%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU129+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 08:46:47 EDT 2022 % Result : Theorem 2.78s 1.43s % Output : Proof 4.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU129+2 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n011.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sun Jun 19 20:30:09 EDT 2022 % 0.13/0.34 % CPUTime : % 0.63/0.64 ____ _ % 0.63/0.64 ___ / __ \_____(_)___ ________ __________ % 0.63/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.63/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.63/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.63/0.64 % 0.63/0.64 A Theorem Prover for First-Order Logic % 0.63/0.64 (ePrincess v.1.0) % 0.63/0.64 % 0.63/0.64 (c) Philipp Rümmer, 2009-2015 % 0.63/0.64 (c) Peter Backeman, 2014-2015 % 0.63/0.64 (contributions by Angelo Brillout, Peter Baumgartner) % 0.63/0.64 Free software under GNU Lesser General Public License (LGPL). % 0.63/0.64 Bug reports to peter@backeman.se % 0.63/0.64 % 0.63/0.64 For more information, visit http://user.uu.se/~petba168/breu/ % 0.63/0.64 % 0.63/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.70/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.63/1.02 Prover 0: Preprocessing ... % 2.33/1.27 Prover 0: Warning: ignoring some quantifiers % 2.33/1.29 Prover 0: Constructing countermodel ... % 2.78/1.43 Prover 0: proved (728ms) % 2.78/1.43 % 2.78/1.43 No countermodel exists, formula is valid % 2.78/1.43 % SZS status Theorem for theBenchmark % 2.78/1.43 % 2.78/1.43 Generating proof ... Warning: ignoring some quantifiers % 4.14/1.71 found it (size 8) % 4.14/1.71 % 4.14/1.71 % SZS output start Proof for theBenchmark % 4.14/1.71 Assumed formulas after preprocessing and simplification: % 4.14/1.71 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (set_intersection2(v1, v2) = v4 & set_intersection2(v0, v2) = v3 & empty(v6) & empty(empty_set) & subset(v0, v1) & ~ empty(v5) & ~ subset(v3, v4) & ! [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] : ( ~ (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_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] : (v9 = v8 | ~ (set_union2(v7, v8) = v9) | ~ subset(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : (v9 = empty_set | ~ (set_intersection2(v7, v8) = v9) | ~ disjoint(v7, 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_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] : ( ~ 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] : (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 = empty_set | ~ (set_intersection2(v7, empty_set) = v8)) & ! [v7] : ! [v8] : ( ~ (set_intersection2(v7, v8) = empty_set) | disjoint(v7, v8)) & ! [v7] : ! [v8] : ( ~ empty(v8) | ~ in(v7, v8)) & ! [v7] : ! [v8] : ( ~ disjoint(v7, v8) | disjoint(v8, v7)) & ! [v7] : ! [v8] : ( ~ in(v8, v7) | ~ in(v7, v8)) & ! [v7] : (v7 = empty_set | ~ empty(v7)) & ! [v7] : (v7 = empty_set | ~ subset(v7, empty_set)) & ! [v7] : ~ in(v7, empty_set) & ? [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)) % 4.14/1.75 | 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: % 4.14/1.75 | (1) set_intersection2(all_0_5_5, all_0_4_4) = all_0_2_2 & set_intersection2(all_0_6_6, all_0_4_4) = all_0_3_3 & empty(all_0_0_0) & empty(empty_set) & subset(all_0_6_6, all_0_5_5) & ~ empty(all_0_1_1) & ~ subset(all_0_3_3, all_0_2_2) & ! [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_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_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 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, 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_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] : ( ~ 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_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 = empty_set | ~ (set_intersection2(v0, empty_set) = 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] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set)) & ! [v0] : ~ in(v0, empty_set) & ? [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) % 4.14/1.76 | % 4.14/1.76 | Applying alpha-rule on (1) yields: % 4.14/1.76 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) % 4.14/1.76 | (3) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 4.14/1.77 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) % 4.14/1.77 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) % 4.14/1.77 | (6) set_intersection2(all_0_6_6, all_0_4_4) = all_0_3_3 % 4.14/1.77 | (7) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 4.14/1.77 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2)) % 4.49/1.77 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) % 4.49/1.77 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) % 4.49/1.77 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) % 4.49/1.77 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) % 4.49/1.77 | (13) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 4.49/1.77 | (14) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 4.49/1.77 | (15) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) % 4.49/1.77 | (16) ? [v0] : subset(v0, v0) % 4.49/1.77 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0)) % 4.49/1.77 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) % 4.49/1.77 | (19) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 4.49/1.77 | (20) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) % 4.49/1.77 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) % 4.49/1.77 | (22) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0)) % 4.49/1.77 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 4.49/1.77 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 4.49/1.77 | (25) ~ empty(all_0_1_1) % 4.49/1.77 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 4.49/1.77 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) % 4.49/1.77 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) % 4.49/1.77 | (29) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 4.49/1.77 | (30) ? [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))))) % 4.49/1.77 | (31) ? [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)))) % 4.49/1.78 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) % 4.49/1.78 | (33) ! [v0] : ~ in(v0, empty_set) % 4.49/1.78 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 4.49/1.78 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) % 4.52/1.78 | (36) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 4.52/1.78 | (37) empty(empty_set) % 4.52/1.78 | (38) empty(all_0_0_0) % 4.52/1.78 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 4.52/1.78 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 4.52/1.78 | (41) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 4.52/1.78 | (42) ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set)) % 4.52/1.78 | (43) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 4.52/1.78 | (44) set_intersection2(all_0_5_5, all_0_4_4) = all_0_2_2 % 4.52/1.78 | (45) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0))) % 4.52/1.78 | (46) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) % 4.52/1.78 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 4.52/1.78 | (48) ~ subset(all_0_3_3, all_0_2_2) % 4.52/1.78 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 4.52/1.78 | (50) subset(all_0_6_6, all_0_5_5) % 4.52/1.78 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) % 4.52/1.78 | (52) ? [v0] : subset(empty_set, v0) % 4.52/1.78 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) % 4.52/1.78 | % 4.52/1.78 | Instantiating formula (35) with all_0_3_3, all_0_6_6, all_0_4_4 and discharging atoms set_intersection2(all_0_6_6, all_0_4_4) = all_0_3_3, yields: % 4.52/1.78 | (54) set_intersection2(all_0_4_4, all_0_6_6) = all_0_3_3 % 4.52/1.78 | % 4.52/1.78 | Instantiating formula (2) with all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms set_intersection2(all_0_6_6, all_0_4_4) = all_0_3_3, yields: % 4.52/1.78 | (55) subset(all_0_3_3, all_0_6_6) % 4.52/1.78 | % 4.52/1.78 | Instantiating formula (2) with all_0_3_3, all_0_6_6, all_0_4_4 and discharging atoms set_intersection2(all_0_4_4, all_0_6_6) = all_0_3_3, yields: % 4.52/1.78 | (56) subset(all_0_3_3, all_0_4_4) % 4.52/1.78 | % 4.52/1.78 | Instantiating formula (51) with all_0_5_5, all_0_6_6, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_6_6), subset(all_0_6_6, all_0_5_5), yields: % 4.52/1.78 | (57) subset(all_0_3_3, all_0_5_5) % 4.52/1.79 | % 4.52/1.79 | Instantiating formula (32) with all_0_2_2, all_0_4_4, all_0_5_5, all_0_3_3 and discharging atoms set_intersection2(all_0_5_5, all_0_4_4) = all_0_2_2, subset(all_0_3_3, all_0_4_4), subset(all_0_3_3, all_0_5_5), ~ subset(all_0_3_3, all_0_2_2), yields: % 4.52/1.79 | (58) $false % 4.52/1.79 | % 4.52/1.79 |-The branch is then unsatisfiable % 4.52/1.79 % SZS output end Proof for theBenchmark % 4.52/1.79 % 4.52/1.79 1131ms %------------------------------------------------------------------------------