%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU245+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n009.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 08:48:06 EDT 2022 % Result : Theorem 2.47s 1.31s % Output : Proof 3.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.14 % Problem : SEU245+1 : TPTP v8.1.0. Released v3.3.0. % 0.12/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.36 % Computer : n009.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 : Mon Jun 20 11:35:37 EDT 2022 % 0.14/0.36 % CPUTime : % 0.54/0.61 ____ _ % 0.54/0.61 ___ / __ \_____(_)___ ________ __________ % 0.54/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.54/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.54/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.54/0.61 % 0.54/0.61 A Theorem Prover for First-Order Logic % 0.54/0.61 (ePrincess v.1.0) % 0.54/0.61 % 0.54/0.61 (c) Philipp Rümmer, 2009-2015 % 0.54/0.61 (c) Peter Backeman, 2014-2015 % 0.54/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.54/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.54/0.61 Bug reports to peter@backeman.se % 0.54/0.61 % 0.54/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.54/0.61 % 0.54/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.74/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.61/0.96 Prover 0: Preprocessing ... % 1.93/1.13 Prover 0: Warning: ignoring some quantifiers % 1.93/1.15 Prover 0: Constructing countermodel ... % 2.47/1.31 Prover 0: proved (643ms) % 2.47/1.31 % 2.47/1.31 No countermodel exists, formula is valid % 2.47/1.31 % SZS status Theorem for theBenchmark % 2.47/1.31 % 2.47/1.31 Generating proof ... Warning: ignoring some quantifiers % 3.42/1.52 found it (size 19) % 3.42/1.52 % 3.42/1.52 % SZS output start Proof for theBenchmark % 3.42/1.52 Assumed formulas after preprocessing and simplification: % 3.42/1.52 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v1, v1) = v4 & relation_restriction(v2, v1) = v3 & empty(v7) & empty(v6) & empty(empty_set) & one_to_one(v9) & function(v9) & function(v8) & function(v7) & relation(v9) & relation(v8) & relation(v7) & relation(v2) & ~ empty(v5) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (cartesian_product2(v13, v12) = v11) | ~ (cartesian_product2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (relation_restriction(v13, v12) = v11) | ~ (relation_restriction(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_intersection2(v13, v12) = v11) | ~ (set_intersection2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v11, v11) = v12) | ~ (set_intersection2(v10, v12) = v13) | ~ relation(v10) | relation_restriction(v10, v11) = v13) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v10, v11) = v12) | ~ in(v13, v12) | in(v13, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v10, v11) = v12) | ~ in(v13, v12) | in(v13, v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v10, v11) = v12) | ~ in(v13, v11) | ~ in(v13, v10) | in(v13, v12)) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (set_intersection2(v11, v12) = v13) | ? [v14] : (( ~ in(v14, v12) | ~ in(v14, v11) | ~ in(v14, v10)) & (in(v14, v10) | (in(v14, v12) & in(v14, v11))))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_restriction(v10, v11) = v12) | ~ relation(v10) | relation(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_restriction(v10, v11) = v12) | ~ relation(v10) | ? [v13] : (cartesian_product2(v11, v11) = v13 & set_intersection2(v10, v13) = v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v11, v10) = v12) | set_intersection2(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v10, v11) = v12) | set_intersection2(v11, v10) = v12) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_intersection2(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ empty(v11) | ~ empty(v10)) & ! [v10] : ! [v11] : (v11 = empty_set | ~ (set_intersection2(v10, empty_set) = v11)) & ! [v10] : ! [v11] : ( ~ in(v11, v10) | ~ in(v10, v11)) & ! [v10] : ! [v11] : ( ~ in(v10, v11) | ~ empty(v11)) & ! [v10] : ! [v11] : ( ~ in(v10, v11) | element(v10, v11)) & ! [v10] : ! [v11] : ( ~ element(v10, v11) | in(v10, v11) | empty(v11)) & ! [v10] : (v10 = empty_set | ~ empty(v10)) & ! [v10] : ( ~ empty(v10) | ~ function(v10) | ~ relation(v10) | one_to_one(v10)) & ! [v10] : ( ~ empty(v10) | function(v10)) & ? [v10] : ? [v11] : element(v11, v10) & ((in(v0, v4) & in(v0, v2) & ~ in(v0, v3)) | (in(v0, v3) & ( ~ in(v0, v4) | ~ in(v0, v2))))) % 3.53/1.56 | 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, all_0_7_7, all_0_8_8, all_0_9_9 yields: % 3.53/1.56 | (1) cartesian_product2(all_0_8_8, all_0_8_8) = all_0_5_5 & relation_restriction(all_0_7_7, all_0_8_8) = all_0_6_6 & empty(all_0_2_2) & empty(all_0_3_3) & empty(empty_set) & one_to_one(all_0_0_0) & function(all_0_0_0) & function(all_0_1_1) & function(all_0_2_2) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_2_2) & relation(all_0_7_7) & ~ empty(all_0_4_4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v1, v1) = v2) | ~ (set_intersection2(v0, v2) = v3) | ~ relation(v0) | relation_restriction(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ~ relation(v0) | ? [v3] : (cartesian_product2(v1, v1) = v3 & set_intersection2(v0, v3) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = 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 | ~ empty(v0)) & ! [v0] : ( ~ empty(v0) | ~ function(v0) | ~ relation(v0) | one_to_one(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ((in(all_0_9_9, all_0_5_5) & in(all_0_9_9, all_0_7_7) & ~ in(all_0_9_9, all_0_6_6)) | (in(all_0_9_9, all_0_6_6) & ( ~ in(all_0_9_9, all_0_5_5) | ~ in(all_0_9_9, all_0_7_7)))) % 3.53/1.57 | % 3.53/1.57 | Applying alpha-rule on (1) yields: % 3.53/1.57 | (2) function(all_0_0_0) % 3.53/1.57 | (3) ! [v0] : ! [v1] : ( ~ in(v0, v1) | ~ empty(v1)) % 3.53/1.57 | (4) empty(all_0_3_3) % 3.53/1.57 | (5) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 3.53/1.57 | (6) function(all_0_1_1) % 3.53/1.57 | (7) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 3.53/1.57 | (8) relation(all_0_7_7) % 3.53/1.57 | (9) function(all_0_2_2) % 3.53/1.57 | (10) (in(all_0_9_9, all_0_5_5) & in(all_0_9_9, all_0_7_7) & ~ in(all_0_9_9, all_0_6_6)) | (in(all_0_9_9, all_0_6_6) & ( ~ in(all_0_9_9, all_0_5_5) | ~ in(all_0_9_9, all_0_7_7))) % 3.53/1.57 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) % 3.53/1.57 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 3.53/1.57 | (13) ! [v0] : ( ~ empty(v0) | ~ function(v0) | ~ relation(v0) | one_to_one(v0)) % 3.53/1.57 | (14) relation(all_0_0_0) % 3.53/1.57 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) = v0)) % 3.53/1.57 | (16) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 3.53/1.57 | (17) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1))))) % 3.53/1.57 | (18) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 3.53/1.57 | (19) empty(all_0_2_2) % 3.53/1.57 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 3.53/1.57 | (21) empty(empty_set) % 3.53/1.57 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 3.53/1.57 | (23) relation(all_0_1_1) % 3.53/1.57 | (24) ? [v0] : ? [v1] : element(v1, v0) % 3.53/1.57 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ~ relation(v0) | ? [v3] : (cartesian_product2(v1, v1) = v3 & set_intersection2(v0, v3) = v2)) % 3.53/1.57 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) % 3.53/1.57 | (27) one_to_one(all_0_0_0) % 3.53/1.57 | (28) ! [v0] : ( ~ empty(v0) | function(v0)) % 3.53/1.57 | (29) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 3.53/1.57 | (30) ! [v0] : ! [v1] : ( ~ element(v0, v1) | in(v0, v1) | empty(v1)) % 3.53/1.57 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v1, v1) = v2) | ~ (set_intersection2(v0, v2) = v3) | ~ relation(v0) | relation_restriction(v0, v1) = v3) % 3.53/1.57 | (32) cartesian_product2(all_0_8_8, all_0_8_8) = all_0_5_5 % 3.53/1.57 | (33) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 3.53/1.57 | (34) relation(all_0_2_2) % 3.53/1.57 | (35) relation_restriction(all_0_7_7, all_0_8_8) = all_0_6_6 % 3.53/1.57 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 3.53/1.58 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) % 3.53/1.58 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) % 3.53/1.58 | (39) ~ empty(all_0_4_4) % 3.53/1.58 | % 3.53/1.58 | Instantiating formula (25) with all_0_6_6, all_0_8_8, all_0_7_7 and discharging atoms relation_restriction(all_0_7_7, all_0_8_8) = all_0_6_6, relation(all_0_7_7), yields: % 3.53/1.58 | (40) ? [v0] : (cartesian_product2(all_0_8_8, all_0_8_8) = v0 & set_intersection2(all_0_7_7, v0) = all_0_6_6) % 3.53/1.58 | % 3.53/1.58 | Instantiating (40) with all_17_0_13 yields: % 3.53/1.58 | (41) cartesian_product2(all_0_8_8, all_0_8_8) = all_17_0_13 & set_intersection2(all_0_7_7, all_17_0_13) = all_0_6_6 % 3.53/1.58 | % 3.53/1.58 | Applying alpha-rule on (41) yields: % 3.53/1.58 | (42) cartesian_product2(all_0_8_8, all_0_8_8) = all_17_0_13 % 3.53/1.58 | (43) set_intersection2(all_0_7_7, all_17_0_13) = all_0_6_6 % 3.53/1.58 | % 3.53/1.58 | Instantiating formula (12) with all_0_8_8, all_0_8_8, all_17_0_13, all_0_5_5 and discharging atoms cartesian_product2(all_0_8_8, all_0_8_8) = all_17_0_13, cartesian_product2(all_0_8_8, all_0_8_8) = all_0_5_5, yields: % 3.53/1.58 | (44) all_17_0_13 = all_0_5_5 % 3.53/1.58 | % 3.53/1.58 | From (44) and (43) follows: % 3.53/1.58 | (45) set_intersection2(all_0_7_7, all_0_5_5) = all_0_6_6 % 3.53/1.58 | % 3.53/1.58 +-Applying beta-rule and splitting (10), into two cases. % 3.53/1.58 |-Branch one: % 3.53/1.58 | (46) in(all_0_9_9, all_0_5_5) & in(all_0_9_9, all_0_7_7) & ~ in(all_0_9_9, all_0_6_6) % 3.53/1.58 | % 3.53/1.58 | Applying alpha-rule on (46) yields: % 3.53/1.58 | (47) in(all_0_9_9, all_0_5_5) % 3.53/1.58 | (48) in(all_0_9_9, all_0_7_7) % 3.53/1.58 | (49) ~ in(all_0_9_9, all_0_6_6) % 3.53/1.58 | % 3.53/1.58 | Instantiating formula (11) with all_0_9_9, all_0_6_6, all_0_5_5, all_0_7_7 and discharging atoms set_intersection2(all_0_7_7, all_0_5_5) = all_0_6_6, in(all_0_9_9, all_0_5_5), in(all_0_9_9, all_0_7_7), ~ in(all_0_9_9, all_0_6_6), yields: % 3.53/1.58 | (50) $false % 3.53/1.58 | % 3.53/1.58 |-The branch is then unsatisfiable % 3.53/1.58 |-Branch two: % 3.53/1.58 | (51) in(all_0_9_9, all_0_6_6) & ( ~ in(all_0_9_9, all_0_5_5) | ~ in(all_0_9_9, all_0_7_7)) % 3.53/1.58 | % 3.53/1.58 | Applying alpha-rule on (51) yields: % 3.53/1.58 | (52) in(all_0_9_9, all_0_6_6) % 3.53/1.58 | (53) ~ in(all_0_9_9, all_0_5_5) | ~ in(all_0_9_9, all_0_7_7) % 3.53/1.58 | % 3.53/1.58 | Instantiating formula (26) with all_0_9_9, all_0_6_6, all_0_5_5, all_0_7_7 and discharging atoms set_intersection2(all_0_7_7, all_0_5_5) = all_0_6_6, in(all_0_9_9, all_0_6_6), yields: % 3.53/1.58 | (47) in(all_0_9_9, all_0_5_5) % 3.53/1.58 | % 3.53/1.58 | Instantiating formula (20) with all_0_9_9, all_0_6_6, all_0_5_5, all_0_7_7 and discharging atoms set_intersection2(all_0_7_7, all_0_5_5) = all_0_6_6, in(all_0_9_9, all_0_6_6), yields: % 3.53/1.58 | (48) in(all_0_9_9, all_0_7_7) % 3.53/1.58 | % 3.53/1.58 +-Applying beta-rule and splitting (53), into two cases. % 3.53/1.58 |-Branch one: % 3.53/1.58 | (56) ~ in(all_0_9_9, all_0_5_5) % 3.53/1.58 | % 3.53/1.58 | Using (47) and (56) yields: % 3.53/1.58 | (50) $false % 3.53/1.58 | % 3.53/1.58 |-The branch is then unsatisfiable % 3.53/1.58 |-Branch two: % 3.53/1.58 | (47) in(all_0_9_9, all_0_5_5) % 3.53/1.58 | (59) ~ in(all_0_9_9, all_0_7_7) % 3.53/1.59 | % 3.53/1.59 | Using (48) and (59) yields: % 3.53/1.59 | (50) $false % 3.53/1.59 | % 3.53/1.59 |-The branch is then unsatisfiable % 3.53/1.59 % SZS output end Proof for theBenchmark % 3.53/1.59 % 3.53/1.59 961ms %------------------------------------------------------------------------------