%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : NUM534+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n013.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Mon Jul 18 08:45:34 EDT 2022 % Result : Theorem 6.52s 2.15s % Output : Proof 9.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : NUM534+1 : TPTP v8.1.0. Released v4.0.0. % 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n013.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 12:54:44 EDT 2022 % 0.12/0.34 % CPUTime : % 0.19/0.58 ____ _ % 0.19/0.58 ___ / __ \_____(_)___ ________ __________ % 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.58 % 0.19/0.58 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 ... % 0.76/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.55/0.91 Prover 0: Preprocessing ... % 2.07/1.13 Prover 0: Constructing countermodel ... % 6.52/2.14 Prover 0: proved (1511ms) % 6.52/2.15 % 6.52/2.15 No countermodel exists, formula is valid % 6.52/2.15 % SZS status Theorem for theBenchmark % 6.52/2.15 % 6.52/2.15 Generating proof ... found it (size 65) % 9.13/2.73 % 9.13/2.73 % SZS output start Proof for theBenchmark % 9.13/2.73 Assumed formulas after preprocessing and simplification: % 9.13/2.73 | (0) ? [v0] : ? [v1] : ( ~ (v1 = xS) & sdtmndt0(xS, xx) = v0 & sdtpldt0(v0, xx) = v1 & isFinite0(slcrc0) & aElementOf0(xx, xS) & aSet0(xS) & aSet0(slcrc0) & ~ isCountable0(slcrc0) & ! [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 = slcrc0 | ~ aSet0(v2) | ? [v3] : aElementOf0(v3, v2)) & ! [v2] : ( ~ isCountable0(v2) | ~ isFinite0(v2) | ~ aSet0(v2)) & ! [v2] : ~ aElementOf0(v2, slcrc0) & ! [v2] : ( ~ aSet0(v2) | aSubsetOf0(v2, v2))) % 9.13/2.77 | Instantiating (0) with all_0_0_0, all_0_1_1 yields: % 9.13/2.77 | (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(xS) & aSet0(slcrc0) & ~ isCountable0(slcrc0) & ! [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 = slcrc0 | ~ aSet0(v0) | ? [v1] : aElementOf0(v1, v0)) & ! [v0] : ( ~ isCountable0(v0) | ~ isFinite0(v0) | ~ aSet0(v0)) & ! [v0] : ~ aElementOf0(v0, slcrc0) & ! [v0] : ( ~ aSet0(v0) | aSubsetOf0(v0, v0)) % 9.13/2.78 | % 9.13/2.78 | Applying alpha-rule on (1) yields: % 9.13/2.78 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v1, v2)) % 9.13/2.78 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2)) % 9.13/2.78 | (4) ! [v0] : ~ aElementOf0(v0, slcrc0) % 9.13/2.78 | (5) aElementOf0(xx, xS) % 9.13/2.78 | (6) sdtmndt0(xS, xx) = all_0_1_1 % 9.13/2.78 | (7) ! [v0] : ! [v1] : ( ~ aElementOf0(v1, v0) | ~ aSet0(v0) | aElement0(v1)) % 9.13/2.78 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) % 9.13/2.78 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElement0(v3)) % 9.13/2.78 | (10) ! [v0] : ( ~ isCountable0(v0) | ~ isFinite0(v0) | ~ aSet0(v0)) % 9.13/2.78 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0)) % 9.13/2.78 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2)) % 9.13/2.79 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) % 9.13/2.79 | (14) ! [v0] : ! [v1] : ( ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2] : (aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 9.13/2.79 | (15) ! [v0] : ! [v1] : ( ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) % 9.13/2.79 | (16) aSet0(xS) % 9.13/2.79 | (17) ! [v0] : ( ~ aSet0(v0) | aSubsetOf0(v0, v0)) % 9.13/2.79 | (18) ! [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))))) % 9.13/2.79 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) % 9.13/2.79 | (20) ~ isCountable0(slcrc0) % 9.13/2.79 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ aSubsetOf0(v1, v0) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v1) | ~ aSet0(v0)) % 9.13/2.79 | (22) sdtpldt0(all_0_1_1, xx) = all_0_0_0 % 9.13/2.79 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0)) % 9.13/2.79 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ aSubsetOf0(v1, v2) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v2) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v0, v2)) % 9.13/2.79 | (25) ! [v0] : (v0 = slcrc0 | ~ aSet0(v0) | ? [v1] : aElementOf0(v1, v0)) % 9.13/2.79 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 9.13/2.79 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | aElementOf0(v2, v0)) % 9.13/2.79 | (28) ~ (all_0_0_0 = xS) % 9.13/2.79 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v1, v2) | ~ aElement0(v1) | ~ aSet0(v0)) % 9.13/2.79 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElement0(v3)) % 9.13/2.79 | (31) ! [v0] : ! [v1] : ( ~ aSubsetOf0(v1, v0) | ~ isFinite0(v0) | ~ aSet0(v0) | isFinite0(v1)) % 9.13/2.79 | (32) ! [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)))))) % 9.13/2.79 | (33) aSet0(slcrc0) % 9.13/2.79 | (34) isFinite0(slcrc0) % 9.13/2.79 | % 9.13/2.79 | Instantiating formula (7) with xx, xS and discharging atoms aElementOf0(xx, xS), aSet0(xS), yields: % 9.13/2.79 | (35) aElement0(xx) % 9.13/2.79 | % 9.13/2.79 | Instantiating formula (18) with xS, all_0_1_1, xx, xS and discharging atoms sdtmndt0(xS, xx) = all_0_1_1, aElement0(xx), aSet0(xS), yields: % 9.13/2.79 | (36) all_0_1_1 = xS | ? [v0] : (aElementOf0(v0, xS) & (v0 = xx | ~ aElement0(v0))) % 9.13/2.79 | % 9.13/2.79 | Instantiating formula (3) with all_0_1_1, xx, xS and discharging atoms sdtmndt0(xS, xx) = all_0_1_1, aElement0(xx), aSet0(xS), yields: % 9.13/2.79 | (37) aSet0(all_0_1_1) % 9.13/2.79 | % 9.13/2.79 | Instantiating formula (32) 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: % 9.13/2.79 | (38) 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))))) % 9.13/2.79 | % 9.13/2.79 | Instantiating formula (14) with all_0_1_1, xS and discharging atoms aSet0(all_0_1_1), aSet0(xS), yields: % 9.13/2.79 | (39) aSubsetOf0(all_0_1_1, xS) | ? [v0] : (aElementOf0(v0, all_0_1_1) & ~ aElementOf0(v0, xS)) % 9.13/2.79 | % 9.13/2.79 | Instantiating formula (14) with xS, all_0_1_1 and discharging atoms aSet0(all_0_1_1), aSet0(xS), yields: % 9.13/2.79 | (40) aSubsetOf0(xS, all_0_1_1) | ? [v0] : (aElementOf0(v0, xS) & ~ aElementOf0(v0, all_0_1_1)) % 9.13/2.79 | % 9.13/2.79 +-Applying beta-rule and splitting (38), into two cases. % 9.13/2.79 |-Branch one: % 9.13/2.79 | (41) all_0_0_0 = xS % 9.13/2.79 | % 9.13/2.80 | Equations (41) can reduce 28 to: % 9.13/2.80 | (42) $false % 9.13/2.80 | % 9.13/2.80 |-The branch is then unsatisfiable % 9.13/2.80 |-Branch two: % 9.13/2.80 | (28) ~ (all_0_0_0 = xS) % 9.13/2.80 | (44) ? [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))))) % 9.13/2.80 | % 9.13/2.80 | Instantiating (44) with all_25_0_2 yields: % 9.13/2.80 | (45) ( ~ aElementOf0(all_25_0_2, xS) | ~ aElement0(all_25_0_2) | ( ~ (all_25_0_2 = xx) & ~ aElementOf0(all_25_0_2, all_0_1_1))) & (aElementOf0(all_25_0_2, xS) | (aElement0(all_25_0_2) & (all_25_0_2 = xx | aElementOf0(all_25_0_2, all_0_1_1)))) % 9.13/2.80 | % 9.13/2.80 | Applying alpha-rule on (45) yields: % 9.13/2.80 | (46) ~ aElementOf0(all_25_0_2, xS) | ~ aElement0(all_25_0_2) | ( ~ (all_25_0_2 = xx) & ~ aElementOf0(all_25_0_2, all_0_1_1)) % 9.13/2.80 | (47) aElementOf0(all_25_0_2, xS) | (aElement0(all_25_0_2) & (all_25_0_2 = xx | aElementOf0(all_25_0_2, all_0_1_1))) % 9.13/2.80 | % 9.13/2.80 +-Applying beta-rule and splitting (36), into two cases. % 9.13/2.80 |-Branch one: % 9.13/2.80 | (48) all_0_1_1 = xS % 9.13/2.80 | % 9.13/2.80 | From (48) and (6) follows: % 9.13/2.80 | (49) sdtmndt0(xS, xx) = xS % 9.13/2.80 | % 9.13/2.80 | From (48) and (37) follows: % 9.13/2.80 | (16) aSet0(xS) % 9.13/2.80 | % 9.13/2.80 | Instantiating formula (29) with xS, xx, xS and discharging atoms sdtmndt0(xS, xx) = xS, aElementOf0(xx, xS), aElement0(xx), aSet0(xS), yields: % 9.13/2.80 | (51) $false % 9.13/2.80 | % 9.13/2.80 |-The branch is then unsatisfiable % 9.13/2.80 |-Branch two: % 9.13/2.80 | (52) ~ (all_0_1_1 = xS) % 9.13/2.80 | (53) ? [v0] : (aElementOf0(v0, xS) & (v0 = xx | ~ aElement0(v0))) % 9.13/2.80 | % 9.13/2.80 | Instantiating (53) with all_102_0_24 yields: % 9.13/2.80 | (54) aElementOf0(all_102_0_24, xS) & (all_102_0_24 = xx | ~ aElement0(all_102_0_24)) % 9.13/2.80 | % 9.13/2.80 | Applying alpha-rule on (54) yields: % 9.13/2.80 | (55) aElementOf0(all_102_0_24, xS) % 9.13/2.80 | (56) all_102_0_24 = xx | ~ aElement0(all_102_0_24) % 9.13/2.80 | % 9.13/2.80 | Instantiating formula (7) with all_102_0_24, xS and discharging atoms aElementOf0(all_102_0_24, xS), aSet0(xS), yields: % 9.13/2.80 | (57) aElement0(all_102_0_24) % 9.13/2.80 | % 9.13/2.80 +-Applying beta-rule and splitting (56), into two cases. % 9.13/2.80 |-Branch one: % 9.13/2.80 | (58) ~ aElement0(all_102_0_24) % 9.13/2.80 | % 9.13/2.80 | Using (57) and (58) yields: % 9.13/2.80 | (51) $false % 9.13/2.80 | % 9.13/2.80 |-The branch is then unsatisfiable % 9.13/2.80 |-Branch two: % 9.13/2.80 | (57) aElement0(all_102_0_24) % 9.13/2.80 | (61) all_102_0_24 = xx % 9.13/2.80 | % 9.13/2.80 | From (61) and (57) follows: % 9.13/2.80 | (35) aElement0(xx) % 9.13/2.80 | % 9.13/2.80 +-Applying beta-rule and splitting (40), into two cases. % 9.13/2.80 |-Branch one: % 9.13/2.80 | (63) aSubsetOf0(xS, all_0_1_1) % 9.13/2.80 | % 9.13/2.80 +-Applying beta-rule and splitting (39), into two cases. % 9.13/2.80 |-Branch one: % 9.13/2.80 | (64) aSubsetOf0(all_0_1_1, xS) % 9.13/2.80 | % 9.13/2.80 | Instantiating formula (21) with all_0_1_1, xS and discharging atoms aSubsetOf0(all_0_1_1, xS), aSubsetOf0(xS, all_0_1_1), aSet0(all_0_1_1), aSet0(xS), yields: % 9.13/2.80 | (48) all_0_1_1 = xS % 9.13/2.80 | % 9.13/2.80 | Equations (48) can reduce 52 to: % 9.13/2.80 | (42) $false % 9.13/2.80 | % 9.13/2.80 |-The branch is then unsatisfiable % 9.13/2.80 |-Branch two: % 9.13/2.80 | (67) ~ aSubsetOf0(all_0_1_1, xS) % 9.13/2.80 | (68) ? [v0] : (aElementOf0(v0, all_0_1_1) & ~ aElementOf0(v0, xS)) % 9.13/2.80 | % 9.13/2.80 | Instantiating (68) with all_141_0_26 yields: % 9.13/2.80 | (69) aElementOf0(all_141_0_26, all_0_1_1) & ~ aElementOf0(all_141_0_26, xS) % 9.13/2.80 | % 9.13/2.80 | Applying alpha-rule on (69) yields: % 9.13/2.80 | (70) aElementOf0(all_141_0_26, all_0_1_1) % 9.13/2.80 | (71) ~ aElementOf0(all_141_0_26, xS) % 9.13/2.80 | % 9.13/2.80 | Instantiating formula (23) with all_141_0_26, all_0_1_1, xx, xS and discharging atoms sdtmndt0(xS, xx) = all_0_1_1, aElementOf0(all_141_0_26, all_0_1_1), aElement0(xx), aSet0(xS), ~ aElementOf0(all_141_0_26, xS), yields: % 9.13/2.80 | (51) $false % 9.13/2.80 | % 9.13/2.80 |-The branch is then unsatisfiable % 9.13/2.80 |-Branch two: % 9.13/2.80 | (73) ~ aSubsetOf0(xS, all_0_1_1) % 9.13/2.80 | (74) ? [v0] : (aElementOf0(v0, xS) & ~ aElementOf0(v0, all_0_1_1)) % 9.13/2.80 | % 9.13/2.80 | Instantiating (74) with all_135_0_33 yields: % 9.13/2.80 | (75) aElementOf0(all_135_0_33, xS) & ~ aElementOf0(all_135_0_33, all_0_1_1) % 9.13/2.80 | % 9.13/2.80 | Applying alpha-rule on (75) yields: % 9.13/2.80 | (76) aElementOf0(all_135_0_33, xS) % 9.13/2.80 | (77) ~ aElementOf0(all_135_0_33, all_0_1_1) % 9.13/2.80 | % 9.13/2.80 +-Applying beta-rule and splitting (39), into two cases. % 9.13/2.80 |-Branch one: % 9.13/2.80 | (64) aSubsetOf0(all_0_1_1, xS) % 9.13/2.80 | % 9.13/2.80 | Instantiating formula (7) with all_135_0_33, xS and discharging atoms aElementOf0(all_135_0_33, xS), aSet0(xS), yields: % 9.13/2.80 | (79) aElement0(all_135_0_33) % 9.13/2.80 | % 9.13/2.80 +-Applying beta-rule and splitting (47), into two cases. % 9.13/2.80 |-Branch one: % 9.13/2.80 | (80) aElementOf0(all_25_0_2, xS) % 9.13/2.80 | % 9.13/2.80 +-Applying beta-rule and splitting (46), into two cases. % 9.13/2.80 |-Branch one: % 9.13/2.80 | (81) ~ aElementOf0(all_25_0_2, xS) % 9.13/2.80 | % 9.13/2.81 | Using (80) and (81) yields: % 9.13/2.81 | (51) $false % 9.13/2.81 | % 9.13/2.81 |-The branch is then unsatisfiable % 9.13/2.81 |-Branch two: % 9.13/2.81 | (80) aElementOf0(all_25_0_2, xS) % 9.13/2.81 | (84) ~ aElement0(all_25_0_2) | ( ~ (all_25_0_2 = xx) & ~ aElementOf0(all_25_0_2, all_0_1_1)) % 9.13/2.81 | % 9.13/2.81 | Instantiating formula (7) with all_25_0_2, xS and discharging atoms aElementOf0(all_25_0_2, xS), aSet0(xS), yields: % 9.13/2.81 | (85) aElement0(all_25_0_2) % 9.13/2.81 | % 9.13/2.81 | Instantiating formula (13) with all_135_0_33, all_0_1_1, xx, xS and discharging atoms sdtmndt0(xS, xx) = all_0_1_1, aElementOf0(all_135_0_33, xS), aElement0(all_135_0_33), aElement0(xx), aSet0(xS), ~ aElementOf0(all_135_0_33, all_0_1_1), yields: % 9.13/2.81 | (86) all_135_0_33 = xx % 9.13/2.81 | % 9.13/2.81 | From (86) and (79) follows: % 9.13/2.81 | (35) aElement0(xx) % 9.13/2.81 | % 9.13/2.81 +-Applying beta-rule and splitting (84), into two cases. % 9.13/2.81 |-Branch one: % 9.13/2.81 | (88) ~ aElement0(all_25_0_2) % 9.13/2.81 | % 9.13/2.81 | Using (85) and (88) yields: % 9.13/2.81 | (51) $false % 9.13/2.81 | % 9.13/2.81 |-The branch is then unsatisfiable % 9.13/2.81 |-Branch two: % 9.13/2.81 | (85) aElement0(all_25_0_2) % 9.13/2.81 | (91) ~ (all_25_0_2 = xx) & ~ aElementOf0(all_25_0_2, all_0_1_1) % 9.13/2.81 | % 9.13/2.81 | Applying alpha-rule on (91) yields: % 9.13/2.81 | (92) ~ (all_25_0_2 = xx) % 9.13/2.81 | (93) ~ aElementOf0(all_25_0_2, all_0_1_1) % 9.13/2.81 | % 9.13/2.81 | Instantiating formula (13) with all_25_0_2, all_0_1_1, xx, xS and discharging atoms sdtmndt0(xS, xx) = all_0_1_1, aElementOf0(all_25_0_2, xS), aElement0(all_25_0_2), aElement0(xx), aSet0(xS), ~ aElementOf0(all_25_0_2, all_0_1_1), yields: % 9.13/2.81 | (94) all_25_0_2 = xx % 9.13/2.81 | % 9.13/2.81 | Equations (94) can reduce 92 to: % 9.13/2.81 | (42) $false % 9.13/2.81 | % 9.13/2.81 |-The branch is then unsatisfiable % 9.13/2.81 |-Branch two: % 9.13/2.81 | (81) ~ aElementOf0(all_25_0_2, xS) % 9.13/2.81 | (97) aElement0(all_25_0_2) & (all_25_0_2 = xx | aElementOf0(all_25_0_2, all_0_1_1)) % 9.13/2.81 | % 9.13/2.81 | Applying alpha-rule on (97) yields: % 9.13/2.81 | (85) aElement0(all_25_0_2) % 9.13/2.81 | (99) all_25_0_2 = xx | aElementOf0(all_25_0_2, all_0_1_1) % 9.13/2.81 | % 9.13/2.81 | Instantiating formula (13) with all_135_0_33, all_0_1_1, xx, xS and discharging atoms sdtmndt0(xS, xx) = all_0_1_1, aElementOf0(all_135_0_33, xS), aElement0(all_135_0_33), aElement0(xx), aSet0(xS), ~ aElementOf0(all_135_0_33, all_0_1_1), yields: % 9.13/2.81 | (86) all_135_0_33 = xx % 9.13/2.81 | % 9.13/2.81 | From (86) and (76) follows: % 9.13/2.81 | (5) aElementOf0(xx, xS) % 9.13/2.81 | % 9.13/2.81 +-Applying beta-rule and splitting (99), into two cases. % 9.13/2.81 |-Branch one: % 9.13/2.81 | (102) aElementOf0(all_25_0_2, all_0_1_1) % 9.13/2.81 | % 9.13/2.81 | Instantiating formula (27) with all_25_0_2, all_0_1_1, xS and discharging atoms aSubsetOf0(all_0_1_1, xS), aElementOf0(all_25_0_2, all_0_1_1), aSet0(xS), ~ aElementOf0(all_25_0_2, xS), yields: % 9.13/2.81 | (51) $false % 9.13/2.81 | % 9.13/2.81 |-The branch is then unsatisfiable % 9.13/2.81 |-Branch two: % 9.13/2.81 | (93) ~ aElementOf0(all_25_0_2, all_0_1_1) % 9.13/2.81 | (94) all_25_0_2 = xx % 9.13/2.81 | % 9.13/2.81 | From (94) and (81) follows: % 9.13/2.81 | (106) ~ aElementOf0(xx, xS) % 9.13/2.81 | % 9.13/2.81 | Using (5) and (106) yields: % 9.13/2.81 | (51) $false % 9.13/2.81 | % 9.13/2.81 |-The branch is then unsatisfiable % 9.13/2.81 |-Branch two: % 9.13/2.81 | (67) ~ aSubsetOf0(all_0_1_1, xS) % 9.13/2.81 | (68) ? [v0] : (aElementOf0(v0, all_0_1_1) & ~ aElementOf0(v0, xS)) % 9.13/2.81 | % 9.13/2.81 | Instantiating (68) with all_143_0_55 yields: % 9.13/2.81 | (110) aElementOf0(all_143_0_55, all_0_1_1) & ~ aElementOf0(all_143_0_55, xS) % 9.13/2.81 | % 9.13/2.81 | Applying alpha-rule on (110) yields: % 9.13/2.81 | (111) aElementOf0(all_143_0_55, all_0_1_1) % 9.13/2.81 | (112) ~ aElementOf0(all_143_0_55, xS) % 9.13/2.81 | % 9.13/2.81 | Instantiating formula (23) with all_143_0_55, all_0_1_1, xx, xS and discharging atoms sdtmndt0(xS, xx) = all_0_1_1, aElementOf0(all_143_0_55, all_0_1_1), aElement0(xx), aSet0(xS), ~ aElementOf0(all_143_0_55, xS), yields: % 9.58/2.81 | (51) $false % 9.58/2.81 | % 9.58/2.81 |-The branch is then unsatisfiable % 9.58/2.81 % SZS output end Proof for theBenchmark % 9.58/2.81 % 9.58/2.81 2217ms %------------------------------------------------------------------------------