%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET902+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n014.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 00:23:01 EDT 2022 % Result : Theorem 2.13s 1.19s % Output : Proof 2.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET902+1 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n014.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 02:20:35 EDT 2022 % 0.12/0.33 % CPUTime : % 0.57/0.58 ____ _ % 0.57/0.58 ___ / __ \_____(_)___ ________ __________ % 0.57/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.57/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.57/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.57/0.58 % 0.57/0.58 A Theorem Prover for First-Order Logic % 0.57/0.58 (ePrincess v.1.0) % 0.57/0.58 % 0.57/0.58 (c) Philipp Rümmer, 2009-2015 % 0.57/0.58 (c) Peter Backeman, 2014-2015 % 0.57/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.57/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.57/0.58 Bug reports to peter@backeman.se % 0.57/0.58 % 0.57/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.57/0.58 % 0.57/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.57/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.30/0.91 Prover 0: Preprocessing ... % 1.66/1.06 Prover 0: Warning: ignoring some quantifiers % 1.66/1.07 Prover 0: Constructing countermodel ... % 2.13/1.19 Prover 0: proved (562ms) % 2.13/1.19 % 2.13/1.19 No countermodel exists, formula is valid % 2.13/1.19 % SZS status Theorem for theBenchmark % 2.13/1.19 % 2.13/1.19 Generating proof ... Warning: ignoring some quantifiers % 2.63/1.39 found it (size 34) % 2.63/1.39 % 2.63/1.39 % SZS output start Proof for theBenchmark % 2.63/1.39 Assumed formulas after preprocessing and simplification: % 2.63/1.39 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (singleton(v0) = v3 & set_union2(v1, v2) = v3 & empty(v5) & empty(empty_set) & ~ empty(v4) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (set_union2(v9, v8) = v7) | ~ (set_union2(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v8 = v6 | v6 = empty_set | ~ (singleton(v7) = v8) | ~ subset(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (singleton(v8) = v7) | ~ (singleton(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v7, v6) = v8) | ~ empty(v8) | empty(v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v7, v6) = v8) | set_union2(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v6, v7) = v8) | ~ empty(v8) | empty(v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v6, v7) = v8) | set_union2(v7, v6) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v6, v7) = v8) | subset(v6, v8)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (set_union2(v6, v6) = v7)) & ! [v6] : ! [v7] : ( ~ (singleton(v7) = v6) | subset(v6, v6)) & ! [v6] : ! [v7] : ( ~ (singleton(v6) = v7) | subset(empty_set, v7)) & ! [v6] : ~ (singleton(v6) = empty_set) & ? [v6] : subset(v6, v6) & ( ~ (v3 = v2) | ~ (v1 = empty_set)) & ( ~ (v3 = v1) | ~ (v2 = v1)) & ( ~ (v3 = v1) | ~ (v2 = empty_set))) % 2.63/1.43 | 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 yields: % 2.63/1.43 | (1) singleton(all_0_5_5) = all_0_2_2 & set_union2(all_0_4_4, all_0_3_3) = all_0_2_2 & empty(all_0_0_0) & empty(empty_set) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [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] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) & ! [v0] : ~ (singleton(v0) = empty_set) & ? [v0] : subset(v0, v0) & ( ~ (all_0_2_2 = all_0_3_3) | ~ (all_0_4_4 = empty_set)) & ( ~ (all_0_2_2 = all_0_4_4) | ~ (all_0_3_3 = all_0_4_4)) & ( ~ (all_0_2_2 = all_0_4_4) | ~ (all_0_3_3 = empty_set)) % 2.63/1.43 | % 2.63/1.43 | Applying alpha-rule on (1) yields: % 2.63/1.43 | (2) empty(all_0_0_0) % 2.63/1.43 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 2.63/1.44 | (4) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) % 2.63/1.44 | (5) ~ empty(all_0_1_1) % 2.63/1.44 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 2.63/1.44 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 2.63/1.44 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 2.63/1.44 | (9) ~ (all_0_2_2 = all_0_4_4) | ~ (all_0_3_3 = all_0_4_4) % 2.63/1.44 | (10) singleton(all_0_5_5) = all_0_2_2 % 2.63/1.44 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) % 2.63/1.44 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 2.63/1.44 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 2.63/1.44 | (14) ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) % 2.63/1.44 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2)) % 2.63/1.44 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 2.63/1.44 | (17) ! [v0] : ~ (singleton(v0) = empty_set) % 2.63/1.44 | (18) ? [v0] : subset(v0, v0) % 2.63/1.44 | (19) empty(empty_set) % 2.63/1.44 | (20) ~ (all_0_2_2 = all_0_4_4) | ~ (all_0_3_3 = empty_set) % 2.63/1.44 | (21) ~ (all_0_2_2 = all_0_3_3) | ~ (all_0_4_4 = empty_set) % 2.63/1.44 | (22) set_union2(all_0_4_4, all_0_3_3) = all_0_2_2 % 2.63/1.44 | % 2.63/1.44 | Instantiating formula (13) with all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms set_union2(all_0_4_4, all_0_3_3) = all_0_2_2, yields: % 2.63/1.44 | (23) set_union2(all_0_3_3, all_0_4_4) = all_0_2_2 % 2.63/1.44 | % 2.63/1.44 | Instantiating formula (11) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms set_union2(all_0_4_4, all_0_3_3) = all_0_2_2, yields: % 2.63/1.44 | (24) subset(all_0_4_4, all_0_2_2) % 2.63/1.44 | % 2.63/1.44 | Instantiating formula (15) with all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms singleton(all_0_5_5) = all_0_2_2, subset(all_0_4_4, all_0_2_2), yields: % 2.63/1.44 | (25) all_0_2_2 = all_0_4_4 | all_0_4_4 = empty_set % 2.63/1.44 | % 2.63/1.44 | Instantiating formula (11) with all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms set_union2(all_0_3_3, all_0_4_4) = all_0_2_2, yields: % 2.63/1.44 | (26) subset(all_0_3_3, all_0_2_2) % 2.63/1.44 | % 2.63/1.44 | Instantiating formula (15) with all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms singleton(all_0_5_5) = all_0_2_2, subset(all_0_3_3, all_0_2_2), yields: % 2.63/1.44 | (27) all_0_2_2 = all_0_3_3 | all_0_3_3 = empty_set % 2.63/1.44 | % 2.63/1.44 +-Applying beta-rule and splitting (20), into two cases. % 2.63/1.44 |-Branch one: % 2.63/1.44 | (28) ~ (all_0_3_3 = empty_set) % 2.63/1.44 | % 2.63/1.44 +-Applying beta-rule and splitting (27), into two cases. % 2.63/1.44 |-Branch one: % 2.63/1.44 | (29) all_0_3_3 = empty_set % 2.63/1.44 | % 2.63/1.44 | Equations (29) can reduce 28 to: % 2.63/1.44 | (30) $false % 2.63/1.44 | % 2.63/1.45 |-The branch is then unsatisfiable % 2.63/1.45 |-Branch two: % 2.63/1.45 | (28) ~ (all_0_3_3 = empty_set) % 2.63/1.45 | (32) all_0_2_2 = all_0_3_3 % 2.63/1.45 | % 2.63/1.45 +-Applying beta-rule and splitting (9), into two cases. % 2.63/1.45 |-Branch one: % 2.63/1.45 | (33) ~ (all_0_2_2 = all_0_4_4) % 2.63/1.45 | % 2.63/1.45 | Equations (32) can reduce 33 to: % 2.63/1.45 | (34) ~ (all_0_3_3 = all_0_4_4) % 2.63/1.45 | % 2.63/1.45 +-Applying beta-rule and splitting (21), into two cases. % 2.63/1.45 |-Branch one: % 2.63/1.45 | (35) ~ (all_0_4_4 = empty_set) % 2.63/1.45 | % 2.63/1.45 +-Applying beta-rule and splitting (25), into two cases. % 2.63/1.45 |-Branch one: % 2.63/1.45 | (36) all_0_4_4 = empty_set % 2.63/1.45 | % 2.63/1.45 | Equations (36) can reduce 35 to: % 2.63/1.45 | (30) $false % 2.63/1.45 | % 2.63/1.45 |-The branch is then unsatisfiable % 2.63/1.45 |-Branch two: % 2.63/1.45 | (35) ~ (all_0_4_4 = empty_set) % 2.63/1.45 | (39) all_0_2_2 = all_0_4_4 % 2.63/1.45 | % 2.63/1.45 | Combining equations (39,32) yields a new equation: % 2.63/1.45 | (40) all_0_3_3 = all_0_4_4 % 2.63/1.45 | % 2.63/1.45 | Equations (40) can reduce 34 to: % 2.63/1.45 | (30) $false % 2.63/1.45 | % 2.63/1.45 |-The branch is then unsatisfiable % 2.63/1.45 |-Branch two: % 2.63/1.45 | (36) all_0_4_4 = empty_set % 2.63/1.45 | (43) ~ (all_0_2_2 = all_0_3_3) % 2.63/1.45 | % 2.63/1.45 | Equations (32) can reduce 43 to: % 2.63/1.45 | (30) $false % 2.63/1.45 | % 2.63/1.45 |-The branch is then unsatisfiable % 2.63/1.45 |-Branch two: % 2.63/1.45 | (39) all_0_2_2 = all_0_4_4 % 2.63/1.45 | (34) ~ (all_0_3_3 = all_0_4_4) % 2.63/1.45 | % 2.63/1.45 | Combining equations (39,32) yields a new equation: % 2.63/1.45 | (40) all_0_3_3 = all_0_4_4 % 2.63/1.45 | % 2.63/1.45 | Equations (40) can reduce 34 to: % 2.63/1.45 | (30) $false % 2.63/1.45 | % 2.63/1.45 |-The branch is then unsatisfiable % 2.63/1.45 |-Branch two: % 2.63/1.45 | (29) all_0_3_3 = empty_set % 2.63/1.45 | (33) ~ (all_0_2_2 = all_0_4_4) % 2.63/1.45 | % 2.63/1.45 | From (29) and (23) follows: % 2.63/1.45 | (51) set_union2(empty_set, all_0_4_4) = all_0_2_2 % 2.63/1.45 | % 2.63/1.45 +-Applying beta-rule and splitting (25), into two cases. % 2.63/1.45 |-Branch one: % 2.63/1.45 | (36) all_0_4_4 = empty_set % 2.63/1.45 | % 2.63/1.45 | Equations (36) can reduce 33 to: % 2.63/1.45 | (53) ~ (all_0_2_2 = empty_set) % 2.63/1.45 | % 2.63/1.45 | From (36) and (51) follows: % 2.63/1.45 | (54) set_union2(empty_set, empty_set) = all_0_2_2 % 2.91/1.45 | % 2.91/1.45 | Instantiating formula (16) with all_0_2_2, empty_set and discharging atoms set_union2(empty_set, empty_set) = all_0_2_2, yields: % 2.91/1.45 | (55) all_0_2_2 = empty_set % 2.91/1.45 | % 2.91/1.45 | Equations (55) can reduce 53 to: % 2.91/1.45 | (30) $false % 2.91/1.45 | % 2.91/1.45 |-The branch is then unsatisfiable % 2.91/1.45 |-Branch two: % 2.91/1.45 | (35) ~ (all_0_4_4 = empty_set) % 2.91/1.45 | (39) all_0_2_2 = all_0_4_4 % 2.91/1.45 | % 2.91/1.45 | Equations (39) can reduce 33 to: % 2.91/1.45 | (30) $false % 2.91/1.45 | % 2.91/1.45 |-The branch is then unsatisfiable % 2.91/1.45 % SZS output end Proof for theBenchmark % 2.91/1.45 % 2.91/1.45 862ms %------------------------------------------------------------------------------