%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU189+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n004.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 08:47:27 EDT 2022 % Result : Theorem 2.49s 1.26s % Output : Proof 3.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU189+1 : TPTP v8.1.0. Released v3.3.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n004.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 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon Jun 20 11:15:23 EDT 2022 % 0.13/0.33 % CPUTime : % 0.19/0.58 ____ _ % 0.19/0.58 ___ / __ \_____(_)___ ________ __________ % 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.58 % 0.19/0.58 A Theorem Prover for First-Order Logic % 0.19/0.58 (ePrincess v.1.0) % 0.19/0.58 % 0.19/0.58 (c) Philipp Rümmer, 2009-2015 % 0.19/0.58 (c) Peter Backeman, 2014-2015 % 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.58 Bug reports to peter@backeman.se % 0.19/0.58 % 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.58 % 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.77/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.58/0.94 Prover 0: Preprocessing ... % 1.97/1.11 Prover 0: Warning: ignoring some quantifiers % 1.97/1.13 Prover 0: Constructing countermodel ... % 2.49/1.26 Prover 0: proved (628ms) % 2.49/1.26 % 2.49/1.26 No countermodel exists, formula is valid % 2.49/1.26 % SZS status Theorem for theBenchmark % 2.49/1.26 % 2.49/1.26 Generating proof ... Warning: ignoring some quantifiers % 3.30/1.52 found it (size 25) % 3.30/1.52 % 3.30/1.52 % SZS output start Proof for theBenchmark % 3.30/1.52 Assumed formulas after preprocessing and simplification: % 3.30/1.52 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v2 & relation_rng(empty_set) = empty_set & relation_dom(v0) = v1 & relation_dom(empty_set) = empty_set & relation(v6) & relation(v5) & relation(v0) & relation(empty_set) & empty(v6) & empty(v4) & empty(empty_set) & ~ empty(v5) & ~ empty(v3) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (relation_rng(v9) = v8) | ~ (relation_rng(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (relation_dom(v9) = v8) | ~ (relation_dom(v9) = v7)) & ! [v7] : ! [v8] : (v8 = v7 | ~ empty(v8) | ~ empty(v7)) & ! [v7] : ! [v8] : (v7 = empty_set | ~ (relation_rng(v7) = v8) | ~ relation(v7) | ? [v9] : ( ~ (v9 = empty_set) & relation_dom(v7) = v9)) & ! [v7] : ! [v8] : (v7 = empty_set | ~ (relation_dom(v7) = v8) | ~ relation(v7) | ? [v9] : ( ~ (v9 = empty_set) & relation_rng(v7) = v9)) & ! [v7] : ! [v8] : ( ~ (relation_rng(v7) = v8) | ~ relation(v7) | ~ empty(v8) | empty(v7)) & ! [v7] : ! [v8] : ( ~ (relation_rng(v7) = v8) | ~ empty(v7) | relation(v8)) & ! [v7] : ! [v8] : ( ~ (relation_rng(v7) = v8) | ~ empty(v7) | empty(v8)) & ! [v7] : ! [v8] : ( ~ (relation_dom(v7) = v8) | ~ relation(v7) | ~ empty(v8) | empty(v7)) & ! [v7] : ! [v8] : ( ~ (relation_dom(v7) = v8) | ~ empty(v7) | relation(v8)) & ! [v7] : ! [v8] : ( ~ (relation_dom(v7) = v8) | ~ empty(v7) | empty(v8)) & ! [v7] : ! [v8] : ( ~ in(v8, v7) | ~ in(v7, v8)) & ! [v7] : ! [v8] : ( ~ in(v7, v8) | ~ empty(v8)) & ! [v7] : ! [v8] : ( ~ in(v7, v8) | element(v7, v8)) & ! [v7] : ! [v8] : ( ~ element(v7, v8) | in(v7, v8) | empty(v8)) & ! [v7] : (v7 = empty_set | ~ (relation_rng(v7) = empty_set) | ~ relation(v7)) & ! [v7] : (v7 = empty_set | ~ (relation_dom(v7) = empty_set) | ~ relation(v7)) & ! [v7] : (v7 = empty_set | ~ empty(v7)) & ! [v7] : ( ~ empty(v7) | relation(v7)) & ? [v7] : ? [v8] : element(v8, v7) & ((v2 = empty_set & ~ (v1 = empty_set)) | (v1 = empty_set & ~ (v2 = empty_set)))) % 3.30/1.56 | 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: % 3.30/1.56 | (1) relation_rng(all_0_6_6) = all_0_4_4 & relation_rng(empty_set) = empty_set & relation_dom(all_0_6_6) = all_0_5_5 & relation_dom(empty_set) = empty_set & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_6_6) & relation(empty_set) & empty(all_0_0_0) & empty(all_0_2_2) & empty(empty_set) & ~ empty(all_0_1_1) & ~ empty(all_0_3_3) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_dom(v0) = v2)) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_rng(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | in(v0, v1) | empty(v1)) & ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0)) & ! [v0] : (v0 = empty_set | ~ (relation_dom(v0) = empty_set) | ~ relation(v0)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ((all_0_4_4 = empty_set & ~ (all_0_5_5 = empty_set)) | (all_0_5_5 = empty_set & ~ (all_0_4_4 = empty_set))) % 3.30/1.56 | % 3.30/1.56 | Applying alpha-rule on (1) yields: % 3.30/1.56 | (2) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) % 3.30/1.56 | (3) empty(all_0_0_0) % 3.30/1.57 | (4) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 3.30/1.57 | (5) ~ empty(all_0_1_1) % 3.30/1.57 | (6) ~ empty(all_0_3_3) % 3.59/1.57 | (7) ! [v0] : (v0 = empty_set | ~ (relation_dom(v0) = empty_set) | ~ relation(v0)) % 3.59/1.57 | (8) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_rng(v0) = v2)) % 3.59/1.57 | (9) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) % 3.59/1.57 | (10) relation_rng(empty_set) = empty_set % 3.59/1.57 | (11) ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0)) % 3.59/1.57 | (12) relation_rng(all_0_6_6) = all_0_4_4 % 3.59/1.57 | (13) ! [v0] : ( ~ empty(v0) | relation(v0)) % 3.59/1.57 | (14) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 3.59/1.57 | (15) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) % 3.59/1.57 | (16) empty(empty_set) % 3.59/1.57 | (17) relation(all_0_6_6) % 3.59/1.57 | (18) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_dom(v0) = v2)) % 3.59/1.57 | (19) (all_0_4_4 = empty_set & ~ (all_0_5_5 = empty_set)) | (all_0_5_5 = empty_set & ~ (all_0_4_4 = empty_set)) % 3.59/1.57 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 3.59/1.57 | (21) relation(all_0_1_1) % 3.59/1.57 | (22) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 3.59/1.57 | (23) ? [v0] : ? [v1] : element(v1, v0) % 3.59/1.57 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 3.59/1.57 | (25) relation(empty_set) % 3.59/1.57 | (26) ! [v0] : ! [v1] : ( ~ element(v0, v1) | in(v0, v1) | empty(v1)) % 3.59/1.57 | (27) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 3.59/1.57 | (28) relation_dom(all_0_6_6) = all_0_5_5 % 3.59/1.57 | (29) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 3.59/1.57 | (30) ! [v0] : ! [v1] : ( ~ in(v0, v1) | ~ empty(v1)) % 3.59/1.57 | (31) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) % 3.59/1.57 | (32) relation_dom(empty_set) = empty_set % 3.59/1.57 | (33) relation(all_0_0_0) % 3.59/1.57 | (34) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 3.59/1.57 | (35) empty(all_0_2_2) % 3.59/1.57 | % 3.59/1.57 | Instantiating formula (18) with all_0_4_4, all_0_6_6 and discharging atoms relation_rng(all_0_6_6) = all_0_4_4, relation(all_0_6_6), yields: % 3.59/1.57 | (36) all_0_6_6 = empty_set | ? [v0] : ( ~ (v0 = empty_set) & relation_dom(all_0_6_6) = v0) % 3.59/1.57 | % 3.59/1.57 | Instantiating formula (8) with all_0_5_5, all_0_6_6 and discharging atoms relation_dom(all_0_6_6) = all_0_5_5, relation(all_0_6_6), yields: % 3.59/1.58 | (37) all_0_6_6 = empty_set | ? [v0] : ( ~ (v0 = empty_set) & relation_rng(all_0_6_6) = v0) % 3.59/1.58 | % 3.59/1.58 +-Applying beta-rule and splitting (19), into two cases. % 3.59/1.58 |-Branch one: % 3.59/1.58 | (38) all_0_4_4 = empty_set & ~ (all_0_5_5 = empty_set) % 3.59/1.58 | % 3.59/1.58 | Applying alpha-rule on (38) yields: % 3.59/1.58 | (39) all_0_4_4 = empty_set % 3.59/1.58 | (40) ~ (all_0_5_5 = empty_set) % 3.59/1.58 | % 3.59/1.58 | From (39) and (12) follows: % 3.59/1.58 | (41) relation_rng(all_0_6_6) = empty_set % 3.59/1.58 | % 3.59/1.58 +-Applying beta-rule and splitting (37), into two cases. % 3.59/1.58 |-Branch one: % 3.59/1.58 | (42) all_0_6_6 = empty_set % 3.59/1.58 | % 3.59/1.58 | From (42) and (28) follows: % 3.59/1.58 | (43) relation_dom(empty_set) = all_0_5_5 % 3.59/1.58 | % 3.59/1.58 | Instantiating formula (24) with empty_set, all_0_5_5, empty_set and discharging atoms relation_dom(empty_set) = all_0_5_5, relation_dom(empty_set) = empty_set, yields: % 3.59/1.58 | (44) all_0_5_5 = empty_set % 3.59/1.58 | % 3.59/1.58 | Equations (44) can reduce 40 to: % 3.59/1.58 | (45) $false % 3.59/1.58 | % 3.59/1.58 |-The branch is then unsatisfiable % 3.59/1.58 |-Branch two: % 3.59/1.58 | (46) ~ (all_0_6_6 = empty_set) % 3.59/1.58 | (47) ? [v0] : ( ~ (v0 = empty_set) & relation_rng(all_0_6_6) = v0) % 3.59/1.58 | % 3.59/1.58 | Instantiating formula (11) with all_0_6_6 and discharging atoms relation_rng(all_0_6_6) = empty_set, relation(all_0_6_6), yields: % 3.59/1.58 | (42) all_0_6_6 = empty_set % 3.59/1.58 | % 3.59/1.58 | Equations (42) can reduce 46 to: % 3.59/1.58 | (45) $false % 3.59/1.58 | % 3.59/1.58 |-The branch is then unsatisfiable % 3.59/1.58 |-Branch two: % 3.59/1.58 | (50) all_0_5_5 = empty_set & ~ (all_0_4_4 = empty_set) % 3.59/1.58 | % 3.59/1.58 | Applying alpha-rule on (50) yields: % 3.59/1.58 | (44) all_0_5_5 = empty_set % 3.59/1.58 | (52) ~ (all_0_4_4 = empty_set) % 3.59/1.58 | % 3.59/1.58 | From (44) and (28) follows: % 3.59/1.58 | (53) relation_dom(all_0_6_6) = empty_set % 3.59/1.58 | % 3.59/1.58 +-Applying beta-rule and splitting (36), into two cases. % 3.59/1.58 |-Branch one: % 3.59/1.58 | (42) all_0_6_6 = empty_set % 3.59/1.58 | % 3.59/1.58 | From (42) and (12) follows: % 3.59/1.58 | (55) relation_rng(empty_set) = all_0_4_4 % 3.59/1.58 | % 3.59/1.58 | Instantiating formula (20) with empty_set, all_0_4_4, empty_set and discharging atoms relation_rng(empty_set) = all_0_4_4, relation_rng(empty_set) = empty_set, yields: % 3.59/1.58 | (39) all_0_4_4 = empty_set % 3.59/1.58 | % 3.59/1.58 | Equations (39) can reduce 52 to: % 3.59/1.58 | (45) $false % 3.59/1.58 | % 3.59/1.58 |-The branch is then unsatisfiable % 3.59/1.58 |-Branch two: % 3.59/1.58 | (46) ~ (all_0_6_6 = empty_set) % 3.59/1.58 | (59) ? [v0] : ( ~ (v0 = empty_set) & relation_dom(all_0_6_6) = v0) % 3.59/1.58 | % 3.59/1.58 | Instantiating formula (7) with all_0_6_6 and discharging atoms relation_dom(all_0_6_6) = empty_set, relation(all_0_6_6), yields: % 3.59/1.58 | (42) all_0_6_6 = empty_set % 3.59/1.58 | % 3.59/1.58 | Equations (42) can reduce 46 to: % 3.59/1.58 | (45) $false % 3.59/1.58 | % 3.59/1.58 |-The branch is then unsatisfiable % 3.59/1.58 % SZS output end Proof for theBenchmark % 3.59/1.58 % 3.59/1.58 994ms %------------------------------------------------------------------------------