%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU219+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n005.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 08:47:46 EDT 2022 % Result : Theorem 2.16s 1.18s % Output : Proof 2.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU219+1 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n005.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sun Jun 19 17:08:23 EDT 2022 % 0.12/0.33 % CPUTime : % 0.56/0.57 ____ _ % 0.56/0.57 ___ / __ \_____(_)___ ________ __________ % 0.56/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.56/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.56/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.56/0.57 % 0.56/0.57 A Theorem Prover for First-Order Logic % 0.56/0.57 (ePrincess v.1.0) % 0.56/0.57 % 0.56/0.57 (c) Philipp Rümmer, 2009-2015 % 0.56/0.57 (c) Peter Backeman, 2014-2015 % 0.56/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.56/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.56/0.57 Bug reports to peter@backeman.se % 0.56/0.57 % 0.56/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.56/0.57 % 0.56/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.61/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.41/0.89 Prover 0: Preprocessing ... % 1.74/1.07 Prover 0: Constructing countermodel ... % 2.16/1.18 Prover 0: proved (563ms) % 2.16/1.18 % 2.16/1.18 No countermodel exists, formula is valid % 2.16/1.18 % SZS status Theorem for theBenchmark % 2.16/1.18 % 2.16/1.18 Generating proof ... found it (size 22) % 2.64/1.36 % 2.64/1.36 % SZS output start Proof for theBenchmark % 2.64/1.36 Assumed formulas after preprocessing and simplification: % 2.64/1.36 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v2) = v3 & relation_dom(v0) = v4 & relation_rng(v2) = v5 & relation_rng(v0) = v1 & function_inverse(v0) = v2 & one_to_one(v6) & one_to_one(v0) & function(v7) & function(v6) & function(v0) & relation(v7) & relation(v6) & relation(v0) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (relation_dom(v10) = v9) | ~ (relation_dom(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (relation_rng(v10) = v9) | ~ (relation_rng(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (relation_inverse(v10) = v9) | ~ (relation_inverse(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (function_inverse(v10) = v9) | ~ (function_inverse(v10) = v8)) & ! [v8] : ! [v9] : ( ~ (relation_dom(v8) = v9) | ~ relation(v8) | ? [v10] : ? [v11] : (relation_dom(v11) = v10 & relation_rng(v11) = v9 & relation_rng(v8) = v10 & relation_inverse(v8) = v11)) & ! [v8] : ! [v9] : ( ~ (relation_rng(v8) = v9) | ~ relation(v8) | ? [v10] : ? [v11] : (relation_dom(v10) = v9 & relation_dom(v8) = v11 & relation_rng(v10) = v11 & relation_inverse(v8) = v10)) & ! [v8] : ! [v9] : ( ~ (relation_inverse(v8) = v9) | ~ one_to_one(v8) | ~ function(v8) | ~ relation(v8) | function_inverse(v8) = v9) & ! [v8] : ! [v9] : ( ~ (relation_inverse(v8) = v9) | ~ one_to_one(v8) | ~ function(v8) | ~ relation(v8) | function(v9)) & ! [v8] : ! [v9] : ( ~ (relation_inverse(v8) = v9) | ~ one_to_one(v8) | ~ function(v8) | ~ relation(v8) | relation(v9)) & ! [v8] : ! [v9] : ( ~ (relation_inverse(v8) = v9) | ~ relation(v8) | relation_inverse(v9) = v8) & ! [v8] : ! [v9] : ( ~ (relation_inverse(v8) = v9) | ~ relation(v8) | relation(v9)) & ! [v8] : ! [v9] : ( ~ (relation_inverse(v8) = v9) | ~ relation(v8) | ? [v10] : ? [v11] : (relation_dom(v9) = v10 & relation_dom(v8) = v11 & relation_rng(v9) = v11 & relation_rng(v8) = v10)) & ! [v8] : ! [v9] : ( ~ (function_inverse(v8) = v9) | ~ one_to_one(v8) | ~ function(v8) | ~ relation(v8) | relation_inverse(v8) = v9) & ! [v8] : ! [v9] : ( ~ (function_inverse(v8) = v9) | ~ function(v8) | ~ relation(v8) | function(v9)) & ! [v8] : ! [v9] : ( ~ (function_inverse(v8) = v9) | ~ function(v8) | ~ relation(v8) | relation(v9)) & ( ~ (v5 = v4) | ~ (v3 = v1))) % 2.84/1.40 | 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 yields: % 2.84/1.40 | (1) relation_dom(all_0_5_5) = all_0_4_4 & relation_dom(all_0_7_7) = all_0_3_3 & relation_rng(all_0_5_5) = all_0_2_2 & relation_rng(all_0_7_7) = all_0_6_6 & function_inverse(all_0_7_7) = all_0_5_5 & one_to_one(all_0_1_1) & one_to_one(all_0_7_7) & function(all_0_0_0) & function(all_0_1_1) & function(all_0_7_7) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_7_7) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v3) = v2 & relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_inverse(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v2) = v1 & relation_dom(v0) = v3 & relation_rng(v2) = v3 & relation_inverse(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ function(v0) | ~ relation(v0) | function_inverse(v0) = v1) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ function(v0) | ~ relation(v0) | function(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ function(v0) | ~ relation(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation_inverse(v1) = v0) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v2 & relation_dom(v0) = v3 & relation_rng(v1) = v3 & relation_rng(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ function(v0) | ~ relation(v0) | relation_inverse(v0) = v1) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ function(v0) | ~ relation(v0) | function(v1)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ function(v0) | ~ relation(v0) | relation(v1)) & ( ~ (all_0_2_2 = all_0_3_3) | ~ (all_0_4_4 = all_0_6_6)) % 2.84/1.41 | % 2.84/1.41 | Applying alpha-rule on (1) yields: % 2.84/1.41 | (2) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation(v1)) % 2.84/1.41 | (3) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ function(v0) | ~ relation(v0) | function(v1)) % 2.84/1.41 | (4) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ function(v0) | ~ relation(v0) | relation_inverse(v0) = v1) % 2.84/1.41 | (5) relation(all_0_7_7) % 2.84/1.41 | (6) relation_dom(all_0_5_5) = all_0_4_4 % 2.84/1.41 | (7) function(all_0_7_7) % 2.84/1.41 | (8) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v2) = v1 & relation_dom(v0) = v3 & relation_rng(v2) = v3 & relation_inverse(v0) = v2)) % 2.84/1.41 | (9) ~ (all_0_2_2 = all_0_3_3) | ~ (all_0_4_4 = all_0_6_6) % 2.84/1.41 | (10) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ function(v0) | ~ relation(v0) | function_inverse(v0) = v1) % 2.84/1.41 | (11) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v2 & relation_dom(v0) = v3 & relation_rng(v1) = v3 & relation_rng(v0) = v2)) % 2.84/1.41 | (12) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ function(v0) | ~ relation(v0) | relation(v1)) % 2.84/1.41 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 2.84/1.41 | (14) relation(all_0_0_0) % 2.84/1.41 | (15) relation_dom(all_0_7_7) = all_0_3_3 % 2.84/1.41 | (16) function(all_0_1_1) % 2.84/1.41 | (17) relation_rng(all_0_5_5) = all_0_2_2 % 2.84/1.41 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) % 2.84/1.42 | (19) function(all_0_0_0) % 2.84/1.42 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) % 2.84/1.42 | (21) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v3) = v2 & relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_inverse(v0) = v3)) % 2.84/1.42 | (22) relation_rng(all_0_7_7) = all_0_6_6 % 2.84/1.42 | (23) relation(all_0_1_1) % 2.84/1.42 | (24) one_to_one(all_0_7_7) % 2.84/1.42 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 2.84/1.42 | (26) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation_inverse(v1) = v0) % 2.84/1.42 | (27) function_inverse(all_0_7_7) = all_0_5_5 % 2.84/1.42 | (28) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ function(v0) | ~ relation(v0) | relation(v1)) % 2.84/1.42 | (29) one_to_one(all_0_1_1) % 2.84/1.42 | (30) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ function(v0) | ~ relation(v0) | function(v1)) % 2.84/1.42 | % 2.84/1.42 | Instantiating formula (21) with all_0_3_3, all_0_7_7 and discharging atoms relation_dom(all_0_7_7) = all_0_3_3, relation(all_0_7_7), yields: % 2.84/1.42 | (31) ? [v0] : ? [v1] : (relation_dom(v1) = v0 & relation_rng(v1) = all_0_3_3 & relation_rng(all_0_7_7) = v0 & relation_inverse(all_0_7_7) = v1) % 2.84/1.42 | % 2.84/1.42 | Instantiating formula (8) with all_0_6_6, all_0_7_7 and discharging atoms relation_rng(all_0_7_7) = all_0_6_6, relation(all_0_7_7), yields: % 2.84/1.42 | (32) ? [v0] : ? [v1] : (relation_dom(v0) = all_0_6_6 & relation_dom(all_0_7_7) = v1 & relation_rng(v0) = v1 & relation_inverse(all_0_7_7) = v0) % 2.84/1.42 | % 2.84/1.42 | Instantiating formula (4) with all_0_5_5, all_0_7_7 and discharging atoms function_inverse(all_0_7_7) = all_0_5_5, one_to_one(all_0_7_7), function(all_0_7_7), relation(all_0_7_7), yields: % 2.84/1.42 | (33) relation_inverse(all_0_7_7) = all_0_5_5 % 2.84/1.42 | % 2.84/1.42 | Instantiating (31) with all_9_0_8, all_9_1_9 yields: % 2.84/1.42 | (34) relation_dom(all_9_0_8) = all_9_1_9 & relation_rng(all_9_0_8) = all_0_3_3 & relation_rng(all_0_7_7) = all_9_1_9 & relation_inverse(all_0_7_7) = all_9_0_8 % 2.84/1.42 | % 2.84/1.42 | Applying alpha-rule on (34) yields: % 2.84/1.42 | (35) relation_dom(all_9_0_8) = all_9_1_9 % 2.84/1.42 | (36) relation_rng(all_9_0_8) = all_0_3_3 % 2.84/1.42 | (37) relation_rng(all_0_7_7) = all_9_1_9 % 2.84/1.42 | (38) relation_inverse(all_0_7_7) = all_9_0_8 % 2.84/1.42 | % 2.84/1.42 | Instantiating (32) with all_11_0_10, all_11_1_11 yields: % 2.84/1.42 | (39) relation_dom(all_11_1_11) = all_0_6_6 & relation_dom(all_0_7_7) = all_11_0_10 & relation_rng(all_11_1_11) = all_11_0_10 & relation_inverse(all_0_7_7) = all_11_1_11 % 2.84/1.42 | % 2.84/1.42 | Applying alpha-rule on (39) yields: % 2.84/1.42 | (40) relation_dom(all_11_1_11) = all_0_6_6 % 2.84/1.42 | (41) relation_dom(all_0_7_7) = all_11_0_10 % 2.84/1.42 | (42) relation_rng(all_11_1_11) = all_11_0_10 % 2.84/1.42 | (43) relation_inverse(all_0_7_7) = all_11_1_11 % 2.84/1.42 | % 2.84/1.42 | Instantiating formula (25) with all_0_7_7, all_9_1_9, all_0_6_6 and discharging atoms relation_rng(all_0_7_7) = all_9_1_9, relation_rng(all_0_7_7) = all_0_6_6, yields: % 2.84/1.42 | (44) all_9_1_9 = all_0_6_6 % 2.84/1.42 | % 2.84/1.42 | Instantiating formula (18) with all_0_7_7, all_9_0_8, all_11_1_11 and discharging atoms relation_inverse(all_0_7_7) = all_11_1_11, relation_inverse(all_0_7_7) = all_9_0_8, yields: % 2.84/1.42 | (45) all_11_1_11 = all_9_0_8 % 2.84/1.42 | % 2.84/1.42 | Instantiating formula (18) with all_0_7_7, all_0_5_5, all_11_1_11 and discharging atoms relation_inverse(all_0_7_7) = all_11_1_11, relation_inverse(all_0_7_7) = all_0_5_5, yields: % 2.84/1.42 | (46) all_11_1_11 = all_0_5_5 % 2.84/1.42 | % 2.84/1.43 | Combining equations (46,45) yields a new equation: % 2.84/1.43 | (47) all_9_0_8 = all_0_5_5 % 2.84/1.43 | % 2.84/1.43 | From (47)(44) and (35) follows: % 2.84/1.43 | (48) relation_dom(all_0_5_5) = all_0_6_6 % 2.84/1.43 | % 2.84/1.43 | From (47) and (36) follows: % 2.84/1.43 | (49) relation_rng(all_0_5_5) = all_0_3_3 % 2.84/1.43 | % 2.84/1.43 | Instantiating formula (13) with all_0_5_5, all_0_6_6, all_0_4_4 and discharging atoms relation_dom(all_0_5_5) = all_0_4_4, relation_dom(all_0_5_5) = all_0_6_6, yields: % 2.84/1.43 | (50) all_0_4_4 = all_0_6_6 % 2.84/1.43 | % 2.84/1.43 | Instantiating formula (25) with all_0_5_5, all_0_3_3, all_0_2_2 and discharging atoms relation_rng(all_0_5_5) = all_0_2_2, relation_rng(all_0_5_5) = all_0_3_3, yields: % 2.84/1.43 | (51) all_0_2_2 = all_0_3_3 % 2.84/1.43 | % 2.84/1.43 +-Applying beta-rule and splitting (9), into two cases. % 2.84/1.43 |-Branch one: % 2.84/1.43 | (52) ~ (all_0_2_2 = all_0_3_3) % 2.84/1.43 | % 2.84/1.43 | Equations (51) can reduce 52 to: % 2.84/1.43 | (53) $false % 2.84/1.43 | % 2.84/1.43 |-The branch is then unsatisfiable % 2.84/1.43 |-Branch two: % 2.84/1.43 | (51) all_0_2_2 = all_0_3_3 % 2.84/1.43 | (55) ~ (all_0_4_4 = all_0_6_6) % 2.84/1.43 | % 2.84/1.43 | Equations (50) can reduce 55 to: % 2.84/1.43 | (53) $false % 2.84/1.43 | % 2.84/1.43 |-The branch is then unsatisfiable % 2.84/1.43 % SZS output end Proof for theBenchmark % 2.84/1.43 % 2.84/1.43 852ms %------------------------------------------------------------------------------