%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET753+4 : TPTP v8.1.0. Bugfixed v2.2.1. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n004.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 00:21:50 EDT 2022 % Result : Theorem 6.66s 2.07s % Output : Proof 9.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SET753+4 : TPTP v8.1.0. Bugfixed v2.2.1. % 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n004.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Mon Jul 11 07:36:22 EDT 2022 % 0.13/0.34 % CPUTime : % 0.66/0.63 ____ _ % 0.66/0.63 ___ / __ \_____(_)___ ________ __________ % 0.66/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.66/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.66/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.66/0.63 % 0.66/0.63 A Theorem Prover for First-Order Logic % 0.66/0.63 (ePrincess v.1.0) % 0.66/0.63 % 0.66/0.63 (c) Philipp Rümmer, 2009-2015 % 0.66/0.63 (c) Peter Backeman, 2014-2015 % 0.66/0.63 (contributions by Angelo Brillout, Peter Baumgartner) % 0.66/0.63 Free software under GNU Lesser General Public License (LGPL). % 0.66/0.63 Bug reports to peter@backeman.se % 0.66/0.63 % 0.66/0.63 For more information, visit http://user.uu.se/~petba168/breu/ % 0.66/0.63 % 0.66/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.74/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.06/1.04 Prover 0: Preprocessing ... % 3.52/1.38 Prover 0: Warning: ignoring some quantifiers % 3.52/1.41 Prover 0: Constructing countermodel ... % 4.89/1.71 Prover 0: gave up % 4.89/1.71 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 4.89/1.76 Prover 1: Preprocessing ... % 6.28/1.99 Prover 1: Constructing countermodel ... % 6.28/2.07 Prover 1: proved (356ms) % 6.66/2.07 % 6.66/2.07 No countermodel exists, formula is valid % 6.66/2.07 % SZS status Theorem for theBenchmark % 6.66/2.07 % 6.66/2.07 Generating proof ... found it (size 42) % 8.74/2.55 % 8.74/2.55 % SZS output start Proof for theBenchmark % 8.74/2.55 Assumed formulas after preprocessing and simplification: % 8.74/2.55 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & image2(v0, v5) = v6 & image2(v0, v4) = v8 & image2(v0, v3) = v7 & maps(v0, v1, v2) = 0 & intersection(v7, v8) = v9 & intersection(v3, v4) = v5 & subset(v6, v9) = v10 & subset(v4, v1) = 0 & subset(v3, v1) = 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)) % 9.08/2.61 | 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: % 9.08/2.61 | (1) ~ (all_0_0_0 = 0) & image2(all_0_10_10, all_0_5_5) = all_0_4_4 & image2(all_0_10_10, all_0_6_6) = all_0_2_2 & image2(all_0_10_10, all_0_7_7) = 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 & subset(all_0_4_4, all_0_1_1) = all_0_0_0 & subset(all_0_6_6, all_0_9_9) = 0 & subset(all_0_7_7, all_0_9_9) = 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) % 9.08/2.65 | % 9.08/2.65 | Applying alpha-rule on (1) yields: % 9.08/2.65 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 9.08/2.65 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 9.08/2.65 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 9.08/2.65 | (5) ! [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)) % 9.08/2.65 | (6) ! [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))) % 9.08/2.65 | (7) ! [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)) % 9.08/2.65 | (8) ! [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)))) % 9.08/2.65 | (9) ~ (all_0_0_0 = 0) % 9.08/2.65 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) % 9.08/2.65 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 9.08/2.65 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 9.08/2.65 | (13) ! [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)) % 9.08/2.65 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 9.08/2.66 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 9.08/2.66 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0)) % 9.08/2.66 | (17) intersection(all_0_7_7, all_0_6_6) = all_0_5_5 % 9.08/2.66 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) % 9.08/2.66 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) % 9.08/2.66 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 9.08/2.66 | (21) ! [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))))) % 9.08/2.66 | (22) ! [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))))) % 9.08/2.66 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) % 9.08/2.66 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 9.08/2.66 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0) % 9.08/2.66 | (26) ! [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))))) % 9.08/2.66 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0)) % 9.08/2.66 | (28) ! [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)))) % 9.08/2.66 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0)) % 9.08/2.66 | (30) maps(all_0_10_10, all_0_9_9, all_0_8_8) = 0 % 9.08/2.66 | (31) ! [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)) % 9.08/2.66 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 9.08/2.66 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 9.08/2.66 | (34) intersection(all_0_3_3, all_0_2_2) = all_0_1_1 % 9.08/2.66 | (35) ! [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)) % 9.08/2.66 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0)) % 9.08/2.66 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0)) % 9.08/2.66 | (38) ! [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)))) % 9.08/2.66 | (39) subset(all_0_4_4, all_0_1_1) = all_0_0_0 % 9.08/2.66 | (40) ! [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)) % 9.08/2.66 | (41) image2(all_0_10_10, all_0_6_6) = all_0_2_2 % 9.08/2.66 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0)) % 9.08/2.67 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) % 9.08/2.67 | (44) ! [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)) % 9.08/2.67 | (45) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 9.08/2.67 | (46) ! [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))))) % 9.08/2.67 | (47) ! [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))))) % 9.08/2.67 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0)) % 9.08/2.67 | (49) ! [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)) % 9.42/2.67 | (50) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 9.42/2.67 | (51) subset(all_0_7_7, all_0_9_9) = 0 % 9.42/2.67 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 9.42/2.67 | (53) ! [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)))) % 9.42/2.67 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0)) % 9.42/2.67 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) % 9.42/2.67 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 9.42/2.67 | (57) image2(all_0_10_10, all_0_5_5) = all_0_4_4 % 9.42/2.67 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 9.42/2.67 | (59) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 9.42/2.67 | (60) ! [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)))) % 9.42/2.67 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0)) % 9.42/2.67 | (62) ! [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))) % 9.42/2.67 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) % 9.42/2.67 | (64) ! [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))))) % 9.42/2.67 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 9.42/2.67 | (66) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 9.42/2.67 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0)) % 9.42/2.67 | (68) ! [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)) % 9.42/2.67 | (69) image2(all_0_10_10, all_0_7_7) = all_0_3_3 % 9.42/2.67 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0)) % 9.42/2.67 | (71) ! [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))))) % 9.42/2.68 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 9.42/2.68 | (73) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 9.42/2.68 | (74) ! [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))) % 9.42/2.68 | (75) ! [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))) % 9.42/2.68 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0) % 9.42/2.68 | (77) ! [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))) % 9.42/2.68 | (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)) % 9.42/2.68 | (79) ! [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)))) % 9.42/2.68 | (80) ! [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)) % 9.42/2.68 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 9.42/2.68 | (82) ! [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))) % 9.42/2.68 | (83) ! [v0] : ~ (member(v0, empty_set) = 0) % 9.42/2.68 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 9.42/2.68 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0)) % 9.42/2.68 | (86) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0)) % 9.42/2.68 | (87) ! [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)) % 9.42/2.68 | (88) ! [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)))) % 9.42/2.68 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0)) % 9.42/2.68 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0)) % 9.42/2.68 | (91) ! [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))))) % 9.42/2.68 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 9.42/2.68 | (93) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 9.42/2.68 | (94) ! [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))))) % 9.42/2.68 | (95) ! [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))) % 9.42/2.68 | (96) subset(all_0_6_6, all_0_9_9) = 0 % 9.42/2.68 | (97) ! [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))) % 9.42/2.69 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) % 9.42/2.69 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 9.42/2.69 | (100) ! [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)) % 9.42/2.69 | % 9.42/2.69 | Instantiating formula (66) with all_0_0_0, all_0_1_1, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_1_1) = all_0_0_0, yields: % 9.42/2.69 | (101) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_4_4) = 0) % 9.42/2.69 | % 9.42/2.69 +-Applying beta-rule and splitting (101), into two cases. % 9.42/2.69 |-Branch one: % 9.42/2.69 | (102) all_0_0_0 = 0 % 9.42/2.69 | % 9.42/2.69 | Equations (102) can reduce 9 to: % 9.42/2.69 | (103) $false % 9.42/2.69 | % 9.42/2.69 |-The branch is then unsatisfiable % 9.42/2.69 |-Branch two: % 9.42/2.69 | (9) ~ (all_0_0_0 = 0) % 9.42/2.69 | (105) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_4_4) = 0) % 9.42/2.69 | % 9.42/2.69 | Instantiating (105) with all_14_0_11, all_14_1_12 yields: % 9.42/2.69 | (106) ~ (all_14_0_11 = 0) & member(all_14_1_12, all_0_1_1) = all_14_0_11 & member(all_14_1_12, all_0_4_4) = 0 % 9.42/2.69 | % 9.42/2.69 | Applying alpha-rule on (106) yields: % 9.42/2.69 | (107) ~ (all_14_0_11 = 0) % 9.42/2.69 | (108) member(all_14_1_12, all_0_1_1) = all_14_0_11 % 9.42/2.69 | (109) member(all_14_1_12, all_0_4_4) = 0 % 9.42/2.69 | % 9.42/2.69 | Instantiating formula (38) with all_14_0_11, all_0_1_1, all_0_2_2, all_0_3_3, all_14_1_12 and discharging atoms intersection(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_14_1_12, all_0_1_1) = all_14_0_11, yields: % 9.42/2.69 | (110) all_14_0_11 = 0 | ? [v0] : ? [v1] : (member(all_14_1_12, all_0_2_2) = v1 & member(all_14_1_12, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 9.42/2.69 | % 9.42/2.69 | Instantiating formula (54) with all_0_4_4, all_14_1_12, all_0_5_5, all_0_10_10 and discharging atoms image2(all_0_10_10, all_0_5_5) = all_0_4_4, member(all_14_1_12, all_0_4_4) = 0, yields: % 9.42/2.69 | (111) ? [v0] : (apply(all_0_10_10, v0, all_14_1_12) = 0 & member(v0, all_0_5_5) = 0) % 9.42/2.69 | % 9.42/2.69 | Instantiating (111) with all_29_0_13 yields: % 9.42/2.69 | (112) apply(all_0_10_10, all_29_0_13, all_14_1_12) = 0 & member(all_29_0_13, all_0_5_5) = 0 % 9.42/2.69 | % 9.42/2.69 | Applying alpha-rule on (112) yields: % 9.42/2.69 | (113) apply(all_0_10_10, all_29_0_13, all_14_1_12) = 0 % 9.42/2.69 | (114) member(all_29_0_13, all_0_5_5) = 0 % 9.42/2.69 | % 9.42/2.69 +-Applying beta-rule and splitting (110), into two cases. % 9.42/2.69 |-Branch one: % 9.42/2.69 | (115) all_14_0_11 = 0 % 9.42/2.69 | % 9.42/2.69 | Equations (115) can reduce 107 to: % 9.42/2.69 | (103) $false % 9.42/2.69 | % 9.42/2.69 |-The branch is then unsatisfiable % 9.42/2.69 |-Branch two: % 9.42/2.69 | (107) ~ (all_14_0_11 = 0) % 9.42/2.69 | (118) ? [v0] : ? [v1] : (member(all_14_1_12, all_0_2_2) = v1 & member(all_14_1_12, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 9.42/2.69 | % 9.42/2.69 | Instantiating (118) with all_35_0_14, all_35_1_15 yields: % 9.42/2.69 | (119) member(all_14_1_12, all_0_2_2) = all_35_0_14 & member(all_14_1_12, all_0_3_3) = all_35_1_15 & ( ~ (all_35_0_14 = 0) | ~ (all_35_1_15 = 0)) % 9.42/2.69 | % 9.42/2.69 | Applying alpha-rule on (119) yields: % 9.42/2.69 | (120) member(all_14_1_12, all_0_2_2) = all_35_0_14 % 9.42/2.69 | (121) member(all_14_1_12, all_0_3_3) = all_35_1_15 % 9.42/2.69 | (122) ~ (all_35_0_14 = 0) | ~ (all_35_1_15 = 0) % 9.42/2.69 | % 9.42/2.69 | Instantiating formula (4) with all_0_5_5, all_0_6_6, all_0_7_7, all_29_0_13 and discharging atoms intersection(all_0_7_7, all_0_6_6) = all_0_5_5, member(all_29_0_13, all_0_5_5) = 0, yields: % 9.42/2.69 | (123) member(all_29_0_13, all_0_6_6) = 0 & member(all_29_0_13, all_0_7_7) = 0 % 9.42/2.69 | % 9.42/2.69 | Applying alpha-rule on (123) yields: % 9.42/2.69 | (124) member(all_29_0_13, all_0_6_6) = 0 % 9.42/2.69 | (125) member(all_29_0_13, all_0_7_7) = 0 % 9.42/2.69 | % 9.42/2.69 | Instantiating formula (84) with all_29_0_13, all_0_9_9, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_9_9) = 0, yields: % 9.42/2.69 | (126) ~ (member(all_29_0_13, all_0_6_6) = 0) | member(all_29_0_13, all_0_9_9) = 0 % 9.42/2.69 | % 9.42/2.69 | Instantiating formula (49) with all_29_0_13, all_35_0_14, all_0_2_2, all_14_1_12, all_0_6_6, all_0_10_10 and discharging atoms image2(all_0_10_10, all_0_6_6) = all_0_2_2, apply(all_0_10_10, all_29_0_13, all_14_1_12) = 0, member(all_14_1_12, all_0_2_2) = all_35_0_14, yields: % 9.42/2.69 | (127) all_35_0_14 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_29_0_13, all_0_6_6) = v0) % 9.42/2.69 | % 9.42/2.69 | Instantiating formula (49) with all_29_0_13, all_35_1_15, all_0_3_3, all_14_1_12, all_0_7_7, all_0_10_10 and discharging atoms image2(all_0_10_10, all_0_7_7) = all_0_3_3, apply(all_0_10_10, all_29_0_13, all_14_1_12) = 0, member(all_14_1_12, all_0_3_3) = all_35_1_15, yields: % 9.42/2.69 | (128) all_35_1_15 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_29_0_13, all_0_7_7) = v0) % 9.42/2.69 | % 9.42/2.69 +-Applying beta-rule and splitting (126), into two cases. % 9.42/2.69 |-Branch one: % 9.42/2.69 | (129) ~ (member(all_29_0_13, all_0_6_6) = 0) % 9.42/2.69 | % 9.42/2.69 | Using (124) and (129) yields: % 9.42/2.69 | (130) $false % 9.42/2.69 | % 9.42/2.69 |-The branch is then unsatisfiable % 9.42/2.69 |-Branch two: % 9.42/2.69 | (124) member(all_29_0_13, all_0_6_6) = 0 % 9.42/2.69 | (132) member(all_29_0_13, all_0_9_9) = 0 % 9.42/2.69 | % 9.42/2.69 +-Applying beta-rule and splitting (128), into two cases. % 9.42/2.69 |-Branch one: % 9.42/2.69 | (133) all_35_1_15 = 0 % 9.42/2.69 | % 9.42/2.69 +-Applying beta-rule and splitting (122), into two cases. % 9.42/2.69 |-Branch one: % 9.42/2.69 | (134) ~ (all_35_0_14 = 0) % 9.42/2.69 | % 9.42/2.69 +-Applying beta-rule and splitting (127), into two cases. % 9.42/2.69 |-Branch one: % 9.42/2.69 | (135) all_35_0_14 = 0 % 9.42/2.69 | % 9.42/2.69 | Equations (135) can reduce 134 to: % 9.42/2.69 | (103) $false % 9.42/2.69 | % 9.42/2.69 |-The branch is then unsatisfiable % 9.42/2.69 |-Branch two: % 9.42/2.69 | (134) ~ (all_35_0_14 = 0) % 9.42/2.69 | (138) ? [v0] : ( ~ (v0 = 0) & member(all_29_0_13, all_0_6_6) = v0) % 9.42/2.69 | % 9.42/2.69 | Instantiating (138) with all_89_0_18 yields: % 9.42/2.69 | (139) ~ (all_89_0_18 = 0) & member(all_29_0_13, all_0_6_6) = all_89_0_18 % 9.42/2.69 | % 9.42/2.69 | Applying alpha-rule on (139) yields: % 9.42/2.69 | (140) ~ (all_89_0_18 = 0) % 9.42/2.69 | (141) member(all_29_0_13, all_0_6_6) = all_89_0_18 % 9.42/2.69 | % 9.42/2.70 | Instantiating formula (92) with all_29_0_13, all_0_6_6, all_89_0_18, 0 and discharging atoms member(all_29_0_13, all_0_6_6) = all_89_0_18, member(all_29_0_13, all_0_6_6) = 0, yields: % 9.42/2.70 | (142) all_89_0_18 = 0 % 9.42/2.70 | % 9.42/2.70 | Equations (142) can reduce 140 to: % 9.42/2.70 | (103) $false % 9.42/2.70 | % 9.42/2.70 |-The branch is then unsatisfiable % 9.42/2.70 |-Branch two: % 9.42/2.70 | (135) all_35_0_14 = 0 % 9.42/2.70 | (145) ~ (all_35_1_15 = 0) % 9.42/2.70 | % 9.42/2.70 | Equations (133) can reduce 145 to: % 9.42/2.70 | (103) $false % 9.42/2.70 | % 9.42/2.70 |-The branch is then unsatisfiable % 9.42/2.70 |-Branch two: % 9.42/2.70 | (145) ~ (all_35_1_15 = 0) % 9.42/2.70 | (148) ? [v0] : ( ~ (v0 = 0) & member(all_29_0_13, all_0_7_7) = v0) % 9.42/2.70 | % 9.42/2.70 | Instantiating (148) with all_68_0_19 yields: % 9.42/2.70 | (149) ~ (all_68_0_19 = 0) & member(all_29_0_13, all_0_7_7) = all_68_0_19 % 9.42/2.70 | % 9.42/2.70 | Applying alpha-rule on (149) yields: % 9.42/2.70 | (150) ~ (all_68_0_19 = 0) % 9.42/2.70 | (151) member(all_29_0_13, all_0_7_7) = all_68_0_19 % 9.42/2.70 | % 9.42/2.70 | Instantiating formula (92) with all_29_0_13, all_0_7_7, all_68_0_19, 0 and discharging atoms member(all_29_0_13, all_0_7_7) = all_68_0_19, member(all_29_0_13, all_0_7_7) = 0, yields: % 9.42/2.70 | (152) all_68_0_19 = 0 % 9.42/2.70 | % 9.42/2.70 | Equations (152) can reduce 150 to: % 9.42/2.70 | (103) $false % 9.42/2.70 | % 9.42/2.70 |-The branch is then unsatisfiable % 9.42/2.70 % SZS output end Proof for theBenchmark % 9.42/2.70 % 9.42/2.70 2053ms %------------------------------------------------------------------------------