%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU134+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n008.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 08:46:50 EDT 2022 % Result : Theorem 3.10s 1.41s % Output : Proof 4.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SEU134+2 : TPTP v8.1.0. Released v3.3.0. % 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n008.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 07:42:52 EDT 2022 % 0.12/0.33 % CPUTime : % 0.19/0.59 ____ _ % 0.19/0.59 ___ / __ \_____(_)___ ________ __________ % 0.19/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic % 0.19/0.59 (ePrincess v.1.0) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2015 % 0.19/0.59 (c) Peter Backeman, 2014-2015 % 0.19/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.59 Bug reports to peter@backeman.se % 0.19/0.59 % 0.19/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.66/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.62/0.98 Prover 0: Preprocessing ... % 2.57/1.26 Prover 0: Warning: ignoring some quantifiers % 2.57/1.28 Prover 0: Constructing countermodel ... % 3.10/1.41 Prover 0: proved (769ms) % 3.10/1.41 % 3.10/1.41 No countermodel exists, formula is valid % 3.10/1.41 % SZS status Theorem for theBenchmark % 3.10/1.41 % 3.10/1.41 Generating proof ... Warning: ignoring some quantifiers % 4.52/1.71 found it (size 11) % 4.52/1.71 % 4.52/1.71 % SZS output start Proof for theBenchmark % 4.52/1.71 Assumed formulas after preprocessing and simplification: % 4.52/1.71 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (set_difference(v0, v1) = v2 & empty(v4) & empty(empty_set) & ~ empty(v3) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (set_difference(v6, v7) = v9) | ~ (set_difference(v5, v7) = v8) | ~ subset(v5, v6) | subset(v8, v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v6, v7) = v9) | ~ (set_intersection2(v5, v7) = v8) | ~ subset(v5, v6) | subset(v8, v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (set_difference(v8, v7) = v6) | ~ (set_difference(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (set_intersection2(v8, v7) = v6) | ~ (set_intersection2(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (set_union2(v8, v7) = v6) | ~ (set_union2(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (set_difference(v5, v6) = v7) | ~ in(v8, v7) | ~ in(v8, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (set_difference(v5, v6) = v7) | ~ in(v8, v7) | in(v8, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (set_difference(v5, v6) = v7) | ~ in(v8, v5) | in(v8, v7) | in(v8, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (set_intersection2(v6, v7) = v8) | ~ subset(v5, v7) | ~ subset(v5, v6) | subset(v5, v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (set_intersection2(v5, v6) = v7) | ~ disjoint(v5, v6) | ~ in(v8, v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (set_intersection2(v5, v6) = v7) | ~ in(v8, v7) | in(v8, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (set_intersection2(v5, v6) = v7) | ~ in(v8, v7) | in(v8, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (set_intersection2(v5, v6) = v7) | ~ in(v8, v6) | ~ in(v8, v5) | in(v8, v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v5, v7) = v8) | ~ subset(v7, v6) | ~ subset(v5, v6) | subset(v8, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v5, v6) = v7) | ~ in(v8, v7) | in(v8, v6) | in(v8, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v5, v6) = v7) | ~ in(v8, v6) | in(v8, v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v5, v6) = v7) | ~ in(v8, v5) | in(v8, v7)) & ? [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v5 | ~ (set_difference(v6, v7) = v8) | ? [v9] : (( ~ in(v9, v6) | ~ in(v9, v5) | in(v9, v7)) & (in(v9, v5) | (in(v9, v6) & ~ in(v9, v7))))) & ? [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v5 | ~ (set_intersection2(v6, v7) = v8) | ? [v9] : (( ~ in(v9, v7) | ~ in(v9, v6) | ~ in(v9, v5)) & (in(v9, v5) | (in(v9, v7) & in(v9, v6))))) & ? [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v5 | ~ (set_union2(v6, v7) = v8) | ? [v9] : (( ~ in(v9, v5) | ( ~ in(v9, v7) & ~ in(v9, v6))) & (in(v9, v7) | in(v9, v6) | in(v9, v5)))) & ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (set_union2(v5, v6) = v7) | ~ subset(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (set_intersection2(v5, v6) = v7) | ~ subset(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : (v7 = empty_set | ~ (set_difference(v5, v6) = v7) | ~ subset(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : (v7 = empty_set | ~ (set_intersection2(v5, v6) = v7) | ~ disjoint(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (set_difference(v5, v6) = v7) | subset(v7, v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (set_intersection2(v6, v5) = v7) | set_intersection2(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (set_intersection2(v5, v6) = v7) | set_intersection2(v6, v5) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (set_intersection2(v5, v6) = v7) | disjoint(v5, v6) | ? [v8] : in(v8, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (set_intersection2(v5, v6) = v7) | subset(v7, v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (set_union2(v6, v5) = v7) | ~ empty(v7) | empty(v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (set_union2(v6, v5) = v7) | set_union2(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (set_union2(v5, v6) = v7) | ~ empty(v7) | empty(v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (set_union2(v5, v6) = v7) | set_union2(v6, v5) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (set_union2(v5, v6) = v7) | subset(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ disjoint(v5, v6) | ~ in(v7, v6) | ~ in(v7, v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ subset(v6, v7) | ~ subset(v5, v6) | subset(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ subset(v5, v6) | ~ in(v7, v5) | in(v7, v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (set_difference(v5, empty_set) = v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (set_intersection2(v5, v5) = v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (set_union2(v5, v5) = v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (set_union2(v5, empty_set) = v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ empty(v6) | ~ empty(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ subset(v6, v5) | ~ subset(v5, v6)) & ! [v5] : ! [v6] : (v6 = empty_set | ~ (set_difference(empty_set, v5) = v6)) & ! [v5] : ! [v6] : (v6 = empty_set | ~ (set_intersection2(v5, empty_set) = v6)) & ! [v5] : ! [v6] : ( ~ (set_difference(v5, v6) = empty_set) | subset(v5, v6)) & ! [v5] : ! [v6] : ( ~ (set_intersection2(v5, v6) = empty_set) | disjoint(v5, v6)) & ! [v5] : ! [v6] : ( ~ empty(v6) | ~ in(v5, v6)) & ! [v5] : ! [v6] : ( ~ disjoint(v5, v6) | disjoint(v6, v5)) & ! [v5] : ! [v6] : ( ~ in(v6, v5) | ~ in(v5, v6)) & ! [v5] : (v5 = empty_set | ~ empty(v5)) & ! [v5] : (v5 = empty_set | ~ subset(v5, empty_set)) & ! [v5] : ~ in(v5, empty_set) & ? [v5] : ? [v6] : (v6 = v5 | ? [v7] : (( ~ in(v7, v6) | ~ in(v7, v5)) & (in(v7, v6) | in(v7, v5)))) & ? [v5] : ? [v6] : (disjoint(v5, v6) | ? [v7] : (in(v7, v6) & in(v7, v5))) & ? [v5] : ? [v6] : (subset(v5, v6) | ? [v7] : (in(v7, v5) & ~ in(v7, v6))) & ? [v5] : (v5 = empty_set | ? [v6] : in(v6, v5)) & ? [v5] : subset(v5, v5) & ? [v5] : subset(empty_set, v5) & ((v2 = empty_set & ~ subset(v0, v1)) | ( ~ (v2 = empty_set) & subset(v0, v1)))) % 4.52/1.76 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 4.52/1.76 | (1) set_difference(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, 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] : (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(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_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_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 = 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] : ( ~ 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] : (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) & ((all_0_2_2 = empty_set & ~ subset(all_0_4_4, all_0_3_3)) | ( ~ (all_0_2_2 = empty_set) & subset(all_0_4_4, all_0_3_3))) % 4.90/1.77 | % 4.90/1.77 | Applying alpha-rule on (1) yields: % 4.90/1.77 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 4.90/1.77 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 4.90/1.77 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) % 4.90/1.77 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) % 4.90/1.77 | (6) empty(empty_set) % 4.90/1.77 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 4.90/1.77 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) % 4.90/1.77 | (9) set_difference(all_0_4_4, all_0_3_3) = all_0_2_2 % 4.90/1.77 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 4.90/1.77 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 4.90/1.77 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 4.90/1.77 | (13) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0)) % 4.90/1.77 | (14) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 4.90/1.77 | (15) ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set)) % 4.90/1.77 | (16) ~ empty(all_0_1_1) % 4.90/1.77 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) % 4.90/1.77 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) % 4.90/1.77 | (19) ? [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)))) % 4.90/1.77 | (20) empty(all_0_0_0) % 4.90/1.77 | (21) ? [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))))) % 4.90/1.78 | (22) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 4.90/1.78 | (23) ? [v0] : subset(v0, v0) % 4.90/1.78 | (24) ! [v0] : ~ in(v0, empty_set) % 4.90/1.78 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) % 4.90/1.78 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 4.90/1.78 | (27) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 4.90/1.78 | (28) ? [v0] : subset(empty_set, v0) % 4.90/1.78 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 4.90/1.78 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 4.90/1.78 | (31) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) % 4.90/1.78 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 4.90/1.78 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) % 4.90/1.78 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) % 4.90/1.78 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) % 4.90/1.78 | (36) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) % 4.90/1.78 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) % 4.90/1.78 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 4.90/1.78 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2)) % 4.90/1.78 | (40) ? [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))))) % 4.90/1.78 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) % 4.90/1.78 | (42) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) % 4.90/1.78 | (43) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 4.90/1.78 | (44) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) % 4.90/1.78 | (45) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0))) % 4.90/1.78 | (46) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 4.90/1.78 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) % 4.90/1.78 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 4.90/1.78 | (49) (all_0_2_2 = empty_set & ~ subset(all_0_4_4, all_0_3_3)) | ( ~ (all_0_2_2 = empty_set) & subset(all_0_4_4, all_0_3_3)) % 4.90/1.78 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) % 4.90/1.78 | (51) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) % 4.90/1.78 | (52) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 4.90/1.78 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) % 4.90/1.78 | (54) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) % 4.90/1.78 | (55) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) % 4.90/1.78 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 4.90/1.79 | (57) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) % 4.90/1.79 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0)) % 4.90/1.79 | (59) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) % 4.90/1.79 | (60) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) % 4.90/1.79 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1)) % 4.90/1.79 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 4.90/1.79 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) % 4.90/1.79 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) % 4.90/1.79 | (65) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 4.90/1.79 | % 4.90/1.79 +-Applying beta-rule and splitting (49), into two cases. % 4.90/1.79 |-Branch one: % 4.90/1.79 | (66) all_0_2_2 = empty_set & ~ subset(all_0_4_4, all_0_3_3) % 4.90/1.79 | % 4.90/1.79 | Applying alpha-rule on (66) yields: % 4.90/1.79 | (67) all_0_2_2 = empty_set % 4.90/1.79 | (68) ~ subset(all_0_4_4, all_0_3_3) % 4.90/1.79 | % 4.90/1.79 | From (67) and (9) follows: % 4.90/1.79 | (69) set_difference(all_0_4_4, all_0_3_3) = empty_set % 4.90/1.79 | % 4.90/1.79 | Instantiating formula (42) with all_0_3_3, all_0_4_4 and discharging atoms set_difference(all_0_4_4, all_0_3_3) = empty_set, ~ subset(all_0_4_4, all_0_3_3), yields: % 4.90/1.79 | (70) $false % 4.90/1.79 | % 4.90/1.79 |-The branch is then unsatisfiable % 4.90/1.79 |-Branch two: % 4.90/1.79 | (71) ~ (all_0_2_2 = empty_set) & subset(all_0_4_4, all_0_3_3) % 4.90/1.79 | % 4.90/1.79 | Applying alpha-rule on (71) yields: % 4.90/1.79 | (72) ~ (all_0_2_2 = empty_set) % 4.90/1.79 | (73) subset(all_0_4_4, all_0_3_3) % 4.90/1.79 | % 4.90/1.79 | Instantiating formula (57) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms set_difference(all_0_4_4, all_0_3_3) = all_0_2_2, subset(all_0_4_4, all_0_3_3), yields: % 4.90/1.79 | (67) all_0_2_2 = empty_set % 4.90/1.79 | % 4.90/1.79 | Equations (67) can reduce 72 to: % 4.90/1.79 | (75) $false % 4.90/1.79 | % 4.90/1.79 |-The branch is then unsatisfiable % 4.90/1.79 % SZS output end Proof for theBenchmark % 4.90/1.79 % 4.90/1.79 1196ms %------------------------------------------------------------------------------