70/3.28 | Equations (312) can reduce 310 to: % 11.70/3.28 | (103) $false % 11.70/3.28 | % 11.70/3.28 |-The branch is then unsatisfiable % 11.70/3.28 |-Branch two: % 11.70/3.28 | (300) ~ (all_80_0_42 = 0) % 11.70/3.28 | (320) ? [v0] : (( ~ (v0 = 0) & member(all_69_0_40, all_0_6_6) = v0) | ( ~ (v0 = 0) & member(all_53_1_39, all_0_9_9) = v0)) % 11.70/3.28 | % 11.70/3.28 | Instantiating (320) with all_104_0_48 yields: % 11.70/3.28 | (321) ( ~ (all_104_0_48 = 0) & member(all_69_0_40, all_0_6_6) = all_104_0_48) | ( ~ (all_104_0_48 = 0) & member(all_53_1_39, all_0_9_9) = all_104_0_48) % 11.70/3.28 | % 11.70/3.28 +-Applying beta-rule and splitting (321), into two cases. % 11.70/3.28 |-Branch one: % 11.70/3.28 | (322) ~ (all_104_0_48 = 0) & member(all_69_0_40, all_0_6_6) = all_104_0_48 % 11.70/3.28 | % 11.70/3.28 | Applying alpha-rule on (322) yields: % 11.70/3.28 | (323) ~ (all_104_0_48 = 0) % 11.70/3.28 | (324) member(all_69_0_40, all_0_6_6) = all_104_0_48 % 11.70/3.28 | % 11.70/3.28 | Instantiating formula (38) with all_69_0_40, all_0_6_6, 0, all_104_0_48 and discharging atoms member(all_69_0_40, all_0_6_6) = all_104_0_48, member(all_69_0_40, all_0_6_6) = 0, yields: % 11.70/3.28 | (325) all_104_0_48 = 0 % 11.70/3.28 | % 11.70/3.28 | Equations (325) can reduce 323 to: % 11.70/3.28 | (103) $false % 11.70/3.28 | % 11.70/3.28 |-The branch is then unsatisfiable % 11.70/3.28 |-Branch two: % 11.70/3.28 | (327) ~ (all_104_0_48 = 0) & member(all_53_1_39, all_0_9_9) = all_104_0_48 % 11.70/3.28 | % 11.70/3.28 | Applying alpha-rule on (327) yields: % 11.70/3.28 | (323) ~ (all_104_0_48 = 0) % 11.70/3.28 | (329) member(all_53_1_39, all_0_9_9) = all_104_0_48 % 11.70/3.28 | % 11.70/3.28 | Instantiating formula (38) with all_53_1_39, all_0_9_9, all_104_0_48, 0 and discharging atoms member(all_53_1_39, all_0_9_9) = all_104_0_48, member(all_53_1_39, all_0_9_9) = 0, yields: % 11.70/3.28 | (325) all_104_0_48 = 0 % 11.70/3.28 | % 11.70/3.28 | Equations (325) can reduce 323 to: % 11.70/3.28 | (103) $false % 11.70/3.28 | % 11.70/3.28 |-The branch is then unsatisfiable % 11.70/3.28 % SZS output end Proof for theBenchmark % 11.70/3.28 % 11.70/3.28 2639ms %------------------------------------------------------------------------------