%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET932+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n004.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 3.45s 1.52s % Output : Proof 4.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET932+1 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n004.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 : Mon Jul 11 05:10:22 EDT 2022 % 0.12/0.33 % CPUTime : % 0.53/0.62 ____ _ % 0.53/0.62 ___ / __ \_____(_)___ ________ __________ % 0.53/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.53/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.53/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.53/0.62 % 0.53/0.62 A Theorem Prover for First-Order Logic % 0.53/0.62 (ePrincess v.1.0) % 0.53/0.62 % 0.53/0.62 (c) Philipp Rümmer, 2009-2015 % 0.53/0.62 (c) Peter Backeman, 2014-2015 % 0.53/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.53/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.53/0.62 Bug reports to peter@backeman.se % 0.53/0.62 % 0.53/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.53/0.62 % 0.53/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.74/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.33/0.89 Prover 0: Preprocessing ... % 1.53/1.01 Prover 0: Warning: ignoring some quantifiers % 1.53/1.02 Prover 0: Constructing countermodel ... % 2.94/1.40 Prover 0: gave up % 2.94/1.41 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.94/1.42 Prover 1: Preprocessing ... % 3.33/1.47 Prover 1: Warning: ignoring some quantifiers % 3.33/1.47 Prover 1: Constructing countermodel ... % 3.45/1.52 Prover 1: proved (111ms) % 3.45/1.52 % 3.45/1.52 No countermodel exists, formula is valid % 3.45/1.52 % SZS status Theorem for theBenchmark % 3.45/1.52 % 3.45/1.52 Generating proof ... Warning: ignoring some quantifiers % 4.12/1.73 found it (size 24) % 4.12/1.73 % 4.12/1.73 % SZS output start Proof for theBenchmark % 4.12/1.73 Assumed formulas after preprocessing and simplification: % 4.12/1.73 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v6 = 0) & ~ (v4 = 0) & empty(v7) = 0 & empty(v5) = v6 & powerset(v1) = v3 & powerset(v0) = v2 & subset(v2, v3) = v4 & subset(v0, v1) = 0 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (powerset(v8) = v9) | ~ (in(v10, v9) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v10, v8) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v8, v10) = v11) | ~ (subset(v8, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & subset(v9, v10) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (subset(v11, v10) = v9) | ~ (subset(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (in(v11, v10) = v9) | ~ (in(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & in(v11, v9) = v12 & in(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (empty(v10) = v9) | ~ (empty(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (powerset(v10) = v9) | ~ (powerset(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v8) = v9) | ~ (in(v10, v9) = 0) | subset(v10, v8) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v8, v9) = 0) | ~ (in(v10, v8) = 0) | in(v10, v9) = 0) & ? [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (powerset(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (subset(v11, v9) = v13 & in(v11, v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)) & (v13 = 0 | v12 = 0))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v8, v8) = v9)) & ! [v8] : ! [v9] : ( ~ (in(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & in(v9, v8) = v10))) % 4.12/1.76 | 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: % 4.12/1.76 | (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 & powerset(all_0_6_6) = all_0_4_4 & powerset(all_0_7_7) = all_0_5_5 & subset(all_0_5_5, all_0_4_4) = all_0_3_3 & subset(all_0_7_7, all_0_6_6) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = 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 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | subset(v2, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 4.12/1.77 | % 4.12/1.77 | Applying alpha-rule on (1) yields: % 4.12/1.77 | (2) subset(all_0_5_5, all_0_4_4) = all_0_3_3 % 4.12/1.77 | (3) ~ (all_0_1_1 = 0) % 4.12/1.77 | (4) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 4.12/1.77 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 4.12/1.77 | (6) ~ (all_0_3_3 = 0) % 4.12/1.77 | (7) subset(all_0_7_7, all_0_6_6) = 0 % 4.53/1.77 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 4.53/1.77 | (9) powerset(all_0_7_7) = all_0_5_5 % 4.53/1.77 | (10) empty(all_0_2_2) = all_0_1_1 % 4.53/1.77 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 4.53/1.77 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 4.53/1.77 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | subset(v2, v0) = 0) % 4.53/1.77 | (14) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 4.53/1.77 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 4.53/1.77 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 4.53/1.77 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v2, v0) = v4)) % 4.53/1.77 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) % 4.53/1.77 | (19) empty(all_0_0_0) = 0 % 4.53/1.77 | (20) powerset(all_0_6_6) = all_0_4_4 % 4.53/1.77 | (21) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) % 4.53/1.77 | % 4.53/1.77 | Instantiating formula (12) with all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 4.53/1.78 | (22) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_5_5) = 0) % 4.53/1.78 | % 4.53/1.78 +-Applying beta-rule and splitting (22), into two cases. % 4.53/1.78 |-Branch one: % 4.53/1.78 | (23) all_0_3_3 = 0 % 4.53/1.78 | % 4.53/1.78 | Equations (23) can reduce 6 to: % 4.53/1.78 | (24) $false % 4.53/1.78 | % 4.53/1.78 |-The branch is then unsatisfiable % 4.53/1.78 |-Branch two: % 4.53/1.78 | (6) ~ (all_0_3_3 = 0) % 4.53/1.78 | (26) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_5_5) = 0) % 4.53/1.78 | % 4.53/1.78 | Instantiating (26) with all_16_0_9, all_16_1_10 yields: % 4.53/1.78 | (27) ~ (all_16_0_9 = 0) & in(all_16_1_10, all_0_4_4) = all_16_0_9 & in(all_16_1_10, all_0_5_5) = 0 % 4.53/1.78 | % 4.53/1.78 | Applying alpha-rule on (27) yields: % 4.53/1.78 | (28) ~ (all_16_0_9 = 0) % 4.53/1.78 | (29) in(all_16_1_10, all_0_4_4) = all_16_0_9 % 4.53/1.78 | (30) in(all_16_1_10, all_0_5_5) = 0 % 4.53/1.78 | % 4.53/1.78 | Instantiating formula (17) with all_16_0_9, all_16_1_10, all_0_4_4, all_0_6_6 and discharging atoms powerset(all_0_6_6) = all_0_4_4, in(all_16_1_10, all_0_4_4) = all_16_0_9, yields: % 4.53/1.78 | (31) all_16_0_9 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_16_1_10, all_0_6_6) = v0) % 4.53/1.78 | % 4.53/1.78 | Instantiating formula (13) with all_16_1_10, all_0_5_5, all_0_7_7 and discharging atoms powerset(all_0_7_7) = all_0_5_5, in(all_16_1_10, all_0_5_5) = 0, yields: % 4.53/1.78 | (32) subset(all_16_1_10, all_0_7_7) = 0 % 4.53/1.78 | % 4.53/1.78 +-Applying beta-rule and splitting (31), into two cases. % 4.53/1.78 |-Branch one: % 4.53/1.78 | (33) all_16_0_9 = 0 % 4.53/1.78 | % 4.53/1.78 | Equations (33) can reduce 28 to: % 4.53/1.78 | (24) $false % 4.53/1.78 | % 4.53/1.78 |-The branch is then unsatisfiable % 4.53/1.78 |-Branch two: % 4.53/1.78 | (28) ~ (all_16_0_9 = 0) % 4.53/1.78 | (36) ? [v0] : ( ~ (v0 = 0) & subset(all_16_1_10, all_0_6_6) = v0) % 4.53/1.78 | % 4.53/1.78 | Instantiating (36) with all_34_0_12 yields: % 4.53/1.78 | (37) ~ (all_34_0_12 = 0) & subset(all_16_1_10, all_0_6_6) = all_34_0_12 % 4.53/1.78 | % 4.53/1.78 | Applying alpha-rule on (37) yields: % 4.53/1.78 | (38) ~ (all_34_0_12 = 0) % 4.53/1.78 | (39) subset(all_16_1_10, all_0_6_6) = all_34_0_12 % 4.53/1.78 | % 4.53/1.78 | Instantiating formula (18) with all_34_0_12, all_0_6_6, all_0_7_7, all_16_1_10 and discharging atoms subset(all_16_1_10, all_0_6_6) = all_34_0_12, subset(all_16_1_10, all_0_7_7) = 0, yields: % 4.53/1.78 | (40) all_34_0_12 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_0_7_7, all_0_6_6) = v0) % 4.53/1.78 | % 4.53/1.78 +-Applying beta-rule and splitting (40), into two cases. % 4.53/1.78 |-Branch one: % 4.53/1.78 | (41) all_34_0_12 = 0 % 4.53/1.78 | % 4.53/1.78 | Equations (41) can reduce 38 to: % 4.53/1.78 | (24) $false % 4.53/1.78 | % 4.53/1.78 |-The branch is then unsatisfiable % 4.53/1.78 |-Branch two: % 4.53/1.78 | (38) ~ (all_34_0_12 = 0) % 4.53/1.78 | (44) ? [v0] : ( ~ (v0 = 0) & subset(all_0_7_7, all_0_6_6) = v0) % 4.53/1.78 | % 4.53/1.78 | Instantiating (44) with all_47_0_13 yields: % 4.53/1.78 | (45) ~ (all_47_0_13 = 0) & subset(all_0_7_7, all_0_6_6) = all_47_0_13 % 4.53/1.78 | % 4.53/1.78 | Applying alpha-rule on (45) yields: % 4.53/1.78 | (46) ~ (all_47_0_13 = 0) % 4.53/1.78 | (47) subset(all_0_7_7, all_0_6_6) = all_47_0_13 % 4.53/1.78 | % 4.53/1.78 | Instantiating formula (16) with all_0_7_7, all_0_6_6, all_47_0_13, 0 and discharging atoms subset(all_0_7_7, all_0_6_6) = all_47_0_13, subset(all_0_7_7, all_0_6_6) = 0, yields: % 4.53/1.78 | (48) all_47_0_13 = 0 % 4.53/1.78 | % 4.53/1.78 | Equations (48) can reduce 46 to: % 4.53/1.78 | (24) $false % 4.53/1.78 | % 4.53/1.78 |-The branch is then unsatisfiable % 4.53/1.78 % SZS output end Proof for theBenchmark % 4.53/1.78 % 4.53/1.78 1157ms %------------------------------------------------------------------------------