%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET958+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n006.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 00:23:27 EDT 2022 % Result : Theorem 3.75s 1.62s % Output : Proof 4.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET958+1 : TPTP v8.1.0. Released v3.2.0. % 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n006.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 08:05:20 EDT 2022 % 0.13/0.33 % CPUTime : % 0.55/0.59 ____ _ % 0.55/0.59 ___ / __ \_____(_)___ ________ __________ % 0.55/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.55/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.55/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.55/0.59 % 0.55/0.59 A Theorem Prover for First-Order Logic % 0.55/0.59 (ePrincess v.1.0) % 0.55/0.59 % 0.55/0.59 (c) Philipp Rümmer, 2009-2015 % 0.55/0.59 (c) Peter Backeman, 2014-2015 % 0.55/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.55/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.55/0.59 Bug reports to peter@backeman.se % 0.55/0.59 % 0.55/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.55/0.59 % 0.55/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.37/0.88 Prover 0: Preprocessing ... % 1.71/1.02 Prover 0: Warning: ignoring some quantifiers % 1.71/1.04 Prover 0: Constructing countermodel ... % 3.62/1.53 Prover 0: gave up % 3.62/1.53 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.75/1.55 Prover 1: Preprocessing ... % 3.75/1.59 Prover 1: Constructing countermodel ... % 3.75/1.61 Prover 1: proved (83ms) % 3.75/1.62 % 3.75/1.62 No countermodel exists, formula is valid % 3.75/1.62 % SZS status Theorem for theBenchmark % 3.75/1.62 % 3.75/1.62 Generating proof ... found it (size 14) % 4.47/1.78 % 4.47/1.78 % SZS output start Proof for theBenchmark % 4.47/1.78 Assumed formulas after preprocessing and simplification: % 4.47/1.78 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v4 = 0) & ~ (v2 = 0) & empty(v5) = 0 & empty(v3) = v4 & subset(v0, v1) = v2 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (singleton(v6) = v9) | ~ (unordered_pair(v8, v9) = v10) | ~ (unordered_pair(v6, v7) = v8) | ordered_pair(v6, v7) = v10) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (ordered_pair(v9, v8) = v7) | ~ (ordered_pair(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (subset(v9, v8) = v7) | ~ (subset(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (unordered_pair(v9, v8) = v7) | ~ (unordered_pair(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (in(v9, v8) = v7) | ~ (in(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v6, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & in(v9, v7) = v10 & in(v9, v6) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (empty(v8) = v7) | ~ (empty(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (singleton(v8) = v7) | ~ (singleton(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (ordered_pair(v6, v7) = v8) | ~ (in(v8, v0) = 0) | in(v8, v1) = 0) & ! [v6] : ! [v7] : ! [v8] : ( ~ (ordered_pair(v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & empty(v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (subset(v6, v7) = 0) | ~ (in(v8, v6) = 0) | in(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ( ~ (unordered_pair(v6, v7) = v8) | unordered_pair(v7, v6) = v8) & ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v6, v6) = v7)) & ! [v6] : ! [v7] : ( ~ (in(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & in(v7, v6) = v8)) & ! [v6] : ( ~ (in(v6, v0) = 0) | ? [v7] : ? [v8] : ordered_pair(v7, v8) = v6)) % 4.89/1.81 | 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: % 4.89/1.81 | (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 & subset(all_0_5_5, all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [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] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_0_5_5) = 0) | in(v2, all_0_4_4) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : ( ~ (in(v0, all_0_5_5) = 0) | ? [v1] : ? [v2] : ordered_pair(v1, v2) = v0) % 4.92/1.82 | % 4.92/1.82 | Applying alpha-rule on (1) yields: % 4.92/1.82 | (2) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 4.92/1.82 | (3) ~ (all_0_3_3 = 0) % 4.92/1.82 | (4) ~ (all_0_1_1 = 0) % 4.92/1.82 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 4.92/1.82 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 4.92/1.82 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_0_5_5) = 0) | in(v2, all_0_4_4) = 0) % 4.92/1.82 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 4.92/1.82 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 4.92/1.82 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 4.92/1.82 | (11) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 4.92/1.82 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 4.92/1.82 | (13) ! [v0] : ( ~ (in(v0, all_0_5_5) = 0) | ? [v1] : ? [v2] : ordered_pair(v1, v2) = v0) % 4.92/1.82 | (14) empty(all_0_2_2) = all_0_1_1 % 4.92/1.82 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 4.92/1.82 | (16) subset(all_0_5_5, all_0_4_4) = all_0_3_3 % 4.92/1.82 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 4.92/1.82 | (18) empty(all_0_0_0) = 0 % 4.92/1.82 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) % 4.92/1.82 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 4.92/1.82 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 4.92/1.82 | % 4.92/1.82 | Instantiating formula (2) with all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 4.92/1.82 | (22) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_5_5) = 0) % 4.92/1.82 | % 4.92/1.82 +-Applying beta-rule and splitting (22), into two cases. % 4.92/1.82 |-Branch one: % 4.92/1.82 | (23) all_0_3_3 = 0 % 4.92/1.82 | % 4.92/1.82 | Equations (23) can reduce 3 to: % 4.92/1.82 | (24) $false % 4.92/1.82 | % 4.92/1.82 |-The branch is then unsatisfiable % 4.92/1.82 |-Branch two: % 4.92/1.82 | (3) ~ (all_0_3_3 = 0) % 4.92/1.82 | (26) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_5_5) = 0) % 4.92/1.82 | % 4.92/1.82 | Instantiating (26) with all_14_0_6, all_14_1_7 yields: % 4.92/1.82 | (27) ~ (all_14_0_6 = 0) & in(all_14_1_7, all_0_4_4) = all_14_0_6 & in(all_14_1_7, all_0_5_5) = 0 % 4.92/1.83 | % 4.92/1.83 | Applying alpha-rule on (27) yields: % 4.92/1.83 | (28) ~ (all_14_0_6 = 0) % 4.92/1.83 | (29) in(all_14_1_7, all_0_4_4) = all_14_0_6 % 4.92/1.83 | (30) in(all_14_1_7, all_0_5_5) = 0 % 4.92/1.83 | % 4.92/1.83 | Instantiating formula (13) with all_14_1_7 and discharging atoms in(all_14_1_7, all_0_5_5) = 0, yields: % 4.92/1.83 | (31) ? [v0] : ? [v1] : ordered_pair(v0, v1) = all_14_1_7 % 4.92/1.83 | % 4.92/1.83 | Instantiating (31) with all_27_0_9, all_27_1_10 yields: % 4.92/1.83 | (32) ordered_pair(all_27_1_10, all_27_0_9) = all_14_1_7 % 4.92/1.83 | % 4.92/1.83 | Instantiating formula (7) with all_14_1_7, all_27_0_9, all_27_1_10 and discharging atoms ordered_pair(all_27_1_10, all_27_0_9) = all_14_1_7, in(all_14_1_7, all_0_5_5) = 0, yields: % 4.92/1.83 | (33) in(all_14_1_7, all_0_4_4) = 0 % 4.92/1.83 | % 4.92/1.83 | Instantiating formula (10) with all_14_1_7, all_0_4_4, 0, all_14_0_6 and discharging atoms in(all_14_1_7, all_0_4_4) = all_14_0_6, in(all_14_1_7, all_0_4_4) = 0, yields: % 4.92/1.83 | (34) all_14_0_6 = 0 % 4.92/1.83 | % 4.92/1.83 | Equations (34) can reduce 28 to: % 4.92/1.83 | (24) $false % 4.92/1.83 | % 4.92/1.83 |-The branch is then unsatisfiable % 4.92/1.83 % SZS output end Proof for theBenchmark % 4.92/1.83 % 4.92/1.83 1230ms %------------------------------------------------------------------------------