%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET617+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n029.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 00:20:51 EDT 2022 % Result : Theorem 2.27s 1.27s % Output : Proof 3.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET617+3 : TPTP v8.1.0. Released v2.2.0. % 0.06/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n029.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 08:07:01 EDT 2022 % 0.12/0.34 % CPUTime : % 0.48/0.59 ____ _ % 0.48/0.59 ___ / __ \_____(_)___ ________ __________ % 0.48/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.48/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.48/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.48/0.59 % 0.48/0.59 A Theorem Prover for First-Order Logic % 0.48/0.59 (ePrincess v.1.0) % 0.48/0.59 % 0.48/0.59 (c) Philipp Rümmer, 2009-2015 % 0.48/0.59 (c) Peter Backeman, 2014-2015 % 0.48/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.48/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.48/0.59 Bug reports to peter@backeman.se % 0.48/0.59 % 0.48/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.48/0.59 % 0.48/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.25/0.92 Prover 0: Preprocessing ... % 1.91/1.13 Prover 0: Warning: ignoring some quantifiers % 1.98/1.15 Prover 0: Constructing countermodel ... % 2.27/1.27 Prover 0: proved (631ms) % 2.27/1.27 % 2.27/1.27 No countermodel exists, formula is valid % 2.27/1.27 % SZS status Theorem for theBenchmark % 2.27/1.28 % 2.27/1.28 Generating proof ... Warning: ignoring some quantifiers % 2.99/1.50 found it (size 24) % 2.99/1.50 % 2.99/1.50 % SZS output start Proof for theBenchmark % 2.99/1.50 Assumed formulas after preprocessing and simplification: % 2.99/1.50 | (0) ? [v0] : ? [v1] : ? [v2] : (symmetric_difference(v0, empty_set) = v1 & symmetric_difference(empty_set, v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (difference(v4, v3) = v6) | ~ (difference(v3, v4) = v5) | ~ (union(v5, v6) = v7) | symmetric_difference(v3, v4) = v7) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (difference(v6, v5) = v4) | ~ (difference(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (union(v6, v5) = v4) | ~ (union(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (symmetric_difference(v6, v5) = v4) | ~ (symmetric_difference(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (union(v4, v3) = v5) | union(v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (union(v3, v4) = v5) | union(v4, v3) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (symmetric_difference(v4, v3) = v5) | symmetric_difference(v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (symmetric_difference(v3, v4) = v5) | symmetric_difference(v4, v3) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (symmetric_difference(v3, v4) = v5) | ? [v6] : ? [v7] : (difference(v4, v3) = v7 & difference(v3, v4) = v6 & union(v6, v7) = v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ subset(v3, v4) | ~ member(v5, v3) | member(v5, v4)) & ! [v3] : ! [v4] : (v4 = v3 | ~ (difference(v3, empty_set) = v4)) & ! [v3] : ! [v4] : (v4 = v3 | ~ (union(v3, empty_set) = v4)) & ! [v3] : ! [v4] : (v4 = v3 | ~ subset(v4, v3) | ~ subset(v3, v4)) & ! [v3] : ! [v4] : (v4 = empty_set | ~ (difference(empty_set, v3) = v4)) & ! [v3] : ! [v4] : ( ~ empty(v3) | ~ member(v4, v3)) & ! [v3] : ~ member(v3, empty_set) & ? [v3] : ? [v4] : (v4 = v3 | ? [v5] : (( ~ member(v5, v4) | ~ member(v5, v3)) & (member(v5, v4) | member(v5, v3)))) & ? [v3] : ? [v4] : (subset(v3, v4) | ? [v5] : (member(v5, v3) & ~ member(v5, v4))) & ? [v3] : (empty(v3) | ? [v4] : member(v4, v3)) & ? [v3] : subset(v3, v3) & ( ~ (v2 = v0) | ~ (v1 = v0))) % 3.29/1.54 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 3.29/1.54 | (1) symmetric_difference(all_0_2_2, empty_set) = all_0_1_1 & symmetric_difference(empty_set, all_0_2_2) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v0) = v3) | ~ (difference(v0, v1) = v2) | ~ (union(v2, v3) = v4) | symmetric_difference(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ member(v2, v0) | member(v2, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (union(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : ( ~ empty(v0) | ~ member(v1, v0)) & ! [v0] : ~ member(v0, empty_set) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) & ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) & ? [v0] : (empty(v0) | ? [v1] : member(v1, v0)) & ? [v0] : subset(v0, v0) & ( ~ (all_0_0_0 = all_0_2_2) | ~ (all_0_1_1 = all_0_2_2)) % 3.29/1.54 | % 3.29/1.54 | Applying alpha-rule on (1) yields: % 3.29/1.54 | (2) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) % 3.29/1.54 | (3) ~ (all_0_0_0 = all_0_2_2) | ~ (all_0_1_1 = all_0_2_2) % 3.29/1.54 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 3.29/1.54 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ (difference(v0, empty_set) = v1)) % 3.29/1.54 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2)) % 3.29/1.54 | (7) symmetric_difference(all_0_2_2, empty_set) = all_0_1_1 % 3.29/1.55 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 3.29/1.55 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ member(v2, v0) | member(v2, v1)) % 3.29/1.55 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2) % 3.29/1.55 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2) % 3.29/1.55 | (12) symmetric_difference(empty_set, all_0_2_2) = all_0_0_0 % 3.29/1.55 | (13) ! [v0] : ! [v1] : ( ~ empty(v0) | ~ member(v1, v0)) % 3.29/1.55 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0)) % 3.29/1.55 | (15) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) % 3.29/1.55 | (16) ! [v0] : ~ member(v0, empty_set) % 3.29/1.55 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) % 3.29/1.55 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) % 3.29/1.55 | (19) ? [v0] : (empty(v0) | ? [v1] : member(v1, v0)) % 3.29/1.55 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ (union(v0, empty_set) = v1)) % 3.29/1.55 | (21) ? [v0] : subset(v0, v0) % 3.29/1.55 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v0) = v3) | ~ (difference(v0, v1) = v2) | ~ (union(v2, v3) = v4) | symmetric_difference(v0, v1) = v4) % 3.29/1.55 | (23) ! [v0] : ! [v1] : (v1 = empty_set | ~ (difference(empty_set, v0) = v1)) % 3.29/1.55 | (24) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 3.29/1.55 | % 3.29/1.55 | Instantiating formula (11) with all_0_1_1, all_0_2_2, empty_set and discharging atoms symmetric_difference(all_0_2_2, empty_set) = all_0_1_1, yields: % 3.29/1.55 | (25) symmetric_difference(empty_set, all_0_2_2) = all_0_1_1 % 3.29/1.55 | % 3.29/1.55 | Instantiating formula (6) with all_0_1_1, empty_set, all_0_2_2 and discharging atoms symmetric_difference(all_0_2_2, empty_set) = all_0_1_1, yields: % 3.29/1.55 | (26) ? [v0] : ? [v1] : (difference(all_0_2_2, empty_set) = v0 & difference(empty_set, all_0_2_2) = v1 & union(v0, v1) = all_0_1_1) % 3.29/1.55 | % 3.29/1.55 | Instantiating formula (6) with all_0_0_0, all_0_2_2, empty_set and discharging atoms symmetric_difference(empty_set, all_0_2_2) = all_0_0_0, yields: % 3.29/1.55 | (27) ? [v0] : ? [v1] : (difference(all_0_2_2, empty_set) = v1 & difference(empty_set, all_0_2_2) = v0 & union(v0, v1) = all_0_0_0) % 3.29/1.55 | % 3.29/1.55 | Instantiating (27) with all_14_0_9, all_14_1_10 yields: % 3.29/1.55 | (28) difference(all_0_2_2, empty_set) = all_14_0_9 & difference(empty_set, all_0_2_2) = all_14_1_10 & union(all_14_1_10, all_14_0_9) = all_0_0_0 % 3.29/1.55 | % 3.29/1.55 | Applying alpha-rule on (28) yields: % 3.29/1.55 | (29) difference(all_0_2_2, empty_set) = all_14_0_9 % 3.29/1.55 | (30) difference(empty_set, all_0_2_2) = all_14_1_10 % 3.29/1.55 | (31) union(all_14_1_10, all_14_0_9) = all_0_0_0 % 3.29/1.56 | % 3.29/1.56 | Instantiating (26) with all_16_0_11, all_16_1_12 yields: % 3.29/1.56 | (32) difference(all_0_2_2, empty_set) = all_16_1_12 & difference(empty_set, all_0_2_2) = all_16_0_11 & union(all_16_1_12, all_16_0_11) = all_0_1_1 % 3.29/1.56 | % 3.29/1.56 | Applying alpha-rule on (32) yields: % 3.29/1.56 | (33) difference(all_0_2_2, empty_set) = all_16_1_12 % 3.29/1.56 | (34) difference(empty_set, all_0_2_2) = all_16_0_11 % 3.29/1.56 | (35) union(all_16_1_12, all_16_0_11) = all_0_1_1 % 3.29/1.56 | % 3.29/1.56 | Instantiating formula (5) with all_16_1_12, all_0_2_2 and discharging atoms difference(all_0_2_2, empty_set) = all_16_1_12, yields: % 3.29/1.56 | (36) all_16_1_12 = all_0_2_2 % 3.29/1.56 | % 3.29/1.56 | Instantiating formula (23) with all_16_0_11, all_0_2_2 and discharging atoms difference(empty_set, all_0_2_2) = all_16_0_11, yields: % 3.29/1.56 | (37) all_16_0_11 = empty_set % 3.29/1.56 | % 3.29/1.56 | Instantiating formula (4) with empty_set, all_0_2_2, all_14_1_10, all_16_0_11 and discharging atoms difference(empty_set, all_0_2_2) = all_16_0_11, difference(empty_set, all_0_2_2) = all_14_1_10, yields: % 3.29/1.56 | (38) all_16_0_11 = all_14_1_10 % 3.29/1.56 | % 3.29/1.56 | Instantiating formula (14) with empty_set, all_0_2_2, all_0_1_1, all_0_0_0 and discharging atoms symmetric_difference(empty_set, all_0_2_2) = all_0_0_0, symmetric_difference(empty_set, all_0_2_2) = all_0_1_1, yields: % 3.29/1.56 | (39) all_0_0_0 = all_0_1_1 % 3.29/1.56 | % 3.29/1.56 | Combining equations (37,38) yields a new equation: % 3.29/1.56 | (40) all_14_1_10 = empty_set % 3.29/1.56 | % 3.29/1.56 | Combining equations (40,38) yields a new equation: % 3.29/1.56 | (37) all_16_0_11 = empty_set % 3.29/1.56 | % 3.29/1.56 | From (36)(37) and (35) follows: % 3.29/1.56 | (42) union(all_0_2_2, empty_set) = all_0_1_1 % 3.29/1.56 | % 3.29/1.56 +-Applying beta-rule and splitting (3), into two cases. % 3.29/1.56 |-Branch one: % 3.29/1.56 | (43) ~ (all_0_0_0 = all_0_2_2) % 3.29/1.56 | % 3.29/1.56 | Equations (39) can reduce 43 to: % 3.29/1.56 | (44) ~ (all_0_1_1 = all_0_2_2) % 3.29/1.56 | % 3.29/1.56 | Instantiating formula (20) with all_0_1_1, all_0_2_2 and discharging atoms union(all_0_2_2, empty_set) = all_0_1_1, yields: % 3.29/1.56 | (45) all_0_1_1 = all_0_2_2 % 3.29/1.56 | % 3.29/1.56 | Equations (45) can reduce 44 to: % 3.29/1.56 | (46) $false % 3.29/1.56 | % 3.29/1.56 |-The branch is then unsatisfiable % 3.29/1.56 |-Branch two: % 3.29/1.56 | (47) all_0_0_0 = all_0_2_2 % 3.29/1.56 | (44) ~ (all_0_1_1 = all_0_2_2) % 3.29/1.56 | % 3.29/1.56 | Combining equations (47,39) yields a new equation: % 3.29/1.56 | (45) all_0_1_1 = all_0_2_2 % 3.29/1.56 | % 3.29/1.56 | Equations (45) can reduce 44 to: % 3.29/1.56 | (46) $false % 3.29/1.56 | % 3.29/1.56 |-The branch is then unsatisfiable % 3.29/1.56 % SZS output end Proof for theBenchmark % 3.29/1.56 % 3.29/1.56 960ms %------------------------------------------------------------------------------