TSTP Solution File: NUM535+2 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM535+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.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 6.15s 2.09s
% Output : Proof 8.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM535+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jul 6 19:48:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.61/0.60 ____ _
% 0.61/0.60 ___ / __ \_____(_)___ ________ __________
% 0.61/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.61/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.61/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.61/0.60
% 0.61/0.60 A Theorem Prover for First-Order Logic
% 0.61/0.60 (ePrincess v.1.0)
% 0.61/0.60
% 0.61/0.60 (c) Philipp Rümmer, 2009-2015
% 0.61/0.60 (c) Peter Backeman, 2014-2015
% 0.61/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.61/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.61/0.60 Bug reports to peter@backeman.se
% 0.61/0.60
% 0.61/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.61/0.60
% 0.61/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.62/0.99 Prover 0: Preprocessing ...
% 2.40/1.24 Prover 0: Constructing countermodel ...
% 6.15/2.09 Prover 0: proved (1434ms)
% 6.15/2.09
% 6.15/2.09 No countermodel exists, formula is valid
% 6.15/2.09 % SZS status Theorem for theBenchmark
% 6.15/2.09
% 6.15/2.09 Generating proof ... found it (size 71)
% 8.84/2.70
% 8.84/2.70 % SZS output start Proof for theBenchmark
% 8.84/2.70 Assumed formulas after preprocessing and simplification:
% 8.84/2.70 | (0) ? [v0] : ? [v1] : ? [v2] : (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) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtmndt0(v3, v4) = v5) | ~ aElement0(v4) | ~ aSet0(v6) | ~ aSet0(v3) | ? [v7] : ((v7 = v4 | ~ aElementOf0(v7, v6) | ~ aElementOf0(v7, v3) | ~ aElement0(v7)) & (aElementOf0(v7, v6) | ( ~ (v7 = v4) & aElementOf0(v7, v3) & aElement0(v7))))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtpldt0(v3, v4) = v5) | ~ aElement0(v4) | ~ aSet0(v6) | ~ aSet0(v3) | ? [v7] : (( ~ aElementOf0(v7, v6) | ~ aElement0(v7) | ( ~ (v7 = v4) & ~ aElementOf0(v7, v3))) & (aElementOf0(v7, v6) | (aElement0(v7) & (v7 = v4 | aElementOf0(v7, v3)))))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v4 | ~ (sdtmndt0(v3, v4) = v5) | ~ aElementOf0(v6, v3) | ~ aElement0(v6) | ~ aElement0(v4) | ~ aSet0(v3) | aElementOf0(v6, v5)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v4 | ~ (sdtpldt0(v3, v4) = v5) | ~ aElementOf0(v6, v5) | ~ aElement0(v4) | ~ aSet0(v3) | aElementOf0(v6, v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (sdtmndt0(v6, v5) = v4) | ~ (sdtmndt0(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (sdtpldt0(v6, v5) = v4) | ~ (sdtpldt0(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtmndt0(v3, v4) = v5) | ~ aElementOf0(v6, v5) | ~ aElement0(v4) | ~ aSet0(v3) | aElementOf0(v6, v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtmndt0(v3, v4) = v5) | ~ aElementOf0(v6, v5) | ~ aElement0(v4) | ~ aSet0(v3) | aElement0(v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v3, v4) = v5) | ~ aElementOf0(v6, v5) | ~ aElement0(v4) | ~ aSet0(v3) | aElement0(v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtpldt0(v3, v4) = v5) | ~ aElementOf0(v6, v3) | ~ aElement0(v6) | ~ aElement0(v4) | ~ aSet0(v3) | aElementOf0(v6, v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtmndt0(v3, v4) = v5) | ~ aElementOf0(v4, v5) | ~ aElement0(v4) | ~ aSet0(v3)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtmndt0(v3, v4) = v5) | ~ aElement0(v4) | ~ aSet0(v3) | aSet0(v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtpldt0(v3, v4) = v5) | ~ aElement0(v4) | ~ aSet0(v3) | aElementOf0(v4, v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtpldt0(v3, v4) = v5) | ~ aElement0(v4) | ~ aSet0(v3) | aSet0(v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ aSubsetOf0(v4, v5) | ~ aSubsetOf0(v3, v4) | ~ aSet0(v5) | ~ aSet0(v4) | ~ aSet0(v3) | aSubsetOf0(v3, v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ aSubsetOf0(v4, v3) | ~ aElementOf0(v5, v4) | ~ aSet0(v3) | aElementOf0(v5, v3)) & ! [v3] : ! [v4] : (v4 = v3 | ~ aSubsetOf0(v4, v3) | ~ aSubsetOf0(v3, v4) | ~ aSet0(v4) | ~ aSet0(v3)) & ! [v3] : ! [v4] : ( ~ aSubsetOf0(v4, v3) | ~ isFinite0(v3) | ~ aSet0(v3) | isFinite0(v4)) & ! [v3] : ! [v4] : ( ~ aSubsetOf0(v4, v3) | ~ aSet0(v3) | aSet0(v4)) & ! [v3] : ! [v4] : ( ~ aElementOf0(v4, v3) | ~ aSet0(v3) | aElement0(v4)) & ! [v3] : ! [v4] : ( ~ aSet0(v4) | ~ aSet0(v3) | aSubsetOf0(v4, v3) | ? [v5] : (aElementOf0(v5, v4) & ~ aElementOf0(v5, v3))) & ! [v3] : (v3 = xx | ~ aElementOf0(v3, v1) | aElementOf0(v3, v0)) & ! [v3] : (v3 = xx | ~ aElementOf0(v3, xS) | ~ aElement0(v3) | aElementOf0(v3, v0)) & ! [v3] : (v3 = slcrc0 | ~ aSet0(v3) | ? [v4] : aElementOf0(v4, v3)) & ! [v3] : ( ~ isCountable0(v3) | ~ isFinite0(v3) | ~ aSet0(v3)) & ! [v3] : ( ~ aElementOf0(v3, v1) | aElement0(v3)) & ! [v3] : ( ~ aElementOf0(v3, v0) | ~ aElement0(v3) | aElementOf0(v3, v1)) & ! [v3] : ( ~ aElementOf0(v3, v0) | aElementOf0(v3, xS)) & ! [v3] : ( ~ aElementOf0(v3, v0) | aElement0(v3)) & ! [v3] : ~ aElementOf0(v3, slcrc0) & ! [v3] : ( ~ aSet0(v3) | aSubsetOf0(v3, v3)) & ( ~ aElement0(xx) | aElementOf0(xx, v1)) & ((aElementOf0(v2, v1) & ~ aSubsetOf0(v1, xS) & ~ aElementOf0(v2, xS)) | (aElementOf0(v2, xS) & ~ aSubsetOf0(xS, v1) & ~ aElementOf0(v2, v1))))
% 8.87/2.73 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 8.87/2.73 | (1) sdtmndt0(xS, xx) = all_0_2_2 & sdtpldt0(all_0_2_2, xx) = all_0_1_1 & isFinite0(slcrc0) & aElementOf0(xx, xS) & aSet0(all_0_1_1) & aSet0(all_0_2_2) & aSet0(xS) & aSet0(slcrc0) & ~ isCountable0(slcrc0) & ~ aElementOf0(xx, all_0_2_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))))) & ! [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_1_1) | aElementOf0(v0, all_0_2_2)) & ! [v0] : (v0 = xx | ~ aElementOf0(v0, xS) | ~ aElement0(v0) | aElementOf0(v0, all_0_2_2)) & ! [v0] : (v0 = slcrc0 | ~ aSet0(v0) | ? [v1] : aElementOf0(v1, v0)) & ! [v0] : ( ~ isCountable0(v0) | ~ isFinite0(v0) | ~ aSet0(v0)) & ! [v0] : ( ~ aElementOf0(v0, all_0_1_1) | aElement0(v0)) & ! [v0] : ( ~ aElementOf0(v0, all_0_2_2) | ~ aElement0(v0) | aElementOf0(v0, all_0_1_1)) & ! [v0] : ( ~ aElementOf0(v0, all_0_2_2) | aElementOf0(v0, xS)) & ! [v0] : ( ~ aElementOf0(v0, all_0_2_2) | aElement0(v0)) & ! [v0] : ~ aElementOf0(v0, slcrc0) & ! [v0] : ( ~ aSet0(v0) | aSubsetOf0(v0, v0)) & ( ~ aElement0(xx) | aElementOf0(xx, all_0_1_1)) & ((aElementOf0(all_0_0_0, all_0_1_1) & ~ aSubsetOf0(all_0_1_1, xS) & ~ aElementOf0(all_0_0_0, xS)) | (aElementOf0(all_0_0_0, xS) & ~ aSubsetOf0(xS, all_0_1_1) & ~ aElementOf0(all_0_0_0, all_0_1_1)))
% 8.87/2.75 |
% 8.87/2.75 | Applying alpha-rule on (1) yields:
% 8.87/2.75 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0))
% 8.87/2.75 | (3) ! [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))))))
% 8.87/2.75 | (4) ! [v0] : (v0 = slcrc0 | ~ aSet0(v0) | ? [v1] : aElementOf0(v1, v0))
% 8.87/2.75 | (5) ! [v0] : ~ aElementOf0(v0, slcrc0)
% 8.87/2.75 | (6) ! [v0] : ! [v1] : ( ~ aSubsetOf0(v1, v0) | ~ isFinite0(v0) | ~ aSet0(v0) | isFinite0(v1))
% 8.87/2.75 | (7) (aElementOf0(all_0_0_0, all_0_1_1) & ~ aSubsetOf0(all_0_1_1, xS) & ~ aElementOf0(all_0_0_0, xS)) | (aElementOf0(all_0_0_0, xS) & ~ aSubsetOf0(xS, all_0_1_1) & ~ aElementOf0(all_0_0_0, all_0_1_1))
% 8.87/2.75 | (8) ! [v0] : ( ~ aSet0(v0) | aSubsetOf0(v0, v0))
% 8.87/2.75 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ aSubsetOf0(v1, v0) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v1) | ~ aSet0(v0))
% 8.87/2.75 | (10) ! [v0] : ! [v1] : ( ~ aElementOf0(v1, v0) | ~ aSet0(v0) | aElement0(v1))
% 8.87/2.75 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v1, v2))
% 8.87/2.75 | (12) ! [v0] : ! [v1] : ( ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1))
% 8.87/2.75 | (13) ! [v0] : ( ~ aElementOf0(v0, all_0_1_1) | aElement0(v0))
% 8.87/2.75 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 8.87/2.75 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ aSubsetOf0(v1, v2) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v2) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v0, v2))
% 8.87/2.75 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2))
% 8.87/2.75 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElement0(v3))
% 8.87/2.75 | (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)))))
% 8.87/2.75 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2))
% 8.87/2.75 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2))
% 8.87/2.75 | (21) aSet0(slcrc0)
% 8.87/2.75 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElement0(v3))
% 8.87/2.75 | (23) ~ aElement0(xx) | aElementOf0(xx, all_0_1_1)
% 8.87/2.75 | (24) isFinite0(slcrc0)
% 8.87/2.75 | (25) ~ aElementOf0(xx, all_0_2_2)
% 8.87/2.75 | (26) aSet0(xS)
% 8.87/2.75 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2))
% 8.87/2.75 | (28) ! [v0] : ( ~ isCountable0(v0) | ~ isFinite0(v0) | ~ aSet0(v0))
% 8.87/2.75 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v1, v2) | ~ aElement0(v1) | ~ aSet0(v0))
% 8.87/2.75 | (30) ! [v0] : ( ~ aElementOf0(v0, all_0_2_2) | aElement0(v0))
% 8.87/2.75 | (31) sdtmndt0(xS, xx) = all_0_2_2
% 8.87/2.75 | (32) aSet0(all_0_2_2)
% 8.87/2.75 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0))
% 8.87/2.75 | (34) ! [v0] : (v0 = xx | ~ aElementOf0(v0, all_0_1_1) | aElementOf0(v0, all_0_2_2))
% 8.87/2.75 | (35) ~ isCountable0(slcrc0)
% 8.87/2.75 | (36) aElementOf0(xx, xS)
% 8.87/2.75 | (37) sdtpldt0(all_0_2_2, xx) = all_0_1_1
% 8.87/2.75 | (38) aSet0(all_0_1_1)
% 8.87/2.75 | (39) ! [v0] : ( ~ aElementOf0(v0, all_0_2_2) | aElementOf0(v0, xS))
% 8.87/2.75 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | aElementOf0(v2, v0))
% 8.87/2.75 | (41) ! [v0] : ( ~ aElementOf0(v0, all_0_2_2) | ~ aElement0(v0) | aElementOf0(v0, all_0_1_1))
% 8.87/2.75 | (42) ! [v0] : ! [v1] : ( ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2] : (aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 8.87/2.76 | (43) ! [v0] : (v0 = xx | ~ aElementOf0(v0, xS) | ~ aElement0(v0) | aElementOf0(v0, all_0_2_2))
% 8.87/2.76 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 8.87/2.76 |
% 8.87/2.76 | Instantiating formula (42) with all_0_2_2, all_0_1_1 and discharging atoms aSet0(all_0_1_1), aSet0(all_0_2_2), yields:
% 8.87/2.76 | (45) aSubsetOf0(all_0_2_2, all_0_1_1) | ? [v0] : (aElementOf0(v0, all_0_2_2) & ~ aElementOf0(v0, all_0_1_1))
% 8.87/2.76 |
% 8.87/2.76 | Instantiating formula (42) with all_0_1_1, all_0_2_2 and discharging atoms aSet0(all_0_1_1), aSet0(all_0_2_2), yields:
% 8.87/2.76 | (46) aSubsetOf0(all_0_1_1, all_0_2_2) | ? [v0] : (aElementOf0(v0, all_0_1_1) & ~ aElementOf0(v0, all_0_2_2))
% 8.87/2.76 |
% 8.87/2.76 | Instantiating formula (10) with xx, xS and discharging atoms aElementOf0(xx, xS), aSet0(xS), yields:
% 8.87/2.76 | (47) aElement0(xx)
% 8.87/2.76 |
% 8.87/2.76 | Instantiating formula (42) with xS, all_0_2_2 and discharging atoms aSet0(all_0_2_2), aSet0(xS), yields:
% 8.87/2.76 | (48) aSubsetOf0(xS, all_0_2_2) | ? [v0] : (aElementOf0(v0, xS) & ~ aElementOf0(v0, all_0_2_2))
% 8.87/2.76 |
% 8.87/2.76 | Instantiating formula (42) with all_0_2_2, xS and discharging atoms aSet0(all_0_2_2), aSet0(xS), yields:
% 8.87/2.76 | (49) aSubsetOf0(all_0_2_2, xS) | ? [v0] : (aElementOf0(v0, all_0_2_2) & ~ aElementOf0(v0, xS))
% 8.87/2.76 |
% 8.87/2.76 +-Applying beta-rule and splitting (23), into two cases.
% 8.87/2.76 |-Branch one:
% 8.87/2.76 | (50) aElementOf0(xx, all_0_1_1)
% 8.87/2.76 |
% 8.87/2.76 | Instantiating formula (18) with xS, all_0_2_2, xx, xS and discharging atoms sdtmndt0(xS, xx) = all_0_2_2, aElement0(xx), aSet0(xS), yields:
% 8.87/2.76 | (51) all_0_2_2 = xS | ? [v0] : (aElementOf0(v0, xS) & (v0 = xx | ~ aElement0(v0)))
% 8.87/2.76 |
% 8.87/2.76 +-Applying beta-rule and splitting (7), into two cases.
% 8.87/2.76 |-Branch one:
% 8.87/2.76 | (52) aElementOf0(all_0_0_0, all_0_1_1) & ~ aSubsetOf0(all_0_1_1, xS) & ~ aElementOf0(all_0_0_0, xS)
% 8.87/2.76 |
% 8.87/2.76 | Applying alpha-rule on (52) yields:
% 8.87/2.76 | (53) aElementOf0(all_0_0_0, all_0_1_1)
% 8.87/2.76 | (54) ~ aSubsetOf0(all_0_1_1, xS)
% 8.87/2.76 | (55) ~ aElementOf0(all_0_0_0, xS)
% 8.87/2.76 |
% 8.87/2.76 | Instantiating formula (34) with all_0_0_0 and discharging atoms aElementOf0(all_0_0_0, all_0_1_1), yields:
% 8.87/2.76 | (56) all_0_0_0 = xx | aElementOf0(all_0_0_0, all_0_2_2)
% 8.87/2.76 |
% 8.87/2.76 +-Applying beta-rule and splitting (46), into two cases.
% 8.87/2.76 |-Branch one:
% 8.87/2.76 | (57) aSubsetOf0(all_0_1_1, all_0_2_2)
% 8.87/2.76 |
% 8.87/2.76 | Instantiating formula (40) with xx, all_0_1_1, all_0_2_2 and discharging atoms aSubsetOf0(all_0_1_1, all_0_2_2), aElementOf0(xx, all_0_1_1), aSet0(all_0_2_2), ~ aElementOf0(xx, all_0_2_2), yields:
% 8.87/2.76 | (58) $false
% 8.87/2.76 |
% 8.87/2.76 |-The branch is then unsatisfiable
% 8.87/2.76 |-Branch two:
% 8.87/2.76 | (59) ~ aSubsetOf0(all_0_1_1, all_0_2_2)
% 8.87/2.76 | (60) ? [v0] : (aElementOf0(v0, all_0_1_1) & ~ aElementOf0(v0, all_0_2_2))
% 8.87/2.76 |
% 8.87/2.76 | Instantiating (60) with all_39_0_4 yields:
% 8.87/2.76 | (61) aElementOf0(all_39_0_4, all_0_1_1) & ~ aElementOf0(all_39_0_4, all_0_2_2)
% 8.87/2.76 |
% 8.87/2.76 | Applying alpha-rule on (61) yields:
% 8.87/2.76 | (62) aElementOf0(all_39_0_4, all_0_1_1)
% 8.87/2.76 | (63) ~ aElementOf0(all_39_0_4, all_0_2_2)
% 8.87/2.76 |
% 8.87/2.76 | Instantiating formula (34) with all_39_0_4 and discharging atoms aElementOf0(all_39_0_4, all_0_1_1), ~ aElementOf0(all_39_0_4, all_0_2_2), yields:
% 8.87/2.76 | (64) all_39_0_4 = xx
% 8.87/2.76 |
% 8.87/2.76 | From (64) and (63) follows:
% 8.87/2.76 | (25) ~ aElementOf0(xx, all_0_2_2)
% 8.87/2.76 |
% 8.87/2.76 +-Applying beta-rule and splitting (48), into two cases.
% 8.87/2.76 |-Branch one:
% 8.87/2.76 | (66) aSubsetOf0(xS, all_0_2_2)
% 8.87/2.76 |
% 8.87/2.76 | Instantiating formula (40) with xx, xS, all_0_2_2 and discharging atoms aSubsetOf0(xS, all_0_2_2), aElementOf0(xx, xS), aSet0(all_0_2_2), ~ aElementOf0(xx, all_0_2_2), yields:
% 8.87/2.76 | (58) $false
% 8.87/2.76 |
% 8.87/2.76 |-The branch is then unsatisfiable
% 8.87/2.76 |-Branch two:
% 8.87/2.76 | (68) ~ aSubsetOf0(xS, all_0_2_2)
% 8.87/2.76 | (69) ? [v0] : (aElementOf0(v0, xS) & ~ aElementOf0(v0, all_0_2_2))
% 8.87/2.76 |
% 8.87/2.76 +-Applying beta-rule and splitting (49), into two cases.
% 8.87/2.76 |-Branch one:
% 8.87/2.76 | (70) aSubsetOf0(all_0_2_2, xS)
% 8.87/2.76 |
% 8.87/2.76 +-Applying beta-rule and splitting (51), into two cases.
% 8.87/2.76 |-Branch one:
% 8.87/2.76 | (71) all_0_2_2 = xS
% 8.87/2.76 |
% 8.87/2.76 | From (71) and (70) follows:
% 8.87/2.76 | (72) aSubsetOf0(xS, xS)
% 8.87/2.76 |
% 8.87/2.76 | From (71) and (68) follows:
% 8.87/2.76 | (73) ~ aSubsetOf0(xS, xS)
% 8.87/2.76 |
% 8.87/2.76 | Using (72) and (73) yields:
% 8.87/2.76 | (58) $false
% 8.87/2.76 |
% 8.87/2.76 |-The branch is then unsatisfiable
% 8.87/2.76 |-Branch two:
% 8.87/2.76 | (75) ~ (all_0_2_2 = xS)
% 8.87/2.76 | (76) ? [v0] : (aElementOf0(v0, xS) & (v0 = xx | ~ aElement0(v0)))
% 8.87/2.76 |
% 8.87/2.76 | Instantiating (76) with all_184_0_23 yields:
% 8.87/2.76 | (77) aElementOf0(all_184_0_23, xS) & (all_184_0_23 = xx | ~ aElement0(all_184_0_23))
% 8.87/2.77 |
% 8.87/2.77 | Applying alpha-rule on (77) yields:
% 8.87/2.77 | (78) aElementOf0(all_184_0_23, xS)
% 8.87/2.77 | (79) all_184_0_23 = xx | ~ aElement0(all_184_0_23)
% 8.87/2.77 |
% 8.87/2.77 | Instantiating formula (10) with all_184_0_23, xS and discharging atoms aElementOf0(all_184_0_23, xS), aSet0(xS), yields:
% 8.87/2.77 | (80) aElement0(all_184_0_23)
% 8.87/2.77 |
% 8.87/2.77 +-Applying beta-rule and splitting (79), into two cases.
% 8.87/2.77 |-Branch one:
% 8.87/2.77 | (81) ~ aElement0(all_184_0_23)
% 8.87/2.77 |
% 8.87/2.77 | Using (80) and (81) yields:
% 8.87/2.77 | (58) $false
% 8.87/2.77 |
% 8.87/2.77 |-The branch is then unsatisfiable
% 8.87/2.77 |-Branch two:
% 8.87/2.77 | (80) aElement0(all_184_0_23)
% 8.87/2.77 | (84) all_184_0_23 = xx
% 8.87/2.77 |
% 8.87/2.77 | From (84) and (78) follows:
% 8.87/2.77 | (36) aElementOf0(xx, xS)
% 8.87/2.77 |
% 8.87/2.77 +-Applying beta-rule and splitting (56), into two cases.
% 8.87/2.77 |-Branch one:
% 8.87/2.77 | (86) aElementOf0(all_0_0_0, all_0_2_2)
% 8.87/2.77 |
% 8.87/2.77 | Instantiating formula (39) with all_0_0_0 and discharging atoms aElementOf0(all_0_0_0, all_0_2_2), ~ aElementOf0(all_0_0_0, xS), yields:
% 8.87/2.77 | (58) $false
% 8.87/2.77 |
% 8.87/2.77 |-The branch is then unsatisfiable
% 8.87/2.77 |-Branch two:
% 8.87/2.77 | (88) ~ aElementOf0(all_0_0_0, all_0_2_2)
% 8.87/2.77 | (89) all_0_0_0 = xx
% 8.87/2.77 |
% 8.87/2.77 | From (89) and (55) follows:
% 8.87/2.77 | (90) ~ aElementOf0(xx, xS)
% 8.87/2.77 |
% 8.87/2.77 | Using (36) and (90) yields:
% 8.87/2.77 | (58) $false
% 8.87/2.77 |
% 8.87/2.77 |-The branch is then unsatisfiable
% 8.87/2.77 |-Branch two:
% 8.87/2.77 | (92) ~ aSubsetOf0(all_0_2_2, xS)
% 8.87/2.77 | (93) ? [v0] : (aElementOf0(v0, all_0_2_2) & ~ aElementOf0(v0, xS))
% 8.87/2.77 |
% 8.87/2.77 | Instantiating (93) with all_144_0_27 yields:
% 8.87/2.77 | (94) aElementOf0(all_144_0_27, all_0_2_2) & ~ aElementOf0(all_144_0_27, xS)
% 8.87/2.77 |
% 8.87/2.77 | Applying alpha-rule on (94) yields:
% 8.87/2.77 | (95) aElementOf0(all_144_0_27, all_0_2_2)
% 8.87/2.77 | (96) ~ aElementOf0(all_144_0_27, xS)
% 8.87/2.77 |
% 8.87/2.77 | Instantiating formula (39) with all_144_0_27 and discharging atoms aElementOf0(all_144_0_27, all_0_2_2), ~ aElementOf0(all_144_0_27, xS), yields:
% 8.87/2.77 | (58) $false
% 8.87/2.77 |
% 8.87/2.77 |-The branch is then unsatisfiable
% 8.87/2.77 |-Branch two:
% 8.87/2.77 | (98) aElementOf0(all_0_0_0, xS) & ~ aSubsetOf0(xS, all_0_1_1) & ~ aElementOf0(all_0_0_0, all_0_1_1)
% 8.87/2.77 |
% 8.87/2.77 | Applying alpha-rule on (98) yields:
% 8.87/2.77 | (99) aElementOf0(all_0_0_0, xS)
% 8.87/2.77 | (100) ~ aSubsetOf0(xS, all_0_1_1)
% 8.87/2.77 | (101) ~ aElementOf0(all_0_0_0, all_0_1_1)
% 8.87/2.77 |
% 8.87/2.77 | Instantiating formula (10) with all_0_0_0, xS and discharging atoms aElementOf0(all_0_0_0, xS), aSet0(xS), yields:
% 8.87/2.77 | (102) aElement0(all_0_0_0)
% 8.87/2.77 |
% 8.87/2.77 | Instantiating formula (43) with all_0_0_0 and discharging atoms aElementOf0(all_0_0_0, xS), aElement0(all_0_0_0), yields:
% 8.87/2.77 | (56) all_0_0_0 = xx | aElementOf0(all_0_0_0, all_0_2_2)
% 8.87/2.77 |
% 8.87/2.77 +-Applying beta-rule and splitting (45), into two cases.
% 8.87/2.77 |-Branch one:
% 8.87/2.77 | (104) aSubsetOf0(all_0_2_2, all_0_1_1)
% 8.87/2.77 |
% 8.87/2.77 +-Applying beta-rule and splitting (46), into two cases.
% 8.87/2.77 |-Branch one:
% 8.87/2.77 | (57) aSubsetOf0(all_0_1_1, all_0_2_2)
% 8.87/2.77 |
% 8.87/2.77 | Instantiating formula (9) with all_0_1_1, all_0_2_2 and discharging atoms aSubsetOf0(all_0_1_1, all_0_2_2), aSubsetOf0(all_0_2_2, all_0_1_1), aSet0(all_0_1_1), aSet0(all_0_2_2), yields:
% 8.87/2.77 | (106) all_0_1_1 = all_0_2_2
% 8.87/2.77 |
% 8.87/2.77 | From (106) and (50) follows:
% 8.87/2.77 | (107) aElementOf0(xx, all_0_2_2)
% 8.87/2.77 |
% 8.87/2.77 | Using (107) and (25) yields:
% 8.87/2.77 | (58) $false
% 8.87/2.77 |
% 8.87/2.77 |-The branch is then unsatisfiable
% 8.87/2.77 |-Branch two:
% 8.87/2.77 | (59) ~ aSubsetOf0(all_0_1_1, all_0_2_2)
% 8.87/2.77 | (60) ? [v0] : (aElementOf0(v0, all_0_1_1) & ~ aElementOf0(v0, all_0_2_2))
% 8.87/2.77 |
% 8.87/2.77 | Instantiating (60) with all_75_0_51 yields:
% 8.87/2.77 | (111) aElementOf0(all_75_0_51, all_0_1_1) & ~ aElementOf0(all_75_0_51, all_0_2_2)
% 8.87/2.77 |
% 8.87/2.77 | Applying alpha-rule on (111) yields:
% 8.87/2.77 | (112) aElementOf0(all_75_0_51, all_0_1_1)
% 8.87/2.77 | (113) ~ aElementOf0(all_75_0_51, all_0_2_2)
% 8.87/2.77 |
% 8.87/2.77 | Instantiating formula (34) with all_75_0_51 and discharging atoms aElementOf0(all_75_0_51, all_0_1_1), ~ aElementOf0(all_75_0_51, all_0_2_2), yields:
% 8.87/2.77 | (114) all_75_0_51 = xx
% 8.87/2.77 |
% 8.87/2.77 | From (114) and (112) follows:
% 8.87/2.77 | (50) aElementOf0(xx, all_0_1_1)
% 8.87/2.77 |
% 8.87/2.77 +-Applying beta-rule and splitting (56), into two cases.
% 8.87/2.77 |-Branch one:
% 8.87/2.77 | (86) aElementOf0(all_0_0_0, all_0_2_2)
% 8.87/2.77 |
% 8.87/2.77 | Instantiating formula (41) with all_0_0_0 and discharging atoms aElementOf0(all_0_0_0, all_0_2_2), aElement0(all_0_0_0), ~ aElementOf0(all_0_0_0, all_0_1_1), yields:
% 8.87/2.77 | (58) $false
% 8.87/2.77 |
% 8.87/2.77 |-The branch is then unsatisfiable
% 8.87/2.77 |-Branch two:
% 8.87/2.77 | (88) ~ aElementOf0(all_0_0_0, all_0_2_2)
% 8.87/2.77 | (89) all_0_0_0 = xx
% 8.87/2.77 |
% 8.87/2.77 | From (89) and (101) follows:
% 8.87/2.77 | (120) ~ aElementOf0(xx, all_0_1_1)
% 8.87/2.77 |
% 8.87/2.77 | Using (50) and (120) yields:
% 8.87/2.77 | (58) $false
% 8.87/2.77 |
% 8.87/2.77 |-The branch is then unsatisfiable
% 8.87/2.77 |-Branch two:
% 8.87/2.78 | (122) ~ aSubsetOf0(all_0_2_2, all_0_1_1)
% 8.87/2.78 | (123) ? [v0] : (aElementOf0(v0, all_0_2_2) & ~ aElementOf0(v0, all_0_1_1))
% 8.87/2.78 |
% 8.87/2.78 | Instantiating (123) with all_46_0_64 yields:
% 8.87/2.78 | (124) aElementOf0(all_46_0_64, all_0_2_2) & ~ aElementOf0(all_46_0_64, all_0_1_1)
% 8.87/2.78 |
% 8.87/2.78 | Applying alpha-rule on (124) yields:
% 8.87/2.78 | (125) aElementOf0(all_46_0_64, all_0_2_2)
% 8.87/2.78 | (126) ~ aElementOf0(all_46_0_64, all_0_1_1)
% 8.87/2.78 |
% 8.87/2.78 | Instantiating formula (30) with all_46_0_64 and discharging atoms aElementOf0(all_46_0_64, all_0_2_2), yields:
% 8.87/2.78 | (127) aElement0(all_46_0_64)
% 8.87/2.78 |
% 8.87/2.78 | Instantiating formula (41) with all_46_0_64 and discharging atoms aElementOf0(all_46_0_64, all_0_2_2), aElement0(all_46_0_64), ~ aElementOf0(all_46_0_64, all_0_1_1), yields:
% 8.87/2.78 | (58) $false
% 8.87/2.78 |
% 8.87/2.78 |-The branch is then unsatisfiable
% 8.87/2.78 |-Branch two:
% 8.87/2.78 | (120) ~ aElementOf0(xx, all_0_1_1)
% 8.87/2.78 | (130) ~ aElement0(xx)
% 8.87/2.78 |
% 8.87/2.78 | Using (47) and (130) yields:
% 8.87/2.78 | (58) $false
% 8.87/2.78 |
% 8.87/2.78 |-The branch is then unsatisfiable
% 8.87/2.78 % SZS output end Proof for theBenchmark
% 8.87/2.78
% 8.87/2.78 2161ms
%------------------------------------------------------------------------------