%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET938+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n025.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 00:23:19 EDT 2022 % Result : Theorem 10.63s 3.32s % Output : Proof 13.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SET938+1 : TPTP v8.1.0. Released v3.2.0. % 0.13/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.35 % Computer : n025.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Sat Jul 9 17:48:30 EDT 2022 % 0.14/0.35 % CPUTime : % 0.69/0.67 ____ _ % 0.69/0.67 ___ / __ \_____(_)___ ________ __________ % 0.69/0.67 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.69/0.67 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.69/0.67 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.69/0.67 % 0.69/0.67 A Theorem Prover for First-Order Logic % 0.69/0.67 (ePrincess v.1.0) % 0.69/0.67 % 0.69/0.67 (c) Philipp Rümmer, 2009-2015 % 0.69/0.67 (c) Peter Backeman, 2014-2015 % 0.69/0.67 (contributions by Angelo Brillout, Peter Baumgartner) % 0.69/0.67 Free software under GNU Lesser General Public License (LGPL). % 0.69/0.67 Bug reports to peter@backeman.se % 0.69/0.67 % 0.69/0.67 For more information, visit http://user.uu.se/~petba168/breu/ % 0.69/0.67 % 0.69/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.72 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.46/1.01 Prover 0: Preprocessing ... % 2.01/1.20 Prover 0: Warning: ignoring some quantifiers % 2.01/1.22 Prover 0: Constructing countermodel ... % 3.60/1.64 Prover 0: gave up % 3.60/1.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.60/1.66 Prover 1: Preprocessing ... % 3.83/1.72 Prover 1: Warning: ignoring some quantifiers % 3.83/1.73 Prover 1: Constructing countermodel ... % 5.18/2.05 Prover 1: gave up % 5.18/2.05 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 5.18/2.06 Prover 2: Preprocessing ... % 5.79/2.13 Prover 2: Warning: ignoring some quantifiers % 5.79/2.14 Prover 2: Constructing countermodel ... % 10.63/3.32 Prover 2: proved (1267ms) % 10.63/3.32 % 10.63/3.32 No countermodel exists, formula is valid % 10.63/3.32 % SZS status Theorem for theBenchmark % 10.63/3.32 % 10.63/3.32 Generating proof ... Warning: ignoring some quantifiers % 13.22/3.84 found it (size 99) % 13.22/3.84 % 13.22/3.84 % SZS output start Proof for theBenchmark % 13.22/3.84 Assumed formulas after preprocessing and simplification: % 13.22/3.84 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ( ~ (v11 = 0) & ~ (v9 = 0) & empty(v12) = 0 & empty(v10) = v11 & set_difference(v1, v0) = v4 & set_difference(v0, v1) = v2 & powerset(v7) = v8 & powerset(v4) = v5 & powerset(v2) = v3 & subset(v6, v8) = v9 & symmetric_difference(v0, v1) = v7 & set_union2(v3, v5) = v6 & ! [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_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 | ~ (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(v13, v14) = 0) | ~ (in(v15, v14) = v16) | ? [v17] : ( ~ (v17 = 0) & in(v15, v13) = v17)) & ! [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 | ~ (symmetric_difference(v16, v15) = v14) | ~ (symmetric_difference(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_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_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 = 0 | ~ (subset(v13, v14) = v15) | ? [v16] : ? [v17] : ( ~ (v17 = 0) & in(v16, v14) = v17 & in(v16, v13) = 0)) & ! [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] : ( ~ (set_difference(v14, v13) = v15) | ? [v16] : ? [v17] : (set_difference(v13, v14) = v17 & symmetric_difference(v13, v14) = v16 & set_union2(v17, v15) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_difference(v13, v14) = v15) | ? [v16] : ? [v17] : (set_difference(v14, v13) = v17 & symmetric_difference(v13, v14) = v16 & set_union2(v15, v17) = v16)) & ! [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(v13, v14) = 0) | ~ (in(v15, v13) = 0) | in(v15, v14) = 0) & ! [v13] : ! [v14] : ! [v15] : ( ~ (symmetric_difference(v14, v13) = v15) | symmetric_difference(v13, v14) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (symmetric_difference(v13, v14) = v15) | symmetric_difference(v14, v13) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (symmetric_difference(v13, v14) = v15) | ? [v16] : ? [v17] : (set_difference(v14, v13) = v17 & set_difference(v13, v14) = v16 & set_union2(v16, v17) = 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] : (v14 = v13 | ~ (set_union2(v13, v13) = v14)) & ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v13, v13) = v14)) & ! [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] : set_difference(v14, v13) = v15 & ? [v13] : ? [v14] : ? [v15] : subset(v14, v13) = v15 & ? [v13] : ? [v14] : ? [v15] : symmetric_difference(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) % 13.42/3.88 | 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: % 13.42/3.88 | (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 & set_difference(all_0_11_11, all_0_12_12) = all_0_8_8 & set_difference(all_0_12_12, all_0_11_11) = all_0_10_10 & powerset(all_0_5_5) = all_0_4_4 & powerset(all_0_8_8) = all_0_7_7 & powerset(all_0_10_10) = all_0_9_9 & subset(all_0_6_6, all_0_4_4) = all_0_3_3 & symmetric_difference(all_0_12_12, all_0_11_11) = all_0_5_5 & set_union2(all_0_9_9, all_0_7_7) = all_0_6_6 & ! [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_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 | ~ (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(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [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 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(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_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_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 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [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] : ( ~ (set_difference(v1, v0) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & symmetric_difference(v0, v1) = v3 & set_union2(v4, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v1, v0) = v4 & symmetric_difference(v0, v1) = v3 & set_union2(v2, v4) = v3)) & ! [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(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v1, v0) = v4 & set_difference(v0, v1) = v3 & set_union2(v3, v4) = 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] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [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] : set_difference(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : symmetric_difference(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 % 13.42/3.89 | % 13.42/3.89 | Applying alpha-rule on (1) yields: % 13.42/3.89 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 13.42/3.90 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 13.42/3.90 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2) % 13.42/3.90 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2) % 13.42/3.90 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 13.42/3.90 | (7) powerset(all_0_8_8) = all_0_7_7 % 13.42/3.90 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0)) % 13.42/3.90 | (9) ! [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))) % 13.42/3.90 | (10) ~ (all_0_1_1 = 0) % 13.42/3.90 | (11) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 13.42/3.90 | (12) subset(all_0_6_6, all_0_4_4) = all_0_3_3 % 13.42/3.90 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v2, v0) = v4)) % 13.42/3.90 | (14) set_difference(all_0_11_11, all_0_12_12) = all_0_8_8 % 13.42/3.90 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 13.42/3.90 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 13.42/3.90 | (17) ! [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))) % 13.42/3.90 | (18) ! [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))) % 13.42/3.90 | (19) empty(all_0_2_2) = all_0_1_1 % 13.42/3.90 | (20) set_difference(all_0_12_12, all_0_11_11) = all_0_10_10 % 13.42/3.90 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 13.42/3.90 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) % 13.42/3.90 | (23) ! [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))) % 13.42/3.90 | (24) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 % 13.42/3.90 | (25) ? [v0] : ? [v1] : ? [v2] : set_difference(v1, v0) = v2 % 13.42/3.90 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v1, v0) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & symmetric_difference(v0, v1) = v3 & set_union2(v4, v2) = v3)) % 13.42/3.90 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v1, v0) = v4 & set_difference(v0, v1) = v3 & set_union2(v3, v4) = v2)) % 13.42/3.90 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 13.42/3.90 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 13.42/3.90 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v1, v0) = v4 & symmetric_difference(v0, v1) = v3 & set_union2(v2, v4) = v3)) % 13.42/3.90 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) % 13.42/3.90 | (32) powerset(all_0_5_5) = all_0_4_4 % 13.42/3.90 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 13.42/3.90 | (34) ! [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)) % 13.42/3.90 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 13.42/3.90 | (36) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 13.42/3.90 | (37) ! [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))) % 13.42/3.91 | (38) powerset(all_0_10_10) = all_0_9_9 % 13.42/3.91 | (39) ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2 % 13.42/3.91 | (40) ? [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)))) % 13.42/3.91 | (41) ? [v0] : ? [v1] : empty(v0) = v1 % 13.42/3.91 | (42) ? [v0] : ? [v1] : powerset(v0) = v1 % 13.42/3.91 | (43) ~ (all_0_3_3 = 0) % 13.42/3.91 | (44) ? [v0] : ? [v1] : ? [v2] : symmetric_difference(v1, v0) = v2 % 13.42/3.91 | (45) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 13.42/3.91 | (46) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 13.42/3.91 | (47) ? [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)))) % 13.42/3.91 | (48) set_union2(all_0_9_9, all_0_7_7) = all_0_6_6 % 13.42/3.91 | (49) symmetric_difference(all_0_12_12, all_0_11_11) = all_0_5_5 % 13.42/3.91 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | subset(v2, v0) = 0) % 13.42/3.91 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0) % 13.42/3.91 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) % 13.42/3.91 | (53) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 % 13.42/3.91 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4)) % 13.42/3.91 | (55) empty(all_0_0_0) = 0 % 13.42/3.91 | % 13.42/3.91 | Instantiating formula (26) with all_0_8_8, all_0_11_11, all_0_12_12 and discharging atoms set_difference(all_0_11_11, all_0_12_12) = all_0_8_8, yields: % 13.42/3.91 | (56) ? [v0] : ? [v1] : (set_difference(all_0_12_12, all_0_11_11) = v1 & symmetric_difference(all_0_12_12, all_0_11_11) = v0 & set_union2(v1, all_0_8_8) = v0) % 13.42/3.91 | % 13.42/3.91 | Instantiating formula (30) with all_0_8_8, all_0_12_12, all_0_11_11 and discharging atoms set_difference(all_0_11_11, all_0_12_12) = all_0_8_8, yields: % 13.42/3.91 | (57) ? [v0] : ? [v1] : (set_difference(all_0_12_12, all_0_11_11) = v1 & symmetric_difference(all_0_11_11, all_0_12_12) = v0 & set_union2(all_0_8_8, v1) = v0) % 13.42/3.91 | % 13.42/3.91 | Instantiating formula (26) with all_0_10_10, all_0_12_12, all_0_11_11 and discharging atoms set_difference(all_0_12_12, all_0_11_11) = all_0_10_10, yields: % 13.42/3.91 | (58) ? [v0] : ? [v1] : (set_difference(all_0_11_11, all_0_12_12) = v1 & symmetric_difference(all_0_11_11, all_0_12_12) = v0 & set_union2(v1, all_0_10_10) = v0) % 13.42/3.91 | % 13.42/3.91 | Instantiating formula (30) with all_0_10_10, all_0_11_11, all_0_12_12 and discharging atoms set_difference(all_0_12_12, all_0_11_11) = all_0_10_10, yields: % 13.42/3.91 | (59) ? [v0] : ? [v1] : (set_difference(all_0_11_11, all_0_12_12) = v1 & symmetric_difference(all_0_12_12, all_0_11_11) = v0 & set_union2(all_0_10_10, v1) = v0) % 13.42/3.91 | % 13.42/3.91 | Instantiating formula (3) with all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_4_4) = all_0_3_3, yields: % 13.42/3.91 | (60) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_6_6) = 0) % 13.42/3.91 | % 13.42/3.91 | Instantiating formula (5) with all_0_5_5, all_0_12_12, all_0_11_11 and discharging atoms symmetric_difference(all_0_12_12, all_0_11_11) = all_0_5_5, yields: % 13.42/3.91 | (61) symmetric_difference(all_0_11_11, all_0_12_12) = all_0_5_5 % 13.42/3.91 | % 13.42/3.91 | Instantiating formula (27) with all_0_5_5, all_0_11_11, all_0_12_12 and discharging atoms symmetric_difference(all_0_12_12, all_0_11_11) = all_0_5_5, yields: % 13.42/3.91 | (62) ? [v0] : ? [v1] : (set_difference(all_0_11_11, all_0_12_12) = v1 & set_difference(all_0_12_12, all_0_11_11) = v0 & set_union2(v0, v1) = all_0_5_5) % 13.42/3.91 | % 13.42/3.91 | Instantiating formula (29) with all_0_6_6, all_0_9_9, all_0_7_7 and discharging atoms set_union2(all_0_9_9, all_0_7_7) = all_0_6_6, yields: % 13.42/3.91 | (63) set_union2(all_0_7_7, all_0_9_9) = all_0_6_6 % 13.42/3.91 | % 13.42/3.91 | Instantiating (59) with all_27_0_34, all_27_1_35 yields: % 13.42/3.91 | (64) set_difference(all_0_11_11, all_0_12_12) = all_27_0_34 & symmetric_difference(all_0_12_12, all_0_11_11) = all_27_1_35 & set_union2(all_0_10_10, all_27_0_34) = all_27_1_35 % 13.42/3.91 | % 13.42/3.91 | Applying alpha-rule on (64) yields: % 13.42/3.91 | (65) set_difference(all_0_11_11, all_0_12_12) = all_27_0_34 % 13.42/3.91 | (66) symmetric_difference(all_0_12_12, all_0_11_11) = all_27_1_35 % 13.42/3.91 | (67) set_union2(all_0_10_10, all_27_0_34) = all_27_1_35 % 13.42/3.91 | % 13.42/3.91 | Instantiating (58) with all_29_0_36, all_29_1_37 yields: % 13.42/3.91 | (68) set_difference(all_0_11_11, all_0_12_12) = all_29_0_36 & symmetric_difference(all_0_11_11, all_0_12_12) = all_29_1_37 & set_union2(all_29_0_36, all_0_10_10) = all_29_1_37 % 13.42/3.91 | % 13.42/3.91 | Applying alpha-rule on (68) yields: % 13.42/3.91 | (69) set_difference(all_0_11_11, all_0_12_12) = all_29_0_36 % 13.42/3.91 | (70) symmetric_difference(all_0_11_11, all_0_12_12) = all_29_1_37 % 13.42/3.91 | (71) set_union2(all_29_0_36, all_0_10_10) = all_29_1_37 % 13.42/3.91 | % 13.42/3.91 | Instantiating (57) with all_31_0_38, all_31_1_39 yields: % 13.42/3.91 | (72) set_difference(all_0_12_12, all_0_11_11) = all_31_0_38 & symmetric_difference(all_0_11_11, all_0_12_12) = all_31_1_39 & set_union2(all_0_8_8, all_31_0_38) = all_31_1_39 % 13.42/3.91 | % 13.42/3.91 | Applying alpha-rule on (72) yields: % 13.42/3.91 | (73) set_difference(all_0_12_12, all_0_11_11) = all_31_0_38 % 13.42/3.91 | (74) symmetric_difference(all_0_11_11, all_0_12_12) = all_31_1_39 % 13.42/3.92 | (75) set_union2(all_0_8_8, all_31_0_38) = all_31_1_39 % 13.42/3.92 | % 13.42/3.92 | Instantiating (62) with all_33_0_40, all_33_1_41 yields: % 13.42/3.92 | (76) set_difference(all_0_11_11, all_0_12_12) = all_33_0_40 & set_difference(all_0_12_12, all_0_11_11) = all_33_1_41 & set_union2(all_33_1_41, all_33_0_40) = all_0_5_5 % 13.42/3.92 | % 13.42/3.92 | Applying alpha-rule on (76) yields: % 13.42/3.92 | (77) set_difference(all_0_11_11, all_0_12_12) = all_33_0_40 % 13.42/3.92 | (78) set_difference(all_0_12_12, all_0_11_11) = all_33_1_41 % 13.42/3.92 | (79) set_union2(all_33_1_41, all_33_0_40) = all_0_5_5 % 13.42/3.92 | % 13.42/3.92 | Instantiating (56) with all_37_0_44, all_37_1_45 yields: % 13.42/3.92 | (80) set_difference(all_0_12_12, all_0_11_11) = all_37_0_44 & symmetric_difference(all_0_12_12, all_0_11_11) = all_37_1_45 & set_union2(all_37_0_44, all_0_8_8) = all_37_1_45 % 13.42/3.92 | % 13.42/3.92 | Applying alpha-rule on (80) yields: % 13.42/3.92 | (81) set_difference(all_0_12_12, all_0_11_11) = all_37_0_44 % 13.42/3.92 | (82) symmetric_difference(all_0_12_12, all_0_11_11) = all_37_1_45 % 13.42/3.92 | (83) set_union2(all_37_0_44, all_0_8_8) = all_37_1_45 % 13.42/3.92 | % 13.42/3.92 +-Applying beta-rule and splitting (60), into two cases. % 13.42/3.92 |-Branch one: % 13.42/3.92 | (84) all_0_3_3 = 0 % 13.42/3.92 | % 13.42/3.92 | Equations (84) can reduce 43 to: % 13.42/3.92 | (85) $false % 13.42/3.92 | % 13.42/3.92 |-The branch is then unsatisfiable % 13.42/3.92 |-Branch two: % 13.42/3.92 | (43) ~ (all_0_3_3 = 0) % 13.42/3.92 | (87) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_6_6) = 0) % 13.42/3.92 | % 13.42/3.92 | Instantiating (87) with all_43_0_46, all_43_1_47 yields: % 13.42/3.92 | (88) ~ (all_43_0_46 = 0) & in(all_43_1_47, all_0_4_4) = all_43_0_46 & in(all_43_1_47, all_0_6_6) = 0 % 13.42/3.92 | % 13.42/3.92 | Applying alpha-rule on (88) yields: % 13.42/3.92 | (89) ~ (all_43_0_46 = 0) % 13.42/3.92 | (90) in(all_43_1_47, all_0_4_4) = all_43_0_46 % 13.42/3.92 | (91) in(all_43_1_47, all_0_6_6) = 0 % 13.42/3.92 | % 13.42/3.92 | Instantiating formula (15) with all_0_11_11, all_0_12_12, all_33_0_40, all_0_8_8 and discharging atoms set_difference(all_0_11_11, all_0_12_12) = all_33_0_40, set_difference(all_0_11_11, all_0_12_12) = all_0_8_8, yields: % 13.42/3.92 | (92) all_33_0_40 = all_0_8_8 % 13.42/3.92 | % 13.42/3.92 | Instantiating formula (15) with all_0_11_11, all_0_12_12, all_29_0_36, all_33_0_40 and discharging atoms set_difference(all_0_11_11, all_0_12_12) = all_33_0_40, set_difference(all_0_11_11, all_0_12_12) = all_29_0_36, yields: % 13.42/3.92 | (93) all_33_0_40 = all_29_0_36 % 13.42/3.92 | % 13.42/3.92 | Instantiating formula (15) with all_0_11_11, all_0_12_12, all_27_0_34, all_33_0_40 and discharging atoms set_difference(all_0_11_11, all_0_12_12) = all_33_0_40, set_difference(all_0_11_11, all_0_12_12) = all_27_0_34, yields: % 13.42/3.92 | (94) all_33_0_40 = all_27_0_34 % 13.42/3.92 | % 13.42/3.92 | Instantiating formula (15) with all_0_12_12, all_0_11_11, all_37_0_44, all_0_10_10 and discharging atoms set_difference(all_0_12_12, all_0_11_11) = all_37_0_44, set_difference(all_0_12_12, all_0_11_11) = all_0_10_10, yields: % 13.42/3.92 | (95) all_37_0_44 = all_0_10_10 % 13.42/3.92 | % 13.42/3.92 | Instantiating formula (15) with all_0_12_12, all_0_11_11, all_33_1_41, all_37_0_44 and discharging atoms set_difference(all_0_12_12, all_0_11_11) = all_37_0_44, set_difference(all_0_12_12, all_0_11_11) = all_33_1_41, yields: % 13.42/3.92 | (96) all_37_0_44 = all_33_1_41 % 13.42/3.92 | % 13.42/3.92 | Instantiating formula (15) with all_0_12_12, all_0_11_11, all_31_0_38, all_33_1_41 and discharging atoms set_difference(all_0_12_12, all_0_11_11) = all_33_1_41, set_difference(all_0_12_12, all_0_11_11) = all_31_0_38, yields: % 13.42/3.92 | (97) all_33_1_41 = all_31_0_38 % 13.42/3.92 | % 13.42/3.92 | Instantiating formula (8) with all_0_11_11, all_0_12_12, all_0_5_5, all_31_1_39 and discharging atoms symmetric_difference(all_0_11_11, all_0_12_12) = all_31_1_39, symmetric_difference(all_0_11_11, all_0_12_12) = all_0_5_5, yields: % 13.42/3.92 | (98) all_31_1_39 = all_0_5_5 % 13.42/3.92 | % 13.42/3.92 | Instantiating formula (8) with all_0_12_12, all_0_11_11, all_37_1_45, all_0_5_5 and discharging atoms symmetric_difference(all_0_12_12, all_0_11_11) = all_37_1_45, symmetric_difference(all_0_12_12, all_0_11_11) = all_0_5_5, yields: % 13.42/3.92 | (99) all_37_1_45 = all_0_5_5 % 13.42/3.92 | % 13.42/3.92 | Instantiating formula (8) with all_0_12_12, all_0_11_11, all_27_1_35, all_37_1_45 and discharging atoms symmetric_difference(all_0_12_12, all_0_11_11) = all_37_1_45, symmetric_difference(all_0_12_12, all_0_11_11) = all_27_1_35, yields: % 13.42/3.92 | (100) all_37_1_45 = all_27_1_35 % 13.42/3.92 | % 13.42/3.92 | Combining equations (96,95) yields a new equation: % 13.42/3.92 | (101) all_33_1_41 = all_0_10_10 % 13.42/3.92 | % 13.42/3.92 | Simplifying 101 yields: % 13.42/3.92 | (102) all_33_1_41 = all_0_10_10 % 13.42/3.92 | % 13.42/3.92 | Combining equations (100,99) yields a new equation: % 13.42/3.92 | (103) all_27_1_35 = all_0_5_5 % 13.42/3.92 | % 13.42/3.92 | Simplifying 103 yields: % 13.42/3.92 | (104) all_27_1_35 = all_0_5_5 % 13.42/3.92 | % 13.42/3.92 | Combining equations (92,93) yields a new equation: % 13.42/3.92 | (105) all_29_0_36 = all_0_8_8 % 13.42/3.92 | % 13.42/3.92 | Combining equations (94,93) yields a new equation: % 13.42/3.92 | (106) all_29_0_36 = all_27_0_34 % 13.42/3.92 | % 13.42/3.92 | Combining equations (97,102) yields a new equation: % 13.42/3.92 | (107) all_31_0_38 = all_0_10_10 % 13.42/3.92 | % 13.42/3.92 | Simplifying 107 yields: % 13.42/3.92 | (108) all_31_0_38 = all_0_10_10 % 13.42/3.92 | % 13.42/3.92 | Combining equations (106,105) yields a new equation: % 13.42/3.92 | (109) all_27_0_34 = all_0_8_8 % 13.42/3.92 | % 13.42/3.92 | Simplifying 109 yields: % 13.42/3.92 | (110) all_27_0_34 = all_0_8_8 % 13.42/3.92 | % 13.42/3.92 | From (108)(98) and (75) follows: % 13.42/3.92 | (111) set_union2(all_0_8_8, all_0_10_10) = all_0_5_5 % 13.42/3.92 | % 13.42/3.92 | From (110)(104) and (67) follows: % 13.42/3.92 | (112) set_union2(all_0_10_10, all_0_8_8) = all_0_5_5 % 13.42/3.92 | % 13.42/3.92 | Instantiating formula (13) with all_43_0_46, all_43_1_47, all_0_4_4, all_0_5_5 and discharging atoms powerset(all_0_5_5) = all_0_4_4, in(all_43_1_47, all_0_4_4) = all_43_0_46, yields: % 13.42/3.92 | (113) all_43_0_46 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_43_1_47, all_0_5_5) = v0) % 13.42/3.92 | % 13.42/3.92 | Instantiating formula (23) with all_43_1_47, all_0_6_6, all_0_9_9, all_0_7_7 and discharging atoms set_union2(all_0_7_7, all_0_9_9) = all_0_6_6, in(all_43_1_47, all_0_6_6) = 0, yields: % 13.42/3.92 | (114) ? [v0] : ((v0 = 0 & in(all_43_1_47, all_0_7_7) = 0) | (v0 = 0 & in(all_43_1_47, all_0_9_9) = 0)) % 13.42/3.92 | % 13.42/3.92 | Instantiating (114) with all_58_0_51 yields: % 13.42/3.92 | (115) (all_58_0_51 = 0 & in(all_43_1_47, all_0_7_7) = 0) | (all_58_0_51 = 0 & in(all_43_1_47, all_0_9_9) = 0) % 13.42/3.93 | % 13.42/3.93 +-Applying beta-rule and splitting (113), into two cases. % 13.42/3.93 |-Branch one: % 13.42/3.93 | (116) all_43_0_46 = 0 % 13.42/3.93 | % 13.42/3.93 | Equations (116) can reduce 89 to: % 13.42/3.93 | (85) $false % 13.42/3.93 | % 13.42/3.93 |-The branch is then unsatisfiable % 13.42/3.93 |-Branch two: % 13.42/3.93 | (89) ~ (all_43_0_46 = 0) % 13.42/3.93 | (119) ? [v0] : ( ~ (v0 = 0) & subset(all_43_1_47, all_0_5_5) = v0) % 13.42/3.93 | % 13.42/3.93 | Instantiating (119) with all_65_0_54 yields: % 13.42/3.93 | (120) ~ (all_65_0_54 = 0) & subset(all_43_1_47, all_0_5_5) = all_65_0_54 % 13.42/3.93 | % 13.42/3.93 | Applying alpha-rule on (120) yields: % 13.42/3.93 | (121) ~ (all_65_0_54 = 0) % 13.42/3.93 | (122) subset(all_43_1_47, all_0_5_5) = all_65_0_54 % 13.42/3.93 | % 13.42/3.93 | Instantiating formula (3) with all_65_0_54, all_0_5_5, all_43_1_47 and discharging atoms subset(all_43_1_47, all_0_5_5) = all_65_0_54, yields: % 13.42/3.93 | (123) all_65_0_54 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_43_1_47) = 0 & in(v0, all_0_5_5) = v1) % 13.42/3.93 | % 13.42/3.93 +-Applying beta-rule and splitting (123), into two cases. % 13.42/3.93 |-Branch one: % 13.42/3.93 | (124) all_65_0_54 = 0 % 13.42/3.93 | % 13.42/3.93 | Equations (124) can reduce 121 to: % 13.42/3.93 | (85) $false % 13.42/3.93 | % 13.42/3.93 |-The branch is then unsatisfiable % 13.42/3.93 |-Branch two: % 13.42/3.93 | (121) ~ (all_65_0_54 = 0) % 13.42/3.93 | (127) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_43_1_47) = 0 & in(v0, all_0_5_5) = v1) % 13.42/3.93 | % 13.42/3.93 | Instantiating (127) with all_78_0_55, all_78_1_56 yields: % 13.42/3.93 | (128) ~ (all_78_0_55 = 0) & in(all_78_1_56, all_43_1_47) = 0 & in(all_78_1_56, all_0_5_5) = all_78_0_55 % 13.42/3.93 | % 13.42/3.93 | Applying alpha-rule on (128) yields: % 13.42/3.93 | (129) ~ (all_78_0_55 = 0) % 13.42/3.93 | (130) in(all_78_1_56, all_43_1_47) = 0 % 13.42/3.93 | (131) in(all_78_1_56, all_0_5_5) = all_78_0_55 % 13.42/3.93 | % 13.42/3.93 | Instantiating formula (34) with all_78_0_55, all_78_1_56, all_0_5_5, all_0_10_10, all_0_8_8 and discharging atoms set_union2(all_0_8_8, all_0_10_10) = all_0_5_5, in(all_78_1_56, all_0_5_5) = all_78_0_55, yields: % 13.42/3.93 | (132) all_78_0_55 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & in(all_78_1_56, all_0_8_8) = v0 & in(all_78_1_56, all_0_10_10) = v1) % 13.42/3.93 | % 13.42/3.93 | Instantiating formula (34) with all_78_0_55, all_78_1_56, all_0_5_5, all_0_8_8, all_0_10_10 and discharging atoms set_union2(all_0_10_10, all_0_8_8) = all_0_5_5, in(all_78_1_56, all_0_5_5) = all_78_0_55, yields: % 13.42/3.93 | (133) all_78_0_55 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & in(all_78_1_56, all_0_8_8) = v1 & in(all_78_1_56, all_0_10_10) = v0) % 13.42/3.93 | % 13.42/3.93 +-Applying beta-rule and splitting (133), into two cases. % 13.42/3.93 |-Branch one: % 13.42/3.93 | (134) all_78_0_55 = 0 % 13.42/3.93 | % 13.42/3.93 | Equations (134) can reduce 129 to: % 13.42/3.93 | (85) $false % 13.42/3.93 | % 13.42/3.93 |-The branch is then unsatisfiable % 13.42/3.93 |-Branch two: % 13.42/3.93 | (129) ~ (all_78_0_55 = 0) % 13.42/3.93 | (137) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & in(all_78_1_56, all_0_8_8) = v1 & in(all_78_1_56, all_0_10_10) = v0) % 13.42/3.93 | % 13.42/3.93 | Instantiating (137) with all_91_0_58, all_91_1_59 yields: % 13.42/3.93 | (138) ~ (all_91_0_58 = 0) & ~ (all_91_1_59 = 0) & in(all_78_1_56, all_0_8_8) = all_91_0_58 & in(all_78_1_56, all_0_10_10) = all_91_1_59 % 13.42/3.93 | % 13.42/3.93 | Applying alpha-rule on (138) yields: % 13.42/3.93 | (139) ~ (all_91_0_58 = 0) % 13.42/3.93 | (140) ~ (all_91_1_59 = 0) % 13.42/3.93 | (141) in(all_78_1_56, all_0_8_8) = all_91_0_58 % 13.42/3.93 | (142) in(all_78_1_56, all_0_10_10) = all_91_1_59 % 13.42/3.93 | % 13.42/3.93 +-Applying beta-rule and splitting (132), into two cases. % 13.42/3.93 |-Branch one: % 13.42/3.93 | (134) all_78_0_55 = 0 % 13.42/3.93 | % 13.42/3.93 | Equations (134) can reduce 129 to: % 13.42/3.93 | (85) $false % 13.42/3.93 | % 13.42/3.93 |-The branch is then unsatisfiable % 13.42/3.93 |-Branch two: % 13.42/3.93 | (129) ~ (all_78_0_55 = 0) % 13.42/3.93 | (146) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & in(all_78_1_56, all_0_8_8) = v0 & in(all_78_1_56, all_0_10_10) = v1) % 13.42/3.93 | % 13.42/3.93 | Instantiating (146) with all_96_0_60, all_96_1_61 yields: % 13.42/3.93 | (147) ~ (all_96_0_60 = 0) & ~ (all_96_1_61 = 0) & in(all_78_1_56, all_0_8_8) = all_96_1_61 & in(all_78_1_56, all_0_10_10) = all_96_0_60 % 13.42/3.93 | % 13.42/3.93 | Applying alpha-rule on (147) yields: % 13.42/3.93 | (148) ~ (all_96_0_60 = 0) % 13.42/3.93 | (149) ~ (all_96_1_61 = 0) % 13.42/3.93 | (150) in(all_78_1_56, all_0_8_8) = all_96_1_61 % 13.42/3.93 | (151) in(all_78_1_56, all_0_10_10) = all_96_0_60 % 13.42/3.93 | % 13.42/3.93 | Instantiating formula (6) with all_78_1_56, all_0_8_8, all_91_0_58, all_96_1_61 and discharging atoms in(all_78_1_56, all_0_8_8) = all_96_1_61, in(all_78_1_56, all_0_8_8) = all_91_0_58, yields: % 13.42/3.93 | (152) all_96_1_61 = all_91_0_58 % 13.42/3.93 | % 13.42/3.93 | Instantiating formula (6) with all_78_1_56, all_0_10_10, all_91_1_59, all_96_0_60 and discharging atoms in(all_78_1_56, all_0_10_10) = all_96_0_60, in(all_78_1_56, all_0_10_10) = all_91_1_59, yields: % 13.42/3.93 | (153) all_96_0_60 = all_91_1_59 % 13.42/3.93 | % 13.42/3.93 | Equations (153) can reduce 148 to: % 13.42/3.93 | (140) ~ (all_91_1_59 = 0) % 13.42/3.93 | % 13.42/3.93 | Equations (152) can reduce 149 to: % 13.42/3.93 | (139) ~ (all_91_0_58 = 0) % 13.42/3.93 | % 13.42/3.93 | From (152) and (150) follows: % 13.42/3.93 | (141) in(all_78_1_56, all_0_8_8) = all_91_0_58 % 13.42/3.93 | % 13.42/3.93 | From (153) and (151) follows: % 13.42/3.93 | (142) in(all_78_1_56, all_0_10_10) = all_91_1_59 % 13.42/3.93 | % 13.42/3.93 +-Applying beta-rule and splitting (115), into two cases. % 13.42/3.93 |-Branch one: % 13.42/3.93 | (158) all_58_0_51 = 0 & in(all_43_1_47, all_0_7_7) = 0 % 13.42/3.93 | % 13.42/3.93 | Applying alpha-rule on (158) yields: % 13.42/3.93 | (159) all_58_0_51 = 0 % 13.42/3.93 | (160) in(all_43_1_47, all_0_7_7) = 0 % 13.42/3.93 | % 13.42/3.93 | Instantiating formula (50) with all_43_1_47, all_0_7_7, all_0_8_8 and discharging atoms powerset(all_0_8_8) = all_0_7_7, in(all_43_1_47, all_0_7_7) = 0, yields: % 13.42/3.93 | (161) subset(all_43_1_47, all_0_8_8) = 0 % 13.42/3.93 | % 13.42/3.93 | Instantiating formula (21) with all_78_1_56, all_0_8_8, all_43_1_47 and discharging atoms subset(all_43_1_47, all_0_8_8) = 0, in(all_78_1_56, all_43_1_47) = 0, yields: % 13.42/3.93 | (162) in(all_78_1_56, all_0_8_8) = 0 % 13.42/3.93 | % 13.42/3.93 | Instantiating formula (22) with all_91_0_58, all_78_1_56, all_0_8_8, all_43_1_47 and discharging atoms subset(all_43_1_47, all_0_8_8) = 0, in(all_78_1_56, all_0_8_8) = all_91_0_58, yields: % 13.42/3.94 | (163) all_91_0_58 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_78_1_56, all_43_1_47) = v0) % 13.42/3.94 | % 13.42/3.94 +-Applying beta-rule and splitting (163), into two cases. % 13.42/3.94 |-Branch one: % 13.42/3.94 | (164) all_91_0_58 = 0 % 13.42/3.94 | % 13.42/3.94 | Equations (164) can reduce 139 to: % 13.42/3.94 | (85) $false % 13.42/3.94 | % 13.42/3.94 |-The branch is then unsatisfiable % 13.42/3.94 |-Branch two: % 13.42/3.94 | (139) ~ (all_91_0_58 = 0) % 13.42/3.94 | (167) ? [v0] : ( ~ (v0 = 0) & in(all_78_1_56, all_43_1_47) = v0) % 13.42/3.94 | % 13.42/3.94 | Instantiating formula (6) with all_78_1_56, all_0_8_8, 0, all_91_0_58 and discharging atoms in(all_78_1_56, all_0_8_8) = all_91_0_58, in(all_78_1_56, all_0_8_8) = 0, yields: % 13.42/3.94 | (164) all_91_0_58 = 0 % 13.42/3.94 | % 13.42/3.94 | Equations (164) can reduce 139 to: % 13.42/3.94 | (85) $false % 13.42/3.94 | % 13.42/3.94 |-The branch is then unsatisfiable % 13.42/3.94 |-Branch two: % 13.42/3.94 | (170) all_58_0_51 = 0 & in(all_43_1_47, all_0_9_9) = 0 % 13.42/3.94 | % 13.42/3.94 | Applying alpha-rule on (170) yields: % 13.42/3.94 | (159) all_58_0_51 = 0 % 13.42/3.94 | (172) in(all_43_1_47, all_0_9_9) = 0 % 13.42/3.94 | % 13.42/3.94 | Instantiating formula (50) with all_43_1_47, all_0_9_9, all_0_10_10 and discharging atoms powerset(all_0_10_10) = all_0_9_9, in(all_43_1_47, all_0_9_9) = 0, yields: % 13.42/3.94 | (173) subset(all_43_1_47, all_0_10_10) = 0 % 13.42/3.94 | % 13.42/3.94 | Instantiating formula (21) with all_78_1_56, all_0_10_10, all_43_1_47 and discharging atoms subset(all_43_1_47, all_0_10_10) = 0, in(all_78_1_56, all_43_1_47) = 0, yields: % 13.42/3.94 | (174) in(all_78_1_56, all_0_10_10) = 0 % 13.42/3.94 | % 13.42/3.94 | Instantiating formula (22) with all_91_1_59, all_78_1_56, all_0_10_10, all_43_1_47 and discharging atoms subset(all_43_1_47, all_0_10_10) = 0, in(all_78_1_56, all_0_10_10) = all_91_1_59, yields: % 13.42/3.94 | (175) all_91_1_59 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_78_1_56, all_43_1_47) = v0) % 13.42/3.94 | % 13.42/3.94 +-Applying beta-rule and splitting (175), into two cases. % 13.42/3.94 |-Branch one: % 13.42/3.94 | (176) all_91_1_59 = 0 % 13.42/3.94 | % 13.42/3.94 | Equations (176) can reduce 140 to: % 13.42/3.94 | (85) $false % 13.42/3.94 | % 13.42/3.94 |-The branch is then unsatisfiable % 13.42/3.94 |-Branch two: % 13.42/3.94 | (140) ~ (all_91_1_59 = 0) % 13.42/3.94 | (167) ? [v0] : ( ~ (v0 = 0) & in(all_78_1_56, all_43_1_47) = v0) % 13.42/3.94 | % 13.42/3.94 | Instantiating formula (6) with all_78_1_56, all_0_10_10, 0, all_91_1_59 and discharging atoms in(all_78_1_56, all_0_10_10) = all_91_1_59, in(all_78_1_56, all_0_10_10) = 0, yields: % 13.42/3.94 | (176) all_91_1_59 = 0 % 13.42/3.94 | % 13.42/3.94 | Equations (176) can reduce 140 to: % 13.42/3.94 | (85) $false % 13.42/3.94 | % 13.42/3.94 |-The branch is then unsatisfiable % 13.42/3.94 % SZS output end Proof for theBenchmark % 13.42/3.94 % 13.42/3.94 3258ms %------------------------------------------------------------------------------