%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET921+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 00:23:10 EDT 2022 % Result : Theorem 2.12s 1.20s % Output : Proof 2.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET921+1 : TPTP v8.1.0. Released v3.2.0. % 0.00/0.12 % 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 21:14:11 EDT 2022 % 0.12/0.33 % CPUTime : % 0.58/0.59 ____ _ % 0.58/0.59 ___ / __ \_____(_)___ ________ __________ % 0.58/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.59 % 0.58/0.59 A Theorem Prover for First-Order Logic % 0.58/0.60 (ePrincess v.1.0) % 0.58/0.60 % 0.58/0.60 (c) Philipp Rümmer, 2009-2015 % 0.58/0.60 (c) Peter Backeman, 2014-2015 % 0.58/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.60 Bug reports to peter@backeman.se % 0.58/0.60 % 0.58/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.60 % 0.58/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.32/0.92 Prover 0: Preprocessing ... % 1.61/1.06 Prover 0: Warning: ignoring some quantifiers % 1.61/1.08 Prover 0: Constructing countermodel ... % 2.12/1.19 Prover 0: proved (551ms) % 2.12/1.20 % 2.12/1.20 No countermodel exists, formula is valid % 2.12/1.20 % SZS status Theorem for theBenchmark % 2.12/1.20 % 2.12/1.20 Generating proof ... Warning: ignoring some quantifiers % 2.61/1.38 found it (size 17) % 2.61/1.38 % 2.61/1.38 % SZS output start Proof for theBenchmark % 2.61/1.38 Assumed formulas after preprocessing and simplification: % 2.61/1.38 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (set_difference(v1, v3) = v4 & singleton(v2) = v3 & empty(v6) & ~ empty(v5) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_difference(v10, v9) = v8) | ~ (set_difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v8) = v9) | ~ in(v10, v9) | ~ in(v10, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v8) = v9) | ~ in(v10, v9) | in(v10, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v8) = v9) | ~ in(v10, v7) | in(v10, v9) | in(v10, v8)) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_difference(v8, v9) = v10) | ? [v11] : (( ~ in(v11, v8) | ~ in(v11, v7) | in(v11, v9)) & (in(v11, v7) | (in(v11, v8) & ~ in(v11, v9))))) & ! [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] : (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)) & (( ~ (v2 = v0) & in(v0, v1) & ~ in(v0, v4)) | (in(v0, v4) & (v2 = v0 | ~ in(v0, v1))))) % 2.82/1.42 | 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: % 2.82/1.42 | (1) set_difference(all_0_5_5, all_0_3_3) = all_0_2_2 & singleton(all_0_4_4) = all_0_3_3 & empty(all_0_0_0) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v1) | ~ in(v4, v0) | in(v4, v2)) & (in(v4, v0) | (in(v4, v1) & ~ in(v4, v2))))) & ! [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] : (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_4_4 = all_0_6_6) & in(all_0_6_6, all_0_5_5) & ~ in(all_0_6_6, all_0_2_2)) | (in(all_0_6_6, all_0_2_2) & (all_0_4_4 = all_0_6_6 | ~ in(all_0_6_6, all_0_5_5)))) % 2.82/1.42 | % 2.82/1.42 | Applying alpha-rule on (1) yields: % 2.82/1.42 | (2) empty(all_0_0_0) % 2.82/1.42 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) % 2.82/1.42 | (4) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) % 2.82/1.42 | (5) ( ~ (all_0_4_4 = all_0_6_6) & in(all_0_6_6, all_0_5_5) & ~ in(all_0_6_6, all_0_2_2)) | (in(all_0_6_6, all_0_2_2) & (all_0_4_4 = all_0_6_6 | ~ in(all_0_6_6, all_0_5_5))) % 2.82/1.42 | (6) singleton(all_0_4_4) = all_0_3_3 % 2.82/1.42 | (7) ~ empty(all_0_1_1) % 2.82/1.43 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 2.82/1.43 | (9) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v1) | ~ in(v4, v0) | in(v4, v2)) & (in(v4, v0) | (in(v4, v1) & ~ in(v4, v2))))) % 2.82/1.43 | (10) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 2.82/1.43 | (11) set_difference(all_0_5_5, all_0_3_3) = all_0_2_2 % 2.82/1.43 | (12) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) % 2.82/1.43 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 2.82/1.43 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1)) % 2.82/1.43 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 2.82/1.43 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) % 2.82/1.43 | % 2.82/1.43 | Instantiating formula (12) with all_0_3_3, all_0_4_4 and discharging atoms singleton(all_0_4_4) = all_0_3_3, yields: % 2.82/1.43 | (17) in(all_0_4_4, all_0_3_3) % 2.82/1.43 | % 2.82/1.43 +-Applying beta-rule and splitting (5), into two cases. % 2.82/1.43 |-Branch one: % 2.82/1.43 | (18) ~ (all_0_4_4 = all_0_6_6) & in(all_0_6_6, all_0_5_5) & ~ in(all_0_6_6, all_0_2_2) % 2.82/1.43 | % 2.82/1.43 | Applying alpha-rule on (18) yields: % 2.82/1.43 | (19) ~ (all_0_4_4 = all_0_6_6) % 2.82/1.43 | (20) in(all_0_6_6, all_0_5_5) % 2.82/1.43 | (21) ~ in(all_0_6_6, all_0_2_2) % 2.82/1.43 | % 2.82/1.43 | Instantiating formula (3) with all_0_6_6, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms set_difference(all_0_5_5, all_0_3_3) = all_0_2_2, in(all_0_6_6, all_0_5_5), ~ in(all_0_6_6, all_0_2_2), yields: % 2.82/1.43 | (22) in(all_0_6_6, all_0_3_3) % 2.82/1.43 | % 2.82/1.43 | Instantiating formula (16) with all_0_6_6, all_0_3_3, all_0_4_4 and discharging atoms singleton(all_0_4_4) = all_0_3_3, in(all_0_6_6, all_0_3_3), yields: % 2.82/1.43 | (23) all_0_4_4 = all_0_6_6 % 2.82/1.43 | % 2.82/1.43 | Equations (23) can reduce 19 to: % 2.82/1.43 | (24) $false % 2.82/1.43 | % 2.82/1.43 |-The branch is then unsatisfiable % 2.82/1.43 |-Branch two: % 2.82/1.43 | (25) in(all_0_6_6, all_0_2_2) & (all_0_4_4 = all_0_6_6 | ~ in(all_0_6_6, all_0_5_5)) % 2.82/1.43 | % 2.82/1.43 | Applying alpha-rule on (25) yields: % 2.82/1.43 | (26) in(all_0_6_6, all_0_2_2) % 2.82/1.43 | (27) all_0_4_4 = all_0_6_6 | ~ in(all_0_6_6, all_0_5_5) % 2.82/1.43 | % 2.82/1.43 | Instantiating formula (8) with all_0_6_6, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms set_difference(all_0_5_5, all_0_3_3) = all_0_2_2, in(all_0_6_6, all_0_2_2), yields: % 2.82/1.43 | (20) in(all_0_6_6, all_0_5_5) % 2.82/1.43 | % 2.82/1.43 +-Applying beta-rule and splitting (27), into two cases. % 2.82/1.43 |-Branch one: % 2.82/1.43 | (29) ~ in(all_0_6_6, all_0_5_5) % 2.82/1.43 | % 2.82/1.44 | Using (20) and (29) yields: % 2.82/1.44 | (30) $false % 2.82/1.44 | % 2.82/1.44 |-The branch is then unsatisfiable % 2.82/1.44 |-Branch two: % 2.82/1.44 | (20) in(all_0_6_6, all_0_5_5) % 2.82/1.44 | (23) all_0_4_4 = all_0_6_6 % 2.82/1.44 | % 2.82/1.44 | From (23) and (17) follows: % 2.82/1.44 | (22) in(all_0_6_6, all_0_3_3) % 2.82/1.44 | % 2.82/1.44 | Instantiating formula (14) with all_0_6_6, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms set_difference(all_0_5_5, all_0_3_3) = all_0_2_2, in(all_0_6_6, all_0_2_2), in(all_0_6_6, all_0_3_3), yields: % 2.82/1.44 | (30) $false % 2.82/1.44 | % 2.82/1.44 |-The branch is then unsatisfiable % 2.82/1.44 % SZS output end Proof for theBenchmark % 2.82/1.44 % 2.82/1.44 830ms %------------------------------------------------------------------------------