%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU355+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n032.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 08:49:08 EDT 2022 % Result : Theorem 3.32s 1.47s % Output : Proof 5.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SEU355+1 : TPTP v8.1.0. Released v3.3.0. % 0.00/0.10 % Command : ePrincess-casc -timeout=%d %s % 0.10/0.29 % Computer : n032.cluster.edu % 0.10/0.29 % Model : x86_64 x86_64 % 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.29 % Memory : 8042.1875MB % 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.29 % CPULimit : 300 % 0.10/0.29 % WCLimit : 600 % 0.10/0.29 % DateTime : Sun Jun 19 10:33:33 EDT 2022 % 0.10/0.29 % CPUTime : % 0.15/0.49 ____ _ % 0.15/0.49 ___ / __ \_____(_)___ ________ __________ % 0.15/0.49 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.15/0.49 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.15/0.49 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.15/0.49 % 0.15/0.49 A Theorem Prover for First-Order Logic % 0.15/0.50 (ePrincess v.1.0) % 0.15/0.50 % 0.15/0.50 (c) Philipp Rümmer, 2009-2015 % 0.15/0.50 (c) Peter Backeman, 2014-2015 % 0.15/0.50 (contributions by Angelo Brillout, Peter Baumgartner) % 0.15/0.50 Free software under GNU Lesser General Public License (LGPL). % 0.15/0.50 Bug reports to peter@backeman.se % 0.15/0.50 % 0.15/0.50 For more information, visit http://user.uu.se/~petba168/breu/ % 0.15/0.50 % 0.15/0.50 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.15/0.54 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.18/0.81 Prover 0: Preprocessing ... % 1.55/0.96 Prover 0: Warning: ignoring some quantifiers % 1.55/0.98 Prover 0: Constructing countermodel ... % 2.30/1.21 Prover 0: gave up % 2.30/1.21 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.39/1.23 Prover 1: Preprocessing ... % 2.66/1.33 Prover 1: Warning: ignoring some quantifiers % 2.66/1.33 Prover 1: Constructing countermodel ... % 3.32/1.47 Prover 1: proved (259ms) % 3.32/1.47 % 3.32/1.47 No countermodel exists, formula is valid % 3.32/1.47 % SZS status Theorem for theBenchmark % 3.32/1.47 % 3.32/1.47 Generating proof ... Warning: ignoring some quantifiers % 4.93/1.87 found it (size 51) % 4.93/1.87 % 4.93/1.87 % SZS output start Proof for theBenchmark % 4.93/1.87 Assumed formulas after preprocessing and simplification: % 4.93/1.87 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v9 = 0) & ~ (v6 = 0) & one_sorted_str(v10) = 0 & relstr_set_smaller(v0, empty_set, v2) = v3 & rel_str(v11) = 0 & rel_str(v0) = 0 & the_carrier(v0) = v1 & relstr_element_smaller(v0, empty_set, v2) = v4 & element(v2, v1) = 0 & finite(v8) = 0 & empty(v8) = v9 & empty(v7) = 0 & empty(v5) = v6 & empty(empty_set) = 0 & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = v12 | ~ (relstr_set_smaller(v16, v15, v14) = v13) | ~ (relstr_set_smaller(v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = v12 | ~ (relstr_element_smaller(v16, v15, v14) = v13) | ~ (relstr_element_smaller(v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = v12 | ~ (related(v16, v15, v14) = v13) | ~ (related(v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (element(v15, v14) = v13) | ~ (element(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (in(v15, v14) = v13) | ~ (in(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (in(v12, v13) = v14) | ? [v15] : ? [v16] : (element(v12, v13) = v15 & empty(v13) = v16 & ( ~ (v15 = 0) | v16 = 0))) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (one_sorted_str(v14) = v13) | ~ (one_sorted_str(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (rel_str(v14) = v13) | ~ (rel_str(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (the_carrier(v14) = v13) | ~ (the_carrier(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (finite(v14) = v13) | ~ (finite(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (empty(v14) = v13) | ~ (empty(v14) = v12)) & ! [v12] : ! [v13] : (v13 = v12 | ~ (empty(v13) = 0) | ~ (empty(v12) = 0)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (one_sorted_str(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & rel_str(v12) = v14)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (finite(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v12) = v14)) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | element(v12, v13) = 0) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & in(v13, v12) = v14)) & ! [v12] : (v12 = empty_set | ~ (empty(v12) = 0)) & ! [v12] : ( ~ (rel_str(v12) = 0) | ? [v13] : (the_carrier(v12) = v13 & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (relstr_set_smaller(v12, v14, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ((v19 = 0 & v18 = 0 & ~ (v20 = 0) & element(v17, v13) = 0 & related(v12, v17, v15) = v20 & in(v17, v14) = 0) | ( ~ (v17 = 0) & element(v15, v13) = v17))) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relstr_set_smaller(v12, v14, v15) = 0) | ~ (element(v16, v13) = 0) | ? [v17] : ? [v18] : (( ~ (v17 = 0) & element(v15, v13) = v17) | (related(v12, v16, v15) = v18 & in(v16, v14) = v17 & ( ~ (v17 = 0) | v18 = 0)))))) & ! [v12] : ( ~ (rel_str(v12) = 0) | ? [v13] : (the_carrier(v12) = v13 & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (relstr_element_smaller(v12, v14, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ((v19 = 0 & v18 = 0 & ~ (v20 = 0) & element(v17, v13) = 0 & related(v12, v15, v17) = v20 & in(v17, v14) = 0) | ( ~ (v17 = 0) & element(v15, v13) = v17))) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relstr_element_smaller(v12, v14, v15) = 0) | ~ (element(v16, v13) = 0) | ? [v17] : ? [v18] : (( ~ (v17 = 0) & element(v15, v13) = v17) | (related(v12, v15, v16) = v18 & in(v16, v14) = v17 & ( ~ (v17 = 0) | v18 = 0)))))) & ? [v12] : ? [v13] : element(v13, v12) = 0 & ( ~ (v4 = 0) | ~ (v3 = 0))) % 5.30/1.91 | 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, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11 yields: % 5.30/1.91 | (1) ~ (all_0_2_2 = 0) & ~ (all_0_5_5 = 0) & one_sorted_str(all_0_1_1) = 0 & relstr_set_smaller(all_0_11_11, empty_set, all_0_9_9) = all_0_8_8 & rel_str(all_0_0_0) = 0 & rel_str(all_0_11_11) = 0 & the_carrier(all_0_11_11) = all_0_10_10 & relstr_element_smaller(all_0_11_11, empty_set, all_0_9_9) = all_0_7_7 & element(all_0_9_9, all_0_10_10) = 0 & finite(all_0_3_3) = 0 & empty(all_0_3_3) = all_0_2_2 & empty(all_0_4_4) = 0 & empty(all_0_6_6) = all_0_5_5 & empty(empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relstr_set_smaller(v4, v3, v2) = v1) | ~ (relstr_set_smaller(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relstr_element_smaller(v4, v3, v2) = v1) | ~ (relstr_element_smaller(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (related(v4, v3, v2) = v1) | ~ (related(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (rel_str(v2) = v1) | ~ (rel_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite(v2) = v1) | ~ (finite(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & rel_str(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (finite(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ( ~ (rel_str(v0) = 0) | ? [v1] : (the_carrier(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relstr_set_smaller(v0, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & ~ (v8 = 0) & element(v5, v1) = 0 & related(v0, v5, v3) = v8 & in(v5, v2) = 0) | ( ~ (v5 = 0) & element(v3, v1) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (relstr_set_smaller(v0, v2, v3) = 0) | ~ (element(v4, v1) = 0) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & element(v3, v1) = v5) | (related(v0, v4, v3) = v6 & in(v4, v2) = v5 & ( ~ (v5 = 0) | v6 = 0)))))) & ! [v0] : ( ~ (rel_str(v0) = 0) | ? [v1] : (the_carrier(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relstr_element_smaller(v0, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & ~ (v8 = 0) & element(v5, v1) = 0 & related(v0, v3, v5) = v8 & in(v5, v2) = 0) | ( ~ (v5 = 0) & element(v3, v1) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (relstr_element_smaller(v0, v2, v3) = 0) | ~ (element(v4, v1) = 0) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & element(v3, v1) = v5) | (related(v0, v3, v4) = v6 & in(v4, v2) = v5 & ( ~ (v5 = 0) | v6 = 0)))))) & ? [v0] : ? [v1] : element(v1, v0) = 0 & ( ~ (all_0_7_7 = 0) | ~ (all_0_8_8 = 0)) % 5.30/1.92 | % 5.30/1.92 | Applying alpha-rule on (1) yields: % 5.30/1.92 | (2) relstr_element_smaller(all_0_11_11, empty_set, all_0_9_9) = all_0_7_7 % 5.30/1.92 | (3) empty(all_0_4_4) = 0 % 5.30/1.92 | (4) ~ (all_0_5_5 = 0) % 5.30/1.92 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (rel_str(v2) = v1) | ~ (rel_str(v2) = v0)) % 5.30/1.92 | (6) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 5.30/1.92 | (7) element(all_0_9_9, all_0_10_10) = 0 % 5.30/1.92 | (8) the_carrier(all_0_11_11) = all_0_10_10 % 5.30/1.92 | (9) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) % 5.30/1.92 | (10) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 5.30/1.92 | (11) empty(all_0_6_6) = all_0_5_5 % 5.30/1.92 | (12) ! [v0] : ( ~ (rel_str(v0) = 0) | ? [v1] : (the_carrier(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relstr_set_smaller(v0, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & ~ (v8 = 0) & element(v5, v1) = 0 & related(v0, v5, v3) = v8 & in(v5, v2) = 0) | ( ~ (v5 = 0) & element(v3, v1) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (relstr_set_smaller(v0, v2, v3) = 0) | ~ (element(v4, v1) = 0) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & element(v3, v1) = v5) | (related(v0, v4, v3) = v6 & in(v4, v2) = v5 & ( ~ (v5 = 0) | v6 = 0)))))) % 5.30/1.92 | (13) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 5.30/1.92 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 5.30/1.92 | (15) one_sorted_str(all_0_1_1) = 0 % 5.30/1.92 | (16) ! [v0] : ( ~ (rel_str(v0) = 0) | ? [v1] : (the_carrier(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relstr_element_smaller(v0, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & ~ (v8 = 0) & element(v5, v1) = 0 & related(v0, v3, v5) = v8 & in(v5, v2) = 0) | ( ~ (v5 = 0) & element(v3, v1) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (relstr_element_smaller(v0, v2, v3) = 0) | ~ (element(v4, v1) = 0) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & element(v3, v1) = v5) | (related(v0, v3, v4) = v6 & in(v4, v2) = v5 & ( ~ (v5 = 0) | v6 = 0)))))) % 5.30/1.92 | (17) ! [v0] : ! [v1] : (v1 = 0 | ~ (finite(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 5.30/1.92 | (18) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 5.30/1.92 | (19) finite(all_0_3_3) = 0 % 5.30/1.92 | (20) rel_str(all_0_0_0) = 0 % 5.30/1.92 | (21) rel_str(all_0_11_11) = 0 % 5.30/1.92 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0)) % 5.30/1.92 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite(v2) = v1) | ~ (finite(v2) = v0)) % 5.30/1.92 | (24) empty(all_0_3_3) = all_0_2_2 % 5.30/1.92 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) % 5.30/1.93 | (26) ? [v0] : ? [v1] : element(v1, v0) = 0 % 5.30/1.93 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relstr_element_smaller(v4, v3, v2) = v1) | ~ (relstr_element_smaller(v4, v3, v2) = v0)) % 5.30/1.93 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (related(v4, v3, v2) = v1) | ~ (related(v4, v3, v2) = v0)) % 5.30/1.93 | (29) ~ (all_0_7_7 = 0) | ~ (all_0_8_8 = 0) % 5.30/1.93 | (30) empty(empty_set) = 0 % 5.30/1.93 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 5.30/1.93 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 5.30/1.93 | (33) ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & rel_str(v0) = v2)) % 5.30/1.93 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 5.30/1.93 | (35) ~ (all_0_2_2 = 0) % 5.30/1.93 | (36) relstr_set_smaller(all_0_11_11, empty_set, all_0_9_9) = all_0_8_8 % 5.30/1.93 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relstr_set_smaller(v4, v3, v2) = v1) | ~ (relstr_set_smaller(v4, v3, v2) = v0)) % 5.30/1.93 | % 5.30/1.93 | Instantiating formula (18) with empty_set, all_0_4_4 and discharging atoms empty(all_0_4_4) = 0, empty(empty_set) = 0, yields: % 5.30/1.93 | (38) all_0_4_4 = empty_set % 5.30/1.93 | % 5.30/1.93 | From (38) and (3) follows: % 5.30/1.93 | (30) empty(empty_set) = 0 % 5.30/1.93 | % 5.30/1.93 | Instantiating formula (12) with all_0_11_11 and discharging atoms rel_str(all_0_11_11) = 0, yields: % 5.30/1.93 | (40) ? [v0] : (the_carrier(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relstr_set_smaller(all_0_11_11, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & ~ (v7 = 0) & element(v4, v0) = 0 & related(all_0_11_11, v4, v2) = v7 & in(v4, v1) = 0) | ( ~ (v4 = 0) & element(v2, v0) = v4))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (relstr_set_smaller(all_0_11_11, v1, v2) = 0) | ~ (element(v3, v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & element(v2, v0) = v4) | (related(all_0_11_11, v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))))) % 5.30/1.93 | % 5.30/1.93 | Instantiating formula (16) with all_0_11_11 and discharging atoms rel_str(all_0_11_11) = 0, yields: % 5.30/1.93 | (41) ? [v0] : (the_carrier(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relstr_element_smaller(all_0_11_11, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & ~ (v7 = 0) & element(v4, v0) = 0 & related(all_0_11_11, v2, v4) = v7 & in(v4, v1) = 0) | ( ~ (v4 = 0) & element(v2, v0) = v4))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (relstr_element_smaller(all_0_11_11, v1, v2) = 0) | ~ (element(v3, v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & element(v2, v0) = v4) | (related(all_0_11_11, v2, v3) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))))) % 5.30/1.93 | % 5.30/1.93 | Instantiating (41) with all_14_0_14 yields: % 5.30/1.93 | (42) the_carrier(all_0_11_11) = all_14_0_14 & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (relstr_element_smaller(all_0_11_11, v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & v4 = 0 & ~ (v6 = 0) & element(v3, all_14_0_14) = 0 & related(all_0_11_11, v1, v3) = v6 & in(v3, v0) = 0) | ( ~ (v3 = 0) & element(v1, all_14_0_14) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relstr_element_smaller(all_0_11_11, v0, v1) = 0) | ~ (element(v2, all_14_0_14) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, all_14_0_14) = v3) | (related(all_0_11_11, v1, v2) = v4 & in(v2, v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))) % 5.30/1.94 | % 5.30/1.94 | Applying alpha-rule on (42) yields: % 5.30/1.94 | (43) the_carrier(all_0_11_11) = all_14_0_14 % 5.30/1.94 | (44) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (relstr_element_smaller(all_0_11_11, v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & v4 = 0 & ~ (v6 = 0) & element(v3, all_14_0_14) = 0 & related(all_0_11_11, v1, v3) = v6 & in(v3, v0) = 0) | ( ~ (v3 = 0) & element(v1, all_14_0_14) = v3))) % 5.30/1.94 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (relstr_element_smaller(all_0_11_11, v0, v1) = 0) | ~ (element(v2, all_14_0_14) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, all_14_0_14) = v3) | (related(all_0_11_11, v1, v2) = v4 & in(v2, v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))) % 5.30/1.94 | % 5.30/1.94 | Instantiating formula (44) with all_0_7_7, all_0_9_9, empty_set and discharging atoms relstr_element_smaller(all_0_11_11, empty_set, all_0_9_9) = all_0_7_7, yields: % 5.30/1.94 | (46) all_0_7_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v2 = 0 & v1 = 0 & ~ (v3 = 0) & element(v0, all_14_0_14) = 0 & related(all_0_11_11, all_0_9_9, v0) = v3 & in(v0, empty_set) = 0) | ( ~ (v0 = 0) & element(all_0_9_9, all_14_0_14) = v0)) % 5.30/1.94 | % 5.30/1.94 | Instantiating (40) with all_17_0_15 yields: % 5.30/1.94 | (47) the_carrier(all_0_11_11) = all_17_0_15 & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (relstr_set_smaller(all_0_11_11, v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & v4 = 0 & ~ (v6 = 0) & element(v3, all_17_0_15) = 0 & related(all_0_11_11, v3, v1) = v6 & in(v3, v0) = 0) | ( ~ (v3 = 0) & element(v1, all_17_0_15) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relstr_set_smaller(all_0_11_11, v0, v1) = 0) | ~ (element(v2, all_17_0_15) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, all_17_0_15) = v3) | (related(all_0_11_11, v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))) % 5.30/1.94 | % 5.30/1.94 | Applying alpha-rule on (47) yields: % 5.30/1.94 | (48) the_carrier(all_0_11_11) = all_17_0_15 % 5.30/1.94 | (49) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (relstr_set_smaller(all_0_11_11, v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & v4 = 0 & ~ (v6 = 0) & element(v3, all_17_0_15) = 0 & related(all_0_11_11, v3, v1) = v6 & in(v3, v0) = 0) | ( ~ (v3 = 0) & element(v1, all_17_0_15) = v3))) % 5.30/1.94 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (relstr_set_smaller(all_0_11_11, v0, v1) = 0) | ~ (element(v2, all_17_0_15) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, all_17_0_15) = v3) | (related(all_0_11_11, v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))) % 5.30/1.94 | % 5.30/1.94 | Instantiating formula (49) with all_0_8_8, all_0_9_9, empty_set and discharging atoms relstr_set_smaller(all_0_11_11, empty_set, all_0_9_9) = all_0_8_8, yields: % 5.30/1.94 | (51) all_0_8_8 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v2 = 0 & v1 = 0 & ~ (v3 = 0) & element(v0, all_17_0_15) = 0 & related(all_0_11_11, v0, all_0_9_9) = v3 & in(v0, empty_set) = 0) | ( ~ (v0 = 0) & element(all_0_9_9, all_17_0_15) = v0)) % 5.30/1.94 | % 5.30/1.94 | Instantiating formula (14) with all_0_11_11, all_17_0_15, all_0_10_10 and discharging atoms the_carrier(all_0_11_11) = all_17_0_15, the_carrier(all_0_11_11) = all_0_10_10, yields: % 5.30/1.94 | (52) all_17_0_15 = all_0_10_10 % 5.30/1.94 | % 5.30/1.94 | Instantiating formula (14) with all_0_11_11, all_14_0_14, all_17_0_15 and discharging atoms the_carrier(all_0_11_11) = all_17_0_15, the_carrier(all_0_11_11) = all_14_0_14, yields: % 5.30/1.94 | (53) all_17_0_15 = all_14_0_14 % 5.30/1.94 | % 5.30/1.94 | Combining equations (53,52) yields a new equation: % 5.30/1.94 | (54) all_14_0_14 = all_0_10_10 % 5.30/1.94 | % 5.30/1.94 | Simplifying 54 yields: % 5.30/1.94 | (55) all_14_0_14 = all_0_10_10 % 5.30/1.94 | % 5.30/1.94 +-Applying beta-rule and splitting (29), into two cases. % 5.30/1.94 |-Branch one: % 5.30/1.94 | (56) ~ (all_0_7_7 = 0) % 5.30/1.94 | % 5.30/1.94 +-Applying beta-rule and splitting (46), into two cases. % 5.30/1.94 |-Branch one: % 5.30/1.94 | (57) all_0_7_7 = 0 % 5.30/1.94 | % 5.30/1.95 | Equations (57) can reduce 56 to: % 5.30/1.95 | (58) $false % 5.30/1.95 | % 5.30/1.95 |-The branch is then unsatisfiable % 5.30/1.95 |-Branch two: % 5.30/1.95 | (56) ~ (all_0_7_7 = 0) % 5.30/1.95 | (60) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v2 = 0 & v1 = 0 & ~ (v3 = 0) & element(v0, all_14_0_14) = 0 & related(all_0_11_11, all_0_9_9, v0) = v3 & in(v0, empty_set) = 0) | ( ~ (v0 = 0) & element(all_0_9_9, all_14_0_14) = v0)) % 5.30/1.95 | % 5.30/1.95 | Instantiating (60) with all_74_0_18, all_74_1_19, all_74_2_20, all_74_3_21 yields: % 5.30/1.95 | (61) (all_74_1_19 = 0 & all_74_2_20 = 0 & ~ (all_74_0_18 = 0) & element(all_74_3_21, all_14_0_14) = 0 & related(all_0_11_11, all_0_9_9, all_74_3_21) = all_74_0_18 & in(all_74_3_21, empty_set) = 0) | ( ~ (all_74_3_21 = 0) & element(all_0_9_9, all_14_0_14) = all_74_3_21) % 5.30/1.95 | % 5.30/1.95 +-Applying beta-rule and splitting (61), into two cases. % 5.30/1.95 |-Branch one: % 5.30/1.95 | (62) all_74_1_19 = 0 & all_74_2_20 = 0 & ~ (all_74_0_18 = 0) & element(all_74_3_21, all_14_0_14) = 0 & related(all_0_11_11, all_0_9_9, all_74_3_21) = all_74_0_18 & in(all_74_3_21, empty_set) = 0 % 5.30/1.95 | % 5.30/1.95 | Applying alpha-rule on (62) yields: % 5.30/1.95 | (63) all_74_1_19 = 0 % 5.30/1.95 | (64) in(all_74_3_21, empty_set) = 0 % 5.30/1.95 | (65) element(all_74_3_21, all_14_0_14) = 0 % 5.30/1.95 | (66) all_74_2_20 = 0 % 5.30/1.95 | (67) related(all_0_11_11, all_0_9_9, all_74_3_21) = all_74_0_18 % 5.30/1.95 | (68) ~ (all_74_0_18 = 0) % 5.30/1.95 | % 5.30/1.95 | Instantiating formula (10) with empty_set, all_74_3_21 and discharging atoms in(all_74_3_21, empty_set) = 0, yields: % 5.30/1.95 | (69) ? [v0] : ( ~ (v0 = 0) & empty(empty_set) = v0) % 5.30/1.95 | % 5.30/1.95 | Instantiating (69) with all_85_0_22 yields: % 5.30/1.95 | (70) ~ (all_85_0_22 = 0) & empty(empty_set) = all_85_0_22 % 5.30/1.95 | % 5.30/1.95 | Applying alpha-rule on (70) yields: % 5.30/1.95 | (71) ~ (all_85_0_22 = 0) % 5.30/1.95 | (72) empty(empty_set) = all_85_0_22 % 5.30/1.95 | % 5.30/1.95 | Instantiating formula (31) with empty_set, all_85_0_22, 0 and discharging atoms empty(empty_set) = all_85_0_22, empty(empty_set) = 0, yields: % 5.30/1.95 | (73) all_85_0_22 = 0 % 5.30/1.95 | % 5.30/1.95 | Equations (73) can reduce 71 to: % 5.30/1.95 | (58) $false % 5.30/1.95 | % 5.30/1.95 |-The branch is then unsatisfiable % 5.30/1.95 |-Branch two: % 5.30/1.95 | (75) ~ (all_74_3_21 = 0) & element(all_0_9_9, all_14_0_14) = all_74_3_21 % 5.30/1.95 | % 5.30/1.95 | Applying alpha-rule on (75) yields: % 5.30/1.95 | (76) ~ (all_74_3_21 = 0) % 5.30/1.95 | (77) element(all_0_9_9, all_14_0_14) = all_74_3_21 % 5.30/1.95 | % 5.30/1.95 | From (55) and (77) follows: % 5.30/1.95 | (78) element(all_0_9_9, all_0_10_10) = all_74_3_21 % 5.30/1.95 | % 5.30/1.95 | Instantiating formula (32) with all_0_9_9, all_0_10_10, all_74_3_21, 0 and discharging atoms element(all_0_9_9, all_0_10_10) = all_74_3_21, element(all_0_9_9, all_0_10_10) = 0, yields: % 5.30/1.95 | (79) all_74_3_21 = 0 % 5.30/1.95 | % 5.30/1.95 | Equations (79) can reduce 76 to: % 5.30/1.95 | (58) $false % 5.30/1.95 | % 5.30/1.95 |-The branch is then unsatisfiable % 5.30/1.95 |-Branch two: % 5.30/1.95 | (57) all_0_7_7 = 0 % 5.30/1.95 | (82) ~ (all_0_8_8 = 0) % 5.30/1.95 | % 5.30/1.95 +-Applying beta-rule and splitting (51), into two cases. % 5.30/1.95 |-Branch one: % 5.30/1.95 | (83) all_0_8_8 = 0 % 5.30/1.95 | % 5.30/1.95 | Equations (83) can reduce 82 to: % 5.30/1.95 | (58) $false % 5.30/1.95 | % 5.30/1.95 |-The branch is then unsatisfiable % 5.30/1.95 |-Branch two: % 5.30/1.95 | (82) ~ (all_0_8_8 = 0) % 5.30/1.95 | (86) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v2 = 0 & v1 = 0 & ~ (v3 = 0) & element(v0, all_17_0_15) = 0 & related(all_0_11_11, v0, all_0_9_9) = v3 & in(v0, empty_set) = 0) | ( ~ (v0 = 0) & element(all_0_9_9, all_17_0_15) = v0)) % 5.30/1.95 | % 5.30/1.95 | Instantiating (86) with all_74_0_24, all_74_1_25, all_74_2_26, all_74_3_27 yields: % 5.30/1.95 | (87) (all_74_1_25 = 0 & all_74_2_26 = 0 & ~ (all_74_0_24 = 0) & element(all_74_3_27, all_17_0_15) = 0 & related(all_0_11_11, all_74_3_27, all_0_9_9) = all_74_0_24 & in(all_74_3_27, empty_set) = 0) | ( ~ (all_74_3_27 = 0) & element(all_0_9_9, all_17_0_15) = all_74_3_27) % 5.30/1.95 | % 5.30/1.95 +-Applying beta-rule and splitting (87), into two cases. % 5.30/1.95 |-Branch one: % 5.30/1.95 | (88) all_74_1_25 = 0 & all_74_2_26 = 0 & ~ (all_74_0_24 = 0) & element(all_74_3_27, all_17_0_15) = 0 & related(all_0_11_11, all_74_3_27, all_0_9_9) = all_74_0_24 & in(all_74_3_27, empty_set) = 0 % 5.30/1.95 | % 5.30/1.95 | Applying alpha-rule on (88) yields: % 5.30/1.95 | (89) related(all_0_11_11, all_74_3_27, all_0_9_9) = all_74_0_24 % 5.30/1.95 | (90) all_74_1_25 = 0 % 5.30/1.95 | (91) in(all_74_3_27, empty_set) = 0 % 5.30/1.95 | (92) element(all_74_3_27, all_17_0_15) = 0 % 5.30/1.96 | (93) ~ (all_74_0_24 = 0) % 5.30/1.96 | (94) all_74_2_26 = 0 % 5.30/1.96 | % 5.30/1.96 | Instantiating formula (10) with empty_set, all_74_3_27 and discharging atoms in(all_74_3_27, empty_set) = 0, yields: % 5.30/1.96 | (69) ? [v0] : ( ~ (v0 = 0) & empty(empty_set) = v0) % 5.30/1.96 | % 5.30/1.96 | Instantiating (69) with all_87_0_29 yields: % 5.30/1.96 | (96) ~ (all_87_0_29 = 0) & empty(empty_set) = all_87_0_29 % 5.30/1.96 | % 5.30/1.96 | Applying alpha-rule on (96) yields: % 5.30/1.96 | (97) ~ (all_87_0_29 = 0) % 5.30/1.96 | (98) empty(empty_set) = all_87_0_29 % 5.30/1.96 | % 5.30/1.96 | Instantiating formula (31) with empty_set, all_87_0_29, 0 and discharging atoms empty(empty_set) = all_87_0_29, empty(empty_set) = 0, yields: % 5.30/1.96 | (99) all_87_0_29 = 0 % 5.30/1.96 | % 5.30/1.96 | Equations (99) can reduce 97 to: % 5.30/1.96 | (58) $false % 5.30/1.96 | % 5.30/1.96 |-The branch is then unsatisfiable % 5.30/1.96 |-Branch two: % 5.30/1.96 | (101) ~ (all_74_3_27 = 0) & element(all_0_9_9, all_17_0_15) = all_74_3_27 % 5.30/1.96 | % 5.30/1.96 | Applying alpha-rule on (101) yields: % 5.30/1.96 | (102) ~ (all_74_3_27 = 0) % 5.30/1.96 | (103) element(all_0_9_9, all_17_0_15) = all_74_3_27 % 5.30/1.96 | % 5.30/1.96 | From (52) and (103) follows: % 5.30/1.96 | (104) element(all_0_9_9, all_0_10_10) = all_74_3_27 % 5.30/1.96 | % 5.30/1.96 | Instantiating formula (32) with all_0_9_9, all_0_10_10, all_74_3_27, 0 and discharging atoms element(all_0_9_9, all_0_10_10) = all_74_3_27, element(all_0_9_9, all_0_10_10) = 0, yields: % 5.30/1.96 | (105) all_74_3_27 = 0 % 5.30/1.96 | % 5.30/1.96 | Equations (105) can reduce 102 to: % 5.30/1.96 | (58) $false % 5.30/1.96 | % 5.30/1.96 |-The branch is then unsatisfiable % 5.30/1.96 % SZS output end Proof for theBenchmark % 5.30/1.96 % 5.30/1.96 1453ms %------------------------------------------------------------------------------