%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU160+3 : TPTP v8.1.0. Released v3.2.0. % 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 08:47:08 EDT 2022 % Result : Theorem 1.56s 0.97s % Output : Proof 1.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.10 % Problem : SEU160+3 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.10 % 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 07:51:02 EDT 2022 % 0.10/0.29 % CPUTime : % 0.14/0.49 ____ _ % 0.14/0.49 ___ / __ \_____(_)___ ________ __________ % 0.14/0.49 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.14/0.49 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.14/0.49 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.14/0.49 % 0.14/0.49 A Theorem Prover for First-Order Logic % 0.14/0.49 (ePrincess v.1.0) % 0.14/0.49 % 0.14/0.49 (c) Philipp Rümmer, 2009-2015 % 0.14/0.49 (c) Peter Backeman, 2014-2015 % 0.14/0.49 (contributions by Angelo Brillout, Peter Baumgartner) % 0.14/0.49 Free software under GNU Lesser General Public License (LGPL). % 0.14/0.49 Bug reports to peter@backeman.se % 0.14/0.49 % 0.14/0.49 For more information, visit http://user.uu.se/~petba168/breu/ % 0.14/0.49 % 0.14/0.49 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.14/0.54 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.01/0.76 Prover 0: Preprocessing ... % 1.26/0.85 Prover 0: Warning: ignoring some quantifiers % 1.26/0.87 Prover 0: Constructing countermodel ... % 1.56/0.97 Prover 0: proved (431ms) % 1.56/0.97 % 1.56/0.97 No countermodel exists, formula is valid % 1.56/0.97 % SZS status Theorem for theBenchmark % 1.56/0.97 % 1.56/0.97 Generating proof ... Warning: ignoring some quantifiers % 1.96/1.10 found it (size 21) % 1.96/1.10 % 1.96/1.10 % SZS output start Proof for theBenchmark % 1.96/1.10 Assumed formulas after preprocessing and simplification: % 1.96/1.10 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (singleton(v1) = v2 & empty(v4) & empty(empty_set) & ~ empty(v3) & ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | v5 = empty_set | ~ (singleton(v6) = v7) | ~ subset(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (singleton(v7) = v6) | ~ (singleton(v7) = v5)) & ! [v5] : ! [v6] : ( ~ (singleton(v6) = v5) | subset(v5, v5)) & ! [v5] : ! [v6] : ( ~ (singleton(v5) = v6) | subset(empty_set, v6)) & ? [v5] : subset(v5, v5) & (( ~ (v2 = v0) & ~ (v0 = empty_set) & subset(v0, v2)) | ( ~ subset(v0, v2) & (v2 = v0 | v0 = empty_set)))) % 1.96/1.14 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 1.96/1.14 | (1) singleton(all_0_3_3) = all_0_2_2 & empty(all_0_0_0) & empty(empty_set) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) & ? [v0] : subset(v0, v0) & (( ~ (all_0_2_2 = all_0_4_4) & ~ (all_0_4_4 = empty_set) & subset(all_0_4_4, all_0_2_2)) | ( ~ subset(all_0_4_4, all_0_2_2) & (all_0_2_2 = all_0_4_4 | all_0_4_4 = empty_set))) % 1.96/1.14 | % 1.96/1.14 | Applying alpha-rule on (1) yields: % 1.96/1.14 | (2) singleton(all_0_3_3) = all_0_2_2 % 1.96/1.14 | (3) ( ~ (all_0_2_2 = all_0_4_4) & ~ (all_0_4_4 = empty_set) & subset(all_0_4_4, all_0_2_2)) | ( ~ subset(all_0_4_4, all_0_2_2) & (all_0_2_2 = all_0_4_4 | all_0_4_4 = empty_set)) % 1.96/1.14 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2)) % 1.96/1.14 | (5) ? [v0] : subset(v0, v0) % 1.96/1.14 | (6) ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) % 1.96/1.14 | (7) ~ empty(all_0_1_1) % 1.96/1.14 | (8) empty(all_0_0_0) % 1.96/1.14 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 1.96/1.14 | (10) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) % 1.96/1.14 | (11) empty(empty_set) % 1.96/1.14 | % 1.96/1.14 | Instantiating formula (6) with all_0_3_3, all_0_2_2 and discharging atoms singleton(all_0_3_3) = all_0_2_2, yields: % 1.96/1.15 | (12) subset(all_0_2_2, all_0_2_2) % 1.96/1.15 | % 1.96/1.15 | Instantiating formula (10) with all_0_2_2, all_0_3_3 and discharging atoms singleton(all_0_3_3) = all_0_2_2, yields: % 1.96/1.15 | (13) subset(empty_set, all_0_2_2) % 1.96/1.15 | % 1.96/1.15 +-Applying beta-rule and splitting (3), into two cases. % 1.96/1.15 |-Branch one: % 1.96/1.15 | (14) ~ (all_0_2_2 = all_0_4_4) & ~ (all_0_4_4 = empty_set) & subset(all_0_4_4, all_0_2_2) % 1.96/1.15 | % 1.96/1.15 | Applying alpha-rule on (14) yields: % 1.96/1.15 | (15) ~ (all_0_2_2 = all_0_4_4) % 1.96/1.15 | (16) ~ (all_0_4_4 = empty_set) % 1.96/1.15 | (17) subset(all_0_4_4, all_0_2_2) % 1.96/1.15 | % 1.96/1.15 | Instantiating formula (4) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms singleton(all_0_3_3) = all_0_2_2, subset(all_0_4_4, all_0_2_2), yields: % 1.96/1.15 | (18) all_0_2_2 = all_0_4_4 | all_0_4_4 = empty_set % 1.96/1.15 | % 1.96/1.15 +-Applying beta-rule and splitting (18), into two cases. % 1.96/1.15 |-Branch one: % 1.96/1.15 | (19) all_0_4_4 = empty_set % 1.96/1.15 | % 1.96/1.15 | Equations (19) can reduce 16 to: % 1.96/1.15 | (20) $false % 1.96/1.15 | % 1.96/1.15 |-The branch is then unsatisfiable % 1.96/1.15 |-Branch two: % 1.96/1.15 | (16) ~ (all_0_4_4 = empty_set) % 1.96/1.15 | (22) all_0_2_2 = all_0_4_4 % 1.96/1.15 | % 1.96/1.15 | Equations (22) can reduce 15 to: % 1.96/1.15 | (20) $false % 1.96/1.15 | % 1.96/1.15 |-The branch is then unsatisfiable % 1.96/1.15 |-Branch two: % 1.96/1.15 | (24) ~ subset(all_0_4_4, all_0_2_2) & (all_0_2_2 = all_0_4_4 | all_0_4_4 = empty_set) % 1.96/1.15 | % 1.96/1.15 | Applying alpha-rule on (24) yields: % 1.96/1.15 | (25) ~ subset(all_0_4_4, all_0_2_2) % 1.96/1.15 | (18) all_0_2_2 = all_0_4_4 | all_0_4_4 = empty_set % 1.96/1.15 | % 1.96/1.15 +-Applying beta-rule and splitting (18), into two cases. % 1.96/1.15 |-Branch one: % 1.96/1.15 | (19) all_0_4_4 = empty_set % 1.96/1.15 | % 1.96/1.15 | From (19) and (25) follows: % 1.96/1.15 | (28) ~ subset(empty_set, all_0_2_2) % 1.96/1.15 | % 1.96/1.15 | Using (13) and (28) yields: % 1.96/1.15 | (29) $false % 1.96/1.15 | % 1.96/1.15 |-The branch is then unsatisfiable % 1.96/1.15 |-Branch two: % 1.96/1.15 | (16) ~ (all_0_4_4 = empty_set) % 1.96/1.15 | (22) all_0_2_2 = all_0_4_4 % 1.96/1.15 | % 1.96/1.15 | From (22)(22) and (12) follows: % 1.96/1.15 | (32) subset(all_0_4_4, all_0_4_4) % 1.96/1.15 | % 1.96/1.15 | From (22) and (25) follows: % 1.96/1.15 | (33) ~ subset(all_0_4_4, all_0_4_4) % 1.96/1.15 | % 1.96/1.15 | Using (32) and (33) yields: % 1.96/1.15 | (29) $false % 1.96/1.15 | % 1.96/1.15 |-The branch is then unsatisfiable % 1.96/1.15 % SZS output end Proof for theBenchmark % 1.96/1.15 % 1.96/1.15 657ms %------------------------------------------------------------------------------