%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU034+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n032.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Tue Jul 19 08:46:18 EDT 2022 % Result : Theorem 4.19s 1.75s % Output : Proof 7.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : SEU034+1 : TPTP v8.1.0. Released v3.2.0. % 0.00/0.10 % Command : ePrincess-casc -timeout=%d %s % 0.10/0.28 % Computer : n032.cluster.edu % 0.10/0.28 % Model : x86_64 x86_64 % 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.28 % Memory : 8042.1875MB % 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.28 % CPULimit : 300 % 0.10/0.28 % WCLimit : 600 % 0.10/0.28 % DateTime : Mon Jun 20 03:21:03 EDT 2022 % 0.14/0.29 % CPUTime : % 0.14/0.54 ____ _ % 0.14/0.54 ___ / __ \_____(_)___ ________ __________ % 0.14/0.54 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.14/0.54 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.14/0.54 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.14/0.54 % 0.14/0.54 A Theorem Prover for First-Order Logic % 0.14/0.54 (ePrincess v.1.0) % 0.14/0.54 % 0.14/0.54 (c) Philipp Rümmer, 2009-2015 % 0.14/0.54 (c) Peter Backeman, 2014-2015 % 0.14/0.54 (contributions by Angelo Brillout, Peter Baumgartner) % 0.14/0.54 Free software under GNU Lesser General Public License (LGPL). % 0.14/0.54 Bug reports to peter@backeman.se % 0.14/0.54 % 0.14/0.54 For more information, visit http://user.uu.se/~petba168/breu/ % 0.14/0.54 % 0.14/0.54 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.58/0.59 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.59/0.99 Prover 0: Preprocessing ... % 2.89/1.40 Prover 0: Warning: ignoring some quantifiers % 2.89/1.44 Prover 0: Constructing countermodel ... % 4.19/1.75 Prover 0: proved (1161ms) % 4.19/1.75 % 4.19/1.75 No countermodel exists, formula is valid % 4.19/1.75 % SZS status Theorem for theBenchmark % 4.19/1.75 % 4.19/1.75 Generating proof ... Warning: ignoring some quantifiers % 6.60/2.26 found it (size 78) % 6.60/2.26 % 6.60/2.26 % SZS output start Proof for theBenchmark % 6.60/2.26 Assumed formulas after preprocessing and simplification: % 6.60/2.26 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v2 = v1) & identity_relation(v0) = v1 & function_inverse(v1) = v2 & relation_empty_yielding(v3) & relation_empty_yielding(empty_set) & one_to_one(v4) & relation(v10) & relation(v9) & relation(v7) & relation(v6) & relation(v4) & relation(v3) & relation(empty_set) & function(v10) & function(v7) & function(v4) & empty(v9) & empty(v8) & empty(v7) & empty(empty_set) & ~ empty(v6) & ~ empty(v5) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (relation_composition(v14, v13) = v12) | ~ (relation_composition(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ element(v12, v14) | ~ empty(v13) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ element(v12, v14) | ~ in(v11, v12) | element(v11, v13)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation_rng(v13) = v12) | ~ (relation_rng(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation_dom(v13) = v12) | ~ (relation_dom(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (powerset(v13) = v12) | ~ (powerset(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (identity_relation(v13) = v12) | ~ (identity_relation(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (function_inverse(v13) = v12) | ~ (function_inverse(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_rng(v11) = v12) | ~ (relation_dom(v13) = v12) | ~ relation(v13) | ~ relation(v11) | ~ function(v13) | ~ function(v11) | ? [v14] : ? [v15] : (identity_relation(v12) = v15 & relation_composition(v11, v13) = v14 & ( ~ (v14 = v11) | v15 = v13))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_rng(v11) = v12) | ~ (relation_composition(v11, v13) = v11) | ~ relation(v13) | ~ relation(v11) | ~ function(v13) | ~ function(v11) | ? [v14] : ? [v15] : (relation_dom(v13) = v14 & identity_relation(v14) = v15 & ( ~ (v14 = v12) | v15 = v13))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ subset(v11, v12) | element(v11, v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ element(v11, v13) | subset(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v12, v11) = v13) | ~ (function_inverse(v11) = v12) | ~ one_to_one(v11) | ~ relation(v11) | ~ function(v11) | ? [v14] : ? [v15] : ? [v16] : (relation_rng(v11) = v16 & relation_dom(v11) = v15 & identity_relation(v16) = v13 & identity_relation(v15) = v14 & relation_composition(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v12, v11) = v13) | ~ relation(v12) | ~ empty(v11) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v12, v11) = v13) | ~ relation(v12) | ~ empty(v11) | empty(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ (function_inverse(v11) = v12) | ~ one_to_one(v11) | ~ relation(v11) | ~ function(v11) | ? [v14] : ? [v15] : ? [v16] : (relation_rng(v11) = v16 & relation_dom(v11) = v14 & identity_relation(v16) = v15 & identity_relation(v14) = v13 & relation_composition(v12, v11) = v15)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ relation(v12) | ~ relation(v11) | ~ function(v12) | ~ function(v11) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ relation(v12) | ~ relation(v11) | ~ function(v12) | ~ function(v11) | function(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ relation(v12) | ~ relation(v11) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ relation(v12) | ~ empty(v11) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ relation(v12) | ~ empty(v11) | empty(v13)) & ! [v11] : ! [v12] : (v12 = v11 | ~ empty(v12) | ~ empty(v11)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ one_to_one(v11) | ~ relation(v11) | ~ function(v11) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (relation_dom(v11) = v15 & identity_relation(v15) = v14 & identity_relation(v12) = v16 & relation_composition(v13, v11) = v16 & relation_composition(v11, v13) = v14 & function_inverse(v11) = v13)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ one_to_one(v11) | ~ relation(v11) | ~ function(v11) | ? [v13] : ? [v14] : (relation_rng(v13) = v14 & relation_dom(v13) = v12 & relation_dom(v11) = v14 & function_inverse(v11) = v13)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ relation(v11) | ~ empty(v12) | empty(v11)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ empty(v11) | relation(v12)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ empty(v11) | empty(v12)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ one_to_one(v11) | ~ relation(v11) | ~ function(v11) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (relation_rng(v11) = v16 & identity_relation(v16) = v15 & identity_relation(v12) = v14 & relation_composition(v13, v11) = v15 & relation_composition(v11, v13) = v14 & function_inverse(v11) = v13)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ one_to_one(v11) | ~ relation(v11) | ~ function(v11) | ? [v13] : ? [v14] : (relation_rng(v14) = v12 & relation_rng(v11) = v13 & relation_dom(v14) = v13 & function_inverse(v11) = v14)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ relation(v11) | ~ empty(v12) | empty(v11)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ empty(v11) | relation(v12)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ empty(v11) | empty(v12)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ empty(v12)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | empty(v11) | ? [v13] : (element(v13, v12) & ~ empty(v13))) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : (element(v13, v12) & empty(v13))) & ! [v11] : ! [v12] : ( ~ (identity_relation(v11) = v12) | relation_rng(v12) = v11) & ! [v11] : ! [v12] : ( ~ (identity_relation(v11) = v12) | relation_dom(v12) = v11) & ! [v11] : ! [v12] : ( ~ (identity_relation(v11) = v12) | one_to_one(v12)) & ! [v11] : ! [v12] : ( ~ (identity_relation(v11) = v12) | relation(v12)) & ! [v11] : ! [v12] : ( ~ (identity_relation(v11) = v12) | function(v12)) & ! [v11] : ! [v12] : ( ~ (function_inverse(v11) = v12) | ~ one_to_one(v11) | ~ relation(v11) | ~ function(v11) | ? [v13] : ? [v14] : (relation_rng(v12) = v14 & relation_rng(v11) = v13 & relation_dom(v12) = v13 & relation_dom(v11) = v14)) & ! [v11] : ! [v12] : ( ~ (function_inverse(v11) = v12) | ~ relation(v11) | ~ function(v11) | relation(v12)) & ! [v11] : ! [v12] : ( ~ (function_inverse(v11) = v12) | ~ relation(v11) | ~ function(v11) | function(v12)) & ! [v11] : ! [v12] : ( ~ element(v11, v12) | empty(v12) | in(v11, v12)) & ! [v11] : ! [v12] : ( ~ empty(v12) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ( ~ in(v12, v11) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ( ~ in(v11, v12) | element(v11, v12)) & ! [v11] : (v11 = empty_set | ~ empty(v11)) & ! [v11] : ( ~ relation(v11) | ~ function(v11) | ~ empty(v11) | one_to_one(v11)) & ! [v11] : ( ~ empty(v11) | relation(v11)) & ! [v11] : ( ~ empty(v11) | function(v11)) & ? [v11] : ? [v12] : element(v12, v11) & ? [v11] : subset(v11, v11)) % 7.01/2.34 | 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: % 7.01/2.34 | (1) ~ (all_0_8_8 = all_0_9_9) & identity_relation(all_0_10_10) = all_0_9_9 & function_inverse(all_0_9_9) = all_0_8_8 & relation_empty_yielding(all_0_7_7) & relation_empty_yielding(empty_set) & one_to_one(all_0_6_6) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_3_3) & relation(all_0_4_4) & relation(all_0_6_6) & relation(all_0_7_7) & relation(empty_set) & function(all_0_0_0) & function(all_0_3_3) & function(all_0_6_6) & empty(all_0_1_1) & empty(all_0_2_2) & empty(all_0_3_3) & empty(empty_set) & ~ empty(all_0_4_4) & ~ empty(all_0_5_5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ (relation_dom(v2) = v1) | ~ relation(v2) | ~ relation(v0) | ~ function(v2) | ~ function(v0) | ? [v3] : ? [v4] : (identity_relation(v1) = v4 & relation_composition(v0, v2) = v3 & ( ~ (v3 = v0) | v4 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ (relation_composition(v0, v2) = v0) | ~ relation(v2) | ~ relation(v0) | ~ function(v2) | ~ function(v0) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & identity_relation(v3) = v4 & ( ~ (v3 = v1) | v4 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v5 & relation_dom(v0) = v4 & identity_relation(v5) = v2 & identity_relation(v4) = v3 & relation_composition(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v5 & relation_dom(v0) = v3 & identity_relation(v5) = v4 & identity_relation(v3) = v2 & relation_composition(v1, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v0) = v4 & identity_relation(v4) = v3 & identity_relation(v1) = v5 & relation_composition(v2, v0) = v5 & relation_composition(v0, v2) = v3 & function_inverse(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3 & function_inverse(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v5 & identity_relation(v5) = v4 & identity_relation(v1) = v3 & relation_composition(v2, v0) = v4 & relation_composition(v0, v2) = v3 & function_inverse(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2 & function_inverse(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | one_to_one(v1)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) % 7.01/2.36 | % 7.01/2.36 | Applying alpha-rule on (1) yields: % 7.01/2.36 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 7.01/2.36 | (3) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) % 7.01/2.36 | (4) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 7.01/2.36 | (5) function(all_0_3_3) % 7.01/2.36 | (6) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3)) % 7.01/2.37 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) % 7.01/2.37 | (8) ~ (all_0_8_8 = all_0_9_9) % 7.01/2.37 | (9) empty(empty_set) % 7.01/2.37 | (10) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) % 7.01/2.37 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v5 & relation_dom(v0) = v3 & identity_relation(v5) = v4 & identity_relation(v3) = v2 & relation_composition(v1, v0) = v4)) % 7.01/2.37 | (12) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) % 7.01/2.37 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ (relation_dom(v2) = v1) | ~ relation(v2) | ~ relation(v0) | ~ function(v2) | ~ function(v0) | ? [v3] : ? [v4] : (identity_relation(v1) = v4 & relation_composition(v0, v2) = v3 & ( ~ (v3 = v0) | v4 = v2))) % 7.01/2.37 | (14) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 7.01/2.37 | (15) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) % 7.01/2.37 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 7.01/2.37 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) % 7.01/2.37 | (18) relation_empty_yielding(all_0_7_7) % 7.01/2.37 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 7.01/2.37 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 7.01/2.37 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2)) % 7.01/2.37 | (22) empty(all_0_2_2) % 7.01/2.37 | (23) function(all_0_0_0) % 7.01/2.37 | (24) relation_empty_yielding(empty_set) % 7.01/2.37 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2)) % 7.01/2.37 | (26) function(all_0_6_6) % 7.01/2.37 | (27) ~ empty(all_0_5_5) % 7.01/2.37 | (28) relation(all_0_4_4) % 7.01/2.37 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) % 7.01/2.37 | (30) relation(all_0_0_0) % 7.01/2.37 | (31) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 7.01/2.37 | (32) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1)) % 7.01/2.38 | (33) ! [v0] : ( ~ empty(v0) | function(v0)) % 7.01/2.38 | (34) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) % 7.01/2.38 | (35) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v5 & identity_relation(v5) = v4 & identity_relation(v1) = v3 & relation_composition(v2, v0) = v4 & relation_composition(v0, v2) = v3 & function_inverse(v0) = v2)) % 7.01/2.38 | (36) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v0) = v4 & identity_relation(v4) = v3 & identity_relation(v1) = v5 & relation_composition(v2, v0) = v5 & relation_composition(v0, v2) = v3 & function_inverse(v0) = v2)) % 7.01/2.38 | (37) ? [v0] : ? [v1] : element(v1, v0) % 7.01/2.38 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 7.01/2.38 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v5 & relation_dom(v0) = v4 & identity_relation(v5) = v2 & identity_relation(v4) = v3 & relation_composition(v0, v1) = v3)) % 7.01/2.38 | (40) relation(empty_set) % 7.01/2.38 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 7.01/2.38 | (42) ! [v0] : ( ~ empty(v0) | relation(v0)) % 7.01/2.38 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 7.01/2.38 | (44) ~ empty(all_0_4_4) % 7.01/2.38 | (45) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3 & function_inverse(v0) = v2)) % 7.01/2.38 | (46) ? [v0] : subset(v0, v0) % 7.01/2.38 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 7.01/2.38 | (48) one_to_one(all_0_6_6) % 7.01/2.38 | (49) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1)) % 7.01/2.38 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ (relation_composition(v0, v2) = v0) | ~ relation(v2) | ~ relation(v0) | ~ function(v2) | ~ function(v0) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & identity_relation(v3) = v4 & ( ~ (v3 = v1) | v4 = v2))) % 7.01/2.38 | (51) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) % 7.01/2.38 | (52) relation(all_0_3_3) % 7.01/2.39 | (53) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0) % 7.01/2.39 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 7.01/2.39 | (55) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 7.01/2.39 | (56) empty(all_0_1_1) % 7.01/2.39 | (57) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 7.01/2.39 | (58) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2 & function_inverse(v0) = v3)) % 7.01/2.39 | (59) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0) % 7.01/2.39 | (60) function_inverse(all_0_9_9) = all_0_8_8 % 7.01/2.39 | (61) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 7.01/2.39 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 7.01/2.39 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 7.01/2.39 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 7.01/2.39 | (65) relation(all_0_1_1) % 7.01/2.39 | (66) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) % 7.01/2.39 | (67) relation(all_0_6_6) % 7.01/2.39 | (68) empty(all_0_3_3) % 7.01/2.39 | (69) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 7.01/2.39 | (70) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 7.01/2.39 | (71) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 7.01/2.39 | (72) identity_relation(all_0_10_10) = all_0_9_9 % 7.01/2.39 | (73) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1)) % 7.01/2.39 | (74) relation(all_0_7_7) % 7.01/2.39 | (75) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1)) % 7.01/2.39 | (76) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | one_to_one(v1)) % 7.01/2.39 | % 7.36/2.39 | Instantiating formula (59) with all_0_9_9, all_0_10_10 and discharging atoms identity_relation(all_0_10_10) = all_0_9_9, yields: % 7.36/2.39 | (77) relation_rng(all_0_9_9) = all_0_10_10 % 7.36/2.39 | % 7.36/2.39 | Instantiating formula (53) with all_0_9_9, all_0_10_10 and discharging atoms identity_relation(all_0_10_10) = all_0_9_9, yields: % 7.36/2.39 | (78) relation_dom(all_0_9_9) = all_0_10_10 % 7.36/2.39 | % 7.36/2.39 | Instantiating formula (76) with all_0_9_9, all_0_10_10 and discharging atoms identity_relation(all_0_10_10) = all_0_9_9, yields: % 7.36/2.40 | (79) one_to_one(all_0_9_9) % 7.36/2.40 | % 7.36/2.40 | Instantiating formula (75) with all_0_9_9, all_0_10_10 and discharging atoms identity_relation(all_0_10_10) = all_0_9_9, yields: % 7.36/2.40 | (80) relation(all_0_9_9) % 7.36/2.40 | % 7.36/2.40 | Instantiating formula (73) with all_0_9_9, all_0_10_10 and discharging atoms identity_relation(all_0_10_10) = all_0_9_9, yields: % 7.36/2.40 | (81) function(all_0_9_9) % 7.36/2.40 | % 7.37/2.40 | Instantiating formula (13) with all_0_9_9, all_0_10_10, all_0_9_9 and discharging atoms relation_rng(all_0_9_9) = all_0_10_10, relation_dom(all_0_9_9) = all_0_10_10, relation(all_0_9_9), function(all_0_9_9), yields: % 7.37/2.40 | (82) ? [v0] : ? [v1] : (identity_relation(all_0_10_10) = v1 & relation_composition(all_0_9_9, all_0_9_9) = v0 & ( ~ (v0 = all_0_9_9) | v1 = all_0_9_9)) % 7.37/2.40 | % 7.37/2.40 | Instantiating formula (36) with all_0_10_10, all_0_9_9 and discharging atoms relation_rng(all_0_9_9) = all_0_10_10, one_to_one(all_0_9_9), relation(all_0_9_9), function(all_0_9_9), yields: % 7.37/2.40 | (83) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_dom(all_0_9_9) = v2 & identity_relation(v2) = v1 & identity_relation(all_0_10_10) = v3 & relation_composition(v0, all_0_9_9) = v3 & relation_composition(all_0_9_9, v0) = v1 & function_inverse(all_0_9_9) = v0) % 7.37/2.40 | % 7.37/2.40 | Instantiating formula (45) with all_0_10_10, all_0_9_9 and discharging atoms relation_rng(all_0_9_9) = all_0_10_10, one_to_one(all_0_9_9), relation(all_0_9_9), function(all_0_9_9), yields: % 7.37/2.40 | (84) ? [v0] : ? [v1] : (relation_rng(v0) = v1 & relation_dom(v0) = all_0_10_10 & relation_dom(all_0_9_9) = v1 & function_inverse(all_0_9_9) = v0) % 7.38/2.40 | % 7.38/2.40 | Instantiating formula (35) with all_0_10_10, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_10_10, one_to_one(all_0_9_9), relation(all_0_9_9), function(all_0_9_9), yields: % 7.38/2.40 | (85) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_rng(all_0_9_9) = v3 & identity_relation(v3) = v2 & identity_relation(all_0_10_10) = v1 & relation_composition(v0, all_0_9_9) = v2 & relation_composition(all_0_9_9, v0) = v1 & function_inverse(all_0_9_9) = v0) % 7.38/2.40 | % 7.38/2.40 | Instantiating formula (58) with all_0_10_10, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_10_10, one_to_one(all_0_9_9), relation(all_0_9_9), function(all_0_9_9), yields: % 7.38/2.40 | (86) ? [v0] : ? [v1] : (relation_rng(v1) = all_0_10_10 & relation_rng(all_0_9_9) = v0 & relation_dom(v1) = v0 & function_inverse(all_0_9_9) = v1) % 7.38/2.40 | % 7.38/2.40 | Instantiating formula (6) with all_0_8_8, all_0_9_9 and discharging atoms function_inverse(all_0_9_9) = all_0_8_8, one_to_one(all_0_9_9), relation(all_0_9_9), function(all_0_9_9), yields: % 7.38/2.40 | (87) ? [v0] : ? [v1] : (relation_rng(all_0_8_8) = v1 & relation_rng(all_0_9_9) = v0 & relation_dom(all_0_8_8) = v0 & relation_dom(all_0_9_9) = v1) % 7.38/2.40 | % 7.38/2.40 | Instantiating formula (49) with all_0_8_8, all_0_9_9 and discharging atoms function_inverse(all_0_9_9) = all_0_8_8, relation(all_0_9_9), function(all_0_9_9), yields: % 7.38/2.40 | (88) relation(all_0_8_8) % 7.38/2.40 | % 7.38/2.40 | Instantiating formula (32) with all_0_8_8, all_0_9_9 and discharging atoms function_inverse(all_0_9_9) = all_0_8_8, relation(all_0_9_9), function(all_0_9_9), yields: % 7.38/2.40 | (89) function(all_0_8_8) % 7.38/2.40 | % 7.38/2.40 | Instantiating (87) with all_23_0_14, all_23_1_15 yields: % 7.38/2.40 | (90) relation_rng(all_0_8_8) = all_23_0_14 & relation_rng(all_0_9_9) = all_23_1_15 & relation_dom(all_0_8_8) = all_23_1_15 & relation_dom(all_0_9_9) = all_23_0_14 % 7.38/2.40 | % 7.38/2.40 | Applying alpha-rule on (90) yields: % 7.38/2.40 | (91) relation_rng(all_0_8_8) = all_23_0_14 % 7.38/2.40 | (92) relation_rng(all_0_9_9) = all_23_1_15 % 7.38/2.40 | (93) relation_dom(all_0_8_8) = all_23_1_15 % 7.38/2.41 | (94) relation_dom(all_0_9_9) = all_23_0_14 % 7.38/2.41 | % 7.38/2.41 | Instantiating (86) with all_25_0_16, all_25_1_17 yields: % 7.38/2.41 | (95) relation_rng(all_25_0_16) = all_0_10_10 & relation_rng(all_0_9_9) = all_25_1_17 & relation_dom(all_25_0_16) = all_25_1_17 & function_inverse(all_0_9_9) = all_25_0_16 % 7.38/2.41 | % 7.38/2.41 | Applying alpha-rule on (95) yields: % 7.38/2.41 | (96) relation_rng(all_25_0_16) = all_0_10_10 % 7.38/2.41 | (97) relation_rng(all_0_9_9) = all_25_1_17 % 7.38/2.41 | (98) relation_dom(all_25_0_16) = all_25_1_17 % 7.38/2.41 | (99) function_inverse(all_0_9_9) = all_25_0_16 % 7.38/2.41 | % 7.38/2.41 | Instantiating (85) with all_27_0_18, all_27_1_19, all_27_2_20, all_27_3_21 yields: % 7.38/2.41 | (100) relation_rng(all_0_9_9) = all_27_0_18 & identity_relation(all_27_0_18) = all_27_1_19 & identity_relation(all_0_10_10) = all_27_2_20 & relation_composition(all_27_3_21, all_0_9_9) = all_27_1_19 & relation_composition(all_0_9_9, all_27_3_21) = all_27_2_20 & function_inverse(all_0_9_9) = all_27_3_21 % 7.38/2.41 | % 7.38/2.41 | Applying alpha-rule on (100) yields: % 7.38/2.41 | (101) relation_composition(all_27_3_21, all_0_9_9) = all_27_1_19 % 7.38/2.41 | (102) relation_composition(all_0_9_9, all_27_3_21) = all_27_2_20 % 7.38/2.41 | (103) function_inverse(all_0_9_9) = all_27_3_21 % 7.38/2.41 | (104) identity_relation(all_27_0_18) = all_27_1_19 % 7.38/2.41 | (105) identity_relation(all_0_10_10) = all_27_2_20 % 7.38/2.41 | (106) relation_rng(all_0_9_9) = all_27_0_18 % 7.38/2.41 | % 7.38/2.41 | Instantiating (84) with all_29_0_22, all_29_1_23 yields: % 7.38/2.41 | (107) relation_rng(all_29_1_23) = all_29_0_22 & relation_dom(all_29_1_23) = all_0_10_10 & relation_dom(all_0_9_9) = all_29_0_22 & function_inverse(all_0_9_9) = all_29_1_23 % 7.38/2.41 | % 7.38/2.41 | Applying alpha-rule on (107) yields: % 7.38/2.41 | (108) relation_rng(all_29_1_23) = all_29_0_22 % 7.38/2.41 | (109) relation_dom(all_29_1_23) = all_0_10_10 % 7.38/2.41 | (110) relation_dom(all_0_9_9) = all_29_0_22 % 7.38/2.41 | (111) function_inverse(all_0_9_9) = all_29_1_23 % 7.38/2.41 | % 7.38/2.41 | Instantiating (83) with all_31_0_24, all_31_1_25, all_31_2_26, all_31_3_27 yields: % 7.38/2.41 | (112) relation_dom(all_0_9_9) = all_31_1_25 & identity_relation(all_31_1_25) = all_31_2_26 & identity_relation(all_0_10_10) = all_31_0_24 & relation_composition(all_31_3_27, all_0_9_9) = all_31_0_24 & relation_composition(all_0_9_9, all_31_3_27) = all_31_2_26 & function_inverse(all_0_9_9) = all_31_3_27 % 7.38/2.41 | % 7.38/2.41 | Applying alpha-rule on (112) yields: % 7.38/2.41 | (113) identity_relation(all_0_10_10) = all_31_0_24 % 7.38/2.41 | (114) relation_composition(all_0_9_9, all_31_3_27) = all_31_2_26 % 7.38/2.41 | (115) relation_dom(all_0_9_9) = all_31_1_25 % 7.38/2.41 | (116) function_inverse(all_0_9_9) = all_31_3_27 % 7.38/2.41 | (117) identity_relation(all_31_1_25) = all_31_2_26 % 7.38/2.41 | (118) relation_composition(all_31_3_27, all_0_9_9) = all_31_0_24 % 7.38/2.41 | % 7.38/2.41 | Instantiating (82) with all_33_0_28, all_33_1_29 yields: % 7.38/2.41 | (119) identity_relation(all_0_10_10) = all_33_0_28 & relation_composition(all_0_9_9, all_0_9_9) = all_33_1_29 & ( ~ (all_33_1_29 = all_0_9_9) | all_33_0_28 = all_0_9_9) % 7.38/2.41 | % 7.38/2.41 | Applying alpha-rule on (119) yields: % 7.38/2.41 | (120) identity_relation(all_0_10_10) = all_33_0_28 % 7.38/2.41 | (121) relation_composition(all_0_9_9, all_0_9_9) = all_33_1_29 % 7.38/2.41 | (122) ~ (all_33_1_29 = all_0_9_9) | all_33_0_28 = all_0_9_9 % 7.38/2.41 | % 7.38/2.41 | Instantiating formula (47) with all_0_9_9, all_27_0_18, all_0_10_10 and discharging atoms relation_rng(all_0_9_9) = all_27_0_18, relation_rng(all_0_9_9) = all_0_10_10, yields: % 7.38/2.41 | (123) all_27_0_18 = all_0_10_10 % 7.38/2.42 | % 7.38/2.42 | Instantiating formula (47) with all_0_9_9, all_25_1_17, all_27_0_18 and discharging atoms relation_rng(all_0_9_9) = all_27_0_18, relation_rng(all_0_9_9) = all_25_1_17, yields: % 7.38/2.42 | (124) all_27_0_18 = all_25_1_17 % 7.38/2.42 | % 7.38/2.42 | Instantiating formula (47) with all_0_9_9, all_23_1_15, all_27_0_18 and discharging atoms relation_rng(all_0_9_9) = all_27_0_18, relation_rng(all_0_9_9) = all_23_1_15, yields: % 7.38/2.42 | (125) all_27_0_18 = all_23_1_15 % 7.38/2.42 | % 7.38/2.42 | Instantiating formula (38) with all_0_9_9, all_31_1_25, all_0_10_10 and discharging atoms relation_dom(all_0_9_9) = all_31_1_25, relation_dom(all_0_9_9) = all_0_10_10, yields: % 7.38/2.42 | (126) all_31_1_25 = all_0_10_10 % 7.38/2.42 | % 7.38/2.42 | Instantiating formula (51) with all_0_10_10, all_33_0_28, all_0_9_9 and discharging atoms identity_relation(all_0_10_10) = all_33_0_28, identity_relation(all_0_10_10) = all_0_9_9, yields: % 7.38/2.42 | (127) all_33_0_28 = all_0_9_9 % 7.38/2.42 | % 7.38/2.42 | Instantiating formula (51) with all_0_10_10, all_31_0_24, all_33_0_28 and discharging atoms identity_relation(all_0_10_10) = all_33_0_28, identity_relation(all_0_10_10) = all_31_0_24, yields: % 7.38/2.42 | (128) all_33_0_28 = all_31_0_24 % 7.38/2.42 | % 7.38/2.42 | Instantiating formula (51) with all_0_10_10, all_27_2_20, all_31_0_24 and discharging atoms identity_relation(all_0_10_10) = all_31_0_24, identity_relation(all_0_10_10) = all_27_2_20, yields: % 7.38/2.42 | (129) all_31_0_24 = all_27_2_20 % 7.38/2.42 | % 7.38/2.42 | Instantiating formula (29) with all_0_9_9, all_29_1_23, all_31_3_27 and discharging atoms function_inverse(all_0_9_9) = all_31_3_27, function_inverse(all_0_9_9) = all_29_1_23, yields: % 7.38/2.42 | (130) all_31_3_27 = all_29_1_23 % 7.38/2.42 | % 7.38/2.42 | Instantiating formula (29) with all_0_9_9, all_27_3_21, all_0_8_8 and discharging atoms function_inverse(all_0_9_9) = all_27_3_21, function_inverse(all_0_9_9) = all_0_8_8, yields: % 7.38/2.42 | (131) all_27_3_21 = all_0_8_8 % 7.38/2.42 | % 7.38/2.42 | Instantiating formula (29) with all_0_9_9, all_27_3_21, all_29_1_23 and discharging atoms function_inverse(all_0_9_9) = all_29_1_23, function_inverse(all_0_9_9) = all_27_3_21, yields: % 7.38/2.42 | (132) all_29_1_23 = all_27_3_21 % 7.38/2.42 | % 7.38/2.42 | Instantiating formula (29) with all_0_9_9, all_25_0_16, all_31_3_27 and discharging atoms function_inverse(all_0_9_9) = all_31_3_27, function_inverse(all_0_9_9) = all_25_0_16, yields: % 7.38/2.42 | (133) all_31_3_27 = all_25_0_16 % 7.38/2.42 | % 7.38/2.42 | Combining equations (128,127) yields a new equation: % 7.38/2.42 | (134) all_31_0_24 = all_0_9_9 % 7.38/2.42 | % 7.38/2.42 | Simplifying 134 yields: % 7.38/2.42 | (135) all_31_0_24 = all_0_9_9 % 7.38/2.42 | % 7.38/2.42 | Combining equations (129,135) yields a new equation: % 7.38/2.42 | (136) all_27_2_20 = all_0_9_9 % 7.38/2.42 | % 7.38/2.42 | Simplifying 136 yields: % 7.38/2.42 | (137) all_27_2_20 = all_0_9_9 % 7.38/2.42 | % 7.38/2.42 | Combining equations (130,133) yields a new equation: % 7.38/2.42 | (138) all_29_1_23 = all_25_0_16 % 7.38/2.42 | % 7.38/2.42 | Simplifying 138 yields: % 7.38/2.42 | (139) all_29_1_23 = all_25_0_16 % 7.38/2.42 | % 7.38/2.42 | Combining equations (132,139) yields a new equation: % 7.38/2.42 | (140) all_27_3_21 = all_25_0_16 % 7.38/2.42 | % 7.38/2.42 | Simplifying 140 yields: % 7.38/2.42 | (141) all_27_3_21 = all_25_0_16 % 7.38/2.42 | % 7.38/2.42 | Combining equations (125,124) yields a new equation: % 7.38/2.42 | (142) all_25_1_17 = all_23_1_15 % 7.38/2.42 | % 7.38/2.42 | Combining equations (123,124) yields a new equation: % 7.38/2.42 | (143) all_25_1_17 = all_0_10_10 % 7.38/2.42 | % 7.38/2.42 | Combining equations (141,131) yields a new equation: % 7.38/2.42 | (144) all_25_0_16 = all_0_8_8 % 7.38/2.42 | % 7.38/2.42 | Simplifying 144 yields: % 7.38/2.42 | (145) all_25_0_16 = all_0_8_8 % 7.38/2.42 | % 7.38/2.42 | Combining equations (142,143) yields a new equation: % 7.38/2.43 | (146) all_23_1_15 = all_0_10_10 % 7.38/2.43 | % 7.38/2.43 | Simplifying 146 yields: % 7.38/2.43 | (147) all_23_1_15 = all_0_10_10 % 7.38/2.43 | % 7.38/2.43 | Combining equations (143,124) yields a new equation: % 7.38/2.43 | (123) all_27_0_18 = all_0_10_10 % 7.38/2.43 | % 7.38/2.43 | Combining equations (145,133) yields a new equation: % 7.38/2.43 | (149) all_31_3_27 = all_0_8_8 % 7.38/2.43 | % 7.38/2.43 | From (147) and (92) follows: % 7.38/2.43 | (77) relation_rng(all_0_9_9) = all_0_10_10 % 7.38/2.43 | % 7.38/2.43 | From (147) and (93) follows: % 7.38/2.43 | (151) relation_dom(all_0_8_8) = all_0_10_10 % 7.38/2.43 | % 7.38/2.43 | From (126) and (117) follows: % 7.38/2.43 | (152) identity_relation(all_0_10_10) = all_31_2_26 % 7.38/2.43 | % 7.38/2.43 | From (123) and (104) follows: % 7.38/2.43 | (153) identity_relation(all_0_10_10) = all_27_1_19 % 7.38/2.43 | % 7.38/2.43 | From (149) and (114) follows: % 7.38/2.43 | (154) relation_composition(all_0_9_9, all_0_8_8) = all_31_2_26 % 7.38/2.43 | % 7.38/2.43 | From (131)(137) and (102) follows: % 7.38/2.43 | (155) relation_composition(all_0_9_9, all_0_8_8) = all_0_9_9 % 7.38/2.43 | % 7.38/2.43 | Instantiating formula (51) with all_0_10_10, all_27_1_19, all_31_2_26 and discharging atoms identity_relation(all_0_10_10) = all_31_2_26, identity_relation(all_0_10_10) = all_27_1_19, yields: % 7.38/2.43 | (156) all_31_2_26 = all_27_1_19 % 7.38/2.43 | % 7.38/2.43 | Instantiating formula (7) with all_0_9_9, all_0_8_8, all_0_9_9, all_31_2_26 and discharging atoms relation_composition(all_0_9_9, all_0_8_8) = all_31_2_26, relation_composition(all_0_9_9, all_0_8_8) = all_0_9_9, yields: % 7.38/2.43 | (157) all_31_2_26 = all_0_9_9 % 7.38/2.43 | % 7.38/2.43 | Combining equations (156,157) yields a new equation: % 7.38/2.43 | (158) all_27_1_19 = all_0_9_9 % 7.38/2.43 | % 7.38/2.43 | Simplifying 158 yields: % 7.38/2.43 | (159) all_27_1_19 = all_0_9_9 % 7.38/2.43 | % 7.38/2.43 | From (159) and (153) follows: % 7.38/2.43 | (72) identity_relation(all_0_10_10) = all_0_9_9 % 7.38/2.43 | % 7.38/2.43 | From (157) and (154) follows: % 7.38/2.43 | (155) relation_composition(all_0_9_9, all_0_8_8) = all_0_9_9 % 7.38/2.43 | % 7.38/2.43 | Instantiating formula (13) with all_0_8_8, all_0_10_10, all_0_9_9 and discharging atoms relation_rng(all_0_9_9) = all_0_10_10, relation_dom(all_0_8_8) = all_0_10_10, relation(all_0_8_8), relation(all_0_9_9), function(all_0_8_8), function(all_0_9_9), yields: % 7.38/2.43 | (162) ? [v0] : ? [v1] : (identity_relation(all_0_10_10) = v1 & relation_composition(all_0_9_9, all_0_8_8) = v0 & ( ~ (v0 = all_0_9_9) | v1 = all_0_8_8)) % 7.38/2.43 | % 7.38/2.43 | Instantiating (162) with all_50_0_32, all_50_1_33 yields: % 7.38/2.43 | (163) identity_relation(all_0_10_10) = all_50_0_32 & relation_composition(all_0_9_9, all_0_8_8) = all_50_1_33 & ( ~ (all_50_1_33 = all_0_9_9) | all_50_0_32 = all_0_8_8) % 7.38/2.43 | % 7.38/2.43 | Applying alpha-rule on (163) yields: % 7.38/2.43 | (164) identity_relation(all_0_10_10) = all_50_0_32 % 7.38/2.43 | (165) relation_composition(all_0_9_9, all_0_8_8) = all_50_1_33 % 7.38/2.43 | (166) ~ (all_50_1_33 = all_0_9_9) | all_50_0_32 = all_0_8_8 % 7.38/2.43 | % 7.38/2.43 | Instantiating formula (51) with all_0_10_10, all_50_0_32, all_0_9_9 and discharging atoms identity_relation(all_0_10_10) = all_50_0_32, identity_relation(all_0_10_10) = all_0_9_9, yields: % 7.38/2.43 | (167) all_50_0_32 = all_0_9_9 % 7.38/2.43 | % 7.38/2.43 | Instantiating formula (7) with all_0_9_9, all_0_8_8, all_50_1_33, all_0_9_9 and discharging atoms relation_composition(all_0_9_9, all_0_8_8) = all_50_1_33, relation_composition(all_0_9_9, all_0_8_8) = all_0_9_9, yields: % 7.38/2.43 | (168) all_50_1_33 = all_0_9_9 % 7.38/2.43 | % 7.38/2.43 +-Applying beta-rule and splitting (166), into two cases. % 7.38/2.43 |-Branch one: % 7.38/2.43 | (169) ~ (all_50_1_33 = all_0_9_9) % 7.38/2.43 | % 7.38/2.43 | Equations (168) can reduce 169 to: % 7.38/2.43 | (170) $false % 7.38/2.43 | % 7.38/2.44 |-The branch is then unsatisfiable % 7.38/2.44 |-Branch two: % 7.38/2.44 | (168) all_50_1_33 = all_0_9_9 % 7.38/2.44 | (172) all_50_0_32 = all_0_8_8 % 7.38/2.44 | % 7.38/2.44 | Combining equations (172,167) yields a new equation: % 7.38/2.44 | (173) all_0_8_8 = all_0_9_9 % 7.38/2.44 | % 7.38/2.44 | Simplifying 173 yields: % 7.38/2.44 | (174) all_0_8_8 = all_0_9_9 % 7.38/2.44 | % 7.38/2.44 | Equations (174) can reduce 8 to: % 7.38/2.44 | (170) $false % 7.38/2.44 | % 7.38/2.44 |-The branch is then unsatisfiable % 7.38/2.44 % SZS output end Proof for theBenchmark % 7.38/2.44 % 7.38/2.44 1889ms %------------------------------------------------------------------------------