%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET975+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n024.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 2.29s 1.21s % Output : Proof 3.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SET975+1 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n024.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 Jul 10 12:58:58 EDT 2022 % 0.12/0.33 % CPUTime : % 0.57/0.57 ____ _ % 0.57/0.57 ___ / __ \_____(_)___ ________ __________ % 0.57/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.57/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.57/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.57/0.57 % 0.57/0.57 A Theorem Prover for First-Order Logic % 0.57/0.57 (ePrincess v.1.0) % 0.57/0.57 % 0.57/0.57 (c) Philipp Rümmer, 2009-2015 % 0.57/0.57 (c) Peter Backeman, 2014-2015 % 0.57/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.57/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.57/0.57 Bug reports to peter@backeman.se % 0.57/0.57 % 0.57/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.57/0.57 % 0.57/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.57/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.32/0.87 Prover 0: Preprocessing ... % 1.79/1.03 Prover 0: Warning: ignoring some quantifiers % 1.79/1.05 Prover 0: Constructing countermodel ... % 2.29/1.21 Prover 0: proved (587ms) % 2.29/1.21 % 2.29/1.21 No countermodel exists, formula is valid % 2.29/1.21 % SZS status Theorem for theBenchmark % 2.29/1.21 % 2.29/1.21 Generating proof ... Warning: ignoring some quantifiers % 2.87/1.44 found it (size 22) % 2.87/1.44 % 2.87/1.44 % SZS output start Proof for theBenchmark % 2.87/1.44 Assumed formulas after preprocessing and simplification: % 2.87/1.44 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cartesian_product2(v5, v3) = v6 & ordered_pair(v0, v1) = v4 & singleton(v2) = 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)) & ((v2 = v0 & in(v1, v3) & ~ in(v4, v6)) | (in(v4, v6) & ( ~ (v2 = v0) | ~ in(v1, v3))))) % 3.17/1.49 | 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: % 3.17/1.49 | (1) cartesian_product2(all_0_3_3, all_0_5_5) = all_0_2_2 & ordered_pair(all_0_8_8, all_0_7_7) = all_0_4_4 & singleton(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(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_6_6 = all_0_8_8 & in(all_0_7_7, all_0_5_5) & ~ in(all_0_4_4, all_0_2_2)) | (in(all_0_4_4, all_0_2_2) & ( ~ (all_0_6_6 = all_0_8_8) | ~ in(all_0_7_7, all_0_5_5)))) % 3.17/1.49 | % 3.17/1.49 | Applying alpha-rule on (1) yields: % 3.17/1.49 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 3.17/1.49 | (3) ! [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)) % 3.17/1.50 | (4) empty(all_0_0_0) % 3.17/1.50 | (5) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 3.17/1.50 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2)) % 3.17/1.50 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 3.17/1.50 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) % 3.17/1.50 | (9) (all_0_6_6 = all_0_8_8 & in(all_0_7_7, all_0_5_5) & ~ in(all_0_4_4, all_0_2_2)) | (in(all_0_4_4, all_0_2_2) & ( ~ (all_0_6_6 = all_0_8_8) | ~ in(all_0_7_7, all_0_5_5))) % 3.17/1.50 | (10) ordered_pair(all_0_8_8, all_0_7_7) = all_0_4_4 % 3.17/1.50 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 3.17/1.50 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 3.17/1.50 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 3.17/1.50 | (14) ~ empty(all_0_1_1) % 3.17/1.50 | (15) cartesian_product2(all_0_3_3, all_0_5_5) = all_0_2_2 % 3.17/1.50 | (16) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) % 3.17/1.50 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 3.17/1.50 | (18) singleton(all_0_6_6) = all_0_3_3 % 3.17/1.50 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3)) % 3.17/1.50 | (20) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) % 3.17/1.50 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 3.17/1.50 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 3.17/1.50 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 3.17/1.50 | % 3.17/1.50 | Instantiating formula (11) with all_0_4_4, all_0_7_7, all_0_8_8 and discharging atoms ordered_pair(all_0_8_8, all_0_7_7) = all_0_4_4, yields: % 3.17/1.50 | (24) ? [v0] : ? [v1] : (singleton(all_0_8_8) = v1 & unordered_pair(v0, v1) = all_0_4_4 & unordered_pair(all_0_8_8, all_0_7_7) = v0) % 3.17/1.50 | % 3.17/1.50 | Instantiating (24) with all_11_0_10, all_11_1_11 yields: % 3.17/1.50 | (25) singleton(all_0_8_8) = all_11_0_10 & unordered_pair(all_11_1_11, all_11_0_10) = all_0_4_4 & unordered_pair(all_0_8_8, all_0_7_7) = all_11_1_11 % 3.17/1.50 | % 3.17/1.50 | Applying alpha-rule on (25) yields: % 3.17/1.50 | (26) singleton(all_0_8_8) = all_11_0_10 % 3.17/1.50 | (27) unordered_pair(all_11_1_11, all_11_0_10) = all_0_4_4 % 3.17/1.50 | (28) unordered_pair(all_0_8_8, all_0_7_7) = all_11_1_11 % 3.17/1.50 | % 3.17/1.50 | Instantiating formula (16) with all_11_0_10, all_0_8_8 and discharging atoms singleton(all_0_8_8) = all_11_0_10, yields: % 3.17/1.51 | (29) in(all_0_8_8, all_11_0_10) % 3.17/1.51 | % 3.17/1.51 +-Applying beta-rule and splitting (9), into two cases. % 3.17/1.51 |-Branch one: % 3.17/1.51 | (30) all_0_6_6 = all_0_8_8 & in(all_0_7_7, all_0_5_5) & ~ in(all_0_4_4, all_0_2_2) % 3.17/1.51 | % 3.17/1.51 | Applying alpha-rule on (30) yields: % 3.17/1.51 | (31) all_0_6_6 = all_0_8_8 % 3.17/1.51 | (32) in(all_0_7_7, all_0_5_5) % 3.17/1.51 | (33) ~ in(all_0_4_4, all_0_2_2) % 3.17/1.51 | % 3.17/1.51 | From (31) and (18) follows: % 3.17/1.51 | (34) singleton(all_0_8_8) = all_0_3_3 % 3.17/1.51 | % 3.17/1.51 | Instantiating formula (23) with all_0_8_8, all_0_3_3, all_11_0_10 and discharging atoms singleton(all_0_8_8) = all_11_0_10, singleton(all_0_8_8) = all_0_3_3, yields: % 3.17/1.51 | (35) all_11_0_10 = all_0_3_3 % 3.17/1.51 | % 3.17/1.51 | From (35) and (29) follows: % 3.17/1.51 | (36) in(all_0_8_8, all_0_3_3) % 3.17/1.51 | % 3.17/1.51 | Instantiating formula (3) with all_0_2_2, all_0_4_4, all_0_5_5, all_0_3_3, all_0_7_7, all_0_8_8 and discharging atoms cartesian_product2(all_0_3_3, all_0_5_5) = 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_5_5), in(all_0_8_8, all_0_3_3), ~ in(all_0_4_4, all_0_2_2), yields: % 3.17/1.51 | (37) $false % 3.17/1.51 | % 3.17/1.51 |-The branch is then unsatisfiable % 3.17/1.51 |-Branch two: % 3.17/1.51 | (38) in(all_0_4_4, all_0_2_2) & ( ~ (all_0_6_6 = all_0_8_8) | ~ in(all_0_7_7, all_0_5_5)) % 3.17/1.51 | % 3.17/1.51 | Applying alpha-rule on (38) yields: % 3.17/1.51 | (39) in(all_0_4_4, all_0_2_2) % 3.17/1.51 | (40) ~ (all_0_6_6 = all_0_8_8) | ~ in(all_0_7_7, all_0_5_5) % 3.17/1.51 | % 3.17/1.51 | Instantiating formula (19) with all_0_2_2, all_0_4_4, all_0_5_5, all_0_3_3, all_0_7_7, all_0_8_8 and discharging atoms cartesian_product2(all_0_3_3, all_0_5_5) = 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: % 3.17/1.51 | (32) in(all_0_7_7, all_0_5_5) % 3.17/1.51 | % 3.17/1.51 | Instantiating formula (6) with all_0_2_2, all_0_4_4, all_0_5_5, all_0_3_3, all_0_7_7, all_0_8_8 and discharging atoms cartesian_product2(all_0_3_3, all_0_5_5) = 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: % 3.17/1.51 | (36) in(all_0_8_8, all_0_3_3) % 3.17/1.51 | % 3.17/1.51 +-Applying beta-rule and splitting (40), into two cases. % 3.17/1.51 |-Branch one: % 3.17/1.51 | (43) ~ in(all_0_7_7, all_0_5_5) % 3.17/1.51 | % 3.17/1.51 | Using (32) and (43) yields: % 3.17/1.51 | (37) $false % 3.17/1.51 | % 3.17/1.51 |-The branch is then unsatisfiable % 3.17/1.51 |-Branch two: % 3.17/1.51 | (32) in(all_0_7_7, all_0_5_5) % 3.17/1.51 | (46) ~ (all_0_6_6 = all_0_8_8) % 3.17/1.51 | % 3.17/1.51 | Instantiating formula (8) with all_0_8_8, all_0_3_3, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_0_3_3, in(all_0_8_8, all_0_3_3), yields: % 3.17/1.51 | (31) all_0_6_6 = all_0_8_8 % 3.17/1.51 | % 3.17/1.51 | Equations (31) can reduce 46 to: % 3.17/1.51 | (48) $false % 3.17/1.51 | % 3.17/1.51 |-The branch is then unsatisfiable % 3.17/1.51 % SZS output end Proof for theBenchmark % 3.17/1.51 % 3.17/1.51 929ms %------------------------------------------------------------------------------