%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEV572+1 : TPTP v9.1.0. Released v9.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n026.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 4.89s 1.70s % Output : Proof 7.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEV572+1 : TPTP v9.1.0. Released v9.1.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n026.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 : 300 % 0.12/0.33 % DateTime : Mon Mar 31 12:49:07 EDT 2025 % 0.12/0.34 % CPUTime : % 0.53/0.57 ____ _ % 0.53/0.57 ___ / __ \_____(_)___ ________ __________ % 0.53/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.53/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.53/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.53/0.57 % 0.53/0.57 A Theorem Prover for First-Order Logic % 0.53/0.58 (ePrincess v.1.0) % 0.53/0.58 % 0.53/0.58 (c) Philipp Rümmer, 2009-2015 % 0.53/0.58 (c) Peter Backeman, 2014-2015 % 0.53/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.53/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.53/0.58 Bug reports to peter@backeman.se % 0.53/0.58 % 0.53/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.53/0.58 % 0.53/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.53/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.60/0.91 Prover 0: Preprocessing ... % 2.60/1.17 Prover 0: Warning: ignoring some quantifiers % 2.60/1.20 Prover 0: Constructing countermodel ... % 4.89/1.70 Prover 0: proved (1075ms) % 4.89/1.70 % 4.89/1.70 No countermodel exists, formula is valid % 4.89/1.70 % SZS status Theorem for theBenchmark % 4.89/1.70 % 4.89/1.70 Generating proof ... Warning: ignoring some quantifiers % 6.63/2.09 found it (size 105) % 6.63/2.09 % 6.63/2.09 % SZS output start Proof for theBenchmark % 6.63/2.09 Assumed formulas after preprocessing and simplification: % 6.63/2.09 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (n(v8) = v9 & n(v4) = v5 & n(v1) = v4 & n(v0) = v7 & n(e) = v0 & a(v15, v11) = v16 & a(v6, v8) = v14 & a(v2, v7) = v11 & a(v0, v7) = v8 & u(v14, v16) = v17 & u(v10, v12) = v13 & u(v6, v9) = v10 & u(v3, v5) = v6 & s(v11) = v12 & s(v7) = v15 & s(v2) = v3 & s(v1) = v2 & s(v0) = v1 & subq(v13, v17) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v19 = v18 | ~ (a(v21, v20) = v19) | ~ (a(v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v19 = v18 | ~ (m(v21, v20) = v19) | ~ (m(v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v19 = v18 | ~ (u(v21, v20) = v19) | ~ (u(v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (m(v19, v20) = v21) | ~ mem(v18, v21) | ~ mem(v18, v20)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (m(v19, v20) = v21) | ~ mem(v18, v21) | mem(v18, v19)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (m(v19, v20) = v21) | ~ mem(v18, v19) | mem(v18, v21) | mem(v18, v20)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (u(v19, v20) = v21) | ~ mem(v18, v21) | mem(v18, v20) | mem(v18, v19)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (u(v19, v20) = v21) | ~ mem(v18, v20) | mem(v18, v21)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (u(v19, v20) = v21) | ~ mem(v18, v19) | mem(v18, v21)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (u(v18, v20) = v21) | ~ (s(v19) = v20) | a(v18, v19) = v21) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (p(v20) = v19) | ~ (p(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (n(v20) = v19) | ~ (n(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (s(v20) = v19) | ~ (s(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (s(v19) = v20) | ~ mem(v18, v20)) & ! [v18] : ! [v19] : ! [v20] : ( ~ (p(v19) = v20) | ~ mem(v19, v18) | atleast2p(v18) | subq(v18, v20)) & ! [v18] : ! [v19] : ! [v20] : ( ~ (p(v19) = v20) | ~ mem(v18, v20) | subq(v18, v19)) & ! [v18] : ! [v19] : ! [v20] : ( ~ (p(v19) = v20) | ~ subq(v18, v19) | mem(v18, v20)) & ! [v18] : ! [v19] : ! [v20] : ( ~ (a(v18, v19) = v20) | ? [v21] : (u(v18, v21) = v20 & s(v19) = v21)) & ! [v18] : ! [v19] : ! [v20] : ( ~ disj(v18, v19) | ~ mem(v20, v19) | ~ mem(v20, v18)) & ! [v18] : ! [v19] : ! [v20] : ( ~ mem(v20, v18) | ~ subq(v18, v19) | mem(v20, v19)) & ! [v18] : ! [v19] : (v19 = v18 | ~ subq(v19, v18) | ~ subq(v18, v19)) & ! [v18] : ! [v19] : ( ~ (n(v18) = v19) | a(v18, v18) = v19) & ! [v18] : ! [v19] : ( ~ (a(v18, v18) = v19) | n(v18) = v19) & ! [v18] : ! [v19] : ( ~ (s(v18) = v19) | mem(v18, v19)) & ! [v18] : ! [v19] : ( ~ atleast15p(v19) | ~ subq(v19, v18) | atleast16p(v18) | subq(v18, v19)) & ! [v18] : ! [v19] : ( ~ atleast14p(v19) | ~ subq(v19, v18) | atleast15p(v18) | subq(v18, v19)) & ! [v18] : ! [v19] : ( ~ atleast13p(v19) | ~ subq(v19, v18) | atleast14p(v18) | subq(v18, v19)) & ! [v18] : ! [v19] : ( ~ atleast12p(v19) | ~ subq(v19, v18) | atleast13p(v18) | subq(v18, v19)) & ! [v18] : ! [v19] : ( ~ atleast11p(v19) | ~ subq(v19, v18) | atleast12p(v18) | subq(v18, v19)) & ! [v18] : ! [v19] : ( ~ atleast10p(v19) | ~ subq(v19, v18) | atleast11p(v18) | subq(v18, v19)) & ! [v18] : ! [v19] : ( ~ atleast9p(v19) | ~ subq(v19, v18) | atleast10p(v18) | subq(v18, v19)) & ! [v18] : ! [v19] : ( ~ atleast8p(v19) | ~ subq(v19, v18) | atleast9p(v18) | subq(v18, v19)) & ! [v18] : ! [v19] : ( ~ atleast7p(v19) | ~ subq(v19, v18) | atleast8p(v18) | subq(v18, v19)) & ! [v18] : ! [v19] : ( ~ atleast6p(v19) | ~ subq(v19, v18) | atleast7p(v18) | subq(v18, v19)) & ! [v18] : ! [v19] : ( ~ atleast5p(v19) | ~ subq(v19, v18) | atleast6p(v18) | subq(v18, v19)) & ! [v18] : ! [v19] : ( ~ atleast4p(v19) | ~ subq(v19, v18) | atleast5p(v18) | subq(v18, v19)) & ! [v18] : ! [v19] : ( ~ atleast3p(v19) | ~ subq(v19, v18) | atleast4p(v18) | subq(v18, v19)) & ! [v18] : ! [v19] : ( ~ atleast2p(v19) | ~ subq(v19, v18) | atleast3p(v18) | subq(v18, v19)) & ! [v18] : ( ~ atleast16p(v18) | ? [v19] : (atleast15p(v19) & subq(v19, v18) & ~ subq(v18, v19))) & ! [v18] : ( ~ atleast15p(v18) | ? [v19] : (atleast14p(v19) & subq(v19, v18) & ~ subq(v18, v19))) & ! [v18] : ( ~ atleast14p(v18) | ? [v19] : (atleast13p(v19) & subq(v19, v18) & ~ subq(v18, v19))) & ! [v18] : ( ~ atleast13p(v18) | ? [v19] : (atleast12p(v19) & subq(v19, v18) & ~ subq(v18, v19))) & ! [v18] : ( ~ atleast12p(v18) | ? [v19] : (atleast11p(v19) & subq(v19, v18) & ~ subq(v18, v19))) & ! [v18] : ( ~ atleast11p(v18) | ? [v19] : (atleast10p(v19) & subq(v19, v18) & ~ subq(v18, v19))) & ! [v18] : ( ~ atleast10p(v18) | ? [v19] : (atleast9p(v19) & subq(v19, v18) & ~ subq(v18, v19))) & ! [v18] : ( ~ atleast9p(v18) | ? [v19] : (atleast8p(v19) & subq(v19, v18) & ~ subq(v18, v19))) & ! [v18] : ( ~ atleast8p(v18) | ? [v19] : (atleast7p(v19) & subq(v19, v18) & ~ subq(v18, v19))) & ! [v18] : ( ~ atleast7p(v18) | ? [v19] : (atleast6p(v19) & subq(v19, v18) & ~ subq(v18, v19))) & ! [v18] : ( ~ atleast6p(v18) | ? [v19] : (atleast5p(v19) & subq(v19, v18) & ~ subq(v18, v19))) & ! [v18] : ( ~ atleast5p(v18) | ? [v19] : (atleast4p(v19) & subq(v19, v18) & ~ subq(v18, v19))) & ! [v18] : ( ~ atleast4p(v18) | ? [v19] : (atleast3p(v19) & subq(v19, v18) & ~ subq(v18, v19))) & ! [v18] : ( ~ atleast3p(v18) | ? [v19] : (atleast2p(v19) & subq(v19, v18) & ~ subq(v18, v19))) & ! [v18] : ( ~ atleast2p(v18) | ? [v19] : ? [v20] : (p(v19) = v20 & mem(v19, v18) & ~ subq(v18, v20))) & ! [v18] : ~ mem(v18, e) & ? [v18] : ? [v19] : (disj(v18, v19) | ? [v20] : (mem(v20, v19) & mem(v20, v18))) & ? [v18] : ? [v19] : (subq(v18, v19) | ? [v20] : (mem(v20, v18) & ~ mem(v20, v19)))) % 6.88/2.14 | 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, all_0_17_17 yields: % 6.88/2.14 | (1) n(all_0_9_9) = all_0_8_8 & n(all_0_13_13) = all_0_12_12 & n(all_0_16_16) = all_0_13_13 & n(all_0_17_17) = all_0_10_10 & n(e) = all_0_17_17 & a(all_0_2_2, all_0_6_6) = all_0_1_1 & a(all_0_11_11, all_0_9_9) = all_0_3_3 & a(all_0_15_15, all_0_10_10) = all_0_6_6 & a(all_0_17_17, all_0_10_10) = all_0_9_9 & u(all_0_3_3, all_0_1_1) = all_0_0_0 & u(all_0_7_7, all_0_5_5) = all_0_4_4 & u(all_0_11_11, all_0_8_8) = all_0_7_7 & u(all_0_14_14, all_0_12_12) = all_0_11_11 & s(all_0_6_6) = all_0_5_5 & s(all_0_10_10) = all_0_2_2 & s(all_0_15_15) = all_0_14_14 & s(all_0_16_16) = all_0_15_15 & s(all_0_17_17) = all_0_16_16 & subq(all_0_4_4, 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))) % 6.88/2.15 | % 6.88/2.15 | Applying alpha-rule on (1) yields: % 6.88/2.15 | (2) u(all_0_3_3, all_0_1_1) = all_0_0_0 % 6.88/2.15 | (3) ! [v0] : ! [v1] : ( ~ atleast6p(v1) | ~ subq(v1, v0) | atleast7p(v0) | subq(v0, v1)) % 6.88/2.15 | (4) ! [v0] : ! [v1] : ( ~ atleast5p(v1) | ~ subq(v1, v0) | atleast6p(v0) | subq(v0, v1)) % 6.88/2.15 | (5) ! [v0] : ! [v1] : ( ~ atleast7p(v1) | ~ subq(v1, v0) | atleast8p(v0) | subq(v0, v1)) % 6.88/2.15 | (6) ! [v0] : ! [v1] : ( ~ (a(v0, v0) = v1) | n(v0) = v1) % 6.88/2.15 | (7) ! [v0] : ! [v1] : ( ~ (n(v0) = v1) | a(v0, v0) = v1) % 6.88/2.15 | (8) ? [v0] : ? [v1] : (disj(v0, v1) | ? [v2] : (mem(v2, v1) & mem(v2, v0))) % 6.88/2.15 | (9) n(all_0_9_9) = all_0_8_8 % 6.88/2.15 | (10) subq(all_0_4_4, all_0_0_0) % 6.88/2.15 | (11) u(all_0_14_14, all_0_12_12) = all_0_11_11 % 6.88/2.15 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ disj(v0, v1) | ~ mem(v2, v1) | ~ mem(v2, v0)) % 6.88/2.15 | (13) n(all_0_13_13) = all_0_12_12 % 6.88/2.15 | (14) a(all_0_2_2, all_0_6_6) = all_0_1_1 % 6.88/2.15 | (15) s(all_0_10_10) = all_0_2_2 % 6.88/2.15 | (16) n(all_0_17_17) = all_0_10_10 % 6.88/2.15 | (17) a(all_0_17_17, all_0_10_10) = all_0_9_9 % 6.88/2.15 | (18) a(all_0_11_11, all_0_9_9) = all_0_3_3 % 6.88/2.15 | (19) n(all_0_16_16) = all_0_13_13 % 6.88/2.15 | (20) ? [v0] : ? [v1] : (subq(v0, v1) | ? [v2] : (mem(v2, v0) & ~ mem(v2, v1))) % 6.88/2.15 | (21) s(all_0_16_16) = all_0_15_15 % 6.88/2.15 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (s(v2) = v1) | ~ (s(v2) = v0)) % 6.88/2.15 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u(v0, v2) = v3) | ~ (s(v1) = v2) | a(v0, v1) = v3) % 6.88/2.15 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (m(v3, v2) = v1) | ~ (m(v3, v2) = v0)) % 6.88/2.16 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u(v1, v2) = v3) | ~ mem(v0, v2) | mem(v0, v3)) % 6.88/2.16 | (26) ! [v0] : ( ~ atleast16p(v0) | ? [v1] : (atleast15p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.88/2.16 | (27) ! [v0] : ~ mem(v0, e) % 6.88/2.16 | (28) ! [v0] : ( ~ atleast9p(v0) | ? [v1] : (atleast8p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.88/2.16 | (29) a(all_0_15_15, all_0_10_10) = all_0_6_6 % 6.88/2.16 | (30) ! [v0] : ( ~ atleast15p(v0) | ? [v1] : (atleast14p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.88/2.16 | (31) ! [v0] : ! [v1] : ( ~ atleast13p(v1) | ~ subq(v1, v0) | atleast14p(v0) | subq(v0, v1)) % 6.88/2.16 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (p(v1) = v2) | ~ subq(v0, v1) | mem(v0, v2)) % 6.88/2.16 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (p(v1) = v2) | ~ mem(v0, v2) | subq(v0, v1)) % 6.88/2.16 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (m(v1, v2) = v3) | ~ mem(v0, v3) | mem(v0, v1)) % 6.88/2.16 | (35) ! [v0] : ! [v1] : ( ~ atleast11p(v1) | ~ subq(v1, v0) | atleast12p(v0) | subq(v0, v1)) % 6.88/2.16 | (36) ! [v0] : ( ~ atleast14p(v0) | ? [v1] : (atleast13p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.88/2.16 | (37) ! [v0] : ( ~ atleast12p(v0) | ? [v1] : (atleast11p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.88/2.16 | (38) ! [v0] : ( ~ atleast6p(v0) | ? [v1] : (atleast5p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.88/2.16 | (39) ! [v0] : ! [v1] : ( ~ (s(v0) = v1) | mem(v0, v1)) % 6.88/2.16 | (40) ! [v0] : ( ~ atleast13p(v0) | ? [v1] : (atleast12p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.88/2.16 | (41) s(all_0_17_17) = all_0_16_16 % 6.88/2.16 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u(v1, v2) = v3) | ~ mem(v0, v3) | mem(v0, v2) | mem(v0, v1)) % 6.88/2.16 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (u(v3, v2) = v1) | ~ (u(v3, v2) = v0)) % 6.88/2.16 | (44) ! [v0] : ! [v1] : ( ~ atleast15p(v1) | ~ subq(v1, v0) | atleast16p(v0) | subq(v0, v1)) % 6.88/2.16 | (45) ! [v0] : ! [v1] : (v1 = v0 | ~ subq(v1, v0) | ~ subq(v0, v1)) % 6.88/2.16 | (46) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) % 6.88/2.16 | (47) u(all_0_7_7, all_0_5_5) = all_0_4_4 % 6.88/2.16 | (48) ! [v0] : ! [v1] : ( ~ atleast9p(v1) | ~ subq(v1, v0) | atleast10p(v0) | subq(v0, v1)) % 6.88/2.16 | (49) ! [v0] : ! [v1] : ( ~ atleast4p(v1) | ~ subq(v1, v0) | atleast5p(v0) | subq(v0, v1)) % 6.88/2.16 | (50) ! [v0] : ( ~ atleast5p(v0) | ? [v1] : (atleast4p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.07/2.16 | (51) u(all_0_11_11, all_0_8_8) = all_0_7_7 % 7.07/2.16 | (52) ! [v0] : ( ~ atleast4p(v0) | ? [v1] : (atleast3p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.07/2.16 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (p(v1) = v2) | ~ mem(v1, v0) | atleast2p(v0) | subq(v0, v2)) % 7.07/2.16 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (a(v3, v2) = v1) | ~ (a(v3, v2) = v0)) % 7.07/2.16 | (55) ! [v0] : ( ~ atleast3p(v0) | ? [v1] : (atleast2p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.07/2.16 | (56) s(all_0_15_15) = all_0_14_14 % 7.07/2.16 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ mem(v2, v0) | ~ subq(v0, v1) | mem(v2, v1)) % 7.07/2.16 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (a(v0, v1) = v2) | ? [v3] : (u(v0, v3) = v2 & s(v1) = v3)) % 7.07/2.16 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (m(v1, v2) = v3) | ~ mem(v0, v3) | ~ mem(v0, v2)) % 7.07/2.16 | (60) ! [v0] : ! [v1] : ( ~ atleast2p(v1) | ~ subq(v1, v0) | atleast3p(v0) | subq(v0, v1)) % 7.07/2.16 | (61) ! [v0] : ! [v1] : ( ~ atleast10p(v1) | ~ subq(v1, v0) | atleast11p(v0) | subq(v0, v1)) % 7.07/2.16 | (62) ! [v0] : ( ~ atleast2p(v0) | ? [v1] : ? [v2] : (p(v1) = v2 & mem(v1, v0) & ~ subq(v0, v2))) % 7.07/2.16 | (63) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (n(v2) = v1) | ~ (n(v2) = v0)) % 7.07/2.17 | (64) ! [v0] : ! [v1] : ( ~ atleast12p(v1) | ~ subq(v1, v0) | atleast13p(v0) | subq(v0, v1)) % 7.07/2.17 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u(v1, v2) = v3) | ~ mem(v0, v1) | mem(v0, v3)) % 7.07/2.17 | (66) ! [v0] : ( ~ atleast10p(v0) | ? [v1] : (atleast9p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.07/2.17 | (67) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (s(v1) = v2) | ~ mem(v0, v2)) % 7.07/2.17 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (m(v1, v2) = v3) | ~ mem(v0, v1) | mem(v0, v3) | mem(v0, v2)) % 7.07/2.17 | (69) ! [v0] : ! [v1] : ( ~ atleast3p(v1) | ~ subq(v1, v0) | atleast4p(v0) | subq(v0, v1)) % 7.07/2.17 | (70) s(all_0_6_6) = all_0_5_5 % 7.07/2.17 | (71) ! [v0] : ! [v1] : ( ~ atleast8p(v1) | ~ subq(v1, v0) | atleast9p(v0) | subq(v0, v1)) % 7.07/2.17 | (72) ! [v0] : ( ~ atleast11p(v0) | ? [v1] : (atleast10p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.07/2.17 | (73) ! [v0] : ( ~ atleast8p(v0) | ? [v1] : (atleast7p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.07/2.17 | (74) ! [v0] : ! [v1] : ( ~ atleast14p(v1) | ~ subq(v1, v0) | atleast15p(v0) | subq(v0, v1)) % 7.07/2.17 | (75) n(e) = all_0_17_17 % 7.07/2.17 | (76) ! [v0] : ( ~ atleast7p(v0) | ? [v1] : (atleast6p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 7.07/2.17 | % 7.07/2.17 | Instantiating formula (7) with all_0_8_8, all_0_9_9 and discharging atoms n(all_0_9_9) = all_0_8_8, yields: % 7.07/2.17 | (77) a(all_0_9_9, all_0_9_9) = all_0_8_8 % 7.07/2.17 | % 7.07/2.17 | Instantiating formula (7) with all_0_12_12, all_0_13_13 and discharging atoms n(all_0_13_13) = all_0_12_12, yields: % 7.07/2.17 | (78) a(all_0_13_13, all_0_13_13) = all_0_12_12 % 7.07/2.17 | % 7.07/2.17 | Instantiating formula (7) with all_0_13_13, all_0_16_16 and discharging atoms n(all_0_16_16) = all_0_13_13, yields: % 7.07/2.17 | (79) a(all_0_16_16, all_0_16_16) = all_0_13_13 % 7.07/2.17 | % 7.07/2.17 | Instantiating formula (7) with all_0_10_10, all_0_17_17 and discharging atoms n(all_0_17_17) = all_0_10_10, yields: % 7.07/2.17 | (80) a(all_0_17_17, all_0_17_17) = all_0_10_10 % 7.07/2.17 | % 7.07/2.17 | Instantiating formula (7) with all_0_17_17, e and discharging atoms n(e) = all_0_17_17, yields: % 7.07/2.17 | (81) a(e, e) = all_0_17_17 % 7.07/2.17 | % 7.07/2.17 | Instantiating formula (58) with all_0_1_1, all_0_6_6, all_0_2_2 and discharging atoms a(all_0_2_2, all_0_6_6) = all_0_1_1, yields: % 7.07/2.17 | (82) ? [v0] : (u(all_0_2_2, v0) = all_0_1_1 & s(all_0_6_6) = v0) % 7.07/2.17 | % 7.07/2.17 | Instantiating formula (58) with all_0_3_3, all_0_9_9, all_0_11_11 and discharging atoms a(all_0_11_11, all_0_9_9) = all_0_3_3, yields: % 7.07/2.17 | (83) ? [v0] : (u(all_0_11_11, v0) = all_0_3_3 & s(all_0_9_9) = v0) % 7.07/2.17 | % 7.07/2.17 | Instantiating formula (58) with all_0_6_6, all_0_10_10, all_0_15_15 and discharging atoms a(all_0_15_15, all_0_10_10) = all_0_6_6, yields: % 7.07/2.17 | (84) ? [v0] : (u(all_0_15_15, v0) = all_0_6_6 & s(all_0_10_10) = v0) % 7.07/2.17 | % 7.07/2.17 | Instantiating formula (58) with all_0_9_9, all_0_10_10, all_0_17_17 and discharging atoms a(all_0_17_17, all_0_10_10) = all_0_9_9, yields: % 7.07/2.17 | (85) ? [v0] : (u(all_0_17_17, v0) = all_0_9_9 & s(all_0_10_10) = v0) % 7.07/2.17 | % 7.07/2.17 | Instantiating formula (39) with all_0_15_15, all_0_16_16 and discharging atoms s(all_0_16_16) = all_0_15_15, yields: % 7.07/2.17 | (86) mem(all_0_16_16, all_0_15_15) % 7.07/2.17 | % 7.07/2.17 | Instantiating formula (39) with all_0_16_16, all_0_17_17 and discharging atoms s(all_0_17_17) = all_0_16_16, yields: % 7.07/2.17 | (87) mem(all_0_17_17, all_0_16_16) % 7.07/2.17 | % 7.07/2.17 | Instantiating (84) with all_11_0_22 yields: % 7.07/2.17 | (88) u(all_0_15_15, all_11_0_22) = all_0_6_6 & s(all_0_10_10) = all_11_0_22 % 7.07/2.17 | % 7.07/2.17 | Applying alpha-rule on (88) yields: % 7.07/2.17 | (89) u(all_0_15_15, all_11_0_22) = all_0_6_6 % 7.07/2.17 | (90) s(all_0_10_10) = all_11_0_22 % 7.07/2.17 | % 7.07/2.17 | Instantiating (83) with all_13_0_23 yields: % 7.07/2.17 | (91) u(all_0_11_11, all_13_0_23) = all_0_3_3 & s(all_0_9_9) = all_13_0_23 % 7.07/2.17 | % 7.07/2.17 | Applying alpha-rule on (91) yields: % 7.07/2.17 | (92) u(all_0_11_11, all_13_0_23) = all_0_3_3 % 7.07/2.17 | (93) s(all_0_9_9) = all_13_0_23 % 7.07/2.17 | % 7.07/2.17 | Instantiating (82) with all_15_0_24 yields: % 7.07/2.17 | (94) u(all_0_2_2, all_15_0_24) = all_0_1_1 & s(all_0_6_6) = all_15_0_24 % 7.07/2.17 | % 7.07/2.17 | Applying alpha-rule on (94) yields: % 7.07/2.17 | (95) u(all_0_2_2, all_15_0_24) = all_0_1_1 % 7.07/2.17 | (96) s(all_0_6_6) = all_15_0_24 % 7.07/2.17 | % 7.07/2.18 | Instantiating (85) with all_17_0_25 yields: % 7.07/2.18 | (97) u(all_0_17_17, all_17_0_25) = all_0_9_9 & s(all_0_10_10) = all_17_0_25 % 7.07/2.18 | % 7.07/2.18 | Applying alpha-rule on (97) yields: % 7.07/2.18 | (98) u(all_0_17_17, all_17_0_25) = all_0_9_9 % 7.07/2.18 | (99) s(all_0_10_10) = all_17_0_25 % 7.07/2.18 | % 7.07/2.18 | Instantiating formula (22) with all_0_6_6, all_15_0_24, all_0_5_5 and discharging atoms s(all_0_6_6) = all_15_0_24, s(all_0_6_6) = all_0_5_5, yields: % 7.07/2.18 | (100) all_15_0_24 = all_0_5_5 % 7.07/2.18 | % 7.07/2.18 | Instantiating formula (22) with all_0_10_10, all_17_0_25, all_0_2_2 and discharging atoms s(all_0_10_10) = all_17_0_25, s(all_0_10_10) = all_0_2_2, yields: % 7.07/2.18 | (101) all_17_0_25 = all_0_2_2 % 7.07/2.18 | % 7.07/2.18 | Instantiating formula (22) with all_0_10_10, all_11_0_22, all_17_0_25 and discharging atoms s(all_0_10_10) = all_17_0_25, s(all_0_10_10) = all_11_0_22, yields: % 7.07/2.18 | (102) all_17_0_25 = all_11_0_22 % 7.07/2.18 | % 7.07/2.18 | Combining equations (101,102) yields a new equation: % 7.07/2.18 | (103) all_11_0_22 = all_0_2_2 % 7.07/2.18 | % 7.07/2.18 | Combining equations (103,102) yields a new equation: % 7.07/2.18 | (101) all_17_0_25 = all_0_2_2 % 7.07/2.18 | % 7.07/2.18 | From (100) and (95) follows: % 7.07/2.18 | (105) u(all_0_2_2, all_0_5_5) = all_0_1_1 % 7.07/2.18 | % 7.07/2.18 | From (103) and (89) follows: % 7.07/2.18 | (106) u(all_0_15_15, all_0_2_2) = all_0_6_6 % 7.07/2.18 | % 7.07/2.18 | From (101) and (98) follows: % 7.07/2.18 | (107) u(all_0_17_17, all_0_2_2) = all_0_9_9 % 7.07/2.18 | % 7.07/2.18 | From (100) and (96) follows: % 7.07/2.18 | (70) s(all_0_6_6) = all_0_5_5 % 7.07/2.18 | % 7.07/2.18 | From (103) and (90) follows: % 7.07/2.18 | (15) s(all_0_10_10) = all_0_2_2 % 7.07/2.18 | % 7.07/2.18 | Instantiating formula (58) 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: % 7.07/2.18 | (110) ? [v0] : (u(all_0_9_9, v0) = all_0_8_8 & s(all_0_9_9) = v0) % 7.07/2.18 | % 7.07/2.18 | Instantiating formula (58) with all_0_12_12, all_0_13_13, all_0_13_13 and discharging atoms a(all_0_13_13, all_0_13_13) = all_0_12_12, yields: % 7.07/2.18 | (111) ? [v0] : (u(all_0_13_13, v0) = all_0_12_12 & s(all_0_13_13) = v0) % 7.07/2.18 | % 7.07/2.18 | Instantiating formula (58) with all_0_13_13, all_0_16_16, all_0_16_16 and discharging atoms a(all_0_16_16, all_0_16_16) = all_0_13_13, yields: % 7.07/2.18 | (112) ? [v0] : (u(all_0_16_16, v0) = all_0_13_13 & s(all_0_16_16) = v0) % 7.07/2.18 | % 7.07/2.18 | Instantiating formula (58) with all_0_10_10, all_0_17_17, all_0_17_17 and discharging atoms a(all_0_17_17, all_0_17_17) = all_0_10_10, yields: % 7.07/2.18 | (113) ? [v0] : (u(all_0_17_17, v0) = all_0_10_10 & s(all_0_17_17) = v0) % 7.07/2.18 | % 7.07/2.18 | Instantiating formula (58) with all_0_17_17, e, e and discharging atoms a(e, e) = all_0_17_17, yields: % 7.07/2.18 | (114) ? [v0] : (u(e, v0) = all_0_17_17 & s(e) = v0) % 7.07/2.18 | % 7.07/2.18 | Instantiating formula (65) with all_0_6_6, 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_6_6, mem(all_0_16_16, all_0_15_15), yields: % 7.07/2.18 | (115) mem(all_0_16_16, all_0_6_6) % 7.07/2.18 | % 7.07/2.18 | Instantiating (113) with all_29_0_26 yields: % 7.07/2.18 | (116) u(all_0_17_17, all_29_0_26) = all_0_10_10 & s(all_0_17_17) = all_29_0_26 % 7.07/2.18 | % 7.07/2.18 | Applying alpha-rule on (116) yields: % 7.07/2.18 | (117) u(all_0_17_17, all_29_0_26) = all_0_10_10 % 7.07/2.18 | (118) s(all_0_17_17) = all_29_0_26 % 7.07/2.18 | % 7.07/2.18 | Instantiating (112) with all_31_0_27 yields: % 7.07/2.18 | (119) u(all_0_16_16, all_31_0_27) = all_0_13_13 & s(all_0_16_16) = all_31_0_27 % 7.07/2.18 | % 7.07/2.18 | Applying alpha-rule on (119) yields: % 7.07/2.18 | (120) u(all_0_16_16, all_31_0_27) = all_0_13_13 % 7.07/2.18 | (121) s(all_0_16_16) = all_31_0_27 % 7.07/2.18 | % 7.07/2.18 | Instantiating (114) with all_33_0_28 yields: % 7.07/2.18 | (122) u(e, all_33_0_28) = all_0_17_17 & s(e) = all_33_0_28 % 7.07/2.18 | % 7.07/2.19 | Applying alpha-rule on (122) yields: % 7.07/2.19 | (123) u(e, all_33_0_28) = all_0_17_17 % 7.07/2.19 | (124) s(e) = all_33_0_28 % 7.07/2.19 | % 7.07/2.19 | Instantiating (111) with all_35_0_29 yields: % 7.07/2.19 | (125) u(all_0_13_13, all_35_0_29) = all_0_12_12 & s(all_0_13_13) = all_35_0_29 % 7.07/2.19 | % 7.07/2.19 | Applying alpha-rule on (125) yields: % 7.07/2.19 | (126) u(all_0_13_13, all_35_0_29) = all_0_12_12 % 7.07/2.19 | (127) s(all_0_13_13) = all_35_0_29 % 7.07/2.19 | % 7.07/2.19 | Instantiating (110) with all_37_0_30 yields: % 7.07/2.19 | (128) u(all_0_9_9, all_37_0_30) = all_0_8_8 & s(all_0_9_9) = all_37_0_30 % 7.07/2.19 | % 7.07/2.19 | Applying alpha-rule on (128) yields: % 7.07/2.19 | (129) u(all_0_9_9, all_37_0_30) = all_0_8_8 % 7.07/2.19 | (130) s(all_0_9_9) = all_37_0_30 % 7.07/2.19 | % 7.07/2.19 | Instantiating formula (22) with all_0_9_9, all_37_0_30, all_13_0_23 and discharging atoms s(all_0_9_9) = all_37_0_30, s(all_0_9_9) = all_13_0_23, yields: % 7.07/2.19 | (131) all_37_0_30 = all_13_0_23 % 7.07/2.19 | % 7.07/2.19 | Instantiating formula (22) with all_0_16_16, all_31_0_27, all_0_15_15 and discharging atoms s(all_0_16_16) = all_31_0_27, s(all_0_16_16) = all_0_15_15, yields: % 7.07/2.19 | (132) all_31_0_27 = all_0_15_15 % 7.07/2.19 | % 7.07/2.19 | Instantiating formula (22) with all_0_17_17, all_29_0_26, all_0_16_16 and discharging atoms s(all_0_17_17) = all_29_0_26, s(all_0_17_17) = all_0_16_16, yields: % 7.07/2.19 | (133) all_29_0_26 = all_0_16_16 % 7.07/2.19 | % 7.07/2.19 | From (131) and (129) follows: % 7.07/2.19 | (134) u(all_0_9_9, all_13_0_23) = all_0_8_8 % 7.07/2.19 | % 7.07/2.19 | From (132) and (120) follows: % 7.07/2.19 | (135) u(all_0_16_16, all_0_15_15) = all_0_13_13 % 7.07/2.19 | % 7.07/2.19 | From (133) and (117) follows: % 7.07/2.19 | (136) u(all_0_17_17, all_0_16_16) = all_0_10_10 % 7.07/2.19 | % 7.07/2.19 | From (131) and (130) follows: % 7.07/2.19 | (93) s(all_0_9_9) = all_13_0_23 % 7.07/2.19 | % 7.07/2.19 | From (132) and (121) follows: % 7.07/2.19 | (21) s(all_0_16_16) = all_0_15_15 % 7.07/2.19 | % 7.07/2.19 | From (133) and (118) follows: % 7.07/2.19 | (41) s(all_0_17_17) = all_0_16_16 % 7.07/2.19 | % 7.07/2.19 | Instantiating formula (65) with all_0_13_13, all_0_15_15, all_0_16_16, all_0_17_17 and discharging atoms u(all_0_16_16, all_0_15_15) = all_0_13_13, mem(all_0_17_17, all_0_16_16), yields: % 7.07/2.19 | (140) mem(all_0_17_17, all_0_13_13) % 7.07/2.19 | % 7.07/2.19 | Instantiating formula (39) with all_33_0_28, e and discharging atoms s(e) = all_33_0_28, yields: % 7.07/2.19 | (141) mem(e, all_33_0_28) % 7.07/2.19 | % 7.07/2.19 | Instantiating formula (25) with all_0_17_17, all_33_0_28, e, e and discharging atoms u(e, all_33_0_28) = all_0_17_17, mem(e, all_33_0_28), yields: % 7.07/2.19 | (142) mem(e, all_0_17_17) % 7.07/2.19 | % 7.07/2.19 | Instantiating formula (65) with all_0_9_9, all_0_2_2, all_0_17_17, e and discharging atoms u(all_0_17_17, all_0_2_2) = all_0_9_9, mem(e, all_0_17_17), yields: % 7.07/2.19 | (143) mem(e, all_0_9_9) % 7.07/2.19 | % 7.07/2.19 | Instantiating formula (65) with all_0_10_10, all_0_16_16, all_0_17_17, e and discharging atoms u(all_0_17_17, all_0_16_16) = all_0_10_10, mem(e, all_0_17_17), yields: % 7.07/2.19 | (144) mem(e, all_0_10_10) % 7.07/2.19 | % 7.07/2.19 | Instantiating formula (65) with all_0_8_8, all_13_0_23, all_0_9_9, e and discharging atoms u(all_0_9_9, all_13_0_23) = all_0_8_8, mem(e, all_0_9_9), yields: % 7.07/2.19 | (145) mem(e, all_0_8_8) % 7.07/2.19 | % 7.07/2.19 | Instantiating formula (25) with all_0_7_7, all_0_8_8, all_0_11_11, e and discharging atoms u(all_0_11_11, all_0_8_8) = all_0_7_7, mem(e, all_0_8_8), yields: % 7.07/2.19 | (146) mem(e, all_0_7_7) % 7.07/2.19 | % 7.07/2.19 | Instantiating formula (65) with all_0_4_4, all_0_5_5, all_0_7_7, e and discharging atoms u(all_0_7_7, all_0_5_5) = all_0_4_4, mem(e, all_0_7_7), yields: % 7.07/2.19 | (147) mem(e, all_0_4_4) % 7.07/2.19 | % 7.07/2.19 | Instantiating formula (57) with e, all_0_0_0, all_0_4_4 and discharging atoms mem(e, all_0_4_4), subq(all_0_4_4, all_0_0_0), yields: % 7.07/2.19 | (148) mem(e, all_0_0_0) % 7.07/2.19 | % 7.07/2.19 | Instantiating formula (42) with all_0_0_0, all_0_1_1, all_0_3_3, e and discharging atoms u(all_0_3_3, all_0_1_1) = all_0_0_0, mem(e, all_0_0_0), yields: % 7.07/2.19 | (149) mem(e, all_0_1_1) | mem(e, all_0_3_3) % 7.07/2.19 | % 7.07/2.19 +-Applying beta-rule and splitting (149), into two cases. % 7.07/2.19 |-Branch one: % 7.07/2.19 | (150) mem(e, all_0_1_1) % 7.07/2.20 | % 7.07/2.20 | Instantiating formula (42) with all_0_1_1, all_0_5_5, all_0_2_2, e and discharging atoms u(all_0_2_2, all_0_5_5) = all_0_1_1, mem(e, all_0_1_1), yields: % 7.07/2.20 | (151) mem(e, all_0_2_2) | mem(e, all_0_5_5) % 7.07/2.20 | % 7.07/2.20 +-Applying beta-rule and splitting (151), into two cases. % 7.07/2.20 |-Branch one: % 7.07/2.20 | (152) mem(e, all_0_2_2) % 7.07/2.20 | % 7.07/2.20 | Instantiating formula (67) with all_0_2_2, all_0_10_10, e and discharging atoms s(all_0_10_10) = all_0_2_2, mem(e, all_0_2_2), yields: % 7.07/2.20 | (153) all_0_10_10 = e % 7.07/2.20 | % 7.07/2.20 | From (153) and (144) follows: % 7.07/2.20 | (154) mem(e, e) % 7.07/2.20 | % 7.07/2.20 | Instantiating formula (27) with e and discharging atoms mem(e, e), yields: % 7.07/2.20 | (155) $false % 7.07/2.20 | % 7.07/2.20 |-The branch is then unsatisfiable % 7.07/2.20 |-Branch two: % 7.07/2.20 | (156) ~ mem(e, all_0_2_2) % 7.07/2.20 | (157) mem(e, all_0_5_5) % 7.07/2.20 | % 7.07/2.20 | Instantiating formula (67) with all_0_5_5, all_0_6_6, e and discharging atoms s(all_0_6_6) = all_0_5_5, mem(e, all_0_5_5), yields: % 7.07/2.20 | (158) all_0_6_6 = e % 7.07/2.20 | % 7.07/2.20 | From (158) and (115) follows: % 7.07/2.20 | (159) mem(all_0_16_16, e) % 7.07/2.20 | % 7.07/2.20 | Instantiating formula (27) with all_0_16_16 and discharging atoms mem(all_0_16_16, e), yields: % 7.07/2.20 | (155) $false % 7.07/2.20 | % 7.07/2.20 |-The branch is then unsatisfiable % 7.07/2.20 |-Branch two: % 7.07/2.20 | (161) ~ mem(e, all_0_1_1) % 7.07/2.20 | (162) mem(e, all_0_3_3) % 7.07/2.20 | % 7.07/2.20 | Instantiating formula (42) with all_0_3_3, all_13_0_23, all_0_11_11, e and discharging atoms u(all_0_11_11, all_13_0_23) = all_0_3_3, mem(e, all_0_3_3), yields: % 7.07/2.20 | (163) mem(e, all_13_0_23) | mem(e, all_0_11_11) % 7.07/2.20 | % 7.07/2.20 +-Applying beta-rule and splitting (163), into two cases. % 7.07/2.20 |-Branch one: % 7.07/2.20 | (164) mem(e, all_13_0_23) % 7.07/2.20 | % 7.07/2.20 | Instantiating formula (67) with all_13_0_23, all_0_9_9, e and discharging atoms s(all_0_9_9) = all_13_0_23, mem(e, all_13_0_23), yields: % 7.07/2.20 | (165) all_0_9_9 = e % 7.07/2.20 | % 7.07/2.20 | From (165) and (143) follows: % 7.07/2.20 | (154) mem(e, e) % 7.07/2.20 | % 7.07/2.20 | Instantiating formula (27) with e and discharging atoms mem(e, e), yields: % 7.07/2.20 | (155) $false % 7.07/2.20 | % 7.07/2.20 |-The branch is then unsatisfiable % 7.07/2.20 |-Branch two: % 7.07/2.20 | (168) ~ mem(e, all_13_0_23) % 7.07/2.20 | (169) mem(e, all_0_11_11) % 7.07/2.20 | % 7.07/2.20 | Instantiating formula (42) with all_0_11_11, all_0_12_12, all_0_14_14, e and discharging atoms u(all_0_14_14, all_0_12_12) = all_0_11_11, mem(e, all_0_11_11), yields: % 7.07/2.20 | (170) mem(e, all_0_12_12) | mem(e, all_0_14_14) % 7.07/2.20 | % 7.07/2.20 +-Applying beta-rule and splitting (170), into two cases. % 7.07/2.20 |-Branch one: % 7.07/2.20 | (171) mem(e, all_0_12_12) % 7.07/2.20 | % 7.07/2.20 | Instantiating formula (42) with all_0_12_12, all_35_0_29, all_0_13_13, e and discharging atoms u(all_0_13_13, all_35_0_29) = all_0_12_12, mem(e, all_0_12_12), yields: % 7.07/2.20 | (172) mem(e, all_35_0_29) | mem(e, all_0_13_13) % 7.07/2.20 | % 7.07/2.20 +-Applying beta-rule and splitting (172), into two cases. % 7.07/2.20 |-Branch one: % 7.07/2.20 | (173) mem(e, all_35_0_29) % 7.07/2.20 | % 7.07/2.20 | Instantiating formula (67) with all_35_0_29, all_0_13_13, e and discharging atoms s(all_0_13_13) = all_35_0_29, mem(e, all_35_0_29), yields: % 7.07/2.20 | (174) all_0_13_13 = e % 7.07/2.20 | % 7.07/2.20 | From (174) and (140) follows: % 7.07/2.20 | (175) mem(all_0_17_17, e) % 7.07/2.20 | % 7.07/2.20 | Instantiating formula (27) with all_0_17_17 and discharging atoms mem(all_0_17_17, e), yields: % 7.07/2.20 | (155) $false % 7.07/2.20 | % 7.07/2.20 |-The branch is then unsatisfiable % 7.07/2.20 |-Branch two: % 7.07/2.20 | (177) ~ mem(e, all_35_0_29) % 7.07/2.20 | (178) mem(e, all_0_13_13) % 7.07/2.20 | % 7.07/2.20 | Instantiating formula (42) with all_0_13_13, all_0_15_15, all_0_16_16, e and discharging atoms u(all_0_16_16, all_0_15_15) = all_0_13_13, mem(e, all_0_13_13), yields: % 7.07/2.20 | (179) mem(e, all_0_15_15) | mem(e, all_0_16_16) % 7.07/2.20 | % 7.07/2.20 +-Applying beta-rule and splitting (179), into two cases. % 7.07/2.20 |-Branch one: % 7.07/2.20 | (180) mem(e, all_0_15_15) % 7.07/2.20 | % 7.07/2.20 | Instantiating formula (67) 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: % 7.07/2.20 | (181) all_0_16_16 = e % 7.07/2.20 | % 7.07/2.20 | From (181) and (87) follows: % 7.07/2.20 | (175) mem(all_0_17_17, e) % 7.07/2.20 | % 7.07/2.20 | Instantiating formula (27) with all_0_17_17 and discharging atoms mem(all_0_17_17, e), yields: % 7.07/2.20 | (155) $false % 7.07/2.20 | % 7.07/2.20 |-The branch is then unsatisfiable % 7.07/2.20 |-Branch two: % 7.07/2.20 | (184) ~ mem(e, all_0_15_15) % 7.07/2.20 | (185) mem(e, all_0_16_16) % 7.07/2.20 | % 7.07/2.20 | Instantiating formula (67) with all_0_16_16, all_0_17_17, e and discharging atoms s(all_0_17_17) = all_0_16_16, mem(e, all_0_16_16), yields: % 7.07/2.20 | (186) all_0_17_17 = e % 7.07/2.20 | % 7.07/2.20 | From (186) and (142) follows: % 7.07/2.20 | (154) mem(e, e) % 7.07/2.20 | % 7.07/2.20 | Instantiating formula (27) with e and discharging atoms mem(e, e), yields: % 7.07/2.20 | (155) $false % 7.07/2.20 | % 7.07/2.20 |-The branch is then unsatisfiable % 7.07/2.20 |-Branch two: % 7.07/2.20 | (189) ~ mem(e, all_0_12_12) % 7.07/2.20 | (190) mem(e, all_0_14_14) % 7.07/2.20 | % 7.07/2.20 | Instantiating formula (67) with all_0_14_14, all_0_15_15, e and discharging atoms s(all_0_15_15) = all_0_14_14, mem(e, all_0_14_14), yields: % 7.07/2.20 | (191) all_0_15_15 = e % 7.07/2.20 | % 7.07/2.20 | From (191) and (86) follows: % 7.07/2.20 | (159) mem(all_0_16_16, e) % 7.07/2.20 | % 7.07/2.20 | Instantiating formula (27) with all_0_16_16 and discharging atoms mem(all_0_16_16, e), yields: % 7.07/2.20 | (155) $false % 7.07/2.20 | % 7.07/2.20 |-The branch is then unsatisfiable % 7.07/2.21 % SZS output end Proof for theBenchmark % 7.07/2.21 % 7.07/2.21 1619ms %------------------------------------------------------------------------------