%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET927+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n028.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 00:23:15 EDT 2022 % Result : Theorem 2.09s 1.18s % Output : Proof 3.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SET927+1 : TPTP v8.1.0. Released v3.2.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.32 % Computer : n028.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 600 % 0.12/0.32 % DateTime : Mon Jul 11 05:04:28 EDT 2022 % 0.12/0.33 % CPUTime : % 0.52/0.57 ____ _ % 0.52/0.57 ___ / __ \_____(_)___ ________ __________ % 0.52/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.52/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.52/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.52/0.57 % 0.52/0.57 A Theorem Prover for First-Order Logic % 0.52/0.57 (ePrincess v.1.0) % 0.52/0.57 % 0.52/0.57 (c) Philipp Rümmer, 2009-2015 % 0.52/0.57 (c) Peter Backeman, 2014-2015 % 0.52/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.52/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.52/0.57 Bug reports to peter@backeman.se % 0.52/0.57 % 0.52/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.52/0.57 % 0.52/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.52/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.26/0.87 Prover 0: Preprocessing ... % 1.56/1.03 Prover 0: Constructing countermodel ... % 2.09/1.18 Prover 0: proved (559ms) % 2.09/1.18 % 2.09/1.18 No countermodel exists, formula is valid % 2.09/1.18 % SZS status Theorem for theBenchmark % 2.09/1.18 % 2.09/1.18 Generating proof ... found it (size 42) % 2.73/1.41 % 2.73/1.41 % SZS output start Proof for theBenchmark % 2.73/1.41 Assumed formulas after preprocessing and simplification: % 2.73/1.41 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (set_difference(v3, v2) = v4 & singleton(v0) = v5 & unordered_pair(v0, v1) = v3 & 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] : (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] : ( ~ in(v9, v8) | ~ in(v8, v9)) & ((v5 = v4 & (in(v0, v2) | ( ~ (v1 = v0) & ~ in(v1, v2)))) | ( ~ (v5 = v4) & ~ in(v0, v2) & (v1 = v0 | in(v1, v2))))) % 2.96/1.45 | 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: % 2.96/1.45 | (1) set_difference(all_0_4_4, all_0_5_5) = all_0_3_3 & singleton(all_0_7_7) = all_0_2_2 & unordered_pair(all_0_7_7, all_0_6_6) = all_0_4_4 & 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] : (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] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ((all_0_2_2 = all_0_3_3 & (in(all_0_7_7, all_0_5_5) | ( ~ (all_0_6_6 = all_0_7_7) & ~ in(all_0_6_6, all_0_5_5)))) | ( ~ (all_0_2_2 = all_0_3_3) & ~ in(all_0_7_7, all_0_5_5) & (all_0_6_6 = all_0_7_7 | in(all_0_6_6, all_0_5_5)))) % 2.96/1.46 | % 2.96/1.46 | Applying alpha-rule on (1) yields: % 2.96/1.46 | (2) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 2.96/1.46 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | singleton(v0) = v4 | in(v0, v2)) % 2.96/1.46 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 2.96/1.46 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 2.96/1.46 | (6) singleton(all_0_7_7) = all_0_2_2 % 2.96/1.46 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 2.96/1.46 | (8) ~ empty(all_0_1_1) % 2.96/1.46 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (unordered_pair(v0, v0) = v2) | singleton(v0) = v3 | in(v0, v1)) % 2.96/1.46 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ in(v0, v2) | ? [v5] : ( ~ (v5 = v4) & singleton(v0) = v5)) % 2.96/1.46 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 2.96/1.46 | (12) empty(all_0_0_0) % 2.96/1.46 | (13) unordered_pair(all_0_7_7, all_0_6_6) = all_0_4_4 % 2.96/1.46 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 2.96/1.46 | (15) ! [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)) % 2.96/1.46 | (16) set_difference(all_0_4_4, all_0_5_5) = all_0_3_3 % 2.96/1.46 | (17) (all_0_2_2 = all_0_3_3 & (in(all_0_7_7, all_0_5_5) | ( ~ (all_0_6_6 = all_0_7_7) & ~ in(all_0_6_6, all_0_5_5)))) | ( ~ (all_0_2_2 = all_0_3_3) & ~ in(all_0_7_7, all_0_5_5) & (all_0_6_6 = all_0_7_7 | in(all_0_6_6, all_0_5_5))) % 2.96/1.46 | % 2.96/1.46 | Instantiating formula (15) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms set_difference(all_0_4_4, all_0_5_5) = all_0_3_3, unordered_pair(all_0_7_7, all_0_6_6) = all_0_4_4, yields: % 2.96/1.46 | (18) all_0_6_6 = all_0_7_7 | in(all_0_6_6, all_0_5_5) | ? [v0] : ( ~ (v0 = all_0_3_3) & singleton(all_0_7_7) = v0) % 3.07/1.47 | % 3.07/1.47 +-Applying beta-rule and splitting (17), into two cases. % 3.07/1.47 |-Branch one: % 3.07/1.47 | (19) all_0_2_2 = all_0_3_3 & (in(all_0_7_7, all_0_5_5) | ( ~ (all_0_6_6 = all_0_7_7) & ~ in(all_0_6_6, all_0_5_5))) % 3.07/1.47 | % 3.07/1.47 | Applying alpha-rule on (19) yields: % 3.07/1.47 | (20) all_0_2_2 = all_0_3_3 % 3.07/1.47 | (21) in(all_0_7_7, all_0_5_5) | ( ~ (all_0_6_6 = all_0_7_7) & ~ in(all_0_6_6, all_0_5_5)) % 3.07/1.47 | % 3.07/1.47 | From (20) and (6) follows: % 3.07/1.47 | (22) singleton(all_0_7_7) = all_0_3_3 % 3.07/1.47 | % 3.07/1.47 +-Applying beta-rule and splitting (18), into two cases. % 3.07/1.47 |-Branch one: % 3.07/1.47 | (23) in(all_0_6_6, all_0_5_5) % 3.07/1.47 | % 3.07/1.47 +-Applying beta-rule and splitting (21), into two cases. % 3.07/1.47 |-Branch one: % 3.07/1.47 | (24) in(all_0_7_7, all_0_5_5) % 3.07/1.47 | % 3.07/1.47 | Instantiating formula (10) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms set_difference(all_0_4_4, all_0_5_5) = all_0_3_3, unordered_pair(all_0_7_7, all_0_6_6) = all_0_4_4, in(all_0_7_7, all_0_5_5), yields: % 3.07/1.47 | (25) ? [v0] : ( ~ (v0 = all_0_3_3) & singleton(all_0_7_7) = v0) % 3.07/1.47 | % 3.07/1.47 | Instantiating (25) with all_32_0_8 yields: % 3.07/1.47 | (26) ~ (all_32_0_8 = all_0_3_3) & singleton(all_0_7_7) = all_32_0_8 % 3.07/1.47 | % 3.07/1.47 | Applying alpha-rule on (26) yields: % 3.07/1.47 | (27) ~ (all_32_0_8 = all_0_3_3) % 3.07/1.47 | (28) singleton(all_0_7_7) = all_32_0_8 % 3.07/1.47 | % 3.07/1.47 | Instantiating formula (11) with all_0_7_7, all_32_0_8, all_0_3_3 and discharging atoms singleton(all_0_7_7) = all_32_0_8, singleton(all_0_7_7) = all_0_3_3, yields: % 3.07/1.47 | (29) all_32_0_8 = all_0_3_3 % 3.07/1.47 | % 3.07/1.47 | Equations (29) can reduce 27 to: % 3.07/1.47 | (30) $false % 3.07/1.47 | % 3.07/1.47 |-The branch is then unsatisfiable % 3.07/1.47 |-Branch two: % 3.07/1.47 | (31) ~ in(all_0_7_7, all_0_5_5) % 3.07/1.47 | (32) ~ (all_0_6_6 = all_0_7_7) & ~ in(all_0_6_6, all_0_5_5) % 3.07/1.47 | % 3.07/1.47 | Applying alpha-rule on (32) yields: % 3.07/1.47 | (33) ~ (all_0_6_6 = all_0_7_7) % 3.07/1.47 | (34) ~ in(all_0_6_6, all_0_5_5) % 3.07/1.47 | % 3.07/1.47 | Using (23) and (34) yields: % 3.07/1.47 | (35) $false % 3.07/1.47 | % 3.07/1.47 |-The branch is then unsatisfiable % 3.07/1.47 |-Branch two: % 3.07/1.47 | (34) ~ in(all_0_6_6, all_0_5_5) % 3.07/1.47 | (37) all_0_6_6 = all_0_7_7 | ? [v0] : ( ~ (v0 = all_0_3_3) & singleton(all_0_7_7) = v0) % 3.07/1.47 | % 3.07/1.47 +-Applying beta-rule and splitting (37), into two cases. % 3.07/1.47 |-Branch one: % 3.07/1.47 | (38) all_0_6_6 = all_0_7_7 % 3.07/1.47 | % 3.07/1.47 | From (38) and (34) follows: % 3.07/1.47 | (31) ~ in(all_0_7_7, all_0_5_5) % 3.07/1.47 | % 3.07/1.47 +-Applying beta-rule and splitting (21), into two cases. % 3.07/1.47 |-Branch one: % 3.07/1.47 | (24) in(all_0_7_7, all_0_5_5) % 3.07/1.47 | % 3.07/1.47 | Using (24) and (31) yields: % 3.07/1.47 | (35) $false % 3.07/1.47 | % 3.07/1.47 |-The branch is then unsatisfiable % 3.07/1.47 |-Branch two: % 3.07/1.47 | (31) ~ in(all_0_7_7, all_0_5_5) % 3.07/1.47 | (32) ~ (all_0_6_6 = all_0_7_7) & ~ in(all_0_6_6, all_0_5_5) % 3.07/1.47 | % 3.07/1.47 | Applying alpha-rule on (32) yields: % 3.07/1.47 | (33) ~ (all_0_6_6 = all_0_7_7) % 3.07/1.47 | (34) ~ in(all_0_6_6, all_0_5_5) % 3.07/1.47 | % 3.07/1.47 | Equations (38) can reduce 33 to: % 3.07/1.47 | (30) $false % 3.07/1.47 | % 3.07/1.47 |-The branch is then unsatisfiable % 3.07/1.47 |-Branch two: % 3.07/1.47 | (33) ~ (all_0_6_6 = all_0_7_7) % 3.07/1.47 | (25) ? [v0] : ( ~ (v0 = all_0_3_3) & singleton(all_0_7_7) = v0) % 3.07/1.47 | % 3.07/1.47 | Instantiating (25) with all_27_0_10 yields: % 3.07/1.47 | (49) ~ (all_27_0_10 = all_0_3_3) & singleton(all_0_7_7) = all_27_0_10 % 3.07/1.47 | % 3.07/1.47 | Applying alpha-rule on (49) yields: % 3.07/1.47 | (50) ~ (all_27_0_10 = all_0_3_3) % 3.07/1.48 | (51) singleton(all_0_7_7) = all_27_0_10 % 3.07/1.48 | % 3.07/1.48 | Instantiating formula (11) with all_0_7_7, all_27_0_10, all_0_3_3 and discharging atoms singleton(all_0_7_7) = all_27_0_10, singleton(all_0_7_7) = all_0_3_3, yields: % 3.07/1.48 | (52) all_27_0_10 = all_0_3_3 % 3.07/1.48 | % 3.07/1.48 | Equations (52) can reduce 50 to: % 3.07/1.48 | (30) $false % 3.07/1.48 | % 3.07/1.48 |-The branch is then unsatisfiable % 3.07/1.48 |-Branch two: % 3.07/1.48 | (54) ~ (all_0_2_2 = all_0_3_3) & ~ in(all_0_7_7, all_0_5_5) & (all_0_6_6 = all_0_7_7 | in(all_0_6_6, all_0_5_5)) % 3.07/1.48 | % 3.07/1.48 | Applying alpha-rule on (54) yields: % 3.07/1.48 | (55) ~ (all_0_2_2 = all_0_3_3) % 3.07/1.48 | (31) ~ in(all_0_7_7, all_0_5_5) % 3.07/1.48 | (57) all_0_6_6 = all_0_7_7 | in(all_0_6_6, all_0_5_5) % 3.07/1.48 | % 3.07/1.48 +-Applying beta-rule and splitting (57), into two cases. % 3.07/1.48 |-Branch one: % 3.07/1.48 | (23) in(all_0_6_6, all_0_5_5) % 3.07/1.48 | % 3.07/1.48 | Instantiating formula (3) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms set_difference(all_0_4_4, all_0_5_5) = all_0_3_3, unordered_pair(all_0_7_7, all_0_6_6) = all_0_4_4, in(all_0_6_6, all_0_5_5), ~ in(all_0_7_7, all_0_5_5), yields: % 3.07/1.48 | (22) singleton(all_0_7_7) = all_0_3_3 % 3.07/1.48 | % 3.07/1.48 | Instantiating formula (11) 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: % 3.07/1.48 | (20) all_0_2_2 = all_0_3_3 % 3.07/1.48 | % 3.07/1.48 | Equations (20) can reduce 55 to: % 3.07/1.48 | (30) $false % 3.07/1.48 | % 3.07/1.48 |-The branch is then unsatisfiable % 3.07/1.48 |-Branch two: % 3.07/1.48 | (34) ~ in(all_0_6_6, all_0_5_5) % 3.07/1.48 | (38) all_0_6_6 = all_0_7_7 % 3.07/1.48 | % 3.07/1.48 | From (38) and (13) follows: % 3.07/1.48 | (64) unordered_pair(all_0_7_7, all_0_7_7) = all_0_4_4 % 3.07/1.48 | % 3.07/1.48 | From (38) and (34) follows: % 3.07/1.48 | (31) ~ in(all_0_7_7, all_0_5_5) % 3.07/1.48 | % 3.07/1.48 | Instantiating formula (9) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_7_7 and discharging atoms set_difference(all_0_4_4, all_0_5_5) = all_0_3_3, unordered_pair(all_0_7_7, all_0_7_7) = all_0_4_4, ~ in(all_0_7_7, all_0_5_5), yields: % 3.07/1.48 | (22) singleton(all_0_7_7) = all_0_3_3 % 3.07/1.48 | % 3.07/1.48 | Instantiating formula (11) 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: % 3.07/1.48 | (20) all_0_2_2 = all_0_3_3 % 3.07/1.48 | % 3.07/1.48 | Equations (20) can reduce 55 to: % 3.07/1.48 | (30) $false % 3.07/1.48 | % 3.07/1.48 |-The branch is then unsatisfiable % 3.07/1.48 % SZS output end Proof for theBenchmark % 3.07/1.48 % 3.07/1.48 902ms %------------------------------------------------------------------------------