%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU157+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n016.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 08:47:05 EDT 2022 % Result : Theorem 2.34s 1.28s % Output : Proof 3.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU157+1 : TPTP v8.1.0. Released v3.3.0. % 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n016.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 Jun 19 11:45:38 EDT 2022 % 0.12/0.34 % CPUTime : % 0.20/0.58 ____ _ % 0.20/0.58 ___ / __ \_____(_)___ ________ __________ % 0.20/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.20/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.20/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.20/0.58 % 0.20/0.58 A Theorem Prover for First-Order Logic % 0.20/0.58 (ePrincess v.1.0) % 0.20/0.58 % 0.20/0.58 (c) Philipp Rümmer, 2009-2015 % 0.20/0.58 (c) Peter Backeman, 2014-2015 % 0.20/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.20/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.20/0.58 Bug reports to peter@backeman.se % 0.20/0.58 % 0.20/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.20/0.58 % 0.20/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.70/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.47/0.94 Prover 0: Preprocessing ... % 1.83/1.13 Prover 0: Warning: ignoring some quantifiers % 1.83/1.14 Prover 0: Constructing countermodel ... % 2.34/1.28 Prover 0: proved (616ms) % 2.34/1.28 % 2.34/1.28 No countermodel exists, formula is valid % 2.34/1.28 % SZS status Theorem for theBenchmark % 2.34/1.28 % 2.34/1.28 Generating proof ... Warning: ignoring some quantifiers % 3.16/1.49 found it (size 19) % 3.16/1.49 % 3.16/1.49 % SZS output start Proof for theBenchmark % 3.16/1.49 Assumed formulas after preprocessing and simplification: % 3.16/1.49 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (cartesian_product2(v2, v3) = v5 & ordered_pair(v0, v1) = v4 & empty(v7) & ~ empty(v6) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v8, v9) = v10) | ~ (ordered_pair(v12, v13) = v11) | ~ in(v13, v9) | ~ in(v12, v8) | in(v11, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v9 | ~ (ordered_pair(v10, v11) = v12) | ~ (ordered_pair(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v8 | ~ (ordered_pair(v10, v11) = v12) | ~ (ordered_pair(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (singleton(v8) = v11) | ~ (unordered_pair(v10, v11) = v12) | ~ (unordered_pair(v8, v9) = v10) | ordered_pair(v8, v9) = v12) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (cartesian_product2(v11, v10) = v9) | ~ (cartesian_product2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (ordered_pair(v11, v10) = v9) | ~ (ordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unordered_pair(v11, v10) = v9) | ~ (unordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (cartesian_product2(v8, v9) = v10) | ~ in(v11, v10) | ? [v12] : ? [v13] : (ordered_pair(v12, v13) = v11 & in(v13, v9) & in(v12, v8))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (cartesian_product2(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (( ~ in(v12, v8) | ! [v16] : ! [v17] : ( ~ (ordered_pair(v16, v17) = v12) | ~ in(v17, v10) | ~ in(v16, v9))) & (in(v12, v8) | (v15 = v12 & ordered_pair(v13, v14) = v12 & in(v14, v10) & in(v13, v9))))) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ empty(v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ? [v11] : ? [v12] : (singleton(v8) = v12 & unordered_pair(v11, v12) = v10 & unordered_pair(v8, v9) = v11)) & ! [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] : ( ~ in(v9, v8) | ~ in(v8, v9)) & ((in(v4, v5) & ( ~ in(v1, v3) | ~ in(v0, v2))) | (in(v1, v3) & in(v0, v2) & ~ in(v4, v5)))) % 3.25/1.53 | 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: % 3.25/1.53 | (1) cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2 & ordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3 & empty(all_0_0_0) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v4, v5) = v3) | ~ in(v5, v1) | ~ in(v4, v0) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [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 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) & in(v4, v0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ in(v4, v0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v9) = v4) | ~ in(v9, v2) | ~ in(v8, v1))) & (in(v4, v0) | (v7 = v4 & ordered_pair(v5, v6) = v4 & in(v6, v2) & in(v5, v1))))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [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] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ((in(all_0_3_3, all_0_2_2) & ( ~ in(all_0_6_6, all_0_4_4) | ~ in(all_0_7_7, all_0_5_5))) | (in(all_0_6_6, all_0_4_4) & in(all_0_7_7, all_0_5_5) & ~ in(all_0_3_3, all_0_2_2))) % 3.36/1.54 | % 3.36/1.54 | Applying alpha-rule on (1) yields: % 3.36/1.54 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 3.36/1.54 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 3.36/1.54 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 3.36/1.54 | (5) (in(all_0_3_3, all_0_2_2) & ( ~ in(all_0_6_6, all_0_4_4) | ~ in(all_0_7_7, all_0_5_5))) | (in(all_0_6_6, all_0_4_4) & in(all_0_7_7, all_0_5_5) & ~ in(all_0_3_3, all_0_2_2)) % 3.36/1.54 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 3.36/1.54 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 3.36/1.54 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 3.36/1.54 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 3.36/1.55 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 3.36/1.55 | (11) ordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3 % 3.36/1.55 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v4, v5) = v3) | ~ in(v5, v1) | ~ in(v4, v0) | in(v3, v2)) % 3.36/1.55 | (13) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 3.36/1.55 | (14) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ in(v4, v0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v9) = v4) | ~ in(v9, v2) | ~ in(v8, v1))) & (in(v4, v0) | (v7 = v4 & ordered_pair(v5, v6) = v4 & in(v6, v2) & in(v5, v1))))) % 3.36/1.55 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 3.36/1.55 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 3.36/1.55 | (17) ~ empty(all_0_1_1) % 3.36/1.55 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) & in(v4, v0))) % 3.36/1.55 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 3.36/1.55 | (20) empty(all_0_0_0) % 3.36/1.55 | (21) cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2 % 3.36/1.55 | % 3.36/1.55 +-Applying beta-rule and splitting (5), into two cases. % 3.36/1.55 |-Branch one: % 3.36/1.55 | (22) in(all_0_3_3, all_0_2_2) & ( ~ in(all_0_6_6, all_0_4_4) | ~ in(all_0_7_7, all_0_5_5)) % 3.36/1.55 | % 3.36/1.55 | Applying alpha-rule on (22) yields: % 3.36/1.55 | (23) in(all_0_3_3, all_0_2_2) % 3.36/1.55 | (24) ~ in(all_0_6_6, all_0_4_4) | ~ in(all_0_7_7, all_0_5_5) % 3.36/1.55 | % 3.36/1.55 | Instantiating formula (18) with all_0_3_3, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2, in(all_0_3_3, all_0_2_2), yields: % 3.36/1.55 | (25) ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_0_3_3 & in(v1, all_0_4_4) & in(v0, all_0_5_5)) % 3.36/1.55 | % 3.36/1.55 | Instantiating (25) with all_30_0_11, all_30_1_12 yields: % 3.36/1.55 | (26) ordered_pair(all_30_1_12, all_30_0_11) = all_0_3_3 & in(all_30_0_11, all_0_4_4) & in(all_30_1_12, all_0_5_5) % 3.36/1.55 | % 3.36/1.55 | Applying alpha-rule on (26) yields: % 3.36/1.55 | (27) ordered_pair(all_30_1_12, all_30_0_11) = all_0_3_3 % 3.36/1.55 | (28) in(all_30_0_11, all_0_4_4) % 3.36/1.55 | (29) in(all_30_1_12, all_0_5_5) % 3.36/1.55 | % 3.36/1.55 | Instantiating formula (9) with all_0_3_3, all_30_0_11, all_30_1_12, all_0_6_6, all_0_7_7 and discharging atoms ordered_pair(all_30_1_12, all_30_0_11) = all_0_3_3, ordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3, yields: % 3.36/1.55 | (30) all_30_0_11 = all_0_6_6 % 3.36/1.55 | % 3.36/1.55 | Instantiating formula (4) with all_0_3_3, all_30_0_11, all_30_1_12, all_0_6_6, all_0_7_7 and discharging atoms ordered_pair(all_30_1_12, all_30_0_11) = all_0_3_3, ordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3, yields: % 3.36/1.55 | (31) all_30_1_12 = all_0_7_7 % 3.36/1.55 | % 3.36/1.55 | From (30) and (28) follows: % 3.36/1.56 | (32) in(all_0_6_6, all_0_4_4) % 3.36/1.56 | % 3.36/1.56 | From (31) and (29) follows: % 3.36/1.56 | (33) in(all_0_7_7, all_0_5_5) % 3.36/1.56 | % 3.36/1.56 +-Applying beta-rule and splitting (24), into two cases. % 3.36/1.56 |-Branch one: % 3.36/1.56 | (34) ~ in(all_0_6_6, all_0_4_4) % 3.36/1.56 | % 3.36/1.56 | Using (32) and (34) yields: % 3.36/1.56 | (35) $false % 3.36/1.56 | % 3.36/1.56 |-The branch is then unsatisfiable % 3.36/1.56 |-Branch two: % 3.36/1.56 | (32) in(all_0_6_6, all_0_4_4) % 3.36/1.56 | (37) ~ in(all_0_7_7, all_0_5_5) % 3.36/1.56 | % 3.36/1.56 | Using (33) and (37) yields: % 3.36/1.56 | (35) $false % 3.36/1.56 | % 3.36/1.56 |-The branch is then unsatisfiable % 3.36/1.56 |-Branch two: % 3.36/1.56 | (39) in(all_0_6_6, all_0_4_4) & in(all_0_7_7, all_0_5_5) & ~ in(all_0_3_3, all_0_2_2) % 3.36/1.56 | % 3.36/1.56 | Applying alpha-rule on (39) yields: % 3.36/1.56 | (32) in(all_0_6_6, all_0_4_4) % 3.36/1.56 | (33) in(all_0_7_7, all_0_5_5) % 3.36/1.56 | (42) ~ in(all_0_3_3, all_0_2_2) % 3.36/1.56 | % 3.36/1.56 | Instantiating formula (12) with all_0_6_6, all_0_7_7, all_0_3_3, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2, ordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3, in(all_0_6_6, all_0_4_4), in(all_0_7_7, all_0_5_5), ~ in(all_0_3_3, all_0_2_2), yields: % 3.36/1.56 | (35) $false % 3.36/1.56 | % 3.36/1.56 |-The branch is then unsatisfiable % 3.36/1.56 % SZS output end Proof for theBenchmark % 3.36/1.56 % 3.36/1.56 960ms %------------------------------------------------------------------------------