%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET638+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n016.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Tue Jul 19 00:21:05 EDT 2022 % Result : Theorem 4.84s 1.88s % Output : Proof 6.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : SET638+3 : TPTP v8.1.0. Released v2.2.0. % 0.08/0.15 % Command : ePrincess-casc -timeout=%d %s % 0.16/0.37 % Computer : n016.cluster.edu % 0.16/0.37 % Model : x86_64 x86_64 % 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.37 % Memory : 8042.1875MB % 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.37 % CPULimit : 300 % 0.16/0.37 % WCLimit : 600 % 0.16/0.37 % DateTime : Mon Jul 11 00:10:57 EDT 2022 % 0.16/0.37 % CPUTime : % 0.60/0.61 ____ _ % 0.60/0.61 ___ / __ \_____(_)___ ________ __________ % 0.60/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.60/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.60/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.60/0.61 % 0.60/0.61 A Theorem Prover for First-Order Logic % 0.60/0.62 (ePrincess v.1.0) % 0.60/0.62 % 0.60/0.62 (c) Philipp Rümmer, 2009-2015 % 0.60/0.62 (c) Peter Backeman, 2014-2015 % 0.60/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.60/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.60/0.62 Bug reports to peter@backeman.se % 0.60/0.62 % 0.60/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.60/0.62 % 0.60/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.67/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.48/0.97 Prover 0: Preprocessing ... % 2.06/1.19 Prover 0: Warning: ignoring some quantifiers % 2.08/1.21 Prover 0: Constructing countermodel ... % 2.79/1.44 Prover 0: gave up % 2.79/1.44 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.12/1.46 Prover 1: Preprocessing ... % 3.48/1.54 Prover 1: Warning: ignoring some quantifiers % 3.48/1.55 Prover 1: Constructing countermodel ... % 4.18/1.72 Prover 1: gave up % 4.18/1.72 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.18/1.74 Prover 2: Preprocessing ... % 4.74/1.81 Prover 2: Warning: ignoring some quantifiers % 4.74/1.81 Prover 2: Constructing countermodel ... % 4.84/1.88 Prover 2: proved (162ms) % 4.84/1.88 % 4.84/1.88 No countermodel exists, formula is valid % 4.84/1.88 % SZS status Theorem for theBenchmark % 4.84/1.88 % 4.84/1.88 Generating proof ... Warning: ignoring some quantifiers % 6.17/2.18 found it (size 29) % 6.17/2.18 % 6.17/2.18 % SZS output start Proof for theBenchmark % 6.17/2.18 Assumed formulas after preprocessing and simplification: % 6.17/2.18 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & union(v1, v2) = v3 & intersection(v0, v2) = empty_set & subset(v0, v3) = 0 & subset(v0, v1) = v4 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v8, v9) = v10) | ~ (intersection(v5, v7) = v9) | ~ (intersection(v5, v6) = v8) | ? [v11] : (union(v6, v7) = v11 & intersection(v5, v11) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (member(v7, v8) = v9) | ~ (union(v5, v6) = v8) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & ~ (v10 = 0) & member(v7, v6) = v11 & member(v7, v5) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (member(v7, v8) = v9) | ~ (intersection(v5, v6) = v8) | ? [v10] : (( ~ (v10 = 0) & member(v7, v6) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (union(v6, v7) = v8) | ~ (intersection(v5, v8) = v9) | ? [v10] : ? [v11] : (union(v10, v11) = v9 & intersection(v5, v7) = v11 & intersection(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (member(v7, v6) = v8) | ~ (subset(v5, v6) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (member(v8, v7) = v6) | ~ (member(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (union(v8, v7) = v6) | ~ (union(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection(v8, v7) = v6) | ~ (intersection(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (subset(v8, v7) = v6) | ~ (subset(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (member(v7, v8) = 0) | ~ (union(v5, v6) = v8) | ? [v9] : ((v9 = 0 & member(v7, v6) = 0) | (v9 = 0 & member(v7, v5) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (member(v7, v8) = 0) | ~ (intersection(v5, v6) = v8) | (member(v7, v6) = 0 & member(v7, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (intersection(v5, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & subset(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & member(v8, v6) = v9 & member(v8, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (empty(v7) = v6) | ~ (empty(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (member(v7, v5) = 0) | ~ (subset(v5, v6) = 0) | member(v7, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v6, v5) = v7) | union(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v5, v6) = v7) | union(v6, v5) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection(v6, v5) = v7) | intersection(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection(v5, v6) = v7) | intersection(v6, v5) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection(v5, v6) = v7) | subset(v7, v5) = 0) & ! [v5] : ! [v6] : (v6 = v5 | ~ (union(v5, empty_set) = v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (subset(v6, v5) = 0) | ? [v7] : ( ~ (v7 = 0) & subset(v5, v6) = v7)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (subset(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & subset(v6, v5) = v7)) & ! [v5] : ! [v6] : (v6 = 0 | ~ (empty(v5) = v6) | ? [v7] : member(v7, v5) = 0) & ! [v5] : ! [v6] : (v6 = 0 | ~ (subset(v5, v5) = v6)) & ! [v5] : ! [v6] : ( ~ (empty(v5) = 0) | ~ (member(v6, v5) = 0)) & ! [v5] : ! [v6] : ( ~ (subset(v5, v6) = 0) | intersection(v5, v6) = v5) & ! [v5] : ~ (member(v5, empty_set) = 0) & ? [v5] : ? [v6] : ? [v7] : member(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : union(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : intersection(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : subset(v6, v5) = v7 & ? [v5] : ? [v6] : (v6 = v5 | ? [v7] : ? [v8] : ? [v9] : (((v9 = 0 & member(v7, v6) = 0) | (v8 = 0 & member(v7, v5) = 0)) & (( ~ (v9 = 0) & member(v7, v6) = v9) | ( ~ (v8 = 0) & member(v7, v5) = v8)))) & ? [v5] : ? [v6] : empty(v5) = v6) % 6.17/2.21 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 6.17/2.21 | (1) ~ (all_0_0_0 = 0) & union(all_0_3_3, all_0_2_2) = all_0_1_1 & intersection(all_0_4_4, all_0_2_2) = empty_set & subset(all_0_4_4, all_0_1_1) = 0 & subset(all_0_4_4, all_0_3_3) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (union(v3, v4) = v5) | ~ (intersection(v0, v2) = v4) | ~ (intersection(v0, v1) = v3) | ? [v6] : (union(v1, v2) = v6 & intersection(v0, v6) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (member(v2, v3) = v4) | ~ (union(v0, v1) = v3) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (member(v2, v3) = v4) | ~ (intersection(v0, v1) = v3) | ? [v5] : (( ~ (v5 = 0) & member(v2, v1) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (union(v1, v2) = v3) | ~ (intersection(v0, v3) = v4) | ? [v5] : ? [v6] : (union(v5, v6) = v4 & intersection(v0, v2) = v6 & intersection(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (member(v2, v1) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (member(v2, v3) = 0) | ~ (union(v0, v1) = v3) | ? [v4] : ((v4 = 0 & member(v2, v1) = 0) | (v4 = 0 & member(v2, v0) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (member(v2, v3) = 0) | ~ (intersection(v0, v1) = v3) | (member(v2, v1) = 0 & member(v2, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (intersection(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (member(v2, v0) = 0) | ~ (subset(v0, v1) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | subset(v2, v0) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (union(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : member(v2, v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (empty(v0) = 0) | ~ (member(v1, v0) = 0)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | intersection(v0, v1) = v0) & ! [v0] : ~ (member(v0, empty_set) = 0) & ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & member(v2, v1) = 0) | (v3 = 0 & member(v2, v0) = 0)) & (( ~ (v4 = 0) & member(v2, v1) = v4) | ( ~ (v3 = 0) & member(v2, v0) = v3)))) & ? [v0] : ? [v1] : empty(v0) = v1 % 6.59/2.22 | % 6.59/2.22 | Applying alpha-rule on (1) yields: % 6.59/2.22 | (2) union(all_0_3_3, all_0_2_2) = all_0_1_1 % 6.59/2.22 | (3) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 % 6.59/2.22 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 6.59/2.22 | (5) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | intersection(v0, v1) = v0) % 6.59/2.22 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) % 6.59/2.22 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) % 6.59/2.23 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | subset(v2, v0) = 0) % 6.59/2.23 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 6.59/2.23 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) % 6.59/2.23 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) % 6.59/2.23 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2) % 6.59/2.23 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (member(v2, v3) = 0) | ~ (union(v0, v1) = v3) | ? [v4] : ((v4 = 0 & member(v2, v1) = 0) | (v4 = 0 & member(v2, v0) = 0))) % 6.59/2.23 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (member(v2, v3) = v4) | ~ (union(v0, v1) = v3) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = v5)) % 6.59/2.23 | (15) ! [v0] : ~ (member(v0, empty_set) = 0) % 6.59/2.23 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (union(v1, v2) = v3) | ~ (intersection(v0, v3) = v4) | ? [v5] : ? [v6] : (union(v5, v6) = v4 & intersection(v0, v2) = v6 & intersection(v0, v1) = v5)) % 6.59/2.23 | (17) ~ (all_0_0_0 = 0) % 6.59/2.23 | (18) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2 % 6.59/2.23 | (19) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & member(v2, v1) = 0) | (v3 = 0 & member(v2, v0) = 0)) & (( ~ (v4 = 0) & member(v2, v1) = v4) | ( ~ (v3 = 0) & member(v2, v0) = v3)))) % 6.59/2.23 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ (union(v0, empty_set) = v1)) % 6.59/2.23 | (21) subset(all_0_4_4, all_0_1_1) = 0 % 6.59/2.23 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (member(v2, v0) = 0) | ~ (subset(v0, v1) = 0) | member(v2, v1) = 0) % 6.59/2.23 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 6.59/2.23 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (member(v2, v1) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) % 6.59/2.23 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (member(v2, v3) = v4) | ~ (intersection(v0, v1) = v3) | ? [v5] : (( ~ (v5 = 0) & member(v2, v1) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5))) % 6.59/2.23 | (26) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 6.59/2.23 | (27) ? [v0] : ? [v1] : empty(v0) = v1 % 6.59/2.23 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (member(v2, v3) = 0) | ~ (intersection(v0, v1) = v3) | (member(v2, v1) = 0 & member(v2, v0) = 0)) % 6.59/2.23 | (29) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2 % 6.59/2.23 | (30) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : member(v2, v0) = 0) % 6.59/2.23 | (31) intersection(all_0_4_4, all_0_2_2) = empty_set % 6.59/2.23 | (32) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 6.59/2.23 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 6.59/2.24 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 6.59/2.24 | (35) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2 % 6.59/2.24 | (36) subset(all_0_4_4, all_0_3_3) = all_0_0_0 % 6.59/2.24 | (37) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) % 6.59/2.24 | (38) ! [v0] : ! [v1] : ( ~ (empty(v0) = 0) | ~ (member(v1, v0) = 0)) % 6.59/2.24 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (union(v3, v4) = v5) | ~ (intersection(v0, v2) = v4) | ~ (intersection(v0, v1) = v3) | ? [v6] : (union(v1, v2) = v6 & intersection(v0, v6) = v5)) % 6.59/2.24 | (40) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (intersection(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 6.59/2.24 | % 6.59/2.24 | Instantiating formula (7) with all_0_1_1, all_0_3_3, all_0_2_2 and discharging atoms union(all_0_3_3, all_0_2_2) = all_0_1_1, yields: % 6.59/2.24 | (41) union(all_0_2_2, all_0_3_3) = all_0_1_1 % 6.59/2.24 | % 6.59/2.24 | Instantiating formula (5) with all_0_1_1, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_1_1) = 0, yields: % 6.59/2.24 | (42) intersection(all_0_4_4, all_0_1_1) = all_0_4_4 % 6.59/2.24 | % 6.59/2.24 | Instantiating formula (34) with all_0_0_0, all_0_3_3, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_3_3) = all_0_0_0, yields: % 6.59/2.24 | (43) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_3_3) = v1 & member(v0, all_0_4_4) = 0) % 6.59/2.24 | % 6.59/2.24 +-Applying beta-rule and splitting (43), into two cases. % 6.59/2.24 |-Branch one: % 6.59/2.24 | (44) all_0_0_0 = 0 % 6.59/2.24 | % 6.59/2.24 | Equations (44) can reduce 17 to: % 6.59/2.24 | (45) $false % 6.59/2.24 | % 6.59/2.24 |-The branch is then unsatisfiable % 6.59/2.24 |-Branch two: % 6.59/2.24 | (17) ~ (all_0_0_0 = 0) % 6.59/2.24 | (47) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_3_3) = v1 & member(v0, all_0_4_4) = 0) % 6.59/2.24 | % 6.59/2.24 | Instantiating (47) with all_24_0_21, all_24_1_22 yields: % 6.59/2.24 | (48) ~ (all_24_0_21 = 0) & member(all_24_1_22, all_0_3_3) = all_24_0_21 & member(all_24_1_22, all_0_4_4) = 0 % 6.59/2.24 | % 6.59/2.24 | Applying alpha-rule on (48) yields: % 6.59/2.24 | (49) ~ (all_24_0_21 = 0) % 6.59/2.24 | (50) member(all_24_1_22, all_0_3_3) = all_24_0_21 % 6.59/2.24 | (51) member(all_24_1_22, all_0_4_4) = 0 % 6.59/2.24 | % 6.59/2.24 | Instantiating formula (16) with all_0_4_4, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms union(all_0_3_3, all_0_2_2) = all_0_1_1, intersection(all_0_4_4, all_0_1_1) = all_0_4_4, yields: % 6.59/2.24 | (52) ? [v0] : ? [v1] : (union(v0, v1) = all_0_4_4 & intersection(all_0_4_4, all_0_2_2) = v1 & intersection(all_0_4_4, all_0_3_3) = v0) % 6.59/2.24 | % 6.59/2.24 | Instantiating formula (16) with all_0_4_4, all_0_1_1, all_0_3_3, all_0_2_2, all_0_4_4 and discharging atoms union(all_0_2_2, all_0_3_3) = all_0_1_1, intersection(all_0_4_4, all_0_1_1) = all_0_4_4, yields: % 6.59/2.24 | (53) ? [v0] : ? [v1] : (union(v0, v1) = all_0_4_4 & intersection(all_0_4_4, all_0_2_2) = v0 & intersection(all_0_4_4, all_0_3_3) = v1) % 6.59/2.24 | % 6.59/2.24 | Instantiating (52) with all_32_0_23, all_32_1_24 yields: % 6.59/2.24 | (54) union(all_32_1_24, all_32_0_23) = all_0_4_4 & intersection(all_0_4_4, all_0_2_2) = all_32_0_23 & intersection(all_0_4_4, all_0_3_3) = all_32_1_24 % 6.59/2.24 | % 6.59/2.24 | Applying alpha-rule on (54) yields: % 6.59/2.24 | (55) union(all_32_1_24, all_32_0_23) = all_0_4_4 % 6.59/2.25 | (56) intersection(all_0_4_4, all_0_2_2) = all_32_0_23 % 6.59/2.25 | (57) intersection(all_0_4_4, all_0_3_3) = all_32_1_24 % 6.59/2.25 | % 6.59/2.25 | Instantiating (53) with all_34_0_25, all_34_1_26 yields: % 6.59/2.25 | (58) union(all_34_1_26, all_34_0_25) = all_0_4_4 & intersection(all_0_4_4, all_0_2_2) = all_34_1_26 & intersection(all_0_4_4, all_0_3_3) = all_34_0_25 % 6.59/2.25 | % 6.59/2.25 | Applying alpha-rule on (58) yields: % 6.59/2.25 | (59) union(all_34_1_26, all_34_0_25) = all_0_4_4 % 6.59/2.25 | (60) intersection(all_0_4_4, all_0_2_2) = all_34_1_26 % 6.59/2.25 | (61) intersection(all_0_4_4, all_0_3_3) = all_34_0_25 % 6.59/2.25 | % 6.59/2.25 | Instantiating formula (23) with all_0_4_4, all_0_2_2, all_34_1_26, empty_set and discharging atoms intersection(all_0_4_4, all_0_2_2) = all_34_1_26, intersection(all_0_4_4, all_0_2_2) = empty_set, yields: % 6.59/2.25 | (62) all_34_1_26 = empty_set % 6.59/2.25 | % 6.59/2.25 | Instantiating formula (23) with all_0_4_4, all_0_2_2, all_32_0_23, all_34_1_26 and discharging atoms intersection(all_0_4_4, all_0_2_2) = all_34_1_26, intersection(all_0_4_4, all_0_2_2) = all_32_0_23, yields: % 6.59/2.25 | (63) all_34_1_26 = all_32_0_23 % 6.59/2.25 | % 6.59/2.25 | Instantiating formula (23) with all_0_4_4, all_0_3_3, all_32_1_24, all_34_0_25 and discharging atoms intersection(all_0_4_4, all_0_3_3) = all_34_0_25, intersection(all_0_4_4, all_0_3_3) = all_32_1_24, yields: % 6.59/2.25 | (64) all_34_0_25 = all_32_1_24 % 6.59/2.25 | % 6.59/2.25 | Combining equations (63,62) yields a new equation: % 6.59/2.25 | (65) all_32_0_23 = empty_set % 6.59/2.25 | % 6.59/2.25 | Simplifying 65 yields: % 6.59/2.25 | (66) all_32_0_23 = empty_set % 6.59/2.25 | % 6.59/2.25 | From (66) and (55) follows: % 6.59/2.25 | (67) union(all_32_1_24, empty_set) = all_0_4_4 % 6.59/2.25 | % 6.59/2.25 | From (64) and (61) follows: % 6.59/2.25 | (57) intersection(all_0_4_4, all_0_3_3) = all_32_1_24 % 6.59/2.25 | % 6.59/2.25 | Instantiating formula (20) with all_0_4_4, all_32_1_24 and discharging atoms union(all_32_1_24, empty_set) = all_0_4_4, yields: % 6.59/2.25 | (69) all_32_1_24 = all_0_4_4 % 6.59/2.25 | % 6.59/2.25 | From (69) and (57) follows: % 6.59/2.25 | (70) intersection(all_0_4_4, all_0_3_3) = all_0_4_4 % 6.59/2.25 | % 6.59/2.25 | Instantiating formula (28) with all_0_4_4, all_24_1_22, all_0_3_3, all_0_4_4 and discharging atoms member(all_24_1_22, all_0_4_4) = 0, intersection(all_0_4_4, all_0_3_3) = all_0_4_4, yields: % 6.59/2.25 | (71) member(all_24_1_22, all_0_3_3) = 0 % 6.59/2.25 | % 6.59/2.25 | Instantiating formula (4) with all_24_1_22, all_0_3_3, 0, all_24_0_21 and discharging atoms member(all_24_1_22, all_0_3_3) = all_24_0_21, member(all_24_1_22, all_0_3_3) = 0, yields: % 6.59/2.25 | (72) all_24_0_21 = 0 % 6.59/2.25 | % 6.59/2.25 | Equations (72) can reduce 49 to: % 6.59/2.25 | (45) $false % 6.59/2.25 | % 6.59/2.25 |-The branch is then unsatisfiable % 6.59/2.25 % SZS output end Proof for theBenchmark % 6.59/2.25 % 6.59/2.25 1625ms %------------------------------------------------------------------------------