%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEV570+1 : TPTP v9.1.0. Released v9.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n013.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 4.35s 1.73s % Output : Proof 6.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEV570+1 : TPTP v9.1.0. Released v9.1.0. % 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n013.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 12:43:47 EDT 2025 % 0.13/0.34 % CPUTime : % 0.62/0.60 ____ _ % 0.62/0.60 ___ / __ \_____(_)___ ________ __________ % 0.62/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.62/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.62/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.62/0.60 % 0.62/0.60 A Theorem Prover for First-Order Logic % 0.62/0.60 (ePrincess v.1.0) % 0.62/0.60 % 0.62/0.60 (c) Philipp Rümmer, 2009-2015 % 0.62/0.60 (c) Peter Backeman, 2014-2015 % 0.62/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.62/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.62/0.60 Bug reports to peter@backeman.se % 0.62/0.60 % 0.62/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.62/0.60 % 0.62/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.68/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.77/1.00 Prover 0: Preprocessing ... % 2.43/1.26 Prover 0: Warning: ignoring some quantifiers % 2.43/1.29 Prover 0: Constructing countermodel ... % 4.35/1.72 Prover 0: proved (1049ms) % 4.35/1.73 % 4.35/1.73 No countermodel exists, formula is valid % 4.35/1.73 % SZS status Theorem for theBenchmark % 4.35/1.73 % 4.35/1.73 Generating proof ... Warning: ignoring some quantifiers % 6.10/2.08 found it (size 73) % 6.10/2.08 % 6.10/2.08 % SZS output start Proof for theBenchmark % 6.10/2.08 Assumed formulas after preprocessing and simplification: % 6.10/2.08 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (n(v1) = v2 & n(v0) = v6 & n(e) = v0 & a(v10, v7) = v11 & a(v3, v4) = v5 & a(v1, v6) = v7 & u(v5, v8) = v9 & u(v0, v2) = v4 & s(v7) = v8 & s(v4) = v10 & s(v2) = v3 & s(v0) = v1 & subq(v9, v11) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (a(v15, v14) = v13) | ~ (a(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (m(v15, v14) = v13) | ~ (m(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (u(v15, v14) = v13) | ~ (u(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (m(v13, v14) = v15) | ~ mem(v12, v15) | ~ mem(v12, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (m(v13, v14) = v15) | ~ mem(v12, v15) | mem(v12, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (m(v13, v14) = v15) | ~ mem(v12, v13) | mem(v12, v15) | mem(v12, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (u(v13, v14) = v15) | ~ mem(v12, v15) | mem(v12, v14) | mem(v12, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (u(v13, v14) = v15) | ~ mem(v12, v14) | mem(v12, v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (u(v13, v14) = v15) | ~ mem(v12, v13) | mem(v12, v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (u(v12, v14) = v15) | ~ (s(v13) = v14) | a(v12, v13) = v15) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (p(v14) = v13) | ~ (p(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (n(v14) = v13) | ~ (n(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (s(v14) = v13) | ~ (s(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (s(v13) = v14) | ~ mem(v12, v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (p(v13) = v14) | ~ mem(v13, v12) | atleast2p(v12) | subq(v12, v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (p(v13) = v14) | ~ mem(v12, v14) | subq(v12, v13)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (p(v13) = v14) | ~ subq(v12, v13) | mem(v12, v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (a(v12, v13) = v14) | ? [v15] : (u(v12, v15) = v14 & s(v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ disj(v12, v13) | ~ mem(v14, v13) | ~ mem(v14, v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ mem(v14, v12) | ~ subq(v12, v13) | mem(v14, v13)) & ! [v12] : ! [v13] : (v13 = v12 | ~ subq(v13, v12) | ~ subq(v12, v13)) & ! [v12] : ! [v13] : ( ~ (n(v12) = v13) | a(v12, v12) = v13) & ! [v12] : ! [v13] : ( ~ (a(v12, v12) = v13) | n(v12) = v13) & ! [v12] : ! [v13] : ( ~ (s(v12) = v13) | mem(v12, v13)) & ! [v12] : ! [v13] : ( ~ atleast15p(v13) | ~ subq(v13, v12) | atleast16p(v12) | subq(v12, v13)) & ! [v12] : ! [v13] : ( ~ atleast14p(v13) | ~ subq(v13, v12) | atleast15p(v12) | subq(v12, v13)) & ! [v12] : ! [v13] : ( ~ atleast13p(v13) | ~ subq(v13, v12) | atleast14p(v12) | subq(v12, v13)) & ! [v12] : ! [v13] : ( ~ atleast12p(v13) | ~ subq(v13, v12) | atleast13p(v12) | subq(v12, v13)) & ! [v12] : ! [v13] : ( ~ atleast11p(v13) | ~ subq(v13, v12) | atleast12p(v12) | subq(v12, v13)) & ! [v12] : ! [v13] : ( ~ atleast10p(v13) | ~ subq(v13, v12) | atleast11p(v12) | subq(v12, v13)) & ! [v12] : ! [v13] : ( ~ atleast9p(v13) | ~ subq(v13, v12) | atleast10p(v12) | subq(v12, v13)) & ! [v12] : ! [v13] : ( ~ atleast8p(v13) | ~ subq(v13, v12) | atleast9p(v12) | subq(v12, v13)) & ! [v12] : ! [v13] : ( ~ atleast7p(v13) | ~ subq(v13, v12) | atleast8p(v12) | subq(v12, v13)) & ! [v12] : ! [v13] : ( ~ atleast6p(v13) | ~ subq(v13, v12) | atleast7p(v12) | subq(v12, v13)) & ! [v12] : ! [v13] : ( ~ atleast5p(v13) | ~ subq(v13, v12) | atleast6p(v12) | subq(v12, v13)) & ! [v12] : ! [v13] : ( ~ atleast4p(v13) | ~ subq(v13, v12) | atleast5p(v12) | subq(v12, v13)) & ! [v12] : ! [v13] : ( ~ atleast3p(v13) | ~ subq(v13, v12) | atleast4p(v12) | subq(v12, v13)) & ! [v12] : ! [v13] : ( ~ atleast2p(v13) | ~ subq(v13, v12) | atleast3p(v12) | subq(v12, v13)) & ! [v12] : ( ~ atleast16p(v12) | ? [v13] : (atleast15p(v13) & subq(v13, v12) & ~ subq(v12, v13))) & ! [v12] : ( ~ atleast15p(v12) | ? [v13] : (atleast14p(v13) & subq(v13, v12) & ~ subq(v12, v13))) & ! [v12] : ( ~ atleast14p(v12) | ? [v13] : (atleast13p(v13) & subq(v13, v12) & ~ subq(v12, v13))) & ! [v12] : ( ~ atleast13p(v12) | ? [v13] : (atleast12p(v13) & subq(v13, v12) & ~ subq(v12, v13))) & ! [v12] : ( ~ atleast12p(v12) | ? [v13] : (atleast11p(v13) & subq(v13, v12) & ~ subq(v12, v13))) & ! [v12] : ( ~ atleast11p(v12) | ? [v13] : (atleast10p(v13) & subq(v13, v12) & ~ subq(v12, v13))) & ! [v12] : ( ~ atleast10p(v12) | ? [v13] : (atleast9p(v13) & subq(v13, v12) & ~ subq(v12, v13))) & ! [v12] : ( ~ atleast9p(v12) | ? [v13] : (atleast8p(v13) & subq(v13, v12) & ~ subq(v12, v13))) & ! [v12] : ( ~ atleast8p(v12) | ? [v13] : (atleast7p(v13) & subq(v13, v12) & ~ subq(v12, v13))) & ! [v12] : ( ~ atleast7p(v12) | ? [v13] : (atleast6p(v13) & subq(v13, v12) & ~ subq(v12, v13))) & ! [v12] : ( ~ atleast6p(v12) | ? [v13] : (atleast5p(v13) & subq(v13, v12) & ~ subq(v12, v13))) & ! [v12] : ( ~ atleast5p(v12) | ? [v13] : (atleast4p(v13) & subq(v13, v12) & ~ subq(v12, v13))) & ! [v12] : ( ~ atleast4p(v12) | ? [v13] : (atleast3p(v13) & subq(v13, v12) & ~ subq(v12, v13))) & ! [v12] : ( ~ atleast3p(v12) | ? [v13] : (atleast2p(v13) & subq(v13, v12) & ~ subq(v12, v13))) & ! [v12] : ( ~ atleast2p(v12) | ? [v13] : ? [v14] : (p(v13) = v14 & mem(v13, v12) & ~ subq(v12, v14))) & ! [v12] : ~ mem(v12, e) & ? [v12] : ? [v13] : (disj(v12, v13) | ? [v14] : (mem(v14, v13) & mem(v14, v12))) & ? [v12] : ? [v13] : (subq(v12, v13) | ? [v14] : (mem(v14, v12) & ~ mem(v14, v13)))) % 6.23/2.13 | 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 yields: % 6.23/2.13 | (1) n(all_0_10_10) = all_0_9_9 & n(all_0_11_11) = all_0_5_5 & n(e) = all_0_11_11 & a(all_0_1_1, all_0_4_4) = all_0_0_0 & a(all_0_8_8, all_0_7_7) = all_0_6_6 & a(all_0_10_10, all_0_5_5) = all_0_4_4 & u(all_0_6_6, all_0_3_3) = all_0_2_2 & u(all_0_11_11, all_0_9_9) = all_0_7_7 & s(all_0_4_4) = all_0_3_3 & s(all_0_7_7) = all_0_1_1 & s(all_0_9_9) = all_0_8_8 & s(all_0_11_11) = all_0_10_10 & 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))) % 6.23/2.15 | % 6.23/2.15 | Applying alpha-rule on (1) yields: % 6.23/2.15 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (p(v1) = v2) | ~ mem(v1, v0) | atleast2p(v0) | subq(v0, v2)) % 6.23/2.15 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u(v0, v2) = v3) | ~ (s(v1) = v2) | a(v0, v1) = v3) % 6.23/2.15 | (4) n(all_0_10_10) = all_0_9_9 % 6.23/2.15 | (5) ! [v0] : ! [v1] : ( ~ atleast13p(v1) | ~ subq(v1, v0) | atleast14p(v0) | subq(v0, v1)) % 6.23/2.15 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (p(v1) = v2) | ~ subq(v0, v1) | mem(v0, v2)) % 6.23/2.15 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (p(v1) = v2) | ~ mem(v0, v2) | subq(v0, v1)) % 6.23/2.15 | (8) ! [v0] : ( ~ atleast8p(v0) | ? [v1] : (atleast7p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.23/2.15 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (s(v2) = v1) | ~ (s(v2) = v0)) % 6.23/2.15 | (10) ! [v0] : ( ~ atleast5p(v0) | ? [v1] : (atleast4p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.23/2.15 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (a(v0, v1) = v2) | ? [v3] : (u(v0, v3) = v2 & s(v1) = v3)) % 6.23/2.15 | (12) ! [v0] : ! [v1] : ( ~ atleast5p(v1) | ~ subq(v1, v0) | atleast6p(v0) | subq(v0, v1)) % 6.23/2.15 | (13) ! [v0] : ! [v1] : ( ~ atleast15p(v1) | ~ subq(v1, v0) | atleast16p(v0) | subq(v0, v1)) % 6.23/2.15 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (m(v1, v2) = v3) | ~ mem(v0, v3) | ~ mem(v0, v2)) % 6.23/2.15 | (15) s(all_0_9_9) = all_0_8_8 % 6.23/2.15 | (16) ! [v0] : ( ~ atleast4p(v0) | ? [v1] : (atleast3p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.23/2.15 | (17) u(all_0_6_6, all_0_3_3) = all_0_2_2 % 6.23/2.15 | (18) ! [v0] : ! [v1] : ( ~ atleast10p(v1) | ~ subq(v1, v0) | atleast11p(v0) | subq(v0, v1)) % 6.23/2.15 | (19) ! [v0] : ( ~ atleast10p(v0) | ? [v1] : (atleast9p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.23/2.15 | (20) ! [v0] : ! [v1] : ( ~ atleast12p(v1) | ~ subq(v1, v0) | atleast13p(v0) | subq(v0, v1)) % 6.23/2.15 | (21) ! [v0] : ! [v1] : ( ~ atleast4p(v1) | ~ subq(v1, v0) | atleast5p(v0) | subq(v0, v1)) % 6.23/2.15 | (22) ! [v0] : ! [v1] : ( ~ atleast11p(v1) | ~ subq(v1, v0) | atleast12p(v0) | subq(v0, v1)) % 6.23/2.15 | (23) ! [v0] : ( ~ atleast3p(v0) | ? [v1] : (atleast2p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.23/2.15 | (24) a(all_0_10_10, all_0_5_5) = all_0_4_4 % 6.23/2.15 | (25) ! [v0] : ! [v1] : (v1 = v0 | ~ subq(v1, v0) | ~ subq(v0, v1)) % 6.23/2.15 | (26) s(all_0_4_4) = all_0_3_3 % 6.23/2.15 | (27) ! [v0] : ( ~ atleast12p(v0) | ? [v1] : (atleast11p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.23/2.15 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) % 6.23/2.15 | (29) ! [v0] : ( ~ atleast14p(v0) | ? [v1] : (atleast13p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.23/2.15 | (30) ! [v0] : ~ mem(v0, e) % 6.23/2.15 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u(v1, v2) = v3) | ~ mem(v0, v3) | mem(v0, v2) | mem(v0, v1)) % 6.23/2.15 | (32) ! [v0] : ! [v1] : ( ~ atleast14p(v1) | ~ subq(v1, v0) | atleast15p(v0) | subq(v0, v1)) % 6.23/2.15 | (33) ! [v0] : ! [v1] : ( ~ atleast8p(v1) | ~ subq(v1, v0) | atleast9p(v0) | subq(v0, v1)) % 6.23/2.15 | (34) ? [v0] : ? [v1] : (subq(v0, v1) | ? [v2] : (mem(v2, v0) & ~ mem(v2, v1))) % 6.23/2.16 | (35) ! [v0] : ( ~ atleast16p(v0) | ? [v1] : (atleast15p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.23/2.16 | (36) a(all_0_1_1, all_0_4_4) = all_0_0_0 % 6.23/2.16 | (37) ! [v0] : ( ~ atleast2p(v0) | ? [v1] : ? [v2] : (p(v1) = v2 & mem(v1, v0) & ~ subq(v0, v2))) % 6.23/2.16 | (38) ! [v0] : ( ~ atleast6p(v0) | ? [v1] : (atleast5p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.23/2.16 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (m(v3, v2) = v1) | ~ (m(v3, v2) = v0)) % 6.23/2.16 | (40) n(all_0_11_11) = all_0_5_5 % 6.23/2.16 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u(v1, v2) = v3) | ~ mem(v0, v2) | mem(v0, v3)) % 6.23/2.16 | (42) ! [v0] : ! [v1] : ( ~ atleast9p(v1) | ~ subq(v1, v0) | atleast10p(v0) | subq(v0, v1)) % 6.23/2.16 | (43) ! [v0] : ! [v1] : ( ~ (s(v0) = v1) | mem(v0, v1)) % 6.23/2.16 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (m(v1, v2) = v3) | ~ mem(v0, v3) | mem(v0, v1)) % 6.23/2.16 | (45) ! [v0] : ( ~ atleast15p(v0) | ? [v1] : (atleast14p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.23/2.16 | (46) u(all_0_11_11, all_0_9_9) = all_0_7_7 % 6.23/2.16 | (47) ! [v0] : ! [v1] : ( ~ atleast3p(v1) | ~ subq(v1, v0) | atleast4p(v0) | subq(v0, v1)) % 6.23/2.16 | (48) ! [v0] : ( ~ atleast9p(v0) | ? [v1] : (atleast8p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.23/2.16 | (49) s(all_0_7_7) = all_0_1_1 % 6.23/2.16 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (u(v3, v2) = v1) | ~ (u(v3, v2) = v0)) % 6.23/2.16 | (51) subq(all_0_2_2, all_0_0_0) % 6.23/2.16 | (52) ! [v0] : ( ~ atleast7p(v0) | ? [v1] : (atleast6p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.23/2.16 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (a(v3, v2) = v1) | ~ (a(v3, v2) = v0)) % 6.23/2.16 | (54) ! [v0] : ( ~ atleast13p(v0) | ? [v1] : (atleast12p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.23/2.16 | (55) ! [v0] : ! [v1] : ( ~ atleast6p(v1) | ~ subq(v1, v0) | atleast7p(v0) | subq(v0, v1)) % 6.23/2.16 | (56) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (s(v1) = v2) | ~ mem(v0, v2)) % 6.23/2.16 | (57) ? [v0] : ? [v1] : (disj(v0, v1) | ? [v2] : (mem(v2, v1) & mem(v2, v0))) % 6.23/2.16 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (m(v1, v2) = v3) | ~ mem(v0, v1) | mem(v0, v3) | mem(v0, v2)) % 6.23/2.16 | (59) s(all_0_11_11) = all_0_10_10 % 6.23/2.16 | (60) ! [v0] : ( ~ atleast11p(v0) | ? [v1] : (atleast10p(v1) & subq(v1, v0) & ~ subq(v0, v1))) % 6.23/2.16 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ disj(v0, v1) | ~ mem(v2, v1) | ~ mem(v2, v0)) % 6.23/2.16 | (62) ! [v0] : ! [v1] : ( ~ (a(v0, v0) = v1) | n(v0) = v1) % 6.23/2.16 | (63) ! [v0] : ! [v1] : ( ~ (n(v0) = v1) | a(v0, v0) = v1) % 6.23/2.16 | (64) ! [v0] : ! [v1] : ( ~ atleast7p(v1) | ~ subq(v1, v0) | atleast8p(v0) | subq(v0, v1)) % 6.23/2.16 | (65) a(all_0_8_8, all_0_7_7) = all_0_6_6 % 6.23/2.16 | (66) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (n(v2) = v1) | ~ (n(v2) = v0)) % 6.23/2.17 | (67) n(e) = all_0_11_11 % 6.23/2.17 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (u(v1, v2) = v3) | ~ mem(v0, v1) | mem(v0, v3)) % 6.23/2.17 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ mem(v2, v0) | ~ subq(v0, v1) | mem(v2, v1)) % 6.23/2.17 | (70) ! [v0] : ! [v1] : ( ~ atleast2p(v1) | ~ subq(v1, v0) | atleast3p(v0) | subq(v0, v1)) % 6.23/2.17 | % 6.23/2.17 | Instantiating formula (63) with all_0_9_9, all_0_10_10 and discharging atoms n(all_0_10_10) = all_0_9_9, yields: % 6.23/2.17 | (71) a(all_0_10_10, all_0_10_10) = all_0_9_9 % 6.23/2.17 | % 6.23/2.17 | Instantiating formula (63) with all_0_5_5, all_0_11_11 and discharging atoms n(all_0_11_11) = all_0_5_5, yields: % 6.23/2.17 | (72) a(all_0_11_11, all_0_11_11) = all_0_5_5 % 6.23/2.17 | % 6.23/2.17 | Instantiating formula (63) with all_0_11_11, e and discharging atoms n(e) = all_0_11_11, yields: % 6.23/2.17 | (73) a(e, e) = all_0_11_11 % 6.23/2.17 | % 6.23/2.17 | Instantiating formula (11) with all_0_0_0, all_0_4_4, all_0_1_1 and discharging atoms a(all_0_1_1, all_0_4_4) = all_0_0_0, yields: % 6.23/2.17 | (74) ? [v0] : (u(all_0_1_1, v0) = all_0_0_0 & s(all_0_4_4) = v0) % 6.23/2.17 | % 6.23/2.17 | Instantiating formula (11) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms a(all_0_8_8, all_0_7_7) = all_0_6_6, yields: % 6.23/2.17 | (75) ? [v0] : (u(all_0_8_8, v0) = all_0_6_6 & s(all_0_7_7) = v0) % 6.23/2.17 | % 6.23/2.17 | Instantiating formula (11) with all_0_4_4, all_0_5_5, all_0_10_10 and discharging atoms a(all_0_10_10, all_0_5_5) = all_0_4_4, yields: % 6.23/2.17 | (76) ? [v0] : (u(all_0_10_10, v0) = all_0_4_4 & s(all_0_5_5) = v0) % 6.23/2.17 | % 6.23/2.17 | Instantiating formula (43) with all_0_8_8, all_0_9_9 and discharging atoms s(all_0_9_9) = all_0_8_8, yields: % 6.23/2.17 | (77) mem(all_0_9_9, all_0_8_8) % 6.23/2.17 | % 6.23/2.17 | Instantiating formula (43) with all_0_10_10, all_0_11_11 and discharging atoms s(all_0_11_11) = all_0_10_10, yields: % 6.23/2.17 | (78) mem(all_0_11_11, all_0_10_10) % 6.23/2.17 | % 6.23/2.17 | Instantiating (76) with all_11_0_16 yields: % 6.23/2.17 | (79) u(all_0_10_10, all_11_0_16) = all_0_4_4 & s(all_0_5_5) = all_11_0_16 % 6.23/2.17 | % 6.23/2.17 | Applying alpha-rule on (79) yields: % 6.23/2.17 | (80) u(all_0_10_10, all_11_0_16) = all_0_4_4 % 6.23/2.17 | (81) s(all_0_5_5) = all_11_0_16 % 6.23/2.17 | % 6.23/2.17 | Instantiating (75) with all_13_0_17 yields: % 6.23/2.17 | (82) u(all_0_8_8, all_13_0_17) = all_0_6_6 & s(all_0_7_7) = all_13_0_17 % 6.23/2.17 | % 6.23/2.17 | Applying alpha-rule on (82) yields: % 6.23/2.17 | (83) u(all_0_8_8, all_13_0_17) = all_0_6_6 % 6.23/2.17 | (84) s(all_0_7_7) = all_13_0_17 % 6.23/2.17 | % 6.23/2.17 | Instantiating (74) with all_15_0_18 yields: % 6.23/2.17 | (85) u(all_0_1_1, all_15_0_18) = all_0_0_0 & s(all_0_4_4) = all_15_0_18 % 6.23/2.17 | % 6.23/2.17 | Applying alpha-rule on (85) yields: % 6.23/2.17 | (86) u(all_0_1_1, all_15_0_18) = all_0_0_0 % 6.23/2.17 | (87) s(all_0_4_4) = all_15_0_18 % 6.23/2.17 | % 6.23/2.17 | Instantiating formula (9) with all_0_4_4, all_15_0_18, all_0_3_3 and discharging atoms s(all_0_4_4) = all_15_0_18, s(all_0_4_4) = all_0_3_3, yields: % 6.23/2.17 | (88) all_15_0_18 = all_0_3_3 % 6.23/2.17 | % 6.23/2.17 | Instantiating formula (9) with all_0_7_7, all_13_0_17, all_0_1_1 and discharging atoms s(all_0_7_7) = all_13_0_17, s(all_0_7_7) = all_0_1_1, yields: % 6.23/2.17 | (89) all_13_0_17 = all_0_1_1 % 6.23/2.17 | % 6.23/2.17 | From (88) and (86) follows: % 6.23/2.17 | (90) u(all_0_1_1, all_0_3_3) = all_0_0_0 % 6.23/2.18 | % 6.23/2.18 | From (89) and (83) follows: % 6.23/2.18 | (91) u(all_0_8_8, all_0_1_1) = all_0_6_6 % 6.23/2.18 | % 6.23/2.18 | From (88) and (87) follows: % 6.23/2.18 | (26) s(all_0_4_4) = all_0_3_3 % 6.23/2.18 | % 6.23/2.18 | From (89) and (84) follows: % 6.23/2.18 | (49) s(all_0_7_7) = all_0_1_1 % 6.23/2.18 | % 6.23/2.18 | Instantiating formula (11) with all_0_9_9, all_0_10_10, all_0_10_10 and discharging atoms a(all_0_10_10, all_0_10_10) = all_0_9_9, yields: % 6.23/2.18 | (94) ? [v0] : (u(all_0_10_10, v0) = all_0_9_9 & s(all_0_10_10) = v0) % 6.23/2.18 | % 6.23/2.18 | Instantiating formula (11) with all_0_5_5, all_0_11_11, all_0_11_11 and discharging atoms a(all_0_11_11, all_0_11_11) = all_0_5_5, yields: % 6.23/2.18 | (95) ? [v0] : (u(all_0_11_11, v0) = all_0_5_5 & s(all_0_11_11) = v0) % 6.23/2.18 | % 6.23/2.18 | Instantiating formula (11) with all_0_11_11, e, e and discharging atoms a(e, e) = all_0_11_11, yields: % 6.23/2.18 | (96) ? [v0] : (u(e, v0) = all_0_11_11 & s(e) = v0) % 6.23/2.18 | % 6.23/2.18 | Instantiating formula (68) with all_0_6_6, all_0_1_1, all_0_8_8, all_0_9_9 and discharging atoms u(all_0_8_8, all_0_1_1) = all_0_6_6, mem(all_0_9_9, all_0_8_8), yields: % 6.23/2.18 | (97) mem(all_0_9_9, all_0_6_6) % 6.23/2.18 | % 6.23/2.18 | Instantiating (95) with all_27_0_19 yields: % 6.23/2.18 | (98) u(all_0_11_11, all_27_0_19) = all_0_5_5 & s(all_0_11_11) = all_27_0_19 % 6.23/2.18 | % 6.23/2.18 | Applying alpha-rule on (98) yields: % 6.23/2.18 | (99) u(all_0_11_11, all_27_0_19) = all_0_5_5 % 6.23/2.18 | (100) s(all_0_11_11) = all_27_0_19 % 6.23/2.18 | % 6.23/2.18 | Instantiating (94) with all_29_0_20 yields: % 6.23/2.18 | (101) u(all_0_10_10, all_29_0_20) = all_0_9_9 & s(all_0_10_10) = all_29_0_20 % 6.23/2.18 | % 6.23/2.18 | Applying alpha-rule on (101) yields: % 6.23/2.18 | (102) u(all_0_10_10, all_29_0_20) = all_0_9_9 % 6.23/2.18 | (103) s(all_0_10_10) = all_29_0_20 % 6.23/2.18 | % 6.23/2.18 | Instantiating (96) with all_31_0_21 yields: % 6.23/2.18 | (104) u(e, all_31_0_21) = all_0_11_11 & s(e) = all_31_0_21 % 6.23/2.18 | % 6.23/2.18 | Applying alpha-rule on (104) yields: % 6.23/2.18 | (105) u(e, all_31_0_21) = all_0_11_11 % 6.23/2.18 | (106) s(e) = all_31_0_21 % 6.23/2.18 | % 6.23/2.18 | Instantiating formula (9) with all_0_11_11, all_27_0_19, all_0_10_10 and discharging atoms s(all_0_11_11) = all_27_0_19, s(all_0_11_11) = all_0_10_10, yields: % 6.23/2.18 | (107) all_27_0_19 = all_0_10_10 % 6.23/2.18 | % 6.23/2.18 | From (107) and (99) follows: % 6.23/2.18 | (108) u(all_0_11_11, all_0_10_10) = all_0_5_5 % 6.23/2.18 | % 6.23/2.18 | From (107) and (100) follows: % 6.23/2.18 | (59) s(all_0_11_11) = all_0_10_10 % 6.23/2.18 | % 6.23/2.18 | Instantiating formula (43) with all_29_0_20, all_0_10_10 and discharging atoms s(all_0_10_10) = all_29_0_20, yields: % 6.23/2.18 | (110) mem(all_0_10_10, all_29_0_20) % 6.23/2.18 | % 6.23/2.18 | Instantiating formula (43) with all_31_0_21, e and discharging atoms s(e) = all_31_0_21, yields: % 6.23/2.18 | (111) mem(e, all_31_0_21) % 6.23/2.18 | % 6.23/2.18 | Instantiating formula (68) with all_0_2_2, all_0_3_3, all_0_6_6, all_0_9_9 and discharging atoms u(all_0_6_6, all_0_3_3) = all_0_2_2, mem(all_0_9_9, all_0_6_6), yields: % 6.23/2.18 | (112) mem(all_0_9_9, all_0_2_2) % 6.23/2.18 | % 6.23/2.18 | Instantiating formula (69) with all_0_9_9, all_0_0_0, all_0_2_2 and discharging atoms mem(all_0_9_9, all_0_2_2), subq(all_0_2_2, all_0_0_0), yields: % 6.23/2.18 | (113) mem(all_0_9_9, all_0_0_0) % 6.23/2.18 | % 6.23/2.18 | Instantiating formula (41) with all_0_9_9, all_29_0_20, all_0_10_10, all_0_10_10 and discharging atoms u(all_0_10_10, all_29_0_20) = all_0_9_9, mem(all_0_10_10, all_29_0_20), yields: % 6.23/2.18 | (114) mem(all_0_10_10, all_0_9_9) % 6.23/2.18 | % 6.23/2.18 | Instantiating formula (41) with all_0_11_11, all_31_0_21, e, e and discharging atoms u(e, all_31_0_21) = all_0_11_11, mem(e, all_31_0_21), yields: % 6.23/2.19 | (115) mem(e, all_0_11_11) % 6.23/2.19 | % 6.23/2.19 | Instantiating formula (31) with all_0_0_0, all_0_3_3, all_0_1_1, all_0_9_9 and discharging atoms u(all_0_1_1, all_0_3_3) = all_0_0_0, mem(all_0_9_9, all_0_0_0), yields: % 6.23/2.19 | (116) mem(all_0_9_9, all_0_1_1) | mem(all_0_9_9, all_0_3_3) % 6.23/2.19 | % 6.23/2.19 | Instantiating formula (68) with all_0_7_7, all_0_9_9, all_0_11_11, e and discharging atoms u(all_0_11_11, all_0_9_9) = all_0_7_7, mem(e, all_0_11_11), yields: % 6.23/2.19 | (117) mem(e, all_0_7_7) % 6.23/2.19 | % 6.23/2.19 | Instantiating formula (68) with all_0_5_5, all_0_10_10, all_0_11_11, e and discharging atoms u(all_0_11_11, all_0_10_10) = all_0_5_5, mem(e, all_0_11_11), yields: % 6.23/2.19 | (118) mem(e, all_0_5_5) % 6.23/2.19 | % 6.23/2.19 +-Applying beta-rule and splitting (116), into two cases. % 6.23/2.19 |-Branch one: % 6.23/2.19 | (119) mem(all_0_9_9, all_0_1_1) % 6.23/2.19 | % 6.23/2.19 | Instantiating formula (56) with all_0_1_1, all_0_7_7, all_0_9_9 and discharging atoms s(all_0_7_7) = all_0_1_1, mem(all_0_9_9, all_0_1_1), yields: % 6.23/2.19 | (120) all_0_7_7 = all_0_9_9 % 6.23/2.19 | % 6.23/2.19 | From (120) and (117) follows: % 6.23/2.19 | (121) mem(e, all_0_9_9) % 6.23/2.19 | % 6.23/2.19 | Instantiating formula (31) with all_0_9_9, all_29_0_20, all_0_10_10, e and discharging atoms u(all_0_10_10, all_29_0_20) = all_0_9_9, mem(e, all_0_9_9), yields: % 6.23/2.19 | (122) mem(e, all_29_0_20) | mem(e, all_0_10_10) % 6.23/2.19 | % 6.23/2.19 +-Applying beta-rule and splitting (122), into two cases. % 6.23/2.19 |-Branch one: % 6.23/2.19 | (123) mem(e, all_29_0_20) % 6.23/2.19 | % 6.23/2.19 | Instantiating formula (56) with all_29_0_20, all_0_10_10, e and discharging atoms s(all_0_10_10) = all_29_0_20, mem(e, all_29_0_20), yields: % 6.23/2.19 | (124) all_0_10_10 = e % 6.23/2.19 | % 6.23/2.19 | From (124) and (78) follows: % 6.23/2.19 | (125) mem(all_0_11_11, e) % 6.23/2.19 | % 6.23/2.19 | Instantiating formula (30) with all_0_11_11 and discharging atoms mem(all_0_11_11, e), yields: % 6.23/2.19 | (126) $false % 6.23/2.19 | % 6.23/2.19 |-The branch is then unsatisfiable % 6.23/2.19 |-Branch two: % 6.23/2.19 | (127) ~ mem(e, all_29_0_20) % 6.23/2.19 | (128) mem(e, all_0_10_10) % 6.23/2.19 | % 6.23/2.19 | Instantiating formula (56) with all_0_10_10, all_0_11_11, e and discharging atoms s(all_0_11_11) = all_0_10_10, mem(e, all_0_10_10), yields: % 6.23/2.19 | (129) all_0_11_11 = e % 6.23/2.19 | % 6.23/2.19 | From (129) and (115) follows: % 6.23/2.19 | (130) mem(e, e) % 6.23/2.19 | % 6.23/2.19 | Instantiating formula (30) with e and discharging atoms mem(e, e), yields: % 6.23/2.19 | (126) $false % 6.23/2.19 | % 6.23/2.19 |-The branch is then unsatisfiable % 6.23/2.19 |-Branch two: % 6.23/2.19 | (132) ~ mem(all_0_9_9, all_0_1_1) % 6.23/2.19 | (133) mem(all_0_9_9, all_0_3_3) % 6.23/2.19 | % 6.23/2.19 | Instantiating formula (56) with all_0_3_3, all_0_4_4, all_0_9_9 and discharging atoms s(all_0_4_4) = all_0_3_3, mem(all_0_9_9, all_0_3_3), yields: % 6.23/2.19 | (134) all_0_4_4 = all_0_9_9 % 6.23/2.19 | % 6.23/2.19 | From (134) and (80) follows: % 6.23/2.19 | (135) u(all_0_10_10, all_11_0_16) = all_0_9_9 % 6.23/2.19 | % 6.23/2.19 | Instantiating formula (31) with all_0_9_9, all_11_0_16, all_0_10_10, all_0_10_10 and discharging atoms u(all_0_10_10, all_11_0_16) = all_0_9_9, mem(all_0_10_10, all_0_9_9), yields: % 6.23/2.19 | (136) mem(all_0_10_10, all_11_0_16) | mem(all_0_10_10, all_0_10_10) % 6.23/2.19 | % 6.23/2.19 +-Applying beta-rule and splitting (136), into two cases. % 6.23/2.19 |-Branch one: % 6.23/2.19 | (137) mem(all_0_10_10, all_11_0_16) % 6.23/2.19 | % 6.23/2.19 | Instantiating formula (56) with all_11_0_16, all_0_5_5, all_0_10_10 and discharging atoms s(all_0_5_5) = all_11_0_16, mem(all_0_10_10, all_11_0_16), yields: % 6.23/2.19 | (138) all_0_5_5 = all_0_10_10 % 6.23/2.19 | % 6.23/2.19 | From (138) and (118) follows: % 6.23/2.19 | (128) mem(e, all_0_10_10) % 6.23/2.19 | % 6.23/2.19 | Instantiating formula (56) with all_0_10_10, all_0_11_11, e and discharging atoms s(all_0_11_11) = all_0_10_10, mem(e, all_0_10_10), yields: % 6.23/2.19 | (129) all_0_11_11 = e % 6.23/2.19 | % 6.23/2.19 | From (129) and (115) follows: % 6.23/2.19 | (130) mem(e, e) % 6.23/2.19 | % 6.23/2.19 | Instantiating formula (30) with e and discharging atoms mem(e, e), yields: % 6.23/2.19 | (126) $false % 6.23/2.19 | % 6.23/2.19 |-The branch is then unsatisfiable % 6.23/2.19 |-Branch two: % 6.23/2.19 | (143) ~ mem(all_0_10_10, all_11_0_16) % 6.23/2.19 | (144) mem(all_0_10_10, all_0_10_10) % 6.23/2.19 | % 6.23/2.19 | Instantiating formula (56) with all_0_10_10, all_0_11_11, all_0_10_10 and discharging atoms s(all_0_11_11) = all_0_10_10, mem(all_0_10_10, all_0_10_10), yields: % 6.23/2.19 | (145) all_0_10_10 = all_0_11_11 % 6.23/2.19 | % 6.23/2.19 | From (145) and (59) follows: % 6.23/2.19 | (146) s(all_0_11_11) = all_0_11_11 % 6.23/2.19 | % 6.23/2.19 | Instantiating formula (56) with all_0_11_11, all_0_11_11, e and discharging atoms s(all_0_11_11) = all_0_11_11, mem(e, all_0_11_11), yields: % 6.23/2.19 | (129) all_0_11_11 = e % 6.23/2.19 | % 6.23/2.19 | From (129) and (115) follows: % 6.23/2.19 | (130) mem(e, e) % 6.23/2.19 | % 6.23/2.19 | Instantiating formula (30) with e and discharging atoms mem(e, e), yields: % 6.23/2.19 | (126) $false % 6.23/2.19 | % 6.23/2.19 |-The branch is then unsatisfiable % 6.23/2.19 % SZS output end Proof for theBenchmark % 6.23/2.20 % 6.23/2.20 1576ms %------------------------------------------------------------------------------