%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEV569+1 : TPTP v9.1.0. Released v9.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n009.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 : 300s % DateTime : Tue Apr 1 02:01:02 AM UTC 2025 % Result : Theorem 5.93s 1.99s % Output : Proof 8.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEV569+1 : TPTP v9.1.0. Released v9.1.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n009.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Mon Mar 31 12:41:13 EDT 2025 % 0.13/0.34 % CPUTime : % 0.20/0.58 ____ _ % 0.20/0.58 ___ / __ \_____(_)___ ________ __________ % 0.20/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.20/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.20/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.20/0.58 % 0.20/0.58 A Theorem Prover for First-Order Logic % 0.20/0.58 (ePrincess v.1.0) % 0.20/0.58 % 0.20/0.58 (c) Philipp Rümmer, 2009-2015 % 0.20/0.58 (c) Peter Backeman, 2014-2015 % 0.20/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.20/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.20/0.59 Bug reports to peter@backeman.se % 0.20/0.59 % 0.20/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.74/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.68/0.97 Prover 0: Preprocessing ... % 2.52/1.24 Prover 0: Warning: ignoring some quantifiers % 2.65/1.27 Prover 0: Constructing countermodel ... % 5.93/1.99 Prover 0: proved (1360ms) % 5.93/1.99 % 5.93/1.99 No countermodel exists, formula is valid % 5.93/1.99 % SZS status Theorem for theBenchmark % 5.93/1.99 % 5.93/1.99 Generating proof ... Warning: ignoring some quantifiers % 7.94/2.44 found it (size 129) % 7.94/2.44 % 7.94/2.44 % SZS output start Proof for theBenchmark % 7.94/2.44 Assumed formulas after preprocessing and simplification: % 7.94/2.44 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (n(v5) = v10 & n(v1) = v2 & n(v0) = v5 & n(e) = v0 & a(v9, v10) = v11 & a(v4, v6) = v7 & a(v1, v5) = v8 & a(v0, v5) = v6 & u(v14, v11) = v15 & u(v8, v11) = v12 & u(v7, v15) = v16 & u(v7, v12) = v13 & u(v0, v2) = v3 & s(v5) = v14 & s(v3) = v4 & s(v2) = v9 & s(v0) = v1 & subq(v13, v16) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (a(v20, v19) = v18) | ~ (a(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (m(v20, v19) = v18) | ~ (m(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (u(v20, v19) = v18) | ~ (u(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (m(v18, v19) = v20) | ~ mem(v17, v20) | ~ mem(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (m(v18, v19) = v20) | ~ mem(v17, v20) | mem(v17, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (m(v18, v19) = v20) | ~ mem(v17, v18) | mem(v17, v20) | mem(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (u(v18, v19) = v20) | ~ mem(v17, v20) | mem(v17, v19) | mem(v17, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (u(v18, v19) = v20) | ~ mem(v17, v19) | mem(v17, v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (u(v18, v19) = v20) | ~ mem(v17, v18) | mem(v17, v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (u(v17, v19) = v20) | ~ (s(v18) = v19) | a(v17, v18) = v20) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (p(v19) = v18) | ~ (p(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (n(v19) = v18) | ~ (n(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (s(v19) = v18) | ~ (s(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (s(v18) = v19) | ~ mem(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (p(v18) = v19) | ~ mem(v18, v17) | atleast2p(v17) | subq(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (p(v18) = v19) | ~ mem(v17, v19) | subq(v17, v18)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (p(v18) = v19) | ~ subq(v17, v18) | mem(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (a(v17, v18) = v19) | ? [v20] : (u(v17, v20) = v19 & s(v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ disj(v17, v18) | ~ mem(v19, v18) | ~ mem(v19, v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ mem(v19, v17) | ~ subq(v17, v18) | mem(v19, v18)) & ! [v17] : ! [v18] : (v18 = v17 | ~ subq(v18, v17) | ~ subq(v17, v18)) & ! [v17] : ! [v18] : ( ~ (n(v17) = v18) | a(v17, v17) = v18) & ! [v17] : ! [v18] : ( ~ (a(v17, v17) = v18) | n(v17) = v18) & ! [v17] : ! [v18] : ( ~ (s(v17) = v18) | mem(v17, v18)) & ! [v17] : ! [v18] : ( ~ atleast15p(v18) | ~ subq(v18, v17) | atleast16p(v17) | subq(v17, v18)) & ! [v17] : ! [v18] : ( ~ atleast14p(v18) | ~ subq(v18, v17) | atleast15p(v17) | subq(v17, v18)) & ! [v17] : ! [v18] : ( ~ atleast13p(v18) | ~ subq(v18, v17) | atleast14p(v17) | subq(v17, v18)) & ! [v17] : ! [v18] : ( ~ atleast12p(v18) | ~ subq(v18, v17) | atleast13p(v17) | subq(v17, v18)) & ! [v17] : ! [v18] : ( ~ atleast11p(v18) | ~ subq(v18, v17) | atleast12p(v17) | subq(v17, v18)) & ! [v17] : ! [v18] : ( ~ atleast10p(v18) | ~ subq(v18, v17) | atleast11p(v17) | subq(v17, v18)) & ! [v17] : ! [v18] : ( ~ atleast9p(v18) | ~ subq(v18, v17) | atleast10p(v17) | subq(v17, v18)) & ! [v17] : ! [v18] : ( ~ atleast8p(v18) | ~ subq(v18, v17) | atleast9p(v17) | subq(v17, v18)) & ! [v17] : ! [v18] : ( ~ atleast7p(v18) | ~ subq(v18, v17) | atleast8p(v17) | subq(v17, v18)) & ! [v17] : ! [v18] : ( ~ atleast6p(v18) | ~ subq(v18, v17) | atleast7p(v17) | subq(v17, v18)) & ! [v17] : ! [v18] : ( ~ atleast5p(v18) | ~ subq(v18, v17) | atleast6p(v17) | subq(v17, v18)) & ! [v17] : ! [v18] : ( ~ atleast4p(v18) | ~ subq(v18, v17) | atleast5p(v17) | subq(v17, v18)) & ! [v17] : ! [v18] : ( ~ atleast3p(v18) | ~ subq(v18, v17) | atleast4p(v17) | subq(v17, v18)) & ! [v17] : ! [v18] : ( ~ atleast2p(v18) | ~ subq(v18, v17) | atleast3p(v17) | subq(v17, v18)) & ! [v17] : ( ~ atleast16p(v17) | ? [v18] : (atleast15p(v18) & subq(v18, v17) & ~ subq(v17, v18))) & ! [v17] : ( ~ atleast15p(v17) | ? [v18] : (atleast14p(v18) & subq(v18, v17) & ~ subq(v17, v18))) & ! [v17] : ( ~ atleast14p(v17) | ? [v18] : (atleast13p(v18) & subq(v18, v17) & ~ subq(v17, v18))) & ! [v17] : ( ~ atleast13p(v17) | ? [v18] : (atleast12p(v18) & subq(v18, v17) & ~ subq(v17, v18))) & ! [v17] : ( ~ atleast12p(v17) | ? [v18] : (atleast11p(v18) & subq(v18, v17) & ~ subq(v17, v18))) & ! [v17] : ( ~ atleast11p(v17) | ? [v18] : (atleast10p(v18) & subq(v18, v17) & ~ subq(v17, v18))) & ! [v17] : ( ~ atleast10p(v17) | ? [v18] : (atleast9p(v18) & subq(v18, v17) & ~ subq(v17, v18))) & ! [v17] : ( ~ atleast9p(v17) | ? [v18] : (atleast8p(v18) & subq(v18, v17) & ~ subq(v17, v18))) & ! [v17] : ( ~ atleast8p(v17) | ? [v18] : (atleast7p(v18) & subq(v18, v17) & ~ subq(v17, v18))) & ! [v17] : ( ~ atleast7p(v17) | ? [v18] : (atleast6p(v18) & subq(v18, v17) & ~ subq(v17, v18))) & ! [v17] : ( ~ atleast6p(v17) | ? [v18] : (atleast5p(v18) & subq(v18, v17) & ~ subq(v17, v18))) & ! [v17] : ( ~ atleast5p(v17) | ? [v18] : (atleast4p(v18) & subq(v18, v17) & ~ subq(v17, v18))) & ! [v17] : ( ~ atleast4p(v17) | ? [v18] : (atleast3p(v18) & subq(v18, v17) & ~ subq(v17, v18))) & ! [v17] : ( ~ atleast3p(v17) | ? [v18] : (atleast2p(v18) & subq(v18, v17) & ~ subq(v17, v18))) & ! [v17] : ( ~ atleast2p(v17) | ? [v18] : ? [v19] : (p(v18) = v19 & mem(v18, v17) & ~ subq(v17, v19))) & ! [v17] : ~ mem(v17, e) & ? [v17] : ? [v18] : (disj(v17, v18) | ? [v19] : (mem(v19, v18) & mem(v19, v17))) & ? [v17] : ? [v18] : (subq(v17, v18) | ? [v19] : (mem(v19, v17) & ~ mem(v19, v18)))) % 7.94/2.49 | 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, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16 yields: % 7.94/2.49 | (1) n(all_0_11_11) = all_0_6_6 & n(all_0_15_15) = all_0_14_14 & n(all_0_16_16) = all_0_11_11 & n(e) = all_0_16_16 & a(all_0_7_7, all_0_6_6) = all_0_5_5 & a(all_0_12_12, all_0_10_10) = all_0_9_9 & a(all_0_15_15, all_0_11_11) = all_0_8_8 & a(all_0_16_16, all_0_11_11) = all_0_10_10 & u(all_0_2_2, all_0_5_5) = all_0_1_1 & u(all_0_8_8, all_0_5_5) = all_0_4_4 & u(all_0_9_9, all_0_1_1) = all_0_0_0 & u(all_0_9_9, all_0_4_4) = all_0_3_3 & u(all_0_16_16, all_0_14_14) = all_0_13_13 & s(all_0_11_11) = all_0_2_2 & s(all_0_13_13) = all_0_12_12 & s(all_0_14_14) = all_0_7_7 & s(all_0_16_16) = all_0_15_15 & subq(all_0_3_3, all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (a(v3, v2) = v1) | ~ (a(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (m(v3, v2) = v1) | ~ (m(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (u(v3, v2) = v1) | ~ (u(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (m(v1, v2) = v3) | ~ mem(v0, v3) | ~ mem(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (m(v1, v2) = v3) | ~ mem(v0, v3) | mem(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (m(v1, v2) = v3) | ~ mem(v0, v1) | mem(v0, v3) | mem(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u(v1, v2) = v3) | ~ mem(v0, v3) | mem(v0, v2) | mem(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u(v1, v2) = v3) | ~ mem(v0, v2) | mem(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u(v1, v2) = v3) | ~ mem(v0, v1) | mem(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u(v0, v2) = v3) | ~ (s(v1) = v2) | a(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (n(v2) = v1) | ~ (n(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (s(v2) = v1) | ~ (s(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (s(v1) = v2) | ~ mem(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (p(v1) = v2) | ~ mem(v1, v0) | atleast2p(v0) | subq(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (p(v1) = v2) | ~ mem(v0, v2) | subq(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (p(v1) = v2) | ~ subq(v0, v1) | mem(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (a(v0, v1) = v2) | ? [v3] : (u(v0, v3) = v2 & s(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ disj(v0, v1) | ~ mem(v2, v1) | ~ mem(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ mem(v2, v0) | ~ subq(v0, v1) | mem(v2, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subq(v1, v0) | ~ subq(v0, v1)) & ! [v0] : ! [v1] : ( ~ (n(v0) = v1) | a(v0, v0) = v1) & ! [v0] : ! [v1] : ( ~ (a(v0, v0) = v1) | n(v0) = v1) & ! [v0] : ! [v1] : ( ~ (s(v0) = v1) | mem(v0, v1)) & ! [v0] : ! [v1] : ( ~ atleast15p(v1) | ~ subq(v1, v0) | atleast16p(v0) | subq(v0, v1)) & ! [v0] : ! [v1] : ( ~ atleast14p(v1) | ~ subq(v1, v0) | atleast15p(v0) | subq(v0, v1)) & ! [v0] : ! [v1] : ( ~ atleast13p(v1) | ~ subq(v1, v0) | atleast14p(v0) | subq(v0, v1)) & ! [v0] : ! [v1] : ( ~ atleast12p(v1) | ~ subq(v1, v0) | atleast13p(v0) | subq(v0, v1)) & ! [v0] : ! [v1] : ( ~ atleast11p(v1) | ~ subq(v1, v0) | atleast12p(v0) | subq(v0, v1)) & ! [v0] : ! [v1] : ( ~ atleast10p(v1) | ~ subq(v1, v0) | atleast11p(v0) | subq(v0, v1)) & ! [v0] : ! [v1] : ( ~ atleast9p(v1) | ~ subq(v1, v0) | atleast10p(v0) | subq(v0, v1)) & ! [v0] : ! [v1] : ( ~ atleast8p(v1) | ~ subq(v1, v0) | atleast9p(v0) | subq(v0, v1)) & ! [v0] : ! [v1] : ( ~ atleast7p(v1) | ~ subq(v1, v0) | atleast8p(v0) | subq(v0, v1)) & ! [v0] : ! [v1] : ( ~ atleast6p(v1) | ~ subq(v1, v0) | atleast7p(v0) | subq(v0, v1)) & ! [v0] : ! [v1] : ( ~ atleast5p(v1) | ~ subq(v1, v0) | atleast6p(v0) | subq(v0, v1)) & ! [v0] : ! [v1] : ( ~ atleast4p(v1) | ~ subq(v1, v0) | atleast5p(v0) | subq(v0, v1)) & ! [v0] : ! [v1] : ( ~ atleast3p(v1) | ~ subq(v1, v0) | atleast4p(v0) | subq(v0, v1)) & ! [v0] : ! [v1] : ( ~ atleast2p(v1) | ~ subq(v1, v0) | atleast3p(v0) | subq(v0, v1)) & ! [v0] : ( ~ atleast16p(v0) | ? [v1] : (atleast15p(v1) & subq(v1, v0) & ~ subq(v0, v1))) & ! [v0] : ( ~ atleast15p(v0) | ? [v1] : (atleast14p(v1) & subq(v1, v0) & ~ subq(v0, v1))) & ! [v0] : ( ~ atleast14p(v0) | ? [v1] : (atleast13p(v1) & subq(v1, v0) & ~ subq(v0, v1))) & ! [v0] : ( ~ atleast13p(v0) | ? [v1] : (atleast12p(v1) & subq(v1, v0) & ~ subq(v0, v1))) & ! [v0] : ( ~ atleast12p(v0) | ? [v1] : (atleast11p(v1) & subq(v1, v0) & ~ subq(v0, v1))) & ! [v0] : ( ~ atleast11p(v0) | ? [v1] : (atleast10p(v1) & subq(v1, v0) & ~ subq(v0, v1))) & ! [v0] : ( ~ atleast10p(v0) | ? [v1] : (atleast9p(v1) & subq(v1, v0) & ~ subq(v0, v1))) & ! [v0] : ( ~ atleast9p(v0) | ? [v1] : (atleast8p(v1) & subq(v1, v0) & ~ subq(v0, v1))) & ! [v0] : ( ~ atleast8p(v0) | ? [v1] : (atleast7p(v1) & subq(v1, v0) & ~ subq(v0, v1))) & ! [v0] : ( ~ atleast7p(v0) | ? [v1] : (atleast6p(v1) & subq(v1, v0) & ~ subq(v0, v1))) & ! [v0] : ( ~ atleast6p(v0) | ? [v1] : (atleast5p(v1) & subq(v1, v0) & ~ subq(v0, v1))) & ! [v0] : ( ~ atleast5p(v0) | ? [v1] : (atleast4p(v1) & subq(v1, v0) & ~ subq(v0, v1))) & ! [v0] : ( ~ atleast4p(v0) | ? [v1] : (atleast3p(v1) & subq(v1, v0) & ~ subq(v0, v1))) & ! [v0] : ( ~ atleast3p(v0) | ? [v1] : (atleast2p(v1) & subq(v1, v0) & ~ subq(v0, v1))) & ! [v0] : ( ~ atleast2p(v0) | ? [v1] : ? [v2] : (p(v1) = v2 & mem(v1, v0) & ~ subq(v0, v2))) & ! [v0] : ~ mem(v0, e) & ? [v0] : ? [v1] : (disj(v0, v1) | ? [v2] : (mem(v2, v1) & mem(v2, v0))) & ? [v0] : ? [v1] : (subq(v0, v1) | ? [v2] : (mem(v2, v0) & ~ mem(v2, v1))) % 8.30/2.50 | % 8.30/2.50 | Applying alpha-rule on (1) yields: % 8.30/2.50 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (s(v1) = v2) | ~ mem(v0, v2)) % 8.30/2.50 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (a(v0, v1) = v2) | ? [v3] : (u(v0, v3) = v2 & s(v1) = v3)) % 8.30/2.50 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (u(v3, v2) = v1) | ~ (u(v3, v2) = v0)) % 8.30/2.50 | (5) ! [v0] : ! [v1] : ( ~ atleast13p(v1) | ~ subq(v1, v0) | atleast14p(v0) | subq(v0, v1)) % 8.30/2.50 | (6) u(all_0_2_2, all_0_5_5) = all_0_1_1 % 8.30/2.50 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u(v1, v2) = v3) | ~ mem(v0, v1) | mem(v0, v3)) % 8.30/2.50 | (8) subq(all_0_3_3, all_0_0_0) % 8.30/2.50 | (9) ! [v0] : ( ~ atleast8p(v0) | ? [v1] : (atleast7p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 8.30/2.50 | (10) ! [v0] : ( ~ atleast5p(v0) | ? [v1] : (atleast4p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 8.30/2.50 | (11) s(all_0_14_14) = all_0_7_7 % 8.30/2.50 | (12) ! [v0] : ! [v1] : ( ~ atleast5p(v1) | ~ subq(v1, v0) | atleast6p(v0) | subq(v0, v1)) % 8.30/2.50 | (13) ! [v0] : ! [v1] : ( ~ atleast15p(v1) | ~ subq(v1, v0) | atleast16p(v0) | subq(v0, v1)) % 8.30/2.50 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (p(v1) = v2) | ~ subq(v0, v1) | mem(v0, v2)) % 8.30/2.50 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (p(v1) = v2) | ~ mem(v0, v2) | subq(v0, v1)) % 8.30/2.50 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (a(v3, v2) = v1) | ~ (a(v3, v2) = v0)) % 8.30/2.50 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (m(v1, v2) = v3) | ~ mem(v0, v3) | ~ mem(v0, v2)) % 8.30/2.51 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (m(v3, v2) = v1) | ~ (m(v3, v2) = v0)) % 8.30/2.51 | (19) ! [v0] : ( ~ atleast4p(v0) | ? [v1] : (atleast3p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 8.30/2.51 | (20) u(all_0_9_9, all_0_4_4) = all_0_3_3 % 8.30/2.51 | (21) u(all_0_16_16, all_0_14_14) = all_0_13_13 % 8.30/2.51 | (22) ! [v0] : ! [v1] : ( ~ atleast10p(v1) | ~ subq(v1, v0) | atleast11p(v0) | subq(v0, v1)) % 8.30/2.51 | (23) ! [v0] : ( ~ atleast10p(v0) | ? [v1] : (atleast9p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 8.30/2.51 | (24) ! [v0] : ! [v1] : ( ~ atleast12p(v1) | ~ subq(v1, v0) | atleast13p(v0) | subq(v0, v1)) % 8.30/2.51 | (25) ! [v0] : ! [v1] : ( ~ atleast4p(v1) | ~ subq(v1, v0) | atleast5p(v0) | subq(v0, v1)) % 8.30/2.51 | (26) ! [v0] : ! [v1] : ( ~ atleast11p(v1) | ~ subq(v1, v0) | atleast12p(v0) | subq(v0, v1)) % 8.30/2.51 | (27) ! [v0] : ( ~ atleast3p(v0) | ? [v1] : (atleast2p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 8.30/2.51 | (28) n(all_0_15_15) = all_0_14_14 % 8.30/2.51 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (m(v1, v2) = v3) | ~ mem(v0, v3) | mem(v0, v1)) % 8.30/2.51 | (30) ! [v0] : ! [v1] : (v1 = v0 | ~ subq(v1, v0) | ~ subq(v0, v1)) % 8.30/2.51 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u(v1, v2) = v3) | ~ mem(v0, v3) | mem(v0, v2) | mem(v0, v1)) % 8.30/2.51 | (32) u(all_0_8_8, all_0_5_5) = all_0_4_4 % 8.30/2.51 | (33) ! [v0] : ( ~ atleast12p(v0) | ? [v1] : (atleast11p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 8.30/2.51 | (34) ! [v0] : ( ~ atleast14p(v0) | ? [v1] : (atleast13p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 8.30/2.51 | (35) ! [v0] : ! [v1] : ( ~ atleast14p(v1) | ~ subq(v1, v0) | atleast15p(v0) | subq(v0, v1)) % 8.30/2.51 | (36) ! [v0] : ! [v1] : ( ~ atleast8p(v1) | ~ subq(v1, v0) | atleast9p(v0) | subq(v0, v1)) % 8.30/2.51 | (37) ? [v0] : ? [v1] : (subq(v0, v1) | ? [v2] : (mem(v2, v0) & ~ mem(v2, v1))) % 8.30/2.51 | (38) s(all_0_16_16) = all_0_15_15 % 8.30/2.51 | (39) a(all_0_12_12, all_0_10_10) = all_0_9_9 % 8.30/2.51 | (40) ! [v0] : ! [v1] : ( ~ (s(v0) = v1) | mem(v0, v1)) % 8.30/2.51 | (41) ! [v0] : ( ~ atleast16p(v0) | ? [v1] : (atleast15p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 8.30/2.51 | (42) a(all_0_16_16, all_0_11_11) = all_0_10_10 % 8.30/2.51 | (43) ! [v0] : ( ~ atleast6p(v0) | ? [v1] : (atleast5p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 8.30/2.51 | (44) ! [v0] : ! [v1] : ( ~ atleast9p(v1) | ~ subq(v1, v0) | atleast10p(v0) | subq(v0, v1)) % 8.30/2.51 | (45) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (n(v2) = v1) | ~ (n(v2) = v0)) % 8.30/2.51 | (46) s(all_0_13_13) = all_0_12_12 % 8.30/2.51 | (47) ! [v0] : ( ~ atleast15p(v0) | ? [v1] : (atleast14p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 8.30/2.51 | (48) ! [v0] : ( ~ atleast2p(v0) | ? [v1] : ? [v2] : (p(v1) = v2 & mem(v1, v0) & ~ subq(v0, v2))) % 8.30/2.51 | (49) ! [v0] : ! [v1] : ( ~ atleast3p(v1) | ~ subq(v1, v0) | atleast4p(v0) | subq(v0, v1)) % 8.30/2.51 | (50) ! [v0] : ( ~ atleast9p(v0) | ? [v1] : (atleast8p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 8.30/2.51 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u(v0, v2) = v3) | ~ (s(v1) = v2) | a(v0, v1) = v3) % 8.30/2.51 | (52) ! [v0] : ( ~ atleast7p(v0) | ? [v1] : (atleast6p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 8.30/2.51 | (53) ! [v0] : ( ~ atleast13p(v0) | ? [v1] : (atleast12p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 8.30/2.51 | (54) n(e) = all_0_16_16 % 8.30/2.52 | (55) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) % 8.30/2.52 | (56) u(all_0_9_9, all_0_1_1) = all_0_0_0 % 8.30/2.52 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (m(v1, v2) = v3) | ~ mem(v0, v1) | mem(v0, v3) | mem(v0, v2)) % 8.30/2.52 | (58) ! [v0] : ! [v1] : ( ~ atleast6p(v1) | ~ subq(v1, v0) | atleast7p(v0) | subq(v0, v1)) % 8.30/2.52 | (59) ! [v0] : ! [v1] : ( ~ (a(v0, v0) = v1) | n(v0) = v1) % 8.30/2.52 | (60) ! [v0] : ! [v1] : ( ~ (n(v0) = v1) | a(v0, v0) = v1) % 8.30/2.52 | (61) a(all_0_7_7, all_0_6_6) = all_0_5_5 % 8.30/2.52 | (62) ? [v0] : ? [v1] : (disj(v0, v1) | ? [v2] : (mem(v2, v1) & mem(v2, v0))) % 8.30/2.52 | (63) s(all_0_11_11) = all_0_2_2 % 8.30/2.52 | (64) a(all_0_15_15, all_0_11_11) = all_0_8_8 % 8.30/2.52 | (65) ! [v0] : ( ~ atleast11p(v0) | ? [v1] : (atleast10p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 8.30/2.52 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ disj(v0, v1) | ~ mem(v2, v1) | ~ mem(v2, v0)) % 8.30/2.52 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (p(v1) = v2) | ~ mem(v1, v0) | atleast2p(v0) | subq(v0, v2)) % 8.30/2.52 | (68) n(all_0_11_11) = all_0_6_6 % 8.30/2.52 | (69) ! [v0] : ! [v1] : ( ~ atleast7p(v1) | ~ subq(v1, v0) | atleast8p(v0) | subq(v0, v1)) % 8.30/2.52 | (70) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (s(v2) = v1) | ~ (s(v2) = v0)) % 8.30/2.52 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u(v1, v2) = v3) | ~ mem(v0, v2) | mem(v0, v3)) % 8.30/2.52 | (72) ! [v0] : ~ mem(v0, e) % 8.30/2.52 | (73) n(all_0_16_16) = all_0_11_11 % 8.30/2.52 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ mem(v2, v0) | ~ subq(v0, v1) | mem(v2, v1)) % 8.30/2.52 | (75) ! [v0] : ! [v1] : ( ~ atleast2p(v1) | ~ subq(v1, v0) | atleast3p(v0) | subq(v0, v1)) % 8.30/2.52 | % 8.30/2.52 | Instantiating formula (60) with all_0_6_6, all_0_11_11 and discharging atoms n(all_0_11_11) = all_0_6_6, yields: % 8.30/2.52 | (76) a(all_0_11_11, all_0_11_11) = all_0_6_6 % 8.30/2.52 | % 8.30/2.52 | Instantiating formula (60) with all_0_14_14, all_0_15_15 and discharging atoms n(all_0_15_15) = all_0_14_14, yields: % 8.30/2.52 | (77) a(all_0_15_15, all_0_15_15) = all_0_14_14 % 8.30/2.52 | % 8.30/2.52 | Instantiating formula (60) with all_0_11_11, all_0_16_16 and discharging atoms n(all_0_16_16) = all_0_11_11, yields: % 8.30/2.52 | (78) a(all_0_16_16, all_0_16_16) = all_0_11_11 % 8.30/2.52 | % 8.30/2.52 | Instantiating formula (60) with all_0_16_16, e and discharging atoms n(e) = all_0_16_16, yields: % 8.30/2.52 | (79) a(e, e) = all_0_16_16 % 8.30/2.52 | % 8.30/2.52 | Instantiating formula (3) with all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms a(all_0_7_7, all_0_6_6) = all_0_5_5, yields: % 8.30/2.52 | (80) ? [v0] : (u(all_0_7_7, v0) = all_0_5_5 & s(all_0_6_6) = v0) % 8.30/2.52 | % 8.30/2.52 | Instantiating formula (3) with all_0_9_9, all_0_10_10, all_0_12_12 and discharging atoms a(all_0_12_12, all_0_10_10) = all_0_9_9, yields: % 8.30/2.52 | (81) ? [v0] : (u(all_0_12_12, v0) = all_0_9_9 & s(all_0_10_10) = v0) % 8.30/2.52 | % 8.30/2.52 | Instantiating formula (3) with all_0_8_8, all_0_11_11, all_0_15_15 and discharging atoms a(all_0_15_15, all_0_11_11) = all_0_8_8, yields: % 8.30/2.52 | (82) ? [v0] : (u(all_0_15_15, v0) = all_0_8_8 & s(all_0_11_11) = v0) % 8.30/2.52 | % 8.30/2.52 | Instantiating formula (3) with all_0_10_10, all_0_11_11, all_0_16_16 and discharging atoms a(all_0_16_16, all_0_11_11) = all_0_10_10, yields: % 8.30/2.52 | (83) ? [v0] : (u(all_0_16_16, v0) = all_0_10_10 & s(all_0_11_11) = v0) % 8.30/2.52 | % 8.30/2.52 | Instantiating formula (40) with all_0_2_2, all_0_11_11 and discharging atoms s(all_0_11_11) = all_0_2_2, yields: % 8.30/2.52 | (84) mem(all_0_11_11, all_0_2_2) % 8.30/2.52 | % 8.30/2.52 | Instantiating formula (40) with all_0_15_15, all_0_16_16 and discharging atoms s(all_0_16_16) = all_0_15_15, yields: % 8.30/2.52 | (85) mem(all_0_16_16, all_0_15_15) % 8.30/2.52 | % 8.30/2.52 | Instantiating (81) with all_11_0_21 yields: % 8.30/2.52 | (86) u(all_0_12_12, all_11_0_21) = all_0_9_9 & s(all_0_10_10) = all_11_0_21 % 8.30/2.52 | % 8.30/2.52 | Applying alpha-rule on (86) yields: % 8.30/2.52 | (87) u(all_0_12_12, all_11_0_21) = all_0_9_9 % 8.30/2.53 | (88) s(all_0_10_10) = all_11_0_21 % 8.30/2.53 | % 8.30/2.53 | Instantiating (83) with all_13_0_22 yields: % 8.30/2.53 | (89) u(all_0_16_16, all_13_0_22) = all_0_10_10 & s(all_0_11_11) = all_13_0_22 % 8.30/2.53 | % 8.30/2.53 | Applying alpha-rule on (89) yields: % 8.30/2.53 | (90) u(all_0_16_16, all_13_0_22) = all_0_10_10 % 8.30/2.53 | (91) s(all_0_11_11) = all_13_0_22 % 8.30/2.53 | % 8.30/2.53 | Instantiating (82) with all_15_0_23 yields: % 8.30/2.53 | (92) u(all_0_15_15, all_15_0_23) = all_0_8_8 & s(all_0_11_11) = all_15_0_23 % 8.30/2.53 | % 8.30/2.53 | Applying alpha-rule on (92) yields: % 8.30/2.53 | (93) u(all_0_15_15, all_15_0_23) = all_0_8_8 % 8.30/2.53 | (94) s(all_0_11_11) = all_15_0_23 % 8.30/2.53 | % 8.30/2.53 | Instantiating (80) with all_17_0_24 yields: % 8.30/2.53 | (95) u(all_0_7_7, all_17_0_24) = all_0_5_5 & s(all_0_6_6) = all_17_0_24 % 8.30/2.53 | % 8.30/2.53 | Applying alpha-rule on (95) yields: % 8.30/2.53 | (96) u(all_0_7_7, all_17_0_24) = all_0_5_5 % 8.30/2.53 | (97) s(all_0_6_6) = all_17_0_24 % 8.30/2.53 | % 8.30/2.53 | Instantiating formula (70) with all_0_11_11, all_15_0_23, all_0_2_2 and discharging atoms s(all_0_11_11) = all_15_0_23, s(all_0_11_11) = all_0_2_2, yields: % 8.30/2.53 | (98) all_15_0_23 = all_0_2_2 % 8.30/2.53 | % 8.30/2.53 | Instantiating formula (70) with all_0_11_11, all_13_0_22, all_15_0_23 and discharging atoms s(all_0_11_11) = all_15_0_23, s(all_0_11_11) = all_13_0_22, yields: % 8.30/2.53 | (99) all_15_0_23 = all_13_0_22 % 8.30/2.53 | % 8.30/2.53 | Combining equations (98,99) yields a new equation: % 8.30/2.53 | (100) all_13_0_22 = all_0_2_2 % 8.30/2.53 | % 8.30/2.53 | Combining equations (100,99) yields a new equation: % 8.30/2.53 | (98) all_15_0_23 = all_0_2_2 % 8.30/2.53 | % 8.30/2.53 | From (98) and (93) follows: % 8.30/2.53 | (102) u(all_0_15_15, all_0_2_2) = all_0_8_8 % 8.30/2.53 | % 8.30/2.53 | From (100) and (90) follows: % 8.30/2.53 | (103) u(all_0_16_16, all_0_2_2) = all_0_10_10 % 8.30/2.53 | % 8.30/2.53 | From (100) and (91) follows: % 8.30/2.53 | (63) s(all_0_11_11) = all_0_2_2 % 8.30/2.53 | % 8.30/2.53 | Instantiating formula (3) with all_0_6_6, all_0_11_11, all_0_11_11 and discharging atoms a(all_0_11_11, all_0_11_11) = all_0_6_6, yields: % 8.30/2.53 | (105) ? [v0] : (u(all_0_11_11, v0) = all_0_6_6 & s(all_0_11_11) = v0) % 8.30/2.53 | % 8.30/2.53 | Instantiating formula (3) with all_0_14_14, all_0_15_15, all_0_15_15 and discharging atoms a(all_0_15_15, all_0_15_15) = all_0_14_14, yields: % 8.30/2.53 | (106) ? [v0] : (u(all_0_15_15, v0) = all_0_14_14 & s(all_0_15_15) = v0) % 8.30/2.53 | % 8.30/2.53 | Instantiating formula (3) with all_0_11_11, all_0_16_16, all_0_16_16 and discharging atoms a(all_0_16_16, all_0_16_16) = all_0_11_11, yields: % 8.30/2.53 | (107) ? [v0] : (u(all_0_16_16, v0) = all_0_11_11 & s(all_0_16_16) = v0) % 8.30/2.53 | % 8.30/2.53 | Instantiating formula (3) with all_0_16_16, e, e and discharging atoms a(e, e) = all_0_16_16, yields: % 8.30/2.53 | (108) ? [v0] : (u(e, v0) = all_0_16_16 & s(e) = v0) % 8.30/2.53 | % 8.30/2.53 | Instantiating formula (71) with all_0_10_10, all_0_2_2, all_0_16_16, all_0_11_11 and discharging atoms u(all_0_16_16, all_0_2_2) = all_0_10_10, mem(all_0_11_11, all_0_2_2), yields: % 8.30/2.53 | (109) mem(all_0_11_11, all_0_10_10) % 8.30/2.53 | % 8.30/2.53 | Instantiating formula (7) with all_0_8_8, all_0_2_2, all_0_15_15, all_0_16_16 and discharging atoms u(all_0_15_15, all_0_2_2) = all_0_8_8, mem(all_0_16_16, all_0_15_15), yields: % 8.30/2.53 | (110) mem(all_0_16_16, all_0_8_8) % 8.30/2.53 | % 8.30/2.53 | Instantiating (106) with all_29_0_25 yields: % 8.30/2.53 | (111) u(all_0_15_15, all_29_0_25) = all_0_14_14 & s(all_0_15_15) = all_29_0_25 % 8.30/2.53 | % 8.30/2.53 | Applying alpha-rule on (111) yields: % 8.30/2.53 | (112) u(all_0_15_15, all_29_0_25) = all_0_14_14 % 8.30/2.53 | (113) s(all_0_15_15) = all_29_0_25 % 8.30/2.53 | % 8.30/2.53 | Instantiating (105) with all_31_0_26 yields: % 8.30/2.53 | (114) u(all_0_11_11, all_31_0_26) = all_0_6_6 & s(all_0_11_11) = all_31_0_26 % 8.30/2.53 | % 8.30/2.53 | Applying alpha-rule on (114) yields: % 8.30/2.53 | (115) u(all_0_11_11, all_31_0_26) = all_0_6_6 % 8.30/2.53 | (116) s(all_0_11_11) = all_31_0_26 % 8.30/2.53 | % 8.30/2.53 | Instantiating (108) with all_33_0_27 yields: % 8.30/2.53 | (117) u(e, all_33_0_27) = all_0_16_16 & s(e) = all_33_0_27 % 8.30/2.53 | % 8.30/2.54 | Applying alpha-rule on (117) yields: % 8.30/2.54 | (118) u(e, all_33_0_27) = all_0_16_16 % 8.30/2.54 | (119) s(e) = all_33_0_27 % 8.30/2.54 | % 8.30/2.54 | Instantiating (107) with all_35_0_28 yields: % 8.30/2.54 | (120) u(all_0_16_16, all_35_0_28) = all_0_11_11 & s(all_0_16_16) = all_35_0_28 % 8.30/2.54 | % 8.30/2.54 | Applying alpha-rule on (120) yields: % 8.30/2.54 | (121) u(all_0_16_16, all_35_0_28) = all_0_11_11 % 8.30/2.54 | (122) s(all_0_16_16) = all_35_0_28 % 8.30/2.54 | % 8.30/2.54 | Instantiating formula (70) with all_0_11_11, all_31_0_26, all_0_2_2 and discharging atoms s(all_0_11_11) = all_31_0_26, s(all_0_11_11) = all_0_2_2, yields: % 8.30/2.54 | (123) all_31_0_26 = all_0_2_2 % 8.30/2.54 | % 8.30/2.54 | Instantiating formula (70) with all_0_16_16, all_35_0_28, all_0_15_15 and discharging atoms s(all_0_16_16) = all_35_0_28, s(all_0_16_16) = all_0_15_15, yields: % 8.30/2.54 | (124) all_35_0_28 = all_0_15_15 % 8.30/2.54 | % 8.30/2.54 | From (123) and (115) follows: % 8.30/2.54 | (125) u(all_0_11_11, all_0_2_2) = all_0_6_6 % 8.30/2.54 | % 8.30/2.54 | From (124) and (121) follows: % 8.30/2.54 | (126) u(all_0_16_16, all_0_15_15) = all_0_11_11 % 8.30/2.54 | % 8.30/2.54 | From (123) and (116) follows: % 8.30/2.54 | (63) s(all_0_11_11) = all_0_2_2 % 8.30/2.54 | % 8.30/2.54 | Instantiating formula (71) with all_0_6_6, all_0_2_2, all_0_11_11, all_0_11_11 and discharging atoms u(all_0_11_11, all_0_2_2) = all_0_6_6, mem(all_0_11_11, all_0_2_2), yields: % 8.30/2.54 | (128) mem(all_0_11_11, all_0_6_6) % 8.30/2.54 | % 8.30/2.54 | Instantiating formula (7) with all_0_14_14, all_29_0_25, all_0_15_15, all_0_16_16 and discharging atoms u(all_0_15_15, all_29_0_25) = all_0_14_14, mem(all_0_16_16, all_0_15_15), yields: % 8.30/2.54 | (129) mem(all_0_16_16, all_0_14_14) % 8.30/2.54 | % 8.30/2.54 | Instantiating formula (40) with all_33_0_27, e and discharging atoms s(e) = all_33_0_27, yields: % 8.30/2.54 | (130) mem(e, all_33_0_27) % 8.30/2.54 | % 8.30/2.54 | Instantiating formula (7) with all_0_4_4, all_0_5_5, all_0_8_8, all_0_16_16 and discharging atoms u(all_0_8_8, all_0_5_5) = all_0_4_4, mem(all_0_16_16, all_0_8_8), yields: % 8.30/2.54 | (131) mem(all_0_16_16, all_0_4_4) % 8.30/2.54 | % 8.30/2.54 | Instantiating formula (71) with all_0_3_3, all_0_4_4, all_0_9_9, all_0_16_16 and discharging atoms u(all_0_9_9, all_0_4_4) = all_0_3_3, mem(all_0_16_16, all_0_4_4), yields: % 8.30/2.54 | (132) mem(all_0_16_16, all_0_3_3) % 8.30/2.54 | % 8.30/2.54 | Instantiating formula (71) with all_0_13_13, all_0_14_14, all_0_16_16, all_0_16_16 and discharging atoms u(all_0_16_16, all_0_14_14) = all_0_13_13, mem(all_0_16_16, all_0_14_14), yields: % 8.30/2.54 | (133) mem(all_0_16_16, all_0_13_13) % 8.30/2.54 | % 8.30/2.54 | Instantiating formula (71) with all_0_16_16, all_33_0_27, e, e and discharging atoms u(e, all_33_0_27) = all_0_16_16, mem(e, all_33_0_27), yields: % 8.30/2.54 | (134) mem(e, all_0_16_16) % 8.30/2.54 | % 8.30/2.54 | Instantiating formula (74) with all_0_16_16, all_0_0_0, all_0_3_3 and discharging atoms mem(all_0_16_16, all_0_3_3), subq(all_0_3_3, all_0_0_0), yields: % 8.30/2.54 | (135) mem(all_0_16_16, all_0_0_0) % 8.30/2.54 | % 8.30/2.54 | Instantiating formula (7) with all_0_10_10, all_0_2_2, all_0_16_16, e and discharging atoms u(all_0_16_16, all_0_2_2) = all_0_10_10, mem(e, all_0_16_16), yields: % 8.30/2.54 | (136) mem(e, all_0_10_10) % 8.30/2.54 | % 8.30/2.54 | Instantiating formula (7) with all_0_13_13, all_0_14_14, all_0_16_16, e and discharging atoms u(all_0_16_16, all_0_14_14) = all_0_13_13, mem(e, all_0_16_16), yields: % 8.30/2.54 | (137) mem(e, all_0_13_13) % 8.30/2.54 | % 8.30/2.54 | Instantiating formula (7) with all_0_11_11, all_0_15_15, all_0_16_16, e and discharging atoms u(all_0_16_16, all_0_15_15) = all_0_11_11, mem(e, all_0_16_16), yields: % 8.30/2.54 | (138) mem(e, all_0_11_11) % 8.30/2.54 | % 8.30/2.54 | Instantiating formula (31) with all_0_0_0, all_0_1_1, all_0_9_9, all_0_16_16 and discharging atoms u(all_0_9_9, all_0_1_1) = all_0_0_0, mem(all_0_16_16, all_0_0_0), yields: % 8.30/2.54 | (139) mem(all_0_16_16, all_0_1_1) | mem(all_0_16_16, all_0_9_9) % 8.30/2.54 | % 8.30/2.54 +-Applying beta-rule and splitting (139), into two cases. % 8.30/2.54 |-Branch one: % 8.30/2.54 | (140) mem(all_0_16_16, all_0_1_1) % 8.30/2.54 | % 8.30/2.54 | Instantiating formula (31) with all_0_1_1, all_0_5_5, all_0_2_2, all_0_16_16 and discharging atoms u(all_0_2_2, all_0_5_5) = all_0_1_1, mem(all_0_16_16, all_0_1_1), yields: % 8.30/2.54 | (141) mem(all_0_16_16, all_0_2_2) | mem(all_0_16_16, all_0_5_5) % 8.30/2.54 | % 8.30/2.54 +-Applying beta-rule and splitting (141), into two cases. % 8.30/2.54 |-Branch one: % 8.30/2.54 | (142) mem(all_0_16_16, all_0_2_2) % 8.30/2.54 | % 8.30/2.54 | Instantiating formula (2) with all_0_2_2, all_0_11_11, all_0_16_16 and discharging atoms s(all_0_11_11) = all_0_2_2, mem(all_0_16_16, all_0_2_2), yields: % 8.30/2.54 | (143) all_0_11_11 = all_0_16_16 % 8.30/2.54 | % 8.30/2.54 | From (143)(143) and (76) follows: % 8.30/2.55 | (144) a(all_0_16_16, all_0_16_16) = all_0_6_6 % 8.30/2.55 | % 8.30/2.55 | From (143) and (78) follows: % 8.30/2.55 | (145) a(all_0_16_16, all_0_16_16) = all_0_16_16 % 8.30/2.55 | % 8.30/2.55 | From (143) and (125) follows: % 8.30/2.55 | (146) u(all_0_16_16, all_0_2_2) = all_0_6_6 % 8.30/2.55 | % 8.30/2.55 | From (143) and (109) follows: % 8.30/2.55 | (147) mem(all_0_16_16, all_0_10_10) % 8.30/2.55 | % 8.30/2.55 | Instantiating formula (16) with all_0_16_16, all_0_16_16, all_0_16_16, all_0_6_6 and discharging atoms a(all_0_16_16, all_0_16_16) = all_0_6_6, a(all_0_16_16, all_0_16_16) = all_0_16_16, yields: % 8.30/2.55 | (148) all_0_6_6 = all_0_16_16 % 8.30/2.55 | % 8.30/2.55 | Instantiating formula (4) with all_0_16_16, all_0_2_2, all_0_6_6, all_0_10_10 and discharging atoms u(all_0_16_16, all_0_2_2) = all_0_6_6, u(all_0_16_16, all_0_2_2) = all_0_10_10, yields: % 8.30/2.55 | (149) all_0_6_6 = all_0_10_10 % 8.30/2.55 | % 8.30/2.55 | Combining equations (148,149) yields a new equation: % 8.30/2.55 | (150) all_0_10_10 = all_0_16_16 % 8.30/2.55 | % 8.30/2.55 | From (150) and (147) follows: % 8.30/2.55 | (151) mem(all_0_16_16, all_0_16_16) % 8.30/2.55 | % 8.30/2.55 | From (150) and (136) follows: % 8.30/2.55 | (134) mem(e, all_0_16_16) % 8.30/2.55 | % 8.30/2.55 | Instantiating formula (31) with all_0_16_16, all_33_0_27, e, all_0_16_16 and discharging atoms u(e, all_33_0_27) = all_0_16_16, mem(all_0_16_16, all_0_16_16), yields: % 8.30/2.55 | (153) mem(all_0_16_16, all_33_0_27) | mem(all_0_16_16, e) % 8.30/2.55 | % 8.30/2.55 +-Applying beta-rule and splitting (153), into two cases. % 8.30/2.55 |-Branch one: % 8.30/2.55 | (154) mem(all_0_16_16, e) % 8.30/2.55 | % 8.30/2.55 | Instantiating formula (72) with all_0_16_16 and discharging atoms mem(all_0_16_16, e), yields: % 8.30/2.55 | (155) $false % 8.30/2.55 | % 8.30/2.55 |-The branch is then unsatisfiable % 8.30/2.55 |-Branch two: % 8.30/2.55 | (156) ~ mem(all_0_16_16, e) % 8.30/2.55 | (157) mem(all_0_16_16, all_33_0_27) % 8.30/2.55 | % 8.30/2.55 | Instantiating formula (2) with all_33_0_27, e, all_0_16_16 and discharging atoms s(e) = all_33_0_27, mem(all_0_16_16, all_33_0_27), yields: % 8.30/2.55 | (158) all_0_16_16 = e % 8.30/2.55 | % 8.30/2.55 | From (158) and (134) follows: % 8.30/2.55 | (159) mem(e, e) % 8.30/2.55 | % 8.30/2.55 | From (158) and (156) follows: % 8.30/2.55 | (160) ~ mem(e, e) % 8.30/2.55 | % 8.30/2.55 | Using (159) and (160) yields: % 8.30/2.55 | (155) $false % 8.30/2.55 | % 8.30/2.55 |-The branch is then unsatisfiable % 8.30/2.55 |-Branch two: % 8.30/2.55 | (162) ~ mem(all_0_16_16, all_0_2_2) % 8.30/2.55 | (163) mem(all_0_16_16, all_0_5_5) % 8.30/2.55 | % 8.30/2.55 | Instantiating formula (31) with all_0_5_5, all_17_0_24, all_0_7_7, all_0_16_16 and discharging atoms u(all_0_7_7, all_17_0_24) = all_0_5_5, mem(all_0_16_16, all_0_5_5), yields: % 8.30/2.55 | (164) mem(all_0_16_16, all_17_0_24) | mem(all_0_16_16, all_0_7_7) % 8.30/2.55 | % 8.30/2.55 +-Applying beta-rule and splitting (164), into two cases. % 8.30/2.55 |-Branch one: % 8.30/2.55 | (165) mem(all_0_16_16, all_17_0_24) % 8.30/2.55 | % 8.30/2.55 | Instantiating formula (2) with all_17_0_24, all_0_6_6, all_0_16_16 and discharging atoms s(all_0_6_6) = all_17_0_24, mem(all_0_16_16, all_17_0_24), yields: % 8.30/2.55 | (148) all_0_6_6 = all_0_16_16 % 8.30/2.55 | % 8.30/2.55 | From (148) and (128) follows: % 8.30/2.55 | (167) mem(all_0_11_11, all_0_16_16) % 8.30/2.55 | % 8.30/2.55 | Instantiating formula (31) with all_0_16_16, all_33_0_27, e, all_0_11_11 and discharging atoms u(e, all_33_0_27) = all_0_16_16, mem(all_0_11_11, all_0_16_16), yields: % 8.30/2.55 | (168) mem(all_0_11_11, all_33_0_27) | mem(all_0_11_11, e) % 8.30/2.55 | % 8.30/2.55 +-Applying beta-rule and splitting (168), into two cases. % 8.30/2.55 |-Branch one: % 8.30/2.55 | (169) mem(all_0_11_11, e) % 8.30/2.55 | % 8.30/2.55 | Instantiating formula (72) with all_0_11_11 and discharging atoms mem(all_0_11_11, e), yields: % 8.30/2.55 | (155) $false % 8.30/2.55 | % 8.30/2.55 |-The branch is then unsatisfiable % 8.30/2.55 |-Branch two: % 8.30/2.55 | (171) ~ mem(all_0_11_11, e) % 8.30/2.55 | (172) mem(all_0_11_11, all_33_0_27) % 8.30/2.55 | % 8.30/2.55 | Instantiating formula (2) with all_33_0_27, e, all_0_11_11 and discharging atoms s(e) = all_33_0_27, mem(all_0_11_11, all_33_0_27), yields: % 8.30/2.55 | (173) all_0_11_11 = e % 8.30/2.55 | % 8.30/2.55 | From (173) and (138) follows: % 8.30/2.55 | (159) mem(e, e) % 8.30/2.55 | % 8.30/2.55 | From (173) and (171) follows: % 8.30/2.55 | (160) ~ mem(e, e) % 8.30/2.55 | % 8.30/2.55 | Using (159) and (160) yields: % 8.30/2.55 | (155) $false % 8.30/2.55 | % 8.30/2.55 |-The branch is then unsatisfiable % 8.30/2.55 |-Branch two: % 8.30/2.55 | (177) ~ mem(all_0_16_16, all_17_0_24) % 8.30/2.55 | (178) mem(all_0_16_16, all_0_7_7) % 8.30/2.55 | % 8.30/2.55 | Instantiating formula (2) with all_0_7_7, all_0_14_14, all_0_16_16 and discharging atoms s(all_0_14_14) = all_0_7_7, mem(all_0_16_16, all_0_7_7), yields: % 8.30/2.55 | (179) all_0_14_14 = all_0_16_16 % 8.30/2.55 | % 8.30/2.55 | From (179) and (129) follows: % 8.30/2.55 | (151) mem(all_0_16_16, all_0_16_16) % 8.30/2.55 | % 8.30/2.55 | Instantiating formula (31) with all_0_16_16, all_33_0_27, e, all_0_16_16 and discharging atoms u(e, all_33_0_27) = all_0_16_16, mem(all_0_16_16, all_0_16_16), yields: % 8.30/2.55 | (153) mem(all_0_16_16, all_33_0_27) | mem(all_0_16_16, e) % 8.30/2.55 | % 8.30/2.55 +-Applying beta-rule and splitting (153), into two cases. % 8.30/2.55 |-Branch one: % 8.30/2.55 | (154) mem(all_0_16_16, e) % 8.30/2.55 | % 8.30/2.55 | Instantiating formula (72) with all_0_16_16 and discharging atoms mem(all_0_16_16, e), yields: % 8.30/2.55 | (155) $false % 8.30/2.55 | % 8.30/2.55 |-The branch is then unsatisfiable % 8.30/2.55 |-Branch two: % 8.30/2.55 | (156) ~ mem(all_0_16_16, e) % 8.30/2.55 | (157) mem(all_0_16_16, all_33_0_27) % 8.30/2.55 | % 8.30/2.55 | Instantiating formula (2) with all_33_0_27, e, all_0_16_16 and discharging atoms s(e) = all_33_0_27, mem(all_0_16_16, all_33_0_27), yields: % 8.30/2.56 | (158) all_0_16_16 = e % 8.30/2.56 | % 8.30/2.56 | From (158) and (134) follows: % 8.30/2.56 | (159) mem(e, e) % 8.30/2.56 | % 8.30/2.56 | From (158) and (156) follows: % 8.30/2.56 | (160) ~ mem(e, e) % 8.30/2.56 | % 8.30/2.56 | Using (159) and (160) yields: % 8.30/2.56 | (155) $false % 8.30/2.56 | % 8.30/2.56 |-The branch is then unsatisfiable % 8.30/2.56 |-Branch two: % 8.30/2.56 | (190) ~ mem(all_0_16_16, all_0_1_1) % 8.30/2.56 | (191) mem(all_0_16_16, all_0_9_9) % 8.30/2.56 | % 8.30/2.56 | Instantiating formula (31) with all_0_9_9, all_11_0_21, all_0_12_12, all_0_16_16 and discharging atoms u(all_0_12_12, all_11_0_21) = all_0_9_9, mem(all_0_16_16, all_0_9_9), yields: % 8.30/2.56 | (192) mem(all_0_16_16, all_11_0_21) | mem(all_0_16_16, all_0_12_12) % 8.30/2.56 | % 8.30/2.56 +-Applying beta-rule and splitting (192), into two cases. % 8.30/2.56 |-Branch one: % 8.30/2.56 | (193) mem(all_0_16_16, all_11_0_21) % 8.30/2.56 | % 8.30/2.56 | Instantiating formula (2) with all_11_0_21, all_0_10_10, all_0_16_16 and discharging atoms s(all_0_10_10) = all_11_0_21, mem(all_0_16_16, all_11_0_21), yields: % 8.30/2.56 | (150) all_0_10_10 = all_0_16_16 % 8.30/2.56 | % 8.30/2.56 | From (150) and (109) follows: % 8.30/2.56 | (167) mem(all_0_11_11, all_0_16_16) % 8.30/2.56 | % 8.30/2.56 | Instantiating formula (31) with all_0_16_16, all_33_0_27, e, all_0_11_11 and discharging atoms u(e, all_33_0_27) = all_0_16_16, mem(all_0_11_11, all_0_16_16), yields: % 8.30/2.56 | (168) mem(all_0_11_11, all_33_0_27) | mem(all_0_11_11, e) % 8.30/2.56 | % 8.30/2.56 +-Applying beta-rule and splitting (168), into two cases. % 8.30/2.56 |-Branch one: % 8.30/2.56 | (169) mem(all_0_11_11, e) % 8.30/2.56 | % 8.30/2.56 | Instantiating formula (72) with all_0_11_11 and discharging atoms mem(all_0_11_11, e), yields: % 8.30/2.56 | (155) $false % 8.30/2.56 | % 8.30/2.56 |-The branch is then unsatisfiable % 8.30/2.56 |-Branch two: % 8.30/2.56 | (171) ~ mem(all_0_11_11, e) % 8.30/2.56 | (172) mem(all_0_11_11, all_33_0_27) % 8.30/2.56 | % 8.30/2.56 | Instantiating formula (2) with all_33_0_27, e, all_0_11_11 and discharging atoms s(e) = all_33_0_27, mem(all_0_11_11, all_33_0_27), yields: % 8.30/2.56 | (173) all_0_11_11 = e % 8.30/2.56 | % 8.30/2.56 | From (173) and (138) follows: % 8.30/2.56 | (159) mem(e, e) % 8.30/2.56 | % 8.30/2.56 | From (173) and (171) follows: % 8.30/2.56 | (160) ~ mem(e, e) % 8.30/2.56 | % 8.30/2.56 | Using (159) and (160) yields: % 8.30/2.56 | (155) $false % 8.30/2.56 | % 8.30/2.56 |-The branch is then unsatisfiable % 8.30/2.56 |-Branch two: % 8.30/2.56 | (205) ~ mem(all_0_16_16, all_11_0_21) % 8.30/2.56 | (206) mem(all_0_16_16, all_0_12_12) % 8.30/2.56 | % 8.30/2.56 | Instantiating formula (2) with all_0_12_12, all_0_13_13, all_0_16_16 and discharging atoms s(all_0_13_13) = all_0_12_12, mem(all_0_16_16, all_0_12_12), yields: % 8.30/2.56 | (207) all_0_13_13 = all_0_16_16 % 8.30/2.56 | % 8.30/2.56 | From (207) and (133) follows: % 8.30/2.56 | (151) mem(all_0_16_16, all_0_16_16) % 8.30/2.56 | % 8.30/2.56 | From (207) and (137) follows: % 8.30/2.56 | (134) mem(e, all_0_16_16) % 8.30/2.56 | % 8.30/2.56 | Instantiating formula (31) with all_0_16_16, all_33_0_27, e, all_0_16_16 and discharging atoms u(e, all_33_0_27) = all_0_16_16, mem(all_0_16_16, all_0_16_16), yields: % 8.30/2.56 | (153) mem(all_0_16_16, all_33_0_27) | mem(all_0_16_16, e) % 8.30/2.56 | % 8.30/2.56 +-Applying beta-rule and splitting (153), into two cases. % 8.30/2.56 |-Branch one: % 8.30/2.56 | (154) mem(all_0_16_16, e) % 8.30/2.56 | % 8.30/2.56 | Instantiating formula (72) with all_0_16_16 and discharging atoms mem(all_0_16_16, e), yields: % 8.30/2.56 | (155) $false % 8.30/2.56 | % 8.30/2.56 |-The branch is then unsatisfiable % 8.30/2.56 |-Branch two: % 8.30/2.56 | (156) ~ mem(all_0_16_16, e) % 8.30/2.56 | (157) mem(all_0_16_16, all_33_0_27) % 8.30/2.56 | % 8.30/2.56 | Instantiating formula (2) with all_33_0_27, e, all_0_16_16 and discharging atoms s(e) = all_33_0_27, mem(all_0_16_16, all_33_0_27), yields: % 8.30/2.56 | (158) all_0_16_16 = e % 8.30/2.56 | % 8.30/2.56 | From (158) and (134) follows: % 8.30/2.56 | (159) mem(e, e) % 8.30/2.56 | % 8.30/2.56 | From (158) and (156) follows: % 8.30/2.56 | (160) ~ mem(e, e) % 8.30/2.56 | % 8.30/2.56 | Using (159) and (160) yields: % 8.30/2.56 | (155) $false % 8.30/2.56 | % 8.30/2.56 |-The branch is then unsatisfiable % 8.30/2.56 % SZS output end Proof for theBenchmark % 8.30/2.56 % 8.30/2.56 1966ms %------------------------------------------------------------------------------