%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET988+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n008.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 00:23:38 EDT 2022 % Result : Theorem 3.85s 1.63s % Output : Proof 5.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SET988+1 : TPTP v8.1.0. Released v3.2.0. % 0.04/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n008.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sun Jul 10 15:09:23 EDT 2022 % 0.12/0.34 % CPUTime : % 0.52/0.58 ____ _ % 0.52/0.58 ___ / __ \_____(_)___ ________ __________ % 0.52/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.52/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.52/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.52/0.58 % 0.52/0.58 A Theorem Prover for First-Order Logic % 0.52/0.58 (ePrincess v.1.0) % 0.52/0.58 % 0.52/0.58 (c) Philipp Rümmer, 2009-2015 % 0.52/0.58 (c) Peter Backeman, 2014-2015 % 0.52/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.52/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.52/0.58 Bug reports to peter@backeman.se % 0.52/0.58 % 0.52/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.52/0.58 % 0.52/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.76/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.53/0.95 Prover 0: Preprocessing ... % 2.09/1.15 Prover 0: Warning: ignoring some quantifiers % 2.09/1.17 Prover 0: Constructing countermodel ... % 2.78/1.33 Prover 0: gave up % 2.78/1.33 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.93/1.37 Prover 1: Preprocessing ... % 3.47/1.48 Prover 1: Warning: ignoring some quantifiers % 3.47/1.49 Prover 1: Constructing countermodel ... % 3.85/1.63 Prover 1: proved (295ms) % 3.85/1.63 % 3.85/1.63 No countermodel exists, formula is valid % 3.85/1.63 % SZS status Theorem for theBenchmark % 3.85/1.63 % 3.85/1.63 Generating proof ... Warning: ignoring some quantifiers % 5.43/1.95 found it (size 37) % 5.43/1.95 % 5.43/1.95 % SZS output start Proof for theBenchmark % 5.43/1.95 Assumed formulas after preprocessing and simplification: % 5.43/1.95 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v8 = 0) & ~ (v4 = 0) & relation_empty_yielding(v6) = 0 & relation_empty_yielding(empty_set) = 0 & relation(v10) = 0 & relation(v9) = 0 & relation(v7) = 0 & relation(v6) = 0 & relation(v0) = v1 & relation(empty_set) = 0 & function(v10) = 0 & function(v0) = v2 & empty(v9) = 0 & empty(v7) = v8 & empty(v5) = 0 & empty(v3) = v4 & empty(empty_set) = 0 & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (ordered_pair(v12, v14) = v16) | ~ (ordered_pair(v12, v13) = v15) | ~ (in(v16, v11) = 0) | ~ (in(v15, v11) = 0) | ~ (function(v11) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (powerset(v13) = v14) | ~ (element(v12, v14) = 0) | ~ (element(v11, v13) = v15) | ? [v16] : ( ~ (v16 = 0) & in(v11, v12) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (ordered_pair(v11, v13) = v15) | ~ (ordered_pair(v11, v12) = v14) | ~ (in(v15, v0) = 0) | ~ (in(v14, v0) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (singleton(v11) = v14) | ~ (unordered_pair(v13, v14) = v15) | ~ (unordered_pair(v11, v12) = v13) | ordered_pair(v11, v12) = v15) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (powerset(v12) = v13) | ~ (element(v11, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & subset(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (ordered_pair(v14, v13) = v12) | ~ (ordered_pair(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (in(v14, v13) = v12) | ~ (in(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (element(v14, v13) = v12) | ~ (element(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 | ~ (subset(v14, v13) = v12) | ~ (subset(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (in(v11, v12) = 0) | ~ (powerset(v13) = v14) | ~ (element(v12, v14) = 0) | ? [v15] : ( ~ (v15 = 0) & empty(v13) = v15)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (element(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation_empty_yielding(v13) = v12) | ~ (relation_empty_yielding(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation(v13) = v12) | ~ (relation(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (singleton(v13) = v12) | ~ (singleton(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (powerset(v13) = v12) | ~ (powerset(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (function(v13) = v12) | ~ (function(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (empty(v13) = v12) | ~ (empty(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (ordered_pair(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ (element(v11, v13) = 0) | subset(v11, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v11, v12) = v13) | unordered_pair(v12, v11) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (empty(v12) = 0) | ~ (empty(v11) = 0)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (relation(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v11) = v13)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (relation(v11) = v12) | ? [v13] : (in(v13, v11) = 0 & ! [v14] : ! [v15] : ~ (ordered_pair(v14, v15) = v13))) & ! [v11] : ! [v12] : (v12 = 0 | ~ (function(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ( ~ (v15 = v14) & ordered_pair(v13, v15) = v17 & ordered_pair(v13, v14) = v16 & in(v17, v11) = 0 & in(v16, v11) = 0)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (function(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v11) = v13)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v11, v11) = v12)) & ! [v11] : ! [v12] : ( ~ (in(v12, v11) = 0) | ~ (relation(v11) = 0) | ? [v13] : ? [v14] : ordered_pair(v13, v14) = v12) & ! [v11] : ! [v12] : ( ~ (in(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & in(v12, v11) = v13)) & ! [v11] : ! [v12] : ( ~ (in(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (singleton(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ((v14 = 0 & ~ (v15 = 0) & empty(v13) = v15 & element(v13, v12) = 0) | (v13 = 0 & empty(v11) = 0))) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : (empty(v13) = 0 & element(v13, v12) = 0)) & ! [v11] : ! [v12] : ( ~ (element(v11, v12) = 0) | ? [v13] : ? [v14] : (in(v11, v12) = v14 & empty(v12) = v13 & (v14 = 0 | v13 = 0))) & ! [v11] : (v11 = empty_set | ~ (empty(v11) = 0)) & ! [v11] : ( ~ (in(v11, v0) = 0) | ? [v12] : ? [v13] : ordered_pair(v12, v13) = v11) & ? [v11] : ? [v12] : element(v12, v11) = 0 & ( ~ (v2 = 0) | ~ (v1 = 0))) % 5.68/2.00 | 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: % 5.68/2.00 | (1) ~ (all_0_2_2 = 0) & ~ (all_0_6_6 = 0) & relation_empty_yielding(all_0_4_4) = 0 & relation_empty_yielding(empty_set) = 0 & relation(all_0_0_0) = 0 & relation(all_0_1_1) = 0 & relation(all_0_3_3) = 0 & relation(all_0_4_4) = 0 & relation(all_0_10_10) = all_0_9_9 & relation(empty_set) = 0 & function(all_0_0_0) = 0 & function(all_0_10_10) = all_0_8_8 & empty(all_0_1_1) = 0 & empty(all_0_3_3) = all_0_2_2 & empty(all_0_5_5) = 0 & empty(all_0_7_7) = all_0_6_6 & empty(empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (ordered_pair(v1, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ (in(v5, v0) = 0) | ~ (in(v4, v0) = 0) | ~ (function(v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (ordered_pair(v0, v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ (in(v4, all_0_10_10) = 0) | ~ (in(v3, all_0_10_10) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(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 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (in(v0, v1) = 0) | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : (in(v2, v0) = 0 & ! [v3] : ! [v4] : ~ (ordered_pair(v3, v4) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v4 = v3) & ordered_pair(v2, v4) = v6 & ordered_pair(v2, v3) = v5 & in(v6, v0) = 0 & in(v5, v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ~ (relation(v0) = 0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (in(v0, v1) = v3 & empty(v1) = v2 & (v3 = 0 | v2 = 0))) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ( ~ (in(v0, all_0_10_10) = 0) | ? [v1] : ? [v2] : ordered_pair(v1, v2) = v0) & ? [v0] : ? [v1] : element(v1, v0) = 0 & ( ~ (all_0_8_8 = 0) | ~ (all_0_9_9 = 0)) % 5.68/2.01 | % 5.68/2.01 | Applying alpha-rule on (1) yields: % 5.68/2.01 | (2) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 5.68/2.01 | (3) empty(all_0_3_3) = all_0_2_2 % 5.68/2.01 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 5.68/2.01 | (5) empty(all_0_7_7) = all_0_6_6 % 5.68/2.01 | (6) relation(all_0_1_1) = 0 % 5.68/2.01 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 5.68/2.01 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 5.68/2.01 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 5.68/2.02 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (ordered_pair(v0, v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ (in(v4, all_0_10_10) = 0) | ~ (in(v3, all_0_10_10) = 0)) % 5.68/2.02 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) % 5.68/2.02 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) % 5.68/2.02 | (13) empty(all_0_5_5) = 0 % 5.68/2.02 | (14) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 5.68/2.02 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) % 5.68/2.02 | (16) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ~ (relation(v0) = 0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1) % 5.68/2.02 | (17) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 5.68/2.02 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 5.68/2.02 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 5.68/2.02 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (in(v0, v1) = 0) | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) % 5.68/2.02 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (ordered_pair(v1, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ (in(v5, v0) = 0) | ~ (in(v4, v0) = 0) | ~ (function(v0) = 0)) % 5.68/2.02 | (22) ~ (all_0_6_6 = 0) % 5.68/2.02 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 5.68/2.02 | (24) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 5.68/2.02 | (25) relation_empty_yielding(all_0_4_4) = 0 % 5.68/2.02 | (26) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0)) % 5.68/2.02 | (27) relation(all_0_3_3) = 0 % 5.68/2.02 | (28) relation(all_0_0_0) = 0 % 5.68/2.02 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) % 5.68/2.02 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 5.68/2.02 | (31) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 5.68/2.02 | (32) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : (in(v2, v0) = 0 & ! [v3] : ! [v4] : ~ (ordered_pair(v3, v4) = v2))) % 5.68/2.02 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 5.68/2.02 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 5.68/2.02 | (35) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 5.68/2.03 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 5.68/2.03 | (37) function(all_0_0_0) = 0 % 5.68/2.03 | (38) relation(all_0_4_4) = 0 % 5.68/2.03 | (39) ! [v0] : ( ~ (in(v0, all_0_10_10) = 0) | ? [v1] : ? [v2] : ordered_pair(v1, v2) = v0) % 5.68/2.03 | (40) relation_empty_yielding(empty_set) = 0 % 5.68/2.03 | (41) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v4 = v3) & ordered_pair(v2, v4) = v6 & ordered_pair(v2, v3) = v5 & in(v6, v0) = 0 & in(v5, v0) = 0)) % 5.68/2.03 | (42) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 5.68/2.03 | (43) relation(all_0_10_10) = all_0_9_9 % 5.68/2.03 | (44) function(all_0_10_10) = all_0_8_8 % 5.68/2.03 | (45) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 5.68/2.03 | (46) ~ (all_0_2_2 = 0) % 5.68/2.03 | (47) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 5.68/2.03 | (48) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 5.68/2.03 | (49) relation(empty_set) = 0 % 5.68/2.03 | (50) empty(all_0_1_1) = 0 % 5.68/2.03 | (51) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0))) % 5.68/2.03 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) % 5.68/2.03 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 5.68/2.03 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 5.68/2.03 | (55) ? [v0] : ? [v1] : element(v1, v0) = 0 % 5.68/2.03 | (56) ~ (all_0_8_8 = 0) | ~ (all_0_9_9 = 0) % 5.68/2.03 | (57) empty(empty_set) = 0 % 5.68/2.03 | (58) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (in(v0, v1) = v3 & empty(v1) = v2 & (v3 = 0 | v2 = 0))) % 5.68/2.03 | % 5.68/2.03 | Instantiating formula (18) with empty_set, 0, all_0_9_9 and discharging atoms relation(empty_set) = 0, yields: % 5.68/2.03 | (59) all_0_9_9 = 0 | ~ (relation(empty_set) = all_0_9_9) % 5.68/2.03 | % 5.68/2.03 | Instantiating formula (35) with empty_set, all_0_1_1 and discharging atoms empty(all_0_1_1) = 0, empty(empty_set) = 0, yields: % 5.68/2.03 | (60) all_0_1_1 = empty_set % 5.68/2.03 | % 5.68/2.03 | From (60) and (6) follows: % 5.68/2.04 | (49) relation(empty_set) = 0 % 5.68/2.04 | % 5.68/2.04 | Instantiating formula (31) with all_0_9_9, all_0_10_10 and discharging atoms relation(all_0_10_10) = all_0_9_9, yields: % 5.68/2.04 | (62) all_0_9_9 = 0 | ? [v0] : ( ~ (v0 = 0) & empty(all_0_10_10) = v0) % 5.68/2.04 | % 5.68/2.04 | Instantiating formula (32) with all_0_9_9, all_0_10_10 and discharging atoms relation(all_0_10_10) = all_0_9_9, yields: % 5.68/2.04 | (63) all_0_9_9 = 0 | ? [v0] : (in(v0, all_0_10_10) = 0 & ! [v1] : ! [v2] : ~ (ordered_pair(v1, v2) = v0)) % 5.68/2.04 | % 5.68/2.04 | Instantiating formula (41) with all_0_8_8, all_0_10_10 and discharging atoms function(all_0_10_10) = all_0_8_8, yields: % 5.68/2.04 | (64) all_0_8_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v2 = v1) & ordered_pair(v0, v2) = v4 & ordered_pair(v0, v1) = v3 & in(v4, all_0_10_10) = 0 & in(v3, all_0_10_10) = 0) % 5.68/2.04 | % 5.68/2.04 | Instantiating formula (45) with all_0_8_8, all_0_10_10 and discharging atoms function(all_0_10_10) = all_0_8_8, yields: % 5.68/2.04 | (65) all_0_8_8 = 0 | ? [v0] : ( ~ (v0 = 0) & empty(all_0_10_10) = v0) % 5.68/2.04 | % 5.68/2.04 +-Applying beta-rule and splitting (59), into two cases. % 5.68/2.04 |-Branch one: % 5.68/2.04 | (66) ~ (relation(empty_set) = all_0_9_9) % 5.68/2.04 | % 5.68/2.04 | Using (49) and (66) yields: % 5.68/2.04 | (67) ~ (all_0_9_9 = 0) % 5.68/2.04 | % 5.68/2.04 +-Applying beta-rule and splitting (62), into two cases. % 5.68/2.04 |-Branch one: % 5.68/2.04 | (68) all_0_9_9 = 0 % 5.68/2.04 | % 5.68/2.04 | Equations (68) can reduce 67 to: % 5.68/2.04 | (69) $false % 5.68/2.04 | % 5.68/2.04 |-The branch is then unsatisfiable % 5.68/2.04 |-Branch two: % 5.68/2.04 | (67) ~ (all_0_9_9 = 0) % 5.68/2.04 | (71) ? [v0] : ( ~ (v0 = 0) & empty(all_0_10_10) = v0) % 5.68/2.04 | % 5.68/2.04 +-Applying beta-rule and splitting (63), into two cases. % 5.68/2.04 |-Branch one: % 5.68/2.04 | (68) all_0_9_9 = 0 % 5.68/2.04 | % 5.68/2.04 | Equations (68) can reduce 67 to: % 5.68/2.04 | (69) $false % 5.68/2.04 | % 5.68/2.04 |-The branch is then unsatisfiable % 5.68/2.04 |-Branch two: % 5.68/2.04 | (67) ~ (all_0_9_9 = 0) % 5.68/2.04 | (75) ? [v0] : (in(v0, all_0_10_10) = 0 & ! [v1] : ! [v2] : ~ (ordered_pair(v1, v2) = v0)) % 5.68/2.04 | % 5.68/2.04 | Instantiating (75) with all_36_0_16 yields: % 5.68/2.04 | (76) in(all_36_0_16, all_0_10_10) = 0 & ! [v0] : ! [v1] : ~ (ordered_pair(v0, v1) = all_36_0_16) % 5.68/2.04 | % 5.68/2.04 | Applying alpha-rule on (76) yields: % 5.68/2.04 | (77) in(all_36_0_16, all_0_10_10) = 0 % 5.68/2.04 | (78) ! [v0] : ! [v1] : ~ (ordered_pair(v0, v1) = all_36_0_16) % 5.68/2.04 | % 5.68/2.04 | Instantiating formula (39) with all_36_0_16 and discharging atoms in(all_36_0_16, all_0_10_10) = 0, yields: % 5.68/2.04 | (79) ? [v0] : ? [v1] : ordered_pair(v0, v1) = all_36_0_16 % 5.68/2.04 | % 5.68/2.04 | Instantiating (79) with all_46_0_18, all_46_1_19 yields: % 5.68/2.04 | (80) ordered_pair(all_46_1_19, all_46_0_18) = all_36_0_16 % 5.68/2.04 | % 5.68/2.04 | Instantiating formula (78) with all_46_0_18, all_46_1_19 and discharging atoms ordered_pair(all_46_1_19, all_46_0_18) = all_36_0_16, yields: % 5.68/2.04 | (81) $false % 5.68/2.04 | % 5.68/2.04 |-The branch is then unsatisfiable % 5.68/2.04 |-Branch two: % 5.68/2.04 | (82) relation(empty_set) = all_0_9_9 % 5.68/2.04 | (68) all_0_9_9 = 0 % 5.68/2.04 | % 5.68/2.04 +-Applying beta-rule and splitting (56), into two cases. % 5.68/2.04 |-Branch one: % 5.68/2.04 | (84) ~ (all_0_8_8 = 0) % 5.68/2.04 | % 5.68/2.04 +-Applying beta-rule and splitting (65), into two cases. % 5.68/2.04 |-Branch one: % 5.68/2.04 | (85) all_0_8_8 = 0 % 5.68/2.04 | % 5.68/2.04 | Equations (85) can reduce 84 to: % 5.68/2.04 | (69) $false % 5.68/2.04 | % 5.68/2.04 |-The branch is then unsatisfiable % 5.68/2.04 |-Branch two: % 5.68/2.04 | (84) ~ (all_0_8_8 = 0) % 5.68/2.04 | (71) ? [v0] : ( ~ (v0 = 0) & empty(all_0_10_10) = v0) % 5.68/2.04 | % 5.68/2.04 +-Applying beta-rule and splitting (64), into two cases. % 5.68/2.04 |-Branch one: % 5.68/2.04 | (85) all_0_8_8 = 0 % 5.68/2.04 | % 5.68/2.04 | Equations (85) can reduce 84 to: % 5.68/2.04 | (69) $false % 5.68/2.05 | % 5.68/2.05 |-The branch is then unsatisfiable % 5.68/2.05 |-Branch two: % 5.68/2.05 | (84) ~ (all_0_8_8 = 0) % 5.68/2.05 | (92) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v2 = v1) & ordered_pair(v0, v2) = v4 & ordered_pair(v0, v1) = v3 & in(v4, all_0_10_10) = 0 & in(v3, all_0_10_10) = 0) % 5.68/2.05 | % 5.68/2.05 | Instantiating (92) with all_36_0_21, all_36_1_22, all_36_2_23, all_36_3_24, all_36_4_25 yields: % 5.68/2.05 | (93) ~ (all_36_2_23 = all_36_3_24) & ordered_pair(all_36_4_25, all_36_2_23) = all_36_0_21 & ordered_pair(all_36_4_25, all_36_3_24) = all_36_1_22 & in(all_36_0_21, all_0_10_10) = 0 & in(all_36_1_22, all_0_10_10) = 0 % 5.68/2.05 | % 5.68/2.05 | Applying alpha-rule on (93) yields: % 5.68/2.05 | (94) in(all_36_1_22, all_0_10_10) = 0 % 5.68/2.05 | (95) ordered_pair(all_36_4_25, all_36_3_24) = all_36_1_22 % 5.68/2.05 | (96) ~ (all_36_2_23 = all_36_3_24) % 5.68/2.05 | (97) ordered_pair(all_36_4_25, all_36_2_23) = all_36_0_21 % 5.68/2.05 | (98) in(all_36_0_21, all_0_10_10) = 0 % 5.68/2.05 | % 5.68/2.05 | Instantiating formula (10) with all_36_0_21, all_36_1_22, all_36_2_23, all_36_3_24, all_36_4_25 and discharging atoms ordered_pair(all_36_4_25, all_36_2_23) = all_36_0_21, ordered_pair(all_36_4_25, all_36_3_24) = all_36_1_22, in(all_36_0_21, all_0_10_10) = 0, in(all_36_1_22, all_0_10_10) = 0, yields: % 5.68/2.05 | (99) all_36_2_23 = all_36_3_24 % 5.68/2.05 | % 5.68/2.05 | Equations (99) can reduce 96 to: % 5.68/2.05 | (69) $false % 5.68/2.05 | % 5.68/2.05 |-The branch is then unsatisfiable % 5.68/2.05 |-Branch two: % 5.68/2.05 | (85) all_0_8_8 = 0 % 5.68/2.05 | (67) ~ (all_0_9_9 = 0) % 5.68/2.05 | % 5.68/2.05 | Equations (68) can reduce 67 to: % 5.68/2.05 | (69) $false % 5.68/2.05 | % 5.68/2.05 |-The branch is then unsatisfiable % 5.68/2.05 % SZS output end Proof for theBenchmark % 5.68/2.05 % 5.68/2.05 1457ms %------------------------------------------------------------------------------