%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU140+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n026.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 08:46:54 EDT 2022 % Result : Theorem 5.33s 1.95s % Output : Proof 6.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SEU140+1 : TPTP v8.1.0. Released v3.3.0. % 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n026.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 : Sun Jun 19 05:13:55 EDT 2022 % 0.13/0.33 % CPUTime : % 0.58/0.59 ____ _ % 0.58/0.59 ___ / __ \_____(_)___ ________ __________ % 0.58/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.59 % 0.58/0.59 A Theorem Prover for First-Order Logic % 0.58/0.59 (ePrincess v.1.0) % 0.58/0.59 % 0.58/0.59 (c) Philipp Rümmer, 2009-2015 % 0.58/0.59 (c) Peter Backeman, 2014-2015 % 0.58/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.59 Bug reports to peter@backeman.se % 0.58/0.59 % 0.58/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.59 % 0.58/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.43/0.90 Prover 0: Preprocessing ... % 1.67/1.03 Prover 0: Warning: ignoring some quantifiers % 1.67/1.05 Prover 0: Constructing countermodel ... % 1.86/1.17 Prover 0: gave up % 1.86/1.17 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.27/1.19 Prover 1: Preprocessing ... % 2.48/1.27 Prover 1: Constructing countermodel ... % 2.73/1.38 Prover 1: gave up % 2.73/1.38 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.97/1.40 Prover 2: Preprocessing ... % 2.97/1.45 Prover 2: Warning: ignoring some quantifiers % 2.97/1.46 Prover 2: Constructing countermodel ... % 3.58/1.56 Prover 2: gave up % 3.58/1.56 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.58/1.57 Prover 3: Preprocessing ... % 3.58/1.59 Prover 3: Warning: ignoring some quantifiers % 3.58/1.59 Prover 3: Constructing countermodel ... % 3.58/1.61 Prover 3: gave up % 3.58/1.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 3.96/1.62 Prover 4: Preprocessing ... % 3.96/1.68 Prover 4: Warning: ignoring some quantifiers % 3.96/1.68 Prover 4: Constructing countermodel ... % 4.89/1.87 Prover 4: gave up % 4.89/1.87 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.89/1.88 Prover 5: Preprocessing ... % 5.33/1.91 Prover 5: Constructing countermodel ... % 5.33/1.95 Prover 5: proved (79ms) % 5.33/1.95 % 5.33/1.95 No countermodel exists, formula is valid % 5.33/1.95 % SZS status Theorem for theBenchmark % 5.33/1.95 % 5.33/1.95 Generating proof ... found it (size 18) % 6.24/2.17 % 6.24/2.17 % SZS output start Proof for theBenchmark % 6.24/2.17 Assumed formulas after preprocessing and simplification: % 6.24/2.17 | (0) empty(empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ? [v5] : ? [v6] : (subset(v3, v4) = v6 & subset(v0, v1) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v0, v1) = 0) | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (subset(v4, v3) = 0 & set_intersection2(v0, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v0, v1) = 0) | ~ (set_intersection2(v0, v2) = v3) | ? [v4] : (subset(v3, v4) = 0 & set_intersection2(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) & ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = 0 & disjoint(v1, v2) = 0 & disjoint(v0, v2) = v3) & ? [v0] : ? [v1] : ( ~ (v1 = 0) & empty(v0) = v1) & ? [v0] : empty(v0) = 0 % 6.24/2.20 | Applying alpha-rule on (0) yields: % 6.24/2.20 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 6.24/2.20 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 6.24/2.20 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v0, v1) = 0) | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (subset(v4, v3) = 0 & set_intersection2(v0, v2) = v4)) % 6.24/2.20 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 6.24/2.21 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 6.24/2.21 | (6) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 6.24/2.21 | (7) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = 0 & disjoint(v1, v2) = 0 & disjoint(v0, v2) = v3) % 6.24/2.21 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) % 6.69/2.21 | (9) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 6.69/2.21 | (10) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) % 6.69/2.21 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ? [v5] : ? [v6] : (subset(v3, v4) = v6 & subset(v0, v1) = v5 & ( ~ (v5 = 0) | v6 = 0))) % 6.69/2.21 | (12) ? [v0] : empty(v0) = 0 % 6.69/2.21 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 6.69/2.21 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) % 6.69/2.21 | (15) ? [v0] : ? [v1] : ( ~ (v1 = 0) & empty(v0) = v1) % 6.69/2.21 | (16) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0)) % 6.69/2.21 | (17) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 6.69/2.21 | (18) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 6.69/2.21 | (19) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 6.69/2.21 | (20) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 6.69/2.21 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v0, v1) = 0) | ~ (set_intersection2(v0, v2) = v3) | ? [v4] : (subset(v3, v4) = 0 & set_intersection2(v1, v2) = v4)) % 6.69/2.21 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 6.69/2.21 | (23) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0) % 6.69/2.21 | (24) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) % 6.69/2.21 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 6.69/2.21 | (26) empty(empty_set) = 0 % 6.69/2.21 | (27) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 6.69/2.21 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) % 6.69/2.21 | (29) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) % 6.69/2.21 | % 6.69/2.21 | Instantiating (7) with all_6_0_3, all_6_1_4, all_6_2_5, all_6_3_6 yields: % 6.69/2.21 | (30) ~ (all_6_0_3 = 0) & subset(all_6_3_6, all_6_2_5) = 0 & disjoint(all_6_2_5, all_6_1_4) = 0 & disjoint(all_6_3_6, all_6_1_4) = all_6_0_3 % 6.69/2.21 | % 6.69/2.21 | Applying alpha-rule on (30) yields: % 6.69/2.21 | (31) ~ (all_6_0_3 = 0) % 6.69/2.21 | (32) subset(all_6_3_6, all_6_2_5) = 0 % 6.69/2.22 | (33) disjoint(all_6_2_5, all_6_1_4) = 0 % 6.69/2.22 | (34) disjoint(all_6_3_6, all_6_1_4) = all_6_0_3 % 6.69/2.22 | % 6.69/2.22 | Instantiating formula (24) with all_6_1_4, all_6_2_5 and discharging atoms disjoint(all_6_2_5, all_6_1_4) = 0, yields: % 6.69/2.22 | (35) set_intersection2(all_6_2_5, all_6_1_4) = empty_set % 6.69/2.22 | % 6.69/2.22 | Instantiating formula (28) with all_6_0_3, all_6_1_4, all_6_3_6 and discharging atoms disjoint(all_6_3_6, all_6_1_4) = all_6_0_3, yields: % 6.69/2.22 | (36) all_6_0_3 = 0 | ? [v0] : ( ~ (v0 = empty_set) & set_intersection2(all_6_3_6, all_6_1_4) = v0) % 6.69/2.22 | % 6.69/2.22 +-Applying beta-rule and splitting (36), into two cases. % 6.69/2.22 |-Branch one: % 6.69/2.22 | (37) all_6_0_3 = 0 % 6.69/2.22 | % 6.69/2.22 | Equations (37) can reduce 31 to: % 6.69/2.22 | (38) $false % 6.69/2.22 | % 6.69/2.22 |-The branch is then unsatisfiable % 6.69/2.22 |-Branch two: % 6.69/2.22 | (31) ~ (all_6_0_3 = 0) % 6.69/2.22 | (40) ? [v0] : ( ~ (v0 = empty_set) & set_intersection2(all_6_3_6, all_6_1_4) = v0) % 6.69/2.22 | % 6.69/2.22 | Instantiating (40) with all_22_0_7 yields: % 6.69/2.22 | (41) ~ (all_22_0_7 = empty_set) & set_intersection2(all_6_3_6, all_6_1_4) = all_22_0_7 % 6.69/2.22 | % 6.69/2.22 | Applying alpha-rule on (41) yields: % 6.69/2.22 | (42) ~ (all_22_0_7 = empty_set) % 6.69/2.22 | (43) set_intersection2(all_6_3_6, all_6_1_4) = all_22_0_7 % 6.69/2.22 | % 6.69/2.22 | Instantiating formula (3) with empty_set, all_6_1_4, all_6_2_5, all_6_3_6 and discharging atoms subset(all_6_3_6, all_6_2_5) = 0, set_intersection2(all_6_2_5, all_6_1_4) = empty_set, yields: % 6.69/2.22 | (44) ? [v0] : (subset(v0, empty_set) = 0 & set_intersection2(all_6_3_6, all_6_1_4) = v0) % 6.69/2.22 | % 6.69/2.22 | Instantiating (44) with all_37_0_10 yields: % 6.69/2.22 | (45) subset(all_37_0_10, empty_set) = 0 & set_intersection2(all_6_3_6, all_6_1_4) = all_37_0_10 % 6.69/2.22 | % 6.69/2.22 | Applying alpha-rule on (45) yields: % 6.69/2.22 | (46) subset(all_37_0_10, empty_set) = 0 % 6.69/2.22 | (47) set_intersection2(all_6_3_6, all_6_1_4) = all_37_0_10 % 6.69/2.22 | % 6.69/2.22 | Instantiating formula (16) with all_37_0_10 and discharging atoms subset(all_37_0_10, empty_set) = 0, yields: % 6.69/2.22 | (48) all_37_0_10 = empty_set % 6.69/2.22 | % 6.69/2.22 | Instantiating formula (22) with all_6_3_6, all_6_1_4, all_37_0_10, all_22_0_7 and discharging atoms set_intersection2(all_6_3_6, all_6_1_4) = all_37_0_10, set_intersection2(all_6_3_6, all_6_1_4) = all_22_0_7, yields: % 6.69/2.22 | (49) all_37_0_10 = all_22_0_7 % 6.69/2.22 | % 6.69/2.22 | Combining equations (48,49) yields a new equation: % 6.69/2.22 | (50) all_22_0_7 = empty_set % 6.69/2.22 | % 6.69/2.22 | Equations (50) can reduce 42 to: % 6.69/2.22 | (38) $false % 6.69/2.22 | % 6.69/2.22 |-The branch is then unsatisfiable % 6.69/2.22 % SZS output end Proof for theBenchmark % 6.69/2.22 % 6.69/2.22 1625ms %------------------------------------------------------------------------------