%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU172+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n020.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 08:47:17 EDT 2022 % Result : Theorem 2.48s 1.30s % Output : Proof 3.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU172+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n020.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Mon Jun 20 01:30:18 EDT 2022 % 0.13/0.34 % CPUTime : % 0.48/0.58 ____ _ % 0.48/0.58 ___ / __ \_____(_)___ ________ __________ % 0.48/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.48/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.48/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.48/0.58 % 0.48/0.58 A Theorem Prover for First-Order Logic % 0.48/0.58 (ePrincess v.1.0) % 0.48/0.58 % 0.48/0.58 (c) Philipp Rümmer, 2009-2015 % 0.48/0.58 (c) Peter Backeman, 2014-2015 % 0.48/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.48/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.48/0.58 Bug reports to peter@backeman.se % 0.48/0.58 % 0.48/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.48/0.58 % 0.48/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.27/0.92 Prover 0: Preprocessing ... % 1.90/1.10 Prover 0: Warning: ignoring some quantifiers % 1.99/1.14 Prover 0: Constructing countermodel ... % 2.48/1.30 Prover 0: proved (665ms) % 2.48/1.30 % 2.48/1.30 No countermodel exists, formula is valid % 2.48/1.30 % SZS status Theorem for theBenchmark % 2.48/1.30 % 2.48/1.30 Generating proof ... Warning: ignoring some quantifiers % 3.01/1.52 found it (size 24) % 3.01/1.52 % 3.01/1.52 % SZS output start Proof for theBenchmark % 3.01/1.52 Assumed formulas after preprocessing and simplification: % 3.01/1.52 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (subset_complement(v0, v2) = v4 & powerset(v0) = v3 & in(v1, v4) & in(v1, v2) & element(v2, v3) & empty(v6) & empty(empty_set) & ~ empty(v5) & ! [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 | ~ (subset_complement(v10, v9) = v8) | ~ (subset_complement(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_difference(v10, v9) = v8) | ~ (set_difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v8) = v9) | ~ in(v10, v9) | ~ in(v10, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v8) = v9) | ~ in(v10, v9) | in(v10, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v8) = v9) | ~ in(v10, v7) | in(v10, v9) | in(v10, v8)) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_difference(v8, v9) = v10) | ? [v11] : (( ~ in(v11, v8) | ~ in(v11, v7) | in(v11, v9)) & (in(v11, v7) | (in(v11, v8) & ~ in(v11, v9))))) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (powerset(v9) = v8) | ~ (powerset(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset_complement(v7, v8) = v9) | ? [v10] : ? [v11] : (powerset(v7) = v10 & set_difference(v7, v8) = v11 & (v11 = v9 | ~ element(v8, v10)))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset_complement(v7, v8) = v9) | ? [v10] : (powerset(v7) = v10 & ( ~ element(v8, v10) | element(v9, v10)))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_difference(v7, v8) = v9) | ? [v10] : ? [v11] : (subset_complement(v7, v8) = v11 & powerset(v7) = v10 & (v11 = v9 | ~ element(v8, v10)))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_difference(v7, empty_set) = v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ empty(v8) | ~ empty(v7)) & ! [v7] : ! [v8] : (v8 = empty_set | ~ (set_difference(empty_set, v7) = v8)) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ~ empty(v8)) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | empty(v7) | ? [v9] : (element(v9, v8) & ~ empty(v9))) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ? [v9] : (element(v9, v8) & empty(v9))) & ! [v7] : ! [v8] : ( ~ in(v8, v7) | ~ in(v7, v8)) & ! [v7] : ! [v8] : ( ~ in(v7, v8) | ~ empty(v8)) & ! [v7] : (v7 = empty_set | ~ empty(v7)) & ? [v7] : ? [v8] : element(v8, v7)) % 3.29/1.56 | 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: % 3.29/1.56 | (1) subset_complement(all_0_6_6, all_0_4_4) = all_0_2_2 & powerset(all_0_6_6) = all_0_3_3 & in(all_0_5_5, all_0_2_2) & in(all_0_5_5, all_0_4_4) & element(all_0_4_4, all_0_3_3) & empty(all_0_0_0) & empty(empty_set) & ~ empty(all_0_1_1) & ! [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 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v1) | ~ in(v4, v0) | in(v4, v2)) & (in(v4, v0) | (in(v4, v1) & ~ in(v4, v2))))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v0) = v3 & set_difference(v0, v1) = v4 & (v4 = v2 | ~ element(v1, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | ~ empty(v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ? [v0] : ? [v1] : element(v1, v0) % 3.29/1.57 | % 3.29/1.57 | Applying alpha-rule on (1) yields: % 3.29/1.57 | (2) in(all_0_5_5, all_0_2_2) % 3.29/1.57 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) % 3.29/1.57 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) % 3.29/1.57 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1)) % 3.29/1.57 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) % 3.29/1.57 | (7) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) % 3.29/1.57 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 3.29/1.57 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 3.29/1.57 | (10) ? [v0] : ? [v1] : element(v1, v0) % 3.29/1.57 | (11) element(all_0_4_4, all_0_3_3) % 3.29/1.57 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) % 3.29/1.57 | (13) powerset(all_0_6_6) = all_0_3_3 % 3.29/1.57 | (14) subset_complement(all_0_6_6, all_0_4_4) = all_0_2_2 % 3.29/1.57 | (15) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) % 3.29/1.57 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 3.29/1.57 | (17) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 3.29/1.57 | (18) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v1) | ~ in(v4, v0) | in(v4, v2)) & (in(v4, v0) | (in(v4, v1) & ~ in(v4, v2))))) % 3.29/1.57 | (19) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 3.29/1.57 | (20) ! [v0] : ! [v1] : ( ~ in(v0, v1) | ~ empty(v1)) % 3.29/1.57 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 3.29/1.57 | (22) in(all_0_5_5, all_0_4_4) % 3.29/1.57 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) % 3.29/1.57 | (24) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 3.29/1.57 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) % 3.29/1.57 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v0) = v3 & set_difference(v0, v1) = v4 & (v4 = v2 | ~ element(v1, v3)))) % 3.29/1.57 | (27) empty(empty_set) % 3.29/1.57 | (28) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 3.29/1.58 | (29) ~ empty(all_0_1_1) % 3.29/1.58 | (30) empty(all_0_0_0) % 3.29/1.58 | % 3.29/1.58 | Instantiating formula (26) with all_0_2_2, all_0_4_4, all_0_6_6 and discharging atoms subset_complement(all_0_6_6, all_0_4_4) = all_0_2_2, yields: % 3.29/1.58 | (31) ? [v0] : ? [v1] : (powerset(all_0_6_6) = v0 & set_difference(all_0_6_6, all_0_4_4) = v1 & (v1 = all_0_2_2 | ~ element(all_0_4_4, v0))) % 3.29/1.58 | % 3.29/1.58 | Instantiating formula (4) with all_0_2_2, all_0_4_4, all_0_6_6 and discharging atoms subset_complement(all_0_6_6, all_0_4_4) = all_0_2_2, yields: % 3.29/1.58 | (32) ? [v0] : (powerset(all_0_6_6) = v0 & ( ~ element(all_0_4_4, v0) | element(all_0_2_2, v0))) % 3.29/1.58 | % 3.29/1.58 | Instantiating (32) with all_18_0_11 yields: % 3.29/1.58 | (33) powerset(all_0_6_6) = all_18_0_11 & ( ~ element(all_0_4_4, all_18_0_11) | element(all_0_2_2, all_18_0_11)) % 3.29/1.58 | % 3.29/1.58 | Applying alpha-rule on (33) yields: % 3.29/1.58 | (34) powerset(all_0_6_6) = all_18_0_11 % 3.29/1.58 | (35) ~ element(all_0_4_4, all_18_0_11) | element(all_0_2_2, all_18_0_11) % 3.29/1.58 | % 3.29/1.58 | Instantiating (31) with all_20_0_12, all_20_1_13 yields: % 3.29/1.58 | (36) powerset(all_0_6_6) = all_20_1_13 & set_difference(all_0_6_6, all_0_4_4) = all_20_0_12 & (all_20_0_12 = all_0_2_2 | ~ element(all_0_4_4, all_20_1_13)) % 3.29/1.58 | % 3.29/1.58 | Applying alpha-rule on (36) yields: % 3.29/1.58 | (37) powerset(all_0_6_6) = all_20_1_13 % 3.29/1.58 | (38) set_difference(all_0_6_6, all_0_4_4) = all_20_0_12 % 3.29/1.58 | (39) all_20_0_12 = all_0_2_2 | ~ element(all_0_4_4, all_20_1_13) % 3.29/1.58 | % 3.29/1.58 | Instantiating formula (21) with all_0_6_6, all_20_1_13, all_0_3_3 and discharging atoms powerset(all_0_6_6) = all_20_1_13, powerset(all_0_6_6) = all_0_3_3, yields: % 3.29/1.58 | (40) all_20_1_13 = all_0_3_3 % 3.29/1.58 | % 3.29/1.58 | Instantiating formula (21) with all_0_6_6, all_18_0_11, all_20_1_13 and discharging atoms powerset(all_0_6_6) = all_20_1_13, powerset(all_0_6_6) = all_18_0_11, yields: % 3.29/1.58 | (41) all_20_1_13 = all_18_0_11 % 3.29/1.58 | % 3.29/1.58 | Combining equations (40,41) yields a new equation: % 3.29/1.58 | (42) all_18_0_11 = all_0_3_3 % 3.29/1.58 | % 3.29/1.58 | Combining equations (42,41) yields a new equation: % 3.29/1.58 | (40) all_20_1_13 = all_0_3_3 % 3.29/1.58 | % 3.29/1.58 +-Applying beta-rule and splitting (35), into two cases. % 3.29/1.58 |-Branch one: % 3.29/1.58 | (44) ~ element(all_0_4_4, all_18_0_11) % 3.29/1.58 | % 3.29/1.58 | From (42) and (44) follows: % 3.29/1.58 | (45) ~ element(all_0_4_4, all_0_3_3) % 3.29/1.58 | % 3.29/1.58 | Using (11) and (45) yields: % 3.48/1.58 | (46) $false % 3.48/1.58 | % 3.48/1.58 |-The branch is then unsatisfiable % 3.48/1.58 |-Branch two: % 3.48/1.58 | (47) element(all_0_4_4, all_18_0_11) % 3.48/1.58 | (48) element(all_0_2_2, all_18_0_11) % 3.48/1.58 | % 3.48/1.58 | From (42) and (47) follows: % 3.48/1.58 | (11) element(all_0_4_4, all_0_3_3) % 3.48/1.58 | % 3.48/1.58 +-Applying beta-rule and splitting (39), into two cases. % 3.48/1.58 |-Branch one: % 3.48/1.58 | (50) ~ element(all_0_4_4, all_20_1_13) % 3.48/1.58 | % 3.48/1.58 | From (40) and (50) follows: % 3.48/1.58 | (45) ~ element(all_0_4_4, all_0_3_3) % 3.48/1.58 | % 3.48/1.58 | Using (11) and (45) yields: % 3.48/1.58 | (46) $false % 3.48/1.58 | % 3.48/1.58 |-The branch is then unsatisfiable % 3.48/1.58 |-Branch two: % 3.48/1.58 | (53) element(all_0_4_4, all_20_1_13) % 3.48/1.58 | (54) all_20_0_12 = all_0_2_2 % 3.48/1.59 | % 3.48/1.59 | From (54) and (38) follows: % 3.48/1.59 | (55) set_difference(all_0_6_6, all_0_4_4) = all_0_2_2 % 3.48/1.59 | % 3.48/1.59 | Instantiating formula (5) with all_0_5_5, all_0_2_2, all_0_4_4, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_0_4_4) = all_0_2_2, in(all_0_5_5, all_0_2_2), in(all_0_5_5, all_0_4_4), yields: % 3.48/1.59 | (46) $false % 3.48/1.59 | % 3.48/1.59 |-The branch is then unsatisfiable % 3.48/1.59 % SZS output end Proof for theBenchmark % 3.48/1.59 % 3.48/1.59 995ms %------------------------------------------------------------------------------