%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU124+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n018.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 08:46:44 EDT 2022 % Result : Theorem 3.26s 1.56s % Output : Proof 4.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SEU124+1 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.35 % Computer : n018.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Sun Jun 19 04:21:34 EDT 2022 % 0.13/0.35 % CPUTime : % 0.52/0.61 ____ _ % 0.52/0.61 ___ / __ \_____(_)___ ________ __________ % 0.52/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.52/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.52/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.52/0.62 % 0.52/0.62 A Theorem Prover for First-Order Logic % 0.52/0.62 (ePrincess v.1.0) % 0.52/0.62 % 0.52/0.62 (c) Philipp Rümmer, 2009-2015 % 0.52/0.62 (c) Peter Backeman, 2014-2015 % 0.52/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.52/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.52/0.62 Bug reports to peter@backeman.se % 0.52/0.62 % 0.52/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.52/0.62 % 0.52/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.76/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.40/0.93 Prover 0: Preprocessing ... % 1.86/1.12 Prover 0: Warning: ignoring some quantifiers % 1.86/1.14 Prover 0: Constructing countermodel ... % 2.48/1.36 Prover 0: gave up % 2.48/1.36 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.65/1.38 Prover 1: Preprocessing ... % 2.97/1.47 Prover 1: Warning: ignoring some quantifiers % 2.97/1.48 Prover 1: Constructing countermodel ... % 3.26/1.56 Prover 1: proved (198ms) % 3.26/1.56 % 3.26/1.56 No countermodel exists, formula is valid % 3.26/1.56 % SZS status Theorem for theBenchmark % 3.26/1.56 % 3.26/1.56 Generating proof ... Warning: ignoring some quantifiers % 4.33/1.79 found it (size 14) % 4.33/1.79 % 4.33/1.79 % SZS output start Proof for theBenchmark % 4.33/1.79 Assumed formulas after preprocessing and simplification: % 4.33/1.79 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = 0) & ~ (v3 = 0) & empty(v6) = 0 & empty(v4) = v5 & empty(empty_set) = 0 & subset(v0, v2) = v3 & set_union2(v0, v1) = v2 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (set_union2(v7, v8) = v9) | ~ (in(v10, v7) = v11) | ? [v12] : ? [v13] : (in(v10, v9) = v12 & in(v10, v8) = v13 & ( ~ (v12 = 0) | v13 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v7, v8) = v9) | ~ (in(v10, v7) = v11) | ? [v12] : ? [v13] : (in(v10, v9) = v13 & in(v10, v8) = v12 & (v13 = 0 | ( ~ (v12 = 0) & ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_union2(v10, v9) = v8) | ~ (set_union2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (in(v10, v9) = v8) | ~ (in(v10, v9) = v7)) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_union2(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (in(v11, v9) = v14 & in(v11, v8) = v13 & in(v11, v7) = v12 & ( ~ (v12 = 0) | ( ~ (v14 = 0) & ~ (v13 = 0))) & (v14 = 0 | v13 = 0 | v12 = 0))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & in(v10, v8) = v11 & in(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (empty(v9) = v8) | ~ (empty(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (in(v9, v7) = 0) | in(v9, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v8, v7) = v9) | ? [v10] : ? [v11] : (empty(v9) = v11 & empty(v7) = v10 & ( ~ (v11 = 0) | v10 = 0))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | set_union2(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | ? [v10] : ? [v11] : (empty(v9) = v11 & empty(v7) = v10 & ( ~ (v11 = 0) | v10 = 0))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (empty(v8) = 0) | ~ (empty(v7) = 0)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_union2(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_union2(v7, empty_set) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v7, v7) = v8)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & empty(v8) = v9)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v7) = v9)) & ! [v7] : (v7 = empty_set | ~ (empty(v7) = 0))) % 4.51/1.83 | 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: % 4.51/1.83 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & subset(all_0_6_6, all_0_4_4) = all_0_3_3 & set_union2(all_0_6_6, all_0_5_5) = all_0_4_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 4.51/1.83 | % 4.51/1.83 | Applying alpha-rule on (1) yields: % 4.51/1.84 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 4.51/1.84 | (3) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 4.51/1.84 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) % 4.51/1.84 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 4.51/1.84 | (6) empty(empty_set) = 0 % 4.51/1.84 | (7) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 4.51/1.84 | (8) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) % 4.51/1.84 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 4.51/1.84 | (10) ~ (all_0_1_1 = 0) % 4.51/1.84 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 4.51/1.84 | (12) ~ (all_0_3_3 = 0) % 4.51/1.84 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 4.51/1.84 | (14) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 4.51/1.84 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 4.51/1.84 | (16) subset(all_0_6_6, all_0_4_4) = all_0_3_3 % 4.51/1.84 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) % 4.51/1.84 | (18) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 4.51/1.84 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) % 4.51/1.84 | (20) empty(all_0_0_0) = 0 % 4.51/1.84 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) % 4.51/1.84 | (22) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 4.51/1.84 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 4.51/1.84 | (24) set_union2(all_0_6_6, all_0_5_5) = all_0_4_4 % 4.51/1.84 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 4.51/1.84 | (26) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 4.51/1.84 | (27) empty(all_0_2_2) = all_0_1_1 % 4.51/1.84 | % 4.51/1.84 | Instantiating formula (22) with all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_4_4) = all_0_3_3, yields: % 4.51/1.84 | (28) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_6_6) = 0) % 4.51/1.84 | % 4.51/1.84 +-Applying beta-rule and splitting (28), into two cases. % 4.51/1.84 |-Branch one: % 4.51/1.84 | (29) all_0_3_3 = 0 % 4.51/1.84 | % 4.51/1.84 | Equations (29) can reduce 12 to: % 4.51/1.84 | (30) $false % 4.51/1.84 | % 4.51/1.85 |-The branch is then unsatisfiable % 4.51/1.85 |-Branch two: % 4.51/1.85 | (12) ~ (all_0_3_3 = 0) % 4.51/1.85 | (32) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_6_6) = 0) % 4.51/1.85 | % 4.51/1.85 | Instantiating (32) with all_43_0_12, all_43_1_13 yields: % 4.51/1.85 | (33) ~ (all_43_0_12 = 0) & in(all_43_1_13, all_0_4_4) = all_43_0_12 & in(all_43_1_13, all_0_6_6) = 0 % 4.51/1.85 | % 4.51/1.85 | Applying alpha-rule on (33) yields: % 4.51/1.85 | (34) ~ (all_43_0_12 = 0) % 4.51/1.85 | (35) in(all_43_1_13, all_0_4_4) = all_43_0_12 % 4.51/1.85 | (36) in(all_43_1_13, all_0_6_6) = 0 % 4.51/1.85 | % 4.51/1.85 | Instantiating formula (21) with 0, all_43_1_13, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms set_union2(all_0_6_6, all_0_5_5) = all_0_4_4, in(all_43_1_13, all_0_6_6) = 0, yields: % 4.51/1.85 | (37) ? [v0] : (in(all_43_1_13, all_0_4_4) = 0 & in(all_43_1_13, all_0_5_5) = v0) % 4.51/1.85 | % 4.51/1.85 | Instantiating (37) with all_68_0_15 yields: % 4.51/1.85 | (38) in(all_43_1_13, all_0_4_4) = 0 & in(all_43_1_13, all_0_5_5) = all_68_0_15 % 4.51/1.85 | % 4.51/1.85 | Applying alpha-rule on (38) yields: % 4.51/1.85 | (39) in(all_43_1_13, all_0_4_4) = 0 % 4.51/1.85 | (40) in(all_43_1_13, all_0_5_5) = all_68_0_15 % 4.51/1.85 | % 4.51/1.85 | Instantiating formula (25) with all_43_1_13, all_0_4_4, 0, all_43_0_12 and discharging atoms in(all_43_1_13, all_0_4_4) = all_43_0_12, in(all_43_1_13, all_0_4_4) = 0, yields: % 4.51/1.85 | (41) all_43_0_12 = 0 % 4.51/1.85 | % 4.51/1.85 | Equations (41) can reduce 34 to: % 4.51/1.85 | (30) $false % 4.51/1.85 | % 4.51/1.85 |-The branch is then unsatisfiable % 4.51/1.85 % SZS output end Proof for theBenchmark % 4.51/1.85 % 4.51/1.85 1222ms %------------------------------------------------------------------------------