%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET929+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n015.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 00:23:16 EDT 2022 % Result : Theorem 1.74s 1.08s % Output : Proof 2.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SET929+1 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n015.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 : Sat Jul 9 21:57:37 EDT 2022 % 0.12/0.33 % CPUTime : % 0.54/0.57 ____ _ % 0.54/0.57 ___ / __ \_____(_)___ ________ __________ % 0.54/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.54/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.54/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.54/0.57 % 0.54/0.57 A Theorem Prover for First-Order Logic % 0.54/0.57 (ePrincess v.1.0) % 0.54/0.57 % 0.54/0.57 (c) Philipp Rümmer, 2009-2015 % 0.54/0.57 (c) Peter Backeman, 2014-2015 % 0.54/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.54/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.54/0.57 Bug reports to peter@backeman.se % 0.54/0.57 % 0.54/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.54/0.57 % 0.54/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.60/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.10/0.84 Prover 0: Preprocessing ... % 1.50/0.95 Prover 0: Warning: ignoring some quantifiers % 1.55/0.97 Prover 0: Constructing countermodel ... % 1.74/1.08 Prover 0: proved (461ms) % 1.74/1.08 % 1.74/1.08 No countermodel exists, formula is valid % 1.74/1.08 % SZS status Theorem for theBenchmark % 1.74/1.08 % 1.74/1.08 Generating proof ... Warning: ignoring some quantifiers % 2.49/1.27 found it (size 18) % 2.49/1.27 % 2.49/1.27 % SZS output start Proof for theBenchmark % 2.49/1.27 Assumed formulas after preprocessing and simplification: % 2.49/1.27 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (set_difference(v3, v2) = v4 & unordered_pair(v0, v1) = v3 & empty(v6) & empty(empty_set) & ~ empty(v5) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_difference(v10, v9) = v8) | ~ (set_difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v7, v8) = v10) | ~ subset(v10, v9) | in(v8, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v7, v8) = v10) | ~ subset(v10, v9) | in(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v7, v8) = v10) | ~ in(v8, v9) | ~ in(v7, v9) | subset(v10, v9)) & ! [v7] : ! [v8] : ! [v9] : (v9 = empty_set | ~ (set_difference(v7, v8) = v9) | ~ subset(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v8, v7) = v9) | unordered_pair(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | unordered_pair(v8, v7) = v9) & ! [v7] : ! [v8] : ( ~ (set_difference(v7, v8) = empty_set) | subset(v7, v8)) & ! [v7] : ! [v8] : ( ~ in(v8, v7) | ~ in(v7, v8)) & ? [v7] : subset(v7, v7) & ((v4 = empty_set & ( ~ in(v1, v2) | ~ in(v0, v2))) | ( ~ (v4 = empty_set) & in(v1, v2) & in(v0, v2)))) % 2.72/1.31 | 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: % 2.72/1.31 | (1) set_difference(all_0_3_3, all_0_4_4) = all_0_2_2 & unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3 & empty(all_0_0_0) & empty(empty_set) & ~ 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] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ? [v0] : subset(v0, v0) & ((all_0_2_2 = empty_set & ( ~ in(all_0_5_5, all_0_4_4) | ~ in(all_0_6_6, all_0_4_4))) | ( ~ (all_0_2_2 = empty_set) & in(all_0_5_5, all_0_4_4) & in(all_0_6_6, all_0_4_4))) % 2.72/1.31 | % 2.72/1.31 | Applying alpha-rule on (1) yields: % 2.72/1.31 | (2) (all_0_2_2 = empty_set & ( ~ in(all_0_5_5, all_0_4_4) | ~ in(all_0_6_6, all_0_4_4))) | ( ~ (all_0_2_2 = empty_set) & in(all_0_5_5, all_0_4_4) & in(all_0_6_6, all_0_4_4)) % 2.72/1.32 | (3) empty(empty_set) % 2.72/1.32 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) % 2.72/1.32 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2)) % 2.72/1.32 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2)) % 2.72/1.32 | (7) ? [v0] : subset(v0, v0) % 2.72/1.32 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 2.72/1.32 | (9) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) % 2.72/1.32 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 2.72/1.32 | (11) empty(all_0_0_0) % 2.72/1.32 | (12) set_difference(all_0_3_3, all_0_4_4) = all_0_2_2 % 2.72/1.32 | (13) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 2.72/1.32 | (14) ~ empty(all_0_1_1) % 2.72/1.32 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2)) % 2.72/1.32 | (16) unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3 % 2.72/1.32 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 2.72/1.32 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 2.72/1.32 | % 2.72/1.32 +-Applying beta-rule and splitting (2), into two cases. % 2.72/1.32 |-Branch one: % 2.72/1.32 | (19) all_0_2_2 = empty_set & ( ~ in(all_0_5_5, all_0_4_4) | ~ in(all_0_6_6, all_0_4_4)) % 2.72/1.32 | % 2.72/1.32 | Applying alpha-rule on (19) yields: % 2.72/1.32 | (20) all_0_2_2 = empty_set % 2.72/1.32 | (21) ~ in(all_0_5_5, all_0_4_4) | ~ in(all_0_6_6, all_0_4_4) % 2.72/1.32 | % 2.72/1.32 | From (20) and (12) follows: % 2.72/1.32 | (22) set_difference(all_0_3_3, all_0_4_4) = empty_set % 2.72/1.32 | % 2.72/1.32 | Instantiating formula (9) with all_0_4_4, all_0_3_3 and discharging atoms set_difference(all_0_3_3, all_0_4_4) = empty_set, yields: % 2.72/1.32 | (23) subset(all_0_3_3, all_0_4_4) % 2.72/1.32 | % 2.72/1.32 | Instantiating formula (5) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3, subset(all_0_3_3, all_0_4_4), yields: % 2.72/1.33 | (24) in(all_0_5_5, all_0_4_4) % 2.72/1.33 | % 2.72/1.33 | Instantiating formula (15) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3, subset(all_0_3_3, all_0_4_4), yields: % 2.72/1.33 | (25) in(all_0_6_6, all_0_4_4) % 2.72/1.33 | % 2.72/1.33 +-Applying beta-rule and splitting (21), into two cases. % 2.72/1.33 |-Branch one: % 2.72/1.33 | (26) ~ in(all_0_5_5, all_0_4_4) % 2.72/1.33 | % 2.72/1.33 | Using (24) and (26) yields: % 2.72/1.33 | (27) $false % 2.72/1.33 | % 2.72/1.33 |-The branch is then unsatisfiable % 2.72/1.33 |-Branch two: % 2.72/1.33 | (24) in(all_0_5_5, all_0_4_4) % 2.72/1.33 | (29) ~ in(all_0_6_6, all_0_4_4) % 2.72/1.33 | % 2.72/1.33 | Using (25) and (29) yields: % 2.72/1.33 | (27) $false % 2.72/1.33 | % 2.72/1.33 |-The branch is then unsatisfiable % 2.72/1.33 |-Branch two: % 2.72/1.33 | (31) ~ (all_0_2_2 = empty_set) & in(all_0_5_5, all_0_4_4) & in(all_0_6_6, all_0_4_4) % 2.72/1.33 | % 2.72/1.33 | Applying alpha-rule on (31) yields: % 2.72/1.33 | (32) ~ (all_0_2_2 = empty_set) % 2.72/1.33 | (24) in(all_0_5_5, all_0_4_4) % 2.72/1.33 | (25) in(all_0_6_6, all_0_4_4) % 2.72/1.33 | % 2.72/1.33 | Instantiating formula (6) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3, in(all_0_5_5, all_0_4_4), in(all_0_6_6, all_0_4_4), yields: % 2.72/1.33 | (23) subset(all_0_3_3, all_0_4_4) % 2.72/1.33 | % 2.72/1.33 | Instantiating formula (4) with all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms set_difference(all_0_3_3, all_0_4_4) = all_0_2_2, subset(all_0_3_3, all_0_4_4), yields: % 2.72/1.33 | (20) all_0_2_2 = empty_set % 2.72/1.33 | % 2.72/1.33 | Equations (20) can reduce 32 to: % 2.72/1.33 | (37) $false % 2.72/1.33 | % 2.72/1.33 |-The branch is then unsatisfiable % 2.72/1.33 % SZS output end Proof for theBenchmark % 2.72/1.33 % 2.72/1.33 754ms %------------------------------------------------------------------------------