%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEV571+1 : TPTP v9.1.0. Released v9.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n028.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 5.14s 1.82s % Output : Proof 7.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : SEV571+1 : TPTP v9.1.0. Released v9.1.0. % 0.13/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.36 % Computer : n028.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Mon Mar 31 12:46:34 EDT 2025 % 0.14/0.36 % CPUTime : % 0.54/0.61 ____ _ % 0.54/0.61 ___ / __ \_____(_)___ ________ __________ % 0.54/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.54/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.54/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.54/0.62 % 0.54/0.62 A Theorem Prover for First-Order Logic % 0.54/0.62 (ePrincess v.1.0) % 0.54/0.62 % 0.54/0.62 (c) Philipp Rümmer, 2009-2015 % 0.54/0.62 (c) Peter Backeman, 2014-2015 % 0.54/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.54/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.54/0.62 Bug reports to peter@backeman.se % 0.54/0.62 % 0.54/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.54/0.62 % 0.54/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.72/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.68/0.99 Prover 0: Preprocessing ... % 2.58/1.26 Prover 0: Warning: ignoring some quantifiers % 2.58/1.28 Prover 0: Constructing countermodel ... % 5.07/1.82 Prover 0: proved (1147ms) % 5.14/1.82 % 5.14/1.82 No countermodel exists, formula is valid % 5.14/1.82 % SZS status Theorem for theBenchmark % 5.14/1.82 % 5.14/1.82 Generating proof ... Warning: ignoring some quantifiers % 6.96/2.26 found it (size 112) % 6.96/2.26 % 6.96/2.26 % SZS output start Proof for theBenchmark % 6.96/2.26 Assumed formulas after preprocessing and simplification: % 6.96/2.26 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (n(v7) = v8 & n(v6) = v12 & n(v1) = v2 & n(v0) = v6 & n(e) = v0 & a(v11, v12) = v13 & u(v10, v15) = v16 & u(v10, v13) = v14 & u(v5, v8) = v9 & u(v4, v9) = v10 & u(v0, v2) = v3 & s(v12) = v15 & s(v6) = v7 & s(v3) = v4 & s(v2) = v5 & s(v1) = v11 & s(v0) = v1 & subq(v14, 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)))) % 7.34/2.32 | 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: % 7.34/2.32 | (1) n(all_0_9_9) = all_0_8_8 & n(all_0_10_10) = all_0_4_4 & n(all_0_15_15) = all_0_14_14 & n(all_0_16_16) = all_0_10_10 & n(e) = all_0_16_16 & a(all_0_5_5, all_0_4_4) = all_0_3_3 & u(all_0_6_6, all_0_1_1) = all_0_0_0 & u(all_0_6_6, all_0_3_3) = all_0_2_2 & u(all_0_11_11, all_0_8_8) = all_0_7_7 & u(all_0_12_12, all_0_7_7) = all_0_6_6 & u(all_0_16_16, all_0_14_14) = all_0_13_13 & s(all_0_4_4) = all_0_1_1 & s(all_0_10_10) = all_0_9_9 & s(all_0_13_13) = all_0_12_12 & s(all_0_14_14) = all_0_11_11 & s(all_0_15_15) = all_0_5_5 & s(all_0_16_16) = all_0_15_15 & subq(all_0_2_2, 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))) % 7.34/2.33 | % 7.34/2.33 | Applying alpha-rule on (1) yields: % 7.34/2.33 | (2) n(all_0_10_10) = all_0_4_4 % 7.34/2.33 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (m(v1, v2) = v3) | ~ mem(v0, v1) | mem(v0, v3) | mem(v0, v2)) % 7.34/2.33 | (4) s(all_0_13_13) = all_0_12_12 % 7.34/2.33 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u(v0, v2) = v3) | ~ (s(v1) = v2) | a(v0, v1) = v3) % 7.34/2.33 | (6) u(all_0_6_6, all_0_3_3) = all_0_2_2 % 7.34/2.33 | (7) u(all_0_16_16, all_0_14_14) = all_0_13_13 % 7.34/2.33 | (8) ! [v0] : ! [v1] : ( ~ atleast13p(v1) | ~ subq(v1, v0) | atleast14p(v0) | subq(v0, v1)) % 7.34/2.33 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (u(v3, v2) = v1) | ~ (u(v3, v2) = v0)) % 7.34/2.33 | (10) n(all_0_16_16) = all_0_10_10 % 7.34/2.33 | (11) ! [v0] : ( ~ atleast8p(v0) | ? [v1] : (atleast7p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.34/2.33 | (12) s(all_0_10_10) = all_0_9_9 % 7.34/2.33 | (13) ! [v0] : ( ~ atleast5p(v0) | ? [v1] : (atleast4p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.34/2.34 | (14) ! [v0] : ! [v1] : ( ~ atleast5p(v1) | ~ subq(v1, v0) | atleast6p(v0) | subq(v0, v1)) % 7.34/2.34 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u(v1, v2) = v3) | ~ mem(v0, v2) | mem(v0, v3)) % 7.34/2.34 | (16) ! [v0] : ! [v1] : ( ~ atleast15p(v1) | ~ subq(v1, v0) | atleast16p(v0) | subq(v0, v1)) % 7.34/2.34 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (a(v0, v1) = v2) | ? [v3] : (u(v0, v3) = v2 & s(v1) = v3)) % 7.34/2.34 | (18) ! [v0] : ( ~ atleast4p(v0) | ? [v1] : (atleast3p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.34/2.34 | (19) ! [v0] : ! [v1] : ( ~ (a(v0, v0) = v1) | n(v0) = v1) % 7.34/2.34 | (20) ! [v0] : ! [v1] : ( ~ (n(v0) = v1) | a(v0, v0) = v1) % 7.34/2.34 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (a(v3, v2) = v1) | ~ (a(v3, v2) = v0)) % 7.34/2.34 | (22) ! [v0] : ! [v1] : ( ~ atleast10p(v1) | ~ subq(v1, v0) | atleast11p(v0) | subq(v0, v1)) % 7.34/2.34 | (23) ! [v0] : ( ~ atleast10p(v0) | ? [v1] : (atleast9p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.34/2.34 | (24) ! [v0] : ! [v1] : ( ~ atleast12p(v1) | ~ subq(v1, v0) | atleast13p(v0) | subq(v0, v1)) % 7.34/2.34 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u(v1, v2) = v3) | ~ mem(v0, v3) | mem(v0, v2) | mem(v0, v1)) % 7.34/2.34 | (26) ! [v0] : ! [v1] : ( ~ atleast4p(v1) | ~ subq(v1, v0) | atleast5p(v0) | subq(v0, v1)) % 7.34/2.34 | (27) ! [v0] : ! [v1] : ( ~ atleast11p(v1) | ~ subq(v1, v0) | atleast12p(v0) | subq(v0, v1)) % 7.34/2.34 | (28) ! [v0] : ( ~ atleast3p(v0) | ? [v1] : (atleast2p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.34/2.34 | (29) a(all_0_5_5, all_0_4_4) = all_0_3_3 % 7.34/2.34 | (30) ! [v0] : ! [v1] : (v1 = v0 | ~ subq(v1, v0) | ~ subq(v0, v1)) % 7.34/2.34 | (31) s(all_0_16_16) = all_0_15_15 % 7.34/2.34 | (32) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) % 7.34/2.34 | (33) ! [v0] : ( ~ atleast12p(v0) | ? [v1] : (atleast11p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.34/2.34 | (34) ! [v0] : ( ~ atleast14p(v0) | ? [v1] : (atleast13p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.34/2.34 | (35) ! [v0] : ~ mem(v0, e) % 7.34/2.34 | (36) ! [v0] : ! [v1] : ( ~ atleast14p(v1) | ~ subq(v1, v0) | atleast15p(v0) | subq(v0, v1)) % 7.34/2.34 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (p(v1) = v2) | ~ subq(v0, v1) | mem(v0, v2)) % 7.34/2.34 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (p(v1) = v2) | ~ mem(v0, v2) | subq(v0, v1)) % 7.34/2.34 | (39) ! [v0] : ! [v1] : ( ~ atleast8p(v1) | ~ subq(v1, v0) | atleast9p(v0) | subq(v0, v1)) % 7.34/2.34 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (m(v3, v2) = v1) | ~ (m(v3, v2) = v0)) % 7.34/2.34 | (41) ? [v0] : ? [v1] : (subq(v0, v1) | ? [v2] : (mem(v2, v0) & ~ mem(v2, v1))) % 7.34/2.34 | (42) ! [v0] : ( ~ atleast2p(v0) | ? [v1] : ? [v2] : (p(v1) = v2 & mem(v1, v0) & ~ subq(v0, v2))) % 7.34/2.34 | (43) ! [v0] : ! [v1] : ( ~ (s(v0) = v1) | mem(v0, v1)) % 7.34/2.34 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u(v1, v2) = v3) | ~ mem(v0, v1) | mem(v0, v3)) % 7.34/2.34 | (45) ! [v0] : ( ~ atleast16p(v0) | ? [v1] : (atleast15p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.34/2.35 | (46) s(all_0_15_15) = all_0_5_5 % 7.34/2.35 | (47) ! [v0] : ( ~ atleast6p(v0) | ? [v1] : (atleast5p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.34/2.35 | (48) ! [v0] : ! [v1] : ( ~ atleast9p(v1) | ~ subq(v1, v0) | atleast10p(v0) | subq(v0, v1)) % 7.34/2.35 | (49) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (s(v1) = v2) | ~ mem(v0, v2)) % 7.34/2.35 | (50) n(e) = all_0_16_16 % 7.34/2.35 | (51) ! [v0] : ( ~ atleast15p(v0) | ? [v1] : (atleast14p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.34/2.35 | (52) s(all_0_14_14) = all_0_11_11 % 7.34/2.35 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (s(v2) = v1) | ~ (s(v2) = v0)) % 7.34/2.35 | (54) n(all_0_9_9) = all_0_8_8 % 7.34/2.35 | (55) ! [v0] : ! [v1] : ( ~ atleast3p(v1) | ~ subq(v1, v0) | atleast4p(v0) | subq(v0, v1)) % 7.34/2.35 | (56) ! [v0] : ( ~ atleast9p(v0) | ? [v1] : (atleast8p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.34/2.35 | (57) ! [v0] : ( ~ atleast7p(v0) | ? [v1] : (atleast6p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.34/2.35 | (58) u(all_0_11_11, all_0_8_8) = all_0_7_7 % 7.34/2.35 | (59) ! [v0] : ( ~ atleast13p(v0) | ? [v1] : (atleast12p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.34/2.35 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (m(v1, v2) = v3) | ~ mem(v0, v3) | ~ mem(v0, v2)) % 7.34/2.35 | (61) subq(all_0_2_2, all_0_0_0) % 7.34/2.35 | (62) s(all_0_4_4) = all_0_1_1 % 7.34/2.35 | (63) ! [v0] : ! [v1] : ( ~ atleast6p(v1) | ~ subq(v1, v0) | atleast7p(v0) | subq(v0, v1)) % 7.34/2.35 | (64) u(all_0_12_12, all_0_7_7) = all_0_6_6 % 7.34/2.35 | (65) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (n(v2) = v1) | ~ (n(v2) = v0)) % 7.34/2.35 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (p(v1) = v2) | ~ mem(v1, v0) | atleast2p(v0) | subq(v0, v2)) % 7.34/2.35 | (67) ? [v0] : ? [v1] : (disj(v0, v1) | ? [v2] : (mem(v2, v1) & mem(v2, v0))) % 7.34/2.35 | (68) ! [v0] : ( ~ atleast11p(v0) | ? [v1] : (atleast10p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.34/2.35 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ disj(v0, v1) | ~ mem(v2, v1) | ~ mem(v2, v0)) % 7.34/2.35 | (70) u(all_0_6_6, all_0_1_1) = all_0_0_0 % 7.34/2.35 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (m(v1, v2) = v3) | ~ mem(v0, v3) | mem(v0, v1)) % 7.34/2.35 | (72) ! [v0] : ! [v1] : ( ~ atleast7p(v1) | ~ subq(v1, v0) | atleast8p(v0) | subq(v0, v1)) % 7.34/2.35 | (73) n(all_0_15_15) = all_0_14_14 % 7.34/2.35 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ mem(v2, v0) | ~ subq(v0, v1) | mem(v2, v1)) % 7.34/2.35 | (75) ! [v0] : ! [v1] : ( ~ atleast2p(v1) | ~ subq(v1, v0) | atleast3p(v0) | subq(v0, v1)) % 7.34/2.35 | % 7.34/2.35 | Instantiating formula (20) with all_0_8_8, all_0_9_9 and discharging atoms n(all_0_9_9) = all_0_8_8, yields: % 7.34/2.35 | (76) a(all_0_9_9, all_0_9_9) = all_0_8_8 % 7.34/2.35 | % 7.34/2.35 | Instantiating formula (20) with all_0_4_4, all_0_10_10 and discharging atoms n(all_0_10_10) = all_0_4_4, yields: % 7.34/2.35 | (77) a(all_0_10_10, all_0_10_10) = all_0_4_4 % 7.34/2.35 | % 7.34/2.35 | Instantiating formula (20) with all_0_14_14, all_0_15_15 and discharging atoms n(all_0_15_15) = all_0_14_14, yields: % 7.34/2.36 | (78) a(all_0_15_15, all_0_15_15) = all_0_14_14 % 7.34/2.36 | % 7.34/2.36 | Instantiating formula (20) with all_0_10_10, all_0_16_16 and discharging atoms n(all_0_16_16) = all_0_10_10, yields: % 7.34/2.36 | (79) a(all_0_16_16, all_0_16_16) = all_0_10_10 % 7.34/2.36 | % 7.34/2.36 | Instantiating formula (20) with all_0_16_16, e and discharging atoms n(e) = all_0_16_16, yields: % 7.34/2.36 | (80) a(e, e) = all_0_16_16 % 7.34/2.36 | % 7.34/2.36 | Instantiating formula (17) with all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms a(all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 7.34/2.36 | (81) ? [v0] : (u(all_0_5_5, v0) = all_0_3_3 & s(all_0_4_4) = v0) % 7.34/2.36 | % 7.34/2.36 | Instantiating formula (43) with all_0_9_9, all_0_10_10 and discharging atoms s(all_0_10_10) = all_0_9_9, yields: % 7.34/2.36 | (82) mem(all_0_10_10, all_0_9_9) % 7.34/2.36 | % 7.34/2.36 | Instantiating formula (43) with all_0_5_5, all_0_15_15 and discharging atoms s(all_0_15_15) = all_0_5_5, yields: % 7.34/2.36 | (83) mem(all_0_15_15, all_0_5_5) % 7.34/2.36 | % 7.34/2.36 | Instantiating (81) with all_11_0_21 yields: % 7.34/2.36 | (84) u(all_0_5_5, all_11_0_21) = all_0_3_3 & s(all_0_4_4) = all_11_0_21 % 7.34/2.36 | % 7.34/2.36 | Applying alpha-rule on (84) yields: % 7.34/2.36 | (85) u(all_0_5_5, all_11_0_21) = all_0_3_3 % 7.34/2.36 | (86) s(all_0_4_4) = all_11_0_21 % 7.34/2.36 | % 7.34/2.36 | Instantiating formula (53) with all_0_4_4, all_11_0_21, all_0_1_1 and discharging atoms s(all_0_4_4) = all_11_0_21, s(all_0_4_4) = all_0_1_1, yields: % 7.34/2.36 | (87) all_11_0_21 = all_0_1_1 % 7.34/2.36 | % 7.34/2.36 | From (87) and (85) follows: % 7.34/2.36 | (88) u(all_0_5_5, all_0_1_1) = all_0_3_3 % 7.34/2.36 | % 7.34/2.36 | From (87) and (86) follows: % 7.34/2.36 | (62) s(all_0_4_4) = all_0_1_1 % 7.34/2.36 | % 7.34/2.36 | Instantiating formula (17) with all_0_8_8, all_0_9_9, all_0_9_9 and discharging atoms a(all_0_9_9, all_0_9_9) = all_0_8_8, yields: % 7.34/2.36 | (90) ? [v0] : (u(all_0_9_9, v0) = all_0_8_8 & s(all_0_9_9) = v0) % 7.34/2.36 | % 7.34/2.36 | Instantiating formula (17) with all_0_4_4, all_0_10_10, all_0_10_10 and discharging atoms a(all_0_10_10, all_0_10_10) = all_0_4_4, yields: % 7.34/2.36 | (91) ? [v0] : (u(all_0_10_10, v0) = all_0_4_4 & s(all_0_10_10) = v0) % 7.34/2.36 | % 7.34/2.36 | Instantiating formula (17) 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: % 7.34/2.36 | (92) ? [v0] : (u(all_0_15_15, v0) = all_0_14_14 & s(all_0_15_15) = v0) % 7.34/2.36 | % 7.34/2.36 | Instantiating formula (17) with all_0_10_10, all_0_16_16, all_0_16_16 and discharging atoms a(all_0_16_16, all_0_16_16) = all_0_10_10, yields: % 7.34/2.36 | (93) ? [v0] : (u(all_0_16_16, v0) = all_0_10_10 & s(all_0_16_16) = v0) % 7.34/2.36 | % 7.34/2.36 | Instantiating formula (17) with all_0_16_16, e, e and discharging atoms a(e, e) = all_0_16_16, yields: % 7.34/2.36 | (94) ? [v0] : (u(e, v0) = all_0_16_16 & s(e) = v0) % 7.34/2.36 | % 7.34/2.36 | Instantiating formula (44) with all_0_3_3, all_0_1_1, all_0_5_5, all_0_15_15 and discharging atoms u(all_0_5_5, all_0_1_1) = all_0_3_3, mem(all_0_15_15, all_0_5_5), yields: % 7.34/2.36 | (95) mem(all_0_15_15, all_0_3_3) % 7.34/2.36 | % 7.34/2.36 | Instantiating (93) with all_23_0_22 yields: % 7.34/2.36 | (96) u(all_0_16_16, all_23_0_22) = all_0_10_10 & s(all_0_16_16) = all_23_0_22 % 7.34/2.36 | % 7.34/2.36 | Applying alpha-rule on (96) yields: % 7.34/2.36 | (97) u(all_0_16_16, all_23_0_22) = all_0_10_10 % 7.34/2.36 | (98) s(all_0_16_16) = all_23_0_22 % 7.34/2.36 | % 7.34/2.36 | Instantiating (92) with all_25_0_23 yields: % 7.34/2.36 | (99) u(all_0_15_15, all_25_0_23) = all_0_14_14 & s(all_0_15_15) = all_25_0_23 % 7.34/2.36 | % 7.34/2.36 | Applying alpha-rule on (99) yields: % 7.34/2.36 | (100) u(all_0_15_15, all_25_0_23) = all_0_14_14 % 7.34/2.36 | (101) s(all_0_15_15) = all_25_0_23 % 7.34/2.36 | % 7.34/2.36 | Instantiating (94) with all_27_0_24 yields: % 7.34/2.36 | (102) u(e, all_27_0_24) = all_0_16_16 & s(e) = all_27_0_24 % 7.34/2.36 | % 7.34/2.36 | Applying alpha-rule on (102) yields: % 7.34/2.36 | (103) u(e, all_27_0_24) = all_0_16_16 % 7.34/2.36 | (104) s(e) = all_27_0_24 % 7.34/2.36 | % 7.34/2.37 | Instantiating (91) with all_29_0_25 yields: % 7.34/2.37 | (105) u(all_0_10_10, all_29_0_25) = all_0_4_4 & s(all_0_10_10) = all_29_0_25 % 7.34/2.37 | % 7.34/2.37 | Applying alpha-rule on (105) yields: % 7.34/2.37 | (106) u(all_0_10_10, all_29_0_25) = all_0_4_4 % 7.34/2.37 | (107) s(all_0_10_10) = all_29_0_25 % 7.34/2.37 | % 7.34/2.37 | Instantiating (90) with all_31_0_26 yields: % 7.34/2.37 | (108) u(all_0_9_9, all_31_0_26) = all_0_8_8 & s(all_0_9_9) = all_31_0_26 % 7.34/2.37 | % 7.34/2.37 | Applying alpha-rule on (108) yields: % 7.34/2.37 | (109) u(all_0_9_9, all_31_0_26) = all_0_8_8 % 7.34/2.37 | (110) s(all_0_9_9) = all_31_0_26 % 7.34/2.37 | % 7.34/2.37 | Instantiating formula (53) with all_0_10_10, all_29_0_25, all_0_9_9 and discharging atoms s(all_0_10_10) = all_29_0_25, s(all_0_10_10) = all_0_9_9, yields: % 7.34/2.37 | (111) all_29_0_25 = all_0_9_9 % 7.34/2.37 | % 7.34/2.37 | Instantiating formula (53) with all_0_15_15, all_25_0_23, all_0_5_5 and discharging atoms s(all_0_15_15) = all_25_0_23, s(all_0_15_15) = all_0_5_5, yields: % 7.34/2.37 | (112) all_25_0_23 = all_0_5_5 % 7.34/2.37 | % 7.34/2.37 | Instantiating formula (53) with all_0_16_16, all_23_0_22, all_0_15_15 and discharging atoms s(all_0_16_16) = all_23_0_22, s(all_0_16_16) = all_0_15_15, yields: % 7.34/2.37 | (113) all_23_0_22 = all_0_15_15 % 7.34/2.37 | % 7.34/2.37 | From (111) and (106) follows: % 7.34/2.37 | (114) u(all_0_10_10, all_0_9_9) = all_0_4_4 % 7.34/2.37 | % 7.34/2.37 | From (112) and (100) follows: % 7.34/2.37 | (115) u(all_0_15_15, all_0_5_5) = all_0_14_14 % 7.34/2.37 | % 7.34/2.37 | From (113) and (97) follows: % 7.34/2.37 | (116) u(all_0_16_16, all_0_15_15) = all_0_10_10 % 7.34/2.37 | % 7.34/2.37 | From (111) and (107) follows: % 7.34/2.37 | (12) s(all_0_10_10) = all_0_9_9 % 7.34/2.37 | % 7.34/2.37 | From (113) and (98) follows: % 7.34/2.37 | (31) s(all_0_16_16) = all_0_15_15 % 7.34/2.37 | % 7.34/2.37 | Instantiating formula (44) with all_0_8_8, all_31_0_26, all_0_9_9, all_0_10_10 and discharging atoms u(all_0_9_9, all_31_0_26) = all_0_8_8, mem(all_0_10_10, all_0_9_9), yields: % 7.34/2.37 | (119) mem(all_0_10_10, all_0_8_8) % 7.34/2.37 | % 7.34/2.37 | Instantiating formula (15) with all_0_4_4, all_0_9_9, all_0_10_10, all_0_10_10 and discharging atoms u(all_0_10_10, all_0_9_9) = all_0_4_4, mem(all_0_10_10, all_0_9_9), yields: % 7.34/2.37 | (120) mem(all_0_10_10, all_0_4_4) % 7.34/2.37 | % 7.34/2.37 | Instantiating formula (15) with all_0_14_14, all_0_5_5, all_0_15_15, all_0_15_15 and discharging atoms u(all_0_15_15, all_0_5_5) = all_0_14_14, mem(all_0_15_15, all_0_5_5), yields: % 7.34/2.37 | (121) mem(all_0_15_15, all_0_14_14) % 7.34/2.37 | % 7.34/2.37 | Instantiating formula (43) with all_27_0_24, e and discharging atoms s(e) = all_27_0_24, yields: % 7.34/2.37 | (122) mem(e, all_27_0_24) % 7.34/2.37 | % 7.34/2.37 | Instantiating formula (15) with all_0_2_2, all_0_3_3, all_0_6_6, all_0_15_15 and discharging atoms u(all_0_6_6, all_0_3_3) = all_0_2_2, mem(all_0_15_15, all_0_3_3), yields: % 7.34/2.37 | (123) mem(all_0_15_15, all_0_2_2) % 7.34/2.37 | % 7.34/2.37 | Instantiating formula (74) with all_0_15_15, all_0_0_0, all_0_2_2 and discharging atoms mem(all_0_15_15, all_0_2_2), subq(all_0_2_2, all_0_0_0), yields: % 7.34/2.37 | (124) mem(all_0_15_15, all_0_0_0) % 7.34/2.37 | % 7.34/2.37 | Instantiating formula (15) with all_0_16_16, all_27_0_24, e, e and discharging atoms u(e, all_27_0_24) = all_0_16_16, mem(e, all_27_0_24), yields: % 7.34/2.37 | (125) mem(e, all_0_16_16) % 7.34/2.37 | % 7.34/2.37 | Instantiating formula (25) with all_0_0_0, all_0_1_1, all_0_6_6, all_0_15_15 and discharging atoms u(all_0_6_6, all_0_1_1) = all_0_0_0, mem(all_0_15_15, all_0_0_0), yields: % 7.34/2.37 | (126) mem(all_0_15_15, all_0_1_1) | mem(all_0_15_15, all_0_6_6) % 7.34/2.37 | % 7.34/2.37 | Instantiating formula (44) 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: % 7.34/2.37 | (127) mem(e, all_0_13_13) % 7.34/2.37 | % 7.34/2.37 | Instantiating formula (44) with all_0_10_10, all_0_15_15, all_0_16_16, e and discharging atoms u(all_0_16_16, all_0_15_15) = all_0_10_10, mem(e, all_0_16_16), yields: % 7.34/2.37 | (128) mem(e, all_0_10_10) % 7.34/2.37 | % 7.34/2.37 | Instantiating formula (44) with all_0_4_4, all_0_9_9, all_0_10_10, e and discharging atoms u(all_0_10_10, all_0_9_9) = all_0_4_4, mem(e, all_0_10_10), yields: % 7.34/2.37 | (129) mem(e, all_0_4_4) % 7.34/2.37 | % 7.34/2.37 +-Applying beta-rule and splitting (126), into two cases. % 7.34/2.37 |-Branch one: % 7.34/2.37 | (130) mem(all_0_15_15, all_0_1_1) % 7.34/2.37 | % 7.34/2.37 | Instantiating formula (49) with all_0_1_1, all_0_4_4, all_0_15_15 and discharging atoms s(all_0_4_4) = all_0_1_1, mem(all_0_15_15, all_0_1_1), yields: % 7.34/2.37 | (131) all_0_4_4 = all_0_15_15 % 7.34/2.37 | % 7.34/2.37 | From (131) and (129) follows: % 7.34/2.37 | (132) mem(e, all_0_15_15) % 7.34/2.37 | % 7.34/2.37 | Instantiating formula (49) with all_0_15_15, all_0_16_16, e and discharging atoms s(all_0_16_16) = all_0_15_15, mem(e, all_0_15_15), yields: % 7.34/2.37 | (133) all_0_16_16 = e % 7.34/2.38 | % 7.34/2.38 | From (133) and (125) follows: % 7.34/2.38 | (134) mem(e, e) % 7.34/2.38 | % 7.34/2.38 | Instantiating formula (35) with e and discharging atoms mem(e, e), yields: % 7.34/2.38 | (135) $false % 7.34/2.38 | % 7.34/2.38 |-The branch is then unsatisfiable % 7.34/2.38 |-Branch two: % 7.34/2.38 | (136) ~ mem(all_0_15_15, all_0_1_1) % 7.34/2.38 | (137) mem(all_0_15_15, all_0_6_6) % 7.34/2.38 | % 7.34/2.38 | Instantiating formula (25) with all_0_6_6, all_0_7_7, all_0_12_12, all_0_15_15 and discharging atoms u(all_0_12_12, all_0_7_7) = all_0_6_6, mem(all_0_15_15, all_0_6_6), yields: % 7.34/2.38 | (138) mem(all_0_15_15, all_0_7_7) | mem(all_0_15_15, all_0_12_12) % 7.34/2.38 | % 7.34/2.38 +-Applying beta-rule and splitting (138), into two cases. % 7.34/2.38 |-Branch one: % 7.34/2.38 | (139) mem(all_0_15_15, all_0_7_7) % 7.34/2.38 | % 7.34/2.38 | Instantiating formula (25) with all_0_7_7, all_0_8_8, all_0_11_11, all_0_15_15 and discharging atoms u(all_0_11_11, all_0_8_8) = all_0_7_7, mem(all_0_15_15, all_0_7_7), yields: % 7.34/2.38 | (140) mem(all_0_15_15, all_0_8_8) | mem(all_0_15_15, all_0_11_11) % 7.34/2.38 | % 7.34/2.38 +-Applying beta-rule and splitting (140), into two cases. % 7.34/2.38 |-Branch one: % 7.34/2.38 | (141) mem(all_0_15_15, all_0_8_8) % 7.34/2.38 | % 7.34/2.38 | Instantiating formula (25) with all_0_8_8, all_31_0_26, all_0_9_9, all_0_15_15 and discharging atoms u(all_0_9_9, all_31_0_26) = all_0_8_8, mem(all_0_15_15, all_0_8_8), yields: % 7.34/2.38 | (142) mem(all_0_15_15, all_31_0_26) | mem(all_0_15_15, all_0_9_9) % 7.34/2.38 | % 7.34/2.38 +-Applying beta-rule and splitting (142), into two cases. % 7.34/2.38 |-Branch one: % 7.34/2.38 | (143) mem(all_0_15_15, all_31_0_26) % 7.34/2.38 | % 7.34/2.38 | Instantiating formula (49) with all_31_0_26, all_0_9_9, all_0_15_15 and discharging atoms s(all_0_9_9) = all_31_0_26, mem(all_0_15_15, all_31_0_26), yields: % 7.34/2.38 | (144) all_0_9_9 = all_0_15_15 % 7.34/2.38 | % 7.34/2.38 | From (144) and (114) follows: % 7.34/2.38 | (145) u(all_0_10_10, all_0_15_15) = all_0_4_4 % 7.34/2.38 | % 7.34/2.38 | From (144) and (82) follows: % 7.34/2.38 | (146) mem(all_0_10_10, all_0_15_15) % 7.34/2.38 | % 7.34/2.38 | Instantiating formula (49) with all_0_15_15, all_0_16_16, all_0_10_10 and discharging atoms s(all_0_16_16) = all_0_15_15, mem(all_0_10_10, all_0_15_15), yields: % 7.34/2.38 | (147) all_0_10_10 = all_0_16_16 % 7.34/2.38 | % 7.34/2.38 | From (147) and (145) follows: % 7.34/2.38 | (148) u(all_0_16_16, all_0_15_15) = all_0_4_4 % 7.34/2.38 | % 7.34/2.38 | From (147) and (116) follows: % 7.34/2.38 | (149) u(all_0_16_16, all_0_15_15) = all_0_16_16 % 7.34/2.38 | % 7.34/2.38 | From (147) and (120) follows: % 7.34/2.38 | (150) mem(all_0_16_16, all_0_4_4) % 7.34/2.38 | % 7.34/2.38 | Instantiating formula (9) with all_0_16_16, all_0_15_15, all_0_16_16, all_0_4_4 and discharging atoms u(all_0_16_16, all_0_15_15) = all_0_4_4, u(all_0_16_16, all_0_15_15) = all_0_16_16, yields: % 7.34/2.38 | (151) all_0_4_4 = all_0_16_16 % 7.34/2.38 | % 7.34/2.38 | From (151) and (150) follows: % 7.34/2.38 | (152) mem(all_0_16_16, all_0_16_16) % 7.34/2.38 | % 7.34/2.38 | From (151) and (129) follows: % 7.34/2.38 | (125) mem(e, all_0_16_16) % 7.34/2.38 | % 7.34/2.38 | Instantiating formula (25) with all_0_16_16, all_27_0_24, e, all_0_16_16 and discharging atoms u(e, all_27_0_24) = all_0_16_16, mem(all_0_16_16, all_0_16_16), yields: % 7.34/2.38 | (154) mem(all_0_16_16, all_27_0_24) | mem(all_0_16_16, e) % 7.34/2.38 | % 7.34/2.38 +-Applying beta-rule and splitting (154), into two cases. % 7.34/2.38 |-Branch one: % 7.34/2.38 | (155) mem(all_0_16_16, e) % 7.34/2.38 | % 7.34/2.38 | Instantiating formula (35) with all_0_16_16 and discharging atoms mem(all_0_16_16, e), yields: % 7.34/2.38 | (135) $false % 7.34/2.38 | % 7.34/2.38 |-The branch is then unsatisfiable % 7.34/2.38 |-Branch two: % 7.34/2.38 | (157) ~ mem(all_0_16_16, e) % 7.34/2.38 | (158) mem(all_0_16_16, all_27_0_24) % 7.34/2.38 | % 7.34/2.38 | Instantiating formula (49) with all_27_0_24, e, all_0_16_16 and discharging atoms s(e) = all_27_0_24, mem(all_0_16_16, all_27_0_24), yields: % 7.34/2.38 | (133) all_0_16_16 = e % 7.34/2.38 | % 7.34/2.38 | From (133) and (125) follows: % 7.34/2.38 | (134) mem(e, e) % 7.34/2.38 | % 7.34/2.38 | From (133) and (157) follows: % 7.34/2.39 | (161) ~ mem(e, e) % 7.34/2.39 | % 7.34/2.39 | Using (134) and (161) yields: % 7.34/2.39 | (135) $false % 7.34/2.39 | % 7.34/2.39 |-The branch is then unsatisfiable % 7.34/2.39 |-Branch two: % 7.34/2.39 | (163) ~ mem(all_0_15_15, all_31_0_26) % 7.34/2.39 | (164) mem(all_0_15_15, all_0_9_9) % 7.34/2.39 | % 7.34/2.39 | Instantiating formula (49) with all_0_9_9, all_0_10_10, all_0_15_15 and discharging atoms s(all_0_10_10) = all_0_9_9, mem(all_0_15_15, all_0_9_9), yields: % 7.34/2.39 | (165) all_0_10_10 = all_0_15_15 % 7.34/2.39 | % 7.34/2.39 | From (165) and (128) follows: % 7.34/2.39 | (132) mem(e, all_0_15_15) % 7.34/2.39 | % 7.34/2.39 | Instantiating formula (49) with all_0_15_15, all_0_16_16, e and discharging atoms s(all_0_16_16) = all_0_15_15, mem(e, all_0_15_15), yields: % 7.34/2.39 | (133) all_0_16_16 = e % 7.34/2.39 | % 7.34/2.39 | From (133) and (125) follows: % 7.34/2.39 | (134) mem(e, e) % 7.34/2.39 | % 7.34/2.39 | Instantiating formula (35) with e and discharging atoms mem(e, e), yields: % 7.34/2.39 | (135) $false % 7.34/2.39 | % 7.34/2.39 |-The branch is then unsatisfiable % 7.34/2.39 |-Branch two: % 7.34/2.39 | (170) ~ mem(all_0_15_15, all_0_8_8) % 7.34/2.39 | (171) mem(all_0_15_15, all_0_11_11) % 7.34/2.39 | % 7.34/2.39 | Instantiating formula (49) with all_0_11_11, all_0_14_14, all_0_15_15 and discharging atoms s(all_0_14_14) = all_0_11_11, mem(all_0_15_15, all_0_11_11), yields: % 7.34/2.39 | (172) all_0_14_14 = all_0_15_15 % 7.34/2.39 | % 7.34/2.39 | From (172) and (78) follows: % 7.76/2.39 | (173) a(all_0_15_15, all_0_15_15) = all_0_15_15 % 7.76/2.39 | % 7.76/2.39 | From (172) and (7) follows: % 7.76/2.39 | (174) u(all_0_16_16, all_0_15_15) = all_0_13_13 % 7.76/2.39 | % 7.76/2.39 | From (172) and (121) follows: % 7.76/2.39 | (175) mem(all_0_15_15, all_0_15_15) % 7.76/2.39 | % 7.76/2.39 | Instantiating formula (9) with all_0_16_16, all_0_15_15, all_0_13_13, all_0_10_10 and discharging atoms u(all_0_16_16, all_0_15_15) = all_0_10_10, u(all_0_16_16, all_0_15_15) = all_0_13_13, yields: % 7.76/2.39 | (176) all_0_10_10 = all_0_13_13 % 7.76/2.39 | % 7.76/2.39 | Instantiating formula (49) with all_0_15_15, all_0_16_16, all_0_15_15 and discharging atoms s(all_0_16_16) = all_0_15_15, mem(all_0_15_15, all_0_15_15), yields: % 7.76/2.39 | (177) all_0_15_15 = all_0_16_16 % 7.76/2.39 | % 7.76/2.39 | From (177)(177)(177) and (173) follows: % 7.76/2.39 | (178) a(all_0_16_16, all_0_16_16) = all_0_16_16 % 7.76/2.39 | % 7.76/2.39 | From (176) and (79) follows: % 7.76/2.39 | (179) a(all_0_16_16, all_0_16_16) = all_0_13_13 % 7.76/2.39 | % 7.76/2.39 | From (177) and (31) follows: % 7.76/2.39 | (180) s(all_0_16_16) = all_0_16_16 % 7.76/2.39 | % 7.76/2.39 | From (176) and (119) follows: % 7.76/2.39 | (181) mem(all_0_13_13, all_0_8_8) % 7.76/2.39 | % 7.76/2.39 | From (177) and (170) follows: % 7.76/2.39 | (182) ~ mem(all_0_16_16, all_0_8_8) % 7.76/2.39 | % 7.76/2.39 | Instantiating formula (21) with all_0_16_16, all_0_16_16, all_0_16_16, all_0_13_13 and discharging atoms a(all_0_16_16, all_0_16_16) = all_0_13_13, a(all_0_16_16, all_0_16_16) = all_0_16_16, yields: % 7.76/2.39 | (183) all_0_13_13 = all_0_16_16 % 7.76/2.39 | % 7.76/2.39 | Instantiating formula (49) with all_0_16_16, all_0_16_16, e and discharging atoms s(all_0_16_16) = all_0_16_16, mem(e, all_0_16_16), yields: % 7.76/2.39 | (133) all_0_16_16 = e % 7.76/2.39 | % 7.76/2.39 | Combining equations (133,183) yields a new equation: % 7.76/2.39 | (185) all_0_13_13 = e % 7.76/2.40 | % 7.76/2.40 | From (185) and (181) follows: % 7.76/2.40 | (186) mem(e, all_0_8_8) % 7.76/2.40 | % 7.76/2.40 | From (133) and (182) follows: % 7.76/2.40 | (187) ~ mem(e, all_0_8_8) % 7.76/2.40 | % 7.76/2.40 | Using (186) and (187) yields: % 7.76/2.40 | (135) $false % 7.76/2.40 | % 7.76/2.40 |-The branch is then unsatisfiable % 7.76/2.40 |-Branch two: % 7.76/2.40 | (189) ~ mem(all_0_15_15, all_0_7_7) % 7.76/2.40 | (190) mem(all_0_15_15, all_0_12_12) % 7.76/2.40 | % 7.76/2.40 | Instantiating formula (49) with all_0_12_12, all_0_13_13, all_0_15_15 and discharging atoms s(all_0_13_13) = all_0_12_12, mem(all_0_15_15, all_0_12_12), yields: % 7.76/2.40 | (191) all_0_13_13 = all_0_15_15 % 7.76/2.40 | % 7.76/2.40 | From (191) and (127) follows: % 7.76/2.40 | (132) mem(e, all_0_15_15) % 7.76/2.40 | % 7.76/2.40 | Instantiating formula (49) with all_0_15_15, all_0_16_16, e and discharging atoms s(all_0_16_16) = all_0_15_15, mem(e, all_0_15_15), yields: % 7.76/2.40 | (133) all_0_16_16 = e % 7.76/2.40 | % 7.76/2.40 | From (133) and (125) follows: % 7.76/2.40 | (134) mem(e, e) % 7.76/2.40 | % 7.76/2.40 | Instantiating formula (35) with e and discharging atoms mem(e, e), yields: % 7.76/2.40 | (135) $false % 7.76/2.40 | % 7.76/2.40 |-The branch is then unsatisfiable % 7.76/2.40 % SZS output end Proof for theBenchmark % 7.76/2.40 % 7.76/2.40 1771ms %------------------------------------------------------------------------------