%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU180+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n007.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 08:47:22 EDT 2022 % Result : Theorem 2.86s 1.40s % Output : Proof 4.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SEU180+1 : TPTP v8.1.0. Released v3.3.0. % 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.35 % Computer : n007.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Sun Jun 19 05:03:43 EDT 2022 % 0.14/0.35 % CPUTime : % 0.62/0.60 ____ _ % 0.62/0.60 ___ / __ \_____(_)___ ________ __________ % 0.62/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.62/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.62/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.62/0.60 % 0.62/0.60 A Theorem Prover for First-Order Logic % 0.62/0.60 (ePrincess v.1.0) % 0.62/0.60 % 0.62/0.60 (c) Philipp Rümmer, 2009-2015 % 0.62/0.60 (c) Peter Backeman, 2014-2015 % 0.62/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.62/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.62/0.60 Bug reports to peter@backeman.se % 0.62/0.60 % 0.62/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.62/0.60 % 0.62/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.71/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.47/0.94 Prover 0: Preprocessing ... % 2.24/1.19 Prover 0: Warning: ignoring some quantifiers % 2.24/1.21 Prover 0: Constructing countermodel ... % 2.86/1.39 Prover 0: proved (747ms) % 2.86/1.40 % 2.86/1.40 No countermodel exists, formula is valid % 2.86/1.40 % SZS status Theorem for theBenchmark % 2.86/1.40 % 2.86/1.40 Generating proof ... Warning: ignoring some quantifiers % 4.22/1.65 found it (size 15) % 4.22/1.65 % 4.22/1.65 % SZS output start Proof for theBenchmark % 4.22/1.65 Assumed formulas after preprocessing and simplification: % 4.22/1.65 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_field(v2) = v4 & ordered_pair(v0, v1) = v3 & empty(v7) & empty(v6) & empty(empty_set) & relation(v7) & relation(v2) & in(v3, v2) & ~ empty(v5) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (singleton(v8) = v11) | ~ (unordered_pair(v10, v11) = v12) | ~ (unordered_pair(v8, v9) = v10) | ordered_pair(v8, v9) = v12) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_rng(v8) = v9) | ~ (ordered_pair(v11, v10) = v12) | ~ relation(v8) | ~ in(v12, v8) | in(v10, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_dom(v8) = v9) | ~ (ordered_pair(v10, v11) = v12) | ~ relation(v8) | ~ in(v12, v8) | in(v10, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (ordered_pair(v11, v10) = v9) | ~ (ordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_union2(v11, v10) = v9) | ~ (set_union2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unordered_pair(v11, v10) = v9) | ~ (unordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (relation_rng(v8) = v10) | ~ (relation_dom(v8) = v9) | ~ (set_union2(v9, v10) = v11) | ~ relation(v8) | relation_field(v8) = v11) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v8, v9) = v10) | ~ in(v11, v10) | in(v11, v9) | in(v11, v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v8, v9) = v10) | ~ in(v11, v9) | in(v11, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v8, v9) = v10) | ~ in(v11, v8) | in(v11, v10)) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (set_union2(v9, v10) = v11) | ? [v12] : (( ~ in(v12, v8) | ( ~ in(v12, v10) & ~ in(v12, v9))) & (in(v12, v10) | in(v12, v9) | in(v12, v8)))) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (relation_field(v10) = v9) | ~ (relation_field(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (relation_rng(v10) = v9) | ~ (relation_rng(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (relation_dom(v10) = v9) | ~ (relation_dom(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (relation_rng(v8) = v9) | ~ relation(v8) | ~ in(v10, v9) | ? [v11] : ? [v12] : (ordered_pair(v11, v10) = v12 & in(v12, v8))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (relation_dom(v8) = v9) | ~ relation(v8) | ~ in(v10, v9) | ? [v11] : ? [v12] : (ordered_pair(v10, v11) = v12 & in(v12, v8))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ empty(v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ? [v11] : ? [v12] : (singleton(v8) = v12 & unordered_pair(v11, v12) = v10 & unordered_pair(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v9, v8) = v10) | ~ empty(v10) | empty(v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v9, v8) = v10) | set_union2(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | ~ empty(v10) | empty(v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | ~ relation(v9) | ~ relation(v8) | relation(v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | set_union2(v9, v8) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v9, v8) = v10) | unordered_pair(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | ~ empty(v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | unordered_pair(v9, v8) = v10) & ? [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (relation_rng(v9) = v10) | ~ relation(v9) | ? [v11] : ? [v12] : ? [v13] : (( ~ in(v11, v8) | ! [v14] : ! [v15] : ( ~ (ordered_pair(v14, v11) = v15) | ~ in(v15, v9))) & (in(v11, v8) | (ordered_pair(v12, v11) = v13 & in(v13, v9))))) & ? [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (relation_dom(v9) = v10) | ~ relation(v9) | ? [v11] : ? [v12] : ? [v13] : (( ~ in(v11, v8) | ! [v14] : ! [v15] : ( ~ (ordered_pair(v11, v14) = v15) | ~ in(v15, v9))) & (in(v11, v8) | (ordered_pair(v11, v12) = v13 & in(v13, v9))))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_union2(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_union2(v8, empty_set) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ empty(v9) | ~ empty(v8)) & ! [v8] : ! [v9] : ( ~ (relation_field(v8) = v9) | ~ relation(v8) | ? [v10] : ? [v11] : (relation_rng(v8) = v11 & relation_dom(v8) = v10 & set_union2(v10, v11) = v9)) & ! [v8] : ! [v9] : ( ~ (singleton(v8) = v9) | ~ empty(v9)) & ! [v8] : ! [v9] : ( ~ empty(v9) | ~ in(v8, v9)) & ! [v8] : ! [v9] : ( ~ element(v8, v9) | empty(v9) | in(v8, v9)) & ! [v8] : ! [v9] : ( ~ in(v9, v8) | ~ in(v8, v9)) & ! [v8] : ! [v9] : ( ~ in(v8, v9) | element(v8, v9)) & ! [v8] : (v8 = empty_set | ~ empty(v8)) & ? [v8] : ? [v9] : element(v9, v8) & ( ~ in(v1, v4) | ~ in(v0, v4))) % 4.22/1.70 | 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, all_0_7_7 yields: % 4.22/1.70 | (1) relation_field(all_0_5_5) = all_0_3_3 & ordered_pair(all_0_7_7, all_0_6_6) = all_0_4_4 & empty(all_0_0_0) & empty(all_0_1_1) & empty(empty_set) & relation(all_0_0_0) & relation(all_0_5_5) & in(all_0_4_4, all_0_5_5) & ~ empty(all_0_2_2) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(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] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ~ relation(v0) | relation_field(v0) = v3) & ! [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_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] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(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) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v3) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & in(v5, v1))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & in(v5, 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] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation_dom(v0) = v2 & set_union2(v2, v3) = v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ( ~ in(all_0_6_6, all_0_3_3) | ~ in(all_0_7_7, all_0_3_3)) % 4.22/1.71 | % 4.22/1.71 | Applying alpha-rule on (1) yields: % 4.22/1.71 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) % 4.22/1.71 | (3) ~ in(all_0_6_6, all_0_3_3) | ~ in(all_0_7_7, all_0_3_3) % 4.22/1.71 | (4) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) % 4.22/1.71 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) % 4.22/1.71 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) % 4.22/1.71 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) % 4.22/1.71 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 4.22/1.71 | (9) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 4.22/1.71 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 4.22/1.71 | (11) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 4.22/1.71 | (12) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation_dom(v0) = v2 & set_union2(v2, v3) = v1)) % 4.22/1.71 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) % 4.22/1.71 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 4.22/1.71 | (15) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & in(v5, v1))))) % 4.22/1.71 | (16) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 4.22/1.71 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 4.22/1.71 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 4.22/1.71 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 4.22/1.71 | (20) in(all_0_4_4, all_0_5_5) % 4.22/1.71 | (21) empty(all_0_0_0) % 4.22/1.71 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 4.22/1.72 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 4.22/1.72 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) % 4.22/1.72 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 4.58/1.72 | (26) ? [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)))) % 4.58/1.72 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 4.58/1.72 | (28) ordered_pair(all_0_7_7, all_0_6_6) = all_0_4_4 % 4.58/1.72 | (29) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 4.58/1.72 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 4.58/1.72 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ~ relation(v0) | relation_field(v0) = v3) % 4.58/1.72 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) % 4.58/1.72 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 4.58/1.72 | (34) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 4.58/1.72 | (35) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 4.58/1.72 | (36) ? [v0] : ? [v1] : element(v1, v0) % 4.58/1.72 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) % 4.58/1.72 | (38) ~ empty(all_0_2_2) % 4.58/1.72 | (39) relation(all_0_5_5) % 4.58/1.72 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 4.58/1.72 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 4.58/1.72 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 4.58/1.72 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) % 4.58/1.72 | (44) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v3) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & in(v5, v1))))) % 4.58/1.72 | (45) relation_field(all_0_5_5) = all_0_3_3 % 4.58/1.72 | (46) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 4.58/1.72 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 4.58/1.72 | (48) empty(all_0_1_1) % 4.58/1.72 | (49) relation(all_0_0_0) % 4.58/1.72 | (50) empty(empty_set) % 4.58/1.72 | (51) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 4.58/1.72 | % 4.58/1.73 | Instantiating formula (12) with all_0_3_3, all_0_5_5 and discharging atoms relation_field(all_0_5_5) = all_0_3_3, relation(all_0_5_5), yields: % 4.58/1.73 | (52) ? [v0] : ? [v1] : (relation_rng(all_0_5_5) = v1 & relation_dom(all_0_5_5) = v0 & set_union2(v0, v1) = all_0_3_3) % 4.58/1.73 | % 4.58/1.73 | Instantiating (52) with all_21_0_13, all_21_1_14 yields: % 4.58/1.73 | (53) relation_rng(all_0_5_5) = all_21_0_13 & relation_dom(all_0_5_5) = all_21_1_14 & set_union2(all_21_1_14, all_21_0_13) = all_0_3_3 % 4.58/1.73 | % 4.58/1.73 | Applying alpha-rule on (53) yields: % 4.58/1.73 | (54) relation_rng(all_0_5_5) = all_21_0_13 % 4.58/1.73 | (55) relation_dom(all_0_5_5) = all_21_1_14 % 4.58/1.73 | (56) set_union2(all_21_1_14, all_21_0_13) = all_0_3_3 % 4.58/1.73 | % 4.58/1.73 | Instantiating formula (43) with all_0_4_4, all_0_7_7, all_0_6_6, all_21_0_13, all_0_5_5 and discharging atoms relation_rng(all_0_5_5) = all_21_0_13, ordered_pair(all_0_7_7, all_0_6_6) = all_0_4_4, relation(all_0_5_5), in(all_0_4_4, all_0_5_5), yields: % 4.58/1.73 | (57) in(all_0_6_6, all_21_0_13) % 4.58/1.73 | % 4.58/1.73 | Instantiating formula (7) with all_0_4_4, all_0_6_6, all_0_7_7, all_21_1_14, all_0_5_5 and discharging atoms relation_dom(all_0_5_5) = all_21_1_14, ordered_pair(all_0_7_7, all_0_6_6) = all_0_4_4, relation(all_0_5_5), in(all_0_4_4, all_0_5_5), yields: % 4.58/1.73 | (58) in(all_0_7_7, all_21_1_14) % 4.58/1.73 | % 4.58/1.73 | Instantiating formula (42) with all_0_3_3, all_21_1_14, all_21_0_13 and discharging atoms set_union2(all_21_1_14, all_21_0_13) = all_0_3_3, yields: % 4.58/1.73 | (59) set_union2(all_21_0_13, all_21_1_14) = all_0_3_3 % 4.58/1.73 | % 4.58/1.73 | Instantiating formula (32) with all_0_6_6, all_0_3_3, all_21_1_14, all_21_0_13 and discharging atoms set_union2(all_21_0_13, all_21_1_14) = all_0_3_3, in(all_0_6_6, all_21_0_13), yields: % 4.58/1.73 | (60) in(all_0_6_6, all_0_3_3) % 4.58/1.73 | % 4.58/1.73 | Instantiating formula (37) with all_0_7_7, all_0_3_3, all_21_1_14, all_21_0_13 and discharging atoms set_union2(all_21_0_13, all_21_1_14) = all_0_3_3, in(all_0_7_7, all_21_1_14), yields: % 4.58/1.73 | (61) in(all_0_7_7, all_0_3_3) % 4.58/1.73 | % 4.58/1.73 +-Applying beta-rule and splitting (3), into two cases. % 4.58/1.73 |-Branch one: % 4.58/1.73 | (62) ~ in(all_0_6_6, all_0_3_3) % 4.58/1.73 | % 4.58/1.73 | Using (60) and (62) yields: % 4.58/1.73 | (63) $false % 4.58/1.73 | % 4.58/1.73 |-The branch is then unsatisfiable % 4.58/1.73 |-Branch two: % 4.58/1.73 | (60) in(all_0_6_6, all_0_3_3) % 4.58/1.73 | (65) ~ in(all_0_7_7, all_0_3_3) % 4.58/1.73 | % 4.58/1.73 | Using (61) and (65) yields: % 4.58/1.73 | (63) $false % 4.58/1.73 | % 4.58/1.73 |-The branch is then unsatisfiable % 4.58/1.73 % SZS output end Proof for theBenchmark % 4.58/1.73 % 4.58/1.73 1124ms %------------------------------------------------------------------------------