%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SYN415+1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n023.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 : Thu Jul 21 05:02:14 EDT 2022 % Result : Theorem 1.56s 1.09s % Output : Proof 2.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN415+1 : TPTP v8.1.0. Released v2.0.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n023.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 : Tue Jul 12 04:40:39 EDT 2022 % 0.12/0.34 % CPUTime : % 0.58/0.60 ____ _ % 0.58/0.60 ___ / __ \_____(_)___ ________ __________ % 0.58/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.60 % 0.58/0.60 A Theorem Prover for First-Order Logic % 0.64/0.60 (ePrincess v.1.0) % 0.64/0.60 % 0.64/0.60 (c) Philipp Rümmer, 2009-2015 % 0.64/0.60 (c) Peter Backeman, 2014-2015 % 0.64/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.64/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.64/0.60 Bug reports to peter@backeman.se % 0.64/0.60 % 0.64/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.64/0.60 % 0.64/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.67/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.32/0.92 Prover 0: Preprocessing ... % 1.37/0.99 Prover 0: Constructing countermodel ... % 1.56/1.09 Prover 0: proved (410ms) % 1.56/1.09 % 1.56/1.09 No countermodel exists, formula is valid % 1.56/1.09 % SZS status Theorem for theBenchmark % 1.56/1.09 % 1.56/1.09 Generating proof ... found it (size 20) % 2.24/1.23 % 2.24/1.23 % SZS output start Proof for theBenchmark % 2.24/1.23 Assumed formulas after preprocessing and simplification: % 2.24/1.23 | (0) ? [v0] : ? [v1] : ? [v2] : ((f(v2) & ! [v3] : (v3 = v2 | ~ f(v3)) & ( ! [v3] : ~ f(v3) | ( ~ (v1 = v0) & f(v1) & f(v0)))) | (f(v0) & ! [v3] : ! [v4] : (v4 = v3 | ~ f(v4) | ~ f(v3)) & ! [v3] : ( ~ f(v3) | ? [v4] : ( ~ (v4 = v3) & f(v4))))) % 2.24/1.23 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 2.24/1.23 | (1) (f(all_0_0_0) & ! [v0] : (v0 = all_0_0_0 | ~ f(v0)) & ( ! [v0] : ~ f(v0) | ( ~ (all_0_1_1 = all_0_2_2) & f(all_0_1_1) & f(all_0_2_2)))) | (f(all_0_2_2) & ! [v0] : ! [v1] : (v1 = v0 | ~ f(v1) | ~ f(v0)) & ! [v0] : ( ~ f(v0) | ? [v1] : ( ~ (v1 = v0) & f(v1)))) % 2.24/1.24 | % 2.24/1.24 +-Applying beta-rule and splitting (1), into two cases. % 2.24/1.24 |-Branch one: % 2.24/1.24 | (2) f(all_0_0_0) & ! [v0] : (v0 = all_0_0_0 | ~ f(v0)) & ( ! [v0] : ~ f(v0) | ( ~ (all_0_1_1 = all_0_2_2) & f(all_0_1_1) & f(all_0_2_2))) % 2.24/1.24 | % 2.24/1.24 | Applying alpha-rule on (2) yields: % 2.24/1.24 | (3) f(all_0_0_0) % 2.24/1.24 | (4) ! [v0] : (v0 = all_0_0_0 | ~ f(v0)) % 2.24/1.24 | (5) ! [v0] : ~ f(v0) | ( ~ (all_0_1_1 = all_0_2_2) & f(all_0_1_1) & f(all_0_2_2)) % 2.24/1.24 | % 2.24/1.24 +-Applying beta-rule and splitting (5), into two cases. % 2.24/1.24 |-Branch one: % 2.24/1.24 | (6) ! [v0] : ~ f(v0) % 2.24/1.24 | % 2.24/1.24 | Instantiating formula (6) with all_0_0_0 and discharging atoms f(all_0_0_0), yields: % 2.24/1.24 | (7) $false % 2.24/1.24 | % 2.24/1.24 |-The branch is then unsatisfiable % 2.24/1.24 |-Branch two: % 2.24/1.24 | (8) ~ (all_0_1_1 = all_0_2_2) & f(all_0_1_1) & f(all_0_2_2) % 2.24/1.24 | % 2.24/1.24 | Applying alpha-rule on (8) yields: % 2.24/1.24 | (9) ~ (all_0_1_1 = all_0_2_2) % 2.24/1.24 | (10) f(all_0_1_1) % 2.24/1.24 | (11) f(all_0_2_2) % 2.24/1.24 | % 2.24/1.24 | Instantiating formula (4) with all_0_1_1 and discharging atoms f(all_0_1_1), yields: % 2.24/1.24 | (12) all_0_0_0 = all_0_1_1 % 2.24/1.24 | % 2.24/1.24 | Instantiating formula (4) with all_0_2_2 and discharging atoms f(all_0_2_2), yields: % 2.24/1.24 | (13) all_0_0_0 = all_0_2_2 % 2.24/1.24 | % 2.24/1.24 | Combining equations (12,13) yields a new equation: % 2.24/1.24 | (14) all_0_1_1 = all_0_2_2 % 2.24/1.24 | % 2.24/1.24 | Simplifying 14 yields: % 2.24/1.24 | (15) all_0_1_1 = all_0_2_2 % 2.24/1.24 | % 2.24/1.24 | Equations (15) can reduce 9 to: % 2.24/1.24 | (16) $false % 2.24/1.24 | % 2.24/1.24 |-The branch is then unsatisfiable % 2.24/1.24 |-Branch two: % 2.24/1.24 | (17) f(all_0_2_2) & ! [v0] : ! [v1] : (v1 = v0 | ~ f(v1) | ~ f(v0)) & ! [v0] : ( ~ f(v0) | ? [v1] : ( ~ (v1 = v0) & f(v1))) % 2.24/1.25 | % 2.24/1.25 | Applying alpha-rule on (17) yields: % 2.24/1.25 | (11) f(all_0_2_2) % 2.24/1.25 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ f(v1) | ~ f(v0)) % 2.24/1.25 | (20) ! [v0] : ( ~ f(v0) | ? [v1] : ( ~ (v1 = v0) & f(v1))) % 2.24/1.25 | % 2.24/1.25 | Instantiating formula (20) with all_0_2_2 and discharging atoms f(all_0_2_2), yields: % 2.24/1.25 | (21) ? [v0] : ( ~ (v0 = all_0_2_2) & f(v0)) % 2.24/1.25 | % 2.24/1.25 | Instantiating (21) with all_9_0_3 yields: % 2.24/1.25 | (22) ~ (all_9_0_3 = all_0_2_2) & f(all_9_0_3) % 2.24/1.25 | % 2.24/1.25 | Applying alpha-rule on (22) yields: % 2.24/1.25 | (23) ~ (all_9_0_3 = all_0_2_2) % 2.24/1.25 | (24) f(all_9_0_3) % 2.24/1.25 | % 2.24/1.25 | Instantiating formula (19) with all_9_0_3, all_0_2_2 and discharging atoms f(all_9_0_3), f(all_0_2_2), yields: % 2.24/1.25 | (25) all_9_0_3 = all_0_2_2 % 2.24/1.25 | % 2.24/1.25 | Equations (25) can reduce 23 to: % 2.24/1.25 | (16) $false % 2.24/1.25 | % 2.24/1.25 |-The branch is then unsatisfiable % 2.24/1.25 % SZS output end Proof for theBenchmark % 2.24/1.25 % 2.24/1.25 629ms %------------------------------------------------------------------------------