%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET944+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n028.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 00:23:21 EDT 2022 % Result : Theorem 16.70s 4.87s % Output : Proof 20.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.08 % Problem : SET944+1 : TPTP v8.1.0. Released v3.2.0. % 0.00/0.08 % Command : ePrincess-casc -timeout=%d %s % 0.08/0.28 % Computer : n028.cluster.edu % 0.08/0.28 % Model : x86_64 x86_64 % 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.28 % Memory : 8042.1875MB % 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.28 % CPULimit : 300 % 0.08/0.28 % WCLimit : 600 % 0.08/0.28 % DateTime : Sun Jul 10 04:33:26 EDT 2022 % 0.08/0.28 % CPUTime : % 0.13/0.52 ____ _ % 0.13/0.52 ___ / __ \_____(_)___ ________ __________ % 0.13/0.52 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.13/0.52 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.13/0.52 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.13/0.52 % 0.13/0.52 A Theorem Prover for First-Order Logic % 0.13/0.53 (ePrincess v.1.0) % 0.13/0.53 % 0.13/0.53 (c) Philipp Rümmer, 2009-2015 % 0.13/0.53 (c) Peter Backeman, 2014-2015 % 0.13/0.53 (contributions by Angelo Brillout, Peter Baumgartner) % 0.13/0.53 Free software under GNU Lesser General Public License (LGPL). % 0.13/0.53 Bug reports to peter@backeman.se % 0.13/0.53 % 0.13/0.53 For more information, visit http://user.uu.se/~petba168/breu/ % 0.13/0.53 % 0.13/0.53 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.13/0.58 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.26/0.89 Prover 0: Preprocessing ... % 1.74/1.10 Prover 0: Warning: ignoring some quantifiers % 1.74/1.13 Prover 0: Constructing countermodel ... % 2.90/1.48 Prover 0: gave up % 2.90/1.49 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.90/1.51 Prover 1: Preprocessing ... % 3.36/1.61 Prover 1: Warning: ignoring some quantifiers % 3.36/1.62 Prover 1: Constructing countermodel ... % 11.30/3.59 Prover 1: gave up % 11.30/3.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 11.30/3.61 Prover 2: Preprocessing ... % 11.89/3.70 Prover 2: Warning: ignoring some quantifiers % 11.89/3.70 Prover 2: Constructing countermodel ... % 16.70/4.87 Prover 2: proved (1282ms) % 16.70/4.87 % 16.70/4.87 No countermodel exists, formula is valid % 16.70/4.87 % SZS status Theorem for theBenchmark % 16.70/4.87 % 16.70/4.87 Generating proof ... Warning: ignoring some quantifiers % 19.94/5.68 found it (size 40) % 19.94/5.68 % 19.94/5.68 % SZS output start Proof for theBenchmark % 19.94/5.68 Assumed formulas after preprocessing and simplification: % 19.94/5.68 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v9 = 0) & ~ (v7 = 0) & empty(v10) = 0 & empty(v8) = v9 & union(v2) = v3 & union(v1) = v5 & union(v0) = v4 & subset(v3, v6) = v7 & set_intersection2(v4, v5) = v6 & set_intersection2(v0, v1) = v2 & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (set_intersection2(v11, v12) = v13) | ~ (in(v14, v13) = v15) | ? [v16] : (( ~ (v16 = 0) & in(v14, v12) = v16) | ( ~ (v16 = 0) & in(v14, v11) = v16))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (union(v11) = v12) | ~ (in(v15, v11) = 0) | ~ (in(v13, v12) = v14) | ? [v16] : ( ~ (v16 = 0) & in(v13, v15) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (union(v11) = v12) | ~ (in(v13, v15) = 0) | ~ (in(v13, v12) = v14) | ? [v16] : ( ~ (v16 = 0) & in(v15, v11) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v11, v12) = v13) | ~ (in(v14, v12) = v15) | ? [v16] : ((v16 = 0 & v15 = 0 & in(v14, v11) = 0) | ( ~ (v16 = 0) & in(v14, v13) = v16))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v11, v12) = v13) | ~ (in(v14, v11) = v15) | ? [v16] : ((v16 = 0 & v15 = 0 & in(v14, v12) = 0) | ( ~ (v16 = 0) & in(v14, v13) = v16))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v11, v12) = 0) | ~ (in(v13, v12) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v13, v11) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (subset(v14, v13) = v12) | ~ (subset(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (set_intersection2(v14, v13) = v12) | ~ (set_intersection2(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (in(v14, v13) = v12) | ~ (in(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v11, v12) = v13) | ~ (in(v14, v13) = 0) | (in(v14, v12) = 0 & in(v14, v11) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v11, v12) = v13) | ~ (in(v14, v12) = 0) | ? [v15] : ((v15 = 0 & in(v14, v13) = 0) | ( ~ (v15 = 0) & in(v14, v11) = v15))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v11, v12) = v13) | ~ (in(v14, v11) = 0) | ? [v15] : ((v15 = 0 & in(v14, v13) = 0) | ( ~ (v15 = 0) & in(v14, v12) = v15))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (set_intersection2(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (((v18 = 0 & v17 = 0 & in(v15, v13) = 0 & in(v15, v12) = 0) | (v16 = 0 & in(v15, v11) = 0)) & (( ~ (v18 = 0) & in(v15, v13) = v18) | ( ~ (v17 = 0) & in(v15, v12) = v17) | ( ~ (v16 = 0) & in(v15, v11) = v16)))) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v11, v12) = v13) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & in(v14, v12) = v15 & in(v14, v11) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (empty(v13) = v12) | ~ (empty(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (union(v13) = v12) | ~ (union(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (union(v11) = v12) | ~ (in(v13, v12) = 0) | ? [v14] : (in(v14, v11) = 0 & in(v13, v14) = 0)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (subset(v11, v12) = 0) | ~ (in(v13, v11) = 0) | in(v13, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v12, v11) = v13) | set_intersection2(v11, v12) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v11, v12) = v13) | set_intersection2(v12, v11) = v13) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (union(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (((v18 = 0 & v17 = 0 & in(v16, v12) = 0 & in(v14, v16) = 0) | (v15 = 0 & in(v14, v11) = 0)) & (( ~ (v15 = 0) & in(v14, v11) = v15) | ( ! [v19] : ( ~ (in(v19, v12) = 0) | ? [v20] : ( ~ (v20 = 0) & in(v14, v19) = v20)) & ! [v19] : ( ~ (in(v14, v19) = 0) | ? [v20] : ( ~ (v20 = 0) & in(v19, v12) = v20)))))) & ! [v11] : ! [v12] : (v12 = v11 | ~ (set_intersection2(v11, v11) = v12)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v11, v11) = v12)) & ! [v11] : ! [v12] : ( ~ (in(v12, v11) = 0) | ? [v13] : ( ~ (v13 = 0) & in(v11, v12) = v13)) & ! [v11] : ! [v12] : ( ~ (in(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & in(v12, v11) = v13)) & ? [v11] : ? [v12] : ? [v13] : subset(v12, v11) = v13 & ? [v11] : ? [v12] : ? [v13] : set_intersection2(v12, v11) = v13 & ? [v11] : ? [v12] : ? [v13] : in(v12, v11) = v13 & ? [v11] : ? [v12] : empty(v11) = v12 & ? [v11] : ? [v12] : union(v11) = v12) % 20.36/5.73 | 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: % 20.36/5.73 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & union(all_0_8_8) = all_0_7_7 & union(all_0_9_9) = all_0_5_5 & union(all_0_10_10) = all_0_6_6 & subset(all_0_7_7, all_0_4_4) = all_0_3_3 & set_intersection2(all_0_6_6, all_0_5_5) = all_0_4_4 & set_intersection2(all_0_10_10, all_0_9_9) = all_0_8_8 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : (( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v4, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v2, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v1) = v4))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v6 = 0 & in(v4, v2) = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & in(v4, v2) = v7) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v4 = 0) & in(v3, v0) = v4) | ( ! [v8] : ( ~ (in(v8, v1) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v3, v8) = v9)) & ! [v8] : ( ~ (in(v3, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v1) = v9)))))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : empty(v0) = v1 & ? [v0] : ? [v1] : union(v0) = v1 % 20.36/5.74 | % 20.36/5.74 | Applying alpha-rule on (1) yields: % 20.36/5.74 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) % 20.36/5.74 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v1) = v4))) % 20.36/5.75 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 20.36/5.75 | (5) union(all_0_10_10) = all_0_6_6 % 20.36/5.75 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 20.36/5.75 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) % 20.36/5.75 | (8) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v6 = 0 & in(v4, v2) = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & in(v4, v2) = v7) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)))) % 20.36/5.75 | (9) ~ (all_0_3_3 = 0) % 20.36/5.75 | (10) set_intersection2(all_0_6_6, all_0_5_5) = all_0_4_4 % 20.36/5.75 | (11) ? [v0] : ? [v1] : empty(v0) = v1 % 20.36/5.75 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 20.36/5.75 | (13) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 % 20.36/5.75 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 20.36/5.75 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 20.36/5.75 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) % 20.36/5.75 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v0) = v4))) % 20.36/5.75 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v4, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v2, v4) = v5)) % 20.36/5.75 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 20.36/5.75 | (20) ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2 % 20.36/5.75 | (21) empty(all_0_2_2) = all_0_1_1 % 20.36/5.75 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = v5)) % 20.36/5.75 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) % 20.36/5.75 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 20.36/5.75 | (25) subset(all_0_7_7, all_0_4_4) = all_0_3_3 % 20.36/5.75 | (26) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v4 = 0) & in(v3, v0) = v4) | ( ! [v8] : ( ~ (in(v8, v1) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v3, v8) = v9)) & ! [v8] : ( ~ (in(v3, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v1) = v9)))))) % 20.36/5.75 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) % 20.36/5.76 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | (in(v3, v1) = 0 & in(v3, v0) = 0)) % 20.36/5.76 | (29) union(all_0_8_8) = all_0_7_7 % 20.36/5.76 | (30) ? [v0] : ? [v1] : union(v0) = v1 % 20.36/5.76 | (31) union(all_0_9_9) = all_0_5_5 % 20.36/5.76 | (32) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 20.36/5.76 | (33) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 20.36/5.76 | (34) empty(all_0_0_0) = 0 % 20.36/5.76 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0)) % 20.36/5.76 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 20.36/5.76 | (37) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 % 20.36/5.76 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 20.36/5.76 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : (( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v0) = v5))) % 20.36/5.76 | (40) ~ (all_0_1_1 = 0) % 20.36/5.76 | (41) set_intersection2(all_0_10_10, all_0_9_9) = all_0_8_8 % 20.36/5.76 | % 20.36/5.76 | Instantiating formula (4) with all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms subset(all_0_7_7, all_0_4_4) = all_0_3_3, yields: % 20.36/5.76 | (42) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_7_7) = 0) % 20.36/5.76 | % 20.36/5.76 | Instantiating formula (16) with all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms set_intersection2(all_0_6_6, all_0_5_5) = all_0_4_4, yields: % 20.36/5.76 | (43) set_intersection2(all_0_5_5, all_0_6_6) = all_0_4_4 % 20.36/5.76 | % 20.36/5.76 +-Applying beta-rule and splitting (42), into two cases. % 20.36/5.76 |-Branch one: % 20.36/5.76 | (44) all_0_3_3 = 0 % 20.36/5.76 | % 20.36/5.76 | Equations (44) can reduce 9 to: % 20.36/5.76 | (45) $false % 20.36/5.76 | % 20.36/5.76 |-The branch is then unsatisfiable % 20.36/5.76 |-Branch two: % 20.36/5.76 | (9) ~ (all_0_3_3 = 0) % 20.36/5.76 | (47) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_7_7) = 0) % 20.36/5.76 | % 20.36/5.76 | Instantiating (47) with all_27_0_26, all_27_1_27 yields: % 20.36/5.76 | (48) ~ (all_27_0_26 = 0) & in(all_27_1_27, all_0_4_4) = all_27_0_26 & in(all_27_1_27, all_0_7_7) = 0 % 20.36/5.76 | % 20.36/5.76 | Applying alpha-rule on (48) yields: % 20.36/5.76 | (49) ~ (all_27_0_26 = 0) % 20.36/5.76 | (50) in(all_27_1_27, all_0_4_4) = all_27_0_26 % 20.36/5.76 | (51) in(all_27_1_27, all_0_7_7) = 0 % 20.36/5.76 | % 20.36/5.76 | Instantiating formula (39) with all_27_0_26, all_27_1_27, all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms set_intersection2(all_0_5_5, all_0_6_6) = all_0_4_4, in(all_27_1_27, all_0_4_4) = all_27_0_26, yields: % 20.36/5.76 | (52) all_27_0_26 = 0 | ? [v0] : (( ~ (v0 = 0) & in(all_27_1_27, all_0_5_5) = v0) | ( ~ (v0 = 0) & in(all_27_1_27, all_0_6_6) = v0)) % 20.36/5.77 | % 20.36/5.77 | Instantiating formula (35) with all_27_1_27, all_0_7_7, all_0_8_8 and discharging atoms union(all_0_8_8) = all_0_7_7, in(all_27_1_27, all_0_7_7) = 0, yields: % 20.36/5.77 | (53) ? [v0] : (in(v0, all_0_8_8) = 0 & in(all_27_1_27, v0) = 0) % 20.36/5.77 | % 20.36/5.77 | Instantiating (53) with all_36_0_29 yields: % 20.36/5.77 | (54) in(all_36_0_29, all_0_8_8) = 0 & in(all_27_1_27, all_36_0_29) = 0 % 20.36/5.77 | % 20.36/5.77 | Applying alpha-rule on (54) yields: % 20.36/5.77 | (55) in(all_36_0_29, all_0_8_8) = 0 % 20.36/5.77 | (56) in(all_27_1_27, all_36_0_29) = 0 % 20.36/5.77 | % 20.36/5.77 +-Applying beta-rule and splitting (52), into two cases. % 20.36/5.77 |-Branch one: % 20.36/5.77 | (57) all_27_0_26 = 0 % 20.36/5.77 | % 20.36/5.77 | Equations (57) can reduce 49 to: % 20.36/5.77 | (45) $false % 20.36/5.77 | % 20.36/5.77 |-The branch is then unsatisfiable % 20.36/5.77 |-Branch two: % 20.36/5.77 | (49) ~ (all_27_0_26 = 0) % 20.36/5.77 | (60) ? [v0] : (( ~ (v0 = 0) & in(all_27_1_27, all_0_5_5) = v0) | ( ~ (v0 = 0) & in(all_27_1_27, all_0_6_6) = v0)) % 20.36/5.77 | % 20.36/5.77 | Instantiating (60) with all_42_0_30 yields: % 20.36/5.77 | (61) ( ~ (all_42_0_30 = 0) & in(all_27_1_27, all_0_5_5) = all_42_0_30) | ( ~ (all_42_0_30 = 0) & in(all_27_1_27, all_0_6_6) = all_42_0_30) % 20.36/5.77 | % 20.36/5.77 | Instantiating formula (28) with all_36_0_29, all_0_8_8, all_0_9_9, all_0_10_10 and discharging atoms set_intersection2(all_0_10_10, all_0_9_9) = all_0_8_8, in(all_36_0_29, all_0_8_8) = 0, yields: % 20.36/5.77 | (62) in(all_36_0_29, all_0_9_9) = 0 & in(all_36_0_29, all_0_10_10) = 0 % 20.36/5.77 | % 20.36/5.77 | Applying alpha-rule on (62) yields: % 20.36/5.77 | (63) in(all_36_0_29, all_0_9_9) = 0 % 20.36/5.77 | (64) in(all_36_0_29, all_0_10_10) = 0 % 20.36/5.77 | % 20.36/5.77 +-Applying beta-rule and splitting (61), into two cases. % 20.36/5.77 |-Branch one: % 20.36/5.77 | (65) ~ (all_42_0_30 = 0) & in(all_27_1_27, all_0_5_5) = all_42_0_30 % 20.36/5.77 | % 20.36/5.77 | Applying alpha-rule on (65) yields: % 20.36/5.77 | (66) ~ (all_42_0_30 = 0) % 20.36/5.77 | (67) in(all_27_1_27, all_0_5_5) = all_42_0_30 % 20.36/5.77 | % 20.36/5.77 | Instantiating formula (22) with all_36_0_29, all_42_0_30, all_27_1_27, all_0_5_5, all_0_9_9 and discharging atoms union(all_0_9_9) = all_0_5_5, in(all_27_1_27, all_36_0_29) = 0, in(all_27_1_27, all_0_5_5) = all_42_0_30, yields: % 20.36/5.77 | (68) all_42_0_30 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_36_0_29, all_0_9_9) = v0) % 20.36/5.77 | % 20.36/5.77 +-Applying beta-rule and splitting (68), into two cases. % 20.36/5.77 |-Branch one: % 20.36/5.77 | (69) all_42_0_30 = 0 % 20.36/5.77 | % 20.36/5.77 | Equations (69) can reduce 66 to: % 20.36/5.77 | (45) $false % 20.36/5.77 | % 20.36/5.77 |-The branch is then unsatisfiable % 20.36/5.77 |-Branch two: % 20.36/5.77 | (66) ~ (all_42_0_30 = 0) % 20.36/5.77 | (72) ? [v0] : ( ~ (v0 = 0) & in(all_36_0_29, all_0_9_9) = v0) % 20.36/5.77 | % 20.36/5.77 | Instantiating (72) with all_209_0_151 yields: % 20.36/5.77 | (73) ~ (all_209_0_151 = 0) & in(all_36_0_29, all_0_9_9) = all_209_0_151 % 20.36/5.77 | % 20.36/5.77 | Applying alpha-rule on (73) yields: % 20.36/5.77 | (74) ~ (all_209_0_151 = 0) % 20.36/5.77 | (75) in(all_36_0_29, all_0_9_9) = all_209_0_151 % 20.36/5.77 | % 20.36/5.77 | Instantiating formula (14) with all_36_0_29, all_0_9_9, all_209_0_151, 0 and discharging atoms in(all_36_0_29, all_0_9_9) = all_209_0_151, in(all_36_0_29, all_0_9_9) = 0, yields: % 20.36/5.77 | (76) all_209_0_151 = 0 % 20.36/5.77 | % 20.36/5.77 | Equations (76) can reduce 74 to: % 20.36/5.77 | (45) $false % 20.36/5.77 | % 20.36/5.77 |-The branch is then unsatisfiable % 20.36/5.77 |-Branch two: % 20.36/5.77 | (78) ~ (all_42_0_30 = 0) & in(all_27_1_27, all_0_6_6) = all_42_0_30 % 20.36/5.77 | % 20.36/5.77 | Applying alpha-rule on (78) yields: % 20.36/5.77 | (66) ~ (all_42_0_30 = 0) % 20.36/5.77 | (80) in(all_27_1_27, all_0_6_6) = all_42_0_30 % 20.36/5.77 | % 20.36/5.77 | Instantiating formula (22) with all_36_0_29, all_42_0_30, all_27_1_27, all_0_6_6, all_0_10_10 and discharging atoms union(all_0_10_10) = all_0_6_6, in(all_27_1_27, all_36_0_29) = 0, in(all_27_1_27, all_0_6_6) = all_42_0_30, yields: % 20.36/5.77 | (81) all_42_0_30 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_36_0_29, all_0_10_10) = v0) % 20.36/5.77 | % 20.36/5.77 +-Applying beta-rule and splitting (81), into two cases. % 20.36/5.77 |-Branch one: % 20.36/5.77 | (69) all_42_0_30 = 0 % 20.36/5.77 | % 20.36/5.77 | Equations (69) can reduce 66 to: % 20.36/5.77 | (45) $false % 20.36/5.77 | % 20.36/5.77 |-The branch is then unsatisfiable % 20.36/5.77 |-Branch two: % 20.36/5.77 | (66) ~ (all_42_0_30 = 0) % 20.36/5.77 | (85) ? [v0] : ( ~ (v0 = 0) & in(all_36_0_29, all_0_10_10) = v0) % 20.36/5.78 | % 20.36/5.78 | Instantiating (85) with all_209_0_165 yields: % 20.36/5.78 | (86) ~ (all_209_0_165 = 0) & in(all_36_0_29, all_0_10_10) = all_209_0_165 % 20.36/5.78 | % 20.36/5.78 | Applying alpha-rule on (86) yields: % 20.36/5.78 | (87) ~ (all_209_0_165 = 0) % 20.36/5.78 | (88) in(all_36_0_29, all_0_10_10) = all_209_0_165 % 20.36/5.78 | % 20.36/5.78 | Instantiating formula (14) with all_36_0_29, all_0_10_10, all_209_0_165, 0 and discharging atoms in(all_36_0_29, all_0_10_10) = all_209_0_165, in(all_36_0_29, all_0_10_10) = 0, yields: % 20.36/5.78 | (89) all_209_0_165 = 0 % 20.36/5.78 | % 20.36/5.78 | Equations (89) can reduce 87 to: % 20.36/5.78 | (45) $false % 20.36/5.78 | % 20.36/5.78 |-The branch is then unsatisfiable % 20.36/5.78 % SZS output end Proof for theBenchmark % 20.36/5.78 % 20.36/5.78 5240ms %------------------------------------------------------------------------------