TSTP Solution File: NUM536+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------