TSTP Solution File: NUM535+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM535+1 : 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 08:45:35 EDT 2022
% Result : Theorem 5.00s 1.90s
% Output : Proof 8.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM535+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12 % 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 : Thu Jul 7 10:39:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.56/0.58 ____ _
% 0.56/0.58 ___ / __ \_____(_)___ ________ __________
% 0.56/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.58
% 0.56/0.58 A Theorem Prover for First-Order Logic
% 0.56/0.58 (ePrincess v.1.0)
% 0.56/0.58
% 0.56/0.58 (c) Philipp Rümmer, 2009-2015
% 0.56/0.58 (c) Peter Backeman, 2014-2015
% 0.56/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.58 Bug reports to peter@backeman.se
% 0.56/0.58
% 0.56/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.58
% 0.56/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.62/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.39/0.91 Prover 0: Preprocessing ...
% 1.89/1.16 Prover 0: Constructing countermodel ...
% 5.00/1.90 Prover 0: proved (1274ms)
% 5.00/1.90
% 5.00/1.90 No countermodel exists, formula is valid
% 5.00/1.90 % SZS status Theorem for theBenchmark
% 5.00/1.90
% 5.00/1.90 Generating proof ... found it (size 69)
% 8.06/2.59
% 8.06/2.59 % SZS output start Proof for theBenchmark
% 8.06/2.59 Assumed formulas after preprocessing and simplification:
% 8.06/2.59 | (0) ? [v0] : ? [v1] : (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)) & ( ~ aSubsetOf0(v1, xS) | ~ aSubsetOf0(xS, v1)))
% 8.49/2.63 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 8.49/2.63 | (1) 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)) & ( ~ aSubsetOf0(all_0_0_0, xS) | ~ aSubsetOf0(xS, all_0_0_0))
% 8.49/2.64 |
% 8.49/2.64 | Applying alpha-rule on (1) yields:
% 8.49/2.64 | (2) isFinite0(slcrc0)
% 8.49/2.64 | (3) ~ isCountable0(slcrc0)
% 8.49/2.64 | (4) aSet0(slcrc0)
% 8.49/2.64 | (5) ! [v0] : ~ aElementOf0(v0, slcrc0)
% 8.49/2.64 | (6) ! [v0] : (v0 = slcrc0 | ~ aSet0(v0) | ? [v1] : aElementOf0(v1, v0))
% 8.49/2.64 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 8.49/2.64 | (8) ! [v0] : ! [v1] : ( ~ aSubsetOf0(v1, v0) | ~ isFinite0(v0) | ~ aSet0(v0) | isFinite0(v1))
% 8.49/2.64 | (9) ! [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)))))
% 8.49/2.64 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElement0(v3))
% 8.49/2.64 | (11) ! [v0] : ( ~ aSet0(v0) | aSubsetOf0(v0, v0))
% 8.49/2.64 | (12) sdtmndt0(xS, xx) = all_0_1_1
% 8.49/2.64 | (13) ! [v0] : ! [v1] : (v1 = v0 | ~ aSubsetOf0(v1, v0) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v1) | ~ aSet0(v0))
% 8.49/2.64 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v1, v2))
% 8.49/2.64 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2))
% 8.49/2.65 | (16) ! [v0] : ! [v1] : ( ~ aElementOf0(v1, v0) | ~ aSet0(v0) | aElement0(v1))
% 8.49/2.65 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0))
% 8.49/2.65 | (18) ! [v0] : ! [v1] : ( ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1))
% 8.49/2.65 | (19) ! [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))))))
% 8.49/2.65 | (20) aElementOf0(xx, xS)
% 8.49/2.65 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2))
% 8.49/2.65 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ aSubsetOf0(v1, v2) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v2) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v0, v2))
% 8.49/2.65 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2))
% 8.49/2.65 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2))
% 8.49/2.65 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElement0(v3))
% 8.49/2.65 | (26) ~ aSubsetOf0(all_0_0_0, xS) | ~ aSubsetOf0(xS, all_0_0_0)
% 8.49/2.65 | (27) ! [v0] : ( ~ isCountable0(v0) | ~ isFinite0(v0) | ~ aSet0(v0))
% 8.49/2.65 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 8.49/2.65 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0))
% 8.49/2.65 | (30) sdtpldt0(all_0_1_1, xx) = all_0_0_0
% 8.49/2.65 | (31) aSet0(xS)
% 8.49/2.65 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | aElementOf0(v2, v0))
% 8.49/2.65 | (33) ! [v0] : ! [v1] : ( ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2] : (aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 8.49/2.65 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v1, v2) | ~ aElement0(v1) | ~ aSet0(v0))
% 8.49/2.65 |
% 8.49/2.65 | Instantiating formula (16) with xx, xS and discharging atoms aElementOf0(xx, xS), aSet0(xS), yields:
% 8.49/2.65 | (35) aElement0(xx)
% 8.49/2.65 |
% 8.49/2.65 | Instantiating formula (9) with xS, all_0_1_1, xx, xS and discharging atoms sdtmndt0(xS, xx) = all_0_1_1, aElement0(xx), aSet0(xS), yields:
% 8.49/2.65 | (36) all_0_1_1 = xS | ? [v0] : (aElementOf0(v0, xS) & (v0 = xx | ~ aElement0(v0)))
% 8.49/2.65 |
% 8.49/2.65 | Instantiating formula (24) with all_0_1_1, xx, xS and discharging atoms sdtmndt0(xS, xx) = all_0_1_1, aElement0(xx), aSet0(xS), yields:
% 8.49/2.65 | (37) aSet0(all_0_1_1)
% 8.49/2.65 |
% 8.49/2.65 | Instantiating formula (14) with 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), yields:
% 8.49/2.65 | (38) aElementOf0(xx, all_0_0_0)
% 8.49/2.65 |
% 8.49/2.65 | Instantiating formula (23) with 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), yields:
% 8.49/2.65 | (39) aSet0(all_0_0_0)
% 8.49/2.65 |
% 8.49/2.65 | Instantiating formula (33) with all_0_1_1, xS and discharging atoms aSet0(all_0_1_1), aSet0(xS), yields:
% 8.49/2.65 | (40) aSubsetOf0(all_0_1_1, xS) | ? [v0] : (aElementOf0(v0, all_0_1_1) & ~ aElementOf0(v0, xS))
% 8.49/2.65 |
% 8.49/2.65 | Instantiating formula (33) with all_0_0_0, xS and discharging atoms aSet0(all_0_0_0), aSet0(xS), yields:
% 8.49/2.65 | (41) aSubsetOf0(all_0_0_0, xS) | ? [v0] : (aElementOf0(v0, all_0_0_0) & ~ aElementOf0(v0, xS))
% 8.49/2.65 |
% 8.49/2.65 | Instantiating formula (33) with xS, all_0_0_0 and discharging atoms aSet0(all_0_0_0), aSet0(xS), yields:
% 8.49/2.65 | (42) aSubsetOf0(xS, all_0_0_0) | ? [v0] : (aElementOf0(v0, xS) & ~ aElementOf0(v0, all_0_0_0))
% 8.49/2.65 |
% 8.49/2.66 +-Applying beta-rule and splitting (26), into two cases.
% 8.49/2.66 |-Branch one:
% 8.49/2.66 | (43) ~ aSubsetOf0(all_0_0_0, xS)
% 8.49/2.66 |
% 8.49/2.66 +-Applying beta-rule and splitting (41), into two cases.
% 8.49/2.66 |-Branch one:
% 8.49/2.66 | (44) aSubsetOf0(all_0_0_0, xS)
% 8.49/2.66 |
% 8.49/2.66 | Using (44) and (43) yields:
% 8.49/2.66 | (45) $false
% 8.49/2.66 |
% 8.49/2.66 |-The branch is then unsatisfiable
% 8.49/2.66 |-Branch two:
% 8.49/2.66 | (43) ~ aSubsetOf0(all_0_0_0, xS)
% 8.49/2.66 | (47) ? [v0] : (aElementOf0(v0, all_0_0_0) & ~ aElementOf0(v0, xS))
% 8.49/2.66 |
% 8.49/2.66 | Instantiating (47) with all_38_0_2 yields:
% 8.49/2.66 | (48) aElementOf0(all_38_0_2, all_0_0_0) & ~ aElementOf0(all_38_0_2, xS)
% 8.49/2.66 |
% 8.49/2.66 | Applying alpha-rule on (48) yields:
% 8.49/2.66 | (49) aElementOf0(all_38_0_2, all_0_0_0)
% 8.49/2.66 | (50) ~ aElementOf0(all_38_0_2, xS)
% 8.49/2.66 |
% 8.49/2.66 | Instantiating formula (29) with all_38_0_2, all_0_0_0, xx, all_0_1_1 and discharging atoms sdtpldt0(all_0_1_1, xx) = all_0_0_0, aElementOf0(all_38_0_2, all_0_0_0), aElement0(xx), aSet0(all_0_1_1), yields:
% 8.49/2.66 | (51) all_38_0_2 = xx | aElementOf0(all_38_0_2, all_0_1_1)
% 8.49/2.66 |
% 8.49/2.66 +-Applying beta-rule and splitting (36), into two cases.
% 8.49/2.66 |-Branch one:
% 8.49/2.66 | (52) all_0_1_1 = xS
% 8.49/2.66 |
% 8.49/2.66 +-Applying beta-rule and splitting (51), into two cases.
% 8.49/2.66 |-Branch one:
% 8.49/2.66 | (53) aElementOf0(all_38_0_2, all_0_1_1)
% 8.49/2.66 |
% 8.49/2.66 | From (52) and (53) follows:
% 8.49/2.66 | (54) aElementOf0(all_38_0_2, xS)
% 8.49/2.66 |
% 8.49/2.66 | Using (54) and (50) yields:
% 8.49/2.66 | (45) $false
% 8.49/2.66 |
% 8.49/2.66 |-The branch is then unsatisfiable
% 8.49/2.66 |-Branch two:
% 8.49/2.66 | (56) ~ aElementOf0(all_38_0_2, all_0_1_1)
% 8.49/2.66 | (57) all_38_0_2 = xx
% 8.49/2.66 |
% 8.49/2.66 | From (57) and (50) follows:
% 8.49/2.66 | (58) ~ aElementOf0(xx, xS)
% 8.49/2.66 |
% 8.49/2.66 | Using (20) and (58) yields:
% 8.49/2.66 | (45) $false
% 8.49/2.66 |
% 8.49/2.66 |-The branch is then unsatisfiable
% 8.49/2.66 |-Branch two:
% 8.49/2.66 | (60) ~ (all_0_1_1 = xS)
% 8.49/2.66 | (61) ? [v0] : (aElementOf0(v0, xS) & (v0 = xx | ~ aElement0(v0)))
% 8.49/2.66 |
% 8.49/2.66 | Instantiating (61) with all_90_0_6 yields:
% 8.49/2.66 | (62) aElementOf0(all_90_0_6, xS) & (all_90_0_6 = xx | ~ aElement0(all_90_0_6))
% 8.49/2.66 |
% 8.49/2.66 | Applying alpha-rule on (62) yields:
% 8.49/2.66 | (63) aElementOf0(all_90_0_6, xS)
% 8.49/2.66 | (64) all_90_0_6 = xx | ~ aElement0(all_90_0_6)
% 8.49/2.66 |
% 8.49/2.66 | Instantiating formula (16) with all_90_0_6, xS and discharging atoms aElementOf0(all_90_0_6, xS), aSet0(xS), yields:
% 8.49/2.66 | (65) aElement0(all_90_0_6)
% 8.49/2.66 |
% 8.49/2.66 +-Applying beta-rule and splitting (64), into two cases.
% 8.49/2.66 |-Branch one:
% 8.49/2.66 | (66) ~ aElement0(all_90_0_6)
% 8.49/2.66 |
% 8.49/2.66 | Using (65) and (66) yields:
% 8.49/2.66 | (45) $false
% 8.49/2.66 |
% 8.49/2.66 |-The branch is then unsatisfiable
% 8.49/2.66 |-Branch two:
% 8.49/2.66 | (65) aElement0(all_90_0_6)
% 8.49/2.66 | (69) all_90_0_6 = xx
% 8.49/2.66 |
% 8.49/2.66 | From (69) and (63) follows:
% 8.49/2.66 | (20) aElementOf0(xx, xS)
% 8.49/2.66 |
% 8.49/2.66 | From (69) and (65) follows:
% 8.49/2.66 | (35) aElement0(xx)
% 8.49/2.66 |
% 8.49/2.66 +-Applying beta-rule and splitting (40), into two cases.
% 8.49/2.66 |-Branch one:
% 8.49/2.66 | (72) aSubsetOf0(all_0_1_1, xS)
% 8.49/2.66 |
% 8.49/2.66 +-Applying beta-rule and splitting (51), into two cases.
% 8.49/2.66 |-Branch one:
% 8.49/2.66 | (53) aElementOf0(all_38_0_2, all_0_1_1)
% 8.49/2.66 |
% 8.49/2.66 | Instantiating formula (32) with all_38_0_2, all_0_1_1, xS and discharging atoms aSubsetOf0(all_0_1_1, xS), aElementOf0(all_38_0_2, all_0_1_1), aSet0(xS), ~ aElementOf0(all_38_0_2, xS), yields:
% 8.49/2.66 | (45) $false
% 8.49/2.66 |
% 8.49/2.66 |-The branch is then unsatisfiable
% 8.49/2.66 |-Branch two:
% 8.49/2.66 | (56) ~ aElementOf0(all_38_0_2, all_0_1_1)
% 8.49/2.66 | (57) all_38_0_2 = xx
% 8.49/2.66 |
% 8.49/2.66 | From (57) and (50) follows:
% 8.49/2.66 | (58) ~ aElementOf0(xx, xS)
% 8.49/2.66 |
% 8.49/2.66 | Using (20) and (58) yields:
% 8.49/2.66 | (45) $false
% 8.49/2.66 |
% 8.49/2.66 |-The branch is then unsatisfiable
% 8.49/2.66 |-Branch two:
% 8.49/2.66 | (79) ~ aSubsetOf0(all_0_1_1, xS)
% 8.49/2.66 | (80) ? [v0] : (aElementOf0(v0, all_0_1_1) & ~ aElementOf0(v0, xS))
% 8.49/2.66 |
% 8.49/2.66 | Instantiating (80) with all_128_0_31 yields:
% 8.49/2.66 | (81) aElementOf0(all_128_0_31, all_0_1_1) & ~ aElementOf0(all_128_0_31, xS)
% 8.49/2.66 |
% 8.49/2.66 | Applying alpha-rule on (81) yields:
% 8.49/2.66 | (82) aElementOf0(all_128_0_31, all_0_1_1)
% 8.49/2.66 | (83) ~ aElementOf0(all_128_0_31, xS)
% 8.49/2.66 |
% 8.49/2.66 | Instantiating formula (17) with all_128_0_31, all_0_1_1, xx, xS and discharging atoms sdtmndt0(xS, xx) = all_0_1_1, aElementOf0(all_128_0_31, all_0_1_1), aElement0(xx), aSet0(xS), ~ aElementOf0(all_128_0_31, xS), yields:
% 8.49/2.66 | (45) $false
% 8.49/2.66 |
% 8.49/2.66 |-The branch is then unsatisfiable
% 8.49/2.66 |-Branch two:
% 8.49/2.66 | (44) aSubsetOf0(all_0_0_0, xS)
% 8.49/2.66 | (86) ~ aSubsetOf0(xS, all_0_0_0)
% 8.49/2.67 |
% 8.49/2.67 +-Applying beta-rule and splitting (42), into two cases.
% 8.49/2.67 |-Branch one:
% 8.49/2.67 | (87) aSubsetOf0(xS, all_0_0_0)
% 8.49/2.67 |
% 8.49/2.67 | Using (87) and (86) yields:
% 8.49/2.67 | (45) $false
% 8.49/2.67 |
% 8.49/2.67 |-The branch is then unsatisfiable
% 8.49/2.67 |-Branch two:
% 8.49/2.67 | (86) ~ aSubsetOf0(xS, all_0_0_0)
% 8.49/2.67 | (90) ? [v0] : (aElementOf0(v0, xS) & ~ aElementOf0(v0, all_0_0_0))
% 8.49/2.67 |
% 8.49/2.67 | Instantiating (90) with all_38_0_41 yields:
% 8.49/2.67 | (91) aElementOf0(all_38_0_41, xS) & ~ aElementOf0(all_38_0_41, all_0_0_0)
% 8.49/2.67 |
% 8.49/2.67 | Applying alpha-rule on (91) yields:
% 8.49/2.67 | (92) aElementOf0(all_38_0_41, xS)
% 8.49/2.67 | (93) ~ aElementOf0(all_38_0_41, all_0_0_0)
% 8.49/2.67 |
% 8.49/2.67 | Instantiating formula (16) with all_38_0_41, xS and discharging atoms aElementOf0(all_38_0_41, xS), aSet0(xS), yields:
% 8.49/2.67 | (94) aElement0(all_38_0_41)
% 8.49/2.67 |
% 8.49/2.67 | Instantiating formula (15) with all_38_0_41, all_0_1_1, xx, xS and discharging atoms sdtmndt0(xS, xx) = all_0_1_1, aElementOf0(all_38_0_41, xS), aElement0(all_38_0_41), aElement0(xx), aSet0(xS), yields:
% 8.49/2.67 | (95) all_38_0_41 = xx | aElementOf0(all_38_0_41, all_0_1_1)
% 8.49/2.67 |
% 8.49/2.67 +-Applying beta-rule and splitting (36), into two cases.
% 8.49/2.67 |-Branch one:
% 8.49/2.67 | (52) all_0_1_1 = xS
% 8.49/2.67 |
% 8.49/2.67 | From (52) and (12) follows:
% 8.49/2.67 | (97) sdtmndt0(xS, xx) = xS
% 8.49/2.67 |
% 8.49/2.67 | From (52) and (37) follows:
% 8.49/2.67 | (31) aSet0(xS)
% 8.49/2.67 |
% 8.49/2.67 | Instantiating formula (34) with xS, xx, xS and discharging atoms sdtmndt0(xS, xx) = xS, aElementOf0(xx, xS), aElement0(xx), aSet0(xS), yields:
% 8.49/2.67 | (45) $false
% 8.49/2.67 |
% 8.49/2.67 |-The branch is then unsatisfiable
% 8.49/2.67 |-Branch two:
% 8.49/2.67 | (60) ~ (all_0_1_1 = xS)
% 8.49/2.67 | (61) ? [v0] : (aElementOf0(v0, xS) & (v0 = xx | ~ aElement0(v0)))
% 8.49/2.67 |
% 8.49/2.67 | Instantiating (61) with all_90_0_48 yields:
% 8.49/2.67 | (102) aElementOf0(all_90_0_48, xS) & (all_90_0_48 = xx | ~ aElement0(all_90_0_48))
% 8.49/2.67 |
% 8.49/2.67 | Applying alpha-rule on (102) yields:
% 8.49/2.67 | (103) aElementOf0(all_90_0_48, xS)
% 8.49/2.67 | (104) all_90_0_48 = xx | ~ aElement0(all_90_0_48)
% 8.49/2.67 |
% 8.49/2.67 | Instantiating formula (16) with all_90_0_48, xS and discharging atoms aElementOf0(all_90_0_48, xS), aSet0(xS), yields:
% 8.49/2.67 | (105) aElement0(all_90_0_48)
% 8.49/2.67 |
% 8.49/2.67 +-Applying beta-rule and splitting (104), into two cases.
% 8.49/2.67 |-Branch one:
% 8.49/2.67 | (106) ~ aElement0(all_90_0_48)
% 8.49/2.67 |
% 8.49/2.67 | Using (105) and (106) yields:
% 8.49/2.67 | (45) $false
% 8.49/2.67 |
% 8.49/2.67 |-The branch is then unsatisfiable
% 8.49/2.67 |-Branch two:
% 8.49/2.67 | (105) aElement0(all_90_0_48)
% 8.49/2.67 | (109) all_90_0_48 = xx
% 8.49/2.67 |
% 8.49/2.67 | From (109) and (105) follows:
% 8.49/2.67 | (35) aElement0(xx)
% 8.49/2.67 |
% 8.49/2.67 +-Applying beta-rule and splitting (95), into two cases.
% 8.49/2.67 |-Branch one:
% 8.49/2.67 | (111) aElementOf0(all_38_0_41, all_0_1_1)
% 8.49/2.67 |
% 8.49/2.67 | Instantiating formula (21) with all_38_0_41, all_0_0_0, xx, all_0_1_1 and discharging atoms sdtpldt0(all_0_1_1, xx) = all_0_0_0, aElementOf0(all_38_0_41, all_0_1_1), aElement0(all_38_0_41), aElement0(xx), aSet0(all_0_1_1), ~ aElementOf0(all_38_0_41, all_0_0_0), yields:
% 8.49/2.67 | (45) $false
% 8.49/2.67 |
% 8.49/2.67 |-The branch is then unsatisfiable
% 8.49/2.67 |-Branch two:
% 8.49/2.67 | (113) ~ aElementOf0(all_38_0_41, all_0_1_1)
% 8.49/2.67 | (114) all_38_0_41 = xx
% 8.49/2.67 |
% 8.49/2.67 | From (114) and (93) follows:
% 8.49/2.67 | (115) ~ aElementOf0(xx, all_0_0_0)
% 8.49/2.67 |
% 8.49/2.67 | Using (38) and (115) yields:
% 8.49/2.67 | (45) $false
% 8.49/2.67 |
% 8.49/2.67 |-The branch is then unsatisfiable
% 8.49/2.67 % SZS output end Proof for theBenchmark
% 8.49/2.67
% 8.49/2.67 2084ms
%------------------------------------------------------------------------------