%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU150+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n021.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 08:47:01 EDT 2022 % Result : Theorem 4.08s 1.58s % Output : Proof 6.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU150+2 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n021.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 : Mon Jun 20 00:04:03 EDT 2022 % 0.12/0.33 % CPUTime : % 0.50/0.58 ____ _ % 0.50/0.58 ___ / __ \_____(_)___ ________ __________ % 0.50/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.50/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.50/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.50/0.58 % 0.50/0.58 A Theorem Prover for First-Order Logic % 0.50/0.58 (ePrincess v.1.0) % 0.50/0.58 % 0.50/0.58 (c) Philipp Rümmer, 2009-2015 % 0.50/0.58 (c) Peter Backeman, 2014-2015 % 0.50/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.50/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.50/0.58 Bug reports to peter@backeman.se % 0.50/0.58 % 0.50/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.50/0.58 % 0.50/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.50/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.69/0.98 Prover 0: Preprocessing ... % 3.17/1.40 Prover 0: Warning: ignoring some quantifiers % 3.42/1.43 Prover 0: Constructing countermodel ... % 4.08/1.58 Prover 0: proved (947ms) % 4.08/1.58 % 4.08/1.58 No countermodel exists, formula is valid % 4.08/1.58 % SZS status Theorem for theBenchmark % 4.08/1.58 % 4.08/1.58 Generating proof ... Warning: ignoring some quantifiers % 5.74/1.94 found it (size 9) % 5.74/1.94 % 5.74/1.94 % SZS output start Proof for theBenchmark % 5.74/1.94 Assumed formulas after preprocessing and simplification: % 5.74/1.94 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v3 = v2) & powerset(empty_set) = v0 & singleton(v1) = v4 & singleton(empty_set) = v0 & unordered_pair(v2, v3) = v4 & empty(v6) & empty(empty_set) & ~ empty(v5) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v8, v10) = v11) | ~ (singleton(v9) = v10) | ~ subset(v7, v8) | subset(v7, v11) | in(v9, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v8, v9) = v11) | ~ (set_difference(v7, v9) = v10) | ~ subset(v7, v8) | subset(v10, v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v8, v9) = v11) | ~ (set_intersection2(v7, v9) = v10) | ~ subset(v7, v8) | subset(v10, v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | v10 = v7 | ~ (unordered_pair(v7, v8) = v9) | ~ in(v10, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (set_difference(v8, v7) = v9) | ~ (set_union2(v7, v9) = v10) | ~ subset(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_difference(v10, v9) = v8) | ~ (set_difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (singleton(v8) = v10) | ~ (singleton(v7) = v9) | ~ subset(v9, v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (singleton(v7) = v10) | ~ (unordered_pair(v8, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_intersection2(v10, v9) = v8) | ~ (set_intersection2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_union2(v10, v9) = v8) | ~ (set_union2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v9, v8) = v10) | ~ (set_union2(v7, v8) = v9) | set_difference(v7, v8) = v10) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v8, v7) = v9) | ~ (set_union2(v7, v9) = v10) | set_union2(v7, v8) = v10) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v9) = v10) | ~ (set_difference(v7, v8) = v9) | set_intersection2(v7, v8) = v10) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v8) = v9) | ~ in(v10, v9) | ~ in(v10, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v8) = v9) | ~ in(v10, v9) | in(v10, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v8) = v9) | ~ in(v10, v7) | in(v10, v9) | in(v10, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) | ~ subset(v7, v9) | ~ subset(v7, v8) | subset(v7, v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) | ~ disjoint(v7, v8) | ~ in(v10, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) | ~ in(v10, v9) | in(v10, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) | ~ in(v10, v9) | in(v10, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) | ~ in(v10, v8) | ~ in(v10, v7) | in(v10, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v7, v9) = v10) | ~ subset(v9, v8) | ~ subset(v7, v8) | subset(v10, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v7, v8) = v9) | ~ in(v10, v9) | in(v10, v8) | in(v10, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v7, v8) = v9) | ~ in(v10, v8) | in(v10, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v7, v8) = v9) | ~ in(v10, v7) | in(v10, v9)) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_difference(v8, v9) = v10) | ? [v11] : (( ~ in(v11, v8) | ~ in(v11, v7) | in(v11, v9)) & (in(v11, v7) | (in(v11, v8) & ~ in(v11, v9))))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_intersection2(v8, v9) = v10) | ? [v11] : (( ~ in(v11, v9) | ~ in(v11, v8) | ~ in(v11, v7)) & (in(v11, v7) | (in(v11, v9) & in(v11, v8))))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_union2(v8, v9) = v10) | ? [v11] : (( ~ in(v11, v7) | ( ~ in(v11, v9) & ~ in(v11, v8))) & (in(v11, v9) | in(v11, v8) | in(v11, v7)))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (unordered_pair(v8, v9) = v10) | ? [v11] : ((v11 = v9 | v11 = v8 | in(v11, v7)) & ( ~ in(v11, v7) | ( ~ (v11 = v9) & ~ (v11 = v8))))) & ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (set_union2(v7, v8) = v9) | ~ subset(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | v7 = empty_set | ~ (singleton(v8) = v9) | ~ subset(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (set_difference(v7, v8) = v9) | ~ disjoint(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (singleton(v7) = v8) | ~ in(v9, v8)) & ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (set_intersection2(v7, v8) = v9) | ~ subset(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : (v9 = empty_set | ~ (set_difference(v7, v8) = v9) | ~ subset(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : (v9 = empty_set | ~ (set_intersection2(v7, v8) = v9) | ~ disjoint(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (powerset(v9) = v8) | ~ (powerset(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_difference(v7, v8) = v9) | subset(v9, v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_difference(v7, v8) = v9) | ? [v10] : (set_difference(v10, v8) = v9 & set_union2(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v7) = v8) | ~ subset(v9, v7) | in(v9, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v7) = v8) | ~ in(v9, v8) | subset(v9, v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (singleton(v7) = v9) | ~ subset(v9, v8) | in(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (singleton(v7) = v9) | ~ in(v7, v8) | subset(v9, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v8, v7) = v9) | set_intersection2(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | set_intersection2(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | disjoint(v7, v8) | ? [v10] : in(v10, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | subset(v9, v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | ? [v10] : (set_difference(v7, v10) = v9 & set_difference(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v8, v7) = v9) | ~ empty(v9) | empty(v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v8, v7) = v9) | set_union2(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | ~ empty(v9) | empty(v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | set_union2(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | subset(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | ? [v10] : (set_difference(v8, v7) = v10 & set_union2(v7, v10) = v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v8, v7) = v9) | unordered_pair(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | unordered_pair(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | in(v8, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | in(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ disjoint(v8, v9) | ~ subset(v7, v8) | disjoint(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ disjoint(v7, v8) | ~ in(v9, v8) | ~ in(v9, v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ subset(v8, v9) | ~ subset(v7, v8) | subset(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ subset(v7, v8) | ~ in(v9, v7) | in(v9, v8)) & ? [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (powerset(v8) = v9) | ? [v10] : (( ~ subset(v10, v8) | ~ in(v10, v7)) & (subset(v10, v8) | in(v10, v7)))) & ? [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (singleton(v8) = v9) | ? [v10] : (( ~ (v10 = v8) | ~ in(v8, v7)) & (v10 = v8 | in(v10, v7)))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_difference(v7, empty_set) = v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_intersection2(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_union2(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_union2(v7, empty_set) = v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ empty(v8) | ~ empty(v7)) & ! [v7] : ! [v8] : (v8 = v7 | ~ subset(v8, v7) | ~ subset(v7, v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ subset(v7, v8) | proper_subset(v7, v8)) & ! [v7] : ! [v8] : (v8 = empty_set | ~ (set_difference(empty_set, v7) = v8)) & ! [v7] : ! [v8] : (v8 = empty_set | ~ (set_intersection2(v7, empty_set) = v8)) & ! [v7] : ! [v8] : ( ~ (set_difference(v7, v8) = v7) | disjoint(v7, v8)) & ! [v7] : ! [v8] : ( ~ (set_difference(v7, v8) = empty_set) | subset(v7, v8)) & ! [v7] : ! [v8] : ( ~ (singleton(v8) = v7) | subset(v7, v7)) & ! [v7] : ! [v8] : ( ~ (singleton(v7) = v8) | unordered_pair(v7, v7) = v8) & ! [v7] : ! [v8] : ( ~ (singleton(v7) = v8) | subset(empty_set, v8)) & ! [v7] : ! [v8] : ( ~ (singleton(v7) = v8) | in(v7, v8)) & ! [v7] : ! [v8] : ( ~ (set_intersection2(v7, v8) = empty_set) | disjoint(v7, v8)) & ! [v7] : ! [v8] : ( ~ (unordered_pair(v7, v7) = v8) | singleton(v7) = v8) & ! [v7] : ! [v8] : ( ~ empty(v8) | ~ in(v7, v8)) & ! [v7] : ! [v8] : ( ~ disjoint(v7, v8) | disjoint(v8, v7)) & ! [v7] : ! [v8] : ( ~ subset(v7, v8) | ~ proper_subset(v8, v7)) & ! [v7] : ! [v8] : ( ~ proper_subset(v8, v7) | ~ proper_subset(v7, v8)) & ! [v7] : ! [v8] : ( ~ proper_subset(v7, v8) | subset(v7, v8)) & ! [v7] : ! [v8] : ( ~ in(v8, v7) | ~ in(v7, v8)) & ! [v7] : (v7 = empty_set | ~ empty(v7)) & ! [v7] : (v7 = empty_set | ~ subset(v7, empty_set)) & ! [v7] : ~ (singleton(v7) = empty_set) & ! [v7] : ~ proper_subset(v7, v7) & ! [v7] : ~ in(v7, empty_set) & ? [v7] : ? [v8] : (v8 = v7 | ? [v9] : (( ~ in(v9, v8) | ~ in(v9, v7)) & (in(v9, v8) | in(v9, v7)))) & ? [v7] : ? [v8] : (disjoint(v7, v8) | ? [v9] : (in(v9, v8) & in(v9, v7))) & ? [v7] : ? [v8] : (subset(v7, v8) | ? [v9] : (in(v9, v7) & ~ in(v9, v8))) & ? [v7] : (v7 = empty_set | ? [v8] : in(v8, v7)) & ? [v7] : subset(v7, v7) & ? [v7] : subset(empty_set, v7)) % 5.94/2.00 | 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 yields: % 5.94/2.00 | (1) ~ (all_0_3_3 = all_0_4_4) & powerset(empty_set) = all_0_6_6 & singleton(all_0_5_5) = all_0_2_2 & singleton(empty_set) = all_0_6_6 & unordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2 & empty(all_0_0_0) & empty(empty_set) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0)) & ! [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 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) & ! [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 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [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] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(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] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, 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] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [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] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1)) & ! [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] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, 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] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0)))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) & ! [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) = v0) | disjoint(v0, v1)) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(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] : ~ (singleton(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) % 5.94/2.02 | % 5.94/2.02 | Applying alpha-rule on (1) yields: % 5.94/2.02 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1)) % 5.94/2.02 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2)) % 5.94/2.02 | (4) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) % 5.94/2.02 | (5) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) % 5.94/2.02 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) % 5.94/2.02 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 5.94/2.02 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) % 5.94/2.02 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1)) % 5.94/2.02 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1)) % 5.94/2.02 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0)) % 5.94/2.02 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) % 5.94/2.02 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 5.94/2.02 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) % 5.94/2.02 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) % 5.94/2.02 | (16) ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) % 5.94/2.02 | (17) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) % 5.94/2.02 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) % 5.94/2.02 | (19) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 5.94/2.02 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 5.94/2.03 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 5.94/2.03 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 5.94/2.03 | (23) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 5.94/2.03 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) % 5.94/2.03 | (25) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) % 5.94/2.03 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) % 5.94/2.03 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) % 5.94/2.03 | (28) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) % 5.94/2.03 | (29) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 5.94/2.03 | (30) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) % 5.94/2.03 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) % 5.94/2.03 | (32) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0))) % 5.94/2.03 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) % 5.94/2.03 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 5.94/2.03 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 5.94/2.03 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) % 5.94/2.03 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 5.94/2.03 | (38) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0)))) % 5.94/2.03 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) % 5.94/2.03 | (40) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0)) % 5.94/2.03 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 5.94/2.03 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 5.94/2.03 | (43) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 5.94/2.03 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3)) % 5.94/2.03 | (45) ? [v0] : subset(empty_set, v0) % 5.94/2.03 | (46) ! [v0] : ~ proper_subset(v0, v0) % 5.94/2.03 | (47) empty(empty_set) % 5.94/2.03 | (48) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 5.94/2.03 | (49) powerset(empty_set) = all_0_6_6 % 5.94/2.03 | (50) ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1)) % 5.94/2.03 | (51) ! [v0] : ~ in(v0, empty_set) % 5.94/2.03 | (52) ! [v0] : ~ (singleton(v0) = empty_set) % 5.94/2.03 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2)) % 5.94/2.03 | (54) ? [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)))) % 5.94/2.03 | (55) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) % 5.94/2.03 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 5.94/2.03 | (57) ~ (all_0_3_3 = all_0_4_4) % 5.94/2.03 | (58) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1)) % 5.94/2.03 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3)) % 5.94/2.04 | (60) unordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2 % 5.94/2.04 | (61) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 5.94/2.04 | (62) ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set)) % 5.94/2.04 | (63) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) % 6.20/2.04 | (64) singleton(all_0_5_5) = all_0_2_2 % 6.20/2.04 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) % 6.20/2.04 | (66) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2)) % 6.20/2.04 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 6.20/2.04 | (68) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) % 6.20/2.04 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2)) % 6.20/2.04 | (70) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) % 6.20/2.04 | (71) empty(all_0_0_0) % 6.20/2.04 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 6.20/2.04 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1)) % 6.20/2.04 | (74) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 6.20/2.04 | (75) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) % 6.20/2.04 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) % 6.20/2.04 | (77) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 6.20/2.04 | (78) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) % 6.20/2.04 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 6.20/2.04 | (80) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) % 6.20/2.04 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) % 6.20/2.04 | (82) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 6.20/2.04 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) % 6.20/2.04 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 6.20/2.04 | (85) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) % 6.20/2.04 | (86) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 6.20/2.04 | (87) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) % 6.20/2.04 | (88) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1)) % 6.20/2.04 | (89) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 6.20/2.04 | (90) singleton(empty_set) = all_0_6_6 % 6.20/2.04 | (91) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0)) % 6.20/2.05 | (92) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) % 6.20/2.05 | (93) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3)) % 6.20/2.05 | (94) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) % 6.20/2.05 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) % 6.20/2.05 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) % 6.20/2.05 | (97) ? [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))))) % 6.20/2.05 | (98) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0)) % 6.20/2.05 | (99) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) % 6.20/2.05 | (100) ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1)) % 6.20/2.05 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 6.20/2.05 | (102) ? [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))))) % 6.20/2.05 | (103) ? [v0] : subset(v0, v0) % 6.20/2.05 | (104) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0)) % 6.20/2.05 | (105) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1)) % 6.20/2.05 | (106) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) % 6.20/2.05 | (107) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) % 6.20/2.05 | (108) ~ empty(all_0_1_1) % 6.20/2.05 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1)) % 6.20/2.05 | % 6.20/2.05 | Instantiating formula (67) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_2_2, unordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2, yields: % 6.20/2.05 | (110) all_0_4_4 = all_0_5_5 % 6.20/2.05 | % 6.20/2.05 | Equations (110) can reduce 57 to: % 6.20/2.05 | (111) ~ (all_0_3_3 = all_0_5_5) % 6.20/2.05 | % 6.20/2.05 | From (110) and (60) follows: % 6.20/2.05 | (112) unordered_pair(all_0_5_5, all_0_3_3) = all_0_2_2 % 6.20/2.05 | % 6.20/2.05 | Instantiating formula (85) with all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms unordered_pair(all_0_5_5, all_0_3_3) = all_0_2_2, yields: % 6.20/2.05 | (113) in(all_0_3_3, all_0_2_2) % 6.20/2.05 | % 6.20/2.05 | Instantiating formula (30) with all_0_3_3, all_0_2_2, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_2_2, in(all_0_3_3, all_0_2_2), yields: % 6.20/2.05 | (114) all_0_3_3 = all_0_5_5 % 6.20/2.05 | % 6.20/2.05 | Equations (114) can reduce 111 to: % 6.20/2.05 | (115) $false % 6.20/2.05 | % 6.20/2.05 |-The branch is then unsatisfiable % 6.20/2.05 % SZS output end Proof for theBenchmark % 6.20/2.05 % 6.20/2.05 1465ms %------------------------------------------------------------------------------