%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET630+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n006.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 00:21:00 EDT 2022 % Result : Theorem 19.95s 6.13s % Output : Proof 21.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.14 % Problem : SET630+3 : TPTP v8.1.0. Released v2.2.0. % 0.04/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.36 % Computer : n006.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Sun Jul 10 19:01:50 EDT 2022 % 0.14/0.36 % CPUTime : % 0.49/0.62 ____ _ % 0.49/0.62 ___ / __ \_____(_)___ ________ __________ % 0.49/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.49/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.49/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.49/0.62 % 0.49/0.62 A Theorem Prover for First-Order Logic % 0.49/0.62 (ePrincess v.1.0) % 0.49/0.62 % 0.49/0.62 (c) Philipp Rümmer, 2009-2015 % 0.49/0.62 (c) Peter Backeman, 2014-2015 % 0.49/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.49/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.49/0.62 Bug reports to peter@backeman.se % 0.49/0.62 % 0.49/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.49/0.62 % 0.49/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.79/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.48/0.95 Prover 0: Preprocessing ... % 2.03/1.15 Prover 0: Warning: ignoring some quantifiers % 2.03/1.17 Prover 0: Constructing countermodel ... % 18.98/5.91 Prover 0: gave up % 18.98/5.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 18.98/5.93 Prover 1: Preprocessing ... % 19.14/5.98 Prover 1: Warning: ignoring some quantifiers % 19.14/5.99 Prover 1: Constructing countermodel ... % 19.14/6.03 Prover 1: gave up % 19.14/6.03 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 19.63/6.04 Prover 2: Preprocessing ... % 19.63/6.09 Prover 2: Warning: ignoring some quantifiers % 19.63/6.09 Prover 2: Constructing countermodel ... % 19.95/6.13 Prover 2: proved (104ms) % 19.95/6.13 % 19.95/6.13 No countermodel exists, formula is valid % 19.95/6.13 % SZS status Theorem for theBenchmark % 19.95/6.13 % 19.95/6.13 Generating proof ... Warning: ignoring some quantifiers % 21.15/6.38 found it (size 50) % 21.15/6.38 % 21.15/6.38 % SZS output start Proof for theBenchmark % 21.15/6.38 Assumed formulas after preprocessing and simplification: % 21.15/6.38 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & intersection(v0, v1) = v2 & disjoint(v2, v3) = v4 & symmetric_difference(v0, v1) = v3 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (member(v7, v8) = v9) | ~ (intersection(v5, v6) = v8) | ? [v10] : (( ~ (v10 = 0) & member(v7, v6) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (intersect(v5, v8) = v9) | ~ (union(v6, v7) = v8) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & ~ (v10 = 0) & intersect(v5, v7) = v11 & intersect(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | ~ (member(v8, v6) = 0) | ~ (intersect(v5, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & member(v8, v5) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | ~ (member(v8, v5) = 0) | ~ (intersect(v5, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & member(v8, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (member(v8, v7) = v6) | ~ (member(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection(v8, v7) = v6) | ~ (intersection(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (disjoint(v8, v7) = v6) | ~ (disjoint(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersect(v8, v7) = v6) | ~ (intersect(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (symmetric_difference(v8, v7) = v6) | ~ (symmetric_difference(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (difference(v8, v7) = v6) | ~ (difference(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (union(v8, v7) = v6) | ~ (union(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (member(v7, v8) = 0) | ~ (intersection(v5, v6) = v8) | (member(v7, v6) = 0 & member(v7, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (intersect(v5, v8) = 0) | ~ (union(v6, v7) = v8) | ? [v9] : ((v9 = 0 & intersect(v5, v7) = 0) | (v9 = 0 & intersect(v5, v6) = 0))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (disjoint(v5, v6) = v7) | intersect(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (intersect(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & intersect(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (intersect(v5, v6) = v7) | disjoint(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection(v6, v5) = v7) | intersection(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection(v5, v6) = v7) | intersection(v6, v5) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection(v5, v6) = v7) | ? [v8] : (disjoint(v7, v8) = 0 & difference(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (symmetric_difference(v6, v5) = v7) | symmetric_difference(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (symmetric_difference(v5, v6) = v7) | symmetric_difference(v6, v5) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (symmetric_difference(v5, v6) = v7) | ? [v8] : ? [v9] : (difference(v6, v5) = v9 & difference(v5, v6) = v8 & union(v8, v9) = v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (difference(v6, v5) = v7) | ? [v8] : ? [v9] : (symmetric_difference(v5, v6) = v8 & difference(v5, v6) = v9 & union(v9, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (difference(v5, v6) = v7) | ? [v8] : ? [v9] : (symmetric_difference(v5, v6) = v8 & difference(v6, v5) = v9 & union(v7, v9) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (difference(v5, v6) = v7) | ? [v8] : (intersection(v5, v6) = v8 & disjoint(v8, v7) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v6, v5) = v7) | union(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v5, v6) = v7) | union(v6, v5) = v7) & ! [v5] : ! [v6] : ( ~ (disjoint(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & intersect(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (intersect(v5, v6) = 0) | intersect(v6, v5) = 0) & ! [v5] : ! [v6] : ( ~ (intersect(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & disjoint(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (intersect(v5, v6) = 0) | ? [v7] : (member(v7, v6) = 0 & member(v7, v5) = 0)) & ? [v5] : ? [v6] : ? [v7] : member(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : intersection(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : disjoint(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : intersect(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : symmetric_difference(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : difference(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : union(v6, v5) = v7 & ? [v5] : ? [v6] : (v6 = v5 | ? [v7] : ? [v8] : ? [v9] : (((v9 = 0 & member(v7, v6) = 0) | (v8 = 0 & member(v7, v5) = 0)) & (( ~ (v9 = 0) & member(v7, v6) = v9) | ( ~ (v8 = 0) & member(v7, v5) = v8))))) % 21.15/6.42 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 21.15/6.42 | (1) ~ (all_0_0_0 = 0) & intersection(all_0_4_4, all_0_3_3) = all_0_2_2 & disjoint(all_0_2_2, all_0_1_1) = all_0_0_0 & symmetric_difference(all_0_4_4, all_0_3_3) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (member(v2, v3) = v4) | ~ (intersection(v0, v1) = v3) | ? [v5] : (( ~ (v5 = 0) & member(v2, v1) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersect(v0, v3) = v4) | ~ (union(v1, v2) = v3) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & intersect(v0, v2) = v6 & intersect(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (member(v3, v1) = 0) | ~ (intersect(v0, v1) = v2) | ? [v4] : ( ~ (v4 = 0) & member(v3, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (member(v3, v0) = 0) | ~ (intersect(v0, v1) = v2) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ (intersect(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (member(v2, v3) = 0) | ~ (intersection(v0, v1) = v3) | (member(v2, v1) = 0 & member(v2, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersect(v0, v3) = 0) | ~ (union(v1, v2) = v3) | ? [v4] : ((v4 = 0 & intersect(v0, v2) = 0) | (v4 = 0 & intersect(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | intersect(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (intersect(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & intersect(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (intersect(v0, v1) = v2) | disjoint(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | ? [v3] : (disjoint(v2, v3) = 0 & difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (difference(v1, v0) = v2) | ? [v3] : ? [v4] : (symmetric_difference(v0, v1) = v3 & difference(v0, v1) = v4 & union(v4, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (difference(v0, v1) = v2) | ? [v3] : ? [v4] : (symmetric_difference(v0, v1) = v3 & difference(v1, v0) = v4 & union(v2, v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (difference(v0, v1) = v2) | ? [v3] : (intersection(v0, v1) = v3 & disjoint(v3, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & intersect(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (intersect(v0, v1) = 0) | intersect(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (intersect(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & disjoint(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (intersect(v0, v1) = 0) | ? [v2] : (member(v2, v1) = 0 & member(v2, v0) = 0)) & ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersect(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : symmetric_difference(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2 & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & member(v2, v1) = 0) | (v3 = 0 & member(v2, v0) = 0)) & (( ~ (v4 = 0) & member(v2, v1) = v4) | ( ~ (v3 = 0) & member(v2, v0) = v3)))) % 21.15/6.43 | % 21.15/6.43 | Applying alpha-rule on (1) yields: % 21.15/6.43 | (2) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2 % 21.15/6.43 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (member(v2, v3) = 0) | ~ (intersection(v0, v1) = v3) | (member(v2, v1) = 0 & member(v2, v0) = 0)) % 21.15/6.43 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (difference(v0, v1) = v2) | ? [v3] : ? [v4] : (symmetric_difference(v0, v1) = v3 & difference(v1, v0) = v4 & union(v2, v4) = v3)) % 21.15/6.43 | (5) ! [v0] : ! [v1] : ( ~ (intersect(v0, v1) = 0) | ? [v2] : (member(v2, v1) = 0 & member(v2, v0) = 0)) % 21.15/6.43 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | ? [v3] : (disjoint(v2, v3) = 0 & difference(v0, v1) = v3)) % 21.15/6.43 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 21.15/6.43 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (difference(v1, v0) = v2) | ? [v3] : ? [v4] : (symmetric_difference(v0, v1) = v3 & difference(v0, v1) = v4 & union(v4, v2) = v3)) % 21.15/6.43 | (9) ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2 % 21.15/6.43 | (10) disjoint(all_0_2_2, all_0_1_1) = all_0_0_0 % 21.15/6.43 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersect(v0, v3) = 0) | ~ (union(v1, v2) = v3) | ? [v4] : ((v4 = 0 & intersect(v0, v2) = 0) | (v4 = 0 & intersect(v0, v1) = 0))) % 21.15/6.43 | (12) ? [v0] : ? [v1] : ? [v2] : symmetric_difference(v1, v0) = v2 % 21.15/6.43 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0)) % 21.15/6.43 | (14) ? [v0] : ? [v1] : ? [v2] : intersect(v1, v0) = v2 % 21.15/6.43 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 21.15/6.43 | (16) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & member(v2, v1) = 0) | (v3 = 0 & member(v2, v0) = 0)) & (( ~ (v4 = 0) & member(v2, v1) = v4) | ( ~ (v3 = 0) & member(v2, v0) = v3)))) % 21.15/6.43 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) % 21.15/6.43 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2) % 21.15/6.43 | (19) ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2 % 21.15/6.43 | (20) ~ (all_0_0_0 = 0) % 21.15/6.43 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (member(v2, v3) = v4) | ~ (intersection(v0, v1) = v3) | ? [v5] : (( ~ (v5 = 0) & member(v2, v1) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5))) % 21.15/6.43 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (difference(v0, v1) = v2) | ? [v3] : (intersection(v0, v1) = v3 & disjoint(v3, v2) = 0)) % 21.15/6.43 | (23) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (intersect(v0, v1) = v2) | disjoint(v0, v1) = 0) % 21.15/6.43 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | intersect(v0, v1) = 0) % 21.15/6.43 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2)) % 21.15/6.43 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (member(v3, v0) = 0) | ~ (intersect(v0, v1) = v2) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4)) % 21.15/6.43 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 21.15/6.43 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) % 21.15/6.43 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) % 21.15/6.43 | (30) ! [v0] : ! [v1] : ( ~ (intersect(v0, v1) = 0) | intersect(v1, v0) = 0) % 21.15/6.43 | (31) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2 % 21.15/6.43 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (member(v3, v1) = 0) | ~ (intersect(v0, v1) = v2) | ? [v4] : ( ~ (v4 = 0) & member(v3, v0) = v4)) % 21.15/6.43 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersect(v0, v3) = v4) | ~ (union(v1, v2) = v3) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & intersect(v0, v2) = v6 & intersect(v0, v1) = v5)) % 21.15/6.43 | (34) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2 % 21.15/6.43 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ (intersect(v3, v2) = v0)) % 21.15/6.44 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 21.15/6.44 | (37) ! [v0] : ! [v1] : ( ~ (intersect(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & disjoint(v0, v1) = v2)) % 21.15/6.44 | (38) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & intersect(v0, v1) = v2)) % 21.15/6.44 | (39) symmetric_difference(all_0_4_4, all_0_3_3) = all_0_1_1 % 21.15/6.44 | (40) intersection(all_0_4_4, all_0_3_3) = all_0_2_2 % 21.15/6.44 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2) % 21.15/6.44 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2) % 21.15/6.44 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 21.15/6.44 | (44) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (intersect(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & intersect(v0, v1) = v3)) % 21.15/6.44 | % 21.15/6.44 | Instantiating formula (18) with all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms intersection(all_0_4_4, all_0_3_3) = all_0_2_2, yields: % 21.15/6.44 | (45) intersection(all_0_3_3, all_0_4_4) = all_0_2_2 % 21.15/6.44 | % 21.15/6.44 | Instantiating formula (6) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms intersection(all_0_4_4, all_0_3_3) = all_0_2_2, yields: % 21.15/6.44 | (46) ? [v0] : (disjoint(all_0_2_2, v0) = 0 & difference(all_0_4_4, all_0_3_3) = v0) % 21.15/6.44 | % 21.15/6.44 | Instantiating formula (24) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms disjoint(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 21.15/6.44 | (47) all_0_0_0 = 0 | intersect(all_0_2_2, all_0_1_1) = 0 % 21.15/6.44 | % 21.15/6.44 | Instantiating formula (42) with all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms symmetric_difference(all_0_4_4, all_0_3_3) = all_0_1_1, yields: % 21.15/6.44 | (48) symmetric_difference(all_0_3_3, all_0_4_4) = all_0_1_1 % 21.15/6.44 | % 21.15/6.44 | Instantiating formula (25) with all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms symmetric_difference(all_0_4_4, all_0_3_3) = all_0_1_1, yields: % 21.15/6.44 | (49) ? [v0] : ? [v1] : (difference(all_0_3_3, all_0_4_4) = v1 & difference(all_0_4_4, all_0_3_3) = v0 & union(v0, v1) = all_0_1_1) % 21.15/6.44 | % 21.15/6.44 | Instantiating (49) with all_24_0_28, all_24_1_29 yields: % 21.15/6.44 | (50) difference(all_0_3_3, all_0_4_4) = all_24_0_28 & difference(all_0_4_4, all_0_3_3) = all_24_1_29 & union(all_24_1_29, all_24_0_28) = all_0_1_1 % 21.15/6.44 | % 21.15/6.44 | Applying alpha-rule on (50) yields: % 21.15/6.44 | (51) difference(all_0_3_3, all_0_4_4) = all_24_0_28 % 21.15/6.44 | (52) difference(all_0_4_4, all_0_3_3) = all_24_1_29 % 21.15/6.44 | (53) union(all_24_1_29, all_24_0_28) = all_0_1_1 % 21.15/6.44 | % 21.15/6.44 | Instantiating (46) with all_26_0_30 yields: % 21.15/6.44 | (54) disjoint(all_0_2_2, all_26_0_30) = 0 & difference(all_0_4_4, all_0_3_3) = all_26_0_30 % 21.15/6.44 | % 21.15/6.44 | Applying alpha-rule on (54) yields: % 21.15/6.44 | (55) disjoint(all_0_2_2, all_26_0_30) = 0 % 21.15/6.44 | (56) difference(all_0_4_4, all_0_3_3) = all_26_0_30 % 21.15/6.44 | % 21.15/6.44 +-Applying beta-rule and splitting (47), into two cases. % 21.15/6.44 |-Branch one: % 21.15/6.44 | (57) intersect(all_0_2_2, all_0_1_1) = 0 % 21.15/6.44 | % 21.15/6.44 | Instantiating formula (15) with all_0_4_4, all_0_3_3, all_24_1_29, all_26_0_30 and discharging atoms difference(all_0_4_4, all_0_3_3) = all_26_0_30, difference(all_0_4_4, all_0_3_3) = all_24_1_29, yields: % 21.15/6.44 | (58) all_26_0_30 = all_24_1_29 % 21.15/6.44 | % 21.15/6.44 | From (58) and (55) follows: % 21.15/6.44 | (59) disjoint(all_0_2_2, all_24_1_29) = 0 % 21.15/6.44 | % 21.15/6.44 | From (58) and (56) follows: % 21.15/6.44 | (52) difference(all_0_4_4, all_0_3_3) = all_24_1_29 % 21.15/6.44 | % 21.15/6.44 | Instantiating formula (6) with all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms intersection(all_0_3_3, all_0_4_4) = all_0_2_2, yields: % 21.15/6.44 | (61) ? [v0] : (disjoint(all_0_2_2, v0) = 0 & difference(all_0_3_3, all_0_4_4) = v0) % 21.15/6.44 | % 21.15/6.44 | Instantiating formula (38) with all_24_1_29, all_0_2_2 and discharging atoms disjoint(all_0_2_2, all_24_1_29) = 0, yields: % 21.15/6.44 | (62) ? [v0] : ( ~ (v0 = 0) & intersect(all_0_2_2, all_24_1_29) = v0) % 21.15/6.44 | % 21.15/6.44 | Instantiating formula (25) with all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms symmetric_difference(all_0_3_3, all_0_4_4) = all_0_1_1, yields: % 21.15/6.44 | (63) ? [v0] : ? [v1] : (difference(all_0_3_3, all_0_4_4) = v0 & difference(all_0_4_4, all_0_3_3) = v1 & union(v0, v1) = all_0_1_1) % 21.15/6.44 | % 21.15/6.44 | Instantiating formula (8) with all_24_1_29, all_0_4_4, all_0_3_3 and discharging atoms difference(all_0_4_4, all_0_3_3) = all_24_1_29, yields: % 21.15/6.44 | (64) ? [v0] : ? [v1] : (symmetric_difference(all_0_3_3, all_0_4_4) = v0 & difference(all_0_3_3, all_0_4_4) = v1 & union(v1, all_24_1_29) = v0) % 21.15/6.44 | % 21.15/6.44 | Instantiating formula (11) with all_0_1_1, all_24_0_28, all_24_1_29, all_0_2_2 and discharging atoms intersect(all_0_2_2, all_0_1_1) = 0, union(all_24_1_29, all_24_0_28) = all_0_1_1, yields: % 21.15/6.44 | (65) ? [v0] : ((v0 = 0 & intersect(all_0_2_2, all_24_0_28) = 0) | (v0 = 0 & intersect(all_0_2_2, all_24_1_29) = 0)) % 21.15/6.44 | % 21.15/6.44 | Instantiating (61) with all_42_0_31 yields: % 21.15/6.44 | (66) disjoint(all_0_2_2, all_42_0_31) = 0 & difference(all_0_3_3, all_0_4_4) = all_42_0_31 % 21.15/6.44 | % 21.15/6.44 | Applying alpha-rule on (66) yields: % 21.15/6.44 | (67) disjoint(all_0_2_2, all_42_0_31) = 0 % 21.15/6.44 | (68) difference(all_0_3_3, all_0_4_4) = all_42_0_31 % 21.15/6.44 | % 21.15/6.44 | Instantiating (65) with all_44_0_32 yields: % 21.15/6.44 | (69) (all_44_0_32 = 0 & intersect(all_0_2_2, all_24_0_28) = 0) | (all_44_0_32 = 0 & intersect(all_0_2_2, all_24_1_29) = 0) % 21.15/6.44 | % 21.15/6.44 | Instantiating (64) with all_45_0_33, all_45_1_34 yields: % 21.15/6.44 | (70) symmetric_difference(all_0_3_3, all_0_4_4) = all_45_1_34 & difference(all_0_3_3, all_0_4_4) = all_45_0_33 & union(all_45_0_33, all_24_1_29) = all_45_1_34 % 21.15/6.44 | % 21.15/6.44 | Applying alpha-rule on (70) yields: % 21.15/6.44 | (71) symmetric_difference(all_0_3_3, all_0_4_4) = all_45_1_34 % 21.15/6.45 | (72) difference(all_0_3_3, all_0_4_4) = all_45_0_33 % 21.15/6.45 | (73) union(all_45_0_33, all_24_1_29) = all_45_1_34 % 21.15/6.45 | % 21.15/6.45 | Instantiating (62) with all_51_0_38 yields: % 21.15/6.45 | (74) ~ (all_51_0_38 = 0) & intersect(all_0_2_2, all_24_1_29) = all_51_0_38 % 21.15/6.45 | % 21.15/6.45 | Applying alpha-rule on (74) yields: % 21.15/6.45 | (75) ~ (all_51_0_38 = 0) % 21.15/6.45 | (76) intersect(all_0_2_2, all_24_1_29) = all_51_0_38 % 21.15/6.45 | % 21.15/6.45 | Instantiating (63) with all_53_0_39, all_53_1_40 yields: % 21.15/6.45 | (77) difference(all_0_3_3, all_0_4_4) = all_53_1_40 & difference(all_0_4_4, all_0_3_3) = all_53_0_39 & union(all_53_1_40, all_53_0_39) = all_0_1_1 % 21.15/6.45 | % 21.15/6.45 | Applying alpha-rule on (77) yields: % 21.15/6.45 | (78) difference(all_0_3_3, all_0_4_4) = all_53_1_40 % 21.15/6.45 | (79) difference(all_0_4_4, all_0_3_3) = all_53_0_39 % 21.15/6.45 | (80) union(all_53_1_40, all_53_0_39) = all_0_1_1 % 21.15/6.45 | % 21.15/6.45 +-Applying beta-rule and splitting (69), into two cases. % 21.15/6.45 |-Branch one: % 21.15/6.45 | (81) all_44_0_32 = 0 & intersect(all_0_2_2, all_24_0_28) = 0 % 21.15/6.45 | % 21.15/6.45 | Applying alpha-rule on (81) yields: % 21.15/6.45 | (82) all_44_0_32 = 0 % 21.15/6.45 | (83) intersect(all_0_2_2, all_24_0_28) = 0 % 21.15/6.45 | % 21.15/6.45 | Instantiating formula (15) with all_0_3_3, all_0_4_4, all_45_0_33, all_24_0_28 and discharging atoms difference(all_0_3_3, all_0_4_4) = all_45_0_33, difference(all_0_3_3, all_0_4_4) = all_24_0_28, yields: % 21.15/6.45 | (84) all_45_0_33 = all_24_0_28 % 21.15/6.45 | % 21.15/6.45 | Instantiating formula (15) with all_0_3_3, all_0_4_4, all_45_0_33, all_53_1_40 and discharging atoms difference(all_0_3_3, all_0_4_4) = all_53_1_40, difference(all_0_3_3, all_0_4_4) = all_45_0_33, yields: % 21.15/6.45 | (85) all_53_1_40 = all_45_0_33 % 21.15/6.45 | % 21.15/6.45 | Instantiating formula (15) with all_0_3_3, all_0_4_4, all_42_0_31, all_53_1_40 and discharging atoms difference(all_0_3_3, all_0_4_4) = all_53_1_40, difference(all_0_3_3, all_0_4_4) = all_42_0_31, yields: % 21.15/6.45 | (86) all_53_1_40 = all_42_0_31 % 21.15/6.45 | % 21.15/6.45 | Combining equations (85,86) yields a new equation: % 21.15/6.45 | (87) all_45_0_33 = all_42_0_31 % 21.15/6.45 | % 21.15/6.45 | Simplifying 87 yields: % 21.15/6.45 | (88) all_45_0_33 = all_42_0_31 % 21.15/6.45 | % 21.15/6.45 | Combining equations (84,88) yields a new equation: % 21.15/6.45 | (89) all_42_0_31 = all_24_0_28 % 21.15/6.45 | % 21.15/6.45 | From (89) and (67) follows: % 21.15/6.45 | (90) disjoint(all_0_2_2, all_24_0_28) = 0 % 21.15/6.45 | % 21.15/6.45 | Instantiating formula (37) with all_24_0_28, all_0_2_2 and discharging atoms intersect(all_0_2_2, all_24_0_28) = 0, yields: % 21.15/6.45 | (91) ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_2_2, all_24_0_28) = v0) % 21.15/6.45 | % 21.15/6.45 | Instantiating (91) with all_73_0_43 yields: % 21.15/6.45 | (92) ~ (all_73_0_43 = 0) & disjoint(all_0_2_2, all_24_0_28) = all_73_0_43 % 21.15/6.45 | % 21.15/6.45 | Applying alpha-rule on (92) yields: % 21.61/6.45 | (93) ~ (all_73_0_43 = 0) % 21.61/6.45 | (94) disjoint(all_0_2_2, all_24_0_28) = all_73_0_43 % 21.61/6.45 | % 21.61/6.45 | Instantiating formula (43) with all_0_2_2, all_24_0_28, all_73_0_43, 0 and discharging atoms disjoint(all_0_2_2, all_24_0_28) = all_73_0_43, disjoint(all_0_2_2, all_24_0_28) = 0, yields: % 21.61/6.45 | (95) all_73_0_43 = 0 % 21.61/6.45 | % 21.61/6.45 | Equations (95) can reduce 93 to: % 21.61/6.45 | (96) $false % 21.61/6.45 | % 21.61/6.45 |-The branch is then unsatisfiable % 21.61/6.45 |-Branch two: % 21.61/6.45 | (97) all_44_0_32 = 0 & intersect(all_0_2_2, all_24_1_29) = 0 % 21.61/6.45 | % 21.61/6.45 | Applying alpha-rule on (97) yields: % 21.61/6.45 | (82) all_44_0_32 = 0 % 21.61/6.45 | (99) intersect(all_0_2_2, all_24_1_29) = 0 % 21.61/6.45 | % 21.61/6.45 | Instantiating formula (35) with all_0_2_2, all_24_1_29, 0, all_51_0_38 and discharging atoms intersect(all_0_2_2, all_24_1_29) = all_51_0_38, intersect(all_0_2_2, all_24_1_29) = 0, yields: % 21.61/6.45 | (100) all_51_0_38 = 0 % 21.61/6.45 | % 21.61/6.45 | Equations (100) can reduce 75 to: % 21.61/6.45 | (96) $false % 21.61/6.45 | % 21.61/6.45 |-The branch is then unsatisfiable % 21.61/6.45 |-Branch two: % 21.61/6.45 | (102) ~ (intersect(all_0_2_2, all_0_1_1) = 0) % 21.61/6.45 | (103) all_0_0_0 = 0 % 21.61/6.45 | % 21.61/6.45 | Equations (103) can reduce 20 to: % 21.61/6.45 | (96) $false % 21.61/6.45 | % 21.61/6.45 |-The branch is then unsatisfiable % 21.61/6.45 % SZS output end Proof for theBenchmark % 21.61/6.45 % 21.61/6.45 5821ms %------------------------------------------------------------------------------