%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU144+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n032.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 08:46:56 EDT 2022 % Result : Theorem 2.60s 1.31s % Output : Proof 3.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.08 % Problem : SEU144+1 : TPTP v8.1.0. Released v3.3.0. % 0.08/0.09 % Command : ePrincess-casc -timeout=%d %s % 0.09/0.28 % Computer : n032.cluster.edu % 0.09/0.28 % Model : x86_64 x86_64 % 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.28 % Memory : 8042.1875MB % 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.28 % CPULimit : 300 % 0.09/0.28 % WCLimit : 600 % 0.09/0.28 % DateTime : Sun Jun 19 06:07:32 EDT 2022 % 0.09/0.28 % CPUTime : % 0.13/0.47 ____ _ % 0.13/0.47 ___ / __ \_____(_)___ ________ __________ % 0.13/0.47 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.13/0.47 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.13/0.47 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.13/0.47 % 0.13/0.47 A Theorem Prover for First-Order Logic % 0.13/0.47 (ePrincess v.1.0) % 0.13/0.47 % 0.13/0.47 (c) Philipp Rümmer, 2009-2015 % 0.13/0.47 (c) Peter Backeman, 2014-2015 % 0.13/0.47 (contributions by Angelo Brillout, Peter Baumgartner) % 0.13/0.47 Free software under GNU Lesser General Public License (LGPL). % 0.13/0.47 Bug reports to peter@backeman.se % 0.13/0.47 % 0.13/0.47 For more information, visit http://user.uu.se/~petba168/breu/ % 0.13/0.47 % 0.13/0.47 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.13/0.52 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 0.95/0.74 Prover 0: Preprocessing ... % 1.26/0.85 Prover 0: Warning: ignoring some quantifiers % 1.26/0.87 Prover 0: Constructing countermodel ... % 1.91/1.06 Prover 0: gave up % 1.91/1.06 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.91/1.09 Prover 1: Preprocessing ... % 2.17/1.14 Prover 1: Warning: ignoring some quantifiers % 2.17/1.15 Prover 1: Constructing countermodel ... % 2.23/1.22 Prover 1: gave up % 2.23/1.22 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.45/1.23 Prover 2: Preprocessing ... % 2.45/1.27 Prover 2: Warning: ignoring some quantifiers % 2.60/1.27 Prover 2: Constructing countermodel ... % 2.60/1.31 Prover 2: proved (96ms) % 2.60/1.31 % 2.60/1.31 No countermodel exists, formula is valid % 2.60/1.31 % SZS status Theorem for theBenchmark % 2.60/1.31 % 2.60/1.31 Generating proof ... Warning: ignoring some quantifiers % 3.22/1.45 found it (size 27) % 3.22/1.45 % 3.22/1.45 % SZS output start Proof for theBenchmark % 3.22/1.45 Assumed formulas after preprocessing and simplification: % 3.22/1.45 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (subset(v2, v1) = v3 & singleton(v0) = v2 & in(v0, v1) = v4 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v5, v6) = 0) | ~ (in(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & in(v7, v5) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (subset(v8, v7) = v6) | ~ (subset(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (in(v8, v7) = v6) | ~ (in(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (singleton(v5) = v6) | ~ (in(v7, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & in(v8, v6) = v9 & in(v8, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (singleton(v5) = v6) | ~ (in(v5, v6) = v7)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (singleton(v7) = v6) | ~ (singleton(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (subset(v5, v6) = 0) | ~ (in(v7, v5) = 0) | in(v7, v6) = 0) & ? [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (singleton(v6) = v7) | ? [v8] : ? [v9] : (( ~ (v8 = v6) | ( ~ (v9 = 0) & in(v6, v5) = v9)) & (v8 = v6 | (v9 = 0 & in(v8, v5) = 0)))) & ! [v5] : ! [v6] : (v6 = 0 | ~ (subset(v5, v5) = v6)) & ! [v5] : ! [v6] : ( ~ (in(v6, v5) = 0) | ? [v7] : ( ~ (v7 = 0) & in(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (in(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & in(v6, v5) = v7)) & ? [v5] : ? [v6] : ? [v7] : subset(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : in(v6, v5) = v7 & ? [v5] : ? [v6] : singleton(v5) = v6 & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0)))) % 3.22/1.48 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 3.22/1.48 | (1) subset(all_0_2_2, all_0_3_3) = all_0_1_1 & singleton(all_0_4_4) = all_0_2_2 & in(all_0_4_4, all_0_3_3) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(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 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = v1) | ( ~ (v4 = 0) & in(v1, v0) = v4)) & (v3 = v1 | (v4 = 0 & in(v3, v0) = 0)))) & ! [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] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : singleton(v0) = v1 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0))) % 3.22/1.49 | % 3.22/1.49 | Applying alpha-rule on (1) yields: % 3.22/1.49 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) % 3.22/1.49 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 3.22/1.49 | (4) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 3.22/1.49 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 3.22/1.49 | (6) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = v1) | ( ~ (v4 = 0) & in(v1, v0) = v4)) & (v3 = v1 | (v4 = 0 & in(v3, v0) = 0)))) % 3.22/1.49 | (7) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 % 3.22/1.49 | (8) ? [v0] : ? [v1] : singleton(v0) = v1 % 3.22/1.49 | (9) singleton(all_0_4_4) = all_0_2_2 % 3.22/1.49 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 3.22/1.49 | (11) (all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)) % 3.22/1.49 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 3.22/1.49 | (13) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 % 3.22/1.49 | (14) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) % 3.22/1.49 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 3.22/1.49 | (16) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 3.22/1.50 | (17) in(all_0_4_4, all_0_3_3) = all_0_0_0 % 3.22/1.50 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) % 3.22/1.50 | (19) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 3.22/1.50 | (20) subset(all_0_2_2, all_0_3_3) = all_0_1_1 % 3.22/1.50 | % 3.22/1.50 | Instantiating formula (15) with all_0_1_1, all_0_3_3, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_3_3) = all_0_1_1, yields: % 3.22/1.50 | (21) all_0_1_1 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_2_2) = 0 & in(v0, all_0_3_3) = v1) % 3.22/1.50 | % 3.22/1.50 +-Applying beta-rule and splitting (11), into two cases. % 3.22/1.50 |-Branch one: % 3.22/1.50 | (22) all_0_0_0 = 0 & ~ (all_0_1_1 = 0) % 3.22/1.50 | % 3.22/1.50 | Applying alpha-rule on (22) yields: % 3.22/1.50 | (23) all_0_0_0 = 0 % 3.22/1.50 | (24) ~ (all_0_1_1 = 0) % 3.22/1.50 | % 3.22/1.50 | From (23) and (17) follows: % 3.22/1.50 | (25) in(all_0_4_4, all_0_3_3) = 0 % 3.22/1.50 | % 3.22/1.50 +-Applying beta-rule and splitting (21), into two cases. % 3.22/1.50 |-Branch one: % 3.22/1.50 | (26) all_0_1_1 = 0 % 3.22/1.50 | % 3.22/1.50 | Equations (26) can reduce 24 to: % 3.22/1.50 | (27) $false % 3.22/1.50 | % 3.22/1.50 |-The branch is then unsatisfiable % 3.22/1.50 |-Branch two: % 3.22/1.50 | (24) ~ (all_0_1_1 = 0) % 3.22/1.50 | (29) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_2_2) = 0 & in(v0, all_0_3_3) = v1) % 3.22/1.50 | % 3.22/1.50 | Instantiating (29) with all_22_0_14, all_22_1_15 yields: % 3.22/1.50 | (30) ~ (all_22_0_14 = 0) & in(all_22_1_15, all_0_2_2) = 0 & in(all_22_1_15, all_0_3_3) = all_22_0_14 % 3.22/1.50 | % 3.22/1.50 | Applying alpha-rule on (30) yields: % 3.22/1.50 | (31) ~ (all_22_0_14 = 0) % 3.22/1.50 | (32) in(all_22_1_15, all_0_2_2) = 0 % 3.22/1.50 | (33) in(all_22_1_15, all_0_3_3) = all_22_0_14 % 3.22/1.50 | % 3.22/1.50 | Instantiating formula (14) with all_22_1_15, all_0_2_2, all_0_4_4 and discharging atoms singleton(all_0_4_4) = all_0_2_2, in(all_22_1_15, all_0_2_2) = 0, yields: % 3.22/1.50 | (34) all_22_1_15 = all_0_4_4 % 3.22/1.50 | % 3.22/1.50 | From (34) and (33) follows: % 3.22/1.50 | (35) in(all_0_4_4, all_0_3_3) = all_22_0_14 % 3.22/1.50 | % 3.22/1.50 | Instantiating formula (3) with all_0_4_4, all_0_3_3, all_22_0_14, 0 and discharging atoms in(all_0_4_4, all_0_3_3) = all_22_0_14, in(all_0_4_4, all_0_3_3) = 0, yields: % 3.22/1.50 | (36) all_22_0_14 = 0 % 3.22/1.50 | % 3.22/1.50 | Equations (36) can reduce 31 to: % 3.22/1.50 | (27) $false % 3.22/1.50 | % 3.22/1.50 |-The branch is then unsatisfiable % 3.22/1.50 |-Branch two: % 3.22/1.50 | (38) all_0_1_1 = 0 & ~ (all_0_0_0 = 0) % 3.22/1.50 | % 3.22/1.50 | Applying alpha-rule on (38) yields: % 3.22/1.50 | (26) all_0_1_1 = 0 % 3.22/1.50 | (40) ~ (all_0_0_0 = 0) % 3.22/1.50 | % 3.22/1.50 | From (26) and (20) follows: % 3.22/1.50 | (41) subset(all_0_2_2, all_0_3_3) = 0 % 3.22/1.50 | % 3.22/1.50 | Instantiating formula (2) with all_0_0_0, all_0_4_4, all_0_3_3, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_3_3) = 0, in(all_0_4_4, all_0_3_3) = all_0_0_0, yields: % 3.22/1.50 | (42) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_0_4_4, all_0_2_2) = v0) % 3.22/1.50 | % 3.22/1.50 +-Applying beta-rule and splitting (42), into two cases. % 3.22/1.50 |-Branch one: % 3.22/1.50 | (23) all_0_0_0 = 0 % 3.22/1.50 | % 3.22/1.50 | Equations (23) can reduce 40 to: % 3.22/1.50 | (27) $false % 3.22/1.50 | % 3.22/1.50 |-The branch is then unsatisfiable % 3.22/1.50 |-Branch two: % 3.22/1.50 | (40) ~ (all_0_0_0 = 0) % 3.22/1.51 | (46) ? [v0] : ( ~ (v0 = 0) & in(all_0_4_4, all_0_2_2) = v0) % 3.22/1.51 | % 3.22/1.51 | Instantiating (46) with all_29_0_16 yields: % 3.22/1.51 | (47) ~ (all_29_0_16 = 0) & in(all_0_4_4, all_0_2_2) = all_29_0_16 % 3.22/1.51 | % 3.22/1.51 | Applying alpha-rule on (47) yields: % 3.22/1.51 | (48) ~ (all_29_0_16 = 0) % 3.22/1.51 | (49) in(all_0_4_4, all_0_2_2) = all_29_0_16 % 3.22/1.51 | % 3.22/1.51 | Instantiating formula (18) with all_29_0_16, all_0_2_2, all_0_4_4 and discharging atoms singleton(all_0_4_4) = all_0_2_2, in(all_0_4_4, all_0_2_2) = all_29_0_16, yields: % 3.22/1.51 | (50) all_29_0_16 = 0 % 3.22/1.51 | % 3.22/1.51 | Equations (50) can reduce 48 to: % 3.22/1.51 | (27) $false % 3.22/1.51 | % 3.22/1.51 |-The branch is then unsatisfiable % 3.22/1.51 % SZS output end Proof for theBenchmark % 3.22/1.51 % 3.22/1.51 1024ms %------------------------------------------------------------------------------