%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : NUM534+2 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n004.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 : Mon Jul 18 08:45:35 EDT 2022 % Result : Theorem 6.01s 2.07s % Output : Proof 9.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM534+2 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n004.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 : Thu Jul 7 06:41:37 EDT 2022 % 0.12/0.33 % CPUTime : % 0.19/0.59 ____ _ % 0.19/0.59 ___ / __ \_____(_)___ ________ __________ % 0.19/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic % 0.19/0.59 (ePrincess v.1.0) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2015 % 0.19/0.59 (c) Peter Backeman, 2014-2015 % 0.19/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.59 Bug reports to peter@backeman.se % 0.19/0.59 % 0.19/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.63/0.93 Prover 0: Preprocessing ... % 2.31/1.18 Prover 0: Constructing countermodel ... % 6.01/2.07 Prover 0: proved (1432ms) % 6.01/2.07 % 6.01/2.07 No countermodel exists, formula is valid % 6.01/2.07 % SZS status Theorem for theBenchmark % 6.01/2.07 % 6.01/2.07 Generating proof ... found it (size 109) % 8.96/2.79 % 8.96/2.79 % SZS output start Proof for theBenchmark % 8.96/2.79 Assumed formulas after preprocessing and simplification: % 8.96/2.79 | (0) ? [v0] : ? [v1] : ( ~ (v1 = xS) & sdtmndt0(xS, xx) = v0 & sdtpldt0(v0, xx) = v1 & isFinite0(slcrc0) & aElementOf0(xx, xS) & aSet0(v1) & aSet0(v0) & aSet0(xS) & aSet0(slcrc0) & ~ isCountable0(slcrc0) & ~ aElementOf0(xx, v0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtmndt0(v2, v3) = v4) | ~ aElement0(v3) | ~ aSet0(v5) | ~ aSet0(v2) | ? [v6] : ((v6 = v3 | ~ aElementOf0(v6, v5) | ~ aElementOf0(v6, v2) | ~ aElement0(v6)) & (aElementOf0(v6, v5) | ( ~ (v6 = v3) & aElementOf0(v6, v2) & aElement0(v6))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (sdtpldt0(v2, v3) = v4) | ~ aElement0(v3) | ~ aSet0(v5) | ~ aSet0(v2) | ? [v6] : (( ~ aElementOf0(v6, v5) | ~ aElement0(v6) | ( ~ (v6 = v3) & ~ aElementOf0(v6, v2))) & (aElementOf0(v6, v5) | (aElement0(v6) & (v6 = v3 | aElementOf0(v6, v2)))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (sdtmndt0(v2, v3) = v4) | ~ aElementOf0(v5, v2) | ~ aElement0(v5) | ~ aElement0(v3) | ~ aSet0(v2) | aElementOf0(v5, v4)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (sdtpldt0(v2, v3) = v4) | ~ aElementOf0(v5, v4) | ~ aElement0(v3) | ~ aSet0(v2) | aElementOf0(v5, v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sdtmndt0(v5, v4) = v3) | ~ (sdtmndt0(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sdtpldt0(v5, v4) = v3) | ~ (sdtpldt0(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtmndt0(v2, v3) = v4) | ~ aElementOf0(v5, v4) | ~ aElement0(v3) | ~ aSet0(v2) | aElementOf0(v5, v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtmndt0(v2, v3) = v4) | ~ aElementOf0(v5, v4) | ~ aElement0(v3) | ~ aSet0(v2) | aElement0(v5)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtpldt0(v2, v3) = v4) | ~ aElementOf0(v5, v4) | ~ aElement0(v3) | ~ aSet0(v2) | aElement0(v5)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtpldt0(v2, v3) = v4) | ~ aElementOf0(v5, v2) | ~ aElement0(v5) | ~ aElement0(v3) | ~ aSet0(v2) | aElementOf0(v5, v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtmndt0(v2, v3) = v4) | ~ aElementOf0(v3, v4) | ~ aElement0(v3) | ~ aSet0(v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtmndt0(v2, v3) = v4) | ~ aElement0(v3) | ~ aSet0(v2) | aSet0(v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v2, v3) = v4) | ~ aElement0(v3) | ~ aSet0(v2) | aElementOf0(v3, v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v2, v3) = v4) | ~ aElement0(v3) | ~ aSet0(v2) | aSet0(v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ aSubsetOf0(v3, v4) | ~ aSubsetOf0(v2, v3) | ~ aSet0(v4) | ~ aSet0(v3) | ~ aSet0(v2) | aSubsetOf0(v2, v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ aSubsetOf0(v3, v2) | ~ aElementOf0(v4, v3) | ~ aSet0(v2) | aElementOf0(v4, v2)) & ! [v2] : ! [v3] : (v3 = v2 | ~ aSubsetOf0(v3, v2) | ~ aSubsetOf0(v2, v3) | ~ aSet0(v3) | ~ aSet0(v2)) & ! [v2] : ! [v3] : ( ~ aSubsetOf0(v3, v2) | ~ isFinite0(v2) | ~ aSet0(v2) | isFinite0(v3)) & ! [v2] : ! [v3] : ( ~ aSubsetOf0(v3, v2) | ~ aSet0(v2) | aSet0(v3)) & ! [v2] : ! [v3] : ( ~ aElementOf0(v3, v2) | ~ aSet0(v2) | aElement0(v3)) & ! [v2] : ! [v3] : ( ~ aSet0(v3) | ~ aSet0(v2) | aSubsetOf0(v3, v2) | ? [v4] : (aElementOf0(v4, v3) & ~ aElementOf0(v4, v2))) & ! [v2] : (v2 = xx | ~ aElementOf0(v2, v1) | aElementOf0(v2, v0)) & ! [v2] : (v2 = xx | ~ aElementOf0(v2, xS) | ~ aElement0(v2) | aElementOf0(v2, v0)) & ! [v2] : (v2 = slcrc0 | ~ aSet0(v2) | ? [v3] : aElementOf0(v3, v2)) & ! [v2] : ( ~ isCountable0(v2) | ~ isFinite0(v2) | ~ aSet0(v2)) & ! [v2] : ( ~ aElementOf0(v2, v1) | aElement0(v2)) & ! [v2] : ( ~ aElementOf0(v2, v0) | ~ aElement0(v2) | aElementOf0(v2, v1)) & ! [v2] : ( ~ aElementOf0(v2, v0) | aElementOf0(v2, xS)) & ! [v2] : ( ~ aElementOf0(v2, v0) | aElement0(v2)) & ! [v2] : ~ aElementOf0(v2, slcrc0) & ! [v2] : ( ~ aSet0(v2) | aSubsetOf0(v2, v2)) & ( ~ aElement0(xx) | aElementOf0(xx, v1))) % 9.35/2.84 | Instantiating (0) with all_0_0_0, all_0_1_1 yields: % 9.35/2.84 | (1) ~ (all_0_0_0 = xS) & sdtmndt0(xS, xx) = all_0_1_1 & sdtpldt0(all_0_1_1, xx) = all_0_0_0 & isFinite0(slcrc0) & aElementOf0(xx, xS) & aSet0(all_0_0_0) & aSet0(all_0_1_1) & aSet0(xS) & aSet0(slcrc0) & ~ isCountable0(slcrc0) & ~ aElementOf0(xx, all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4] : ((v4 = v1 | ~ aElementOf0(v4, v3) | ~ aElementOf0(v4, v0) | ~ aElement0(v4)) & (aElementOf0(v4, v3) | ( ~ (v4 = v1) & aElementOf0(v4, v0) & aElement0(v4))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4] : (( ~ aElementOf0(v4, v3) | ~ aElement0(v4) | ( ~ (v4 = v1) & ~ aElementOf0(v4, v0))) & (aElementOf0(v4, v3) | (aElement0(v4) & (v4 = v1 | aElementOf0(v4, v0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElement0(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElement0(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v1, v2) | ~ aElement0(v1) | ~ aSet0(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ aSubsetOf0(v1, v2) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v2) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | aElementOf0(v2, v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ aSubsetOf0(v1, v0) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v1) | ~ aSet0(v0)) & ! [v0] : ! [v1] : ( ~ aSubsetOf0(v1, v0) | ~ isFinite0(v0) | ~ aSet0(v0) | isFinite0(v1)) & ! [v0] : ! [v1] : ( ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0] : ! [v1] : ( ~ aElementOf0(v1, v0) | ~ aSet0(v0) | aElement0(v1)) & ! [v0] : ! [v1] : ( ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2] : (aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) & ! [v0] : (v0 = xx | ~ aElementOf0(v0, all_0_0_0) | aElementOf0(v0, all_0_1_1)) & ! [v0] : (v0 = xx | ~ aElementOf0(v0, xS) | ~ aElement0(v0) | aElementOf0(v0, all_0_1_1)) & ! [v0] : (v0 = slcrc0 | ~ aSet0(v0) | ? [v1] : aElementOf0(v1, v0)) & ! [v0] : ( ~ isCountable0(v0) | ~ isFinite0(v0) | ~ aSet0(v0)) & ! [v0] : ( ~ aElementOf0(v0, all_0_0_0) | aElement0(v0)) & ! [v0] : ( ~ aElementOf0(v0, all_0_1_1) | ~ aElement0(v0) | aElementOf0(v0, all_0_0_0)) & ! [v0] : ( ~ aElementOf0(v0, all_0_1_1) | aElementOf0(v0, xS)) & ! [v0] : ( ~ aElementOf0(v0, all_0_1_1) | aElement0(v0)) & ! [v0] : ~ aElementOf0(v0, slcrc0) & ! [v0] : ( ~ aSet0(v0) | aSubsetOf0(v0, v0)) & ( ~ aElement0(xx) | aElementOf0(xx, all_0_0_0)) % 9.35/2.84 | % 9.35/2.84 | Applying alpha-rule on (1) yields: % 9.35/2.85 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0)) % 9.35/2.85 | (3) ! [v0] : ( ~ aElementOf0(v0, all_0_1_1) | aElement0(v0)) % 9.35/2.85 | (4) aSet0(all_0_0_0) % 9.35/2.85 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) % 9.35/2.85 | (6) ! [v0] : (v0 = xx | ~ aElementOf0(v0, xS) | ~ aElement0(v0) | aElementOf0(v0, all_0_1_1)) % 9.35/2.85 | (7) ! [v0] : (v0 = xx | ~ aElementOf0(v0, all_0_0_0) | aElementOf0(v0, all_0_1_1)) % 9.35/2.85 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4] : ((v4 = v1 | ~ aElementOf0(v4, v3) | ~ aElementOf0(v4, v0) | ~ aElement0(v4)) & (aElementOf0(v4, v3) | ( ~ (v4 = v1) & aElementOf0(v4, v0) & aElement0(v4))))) % 9.35/2.85 | (9) ! [v0] : ! [v1] : ( ~ aElementOf0(v1, v0) | ~ aSet0(v0) | aElement0(v1)) % 9.35/2.85 | (10) sdtmndt0(xS, xx) = all_0_1_1 % 9.35/2.85 | (11) ! [v0] : ( ~ aElementOf0(v0, all_0_1_1) | aElementOf0(v0, xS)) % 9.35/2.85 | (12) aSet0(slcrc0) % 9.35/2.85 | (13) aElementOf0(xx, xS) % 9.35/2.85 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v1, v2) | ~ aElement0(v1) | ~ aSet0(v0)) % 9.35/2.85 | (15) ! [v0] : ( ~ isCountable0(v0) | ~ isFinite0(v0) | ~ aSet0(v0)) % 9.35/2.85 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElement0(v3)) % 9.35/2.85 | (17) ~ aElement0(xx) | aElementOf0(xx, all_0_0_0) % 9.35/2.85 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 9.35/2.85 | (19) aSet0(xS) % 9.35/2.85 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElement0(v3)) % 9.35/2.85 | (21) ! [v0] : ! [v1] : ( ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2] : (aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 9.35/2.85 | (22) ! [v0] : ! [v1] : ( ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) % 9.35/2.85 | (23) ! [v0] : ( ~ aSet0(v0) | aSubsetOf0(v0, v0)) % 9.35/2.85 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2)) % 9.35/2.85 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) % 9.35/2.85 | (26) ~ isCountable0(slcrc0) % 9.35/2.85 | (27) ! [v0] : ! [v1] : (v1 = v0 | ~ aSubsetOf0(v1, v0) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v1) | ~ aSet0(v0)) % 9.35/2.85 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2)) % 9.35/2.85 | (29) isFinite0(slcrc0) % 9.35/2.85 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ aSubsetOf0(v1, v2) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v2) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v0, v2)) % 9.35/2.85 | (31) ~ (all_0_0_0 = xS) % 9.35/2.85 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) % 9.35/2.85 | (33) ! [v0] : ( ~ aElementOf0(v0, all_0_1_1) | ~ aElement0(v0) | aElementOf0(v0, all_0_0_0)) % 9.35/2.85 | (34) sdtpldt0(all_0_1_1, xx) = all_0_0_0 % 9.35/2.85 | (35) ! [v0] : (v0 = slcrc0 | ~ aSet0(v0) | ? [v1] : aElementOf0(v1, v0)) % 9.35/2.85 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | aElementOf0(v2, v0)) % 9.35/2.85 | (37) ~ aElementOf0(xx, all_0_1_1) % 9.35/2.85 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0)) % 9.35/2.85 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4] : (( ~ aElementOf0(v4, v3) | ~ aElement0(v4) | ( ~ (v4 = v1) & ~ aElementOf0(v4, v0))) & (aElementOf0(v4, v3) | (aElement0(v4) & (v4 = v1 | aElementOf0(v4, v0)))))) % 9.35/2.85 | (40) ! [v0] : ( ~ aElementOf0(v0, all_0_0_0) | aElement0(v0)) % 9.35/2.85 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v1, v2)) % 9.35/2.86 | (42) ! [v0] : ! [v1] : ( ~ aSubsetOf0(v1, v0) | ~ isFinite0(v0) | ~ aSet0(v0) | isFinite0(v1)) % 9.35/2.86 | (43) ! [v0] : ~ aElementOf0(v0, slcrc0) % 9.35/2.86 | (44) aSet0(all_0_1_1) % 9.35/2.86 | % 9.35/2.86 | Instantiating formula (21) with all_0_1_1, all_0_0_0 and discharging atoms aSet0(all_0_0_0), aSet0(all_0_1_1), yields: % 9.35/2.86 | (45) aSubsetOf0(all_0_1_1, all_0_0_0) | ? [v0] : (aElementOf0(v0, all_0_1_1) & ~ aElementOf0(v0, all_0_0_0)) % 9.35/2.86 | % 9.35/2.86 | Instantiating formula (21) with all_0_0_0, all_0_1_1 and discharging atoms aSet0(all_0_0_0), aSet0(all_0_1_1), yields: % 9.35/2.86 | (46) aSubsetOf0(all_0_0_0, all_0_1_1) | ? [v0] : (aElementOf0(v0, all_0_0_0) & ~ aElementOf0(v0, all_0_1_1)) % 9.35/2.86 | % 9.35/2.86 | Instantiating formula (9) with xx, xS and discharging atoms aElementOf0(xx, xS), aSet0(xS), yields: % 9.35/2.86 | (47) aElement0(xx) % 9.35/2.86 | % 9.35/2.86 | Instantiating formula (21) with all_0_0_0, xS and discharging atoms aSet0(all_0_0_0), aSet0(xS), yields: % 9.35/2.86 | (48) aSubsetOf0(all_0_0_0, xS) | ? [v0] : (aElementOf0(v0, all_0_0_0) & ~ aElementOf0(v0, xS)) % 9.35/2.86 | % 9.35/2.86 | Instantiating formula (21) with xS, all_0_1_1 and discharging atoms aSet0(all_0_1_1), aSet0(xS), yields: % 9.35/2.86 | (49) aSubsetOf0(xS, all_0_1_1) | ? [v0] : (aElementOf0(v0, xS) & ~ aElementOf0(v0, all_0_1_1)) % 9.35/2.86 | % 9.35/2.86 | Instantiating formula (21) with all_0_1_1, xS and discharging atoms aSet0(all_0_1_1), aSet0(xS), yields: % 9.35/2.86 | (50) aSubsetOf0(all_0_1_1, xS) | ? [v0] : (aElementOf0(v0, all_0_1_1) & ~ aElementOf0(v0, xS)) % 9.35/2.86 | % 9.35/2.86 +-Applying beta-rule and splitting (17), into two cases. % 9.35/2.86 |-Branch one: % 9.35/2.86 | (51) ~ aElement0(xx) % 9.35/2.86 | % 9.35/2.86 | Using (47) and (51) yields: % 9.35/2.86 | (52) $false % 9.35/2.86 | % 9.35/2.86 |-The branch is then unsatisfiable % 9.35/2.86 |-Branch two: % 9.35/2.86 | (47) aElement0(xx) % 9.35/2.86 | (54) aElementOf0(xx, all_0_0_0) % 9.35/2.86 | % 9.35/2.86 | Instantiating formula (8) with all_0_0_0, all_0_1_1, xx, xS and discharging atoms sdtmndt0(xS, xx) = all_0_1_1, aElement0(xx), aSet0(all_0_0_0), aSet0(xS), yields: % 9.35/2.86 | (55) all_0_0_0 = all_0_1_1 | ? [v0] : ((v0 = xx | ~ aElementOf0(v0, all_0_0_0) | ~ aElementOf0(v0, xS) | ~ aElement0(v0)) & (aElementOf0(v0, all_0_0_0) | ( ~ (v0 = xx) & aElementOf0(v0, xS) & aElement0(v0)))) % 9.35/2.86 | % 9.35/2.86 | Instantiating formula (8) with xS, all_0_1_1, xx, xS and discharging atoms sdtmndt0(xS, xx) = all_0_1_1, aElement0(xx), aSet0(xS), yields: % 9.35/2.86 | (56) all_0_1_1 = xS | ? [v0] : (aElementOf0(v0, xS) & (v0 = xx | ~ aElement0(v0))) % 9.35/2.86 | % 9.35/2.86 | Instantiating formula (39) with xS, all_0_0_0, xx, all_0_1_1 and discharging atoms sdtpldt0(all_0_1_1, xx) = all_0_0_0, aElement0(xx), aSet0(all_0_1_1), aSet0(xS), yields: % 9.35/2.86 | (57) all_0_0_0 = xS | ? [v0] : (( ~ aElementOf0(v0, xS) | ~ aElement0(v0) | ( ~ (v0 = xx) & ~ aElementOf0(v0, all_0_1_1))) & (aElementOf0(v0, xS) | (aElement0(v0) & (v0 = xx | aElementOf0(v0, all_0_1_1))))) % 9.35/2.86 | % 9.35/2.86 +-Applying beta-rule and splitting (49), into two cases. % 9.35/2.86 |-Branch one: % 9.35/2.86 | (58) aSubsetOf0(xS, all_0_1_1) % 9.35/2.86 | % 9.35/2.86 | Instantiating formula (36) with xx, xS, all_0_1_1 and discharging atoms aSubsetOf0(xS, all_0_1_1), aElementOf0(xx, xS), aSet0(all_0_1_1), ~ aElementOf0(xx, all_0_1_1), yields: % 9.35/2.86 | (52) $false % 9.35/2.86 | % 9.35/2.86 |-The branch is then unsatisfiable % 9.35/2.86 |-Branch two: % 9.35/2.86 | (60) ~ aSubsetOf0(xS, all_0_1_1) % 9.35/2.86 | (61) ? [v0] : (aElementOf0(v0, xS) & ~ aElementOf0(v0, all_0_1_1)) % 9.35/2.86 | % 9.35/2.86 | Instantiating (61) with all_20_0_3 yields: % 9.35/2.86 | (62) aElementOf0(all_20_0_3, xS) & ~ aElementOf0(all_20_0_3, all_0_1_1) % 9.35/2.86 | % 9.35/2.86 | Applying alpha-rule on (62) yields: % 9.35/2.86 | (63) aElementOf0(all_20_0_3, xS) % 9.35/2.86 | (64) ~ aElementOf0(all_20_0_3, all_0_1_1) % 9.35/2.86 | % 9.35/2.86 +-Applying beta-rule and splitting (57), into two cases. % 9.35/2.86 |-Branch one: % 9.35/2.86 | (65) all_0_0_0 = xS % 9.35/2.86 | % 9.35/2.86 | Equations (65) can reduce 31 to: % 9.35/2.86 | (66) $false % 9.35/2.86 | % 9.35/2.86 |-The branch is then unsatisfiable % 9.35/2.86 |-Branch two: % 9.35/2.86 | (31) ~ (all_0_0_0 = xS) % 9.35/2.86 | (68) ? [v0] : (( ~ aElementOf0(v0, xS) | ~ aElement0(v0) | ( ~ (v0 = xx) & ~ aElementOf0(v0, all_0_1_1))) & (aElementOf0(v0, xS) | (aElement0(v0) & (v0 = xx | aElementOf0(v0, all_0_1_1))))) % 9.35/2.86 | % 9.35/2.86 | Instantiating (68) with all_26_0_4 yields: % 9.35/2.86 | (69) ( ~ aElementOf0(all_26_0_4, xS) | ~ aElement0(all_26_0_4) | ( ~ (all_26_0_4 = xx) & ~ aElementOf0(all_26_0_4, all_0_1_1))) & (aElementOf0(all_26_0_4, xS) | (aElement0(all_26_0_4) & (all_26_0_4 = xx | aElementOf0(all_26_0_4, all_0_1_1)))) % 9.35/2.86 | % 9.35/2.86 | Applying alpha-rule on (69) yields: % 9.35/2.86 | (70) ~ aElementOf0(all_26_0_4, xS) | ~ aElement0(all_26_0_4) | ( ~ (all_26_0_4 = xx) & ~ aElementOf0(all_26_0_4, all_0_1_1)) % 9.35/2.87 | (71) aElementOf0(all_26_0_4, xS) | (aElement0(all_26_0_4) & (all_26_0_4 = xx | aElementOf0(all_26_0_4, all_0_1_1))) % 9.35/2.87 | % 9.35/2.87 | Instantiating formula (9) with all_20_0_3, xS and discharging atoms aElementOf0(all_20_0_3, xS), aSet0(xS), yields: % 9.35/2.87 | (72) aElement0(all_20_0_3) % 9.35/2.87 | % 9.35/2.87 | Instantiating formula (6) with all_20_0_3 and discharging atoms aElementOf0(all_20_0_3, xS), aElement0(all_20_0_3), ~ aElementOf0(all_20_0_3, all_0_1_1), yields: % 9.35/2.87 | (73) all_20_0_3 = xx % 9.35/2.87 | % 9.35/2.87 | From (73) and (64) follows: % 9.35/2.87 | (37) ~ aElementOf0(xx, all_0_1_1) % 9.35/2.87 | % 9.35/2.87 +-Applying beta-rule and splitting (50), into two cases. % 9.35/2.87 |-Branch one: % 9.35/2.87 | (75) aSubsetOf0(all_0_1_1, xS) % 9.35/2.87 | % 9.35/2.87 +-Applying beta-rule and splitting (48), into two cases. % 9.35/2.87 |-Branch one: % 9.35/2.87 | (76) aSubsetOf0(all_0_0_0, xS) % 9.35/2.87 | % 9.35/2.87 +-Applying beta-rule and splitting (46), into two cases. % 9.35/2.87 |-Branch one: % 9.35/2.87 | (77) aSubsetOf0(all_0_0_0, all_0_1_1) % 9.35/2.87 | % 9.35/2.87 | Instantiating formula (36) with xx, all_0_0_0, all_0_1_1 and discharging atoms aSubsetOf0(all_0_0_0, all_0_1_1), aElementOf0(xx, all_0_0_0), aSet0(all_0_1_1), ~ aElementOf0(xx, all_0_1_1), yields: % 9.35/2.87 | (52) $false % 9.35/2.87 | % 9.35/2.87 |-The branch is then unsatisfiable % 9.35/2.87 |-Branch two: % 9.35/2.87 | (79) ~ aSubsetOf0(all_0_0_0, all_0_1_1) % 9.35/2.87 | (80) ? [v0] : (aElementOf0(v0, all_0_0_0) & ~ aElementOf0(v0, all_0_1_1)) % 9.35/2.87 | % 9.35/2.87 +-Applying beta-rule and splitting (45), into two cases. % 9.35/2.87 |-Branch one: % 9.35/2.87 | (81) aSubsetOf0(all_0_1_1, all_0_0_0) % 9.35/2.87 | % 9.35/2.87 +-Applying beta-rule and splitting (55), into two cases. % 9.35/2.87 |-Branch one: % 9.35/2.87 | (82) all_0_0_0 = all_0_1_1 % 9.35/2.87 | % 9.35/2.87 | From (82) and (81) follows: % 9.35/2.87 | (83) aSubsetOf0(all_0_1_1, all_0_1_1) % 9.35/2.87 | % 9.35/2.87 | From (82) and (79) follows: % 9.35/2.87 | (84) ~ aSubsetOf0(all_0_1_1, all_0_1_1) % 9.35/2.87 | % 9.35/2.87 | Using (83) and (84) yields: % 9.35/2.87 | (52) $false % 9.35/2.87 | % 9.35/2.87 |-The branch is then unsatisfiable % 9.35/2.87 |-Branch two: % 9.35/2.87 | (86) ~ (all_0_0_0 = all_0_1_1) % 9.35/2.87 | (87) ? [v0] : ((v0 = xx | ~ aElementOf0(v0, all_0_0_0) | ~ aElementOf0(v0, xS) | ~ aElement0(v0)) & (aElementOf0(v0, all_0_0_0) | ( ~ (v0 = xx) & aElementOf0(v0, xS) & aElement0(v0)))) % 9.35/2.87 | % 9.35/2.87 | Instantiating (87) with all_198_0_27 yields: % 9.35/2.87 | (88) (all_198_0_27 = xx | ~ aElementOf0(all_198_0_27, all_0_0_0) | ~ aElementOf0(all_198_0_27, xS) | ~ aElement0(all_198_0_27)) & (aElementOf0(all_198_0_27, all_0_0_0) | ( ~ (all_198_0_27 = xx) & aElementOf0(all_198_0_27, xS) & aElement0(all_198_0_27))) % 9.35/2.87 | % 9.35/2.87 | Applying alpha-rule on (88) yields: % 9.35/2.87 | (89) all_198_0_27 = xx | ~ aElementOf0(all_198_0_27, all_0_0_0) | ~ aElementOf0(all_198_0_27, xS) | ~ aElement0(all_198_0_27) % 9.35/2.87 | (90) aElementOf0(all_198_0_27, all_0_0_0) | ( ~ (all_198_0_27 = xx) & aElementOf0(all_198_0_27, xS) & aElement0(all_198_0_27)) % 9.35/2.87 | % 9.35/2.87 +-Applying beta-rule and splitting (71), into two cases. % 9.35/2.87 |-Branch one: % 9.35/2.87 | (91) aElementOf0(all_26_0_4, xS) % 9.35/2.87 | % 9.35/2.87 +-Applying beta-rule and splitting (70), into two cases. % 9.35/2.87 |-Branch one: % 9.35/2.87 | (92) ~ aElementOf0(all_26_0_4, xS) % 9.35/2.87 | % 9.35/2.87 | Using (91) and (92) yields: % 9.35/2.87 | (52) $false % 9.35/2.87 | % 9.35/2.87 |-The branch is then unsatisfiable % 9.35/2.87 |-Branch two: % 9.35/2.87 | (91) aElementOf0(all_26_0_4, xS) % 9.35/2.87 | (95) ~ aElement0(all_26_0_4) | ( ~ (all_26_0_4 = xx) & ~ aElementOf0(all_26_0_4, all_0_1_1)) % 9.35/2.87 | % 9.35/2.87 | Instantiating formula (9) with all_26_0_4, xS and discharging atoms aElementOf0(all_26_0_4, xS), aSet0(xS), yields: % 9.35/2.87 | (96) aElement0(all_26_0_4) % 9.35/2.87 | % 9.35/2.87 +-Applying beta-rule and splitting (95), into two cases. % 9.35/2.87 |-Branch one: % 9.35/2.87 | (97) ~ aElement0(all_26_0_4) % 9.35/2.87 | % 9.35/2.87 | Using (96) and (97) yields: % 9.35/2.87 | (52) $false % 9.35/2.87 | % 9.35/2.87 |-The branch is then unsatisfiable % 9.35/2.87 |-Branch two: % 9.35/2.87 | (96) aElement0(all_26_0_4) % 9.35/2.87 | (100) ~ (all_26_0_4 = xx) & ~ aElementOf0(all_26_0_4, all_0_1_1) % 9.35/2.87 | % 9.35/2.87 | Applying alpha-rule on (100) yields: % 9.35/2.87 | (101) ~ (all_26_0_4 = xx) % 9.35/2.87 | (102) ~ aElementOf0(all_26_0_4, all_0_1_1) % 9.35/2.87 | % 9.35/2.87 | Instantiating formula (6) with all_26_0_4 and discharging atoms aElementOf0(all_26_0_4, xS), aElement0(all_26_0_4), ~ aElementOf0(all_26_0_4, all_0_1_1), yields: % 9.35/2.87 | (103) all_26_0_4 = xx % 9.35/2.87 | % 9.35/2.87 | Equations (103) can reduce 101 to: % 9.35/2.87 | (66) $false % 9.35/2.87 | % 9.35/2.87 |-The branch is then unsatisfiable % 9.35/2.87 |-Branch two: % 9.35/2.87 | (92) ~ aElementOf0(all_26_0_4, xS) % 9.35/2.87 | (106) aElement0(all_26_0_4) & (all_26_0_4 = xx | aElementOf0(all_26_0_4, all_0_1_1)) % 9.35/2.87 | % 9.35/2.87 | Applying alpha-rule on (106) yields: % 9.35/2.87 | (96) aElement0(all_26_0_4) % 9.35/2.87 | (108) all_26_0_4 = xx | aElementOf0(all_26_0_4, all_0_1_1) % 9.35/2.87 | % 9.35/2.87 +-Applying beta-rule and splitting (90), into two cases. % 9.35/2.87 |-Branch one: % 9.35/2.87 | (109) aElementOf0(all_198_0_27, all_0_0_0) % 9.35/2.87 | % 9.35/2.87 | Instantiating formula (36) with all_198_0_27, all_0_0_0, xS and discharging atoms aSubsetOf0(all_0_0_0, xS), aElementOf0(all_198_0_27, all_0_0_0), aSet0(xS), yields: % 9.35/2.87 | (110) aElementOf0(all_198_0_27, xS) % 9.35/2.87 | % 9.35/2.87 | Instantiating formula (40) with all_198_0_27 and discharging atoms aElementOf0(all_198_0_27, all_0_0_0), yields: % 9.35/2.88 | (111) aElement0(all_198_0_27) % 9.35/2.88 | % 9.35/2.88 +-Applying beta-rule and splitting (89), into two cases. % 9.35/2.88 |-Branch one: % 9.35/2.88 | (112) ~ aElementOf0(all_198_0_27, all_0_0_0) % 9.35/2.88 | % 9.35/2.88 | Using (109) and (112) yields: % 9.35/2.88 | (52) $false % 9.35/2.88 | % 9.35/2.88 |-The branch is then unsatisfiable % 9.35/2.88 |-Branch two: % 9.35/2.88 | (109) aElementOf0(all_198_0_27, all_0_0_0) % 9.35/2.88 | (115) all_198_0_27 = xx | ~ aElementOf0(all_198_0_27, xS) | ~ aElement0(all_198_0_27) % 9.35/2.88 | % 9.35/2.88 +-Applying beta-rule and splitting (115), into two cases. % 9.35/2.88 |-Branch one: % 9.35/2.88 | (116) ~ aElementOf0(all_198_0_27, xS) % 9.35/2.88 | % 9.35/2.88 | Using (110) and (116) yields: % 9.35/2.88 | (52) $false % 9.35/2.88 | % 9.35/2.88 |-The branch is then unsatisfiable % 9.35/2.88 |-Branch two: % 9.35/2.88 | (110) aElementOf0(all_198_0_27, xS) % 9.35/2.88 | (119) all_198_0_27 = xx | ~ aElement0(all_198_0_27) % 9.35/2.88 | % 9.35/2.88 +-Applying beta-rule and splitting (119), into two cases. % 9.35/2.88 |-Branch one: % 9.35/2.88 | (120) ~ aElement0(all_198_0_27) % 9.35/2.88 | % 9.35/2.88 | Using (111) and (120) yields: % 9.35/2.88 | (52) $false % 9.35/2.88 | % 9.35/2.88 |-The branch is then unsatisfiable % 9.35/2.88 |-Branch two: % 9.35/2.88 | (111) aElement0(all_198_0_27) % 9.35/2.88 | (123) all_198_0_27 = xx % 9.35/2.88 | % 9.35/2.88 | From (123) and (110) follows: % 9.35/2.88 | (13) aElementOf0(xx, xS) % 9.35/2.88 | % 9.35/2.88 +-Applying beta-rule and splitting (108), into two cases. % 9.35/2.88 |-Branch one: % 9.35/2.88 | (125) aElementOf0(all_26_0_4, all_0_1_1) % 9.35/2.88 | % 9.35/2.88 | Instantiating formula (11) with all_26_0_4 and discharging atoms aElementOf0(all_26_0_4, all_0_1_1), ~ aElementOf0(all_26_0_4, xS), yields: % 9.35/2.88 | (52) $false % 9.35/2.88 | % 9.35/2.88 |-The branch is then unsatisfiable % 9.35/2.88 |-Branch two: % 9.35/2.88 | (102) ~ aElementOf0(all_26_0_4, all_0_1_1) % 9.35/2.88 | (103) all_26_0_4 = xx % 9.35/2.88 | % 9.35/2.88 | From (103) and (92) follows: % 9.35/2.88 | (129) ~ aElementOf0(xx, xS) % 9.35/2.88 | % 9.35/2.88 | Using (13) and (129) yields: % 9.35/2.88 | (52) $false % 9.35/2.88 | % 9.35/2.88 |-The branch is then unsatisfiable % 9.35/2.88 |-Branch two: % 9.35/2.88 | (112) ~ aElementOf0(all_198_0_27, all_0_0_0) % 9.35/2.88 | (132) ~ (all_198_0_27 = xx) & aElementOf0(all_198_0_27, xS) & aElement0(all_198_0_27) % 9.35/2.88 | % 9.35/2.88 | Applying alpha-rule on (132) yields: % 9.35/2.88 | (133) ~ (all_198_0_27 = xx) % 9.35/2.88 | (110) aElementOf0(all_198_0_27, xS) % 9.35/2.88 | (111) aElement0(all_198_0_27) % 9.35/2.88 | % 9.35/2.88 | Instantiating formula (6) with all_198_0_27 and discharging atoms aElementOf0(all_198_0_27, xS), aElement0(all_198_0_27), yields: % 9.35/2.88 | (136) all_198_0_27 = xx | aElementOf0(all_198_0_27, all_0_1_1) % 9.35/2.88 | % 9.35/2.88 +-Applying beta-rule and splitting (136), into two cases. % 9.35/2.88 |-Branch one: % 9.35/2.88 | (137) aElementOf0(all_198_0_27, all_0_1_1) % 9.35/2.88 | % 9.35/2.88 | Instantiating formula (33) with all_198_0_27 and discharging atoms aElementOf0(all_198_0_27, all_0_1_1), aElement0(all_198_0_27), ~ aElementOf0(all_198_0_27, all_0_0_0), yields: % 9.35/2.88 | (52) $false % 9.35/2.88 | % 9.35/2.88 |-The branch is then unsatisfiable % 9.35/2.88 |-Branch two: % 9.35/2.88 | (139) ~ aElementOf0(all_198_0_27, all_0_1_1) % 9.35/2.88 | (123) all_198_0_27 = xx % 9.35/2.88 | % 9.35/2.88 | Equations (123) can reduce 133 to: % 9.35/2.88 | (66) $false % 9.35/2.88 | % 9.35/2.88 |-The branch is then unsatisfiable % 9.35/2.88 |-Branch two: % 9.35/2.88 | (142) ~ aSubsetOf0(all_0_1_1, all_0_0_0) % 9.35/2.88 | (143) ? [v0] : (aElementOf0(v0, all_0_1_1) & ~ aElementOf0(v0, all_0_0_0)) % 9.35/2.88 | % 9.35/2.88 | Instantiating (143) with all_122_0_29 yields: % 9.35/2.88 | (144) aElementOf0(all_122_0_29, all_0_1_1) & ~ aElementOf0(all_122_0_29, all_0_0_0) % 9.35/2.88 | % 9.35/2.88 | Applying alpha-rule on (144) yields: % 9.35/2.88 | (145) aElementOf0(all_122_0_29, all_0_1_1) % 9.35/2.88 | (146) ~ aElementOf0(all_122_0_29, all_0_0_0) % 9.35/2.88 | % 9.35/2.88 | Instantiating formula (3) with all_122_0_29 and discharging atoms aElementOf0(all_122_0_29, all_0_1_1), yields: % 9.35/2.88 | (147) aElement0(all_122_0_29) % 9.35/2.88 | % 9.35/2.88 | Instantiating formula (33) with all_122_0_29 and discharging atoms aElementOf0(all_122_0_29, all_0_1_1), aElement0(all_122_0_29), ~ aElementOf0(all_122_0_29, all_0_0_0), yields: % 9.35/2.88 | (52) $false % 9.35/2.88 | % 9.35/2.88 |-The branch is then unsatisfiable % 9.35/2.89 |-Branch two: % 9.35/2.89 | (149) ~ aSubsetOf0(all_0_0_0, xS) % 9.35/2.89 | (150) ? [v0] : (aElementOf0(v0, all_0_0_0) & ~ aElementOf0(v0, xS)) % 9.35/2.89 | % 9.35/2.89 | Instantiating (150) with all_68_0_40 yields: % 9.35/2.89 | (151) aElementOf0(all_68_0_40, all_0_0_0) & ~ aElementOf0(all_68_0_40, xS) % 9.35/2.89 | % 9.35/2.89 | Applying alpha-rule on (151) yields: % 9.35/2.89 | (152) aElementOf0(all_68_0_40, all_0_0_0) % 9.35/2.89 | (153) ~ aElementOf0(all_68_0_40, xS) % 9.35/2.89 | % 9.35/2.89 | Instantiating formula (7) with all_68_0_40 and discharging atoms aElementOf0(all_68_0_40, all_0_0_0), yields: % 9.35/2.89 | (154) all_68_0_40 = xx | aElementOf0(all_68_0_40, all_0_1_1) % 9.35/2.89 | % 9.35/2.89 +-Applying beta-rule and splitting (56), into two cases. % 9.35/2.89 |-Branch one: % 9.35/2.89 | (155) all_0_1_1 = xS % 9.35/2.89 | % 9.35/2.89 | From (155) and (75) follows: % 9.35/2.89 | (156) aSubsetOf0(xS, xS) % 9.35/2.89 | % 9.35/2.89 | From (155) and (60) follows: % 9.35/2.89 | (157) ~ aSubsetOf0(xS, xS) % 9.35/2.89 | % 9.35/2.89 | Using (156) and (157) yields: % 9.35/2.89 | (52) $false % 9.35/2.89 | % 9.35/2.89 |-The branch is then unsatisfiable % 9.35/2.89 |-Branch two: % 9.35/2.89 | (159) ~ (all_0_1_1 = xS) % 9.35/2.89 | (160) ? [v0] : (aElementOf0(v0, xS) & (v0 = xx | ~ aElement0(v0))) % 9.35/2.89 | % 9.35/2.89 | Instantiating (160) with all_197_0_58 yields: % 9.35/2.89 | (161) aElementOf0(all_197_0_58, xS) & (all_197_0_58 = xx | ~ aElement0(all_197_0_58)) % 9.35/2.89 | % 9.35/2.89 | Applying alpha-rule on (161) yields: % 9.35/2.89 | (162) aElementOf0(all_197_0_58, xS) % 9.35/2.89 | (163) all_197_0_58 = xx | ~ aElement0(all_197_0_58) % 9.73/2.89 | % 9.73/2.89 | Instantiating formula (9) with all_197_0_58, xS and discharging atoms aElementOf0(all_197_0_58, xS), aSet0(xS), yields: % 9.73/2.89 | (164) aElement0(all_197_0_58) % 9.73/2.89 | % 9.73/2.89 +-Applying beta-rule and splitting (163), into two cases. % 9.73/2.89 |-Branch one: % 9.73/2.89 | (165) ~ aElement0(all_197_0_58) % 9.73/2.89 | % 9.73/2.89 | Using (164) and (165) yields: % 9.73/2.89 | (52) $false % 9.73/2.89 | % 9.73/2.89 |-The branch is then unsatisfiable % 9.73/2.89 |-Branch two: % 9.73/2.89 | (164) aElement0(all_197_0_58) % 9.73/2.89 | (168) all_197_0_58 = xx % 9.73/2.89 | % 9.73/2.89 | From (168) and (162) follows: % 9.73/2.89 | (13) aElementOf0(xx, xS) % 9.73/2.89 | % 9.73/2.89 +-Applying beta-rule and splitting (154), into two cases. % 9.73/2.89 |-Branch one: % 9.73/2.89 | (170) aElementOf0(all_68_0_40, all_0_1_1) % 9.73/2.89 | % 9.73/2.89 | Instantiating formula (11) with all_68_0_40 and discharging atoms aElementOf0(all_68_0_40, all_0_1_1), ~ aElementOf0(all_68_0_40, xS), yields: % 9.73/2.89 | (52) $false % 9.73/2.89 | % 9.73/2.89 |-The branch is then unsatisfiable % 9.73/2.89 |-Branch two: % 9.73/2.89 | (172) ~ aElementOf0(all_68_0_40, all_0_1_1) % 9.73/2.89 | (173) all_68_0_40 = xx % 9.73/2.89 | % 9.73/2.89 | From (173) and (153) follows: % 9.73/2.89 | (129) ~ aElementOf0(xx, xS) % 9.73/2.89 | % 9.73/2.89 | Using (13) and (129) yields: % 9.73/2.89 | (52) $false % 9.73/2.89 | % 9.73/2.89 |-The branch is then unsatisfiable % 9.73/2.89 |-Branch two: % 9.73/2.89 | (176) ~ aSubsetOf0(all_0_1_1, xS) % 9.73/2.89 | (177) ? [v0] : (aElementOf0(v0, all_0_1_1) & ~ aElementOf0(v0, xS)) % 9.73/2.89 | % 9.73/2.89 | Instantiating (177) with all_46_0_59 yields: % 9.73/2.89 | (178) aElementOf0(all_46_0_59, all_0_1_1) & ~ aElementOf0(all_46_0_59, xS) % 9.73/2.89 | % 9.73/2.89 | Applying alpha-rule on (178) yields: % 9.73/2.89 | (179) aElementOf0(all_46_0_59, all_0_1_1) % 9.73/2.89 | (180) ~ aElementOf0(all_46_0_59, xS) % 9.73/2.89 | % 9.73/2.89 | Instantiating formula (11) with all_46_0_59 and discharging atoms aElementOf0(all_46_0_59, all_0_1_1), ~ aElementOf0(all_46_0_59, xS), yields: % 9.73/2.89 | (52) $false % 9.73/2.89 | % 9.73/2.89 |-The branch is then unsatisfiable % 9.73/2.89 % SZS output end Proof for theBenchmark % 9.73/2.89 % 9.73/2.89 2294ms %------------------------------------------------------------------------------