%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET882+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n011.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 00:22:54 EDT 2022 % Result : Theorem 1.93s 1.15s % Output : Proof 2.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET882+1 : TPTP v8.1.0. Released v3.2.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n011.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon Jul 11 08:48:27 EDT 2022 % 0.13/0.33 % CPUTime : % 0.19/0.57 ____ _ % 0.19/0.57 ___ / __ \_____(_)___ ________ __________ % 0.19/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.57 % 0.19/0.57 A Theorem Prover for First-Order Logic % 0.19/0.57 (ePrincess v.1.0) % 0.19/0.57 % 0.19/0.57 (c) Philipp Rümmer, 2009-2015 % 0.19/0.57 (c) Peter Backeman, 2014-2015 % 0.19/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.57 Bug reports to peter@backeman.se % 0.19/0.57 % 0.19/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.57 % 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.21/0.85 Prover 0: Preprocessing ... % 1.53/1.01 Prover 0: Warning: ignoring some quantifiers % 1.72/1.03 Prover 0: Constructing countermodel ... % 1.93/1.14 Prover 0: proved (523ms) % 1.93/1.15 % 1.93/1.15 No countermodel exists, formula is valid % 1.93/1.15 % SZS status Theorem for theBenchmark % 1.93/1.15 % 1.93/1.15 Generating proof ... Warning: ignoring some quantifiers % 2.64/1.36 found it (size 11) % 2.64/1.36 % 2.64/1.36 % SZS output start Proof for theBenchmark % 2.64/1.36 Assumed formulas after preprocessing and simplification: % 2.64/1.36 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v5 = v4) & ~ (v1 = v0) & set_difference(v2, v3) = v4 & singleton(v1) = v3 & singleton(v0) = v5 & unordered_pair(v0, v1) = v2 & empty(v7) & ~ empty(v6) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (set_difference(v11, v10) = v12) | ~ (unordered_pair(v8, v9) = v11) | in(v9, v10) | ? [v13] : ( ~ (v13 = v12) & singleton(v8) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v11, v10) = v12) | ~ (unordered_pair(v8, v9) = v11) | ~ in(v9, v10) | singleton(v8) = v12 | in(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v11, v10) = v12) | ~ (unordered_pair(v8, v9) = v11) | ~ in(v8, v10) | ? [v13] : ( ~ (v13 = v12) & singleton(v8) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_difference(v11, v10) = v9) | ~ (set_difference(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unordered_pair(v11, v10) = v9) | ~ (unordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v10, v9) = v11) | ~ (unordered_pair(v8, v8) = v10) | singleton(v8) = v11 | in(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (singleton(v8) = v9) | ~ in(v10, v9)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v9, v8) = v10) | unordered_pair(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | unordered_pair(v9, v8) = v10) & ? [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (singleton(v9) = v10) | ? [v11] : (( ~ (v11 = v9) | ~ in(v9, v8)) & (v11 = v9 | in(v11, v8)))) & ! [v8] : ! [v9] : ( ~ (singleton(v8) = v9) | in(v8, v9)) & ! [v8] : ! [v9] : ( ~ in(v9, v8) | ~ in(v8, v9))) % 2.84/1.40 | 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, all_0_7_7 yields: % 2.84/1.40 | (1) ~ (all_0_2_2 = all_0_3_3) & ~ (all_0_6_6 = all_0_7_7) & set_difference(all_0_5_5, all_0_4_4) = all_0_3_3 & singleton(all_0_6_6) = all_0_4_4 & singleton(all_0_7_7) = all_0_2_2 & unordered_pair(all_0_7_7, all_0_6_6) = all_0_5_5 & empty(all_0_0_0) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | in(v1, v2) | ? [v5] : ( ~ (v5 = v4) & singleton(v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | singleton(v0) = v4 | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ in(v0, v2) | ? [v5] : ( ~ (v5 = v4) & singleton(v0) = v5)) & ! [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] : ( ~ (set_difference(v2, v1) = v3) | ~ (unordered_pair(v0, v0) = v2) | singleton(v0) = v3 | in(v0, v1)) & ! [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] : ( ~ (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] : ! [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)) % 2.84/1.41 | % 2.84/1.41 | Applying alpha-rule on (1) yields: % 2.84/1.41 | (2) ~ (all_0_6_6 = all_0_7_7) % 2.84/1.41 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) % 2.84/1.41 | (4) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) % 2.84/1.41 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | singleton(v0) = v4 | in(v0, v2)) % 2.84/1.41 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 2.84/1.41 | (7) empty(all_0_0_0) % 2.84/1.41 | (8) set_difference(all_0_5_5, all_0_4_4) = all_0_3_3 % 2.84/1.41 | (9) singleton(all_0_6_6) = all_0_4_4 % 2.84/1.41 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 2.84/1.41 | (11) ~ empty(all_0_1_1) % 2.84/1.41 | (12) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) % 2.84/1.41 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 2.84/1.41 | (14) ~ (all_0_2_2 = all_0_3_3) % 2.84/1.41 | (15) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 2.84/1.41 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | in(v1, v2) | ? [v5] : ( ~ (v5 = v4) & singleton(v0) = v5)) % 2.84/1.41 | (17) singleton(all_0_7_7) = all_0_2_2 % 2.84/1.41 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ in(v0, v2) | ? [v5] : ( ~ (v5 = v4) & singleton(v0) = v5)) % 2.84/1.42 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (unordered_pair(v0, v0) = v2) | singleton(v0) = v3 | in(v0, v1)) % 2.84/1.42 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 2.84/1.42 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 2.84/1.42 | (22) unordered_pair(all_0_7_7, all_0_6_6) = all_0_5_5 % 2.84/1.42 | % 2.84/1.42 | Instantiating formula (12) with all_0_4_4, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_0_4_4, yields: % 2.84/1.42 | (23) in(all_0_6_6, all_0_4_4) % 2.84/1.42 | % 2.84/1.42 | Instantiating formula (5) with all_0_3_3, all_0_5_5, all_0_4_4, all_0_6_6, all_0_7_7 and discharging atoms set_difference(all_0_5_5, all_0_4_4) = all_0_3_3, unordered_pair(all_0_7_7, all_0_6_6) = all_0_5_5, in(all_0_6_6, all_0_4_4), yields: % 2.84/1.42 | (24) singleton(all_0_7_7) = all_0_3_3 | in(all_0_7_7, all_0_4_4) % 2.84/1.42 | % 2.84/1.42 +-Applying beta-rule and splitting (24), into two cases. % 2.84/1.42 |-Branch one: % 2.84/1.42 | (25) singleton(all_0_7_7) = all_0_3_3 % 2.84/1.42 | % 2.84/1.42 | Instantiating formula (10) with all_0_7_7, all_0_3_3, all_0_2_2 and discharging atoms singleton(all_0_7_7) = all_0_2_2, singleton(all_0_7_7) = all_0_3_3, yields: % 2.84/1.42 | (26) all_0_2_2 = all_0_3_3 % 2.84/1.42 | % 2.84/1.42 | Equations (26) can reduce 14 to: % 2.84/1.42 | (27) $false % 2.84/1.42 | % 2.84/1.42 |-The branch is then unsatisfiable % 2.84/1.42 |-Branch two: % 2.84/1.42 | (28) ~ (singleton(all_0_7_7) = all_0_3_3) % 2.84/1.42 | (29) in(all_0_7_7, all_0_4_4) % 2.84/1.42 | % 2.84/1.42 | Instantiating formula (3) with all_0_7_7, all_0_4_4, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_0_4_4, in(all_0_7_7, all_0_4_4), yields: % 2.84/1.42 | (30) all_0_6_6 = all_0_7_7 % 2.84/1.42 | % 2.84/1.42 | Equations (30) can reduce 2 to: % 2.84/1.42 | (27) $false % 2.84/1.42 | % 2.84/1.42 |-The branch is then unsatisfiable % 2.84/1.42 % SZS output end Proof for theBenchmark % 2.84/1.42 % 2.84/1.42 838ms %------------------------------------------------------------------------------