%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET937+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n021.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Tue Jul 19 00:23:18 EDT 2022 % Result : Theorem 21.41s 6.12s % Output : Proof 23.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET937+1 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n021.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 : 600 % 0.12/0.33 % DateTime : Sat Jul 9 21:33:51 EDT 2022 % 0.12/0.33 % CPUTime : % 0.19/0.57 ____ _ % 0.19/0.57 ___ / __ \_____(_)___ ________ __________ % 0.19/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.57 % 0.19/0.57 A Theorem Prover for First-Order Logic % 0.19/0.58 (ePrincess v.1.0) % 0.19/0.58 % 0.19/0.58 (c) Philipp Rümmer, 2009-2015 % 0.19/0.58 (c) Peter Backeman, 2014-2015 % 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.58 Bug reports to peter@backeman.se % 0.19/0.58 % 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.58 % 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.72/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.45/0.91 Prover 0: Preprocessing ... % 1.95/1.14 Prover 0: Warning: ignoring some quantifiers % 1.95/1.16 Prover 0: Constructing countermodel ... % 19.20/5.63 Prover 0: gave up % 19.20/5.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 19.28/5.66 Prover 1: Preprocessing ... % 19.67/5.74 Prover 1: Warning: ignoring some quantifiers % 19.67/5.74 Prover 1: Constructing countermodel ... % 20.61/5.93 Prover 1: gave up % 20.61/5.93 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 20.69/5.95 Prover 2: Preprocessing ... % 21.06/6.04 Prover 2: Warning: ignoring some quantifiers % 21.06/6.04 Prover 2: Constructing countermodel ... % 21.41/6.12 Prover 2: proved (187ms) % 21.41/6.12 % 21.41/6.12 No countermodel exists, formula is valid % 21.41/6.12 % SZS status Theorem for theBenchmark % 21.41/6.12 % 21.41/6.12 Generating proof ... Warning: ignoring some quantifiers % 22.75/6.42 found it (size 57) % 22.75/6.42 % 22.75/6.42 % SZS output start Proof for theBenchmark % 22.75/6.42 Assumed formulas after preprocessing and simplification: % 22.75/6.42 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ( ~ (v11 = 0) & ~ (v9 = 0) & empty(v12) = 0 & empty(v10) = v11 & empty(empty_set) = 0 & set_difference(v5, v6) = v7 & set_difference(v1, v2) = v3 & powerset(v3) = v4 & powerset(v2) = v6 & powerset(v1) = v5 & subset(v4, v8) = v9 & singleton(empty_set) = v0 & set_union2(v0, v7) = v8 & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (set_difference(v13, v14) = v15) | ~ (in(v16, v15) = v17) | ? [v18] : ((v18 = 0 & in(v16, v14) = 0) | ( ~ (v18 = 0) & in(v16, v13) = v18))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (set_difference(v13, v14) = v15) | ~ (in(v16, v14) = v17) | ? [v18] : ((v18 = 0 & in(v16, v15) = 0) | ( ~ (v18 = 0) & in(v16, v13) = v18))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (set_union2(v13, v14) = v15) | ~ (in(v16, v15) = v17) | ? [v18] : ? [v19] : ( ~ (v19 = 0) & ~ (v18 = 0) & in(v16, v14) = v19 & in(v16, v13) = v18)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (set_union2(v13, v14) = v15) | ~ (in(v16, v14) = v17) | ? [v18] : ((v18 = 0 & in(v16, v13) = 0) | ( ~ (v18 = 0) & in(v16, v15) = v18))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (set_union2(v13, v14) = v15) | ~ (in(v16, v13) = v17) | ? [v18] : ((v18 = 0 & in(v16, v14) = 0) | ( ~ (v18 = 0) & in(v16, v15) = v18))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (set_difference(v13, v14) = v15) | ~ (in(v16, v14) = v17) | ? [v18] : ((v18 = 0 & ~ (v17 = 0) & in(v16, v13) = 0) | ( ~ (v18 = 0) & in(v16, v15) = v18))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (set_difference(v13, v14) = v15) | ~ (in(v16, v13) = v17) | ? [v18] : ((v17 = 0 & ~ (v18 = 0) & in(v16, v14) = v18) | ( ~ (v18 = 0) & in(v16, v15) = v18))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v13, v14) = v15) | ~ (in(v16, v14) = v17) | ? [v18] : ((v18 = 0 & in(v16, v15) = 0) | ( ~ (v18 = 0) & ~ (v17 = 0) & in(v16, v13) = v18))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v13, v14) = v15) | ~ (in(v16, v13) = v17) | ? [v18] : ((v18 = 0 & in(v16, v15) = 0) | ( ~ (v18 = 0) & ~ (v17 = 0) & in(v16, v14) = v18))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (disjoint(v14, v15) = 0) | ~ (disjoint(v13, v15) = v16) | ? [v17] : ( ~ (v17 = 0) & subset(v13, v14) = v17)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (disjoint(v13, v15) = v16) | ~ (subset(v13, v14) = 0) | ? [v17] : ( ~ (v17 = 0) & disjoint(v14, v15) = v17)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (powerset(v13) = v14) | ~ (subset(v15, v13) = v16) | ? [v17] : ( ~ (v17 = 0) & in(v15, v14) = v17)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (powerset(v13) = v14) | ~ (in(v15, v14) = v16) | ? [v17] : ( ~ (v17 = 0) & subset(v15, v13) = v17)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (subset(v14, v15) = 0) | ~ (subset(v13, v15) = v16) | ? [v17] : ( ~ (v17 = 0) & subset(v13, v14) = v17)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (subset(v13, v15) = v16) | ~ (subset(v13, v14) = 0) | ? [v17] : ( ~ (v17 = 0) & subset(v14, v15) = v17)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (subset(v13, v14) = 0) | ~ (in(v15, v14) = v16) | ? [v17] : ( ~ (v17 = 0) & in(v15, v13) = v17)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (disjoint(v16, v15) = v14) | ~ (disjoint(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (set_difference(v16, v15) = v14) | ~ (set_difference(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (subset(v16, v15) = v14) | ~ (subset(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (set_intersection2(v16, v15) = v14) | ~ (set_intersection2(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (set_union2(v16, v15) = v14) | ~ (set_union2(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (in(v16, v15) = v14) | ~ (in(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (set_difference(v13, v14) = v15) | ~ (in(v16, v15) = 0) | ? [v17] : ( ~ (v17 = 0) & in(v16, v14) = v17 & in(v16, v13) = 0)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (set_difference(v13, v14) = v15) | ~ (in(v16, v13) = 0) | ? [v17] : ((v17 = 0 & in(v16, v15) = 0) | (v17 = 0 & in(v16, v14) = 0))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (set_union2(v13, v14) = v15) | ~ (in(v16, v15) = 0) | ? [v17] : ((v17 = 0 & in(v16, v14) = 0) | (v17 = 0 & in(v16, v13) = 0))) & ? [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v13 | ~ (set_difference(v14, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : (((v20 = 0 & in(v17, v15) = 0) | ( ~ (v19 = 0) & in(v17, v14) = v19) | ( ~ (v18 = 0) & in(v17, v13) = v18)) & ((v19 = 0 & ~ (v20 = 0) & in(v17, v15) = v20 & in(v17, v14) = 0) | (v18 = 0 & in(v17, v13) = 0)))) & ? [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v13 | ~ (set_union2(v14, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : (((v20 = 0 & in(v17, v15) = 0) | (v19 = 0 & in(v17, v14) = 0) | (v18 = 0 & in(v17, v13) = 0)) & (( ~ (v20 = 0) & ~ (v19 = 0) & in(v17, v15) = v20 & in(v17, v14) = v19) | ( ~ (v18 = 0) & in(v17, v13) = v18)))) & ! [v13] : ! [v14] : ! [v15] : (v15 = v13 | ~ (singleton(v13) = v14) | ~ (in(v15, v14) = 0)) & ! [v13] : ! [v14] : ! [v15] : (v15 = v13 | ~ (set_intersection2(v13, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & subset(v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : (v15 = empty_set | ~ (set_intersection2(v13, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & disjoint(v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (disjoint(v14, v13) = v15) | ? [v16] : ( ~ (v16 = 0) & disjoint(v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (disjoint(v13, v14) = v15) | ? [v16] : ( ~ (v16 = empty_set) & set_intersection2(v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v13, v14) = v15) | ? [v16] : ? [v17] : ( ~ (v17 = 0) & in(v16, v14) = v17 & in(v16, v13) = 0)) & ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (singleton(v13) = v14) | ~ (in(v13, v14) = v15)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (empty(v15) = v14) | ~ (empty(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (powerset(v15) = v14) | ~ (powerset(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (singleton(v15) = v14) | ~ (singleton(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (disjoint(v14, v15) = 0) | ~ (subset(v13, v14) = 0) | disjoint(v13, v15) = 0) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_difference(v13, v14) = v15) | disjoint(v15, v14) = 0) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_difference(v13, v14) = v15) | subset(v15, v13) = 0) & ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v13) = v14) | ~ (subset(v15, v13) = 0) | in(v15, v14) = 0) & ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v13) = v14) | ~ (in(v15, v14) = 0) | subset(v15, v13) = 0) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset(v14, v15) = 0) | ~ (subset(v13, v14) = 0) | subset(v13, v15) = 0) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset(v13, v14) = 0) | ~ (in(v15, v13) = 0) | in(v15, v14) = 0) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v14, v13) = v15) | set_intersection2(v13, v14) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v13, v14) = v15) | set_intersection2(v14, v13) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v14, v13) = v15) | set_union2(v13, v14) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v14, v13) = v15) | ? [v16] : ((v16 = 0 & empty(v13) = 0) | ( ~ (v16 = 0) & empty(v15) = v16))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v13, v14) = v15) | set_union2(v14, v13) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v13, v14) = v15) | ? [v16] : ((v16 = 0 & empty(v13) = 0) | ( ~ (v16 = 0) & empty(v15) = v16))) & ? [v13] : ! [v14] : ! [v15] : (v15 = v13 | ~ (powerset(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : (((v18 = 0 & subset(v16, v14) = 0) | (v17 = 0 & in(v16, v13) = 0)) & (( ~ (v18 = 0) & subset(v16, v14) = v18) | ( ~ (v17 = 0) & in(v16, v13) = v17)))) & ? [v13] : ! [v14] : ! [v15] : (v15 = v13 | ~ (singleton(v14) = v15) | ? [v16] : ? [v17] : (( ~ (v16 = v14) | ( ~ (v17 = 0) & in(v14, v13) = v17)) & (v16 = v14 | (v17 = 0 & in(v16, v13) = 0)))) & ! [v13] : ! [v14] : (v14 = v13 | ~ (set_intersection2(v13, v13) = v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ (set_union2(v13, v13) = v14)) & ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v13, v13) = v14)) & ! [v13] : ! [v14] : ( ~ (disjoint(v13, v14) = 0) | disjoint(v14, v13) = 0) & ! [v13] : ! [v14] : ( ~ (disjoint(v13, v14) = 0) | set_intersection2(v13, v14) = empty_set) & ! [v13] : ! [v14] : ( ~ (subset(v13, v14) = 0) | set_intersection2(v13, v14) = v13) & ! [v13] : ! [v14] : ( ~ (set_intersection2(v13, v14) = empty_set) | disjoint(v13, v14) = 0) & ! [v13] : ! [v14] : ( ~ (in(v14, v13) = 0) | ? [v15] : ( ~ (v15 = 0) & in(v13, v14) = v15)) & ! [v13] : ! [v14] : ( ~ (in(v13, v14) = 0) | ? [v15] : ( ~ (v15 = 0) & in(v14, v13) = v15)) & ? [v13] : ? [v14] : ? [v15] : disjoint(v14, v13) = v15 & ? [v13] : ? [v14] : ? [v15] : set_difference(v14, v13) = v15 & ? [v13] : ? [v14] : ? [v15] : subset(v14, v13) = v15 & ? [v13] : ? [v14] : ? [v15] : set_intersection2(v14, v13) = v15 & ? [v13] : ? [v14] : ? [v15] : set_union2(v14, v13) = v15 & ? [v13] : ? [v14] : ? [v15] : in(v14, v13) = v15 & ? [v13] : ? [v14] : empty(v13) = v14 & ? [v13] : ? [v14] : powerset(v13) = v14 & ? [v13] : ? [v14] : singleton(v13) = v14) % 22.75/6.46 | 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 yields: % 22.75/6.46 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & set_difference(all_0_7_7, all_0_6_6) = all_0_5_5 & set_difference(all_0_11_11, all_0_10_10) = all_0_9_9 & powerset(all_0_9_9) = all_0_8_8 & powerset(all_0_10_10) = all_0_6_6 & powerset(all_0_11_11) = all_0_7_7 & subset(all_0_8_8, all_0_4_4) = all_0_3_3 & singleton(empty_set) = all_0_12_12 & set_union2(all_0_12_12, all_0_5_5) = all_0_4_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & in(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & ~ (v4 = 0) & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v4 = 0 & ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v4 = 0 & in(v3, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ((v4 = 0 & in(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)) & ((v6 = 0 & ~ (v7 = 0) & in(v4, v2) = v7 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | (v6 = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & ~ (v6 = 0) & in(v4, v2) = v7 & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | disjoint(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | disjoint(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | subset(v2, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & subset(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v5 = 0) & subset(v3, v1) = v5) | ( ~ (v4 = 0) & in(v3, v0) = v4)))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = v1) | ( ~ (v4 = 0) & in(v1, v0) = v4)) & (v3 = v1 | (v4 = 0 & in(v3, v0) = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_intersection2(v0, v1) = v0) & ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_difference(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : empty(v0) = v1 & ? [v0] : ? [v1] : powerset(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 % 23.12/6.48 | % 23.12/6.48 | Applying alpha-rule on (1) yields: % 23.12/6.48 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 23.12/6.48 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 23.12/6.48 | (4) powerset(all_0_9_9) = all_0_8_8 % 23.12/6.48 | (5) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | (v6 = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & ~ (v6 = 0) & in(v4, v2) = v7 & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)))) % 23.12/6.48 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) % 23.12/6.48 | (7) empty(all_0_0_0) = 0 % 23.12/6.48 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v0) = v5))) % 23.12/6.48 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & in(v3, v0) = v5))) % 23.12/6.48 | (10) ~ (all_0_3_3 = 0) % 23.12/6.48 | (11) set_union2(all_0_12_12, all_0_5_5) = all_0_4_4 % 23.12/6.48 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 23.12/6.48 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) % 23.12/6.48 | (14) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = v1) | ( ~ (v4 = 0) & in(v1, v0) = v4)) & (v3 = v1 | (v4 = 0 & in(v3, v0) = 0)))) % 23.12/6.48 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v0) = v5))) % 23.12/6.48 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) % 23.12/6.48 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v2, v0) = v4)) % 23.12/6.48 | (18) ? [v0] : ? [v1] : ? [v2] : set_difference(v1, v0) = v2 % 23.12/6.48 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v4 = 0 & in(v3, v1) = 0))) % 23.12/6.49 | (20) ? [v0] : ? [v1] : powerset(v0) = v1 % 23.12/6.49 | (21) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0) % 23.12/6.49 | (22) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) % 23.12/6.49 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | subset(v2, v0) = 0) % 23.12/6.49 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0) % 23.12/6.49 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 23.12/6.49 | (26) ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2 % 23.12/6.49 | (27) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) % 23.12/6.49 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) % 23.12/6.49 | (29) ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2 % 23.12/6.49 | (30) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 23.12/6.49 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0) % 23.12/6.49 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v1, v2) = v4)) % 23.12/6.49 | (33) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) % 23.12/6.49 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) % 23.12/6.49 | (35) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 23.12/6.49 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 23.12/6.49 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 23.12/6.49 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 23.12/6.49 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 23.12/6.49 | (40) ? [v0] : ? [v1] : empty(v0) = v1 % 23.12/6.49 | (41) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 % 23.12/6.49 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 23.12/6.49 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v1) = v5))) % 23.12/6.49 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 23.12/6.49 | (45) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & subset(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v5 = 0) & subset(v3, v1) = v5) | ( ~ (v4 = 0) & in(v3, v0) = v4)))) % 23.12/6.49 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 23.12/6.49 | (47) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 23.12/6.49 | (48) set_difference(all_0_11_11, all_0_10_10) = all_0_9_9 % 23.12/6.49 | (49) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_intersection2(v0, v1) = v0) % 23.12/6.49 | (50) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) % 23.12/6.49 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 23.12/6.49 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) % 23.12/6.49 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 23.12/6.49 | (54) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 23.12/6.49 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) % 23.12/6.49 | (56) powerset(all_0_10_10) = all_0_6_6 % 23.12/6.49 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | disjoint(v0, v2) = 0) % 23.12/6.49 | (58) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 % 23.12/6.49 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 23.12/6.49 | (60) singleton(empty_set) = all_0_12_12 % 23.12/6.49 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4)) % 23.12/6.49 | (62) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 23.12/6.49 | (63) ? [v0] : ? [v1] : singleton(v0) = v1 % 23.12/6.49 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) % 23.12/6.49 | (65) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 23.12/6.50 | (66) subset(all_0_8_8, all_0_4_4) = all_0_3_3 % 23.12/6.50 | (67) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 23.12/6.50 | (68) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 23.12/6.50 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0) = 0) % 23.12/6.50 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ((v4 = 0 & in(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0))) % 23.12/6.50 | (71) empty(all_0_2_2) = all_0_1_1 % 23.12/6.50 | (72) empty(empty_set) = 0 % 23.12/6.50 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v4 = 0 & ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v2) = v5))) % 23.12/6.50 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) % 23.12/6.50 | (75) ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2 % 23.12/6.50 | (76) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)) & ((v6 = 0 & ~ (v7 = 0) & in(v4, v2) = v7 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)))) % 23.24/6.50 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 23.24/6.50 | (78) set_difference(all_0_7_7, all_0_6_6) = all_0_5_5 % 23.24/6.50 | (79) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) % 23.24/6.50 | (80) ~ (all_0_1_1 = 0) % 23.24/6.50 | (81) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | disjoint(v2, v1) = 0) % 23.24/6.50 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & ~ (v4 = 0) & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) % 23.24/6.50 | (83) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) % 23.24/6.50 | (84) powerset(all_0_11_11) = all_0_7_7 % 23.24/6.50 | % 23.24/6.50 | Instantiating formula (81) with all_0_9_9, all_0_10_10, all_0_11_11 and discharging atoms set_difference(all_0_11_11, all_0_10_10) = all_0_9_9, yields: % 23.24/6.50 | (85) disjoint(all_0_9_9, all_0_10_10) = 0 % 23.24/6.50 | % 23.24/6.50 | Instantiating formula (69) with all_0_9_9, all_0_10_10, all_0_11_11 and discharging atoms set_difference(all_0_11_11, all_0_10_10) = all_0_9_9, yields: % 23.24/6.50 | (86) subset(all_0_9_9, all_0_11_11) = 0 % 23.24/6.50 | % 23.24/6.50 | Instantiating formula (68) with all_0_3_3, all_0_4_4, all_0_8_8 and discharging atoms subset(all_0_8_8, all_0_4_4) = all_0_3_3, yields: % 23.24/6.50 | (87) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_8_8) = 0) % 23.24/6.50 | % 23.24/6.50 | Instantiating formula (37) with all_0_4_4, all_0_12_12, all_0_5_5 and discharging atoms set_union2(all_0_12_12, all_0_5_5) = all_0_4_4, yields: % 23.24/6.50 | (88) set_union2(all_0_5_5, all_0_12_12) = all_0_4_4 % 23.24/6.50 | % 23.24/6.50 +-Applying beta-rule and splitting (87), into two cases. % 23.24/6.50 |-Branch one: % 23.24/6.50 | (89) all_0_3_3 = 0 % 23.24/6.50 | % 23.24/6.50 | Equations (89) can reduce 10 to: % 23.24/6.50 | (90) $false % 23.24/6.50 | % 23.24/6.50 |-The branch is then unsatisfiable % 23.24/6.50 |-Branch two: % 23.24/6.50 | (10) ~ (all_0_3_3 = 0) % 23.24/6.50 | (92) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_8_8) = 0) % 23.24/6.50 | % 23.24/6.50 | Instantiating (92) with all_41_0_43, all_41_1_44 yields: % 23.24/6.50 | (93) ~ (all_41_0_43 = 0) & in(all_41_1_44, all_0_4_4) = all_41_0_43 & in(all_41_1_44, all_0_8_8) = 0 % 23.24/6.50 | % 23.24/6.50 | Applying alpha-rule on (93) yields: % 23.24/6.50 | (94) ~ (all_41_0_43 = 0) % 23.24/6.50 | (95) in(all_41_1_44, all_0_4_4) = all_41_0_43 % 23.24/6.50 | (96) in(all_41_1_44, all_0_8_8) = 0 % 23.24/6.50 | % 23.24/6.50 | Instantiating formula (64) with all_41_0_43, all_41_1_44, all_0_4_4, all_0_5_5, all_0_12_12 and discharging atoms set_union2(all_0_12_12, all_0_5_5) = all_0_4_4, in(all_41_1_44, all_0_4_4) = all_41_0_43, yields: % 23.24/6.50 | (97) all_41_0_43 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & in(all_41_1_44, all_0_5_5) = v1 & in(all_41_1_44, all_0_12_12) = v0) % 23.24/6.50 | % 23.24/6.50 | Instantiating formula (64) with all_41_0_43, all_41_1_44, all_0_4_4, all_0_12_12, all_0_5_5 and discharging atoms set_union2(all_0_5_5, all_0_12_12) = all_0_4_4, in(all_41_1_44, all_0_4_4) = all_41_0_43, yields: % 23.24/6.50 | (98) all_41_0_43 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & in(all_41_1_44, all_0_5_5) = v0 & in(all_41_1_44, all_0_12_12) = v1) % 23.24/6.50 | % 23.24/6.50 | Instantiating formula (23) with all_41_1_44, all_0_8_8, all_0_9_9 and discharging atoms powerset(all_0_9_9) = all_0_8_8, in(all_41_1_44, all_0_8_8) = 0, yields: % 23.24/6.50 | (99) subset(all_41_1_44, all_0_9_9) = 0 % 23.24/6.50 | % 23.24/6.50 +-Applying beta-rule and splitting (97), into two cases. % 23.24/6.50 |-Branch one: % 23.24/6.50 | (100) all_41_0_43 = 0 % 23.24/6.50 | % 23.24/6.50 | Equations (100) can reduce 94 to: % 23.24/6.50 | (90) $false % 23.24/6.50 | % 23.24/6.50 |-The branch is then unsatisfiable % 23.24/6.50 |-Branch two: % 23.24/6.50 | (94) ~ (all_41_0_43 = 0) % 23.24/6.50 | (103) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & in(all_41_1_44, all_0_5_5) = v1 & in(all_41_1_44, all_0_12_12) = v0) % 23.24/6.50 | % 23.24/6.50 | Instantiating (103) with all_57_0_48, all_57_1_49 yields: % 23.24/6.50 | (104) ~ (all_57_0_48 = 0) & ~ (all_57_1_49 = 0) & in(all_41_1_44, all_0_5_5) = all_57_0_48 & in(all_41_1_44, all_0_12_12) = all_57_1_49 % 23.24/6.50 | % 23.24/6.50 | Applying alpha-rule on (104) yields: % 23.24/6.50 | (105) ~ (all_57_0_48 = 0) % 23.24/6.50 | (106) ~ (all_57_1_49 = 0) % 23.24/6.50 | (107) in(all_41_1_44, all_0_5_5) = all_57_0_48 % 23.24/6.50 | (108) in(all_41_1_44, all_0_12_12) = all_57_1_49 % 23.24/6.50 | % 23.24/6.50 +-Applying beta-rule and splitting (98), into two cases. % 23.24/6.50 |-Branch one: % 23.24/6.50 | (100) all_41_0_43 = 0 % 23.24/6.50 | % 23.24/6.50 | Equations (100) can reduce 94 to: % 23.24/6.50 | (90) $false % 23.24/6.50 | % 23.24/6.50 |-The branch is then unsatisfiable % 23.24/6.50 |-Branch two: % 23.24/6.50 | (94) ~ (all_41_0_43 = 0) % 23.24/6.50 | (112) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & in(all_41_1_44, all_0_5_5) = v0 & in(all_41_1_44, all_0_12_12) = v1) % 23.24/6.50 | % 23.24/6.50 | Instantiating (112) with all_62_0_50, all_62_1_51 yields: % 23.24/6.50 | (113) ~ (all_62_0_50 = 0) & ~ (all_62_1_51 = 0) & in(all_41_1_44, all_0_5_5) = all_62_1_51 & in(all_41_1_44, all_0_12_12) = all_62_0_50 % 23.24/6.51 | % 23.24/6.51 | Applying alpha-rule on (113) yields: % 23.24/6.51 | (114) ~ (all_62_0_50 = 0) % 23.24/6.51 | (115) ~ (all_62_1_51 = 0) % 23.24/6.51 | (116) in(all_41_1_44, all_0_5_5) = all_62_1_51 % 23.24/6.51 | (117) in(all_41_1_44, all_0_12_12) = all_62_0_50 % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (25) with all_41_1_44, all_0_5_5, all_57_0_48, all_62_1_51 and discharging atoms in(all_41_1_44, all_0_5_5) = all_62_1_51, in(all_41_1_44, all_0_5_5) = all_57_0_48, yields: % 23.24/6.51 | (118) all_62_1_51 = all_57_0_48 % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (25) with all_41_1_44, all_0_12_12, all_57_1_49, all_62_0_50 and discharging atoms in(all_41_1_44, all_0_12_12) = all_62_0_50, in(all_41_1_44, all_0_12_12) = all_57_1_49, yields: % 23.24/6.51 | (119) all_62_0_50 = all_57_1_49 % 23.24/6.51 | % 23.24/6.51 | Equations (119) can reduce 114 to: % 23.24/6.51 | (106) ~ (all_57_1_49 = 0) % 23.24/6.51 | % 23.24/6.51 | Equations (118) can reduce 115 to: % 23.24/6.51 | (105) ~ (all_57_0_48 = 0) % 23.24/6.51 | % 23.24/6.51 | From (118) and (116) follows: % 23.24/6.51 | (107) in(all_41_1_44, all_0_5_5) = all_57_0_48 % 23.24/6.51 | % 23.24/6.51 | From (119) and (117) follows: % 23.24/6.51 | (108) in(all_41_1_44, all_0_12_12) = all_57_1_49 % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (57) with all_0_10_10, all_0_9_9, all_41_1_44 and discharging atoms disjoint(all_0_9_9, all_0_10_10) = 0, subset(all_41_1_44, all_0_9_9) = 0, yields: % 23.24/6.51 | (124) disjoint(all_41_1_44, all_0_10_10) = 0 % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (31) with all_0_11_11, all_0_9_9, all_41_1_44 and discharging atoms subset(all_41_1_44, all_0_9_9) = 0, subset(all_0_9_9, all_0_11_11) = 0, yields: % 23.24/6.51 | (125) subset(all_41_1_44, all_0_11_11) = 0 % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (8) with all_57_0_48, all_41_1_44, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms set_difference(all_0_7_7, all_0_6_6) = all_0_5_5, in(all_41_1_44, all_0_5_5) = all_57_0_48, yields: % 23.24/6.51 | (126) all_57_0_48 = 0 | ? [v0] : ((v0 = 0 & in(all_41_1_44, all_0_6_6) = 0) | ( ~ (v0 = 0) & in(all_41_1_44, all_0_7_7) = v0)) % 23.24/6.51 | % 23.24/6.51 +-Applying beta-rule and splitting (126), into two cases. % 23.24/6.51 |-Branch one: % 23.24/6.51 | (127) all_57_0_48 = 0 % 23.24/6.51 | % 23.24/6.51 | Equations (127) can reduce 105 to: % 23.24/6.51 | (90) $false % 23.24/6.51 | % 23.24/6.51 |-The branch is then unsatisfiable % 23.24/6.51 |-Branch two: % 23.24/6.51 | (105) ~ (all_57_0_48 = 0) % 23.24/6.51 | (130) ? [v0] : ((v0 = 0 & in(all_41_1_44, all_0_6_6) = 0) | ( ~ (v0 = 0) & in(all_41_1_44, all_0_7_7) = v0)) % 23.24/6.51 | % 23.24/6.51 | Instantiating (130) with all_82_0_55 yields: % 23.24/6.51 | (131) (all_82_0_55 = 0 & in(all_41_1_44, all_0_6_6) = 0) | ( ~ (all_82_0_55 = 0) & in(all_41_1_44, all_0_7_7) = all_82_0_55) % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (22) with all_0_10_10, all_41_1_44 and discharging atoms disjoint(all_41_1_44, all_0_10_10) = 0, yields: % 23.24/6.51 | (132) set_intersection2(all_41_1_44, all_0_10_10) = empty_set % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (24) with all_41_1_44, all_0_7_7, all_0_11_11 and discharging atoms powerset(all_0_11_11) = all_0_7_7, subset(all_41_1_44, all_0_11_11) = 0, yields: % 23.24/6.51 | (133) in(all_41_1_44, all_0_7_7) = 0 % 23.24/6.51 | % 23.24/6.51 +-Applying beta-rule and splitting (131), into two cases. % 23.24/6.51 |-Branch one: % 23.24/6.51 | (134) all_82_0_55 = 0 & in(all_41_1_44, all_0_6_6) = 0 % 23.24/6.51 | % 23.24/6.51 | Applying alpha-rule on (134) yields: % 23.24/6.51 | (135) all_82_0_55 = 0 % 23.24/6.51 | (136) in(all_41_1_44, all_0_6_6) = 0 % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (65) with empty_set, all_0_10_10, all_41_1_44 and discharging atoms set_intersection2(all_41_1_44, all_0_10_10) = empty_set, yields: % 23.24/6.51 | (137) all_41_1_44 = empty_set | ? [v0] : ( ~ (v0 = 0) & subset(all_41_1_44, all_0_10_10) = v0) % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (23) with all_41_1_44, all_0_6_6, all_0_10_10 and discharging atoms powerset(all_0_10_10) = all_0_6_6, in(all_41_1_44, all_0_6_6) = 0, yields: % 23.24/6.51 | (138) subset(all_41_1_44, all_0_10_10) = 0 % 23.24/6.51 | % 23.24/6.51 +-Applying beta-rule and splitting (137), into two cases. % 23.24/6.51 |-Branch one: % 23.24/6.51 | (139) all_41_1_44 = empty_set % 23.24/6.51 | % 23.24/6.51 | From (139) and (108) follows: % 23.24/6.51 | (140) in(empty_set, all_0_12_12) = all_57_1_49 % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (50) with all_57_1_49, all_0_12_12, empty_set and discharging atoms singleton(empty_set) = all_0_12_12, in(empty_set, all_0_12_12) = all_57_1_49, yields: % 23.24/6.51 | (141) all_57_1_49 = 0 % 23.24/6.51 | % 23.24/6.51 | Equations (141) can reduce 106 to: % 23.24/6.51 | (90) $false % 23.24/6.51 | % 23.24/6.51 |-The branch is then unsatisfiable % 23.24/6.51 |-Branch two: % 23.24/6.51 | (143) ~ (all_41_1_44 = empty_set) % 23.24/6.51 | (144) ? [v0] : ( ~ (v0 = 0) & subset(all_41_1_44, all_0_10_10) = v0) % 23.24/6.51 | % 23.24/6.51 | Instantiating (144) with all_114_0_59 yields: % 23.24/6.51 | (145) ~ (all_114_0_59 = 0) & subset(all_41_1_44, all_0_10_10) = all_114_0_59 % 23.24/6.51 | % 23.24/6.51 | Applying alpha-rule on (145) yields: % 23.24/6.51 | (146) ~ (all_114_0_59 = 0) % 23.24/6.51 | (147) subset(all_41_1_44, all_0_10_10) = all_114_0_59 % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (53) with all_41_1_44, all_0_10_10, 0, all_114_0_59 and discharging atoms subset(all_41_1_44, all_0_10_10) = all_114_0_59, subset(all_41_1_44, all_0_10_10) = 0, yields: % 23.24/6.51 | (148) all_114_0_59 = 0 % 23.24/6.51 | % 23.24/6.51 | Equations (148) can reduce 146 to: % 23.24/6.51 | (90) $false % 23.24/6.51 | % 23.24/6.51 |-The branch is then unsatisfiable % 23.24/6.51 |-Branch two: % 23.24/6.51 | (150) ~ (all_82_0_55 = 0) & in(all_41_1_44, all_0_7_7) = all_82_0_55 % 23.24/6.51 | % 23.24/6.51 | Applying alpha-rule on (150) yields: % 23.24/6.51 | (151) ~ (all_82_0_55 = 0) % 23.24/6.51 | (152) in(all_41_1_44, all_0_7_7) = all_82_0_55 % 23.24/6.51 | % 23.24/6.51 | Instantiating formula (25) with all_41_1_44, all_0_7_7, 0, all_82_0_55 and discharging atoms in(all_41_1_44, all_0_7_7) = all_82_0_55, in(all_41_1_44, all_0_7_7) = 0, yields: % 23.24/6.51 | (135) all_82_0_55 = 0 % 23.24/6.51 | % 23.24/6.51 | Equations (135) can reduce 151 to: % 23.24/6.51 | (90) $false % 23.24/6.51 | % 23.24/6.51 |-The branch is then unsatisfiable % 23.24/6.51 % SZS output end Proof for theBenchmark % 23.24/6.51 % 23.24/6.51 5925ms %------------------------------------------------------------------------------