%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET933+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n020.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 00:23:17 EDT 2022 % Result : Theorem 2.98s 1.49s % Output : Proof 3.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SET933+1 : TPTP v8.1.0. Released v3.2.0. % 0.06/0.11 % Command : ePrincess-casc -timeout=%d %s % 0.11/0.32 % Computer : n020.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 600 % 0.11/0.32 % DateTime : Sat Jul 9 17:00:13 EDT 2022 % 0.11/0.32 % CPUTime : % 0.50/0.58 ____ _ % 0.50/0.58 ___ / __ \_____(_)___ ________ __________ % 0.50/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.50/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.50/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.50/0.58 % 0.50/0.58 A Theorem Prover for First-Order Logic % 0.50/0.58 (ePrincess v.1.0) % 0.50/0.58 % 0.50/0.58 (c) Philipp Rümmer, 2009-2015 % 0.50/0.58 (c) Peter Backeman, 2014-2015 % 0.50/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.50/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.50/0.58 Bug reports to peter@backeman.se % 0.50/0.58 % 0.50/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.50/0.58 % 0.50/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.33/0.94 Prover 0: Preprocessing ... % 1.59/1.06 Prover 0: Warning: ignoring some quantifiers % 1.59/1.07 Prover 0: Constructing countermodel ... % 2.10/1.24 Prover 0: gave up % 2.10/1.24 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.18/1.25 Prover 1: Preprocessing ... % 2.18/1.31 Prover 1: Warning: ignoring some quantifiers % 2.18/1.31 Prover 1: Constructing countermodel ... % 2.62/1.38 Prover 1: gave up % 2.62/1.38 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.62/1.39 Prover 2: Preprocessing ... % 2.62/1.44 Prover 2: Warning: ignoring some quantifiers % 2.89/1.45 Prover 2: Constructing countermodel ... % 2.98/1.49 Prover 2: proved (109ms) % 2.98/1.49 % 2.98/1.49 No countermodel exists, formula is valid % 2.98/1.49 % SZS status Theorem for theBenchmark % 2.98/1.49 % 2.98/1.49 Generating proof ... Warning: ignoring some quantifiers % 3.57/1.67 found it (size 17) % 3.57/1.67 % 3.57/1.67 % SZS output start Proof for theBenchmark % 3.57/1.67 Assumed formulas after preprocessing and simplification: % 3.57/1.67 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = 0) & ~ (v3 = 0) & empty(v6) = 0 & empty(v4) = v5 & singleton(v0) = v1 & powerset(v0) = v2 & subset(v1, v2) = v3 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (singleton(v7) = v9) | ~ (subset(v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & in(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (powerset(v7) = v8) | ~ (subset(v9, v7) = v10) | ? [v11] : ( ~ (v11 = 0) & in(v9, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (powerset(v7) = v8) | ~ (in(v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v9, v7) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (in(v10, v9) = v8) | ~ (in(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (in(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & singleton(v7) = v10 & subset(v10, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (empty(v9) = v8) | ~ (empty(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (powerset(v9) = v8) | ~ (powerset(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (singleton(v7) = v9) | ~ (subset(v9, v8) = 0) | in(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v7) = v8) | ~ (subset(v9, v7) = 0) | in(v9, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v7) = v8) | ~ (in(v9, v8) = 0) | subset(v9, v7) = 0) & ? [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (powerset(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (((v12 = 0 & subset(v10, v8) = 0) | (v11 = 0 & in(v10, v7) = 0)) & (( ~ (v12 = 0) & subset(v10, v8) = v12) | ( ~ (v11 = 0) & in(v10, v7) = v11)))) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v7, v7) = v8)) & ! [v7] : ! [v8] : ( ~ (in(v8, v7) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v7) = v9)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : (singleton(v7) = v9 & subset(v9, v8) = 0)) & ? [v7] : ? [v8] : ? [v9] : subset(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : in(v8, v7) = v9 & ? [v7] : ? [v8] : empty(v7) = v8 & ? [v7] : ? [v8] : singleton(v7) = v8 & ? [v7] : ? [v8] : powerset(v7) = v8) % 3.73/1.70 | 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 yields: % 3.73/1.70 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & singleton(all_0_6_6) = all_0_5_5 & powerset(all_0_6_6) = all_0_4_4 & subset(all_0_5_5, all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & singleton(v0) = v3 & subset(v3, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | subset(v2, v0) = 0) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & subset(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v5 = 0) & subset(v3, v1) = v5) | ( ~ (v4 = 0) & in(v3, v0) = v4)))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : (singleton(v0) = v2 & subset(v2, v1) = 0)) & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : empty(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : powerset(v0) = v1 % 3.73/1.71 | % 3.73/1.71 | Applying alpha-rule on (1) yields: % 3.73/1.71 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0) % 3.73/1.71 | (3) ~ (all_0_1_1 = 0) % 3.73/1.71 | (4) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & subset(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v5 = 0) & subset(v3, v1) = v5) | ( ~ (v4 = 0) & in(v3, v0) = v4)))) % 3.73/1.71 | (5) subset(all_0_5_5, all_0_4_4) = all_0_3_3 % 3.73/1.71 | (6) empty(all_0_0_0) = 0 % 3.73/1.71 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & singleton(v0) = v3 & subset(v3, v1) = v4)) % 3.73/1.71 | (8) ? [v0] : ? [v1] : singleton(v0) = v1 % 3.73/1.71 | (9) singleton(all_0_6_6) = all_0_5_5 % 3.73/1.71 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 3.73/1.71 | (11) powerset(all_0_6_6) = all_0_4_4 % 3.73/1.71 | (12) ~ (all_0_3_3 = 0) % 3.73/1.71 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4)) % 3.73/1.71 | (14) ? [v0] : ? [v1] : empty(v0) = v1 % 3.73/1.71 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 3.73/1.71 | (16) empty(all_0_2_2) = all_0_1_1 % 3.73/1.71 | (17) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 % 3.73/1.71 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v2, v0) = v4)) % 3.73/1.72 | (19) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 3.73/1.72 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | subset(v2, v0) = 0) % 3.73/1.72 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0) % 3.73/1.72 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 3.73/1.72 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 3.73/1.72 | (24) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 3.73/1.72 | (25) ? [v0] : ? [v1] : powerset(v0) = v1 % 3.73/1.72 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 3.73/1.72 | (27) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : (singleton(v0) = v2 & subset(v2, v1) = 0)) % 3.73/1.72 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) % 3.73/1.72 | (29) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 % 3.73/1.72 | (30) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 3.73/1.72 | % 3.73/1.72 | Instantiating formula (28) with all_0_3_3, all_0_5_5, all_0_4_4, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_0_5_5, subset(all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 3.73/1.72 | (31) all_0_3_3 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_0_6_6, all_0_4_4) = v0) % 3.73/1.72 | % 3.73/1.72 +-Applying beta-rule and splitting (31), into two cases. % 3.73/1.72 |-Branch one: % 3.73/1.72 | (32) all_0_3_3 = 0 % 3.73/1.72 | % 3.73/1.72 | Equations (32) can reduce 12 to: % 3.73/1.72 | (33) $false % 3.73/1.72 | % 3.73/1.72 |-The branch is then unsatisfiable % 3.73/1.72 |-Branch two: % 3.73/1.72 | (12) ~ (all_0_3_3 = 0) % 3.73/1.72 | (35) ? [v0] : ( ~ (v0 = 0) & in(all_0_6_6, all_0_4_4) = v0) % 3.73/1.72 | % 3.73/1.72 | Instantiating (35) with all_22_0_20 yields: % 3.73/1.72 | (36) ~ (all_22_0_20 = 0) & in(all_0_6_6, all_0_4_4) = all_22_0_20 % 3.73/1.72 | % 3.73/1.72 | Applying alpha-rule on (36) yields: % 3.73/1.72 | (37) ~ (all_22_0_20 = 0) % 3.73/1.72 | (38) in(all_0_6_6, all_0_4_4) = all_22_0_20 % 3.73/1.72 | % 3.73/1.72 | Instantiating formula (18) with all_22_0_20, all_0_6_6, all_0_4_4, all_0_6_6 and discharging atoms powerset(all_0_6_6) = all_0_4_4, in(all_0_6_6, all_0_4_4) = all_22_0_20, yields: % 3.73/1.72 | (39) all_22_0_20 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_0_6_6, all_0_6_6) = v0) % 3.73/1.72 | % 3.73/1.72 +-Applying beta-rule and splitting (39), into two cases. % 3.73/1.72 |-Branch one: % 3.73/1.72 | (40) all_22_0_20 = 0 % 3.73/1.72 | % 3.73/1.72 | Equations (40) can reduce 37 to: % 3.73/1.72 | (33) $false % 3.73/1.72 | % 3.73/1.72 |-The branch is then unsatisfiable % 3.73/1.72 |-Branch two: % 3.73/1.72 | (37) ~ (all_22_0_20 = 0) % 3.73/1.72 | (43) ? [v0] : ( ~ (v0 = 0) & subset(all_0_6_6, all_0_6_6) = v0) % 3.73/1.72 | % 3.73/1.72 | Instantiating (43) with all_35_0_21 yields: % 3.73/1.72 | (44) ~ (all_35_0_21 = 0) & subset(all_0_6_6, all_0_6_6) = all_35_0_21 % 3.73/1.72 | % 3.73/1.72 | Applying alpha-rule on (44) yields: % 3.73/1.72 | (45) ~ (all_35_0_21 = 0) % 3.73/1.72 | (46) subset(all_0_6_6, all_0_6_6) = all_35_0_21 % 3.73/1.72 | % 3.73/1.72 | Instantiating formula (30) with all_35_0_21, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_6_6) = all_35_0_21, yields: % 3.73/1.72 | (47) all_35_0_21 = 0 % 3.73/1.73 | % 3.73/1.73 | Equations (47) can reduce 45 to: % 3.73/1.73 | (33) $false % 3.73/1.73 | % 3.73/1.73 |-The branch is then unsatisfiable % 3.73/1.73 % SZS output end Proof for theBenchmark % 3.73/1.73 % 3.73/1.73 1132ms %------------------------------------------------------------------------------