%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : NUM536+2 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n026.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Mon Jul 18 08:45:36 EDT 2022 % Result : Theorem 3.52s 1.49s % Output : Proof 7.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : NUM536+2 : TPTP v8.1.0. Released v4.0.0. % 0.10/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n026.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Tue Jul 5 22:07:08 EDT 2022 % 0.13/0.34 % CPUTime : % 0.20/0.60 ____ _ % 0.20/0.60 ___ / __ \_____(_)___ ________ __________ % 0.20/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.20/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.20/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic % 0.20/0.60 (ePrincess v.1.0) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2015 % 0.20/0.60 (c) Peter Backeman, 2014-2015 % 0.20/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.20/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.20/0.60 Bug reports to peter@backeman.se % 0.20/0.60 % 0.20/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.64/0.94 Prover 0: Preprocessing ... % 2.39/1.21 Prover 0: Constructing countermodel ... % 3.52/1.49 Prover 0: proved (838ms) % 3.52/1.49 % 3.52/1.49 No countermodel exists, formula is valid % 3.52/1.49 % SZS status Theorem for theBenchmark % 3.52/1.49 % 3.52/1.49 Generating proof ... found it (size 61) % 6.79/2.30 % 6.79/2.30 % SZS output start Proof for theBenchmark % 6.79/2.30 Assumed formulas after preprocessing and simplification: % 6.79/2.30 | (0) ? [v0] : ? [v1] : ( ~ (v1 = xS) & sdtmndt0(v0, xx) = v1 & sdtpldt0(xS, xx) = v0 & isFinite0(slcrc0) & aElementOf0(xx, v0) & aElement0(xx) & aSet0(v1) & aSet0(v0) & aSet0(xS) & aSet0(slcrc0) & ~ isCountable0(slcrc0) & ~ aElementOf0(xx, v1) & ~ aElementOf0(xx, xS) & ! [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] : (v5 = v2 | ~ (sdtmndt0(v2, v3) = v4) | ~ (sdtpldt0(v4, v3) = v5) | ~ aElementOf0(v3, v2) | ~ aSet0(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, v0) | ~ aElement0(v2) | aElementOf0(v2, v1)) & ! [v2] : (v2 = xx | ~ aElementOf0(v2, v0) | aElementOf0(v2, xS)) & ! [v2] : (v2 = slcrc0 | ~ aSet0(v2) | ? [v3] : aElementOf0(v3, v2)) & ! [v2] : ( ~ isCountable0(v2) | ~ isFinite0(v2) | ~ aSet0(v2)) & ! [v2] : ( ~ aElementOf0(v2, v1) | aElementOf0(v2, v0)) & ! [v2] : ( ~ aElementOf0(v2, v1) | aElement0(v2)) & ! [v2] : ( ~ aElementOf0(v2, v0) | aElement0(v2)) & ! [v2] : ( ~ aElementOf0(v2, xS) | ~ aElement0(v2) | aElementOf0(v2, v0)) & ! [v2] : ~ aElementOf0(v2, slcrc0) & ! [v2] : ( ~ aSet0(v2) | aSubsetOf0(v2, v2))) % 7.16/2.34 | Instantiating (0) with all_0_0_0, all_0_1_1 yields: % 7.16/2.34 | (1) ~ (all_0_0_0 = xS) & sdtmndt0(all_0_1_1, xx) = all_0_0_0 & sdtpldt0(xS, xx) = all_0_1_1 & isFinite0(slcrc0) & aElementOf0(xx, all_0_1_1) & aElement0(xx) & aSet0(all_0_0_0) & aSet0(all_0_1_1) & aSet0(xS) & aSet0(slcrc0) & ~ isCountable0(slcrc0) & ~ aElementOf0(xx, all_0_0_0) & ~ aElementOf0(xx, xS) & ! [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] : (v3 = v0 | ~ (sdtmndt0(v0, v1) = v2) | ~ (sdtpldt0(v2, v1) = v3) | ~ aElementOf0(v1, v0) | ~ aSet0(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_1_1) | ~ aElement0(v0) | aElementOf0(v0, all_0_0_0)) & ! [v0] : (v0 = xx | ~ aElementOf0(v0, all_0_1_1) | aElementOf0(v0, xS)) & ! [v0] : (v0 = slcrc0 | ~ aSet0(v0) | ? [v1] : aElementOf0(v1, v0)) & ! [v0] : ( ~ isCountable0(v0) | ~ isFinite0(v0) | ~ aSet0(v0)) & ! [v0] : ( ~ aElementOf0(v0, all_0_0_0) | aElementOf0(v0, all_0_1_1)) & ! [v0] : ( ~ aElementOf0(v0, all_0_0_0) | aElement0(v0)) & ! [v0] : ( ~ aElementOf0(v0, all_0_1_1) | aElement0(v0)) & ! [v0] : ( ~ aElementOf0(v0, xS) | ~ aElement0(v0) | aElementOf0(v0, all_0_1_1)) & ! [v0] : ~ aElementOf0(v0, slcrc0) & ! [v0] : ( ~ aSet0(v0) | aSubsetOf0(v0, v0)) % 7.16/2.35 | % 7.16/2.35 | Applying alpha-rule on (1) yields: % 7.16/2.35 | (2) ! [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))))) % 7.16/2.35 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElement0(v3)) % 7.16/2.35 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v1, v2) | ~ aElement0(v1) | ~ aSet0(v0)) % 7.16/2.35 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2)) % 7.16/2.36 | (6) ! [v0] : ! [v1] : ( ~ aSubsetOf0(v1, v0) | ~ isFinite0(v0) | ~ aSet0(v0) | isFinite0(v1)) % 7.16/2.36 | (7) ! [v0] : ( ~ aSet0(v0) | aSubsetOf0(v0, v0)) % 7.16/2.36 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) % 7.16/2.36 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) % 7.16/2.36 | (10) ! [v0] : ( ~ aElementOf0(v0, xS) | ~ aElement0(v0) | aElementOf0(v0, all_0_1_1)) % 7.16/2.36 | (11) ! [v0] : ! [v1] : (v1 = v0 | ~ aSubsetOf0(v1, v0) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v1) | ~ aSet0(v0)) % 7.16/2.36 | (12) ! [v0] : ( ~ aElementOf0(v0, all_0_1_1) | aElement0(v0)) % 7.16/2.36 | (13) ! [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)))))) % 7.16/2.36 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0)) % 7.16/2.36 | (15) ! [v0] : ~ aElementOf0(v0, slcrc0) % 7.16/2.36 | (16) aElementOf0(xx, all_0_1_1) % 7.16/2.36 | (17) ! [v0] : ( ~ aElementOf0(v0, all_0_0_0) | aElement0(v0)) % 7.16/2.36 | (18) sdtmndt0(all_0_1_1, xx) = all_0_0_0 % 7.16/2.36 | (19) ! [v0] : ! [v1] : ( ~ aElementOf0(v1, v0) | ~ aSet0(v0) | aElement0(v1)) % 7.16/2.36 | (20) ! [v0] : (v0 = xx | ~ aElementOf0(v0, all_0_1_1) | aElementOf0(v0, xS)) % 7.16/2.36 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 7.16/2.36 | (22) ! [v0] : ! [v1] : ( ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) % 7.16/2.36 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (sdtmndt0(v0, v1) = v2) | ~ (sdtpldt0(v2, v1) = v3) | ~ aElementOf0(v1, v0) | ~ aSet0(v0)) % 7.16/2.36 | (24) ~ aElementOf0(xx, xS) % 7.16/2.36 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ aSubsetOf0(v1, v2) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v2) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v0, v2)) % 7.16/2.36 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) % 7.16/2.36 | (27) aSet0(all_0_0_0) % 7.16/2.36 | (28) isFinite0(slcrc0) % 7.16/2.36 | (29) ~ (all_0_0_0 = xS) % 7.16/2.36 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v1, v2)) % 7.16/2.36 | (31) ~ isCountable0(slcrc0) % 7.16/2.36 | (32) aSet0(all_0_1_1) % 7.16/2.36 | (33) aSet0(slcrc0) % 7.16/2.36 | (34) ! [v0] : ( ~ isCountable0(v0) | ~ isFinite0(v0) | ~ aSet0(v0)) % 7.16/2.36 | (35) ! [v0] : (v0 = xx | ~ aElementOf0(v0, all_0_1_1) | ~ aElement0(v0) | aElementOf0(v0, all_0_0_0)) % 7.16/2.36 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0)) % 7.16/2.36 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElement0(v3)) % 7.16/2.36 | (38) sdtpldt0(xS, xx) = all_0_1_1 % 7.16/2.36 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2)) % 7.16/2.36 | (40) ! [v0] : ( ~ aElementOf0(v0, all_0_0_0) | aElementOf0(v0, all_0_1_1)) % 7.16/2.36 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | aElementOf0(v2, v0)) % 7.16/2.36 | (42) ! [v0] : (v0 = slcrc0 | ~ aSet0(v0) | ? [v1] : aElementOf0(v1, v0)) % 7.16/2.36 | (43) ! [v0] : ! [v1] : ( ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2] : (aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 7.16/2.36 | (44) aSet0(xS) % 7.16/2.36 | (45) ~ aElementOf0(xx, all_0_0_0) % 7.16/2.36 | (46) aElement0(xx) % 7.16/2.36 | % 7.16/2.37 | Instantiating formula (43) with all_0_1_1, all_0_0_0 and discharging atoms aSet0(all_0_0_0), aSet0(all_0_1_1), yields: % 7.16/2.37 | (47) aSubsetOf0(all_0_1_1, all_0_0_0) | ? [v0] : (aElementOf0(v0, all_0_1_1) & ~ aElementOf0(v0, all_0_0_0)) % 7.16/2.37 | % 7.16/2.37 | Instantiating formula (43) with all_0_0_0, all_0_1_1 and discharging atoms aSet0(all_0_0_0), aSet0(all_0_1_1), yields: % 7.16/2.37 | (48) aSubsetOf0(all_0_0_0, all_0_1_1) | ? [v0] : (aElementOf0(v0, all_0_0_0) & ~ aElementOf0(v0, all_0_1_1)) % 7.16/2.37 | % 7.16/2.37 | Instantiating formula (2) with xS, all_0_0_0, xx, all_0_1_1 and discharging atoms sdtmndt0(all_0_1_1, xx) = all_0_0_0, aElement0(xx), aSet0(all_0_1_1), aSet0(xS), yields: % 7.16/2.37 | (49) all_0_0_0 = xS | ? [v0] : ((v0 = xx | ~ aElementOf0(v0, all_0_1_1) | ~ aElementOf0(v0, xS) | ~ aElement0(v0)) & (aElementOf0(v0, xS) | ( ~ (v0 = xx) & aElementOf0(v0, all_0_1_1) & aElement0(v0)))) % 7.16/2.37 | % 7.16/2.37 | Instantiating formula (43) with xS, all_0_0_0 and discharging atoms aSet0(all_0_0_0), aSet0(xS), yields: % 7.16/2.37 | (50) aSubsetOf0(xS, all_0_0_0) | ? [v0] : (aElementOf0(v0, xS) & ~ aElementOf0(v0, all_0_0_0)) % 7.16/2.37 | % 7.16/2.37 | Instantiating formula (43) with all_0_0_0, xS and discharging atoms aSet0(all_0_0_0), aSet0(xS), yields: % 7.16/2.37 | (51) aSubsetOf0(all_0_0_0, xS) | ? [v0] : (aElementOf0(v0, all_0_0_0) & ~ aElementOf0(v0, xS)) % 7.16/2.37 | % 7.16/2.37 | Instantiating formula (43) with xS, all_0_1_1 and discharging atoms aSet0(all_0_1_1), aSet0(xS), yields: % 7.16/2.37 | (52) aSubsetOf0(xS, all_0_1_1) | ? [v0] : (aElementOf0(v0, xS) & ~ aElementOf0(v0, all_0_1_1)) % 7.16/2.37 | % 7.16/2.37 | Instantiating formula (43) with all_0_1_1, xS and discharging atoms aSet0(all_0_1_1), aSet0(xS), yields: % 7.16/2.37 | (53) aSubsetOf0(all_0_1_1, xS) | ? [v0] : (aElementOf0(v0, all_0_1_1) & ~ aElementOf0(v0, xS)) % 7.16/2.37 | % 7.16/2.37 +-Applying beta-rule and splitting (49), into two cases. % 7.16/2.37 |-Branch one: % 7.16/2.37 | (54) all_0_0_0 = xS % 7.16/2.37 | % 7.16/2.37 | Equations (54) can reduce 29 to: % 7.16/2.37 | (55) $false % 7.16/2.37 | % 7.16/2.37 |-The branch is then unsatisfiable % 7.16/2.37 |-Branch two: % 7.16/2.37 | (29) ~ (all_0_0_0 = xS) % 7.16/2.37 | (57) ? [v0] : ((v0 = xx | ~ aElementOf0(v0, all_0_1_1) | ~ aElementOf0(v0, xS) | ~ aElement0(v0)) & (aElementOf0(v0, xS) | ( ~ (v0 = xx) & aElementOf0(v0, all_0_1_1) & aElement0(v0)))) % 7.16/2.37 | % 7.16/2.37 +-Applying beta-rule and splitting (53), into two cases. % 7.16/2.37 |-Branch one: % 7.16/2.37 | (58) aSubsetOf0(all_0_1_1, xS) % 7.16/2.37 | % 7.16/2.37 | Instantiating formula (41) with xx, all_0_1_1, xS and discharging atoms aSubsetOf0(all_0_1_1, xS), aElementOf0(xx, all_0_1_1), aSet0(xS), ~ aElementOf0(xx, xS), yields: % 7.16/2.37 | (59) $false % 7.16/2.37 | % 7.16/2.37 |-The branch is then unsatisfiable % 7.16/2.37 |-Branch two: % 7.16/2.37 | (60) ~ aSubsetOf0(all_0_1_1, xS) % 7.16/2.37 | (61) ? [v0] : (aElementOf0(v0, all_0_1_1) & ~ aElementOf0(v0, xS)) % 7.16/2.37 | % 7.16/2.37 | Instantiating (61) with all_57_0_20 yields: % 7.16/2.37 | (62) aElementOf0(all_57_0_20, all_0_1_1) & ~ aElementOf0(all_57_0_20, xS) % 7.16/2.37 | % 7.16/2.37 | Applying alpha-rule on (62) yields: % 7.16/2.37 | (63) aElementOf0(all_57_0_20, all_0_1_1) % 7.16/2.37 | (64) ~ aElementOf0(all_57_0_20, xS) % 7.16/2.37 | % 7.16/2.37 | Instantiating formula (20) with all_57_0_20 and discharging atoms aElementOf0(all_57_0_20, all_0_1_1), ~ aElementOf0(all_57_0_20, xS), yields: % 7.16/2.37 | (65) all_57_0_20 = xx % 7.16/2.37 | % 7.16/2.37 | From (65) and (63) follows: % 7.16/2.37 | (16) aElementOf0(xx, all_0_1_1) % 7.16/2.37 | % 7.16/2.37 | From (65) and (64) follows: % 7.16/2.37 | (24) ~ aElementOf0(xx, xS) % 7.16/2.37 | % 7.16/2.37 +-Applying beta-rule and splitting (52), into two cases. % 7.16/2.37 |-Branch one: % 7.16/2.37 | (68) aSubsetOf0(xS, all_0_1_1) % 7.16/2.37 | % 7.16/2.37 +-Applying beta-rule and splitting (51), into two cases. % 7.16/2.37 |-Branch one: % 7.16/2.37 | (69) aSubsetOf0(all_0_0_0, xS) % 7.16/2.37 | % 7.16/2.37 +-Applying beta-rule and splitting (50), into two cases. % 7.16/2.37 |-Branch one: % 7.16/2.37 | (70) aSubsetOf0(xS, all_0_0_0) % 7.16/2.37 | % 7.16/2.37 | Instantiating formula (11) with all_0_0_0, xS and discharging atoms aSubsetOf0(all_0_0_0, xS), aSubsetOf0(xS, all_0_0_0), aSet0(all_0_0_0), aSet0(xS), yields: % 7.16/2.37 | (54) all_0_0_0 = xS % 7.16/2.37 | % 7.16/2.37 | Equations (54) can reduce 29 to: % 7.16/2.37 | (55) $false % 7.16/2.37 | % 7.16/2.37 |-The branch is then unsatisfiable % 7.16/2.37 |-Branch two: % 7.16/2.38 | (73) ~ aSubsetOf0(xS, all_0_0_0) % 7.16/2.38 | (74) ? [v0] : (aElementOf0(v0, xS) & ~ aElementOf0(v0, all_0_0_0)) % 7.16/2.38 | % 7.16/2.38 | Instantiating (74) with all_134_0_24 yields: % 7.16/2.38 | (75) aElementOf0(all_134_0_24, xS) & ~ aElementOf0(all_134_0_24, all_0_0_0) % 7.16/2.38 | % 7.16/2.38 | Applying alpha-rule on (75) yields: % 7.16/2.38 | (76) aElementOf0(all_134_0_24, xS) % 7.16/2.38 | (77) ~ aElementOf0(all_134_0_24, all_0_0_0) % 7.16/2.38 | % 7.16/2.38 | Instantiating formula (41) with all_134_0_24, xS, all_0_1_1 and discharging atoms aSubsetOf0(xS, all_0_1_1), aElementOf0(all_134_0_24, xS), aSet0(all_0_1_1), yields: % 7.16/2.38 | (78) aElementOf0(all_134_0_24, all_0_1_1) % 7.16/2.38 | % 7.16/2.38 | Instantiating formula (19) with all_134_0_24, xS and discharging atoms aElementOf0(all_134_0_24, xS), aSet0(xS), yields: % 7.16/2.38 | (79) aElement0(all_134_0_24) % 7.16/2.38 | % 7.16/2.38 | Instantiating formula (35) with all_134_0_24 and discharging atoms aElementOf0(all_134_0_24, all_0_1_1), aElement0(all_134_0_24), ~ aElementOf0(all_134_0_24, all_0_0_0), yields: % 7.16/2.38 | (80) all_134_0_24 = xx % 7.16/2.38 | % 7.16/2.38 | From (80) and (76) follows: % 7.16/2.38 | (81) aElementOf0(xx, xS) % 7.16/2.38 | % 7.16/2.38 | Using (81) and (24) yields: % 7.16/2.38 | (59) $false % 7.16/2.38 | % 7.16/2.38 |-The branch is then unsatisfiable % 7.16/2.38 |-Branch two: % 7.16/2.38 | (83) ~ aSubsetOf0(all_0_0_0, xS) % 7.16/2.38 | (84) ? [v0] : (aElementOf0(v0, all_0_0_0) & ~ aElementOf0(v0, xS)) % 7.16/2.38 | % 7.16/2.38 | Instantiating (84) with all_114_0_33 yields: % 7.16/2.38 | (85) aElementOf0(all_114_0_33, all_0_0_0) & ~ aElementOf0(all_114_0_33, xS) % 7.16/2.38 | % 7.16/2.38 | Applying alpha-rule on (85) yields: % 7.16/2.38 | (86) aElementOf0(all_114_0_33, all_0_0_0) % 7.16/2.38 | (87) ~ aElementOf0(all_114_0_33, xS) % 7.16/2.38 | % 7.16/2.38 +-Applying beta-rule and splitting (48), into two cases. % 7.16/2.38 |-Branch one: % 7.16/2.38 | (88) aSubsetOf0(all_0_0_0, all_0_1_1) % 7.16/2.38 | % 7.16/2.38 +-Applying beta-rule and splitting (47), into two cases. % 7.16/2.38 |-Branch one: % 7.16/2.38 | (89) aSubsetOf0(all_0_1_1, all_0_0_0) % 7.16/2.38 | % 7.16/2.38 | Instantiating formula (11) with all_0_0_0, all_0_1_1 and discharging atoms aSubsetOf0(all_0_0_0, all_0_1_1), aSubsetOf0(all_0_1_1, all_0_0_0), aSet0(all_0_0_0), aSet0(all_0_1_1), yields: % 7.16/2.38 | (90) all_0_0_0 = all_0_1_1 % 7.16/2.38 | % 7.16/2.38 | From (90) and (45) follows: % 7.16/2.38 | (91) ~ aElementOf0(xx, all_0_1_1) % 7.16/2.38 | % 7.16/2.38 | Using (16) and (91) yields: % 7.16/2.38 | (59) $false % 7.16/2.38 | % 7.16/2.38 |-The branch is then unsatisfiable % 7.16/2.38 |-Branch two: % 7.16/2.38 | (93) ~ aSubsetOf0(all_0_1_1, all_0_0_0) % 7.16/2.38 | (94) ? [v0] : (aElementOf0(v0, all_0_1_1) & ~ aElementOf0(v0, all_0_0_0)) % 7.16/2.38 | % 7.16/2.38 | Instantiating (94) with all_128_0_34 yields: % 7.16/2.38 | (95) aElementOf0(all_128_0_34, all_0_1_1) & ~ aElementOf0(all_128_0_34, all_0_0_0) % 7.16/2.38 | % 7.16/2.38 | Applying alpha-rule on (95) yields: % 7.16/2.38 | (96) aElementOf0(all_128_0_34, all_0_1_1) % 7.16/2.38 | (97) ~ aElementOf0(all_128_0_34, all_0_0_0) % 7.16/2.38 | % 7.16/2.38 | Instantiating formula (12) with all_128_0_34 and discharging atoms aElementOf0(all_128_0_34, all_0_1_1), yields: % 7.16/2.38 | (98) aElement0(all_128_0_34) % 7.16/2.38 | % 7.16/2.38 | Instantiating formula (40) with all_114_0_33 and discharging atoms aElementOf0(all_114_0_33, all_0_0_0), yields: % 7.16/2.38 | (99) aElementOf0(all_114_0_33, all_0_1_1) % 7.16/2.38 | % 7.16/2.38 | Instantiating formula (20) with all_114_0_33 and discharging atoms aElementOf0(all_114_0_33, all_0_1_1), ~ aElementOf0(all_114_0_33, xS), yields: % 7.16/2.38 | (100) all_114_0_33 = xx % 7.16/2.38 | % 7.16/2.38 | Instantiating formula (35) with all_128_0_34 and discharging atoms aElementOf0(all_128_0_34, all_0_1_1), aElement0(all_128_0_34), ~ aElementOf0(all_128_0_34, all_0_0_0), yields: % 7.16/2.38 | (101) all_128_0_34 = xx % 7.16/2.38 | % 7.16/2.38 | From (100) and (86) follows: % 7.16/2.38 | (102) aElementOf0(xx, all_0_0_0) % 7.16/2.38 | % 7.16/2.38 | From (101) and (97) follows: % 7.16/2.38 | (45) ~ aElementOf0(xx, all_0_0_0) % 7.16/2.38 | % 7.16/2.38 | Using (102) and (45) yields: % 7.16/2.38 | (59) $false % 7.16/2.38 | % 7.16/2.38 |-The branch is then unsatisfiable % 7.16/2.38 |-Branch two: % 7.16/2.38 | (105) ~ aSubsetOf0(all_0_0_0, all_0_1_1) % 7.16/2.38 | (106) ? [v0] : (aElementOf0(v0, all_0_0_0) & ~ aElementOf0(v0, all_0_1_1)) % 7.16/2.38 | % 7.16/2.38 | Instantiating (106) with all_122_0_43 yields: % 7.16/2.38 | (107) aElementOf0(all_122_0_43, all_0_0_0) & ~ aElementOf0(all_122_0_43, all_0_1_1) % 7.16/2.38 | % 7.16/2.38 | Applying alpha-rule on (107) yields: % 7.16/2.38 | (108) aElementOf0(all_122_0_43, all_0_0_0) % 7.16/2.38 | (109) ~ aElementOf0(all_122_0_43, all_0_1_1) % 7.16/2.38 | % 7.16/2.38 | Instantiating formula (40) with all_122_0_43 and discharging atoms aElementOf0(all_122_0_43, all_0_0_0), ~ aElementOf0(all_122_0_43, all_0_1_1), yields: % 7.16/2.38 | (59) $false % 7.16/2.38 | % 7.16/2.38 |-The branch is then unsatisfiable % 7.16/2.38 |-Branch two: % 7.16/2.38 | (111) ~ aSubsetOf0(xS, all_0_1_1) % 7.16/2.38 | (112) ? [v0] : (aElementOf0(v0, xS) & ~ aElementOf0(v0, all_0_1_1)) % 7.16/2.39 | % 7.16/2.39 | Instantiating (112) with all_101_0_52 yields: % 7.16/2.39 | (113) aElementOf0(all_101_0_52, xS) & ~ aElementOf0(all_101_0_52, all_0_1_1) % 7.16/2.39 | % 7.16/2.39 | Applying alpha-rule on (113) yields: % 7.16/2.39 | (114) aElementOf0(all_101_0_52, xS) % 7.16/2.39 | (115) ~ aElementOf0(all_101_0_52, all_0_1_1) % 7.16/2.39 | % 7.16/2.39 | Instantiating formula (19) with all_101_0_52, xS and discharging atoms aElementOf0(all_101_0_52, xS), aSet0(xS), yields: % 7.16/2.39 | (116) aElement0(all_101_0_52) % 7.16/2.39 | % 7.16/2.39 | Instantiating formula (10) with all_101_0_52 and discharging atoms aElementOf0(all_101_0_52, xS), aElement0(all_101_0_52), ~ aElementOf0(all_101_0_52, all_0_1_1), yields: % 7.16/2.39 | (59) $false % 7.16/2.39 | % 7.16/2.39 |-The branch is then unsatisfiable % 7.16/2.39 % SZS output end Proof for theBenchmark % 7.16/2.39 % 7.16/2.39 1779ms %------------------------------------------------------------------------------