%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : NUN073+2 : TPTP v8.1.0. Released v7.3.0. % 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 : Mon Jul 18 16:25:09 EDT 2022 % Result : Theorem 2.37s 1.24s % Output : Proof 3.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUN073+2 : TPTP v8.1.0. Released v7.3.0. % 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n020.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Thu Jun 2 06:36:23 EDT 2022 % 0.12/0.34 % CPUTime : % 0.58/0.58 ____ _ % 0.58/0.58 ___ / __ \_____(_)___ ________ __________ % 0.58/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.58 % 0.58/0.58 A Theorem Prover for First-Order Logic % 0.58/0.59 (ePrincess v.1.0) % 0.58/0.59 % 0.58/0.59 (c) Philipp Rümmer, 2009-2015 % 0.58/0.59 (c) Peter Backeman, 2014-2015 % 0.58/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.59 Bug reports to peter@backeman.se % 0.58/0.59 % 0.58/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.59 % 0.58/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.80/0.98 Prover 0: Preprocessing ... % 1.98/1.13 Prover 0: Warning: ignoring some quantifiers % 2.21/1.14 Prover 0: Constructing countermodel ... % 2.37/1.24 Prover 0: proved (602ms) % 2.37/1.24 % 2.37/1.24 No countermodel exists, formula is valid % 2.37/1.24 % SZS status Theorem for theBenchmark % 2.37/1.24 % 2.37/1.24 Generating proof ... Warning: ignoring some quantifiers % 3.20/1.44 found it (size 12) % 3.20/1.44 % 3.20/1.44 % SZS output start Proof for theBenchmark % 3.20/1.44 Assumed formulas after preprocessing and simplification: % 3.20/1.44 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (r2(v3, v0) & r2(v2, v1) & r2(v1, v0) & r1(v4) & r1(v3) & r1(v2) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ r2(v6, v7) | ~ r2(v5, v7)) & ! [v5] : ! [v6] : ( ~ r2(v5, v6) | ~ r1(v6)) & ! [v5] : (v5 = v4 | ~ r1(v5)) & ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (r4(v5, v9, v7) & r4(v5, v6, v8) & r3(v8, v5, v7) & r2(v6, v9)) & ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (r3(v5, v9, v7) & r3(v5, v6, v8) & r2(v8, v7) & r2(v6, v9)) & ? [v5] : ? [v6] : ? [v7] : ((v7 = v5 & r2(v6, v5)) | (v6 = v5 & r1(v5))) & ? [v5] : ? [v6] : ? [v7] : (r4(v5, v7, v6) & r1(v7) & r1(v6)) & ? [v5] : ? [v6] : ? [v7] : (r4(v5, v6, v7) & ! [v8] : (v8 = v7 | ~ r4(v5, v6, v8))) & ? [v5] : ? [v6] : ? [v7] : (r3(v5, v6, v7) & ! [v8] : (v8 = v7 | ~ r3(v5, v6, v8))) & ? [v5] : ? [v6] : (r3(v5, v6, v5) & r1(v6)) & ? [v5] : ? [v6] : (r2(v5, v6) & ! [v7] : (v7 = v6 | ~ r2(v5, v7)))) % 3.20/1.45 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 3.20/1.45 | (1) r2(all_0_1_1, all_0_4_4) & r2(all_0_2_2, all_0_3_3) & r2(all_0_3_3, all_0_4_4) & r1(all_0_0_0) & r1(all_0_1_1) & r1(all_0_2_2) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ r2(v1, v2) | ~ r2(v0, v2)) & ! [v0] : ! [v1] : ( ~ r2(v0, v1) | ~ r1(v1)) & ! [v0] : (v0 = all_0_0_0 | ~ r1(v0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (r4(v0, v4, v2) & r4(v0, v1, v3) & r3(v3, v0, v2) & r2(v1, v4)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (r3(v0, v4, v2) & r3(v0, v1, v3) & r2(v3, v2) & r2(v1, v4)) & ? [v0] : ? [v1] : ? [v2] : ((v2 = v0 & r2(v1, v0)) | (v1 = v0 & r1(v0))) & ? [v0] : ? [v1] : ? [v2] : (r4(v0, v2, v1) & r1(v2) & r1(v1)) & ? [v0] : ? [v1] : ? [v2] : (r4(v0, v1, v2) & ! [v3] : (v3 = v2 | ~ r4(v0, v1, v3))) & ? [v0] : ? [v1] : ? [v2] : (r3(v0, v1, v2) & ! [v3] : (v3 = v2 | ~ r3(v0, v1, v3))) & ? [v0] : ? [v1] : (r3(v0, v1, v0) & r1(v1)) & ? [v0] : ? [v1] : (r2(v0, v1) & ! [v2] : (v2 = v1 | ~ r2(v0, v2))) % 3.20/1.46 | % 3.20/1.46 | Applying alpha-rule on (1) yields: % 3.20/1.46 | (2) ? [v0] : ? [v1] : ? [v2] : (r3(v0, v1, v2) & ! [v3] : (v3 = v2 | ~ r3(v0, v1, v3))) % 3.20/1.46 | (3) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (r4(v0, v4, v2) & r4(v0, v1, v3) & r3(v3, v0, v2) & r2(v1, v4)) % 3.20/1.46 | (4) ? [v0] : ? [v1] : ? [v2] : ((v2 = v0 & r2(v1, v0)) | (v1 = v0 & r1(v0))) % 3.20/1.46 | (5) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (r3(v0, v4, v2) & r3(v0, v1, v3) & r2(v3, v2) & r2(v1, v4)) % 3.20/1.46 | (6) r2(all_0_2_2, all_0_3_3) % 3.20/1.46 | (7) ! [v0] : (v0 = all_0_0_0 | ~ r1(v0)) % 3.20/1.46 | (8) r2(all_0_3_3, all_0_4_4) % 3.20/1.46 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ r2(v1, v2) | ~ r2(v0, v2)) % 3.20/1.46 | (10) ? [v0] : ? [v1] : (r3(v0, v1, v0) & r1(v1)) % 3.20/1.46 | (11) r1(all_0_0_0) % 3.20/1.46 | (12) ? [v0] : ? [v1] : ? [v2] : (r4(v0, v1, v2) & ! [v3] : (v3 = v2 | ~ r4(v0, v1, v3))) % 3.20/1.46 | (13) r2(all_0_1_1, all_0_4_4) % 3.20/1.46 | (14) ? [v0] : ? [v1] : ? [v2] : (r4(v0, v2, v1) & r1(v2) & r1(v1)) % 3.20/1.46 | (15) ? [v0] : ? [v1] : (r2(v0, v1) & ! [v2] : (v2 = v1 | ~ r2(v0, v2))) % 3.20/1.46 | (16) r1(all_0_2_2) % 3.20/1.46 | (17) ! [v0] : ! [v1] : ( ~ r2(v0, v1) | ~ r1(v1)) % 3.20/1.46 | (18) r1(all_0_1_1) % 3.20/1.46 | % 3.20/1.46 | Instantiating formula (9) with all_0_4_4, all_0_3_3, all_0_1_1 and discharging atoms r2(all_0_1_1, all_0_4_4), r2(all_0_3_3, all_0_4_4), yields: % 3.20/1.46 | (19) all_0_1_1 = all_0_3_3 % 3.20/1.46 | % 3.20/1.46 | Instantiating formula (7) with all_0_1_1 and discharging atoms r1(all_0_1_1), yields: % 3.20/1.46 | (20) all_0_0_0 = all_0_1_1 % 3.20/1.46 | % 3.20/1.46 | Instantiating formula (7) with all_0_2_2 and discharging atoms r1(all_0_2_2), yields: % 3.20/1.46 | (21) all_0_0_0 = all_0_2_2 % 3.20/1.46 | % 3.20/1.46 | Combining equations (21,20) yields a new equation: % 3.20/1.46 | (22) all_0_1_1 = all_0_2_2 % 3.20/1.46 | % 3.20/1.46 | Combining equations (22,19) yields a new equation: % 3.20/1.46 | (23) all_0_2_2 = all_0_3_3 % 3.20/1.46 | % 3.20/1.46 | Simplifying 23 yields: % 3.20/1.46 | (24) all_0_2_2 = all_0_3_3 % 3.20/1.46 | % 3.20/1.46 | From (24) and (6) follows: % 3.20/1.47 | (25) r2(all_0_3_3, all_0_3_3) % 3.20/1.47 | % 3.20/1.47 | From (24) and (16) follows: % 3.20/1.47 | (26) r1(all_0_3_3) % 3.20/1.47 | % 3.20/1.47 | Instantiating formula (17) with all_0_3_3, all_0_3_3 and discharging atoms r2(all_0_3_3, all_0_3_3), r1(all_0_3_3), yields: % 3.20/1.47 | (27) $false % 3.20/1.47 | % 3.20/1.47 |-The branch is then unsatisfiable % 3.20/1.47 % SZS output end Proof for theBenchmark % 3.20/1.47 % 3.20/1.47 871ms %------------------------------------------------------------------------------