%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET976+1 : TPTP v8.1.0. Released v3.2.0. % 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 00:23:33 EDT 2022 % Result : Theorem 2.28s 1.30s % Output : Proof 3.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET976+1 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n029.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Mon Jul 11 09:47:47 EDT 2022 % 0.12/0.34 % CPUTime : % 0.58/0.60 ____ _ % 0.58/0.60 ___ / __ \_____(_)___ ________ __________ % 0.58/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.60 % 0.58/0.60 A Theorem Prover for First-Order Logic % 0.58/0.60 (ePrincess v.1.0) % 0.58/0.60 % 0.58/0.60 (c) Philipp Rümmer, 2009-2015 % 0.58/0.60 (c) Peter Backeman, 2014-2015 % 0.58/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.60 Bug reports to peter@backeman.se % 0.58/0.60 % 0.58/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.60 % 0.58/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.41/0.93 Prover 0: Preprocessing ... % 1.82/1.11 Prover 0: Warning: ignoring some quantifiers % 1.82/1.13 Prover 0: Constructing countermodel ... % 2.28/1.30 Prover 0: proved (642ms) % 2.28/1.30 % 2.28/1.30 No countermodel exists, formula is valid % 2.28/1.30 % SZS status Theorem for theBenchmark % 2.28/1.30 % 2.28/1.30 Generating proof ... Warning: ignoring some quantifiers % 3.12/1.51 found it (size 17) % 3.12/1.51 % 3.12/1.51 % SZS output start Proof for theBenchmark % 3.12/1.51 Assumed formulas after preprocessing and simplification: % 3.12/1.51 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cartesian_product2(v2, v5) = v6 & ordered_pair(v0, v1) = v4 & singleton(v3) = v5 & empty(v8) & ~ empty(v7) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cartesian_product2(v11, v12) = v14) | ~ (ordered_pair(v9, v10) = v13) | ~ in(v13, v14) | in(v10, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cartesian_product2(v11, v12) = v14) | ~ (ordered_pair(v9, v10) = v13) | ~ in(v13, v14) | in(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cartesian_product2(v11, v12) = v14) | ~ (ordered_pair(v9, v10) = v13) | ~ in(v10, v12) | ~ in(v9, v11) | in(v13, v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (singleton(v9) = v12) | ~ (unordered_pair(v11, v12) = v13) | ~ (unordered_pair(v9, v10) = v11) | ordered_pair(v9, v10) = v13) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (cartesian_product2(v12, v11) = v10) | ~ (cartesian_product2(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (ordered_pair(v12, v11) = v10) | ~ (ordered_pair(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (unordered_pair(v12, v11) = v10) | ~ (unordered_pair(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (singleton(v9) = v10) | ~ in(v11, v10)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (singleton(v11) = v10) | ~ (singleton(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ~ empty(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ? [v12] : ? [v13] : (singleton(v9) = v13 & unordered_pair(v12, v13) = v11 & unordered_pair(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v10, v9) = v11) | unordered_pair(v9, v10) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | unordered_pair(v10, v9) = v11) & ? [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (singleton(v10) = v11) | ? [v12] : (( ~ (v12 = v10) | ~ in(v10, v9)) & (v12 = v10 | in(v12, v9)))) & ! [v9] : ! [v10] : ( ~ (singleton(v9) = v10) | in(v9, v10)) & ! [v9] : ! [v10] : ( ~ in(v10, v9) | ~ in(v9, v10)) & ((v3 = v1 & in(v0, v2) & ~ in(v4, v6)) | (in(v4, v6) & ( ~ (v3 = v1) | ~ in(v0, v2))))) % 3.23/1.54 | 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, all_0_8_8 yields: % 3.23/1.54 | (1) cartesian_product2(all_0_6_6, all_0_3_3) = all_0_2_2 & ordered_pair(all_0_8_8, all_0_7_7) = all_0_4_4 & singleton(all_0_5_5) = all_0_3_3 & empty(all_0_0_0) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5)) & ! [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] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, 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] : ! [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)) & ((all_0_5_5 = all_0_7_7 & in(all_0_8_8, all_0_6_6) & ~ in(all_0_4_4, all_0_2_2)) | (in(all_0_4_4, all_0_2_2) & ( ~ (all_0_5_5 = all_0_7_7) | ~ in(all_0_8_8, all_0_6_6)))) % 3.23/1.55 | % 3.23/1.55 | Applying alpha-rule on (1) yields: % 3.23/1.55 | (2) (all_0_5_5 = all_0_7_7 & in(all_0_8_8, all_0_6_6) & ~ in(all_0_4_4, all_0_2_2)) | (in(all_0_4_4, all_0_2_2) & ( ~ (all_0_5_5 = all_0_7_7) | ~ in(all_0_8_8, all_0_6_6))) % 3.23/1.55 | (3) cartesian_product2(all_0_6_6, all_0_3_3) = all_0_2_2 % 3.23/1.55 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 3.23/1.55 | (5) ~ empty(all_0_1_1) % 3.23/1.55 | (6) empty(all_0_0_0) % 3.23/1.55 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 3.23/1.55 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 3.23/1.55 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2)) % 3.23/1.56 | (10) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) % 3.23/1.56 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 3.23/1.56 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 3.23/1.56 | (13) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 3.23/1.56 | (14) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) % 3.23/1.56 | (15) ordered_pair(all_0_8_8, all_0_7_7) = all_0_4_4 % 3.23/1.56 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 3.23/1.56 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5)) % 3.23/1.56 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 3.23/1.56 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 3.23/1.56 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 3.23/1.56 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3)) % 3.23/1.56 | (22) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) % 3.23/1.56 | (23) singleton(all_0_5_5) = all_0_3_3 % 3.23/1.56 | % 3.23/1.56 | Instantiating formula (14) with all_0_3_3, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_3_3, yields: % 3.23/1.56 | (24) in(all_0_5_5, all_0_3_3) % 3.23/1.56 | % 3.23/1.56 +-Applying beta-rule and splitting (2), into two cases. % 3.23/1.56 |-Branch one: % 3.23/1.56 | (25) all_0_5_5 = all_0_7_7 & in(all_0_8_8, all_0_6_6) & ~ in(all_0_4_4, all_0_2_2) % 3.23/1.56 | % 3.23/1.56 | Applying alpha-rule on (25) yields: % 3.23/1.56 | (26) all_0_5_5 = all_0_7_7 % 3.23/1.56 | (27) in(all_0_8_8, all_0_6_6) % 3.23/1.56 | (28) ~ in(all_0_4_4, all_0_2_2) % 3.23/1.56 | % 3.23/1.56 | From (26) and (24) follows: % 3.23/1.56 | (29) in(all_0_7_7, all_0_3_3) % 3.23/1.56 | % 3.23/1.56 | Instantiating formula (17) with all_0_2_2, all_0_4_4, all_0_3_3, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms cartesian_product2(all_0_6_6, all_0_3_3) = all_0_2_2, ordered_pair(all_0_8_8, all_0_7_7) = all_0_4_4, in(all_0_7_7, all_0_3_3), in(all_0_8_8, all_0_6_6), ~ in(all_0_4_4, all_0_2_2), yields: % 3.23/1.56 | (30) $false % 3.23/1.56 | % 3.23/1.56 |-The branch is then unsatisfiable % 3.23/1.56 |-Branch two: % 3.23/1.56 | (31) in(all_0_4_4, all_0_2_2) & ( ~ (all_0_5_5 = all_0_7_7) | ~ in(all_0_8_8, all_0_6_6)) % 3.23/1.56 | % 3.23/1.56 | Applying alpha-rule on (31) yields: % 3.23/1.56 | (32) in(all_0_4_4, all_0_2_2) % 3.23/1.56 | (33) ~ (all_0_5_5 = all_0_7_7) | ~ in(all_0_8_8, all_0_6_6) % 3.23/1.56 | % 3.23/1.56 | Instantiating formula (21) with all_0_2_2, all_0_4_4, all_0_3_3, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms cartesian_product2(all_0_6_6, all_0_3_3) = all_0_2_2, ordered_pair(all_0_8_8, all_0_7_7) = all_0_4_4, in(all_0_4_4, all_0_2_2), yields: % 3.23/1.57 | (29) in(all_0_7_7, all_0_3_3) % 3.23/1.57 | % 3.23/1.57 | Instantiating formula (9) with all_0_2_2, all_0_4_4, all_0_3_3, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms cartesian_product2(all_0_6_6, all_0_3_3) = all_0_2_2, ordered_pair(all_0_8_8, all_0_7_7) = all_0_4_4, in(all_0_4_4, all_0_2_2), yields: % 3.23/1.57 | (27) in(all_0_8_8, all_0_6_6) % 3.23/1.57 | % 3.23/1.57 +-Applying beta-rule and splitting (33), into two cases. % 3.23/1.57 |-Branch one: % 3.23/1.57 | (36) ~ in(all_0_8_8, all_0_6_6) % 3.23/1.57 | % 3.23/1.57 | Using (27) and (36) yields: % 3.23/1.57 | (30) $false % 3.23/1.57 | % 3.23/1.57 |-The branch is then unsatisfiable % 3.23/1.57 |-Branch two: % 3.23/1.57 | (27) in(all_0_8_8, all_0_6_6) % 3.23/1.57 | (39) ~ (all_0_5_5 = all_0_7_7) % 3.23/1.57 | % 3.23/1.57 | Instantiating formula (22) with all_0_7_7, all_0_3_3, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_3_3, in(all_0_7_7, all_0_3_3), yields: % 3.23/1.57 | (26) all_0_5_5 = all_0_7_7 % 3.23/1.57 | % 3.23/1.57 | Equations (26) can reduce 39 to: % 3.23/1.57 | (41) $false % 3.23/1.57 | % 3.23/1.57 |-The branch is then unsatisfiable % 3.23/1.57 % SZS output end Proof for theBenchmark % 3.23/1.57 % 3.23/1.57 955ms %------------------------------------------------------------------------------