%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET183+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n027.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 00:18:13 EDT 2022 % Result : Theorem 3.29s 1.54s % Output : Proof 4.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : SET183+3 : TPTP v8.1.0. Released v2.2.0. % 0.08/0.15 % Command : ePrincess-casc -timeout=%d %s % 0.15/0.36 % Computer : n027.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 600 % 0.15/0.37 % DateTime : Sun Jul 10 22:12:03 EDT 2022 % 0.15/0.37 % CPUTime : % 0.58/0.62 ____ _ % 0.58/0.62 ___ / __ \_____(_)___ ________ __________ % 0.58/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.62 % 0.58/0.62 A Theorem Prover for First-Order Logic % 0.58/0.62 (ePrincess v.1.0) % 0.58/0.62 % 0.58/0.62 (c) Philipp Rümmer, 2009-2015 % 0.58/0.62 (c) Peter Backeman, 2014-2015 % 0.58/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.62 Bug reports to peter@backeman.se % 0.58/0.62 % 0.58/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.62 % 0.58/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.68/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.26/0.94 Prover 0: Preprocessing ... % 1.64/1.09 Prover 0: Warning: ignoring some quantifiers % 1.64/1.10 Prover 0: Constructing countermodel ... % 2.10/1.26 Prover 0: gave up % 2.10/1.26 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.30/1.28 Prover 1: Preprocessing ... % 2.30/1.35 Prover 1: Warning: ignoring some quantifiers % 2.30/1.36 Prover 1: Constructing countermodel ... % 2.70/1.39 Prover 1: gave up % 2.70/1.40 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.70/1.41 Prover 2: Preprocessing ... % 2.94/1.48 Prover 2: Warning: ignoring some quantifiers % 2.94/1.48 Prover 2: Constructing countermodel ... % 3.29/1.54 Prover 2: proved (143ms) % 3.29/1.54 % 3.29/1.54 No countermodel exists, formula is valid % 3.29/1.54 % SZS status Theorem for theBenchmark % 3.29/1.54 % 3.29/1.54 Generating proof ... Warning: ignoring some quantifiers % 4.21/1.75 found it (size 30) % 4.21/1.75 % 4.21/1.75 % SZS output start Proof for theBenchmark % 4.21/1.75 Assumed formulas after preprocessing and simplification: % 4.21/1.75 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v0) & subset(v0, v1) = 0 & intersection(v0, v1) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (intersection(v3, v4) = v6) | ~ (member(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & member(v5, v4) = v8) | ( ~ (v8 = 0) & member(v5, v3) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (subset(v3, v4) = 0) | ~ (member(v5, v4) = v6) | ? [v7] : ( ~ (v7 = 0) & member(v5, v3) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (subset(v6, v5) = v4) | ~ (subset(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (intersection(v6, v5) = v4) | ~ (intersection(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (member(v6, v5) = v4) | ~ (member(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection(v3, v4) = v6) | ~ (member(v5, v6) = 0) | (member(v5, v4) = 0 & member(v5, v3) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & member(v6, v4) = v7 & member(v6, v3) = 0)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (subset(v3, v4) = 0) | ~ (member(v5, v3) = 0) | member(v5, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : ( ~ (intersection(v4, v3) = v5) | intersection(v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (intersection(v3, v4) = v5) | subset(v5, v3) = 0) & ! [v3] : ! [v4] : ! [v5] : ( ~ (intersection(v3, v4) = v5) | intersection(v4, v3) = v5) & ! [v3] : ! [v4] : (v4 = v3 | ~ (subset(v4, v3) = 0) | ? [v5] : ( ~ (v5 = 0) & subset(v3, v4) = v5)) & ! [v3] : ! [v4] : (v4 = v3 | ~ (subset(v3, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & subset(v4, v3) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v3) = v4)) & ? [v3] : ? [v4] : ? [v5] : subset(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : intersection(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : member(v4, v3) = v5 & ? [v3] : ? [v4] : (v4 = v3 | ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & member(v5, v4) = 0) | (v6 = 0 & member(v5, v3) = 0)) & (( ~ (v7 = 0) & member(v5, v4) = v7) | ( ~ (v6 = 0) & member(v5, v3) = v6))))) % 4.21/1.78 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 4.21/1.78 | (1) ~ (all_0_0_0 = all_0_2_2) & subset(all_0_2_2, all_0_1_1) = 0 & intersection(all_0_2_2, all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & member(v2, v1) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & member(v2, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | subset(v2, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2 & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & member(v2, v1) = 0) | (v3 = 0 & member(v2, v0) = 0)) & (( ~ (v4 = 0) & member(v2, v1) = v4) | ( ~ (v3 = 0) & member(v2, v0) = v3)))) % 4.21/1.79 | % 4.21/1.79 | Applying alpha-rule on (1) yields: % 4.21/1.79 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) % 4.21/1.79 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | subset(v2, v0) = 0) % 4.21/1.79 | (4) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2 % 4.21/1.79 | (5) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 % 4.21/1.79 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 4.21/1.79 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) % 4.21/1.79 | (8) subset(all_0_2_2, all_0_1_1) = 0 % 4.21/1.79 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 4.21/1.79 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) % 4.21/1.79 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 4.21/1.79 | (12) intersection(all_0_2_2, all_0_1_1) = all_0_0_0 % 4.21/1.79 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & member(v2, v0) = 0)) % 4.21/1.79 | (14) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 4.21/1.79 | (15) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & member(v2, v1) = 0) | (v3 = 0 & member(v2, v0) = 0)) & (( ~ (v4 = 0) & member(v2, v1) = v4) | ( ~ (v3 = 0) & member(v2, v0) = v3)))) % 4.21/1.80 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 4.21/1.80 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 4.21/1.80 | (18) ~ (all_0_0_0 = all_0_2_2) % 4.21/1.80 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) % 4.21/1.80 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2) % 4.21/1.80 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & member(v2, v1) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5))) % 4.21/1.80 | (22) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2 % 4.21/1.80 | % 4.21/1.80 | Instantiating formula (3) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms intersection(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 4.21/1.80 | (23) subset(all_0_0_0, all_0_2_2) = 0 % 4.21/1.80 | % 4.21/1.80 | Instantiating formula (10) with all_0_0_0, all_0_2_2 and discharging atoms subset(all_0_0_0, all_0_2_2) = 0, yields: % 4.21/1.80 | (24) all_0_0_0 = all_0_2_2 | ? [v0] : ( ~ (v0 = 0) & subset(all_0_2_2, all_0_0_0) = v0) % 4.21/1.80 | % 4.21/1.80 +-Applying beta-rule and splitting (24), into two cases. % 4.21/1.80 |-Branch one: % 4.21/1.80 | (25) all_0_0_0 = all_0_2_2 % 4.21/1.80 | % 4.21/1.80 | Equations (25) can reduce 18 to: % 4.21/1.80 | (26) $false % 4.21/1.80 | % 4.21/1.80 |-The branch is then unsatisfiable % 4.21/1.80 |-Branch two: % 4.21/1.80 | (18) ~ (all_0_0_0 = all_0_2_2) % 4.21/1.80 | (28) ? [v0] : ( ~ (v0 = 0) & subset(all_0_2_2, all_0_0_0) = v0) % 4.21/1.80 | % 4.21/1.80 | Instantiating (28) with all_26_0_14 yields: % 4.21/1.80 | (29) ~ (all_26_0_14 = 0) & subset(all_0_2_2, all_0_0_0) = all_26_0_14 % 4.21/1.80 | % 4.21/1.80 | Applying alpha-rule on (29) yields: % 4.21/1.80 | (30) ~ (all_26_0_14 = 0) % 4.21/1.80 | (31) subset(all_0_2_2, all_0_0_0) = all_26_0_14 % 4.21/1.80 | % 4.21/1.80 | Instantiating formula (6) with all_26_0_14, all_0_0_0, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_0_0) = all_26_0_14, yields: % 4.21/1.80 | (32) all_26_0_14 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_0_0) = v1 & member(v0, all_0_2_2) = 0) % 4.21/1.80 | % 4.21/1.80 +-Applying beta-rule and splitting (32), into two cases. % 4.21/1.80 |-Branch one: % 4.21/1.80 | (33) all_26_0_14 = 0 % 4.21/1.80 | % 4.21/1.80 | Equations (33) can reduce 30 to: % 4.21/1.80 | (26) $false % 4.21/1.80 | % 4.21/1.80 |-The branch is then unsatisfiable % 4.21/1.80 |-Branch two: % 4.21/1.80 | (30) ~ (all_26_0_14 = 0) % 4.21/1.80 | (36) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_0_0) = v1 & member(v0, all_0_2_2) = 0) % 4.21/1.80 | % 4.21/1.80 | Instantiating (36) with all_39_0_15, all_39_1_16 yields: % 4.21/1.80 | (37) ~ (all_39_0_15 = 0) & member(all_39_1_16, all_0_0_0) = all_39_0_15 & member(all_39_1_16, all_0_2_2) = 0 % 4.21/1.80 | % 4.21/1.80 | Applying alpha-rule on (37) yields: % 4.21/1.80 | (38) ~ (all_39_0_15 = 0) % 4.21/1.80 | (39) member(all_39_1_16, all_0_0_0) = all_39_0_15 % 4.21/1.80 | (40) member(all_39_1_16, all_0_2_2) = 0 % 4.21/1.80 | % 4.21/1.80 | Instantiating formula (21) with all_39_0_15, all_0_0_0, all_39_1_16, all_0_1_1, all_0_2_2 and discharging atoms intersection(all_0_2_2, all_0_1_1) = all_0_0_0, member(all_39_1_16, all_0_0_0) = all_39_0_15, yields: % 4.21/1.80 | (41) all_39_0_15 = 0 | ? [v0] : (( ~ (v0 = 0) & member(all_39_1_16, all_0_1_1) = v0) | ( ~ (v0 = 0) & member(all_39_1_16, all_0_2_2) = v0)) % 4.21/1.81 | % 4.21/1.81 | Instantiating formula (17) with all_39_1_16, all_0_1_1, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_1_1) = 0, member(all_39_1_16, all_0_2_2) = 0, yields: % 4.21/1.81 | (42) member(all_39_1_16, all_0_1_1) = 0 % 4.21/1.81 | % 4.21/1.81 +-Applying beta-rule and splitting (41), into two cases. % 4.21/1.81 |-Branch one: % 4.21/1.81 | (43) all_39_0_15 = 0 % 4.21/1.81 | % 4.21/1.81 | Equations (43) can reduce 38 to: % 4.21/1.81 | (26) $false % 4.21/1.81 | % 4.21/1.81 |-The branch is then unsatisfiable % 4.21/1.81 |-Branch two: % 4.21/1.81 | (38) ~ (all_39_0_15 = 0) % 4.21/1.81 | (46) ? [v0] : (( ~ (v0 = 0) & member(all_39_1_16, all_0_1_1) = v0) | ( ~ (v0 = 0) & member(all_39_1_16, all_0_2_2) = v0)) % 4.21/1.81 | % 4.21/1.81 | Instantiating (46) with all_51_0_17 yields: % 4.21/1.81 | (47) ( ~ (all_51_0_17 = 0) & member(all_39_1_16, all_0_1_1) = all_51_0_17) | ( ~ (all_51_0_17 = 0) & member(all_39_1_16, all_0_2_2) = all_51_0_17) % 4.21/1.81 | % 4.21/1.81 +-Applying beta-rule and splitting (47), into two cases. % 4.21/1.81 |-Branch one: % 4.21/1.81 | (48) ~ (all_51_0_17 = 0) & member(all_39_1_16, all_0_1_1) = all_51_0_17 % 4.21/1.81 | % 4.21/1.81 | Applying alpha-rule on (48) yields: % 4.21/1.81 | (49) ~ (all_51_0_17 = 0) % 4.21/1.81 | (50) member(all_39_1_16, all_0_1_1) = all_51_0_17 % 4.21/1.81 | % 4.21/1.81 | Instantiating formula (16) with all_39_1_16, all_0_1_1, 0, all_51_0_17 and discharging atoms member(all_39_1_16, all_0_1_1) = all_51_0_17, member(all_39_1_16, all_0_1_1) = 0, yields: % 4.21/1.81 | (51) all_51_0_17 = 0 % 4.21/1.81 | % 4.21/1.81 | Equations (51) can reduce 49 to: % 4.21/1.81 | (26) $false % 4.21/1.81 | % 4.21/1.81 |-The branch is then unsatisfiable % 4.21/1.81 |-Branch two: % 4.21/1.81 | (53) ~ (all_51_0_17 = 0) & member(all_39_1_16, all_0_2_2) = all_51_0_17 % 4.21/1.81 | % 4.21/1.81 | Applying alpha-rule on (53) yields: % 4.21/1.81 | (49) ~ (all_51_0_17 = 0) % 4.21/1.81 | (55) member(all_39_1_16, all_0_2_2) = all_51_0_17 % 4.21/1.81 | % 4.21/1.81 | Instantiating formula (16) with all_39_1_16, all_0_2_2, all_51_0_17, 0 and discharging atoms member(all_39_1_16, all_0_2_2) = all_51_0_17, member(all_39_1_16, all_0_2_2) = 0, yields: % 4.21/1.81 | (51) all_51_0_17 = 0 % 4.21/1.81 | % 4.21/1.81 | Equations (51) can reduce 49 to: % 4.21/1.81 | (26) $false % 4.21/1.81 | % 4.21/1.81 |-The branch is then unsatisfiable % 4.21/1.81 % SZS output end Proof for theBenchmark % 4.21/1.81 % 4.21/1.81 1175ms %------------------------------------------------------------------------------