%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET879+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n026.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 00:22:53 EDT 2022 % Result : Theorem 1.92s 1.11s % Output : Proof 2.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET879+1 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n026.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 Jul 10 17:40:26 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.57 ____ _ % 0.18/0.57 ___ / __ \_____(_)___ ________ __________ % 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.57 % 0.18/0.57 A Theorem Prover for First-Order Logic % 0.18/0.57 (ePrincess v.1.0) % 0.18/0.57 % 0.18/0.57 (c) Philipp Rümmer, 2009-2015 % 0.18/0.57 (c) Peter Backeman, 2014-2015 % 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.57 Bug reports to peter@backeman.se % 0.18/0.57 % 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.57 % 0.18/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.73/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.18/0.85 Prover 0: Preprocessing ... % 1.54/0.98 Prover 0: Warning: ignoring some quantifiers % 1.54/1.00 Prover 0: Constructing countermodel ... % 1.92/1.11 Prover 0: proved (491ms) % 1.92/1.11 % 1.92/1.11 No countermodel exists, formula is valid % 1.92/1.11 % SZS status Theorem for theBenchmark % 1.92/1.11 % 1.92/1.11 Generating proof ... Warning: ignoring some quantifiers % 2.38/1.30 found it (size 17) % 2.38/1.30 % 2.38/1.30 % SZS output start Proof for theBenchmark % 2.38/1.30 Assumed formulas after preprocessing and simplification: % 2.38/1.30 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (set_difference(v2, v3) = v4 & singleton(v1) = v3 & singleton(v0) = v2 & empty(v6) & ~ empty(v5) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (set_difference(v9, v8) = v10) | ~ (singleton(v7) = v9) | in(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_difference(v10, v9) = v8) | ~ (set_difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (singleton(v7) = v8) | ~ in(v9, v8)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_difference(v9, v8) = v9) | ~ (singleton(v7) = v9) | ~ in(v7, v8)) & ? [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (singleton(v8) = v9) | ? [v10] : (( ~ (v10 = v8) | ~ in(v8, v7)) & (v10 = v8 | in(v10, v7)))) & ! [v7] : ! [v8] : ( ~ (singleton(v7) = v8) | in(v7, v8)) & ! [v7] : ! [v8] : ( ~ in(v8, v7) | ~ in(v7, v8)) & ((v4 = v2 & v1 = v0) | ( ~ (v4 = v2) & ~ (v1 = v0)))) % 2.38/1.33 | 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: % 2.38/1.33 | (1) set_difference(all_0_4_4, all_0_3_3) = all_0_2_2 & singleton(all_0_5_5) = all_0_3_3 & singleton(all_0_6_6) = all_0_4_4 & empty(all_0_0_0) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (set_difference(v2, v1) = v3) | ~ (singleton(v0) = v2) | in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v2, v1) = v2) | ~ (singleton(v0) = v2) | ~ in(v0, v1)) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ((all_0_2_2 = all_0_4_4 & all_0_5_5 = all_0_6_6) | ( ~ (all_0_2_2 = all_0_4_4) & ~ (all_0_5_5 = all_0_6_6))) % 2.62/1.33 | % 2.62/1.33 | Applying alpha-rule on (1) yields: % 2.62/1.33 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 2.62/1.34 | (3) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) % 2.62/1.34 | (4) singleton(all_0_5_5) = all_0_3_3 % 2.62/1.34 | (5) set_difference(all_0_4_4, all_0_3_3) = all_0_2_2 % 2.62/1.34 | (6) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 2.62/1.34 | (7) empty(all_0_0_0) % 2.62/1.34 | (8) ~ empty(all_0_1_1) % 2.62/1.34 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 2.62/1.34 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) % 2.62/1.34 | (11) (all_0_2_2 = all_0_4_4 & all_0_5_5 = all_0_6_6) | ( ~ (all_0_2_2 = all_0_4_4) & ~ (all_0_5_5 = all_0_6_6)) % 2.62/1.34 | (12) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) % 2.62/1.34 | (13) singleton(all_0_6_6) = all_0_4_4 % 2.62/1.34 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (set_difference(v2, v1) = v3) | ~ (singleton(v0) = v2) | in(v0, v1)) % 2.62/1.34 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v2, v1) = v2) | ~ (singleton(v0) = v2) | ~ in(v0, v1)) % 2.62/1.34 | % 2.62/1.34 | Instantiating formula (3) with all_0_3_3, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_3_3, yields: % 2.62/1.34 | (16) in(all_0_5_5, all_0_3_3) % 2.62/1.34 | % 2.62/1.34 | Instantiating formula (14) with all_0_2_2, all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms set_difference(all_0_4_4, all_0_3_3) = all_0_2_2, singleton(all_0_6_6) = all_0_4_4, yields: % 2.62/1.34 | (17) all_0_2_2 = all_0_4_4 | in(all_0_6_6, all_0_3_3) % 2.62/1.34 | % 2.62/1.34 +-Applying beta-rule and splitting (11), into two cases. % 2.62/1.34 |-Branch one: % 2.62/1.34 | (18) all_0_2_2 = all_0_4_4 & all_0_5_5 = all_0_6_6 % 2.62/1.34 | % 2.62/1.34 | Applying alpha-rule on (18) yields: % 2.62/1.34 | (19) all_0_2_2 = all_0_4_4 % 2.62/1.34 | (20) all_0_5_5 = all_0_6_6 % 2.62/1.34 | % 2.62/1.34 | From (19) and (5) follows: % 2.62/1.34 | (21) set_difference(all_0_4_4, all_0_3_3) = all_0_4_4 % 2.62/1.34 | % 2.62/1.34 | From (20) and (16) follows: % 2.62/1.34 | (22) in(all_0_6_6, all_0_3_3) % 2.62/1.34 | % 2.62/1.34 | Instantiating formula (15) with all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms set_difference(all_0_4_4, all_0_3_3) = all_0_4_4, singleton(all_0_6_6) = all_0_4_4, in(all_0_6_6, all_0_3_3), yields: % 2.62/1.35 | (23) $false % 2.62/1.35 | % 2.62/1.35 |-The branch is then unsatisfiable % 2.62/1.35 |-Branch two: % 2.62/1.35 | (24) ~ (all_0_2_2 = all_0_4_4) & ~ (all_0_5_5 = all_0_6_6) % 2.62/1.35 | % 2.62/1.35 | Applying alpha-rule on (24) yields: % 2.62/1.35 | (25) ~ (all_0_2_2 = all_0_4_4) % 2.62/1.35 | (26) ~ (all_0_5_5 = all_0_6_6) % 2.62/1.35 | % 2.62/1.35 +-Applying beta-rule and splitting (17), into two cases. % 2.62/1.35 |-Branch one: % 2.62/1.35 | (22) in(all_0_6_6, all_0_3_3) % 2.62/1.35 | % 2.62/1.35 | Instantiating formula (10) with all_0_6_6, all_0_3_3, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_3_3, in(all_0_6_6, all_0_3_3), yields: % 2.62/1.35 | (20) all_0_5_5 = all_0_6_6 % 2.62/1.35 | % 2.62/1.35 | Equations (20) can reduce 26 to: % 2.62/1.35 | (29) $false % 2.62/1.35 | % 2.62/1.35 |-The branch is then unsatisfiable % 2.62/1.35 |-Branch two: % 2.62/1.35 | (30) ~ in(all_0_6_6, all_0_3_3) % 2.62/1.35 | (19) all_0_2_2 = all_0_4_4 % 2.62/1.35 | % 2.62/1.35 | Equations (19) can reduce 25 to: % 2.62/1.35 | (29) $false % 2.62/1.35 | % 2.62/1.35 |-The branch is then unsatisfiable % 2.62/1.35 % SZS output end Proof for theBenchmark % 2.62/1.35 % 2.62/1.35 765ms %------------------------------------------------------------------------------