%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU319+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n029.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 08:48:48 EDT 2022 % Result : Theorem 2.41s 1.32s % Output : Proof 4.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SEU319+1 : TPTP v8.1.0. Released v3.3.0. % 0.10/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.33 % Computer : n029.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Mon Jun 20 10:55:30 EDT 2022 % 0.14/0.34 % CPUTime : % 0.20/0.58 ____ _ % 0.20/0.58 ___ / __ \_____(_)___ ________ __________ % 0.20/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.20/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.20/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.20/0.58 % 0.20/0.58 A Theorem Prover for First-Order Logic % 0.20/0.58 (ePrincess v.1.0) % 0.20/0.58 % 0.20/0.58 (c) Philipp Rümmer, 2009-2015 % 0.20/0.58 (c) Peter Backeman, 2014-2015 % 0.20/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.20/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.20/0.58 Bug reports to peter@backeman.se % 0.20/0.58 % 0.20/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.20/0.58 % 0.20/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.74/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.51/0.93 Prover 0: Preprocessing ... % 1.93/1.13 Prover 0: Warning: ignoring some quantifiers % 1.93/1.15 Prover 0: Constructing countermodel ... % 2.41/1.32 Prover 0: proved (689ms) % 2.41/1.32 % 2.41/1.32 No countermodel exists, formula is valid % 2.41/1.32 % SZS status Theorem for theBenchmark % 2.41/1.32 % 2.41/1.32 Generating proof ... Warning: ignoring some quantifiers % 4.53/1.75 found it (size 58) % 4.53/1.75 % 4.53/1.75 % SZS output start Proof for theBenchmark % 4.53/1.75 Assumed formulas after preprocessing and simplification: % 4.53/1.75 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (subset_complement(v1, v3) = v4 & the_carrier(v0) = v1 & powerset(v1) = v2 & one_sorted_str(v5) & element(v3, v2) & top_str(v6) & top_str(v0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (subset_difference(v11, v10, v9) = v8) | ~ (subset_difference(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v8, v9) = v11) | ~ (powerset(v7) = v10) | ~ element(v9, v10) | ~ element(v8, v10) | subset_difference(v7, v8, v9) = v11) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (subset_complement(v7, v9) = v10) | ~ (subset_complement(v7, v8) = v9) | ? [v11] : (powerset(v7) = v11 & ~ element(v8, v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_difference(v10, v9) = v8) | ~ (set_difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset_complement(v10, v9) = v8) | ~ (subset_complement(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (subset_difference(v7, v8, v9) = v10) | ? [v11] : ? [v12] : (set_difference(v8, v9) = v12 & powerset(v7) = v11 & (v12 = v10 | ~ element(v9, v11) | ~ element(v8, v11)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (subset_difference(v7, v8, v9) = v10) | ? [v11] : (powerset(v7) = v11 & ( ~ element(v9, v11) | ~ element(v8, v11) | element(v10, v11)))) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (cast_as_carrier_subset(v9) = v8) | ~ (cast_as_carrier_subset(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (the_carrier(v9) = v8) | ~ (the_carrier(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (powerset(v9) = v8) | ~ (powerset(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset_complement(v7, v8) = v9) | ? [v10] : (powerset(v7) = v10 & ( ~ element(v8, v10) | element(v9, v10)))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ~ subset(v7, v8) | element(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ~ element(v7, v9) | subset(v7, v8)) & ! [v7] : ! [v8] : ( ~ (cast_as_carrier_subset(v7) = v8) | ~ one_sorted_str(v7) | ? [v9] : ? [v10] : (the_carrier(v7) = v9 & powerset(v9) = v10 & element(v8, v10))) & ! [v7] : ! [v8] : ( ~ (cast_as_carrier_subset(v7) = v8) | ~ one_sorted_str(v7) | ? [v9] : ? [v10] : (the_carrier(v7) = v9 & powerset(v9) = v10 & ! [v11] : ! [v12] : ( ~ (subset_complement(v9, v11) = v12) | ~ element(v11, v10) | subset_difference(v9, v8, v11) = v12) & ! [v11] : ! [v12] : ( ~ (subset_difference(v9, v8, v11) = v12) | ~ element(v11, v10) | subset_complement(v9, v11) = v12))) & ! [v7] : ! [v8] : ( ~ (cast_as_carrier_subset(v7) = v8) | ~ top_str(v7) | ? [v9] : ? [v10] : (the_carrier(v7) = v9 & powerset(v9) = v10 & ! [v11] : ! [v12] : ( ~ (subset_difference(v9, v8, v11) = v12) | ~ open_subset(v12, v7) | ~ element(v11, v10) | closed_subset(v11, v7)) & ! [v11] : ! [v12] : ( ~ (subset_difference(v9, v8, v11) = v12) | ~ closed_subset(v11, v7) | ~ element(v11, v10) | open_subset(v12, v7)))) & ! [v7] : ! [v8] : ( ~ (the_carrier(v7) = v8) | ~ one_sorted_str(v7) | ? [v9] : ? [v10] : (cast_as_carrier_subset(v7) = v10 & powerset(v8) = v9 & ! [v11] : ! [v12] : ( ~ (subset_complement(v8, v11) = v12) | ~ element(v11, v9) | subset_difference(v8, v10, v11) = v12) & ! [v11] : ! [v12] : ( ~ (subset_difference(v8, v10, v11) = v12) | ~ element(v11, v9) | subset_complement(v8, v11) = v12))) & ! [v7] : ! [v8] : ( ~ (the_carrier(v7) = v8) | ~ one_sorted_str(v7) | ? [v9] : ? [v10] : (cast_as_carrier_subset(v7) = v9 & powerset(v8) = v10 & element(v9, v10))) & ! [v7] : ! [v8] : ( ~ (the_carrier(v7) = v8) | ~ top_str(v7) | ? [v9] : ? [v10] : (cast_as_carrier_subset(v7) = v10 & powerset(v8) = v9 & ! [v11] : ! [v12] : ( ~ (subset_difference(v8, v10, v11) = v12) | ~ open_subset(v12, v7) | ~ element(v11, v9) | closed_subset(v11, v7)) & ! [v11] : ! [v12] : ( ~ (subset_difference(v8, v10, v11) = v12) | ~ closed_subset(v11, v7) | ~ element(v11, v9) | open_subset(v12, v7)))) & ! [v7] : ( ~ top_str(v7) | one_sorted_str(v7)) & ? [v7] : ? [v8] : element(v8, v7) & ? [v7] : subset(v7, v7) & ((open_subset(v4, v0) & ~ closed_subset(v3, v0)) | (closed_subset(v3, v0) & ~ open_subset(v4, v0)))) % 4.53/1.79 | 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: % 4.53/1.79 | (1) subset_complement(all_0_5_5, all_0_3_3) = all_0_2_2 & the_carrier(all_0_6_6) = all_0_5_5 & powerset(all_0_5_5) = all_0_4_4 & one_sorted_str(all_0_1_1) & element(all_0_3_3, all_0_4_4) & top_str(all_0_0_0) & top_str(all_0_6_6) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_difference(v0, v1, v2) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_difference(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_as_carrier_subset(v2) = v1) | ~ (cast_as_carrier_subset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & element(v1, v3))) & ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & ! [v4] : ! [v5] : ( ~ (subset_complement(v2, v4) = v5) | ~ element(v4, v3) | subset_difference(v2, v1, v4) = v5) & ! [v4] : ! [v5] : ( ~ (subset_difference(v2, v1, v4) = v5) | ~ element(v4, v3) | subset_complement(v2, v4) = v5))) & ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ top_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & ! [v4] : ! [v5] : ( ~ (subset_difference(v2, v1, v4) = v5) | ~ open_subset(v5, v0) | ~ element(v4, v3) | closed_subset(v4, v0)) & ! [v4] : ! [v5] : ( ~ (subset_difference(v2, v1, v4) = v5) | ~ closed_subset(v4, v0) | ~ element(v4, v3) | open_subset(v5, v0)))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (cast_as_carrier_subset(v0) = v3 & powerset(v1) = v2 & ! [v4] : ! [v5] : ( ~ (subset_complement(v1, v4) = v5) | ~ element(v4, v2) | subset_difference(v1, v3, v4) = v5) & ! [v4] : ! [v5] : ( ~ (subset_difference(v1, v3, v4) = v5) | ~ element(v4, v2) | subset_complement(v1, v4) = v5))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (cast_as_carrier_subset(v0) = v2 & powerset(v1) = v3 & element(v2, v3))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ top_str(v0) | ? [v2] : ? [v3] : (cast_as_carrier_subset(v0) = v3 & powerset(v1) = v2 & ! [v4] : ! [v5] : ( ~ (subset_difference(v1, v3, v4) = v5) | ~ open_subset(v5, v0) | ~ element(v4, v2) | closed_subset(v4, v0)) & ! [v4] : ! [v5] : ( ~ (subset_difference(v1, v3, v4) = v5) | ~ closed_subset(v4, v0) | ~ element(v4, v2) | open_subset(v5, v0)))) & ! [v0] : ( ~ top_str(v0) | one_sorted_str(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) & ((open_subset(all_0_2_2, all_0_6_6) & ~ closed_subset(all_0_3_3, all_0_6_6)) | (closed_subset(all_0_3_3, all_0_6_6) & ~ open_subset(all_0_2_2, all_0_6_6))) % 4.83/1.80 | % 4.83/1.80 | Applying alpha-rule on (1) yields: % 4.83/1.80 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 4.83/1.80 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 4.83/1.80 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) % 4.83/1.80 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) % 4.83/1.80 | (6) ! [v0] : ( ~ top_str(v0) | one_sorted_str(v0)) % 4.83/1.80 | (7) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (cast_as_carrier_subset(v0) = v3 & powerset(v1) = v2 & ! [v4] : ! [v5] : ( ~ (subset_complement(v1, v4) = v5) | ~ element(v4, v2) | subset_difference(v1, v3, v4) = v5) & ! [v4] : ! [v5] : ( ~ (subset_difference(v1, v3, v4) = v5) | ~ element(v4, v2) | subset_complement(v1, v4) = v5))) % 4.83/1.80 | (8) the_carrier(all_0_6_6) = all_0_5_5 % 4.83/1.80 | (9) ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ top_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & ! [v4] : ! [v5] : ( ~ (subset_difference(v2, v1, v4) = v5) | ~ open_subset(v5, v0) | ~ element(v4, v3) | closed_subset(v4, v0)) & ! [v4] : ! [v5] : ( ~ (subset_difference(v2, v1, v4) = v5) | ~ closed_subset(v4, v0) | ~ element(v4, v3) | open_subset(v5, v0)))) % 4.83/1.80 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) % 4.83/1.80 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_as_carrier_subset(v2) = v1) | ~ (cast_as_carrier_subset(v2) = v0)) % 4.83/1.80 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 4.83/1.80 | (13) top_str(all_0_6_6) % 4.83/1.80 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_difference(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) % 4.83/1.81 | (15) ? [v0] : subset(v0, v0) % 4.83/1.81 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 4.83/1.81 | (17) (open_subset(all_0_2_2, all_0_6_6) & ~ closed_subset(all_0_3_3, all_0_6_6)) | (closed_subset(all_0_3_3, all_0_6_6) & ~ open_subset(all_0_2_2, all_0_6_6)) % 4.83/1.81 | (18) ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & ! [v4] : ! [v5] : ( ~ (subset_complement(v2, v4) = v5) | ~ element(v4, v3) | subset_difference(v2, v1, v4) = v5) & ! [v4] : ! [v5] : ( ~ (subset_difference(v2, v1, v4) = v5) | ~ element(v4, v3) | subset_complement(v2, v4) = v5))) % 4.83/1.81 | (19) ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & element(v1, v3))) % 4.83/1.81 | (20) element(all_0_3_3, all_0_4_4) % 4.83/1.81 | (21) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (cast_as_carrier_subset(v0) = v2 & powerset(v1) = v3 & element(v2, v3))) % 4.83/1.81 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 4.83/1.81 | (23) subset_complement(all_0_5_5, all_0_3_3) = all_0_2_2 % 4.83/1.81 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_difference(v0, v1, v2) = v4) % 4.83/1.81 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) % 4.83/1.81 | (26) top_str(all_0_0_0) % 4.83/1.81 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) % 4.83/1.81 | (28) one_sorted_str(all_0_1_1) % 4.83/1.81 | (29) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ top_str(v0) | ? [v2] : ? [v3] : (cast_as_carrier_subset(v0) = v3 & powerset(v1) = v2 & ! [v4] : ! [v5] : ( ~ (subset_difference(v1, v3, v4) = v5) | ~ open_subset(v5, v0) | ~ element(v4, v2) | closed_subset(v4, v0)) & ! [v4] : ! [v5] : ( ~ (subset_difference(v1, v3, v4) = v5) | ~ closed_subset(v4, v0) | ~ element(v4, v2) | open_subset(v5, v0)))) % 4.83/1.81 | (30) ? [v0] : ? [v1] : element(v1, v0) % 4.83/1.81 | (31) powerset(all_0_5_5) = all_0_4_4 % 4.83/1.81 | % 4.83/1.81 | Instantiating formula (5) with all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms subset_complement(all_0_5_5, all_0_3_3) = all_0_2_2, yields: % 4.83/1.81 | (32) ? [v0] : (powerset(all_0_5_5) = v0 & ( ~ element(all_0_3_3, v0) | element(all_0_2_2, v0))) % 4.83/1.81 | % 4.83/1.81 | Instantiating formula (29) with all_0_5_5, all_0_6_6 and discharging atoms the_carrier(all_0_6_6) = all_0_5_5, top_str(all_0_6_6), yields: % 4.83/1.81 | (33) ? [v0] : ? [v1] : (cast_as_carrier_subset(all_0_6_6) = v1 & powerset(all_0_5_5) = v0 & ! [v2] : ! [v3] : ( ~ (subset_difference(all_0_5_5, v1, v2) = v3) | ~ open_subset(v3, all_0_6_6) | ~ element(v2, v0) | closed_subset(v2, all_0_6_6)) & ! [v2] : ! [v3] : ( ~ (subset_difference(all_0_5_5, v1, v2) = v3) | ~ closed_subset(v2, all_0_6_6) | ~ element(v2, v0) | open_subset(v3, all_0_6_6))) % 4.83/1.81 | % 4.83/1.81 | Instantiating formula (6) with all_0_6_6 and discharging atoms top_str(all_0_6_6), yields: % 4.83/1.81 | (34) one_sorted_str(all_0_6_6) % 4.83/1.81 | % 4.83/1.81 | Instantiating (32) with all_13_0_10 yields: % 4.83/1.81 | (35) powerset(all_0_5_5) = all_13_0_10 & ( ~ element(all_0_3_3, all_13_0_10) | element(all_0_2_2, all_13_0_10)) % 4.83/1.81 | % 4.83/1.81 | Applying alpha-rule on (35) yields: % 4.83/1.81 | (36) powerset(all_0_5_5) = all_13_0_10 % 4.83/1.81 | (37) ~ element(all_0_3_3, all_13_0_10) | element(all_0_2_2, all_13_0_10) % 4.83/1.81 | % 4.83/1.81 | Instantiating (33) with all_15_0_11, all_15_1_12 yields: % 4.83/1.81 | (38) cast_as_carrier_subset(all_0_6_6) = all_15_0_11 & powerset(all_0_5_5) = all_15_1_12 & ! [v0] : ! [v1] : ( ~ (subset_difference(all_0_5_5, all_15_0_11, v0) = v1) | ~ open_subset(v1, all_0_6_6) | ~ element(v0, all_15_1_12) | closed_subset(v0, all_0_6_6)) & ! [v0] : ! [v1] : ( ~ (subset_difference(all_0_5_5, all_15_0_11, v0) = v1) | ~ closed_subset(v0, all_0_6_6) | ~ element(v0, all_15_1_12) | open_subset(v1, all_0_6_6)) % 4.83/1.82 | % 4.83/1.82 | Applying alpha-rule on (38) yields: % 4.83/1.82 | (39) cast_as_carrier_subset(all_0_6_6) = all_15_0_11 % 4.83/1.82 | (40) powerset(all_0_5_5) = all_15_1_12 % 4.83/1.82 | (41) ! [v0] : ! [v1] : ( ~ (subset_difference(all_0_5_5, all_15_0_11, v0) = v1) | ~ open_subset(v1, all_0_6_6) | ~ element(v0, all_15_1_12) | closed_subset(v0, all_0_6_6)) % 4.83/1.82 | (42) ! [v0] : ! [v1] : ( ~ (subset_difference(all_0_5_5, all_15_0_11, v0) = v1) | ~ closed_subset(v0, all_0_6_6) | ~ element(v0, all_15_1_12) | open_subset(v1, all_0_6_6)) % 4.83/1.82 | % 4.83/1.82 | Instantiating formula (12) with all_0_5_5, all_15_1_12, all_0_4_4 and discharging atoms powerset(all_0_5_5) = all_15_1_12, powerset(all_0_5_5) = all_0_4_4, yields: % 4.83/1.82 | (43) all_15_1_12 = all_0_4_4 % 4.83/1.82 | % 4.83/1.82 | Instantiating formula (12) with all_0_5_5, all_13_0_10, all_15_1_12 and discharging atoms powerset(all_0_5_5) = all_15_1_12, powerset(all_0_5_5) = all_13_0_10, yields: % 4.83/1.82 | (44) all_15_1_12 = all_13_0_10 % 4.83/1.82 | % 4.83/1.82 | Combining equations (43,44) yields a new equation: % 4.83/1.82 | (45) all_13_0_10 = all_0_4_4 % 4.83/1.82 | % 4.83/1.82 | Combining equations (45,44) yields a new equation: % 4.83/1.82 | (43) all_15_1_12 = all_0_4_4 % 4.83/1.82 | % 4.83/1.82 | From (45) and (36) follows: % 4.83/1.82 | (31) powerset(all_0_5_5) = all_0_4_4 % 4.83/1.82 | % 4.83/1.82 +-Applying beta-rule and splitting (37), into two cases. % 4.83/1.82 |-Branch one: % 4.83/1.82 | (48) ~ element(all_0_3_3, all_13_0_10) % 4.83/1.82 | % 4.83/1.82 | From (45) and (48) follows: % 4.83/1.82 | (49) ~ element(all_0_3_3, all_0_4_4) % 4.83/1.82 | % 4.83/1.82 | Using (20) and (49) yields: % 4.83/1.82 | (50) $false % 4.83/1.82 | % 4.83/1.82 |-The branch is then unsatisfiable % 4.83/1.82 |-Branch two: % 4.83/1.82 | (51) element(all_0_3_3, all_13_0_10) % 4.83/1.82 | (52) element(all_0_2_2, all_13_0_10) % 4.83/1.82 | % 4.83/1.82 | From (45) and (51) follows: % 4.83/1.82 | (20) element(all_0_3_3, all_0_4_4) % 4.83/1.82 | % 4.83/1.82 | Instantiating formula (7) with all_0_5_5, all_0_6_6 and discharging atoms the_carrier(all_0_6_6) = all_0_5_5, one_sorted_str(all_0_6_6), yields: % 4.83/1.82 | (54) ? [v0] : ? [v1] : (cast_as_carrier_subset(all_0_6_6) = v1 & powerset(all_0_5_5) = v0 & ! [v2] : ! [v3] : ( ~ (subset_complement(all_0_5_5, v2) = v3) | ~ element(v2, v0) | subset_difference(all_0_5_5, v1, v2) = v3) & ! [v2] : ! [v3] : ( ~ (subset_difference(all_0_5_5, v1, v2) = v3) | ~ element(v2, v0) | subset_complement(all_0_5_5, v2) = v3)) % 4.83/1.82 | % 4.83/1.82 | Instantiating formula (21) with all_0_5_5, all_0_6_6 and discharging atoms the_carrier(all_0_6_6) = all_0_5_5, one_sorted_str(all_0_6_6), yields: % 4.83/1.82 | (55) ? [v0] : ? [v1] : (cast_as_carrier_subset(all_0_6_6) = v0 & powerset(all_0_5_5) = v1 & element(v0, v1)) % 4.83/1.82 | % 4.83/1.82 | Instantiating (55) with all_40_0_19, all_40_1_20 yields: % 4.83/1.82 | (56) cast_as_carrier_subset(all_0_6_6) = all_40_1_20 & powerset(all_0_5_5) = all_40_0_19 & element(all_40_1_20, all_40_0_19) % 4.83/1.82 | % 4.83/1.82 | Applying alpha-rule on (56) yields: % 4.83/1.82 | (57) cast_as_carrier_subset(all_0_6_6) = all_40_1_20 % 4.83/1.82 | (58) powerset(all_0_5_5) = all_40_0_19 % 4.83/1.82 | (59) element(all_40_1_20, all_40_0_19) % 4.83/1.82 | % 4.83/1.82 | Instantiating (54) with all_42_0_21, all_42_1_22 yields: % 4.83/1.82 | (60) cast_as_carrier_subset(all_0_6_6) = all_42_0_21 & powerset(all_0_5_5) = all_42_1_22 & ! [v0] : ! [v1] : ( ~ (subset_complement(all_0_5_5, v0) = v1) | ~ element(v0, all_42_1_22) | subset_difference(all_0_5_5, all_42_0_21, v0) = v1) & ! [v0] : ! [v1] : ( ~ (subset_difference(all_0_5_5, all_42_0_21, v0) = v1) | ~ element(v0, all_42_1_22) | subset_complement(all_0_5_5, v0) = v1) % 4.83/1.82 | % 4.83/1.82 | Applying alpha-rule on (60) yields: % 4.83/1.82 | (61) cast_as_carrier_subset(all_0_6_6) = all_42_0_21 % 4.83/1.82 | (62) powerset(all_0_5_5) = all_42_1_22 % 4.83/1.82 | (63) ! [v0] : ! [v1] : ( ~ (subset_complement(all_0_5_5, v0) = v1) | ~ element(v0, all_42_1_22) | subset_difference(all_0_5_5, all_42_0_21, v0) = v1) % 4.83/1.82 | (64) ! [v0] : ! [v1] : ( ~ (subset_difference(all_0_5_5, all_42_0_21, v0) = v1) | ~ element(v0, all_42_1_22) | subset_complement(all_0_5_5, v0) = v1) % 4.83/1.82 | % 4.83/1.82 | Instantiating formula (11) with all_0_6_6, all_42_0_21, all_15_0_11 and discharging atoms cast_as_carrier_subset(all_0_6_6) = all_42_0_21, cast_as_carrier_subset(all_0_6_6) = all_15_0_11, yields: % 4.83/1.82 | (65) all_42_0_21 = all_15_0_11 % 4.83/1.82 | % 4.83/1.82 | Instantiating formula (11) with all_0_6_6, all_40_1_20, all_42_0_21 and discharging atoms cast_as_carrier_subset(all_0_6_6) = all_42_0_21, cast_as_carrier_subset(all_0_6_6) = all_40_1_20, yields: % 4.83/1.82 | (66) all_42_0_21 = all_40_1_20 % 4.83/1.82 | % 4.83/1.82 | Instantiating formula (12) with all_0_5_5, all_42_1_22, all_0_4_4 and discharging atoms powerset(all_0_5_5) = all_42_1_22, powerset(all_0_5_5) = all_0_4_4, yields: % 4.83/1.82 | (67) all_42_1_22 = all_0_4_4 % 4.83/1.82 | % 4.83/1.82 | Instantiating formula (12) with all_0_5_5, all_40_0_19, all_42_1_22 and discharging atoms powerset(all_0_5_5) = all_42_1_22, powerset(all_0_5_5) = all_40_0_19, yields: % 4.83/1.82 | (68) all_42_1_22 = all_40_0_19 % 4.83/1.83 | % 4.83/1.83 | Combining equations (65,66) yields a new equation: % 4.83/1.83 | (69) all_40_1_20 = all_15_0_11 % 4.83/1.83 | % 4.83/1.83 | Combining equations (67,68) yields a new equation: % 4.83/1.83 | (70) all_40_0_19 = all_0_4_4 % 4.83/1.83 | % 4.83/1.83 | Combining equations (70,68) yields a new equation: % 4.83/1.83 | (67) all_42_1_22 = all_0_4_4 % 4.83/1.83 | % 4.83/1.83 | Combining equations (69,66) yields a new equation: % 4.83/1.83 | (65) all_42_0_21 = all_15_0_11 % 4.83/1.83 | % 4.83/1.83 +-Applying beta-rule and splitting (17), into two cases. % 4.83/1.83 |-Branch one: % 4.83/1.83 | (73) open_subset(all_0_2_2, all_0_6_6) & ~ closed_subset(all_0_3_3, all_0_6_6) % 4.83/1.83 | % 4.83/1.83 | Applying alpha-rule on (73) yields: % 4.83/1.83 | (74) open_subset(all_0_2_2, all_0_6_6) % 4.83/1.83 | (75) ~ closed_subset(all_0_3_3, all_0_6_6) % 4.83/1.83 | % 4.83/1.83 | Instantiating formula (63) with all_0_2_2, all_0_3_3 and discharging atoms subset_complement(all_0_5_5, all_0_3_3) = all_0_2_2, yields: % 4.83/1.83 | (76) ~ element(all_0_3_3, all_42_1_22) | subset_difference(all_0_5_5, all_42_0_21, all_0_3_3) = all_0_2_2 % 4.83/1.83 | % 4.83/1.83 +-Applying beta-rule and splitting (76), into two cases. % 4.83/1.83 |-Branch one: % 4.83/1.83 | (77) ~ element(all_0_3_3, all_42_1_22) % 4.83/1.83 | % 4.83/1.83 | From (67) and (77) follows: % 4.83/1.83 | (49) ~ element(all_0_3_3, all_0_4_4) % 4.83/1.83 | % 4.83/1.83 | Using (20) and (49) yields: % 4.83/1.83 | (50) $false % 4.83/1.83 | % 4.83/1.83 |-The branch is then unsatisfiable % 4.83/1.83 |-Branch two: % 4.83/1.83 | (80) element(all_0_3_3, all_42_1_22) % 4.83/1.83 | (81) subset_difference(all_0_5_5, all_42_0_21, all_0_3_3) = all_0_2_2 % 4.83/1.83 | % 4.83/1.83 | From (65) and (81) follows: % 4.83/1.83 | (82) subset_difference(all_0_5_5, all_15_0_11, all_0_3_3) = all_0_2_2 % 4.83/1.83 | % 4.83/1.83 | From (67) and (80) follows: % 4.83/1.83 | (20) element(all_0_3_3, all_0_4_4) % 4.83/1.83 | % 4.83/1.83 | Instantiating formula (41) with all_0_2_2, all_0_3_3 and discharging atoms subset_difference(all_0_5_5, all_15_0_11, all_0_3_3) = all_0_2_2, open_subset(all_0_2_2, all_0_6_6), ~ closed_subset(all_0_3_3, all_0_6_6), yields: % 4.83/1.83 | (84) ~ element(all_0_3_3, all_15_1_12) % 4.83/1.83 | % 4.83/1.83 | From (43) and (84) follows: % 4.83/1.83 | (49) ~ element(all_0_3_3, all_0_4_4) % 4.83/1.83 | % 4.83/1.83 | Using (20) and (49) yields: % 4.83/1.83 | (50) $false % 4.83/1.83 | % 4.83/1.83 |-The branch is then unsatisfiable % 4.83/1.83 |-Branch two: % 4.83/1.83 | (87) closed_subset(all_0_3_3, all_0_6_6) & ~ open_subset(all_0_2_2, all_0_6_6) % 4.83/1.83 | % 4.83/1.83 | Applying alpha-rule on (87) yields: % 4.83/1.83 | (88) closed_subset(all_0_3_3, all_0_6_6) % 4.83/1.83 | (89) ~ open_subset(all_0_2_2, all_0_6_6) % 4.83/1.83 | % 4.83/1.83 | Instantiating formula (63) with all_0_2_2, all_0_3_3 and discharging atoms subset_complement(all_0_5_5, all_0_3_3) = all_0_2_2, yields: % 4.83/1.83 | (76) ~ element(all_0_3_3, all_42_1_22) | subset_difference(all_0_5_5, all_42_0_21, all_0_3_3) = all_0_2_2 % 4.83/1.83 | % 4.83/1.83 +-Applying beta-rule and splitting (76), into two cases. % 4.83/1.83 |-Branch one: % 4.83/1.83 | (77) ~ element(all_0_3_3, all_42_1_22) % 4.83/1.83 | % 4.83/1.83 | From (67) and (77) follows: % 4.83/1.83 | (49) ~ element(all_0_3_3, all_0_4_4) % 4.83/1.83 | % 4.83/1.83 | Using (20) and (49) yields: % 4.83/1.83 | (50) $false % 4.83/1.83 | % 4.83/1.83 |-The branch is then unsatisfiable % 4.83/1.83 |-Branch two: % 4.83/1.83 | (80) element(all_0_3_3, all_42_1_22) % 4.83/1.83 | (81) subset_difference(all_0_5_5, all_42_0_21, all_0_3_3) = all_0_2_2 % 4.83/1.83 | % 4.83/1.83 | From (65) and (81) follows: % 4.83/1.83 | (82) subset_difference(all_0_5_5, all_15_0_11, all_0_3_3) = all_0_2_2 % 4.83/1.83 | % 4.83/1.83 | From (67) and (80) follows: % 4.83/1.83 | (20) element(all_0_3_3, all_0_4_4) % 4.83/1.83 | % 4.83/1.83 | Instantiating formula (42) with all_0_2_2, all_0_3_3 and discharging atoms subset_difference(all_0_5_5, all_15_0_11, all_0_3_3) = all_0_2_2, closed_subset(all_0_3_3, all_0_6_6), ~ open_subset(all_0_2_2, all_0_6_6), yields: % 4.83/1.83 | (84) ~ element(all_0_3_3, all_15_1_12) % 4.83/1.83 | % 4.83/1.83 | From (43) and (84) follows: % 4.83/1.83 | (49) ~ element(all_0_3_3, all_0_4_4) % 4.83/1.83 | % 4.83/1.83 | Using (20) and (49) yields: % 4.83/1.83 | (50) $false % 4.83/1.83 | % 4.83/1.83 |-The branch is then unsatisfiable % 4.83/1.83 % SZS output end Proof for theBenchmark % 4.83/1.83 % 4.83/1.83 1238ms %------------------------------------------------------------------------------