%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU139+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n011.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 08:46:53 EDT 2022 % Result : Theorem 3.13s 1.38s % Output : Proof 4.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU139+2 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n011.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 Jun 19 01:17:23 EDT 2022 % 0.12/0.33 % CPUTime : % 0.54/0.57 ____ _ % 0.54/0.57 ___ / __ \_____(_)___ ________ __________ % 0.54/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.54/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.54/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.54/0.57 % 0.54/0.57 A Theorem Prover for First-Order Logic % 0.54/0.58 (ePrincess v.1.0) % 0.54/0.58 % 0.54/0.58 (c) Philipp Rümmer, 2009-2015 % 0.54/0.58 (c) Peter Backeman, 2014-2015 % 0.54/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.54/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.54/0.58 Bug reports to peter@backeman.se % 0.54/0.58 % 0.54/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.54/0.58 % 0.54/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.59/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.65/0.94 Prover 0: Preprocessing ... % 2.75/1.24 Prover 0: Warning: ignoring some quantifiers % 2.75/1.27 Prover 0: Constructing countermodel ... % 3.13/1.38 Prover 0: proved (755ms) % 3.13/1.38 % 3.13/1.38 No countermodel exists, formula is valid % 3.13/1.38 % SZS status Theorem for theBenchmark % 3.13/1.38 % 3.13/1.38 Generating proof ... Warning: ignoring some quantifiers % 4.45/1.68 found it (size 7) % 4.45/1.68 % 4.45/1.68 % SZS output start Proof for theBenchmark % 4.45/1.68 Assumed formulas after preprocessing and simplification: % 4.45/1.68 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (empty(v3) & empty(empty_set) & subset(v0, v1) & proper_subset(v1, v0) & ~ empty(v2) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (set_difference(v5, v6) = v8) | ~ (set_difference(v4, v6) = v7) | ~ subset(v4, v5) | subset(v7, v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (set_intersection2(v5, v6) = v8) | ~ (set_intersection2(v4, v6) = v7) | ~ subset(v4, v5) | subset(v7, v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (set_difference(v5, v4) = v6) | ~ (set_union2(v4, v6) = v7) | ~ subset(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (set_difference(v7, v6) = v5) | ~ (set_difference(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (set_intersection2(v7, v6) = v5) | ~ (set_intersection2(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (set_union2(v7, v6) = v5) | ~ (set_union2(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (set_difference(v6, v5) = v7) | ~ (set_union2(v4, v5) = v6) | set_difference(v4, v5) = v7) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (set_difference(v5, v4) = v6) | ~ (set_union2(v4, v6) = v7) | set_union2(v4, v5) = v7) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (set_difference(v4, v6) = v7) | ~ (set_difference(v4, v5) = v6) | set_intersection2(v4, v5) = v7) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (set_difference(v4, v5) = v6) | ~ in(v7, v6) | ~ in(v7, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (set_difference(v4, v5) = v6) | ~ in(v7, v6) | in(v7, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (set_difference(v4, v5) = v6) | ~ in(v7, v4) | in(v7, v6) | in(v7, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (set_intersection2(v5, v6) = v7) | ~ subset(v4, v6) | ~ subset(v4, v5) | subset(v4, v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (set_intersection2(v4, v5) = v6) | ~ disjoint(v4, v5) | ~ in(v7, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (set_intersection2(v4, v5) = v6) | ~ in(v7, v6) | in(v7, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (set_intersection2(v4, v5) = v6) | ~ in(v7, v6) | in(v7, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (set_intersection2(v4, v5) = v6) | ~ in(v7, v5) | ~ in(v7, v4) | in(v7, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (set_union2(v4, v6) = v7) | ~ subset(v6, v5) | ~ subset(v4, v5) | subset(v7, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (set_union2(v4, v5) = v6) | ~ in(v7, v6) | in(v7, v5) | in(v7, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (set_union2(v4, v5) = v6) | ~ in(v7, v5) | in(v7, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (set_union2(v4, v5) = v6) | ~ in(v7, v4) | in(v7, v6)) & ? [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v4 | ~ (set_difference(v5, v6) = v7) | ? [v8] : (( ~ in(v8, v5) | ~ in(v8, v4) | in(v8, v6)) & (in(v8, v4) | (in(v8, v5) & ~ in(v8, v6))))) & ? [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v4 | ~ (set_intersection2(v5, v6) = v7) | ? [v8] : (( ~ in(v8, v6) | ~ in(v8, v5) | ~ in(v8, v4)) & (in(v8, v4) | (in(v8, v6) & in(v8, v5))))) & ? [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v4 | ~ (set_union2(v5, v6) = v7) | ? [v8] : (( ~ in(v8, v4) | ( ~ in(v8, v6) & ~ in(v8, v5))) & (in(v8, v6) | in(v8, v5) | in(v8, v4)))) & ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (set_union2(v4, v5) = v6) | ~ subset(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : (v6 = v4 | ~ (set_intersection2(v4, v5) = v6) | ~ subset(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : (v6 = empty_set | ~ (set_difference(v4, v5) = v6) | ~ subset(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : (v6 = empty_set | ~ (set_intersection2(v4, v5) = v6) | ~ disjoint(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (set_difference(v4, v5) = v6) | subset(v6, v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (set_difference(v4, v5) = v6) | ? [v7] : (set_difference(v7, v5) = v6 & set_union2(v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (set_intersection2(v5, v4) = v6) | set_intersection2(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (set_intersection2(v4, v5) = v6) | set_intersection2(v5, v4) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (set_intersection2(v4, v5) = v6) | disjoint(v4, v5) | ? [v7] : in(v7, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (set_intersection2(v4, v5) = v6) | subset(v6, v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (set_intersection2(v4, v5) = v6) | ? [v7] : (set_difference(v4, v7) = v6 & set_difference(v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (set_union2(v5, v4) = v6) | ~ empty(v6) | empty(v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (set_union2(v5, v4) = v6) | set_union2(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (set_union2(v4, v5) = v6) | ~ empty(v6) | empty(v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (set_union2(v4, v5) = v6) | set_union2(v5, v4) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (set_union2(v4, v5) = v6) | subset(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (set_union2(v4, v5) = v6) | ? [v7] : (set_difference(v5, v4) = v7 & set_union2(v4, v7) = v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ disjoint(v4, v5) | ~ in(v6, v5) | ~ in(v6, v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ subset(v5, v6) | ~ subset(v4, v5) | subset(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ subset(v4, v5) | ~ in(v6, v4) | in(v6, v5)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (set_difference(v4, empty_set) = v5)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (set_intersection2(v4, v4) = v5)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (set_union2(v4, v4) = v5)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (set_union2(v4, empty_set) = v5)) & ! [v4] : ! [v5] : (v5 = v4 | ~ empty(v5) | ~ empty(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ subset(v5, v4) | ~ subset(v4, v5)) & ! [v4] : ! [v5] : (v5 = v4 | ~ subset(v4, v5) | proper_subset(v4, v5)) & ! [v4] : ! [v5] : (v5 = empty_set | ~ (set_difference(empty_set, v4) = v5)) & ! [v4] : ! [v5] : (v5 = empty_set | ~ (set_intersection2(v4, empty_set) = v5)) & ! [v4] : ! [v5] : ( ~ (set_difference(v4, v5) = empty_set) | subset(v4, v5)) & ! [v4] : ! [v5] : ( ~ (set_intersection2(v4, v5) = empty_set) | disjoint(v4, v5)) & ! [v4] : ! [v5] : ( ~ empty(v5) | ~ in(v4, v5)) & ! [v4] : ! [v5] : ( ~ disjoint(v4, v5) | disjoint(v5, v4)) & ! [v4] : ! [v5] : ( ~ proper_subset(v5, v4) | ~ proper_subset(v4, v5)) & ! [v4] : ! [v5] : ( ~ proper_subset(v4, v5) | subset(v4, v5)) & ! [v4] : ! [v5] : ( ~ in(v5, v4) | ~ in(v4, v5)) & ! [v4] : (v4 = empty_set | ~ empty(v4)) & ! [v4] : (v4 = empty_set | ~ subset(v4, empty_set)) & ! [v4] : ~ proper_subset(v4, v4) & ! [v4] : ~ in(v4, empty_set) & ? [v4] : ? [v5] : (v5 = v4 | ? [v6] : (( ~ in(v6, v5) | ~ in(v6, v4)) & (in(v6, v5) | in(v6, v4)))) & ? [v4] : ? [v5] : (disjoint(v4, v5) | ? [v6] : (in(v6, v5) & in(v6, v4))) & ? [v4] : ? [v5] : (subset(v4, v5) | ? [v6] : (in(v6, v4) & ~ in(v6, v5))) & ? [v4] : (v4 = empty_set | ? [v5] : in(v5, v4)) & ? [v4] : subset(v4, v4) & ? [v4] : subset(empty_set, v4)) % 4.85/1.74 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 4.85/1.74 | (1) empty(all_0_0_0) & empty(empty_set) & subset(all_0_3_3, all_0_2_2) & proper_subset(all_0_2_2, all_0_3_3) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(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 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v1) | ~ in(v4, v0) | in(v4, v2)) & (in(v4, v0) | (in(v4, v1) & ~ in(v4, v2))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3)) & ! [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] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) & ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set)) & ! [v0] : ~ proper_subset(v0, v0) & ! [v0] : ~ in(v0, empty_set) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) & ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0))) & ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0)) & ? [v0] : subset(v0, v0) & ? [v0] : subset(empty_set, v0) % 4.85/1.76 | % 4.85/1.76 | Applying alpha-rule on (1) yields: % 4.85/1.76 | (2) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) % 4.85/1.76 | (3) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) % 4.85/1.76 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 4.85/1.76 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) % 4.85/1.76 | (6) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) % 4.85/1.76 | (7) ~ empty(all_0_1_1) % 4.85/1.76 | (8) empty(empty_set) % 4.85/1.76 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 4.85/1.76 | (10) ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1)) % 4.85/1.76 | (11) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0)))) % 4.85/1.76 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) % 4.85/1.76 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) % 4.85/1.76 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2)) % 4.85/1.76 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) % 4.85/1.76 | (16) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1))))) % 4.85/1.77 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) % 4.85/1.77 | (18) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 4.85/1.77 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 4.85/1.77 | (20) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) % 4.85/1.77 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) % 4.85/1.77 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) % 4.85/1.77 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 4.85/1.77 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 4.85/1.77 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1)) % 4.85/1.77 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) % 4.85/1.77 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) % 4.85/1.77 | (28) subset(all_0_3_3, all_0_2_2) % 4.85/1.77 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1)) % 4.85/1.77 | (30) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 4.85/1.77 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) % 4.85/1.77 | (32) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 4.85/1.77 | (33) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 4.85/1.77 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 4.85/1.77 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 4.85/1.77 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) % 4.85/1.77 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) % 4.85/1.77 | (38) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1)) % 4.85/1.77 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2)) % 4.85/1.77 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) % 4.85/1.77 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) % 4.85/1.77 | (42) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) % 4.85/1.78 | (43) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0))) % 4.85/1.78 | (44) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v1) | ~ in(v4, v0) | in(v4, v2)) & (in(v4, v0) | (in(v4, v1) & ~ in(v4, v2))))) % 4.85/1.78 | (45) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) % 4.85/1.78 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3)) % 4.85/1.78 | (47) ? [v0] : subset(v0, v0) % 4.85/1.78 | (48) ! [v0] : ~ in(v0, empty_set) % 4.85/1.78 | (49) empty(all_0_0_0) % 4.85/1.78 | (50) ? [v0] : subset(empty_set, v0) % 4.85/1.78 | (51) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 4.85/1.78 | (52) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) % 4.85/1.78 | (53) ! [v0] : ~ proper_subset(v0, v0) % 4.85/1.78 | (54) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 4.85/1.78 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 4.85/1.78 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) % 4.85/1.78 | (57) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) % 4.85/1.78 | (58) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0)) % 4.85/1.78 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) % 4.85/1.78 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3)) % 4.85/1.78 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 4.85/1.78 | (62) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) % 4.85/1.78 | (63) proper_subset(all_0_2_2, all_0_3_3) % 4.85/1.78 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0)) % 4.85/1.78 | (65) ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1)) % 4.85/1.78 | (66) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) % 4.85/1.78 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 4.85/1.78 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) % 4.85/1.78 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) % 4.85/1.78 | (70) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 4.85/1.79 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 4.85/1.79 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) % 4.85/1.79 | (73) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 4.85/1.79 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 4.85/1.79 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 4.85/1.79 | (76) ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set)) % 4.85/1.79 | % 4.85/1.79 | Instantiating formula (10) with all_0_3_3, all_0_2_2 and discharging atoms proper_subset(all_0_2_2, all_0_3_3), yields: % 4.85/1.79 | (77) subset(all_0_2_2, all_0_3_3) % 4.85/1.79 | % 4.85/1.79 | Instantiating formula (9) with all_0_2_2, all_0_3_3 and discharging atoms subset(all_0_2_2, all_0_3_3), subset(all_0_3_3, all_0_2_2), yields: % 4.85/1.79 | (78) all_0_2_2 = all_0_3_3 % 4.85/1.79 | % 4.85/1.79 | From (78) and (63) follows: % 4.85/1.79 | (79) proper_subset(all_0_3_3, all_0_3_3) % 4.85/1.79 | % 4.85/1.79 | Instantiating formula (65) with all_0_3_3, all_0_3_3 and discharging atoms proper_subset(all_0_3_3, all_0_3_3), yields: % 4.85/1.79 | (80) $false % 4.85/1.79 | % 4.85/1.79 |-The branch is then unsatisfiable % 4.85/1.79 % SZS output end Proof for theBenchmark % 4.85/1.79 % 4.85/1.79 1205ms %------------------------------------------------------------------------------