TSTP Solution File: NUM536+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM536+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 7.66s 2.48s
% Output : Proof 10.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM536+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n029.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 05:58:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.49/0.58 ____ _
% 0.49/0.58 ___ / __ \_____(_)___ ________ __________
% 0.49/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.49/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.49/0.58
% 0.49/0.58 A Theorem Prover for First-Order Logic
% 0.49/0.58 (ePrincess v.1.0)
% 0.49/0.58
% 0.49/0.58 (c) Philipp Rümmer, 2009-2015
% 0.49/0.58 (c) Peter Backeman, 2014-2015
% 0.49/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.58 Bug reports to peter@backeman.se
% 0.49/0.58
% 0.49/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.58
% 0.49/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.49/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.29/0.93 Prover 0: Preprocessing ...
% 2.13/1.18 Prover 0: Constructing countermodel ...
% 7.66/2.48 Prover 0: proved (1852ms)
% 7.66/2.48
% 7.66/2.48 No countermodel exists, formula is valid
% 7.66/2.48 % SZS status Theorem for theBenchmark
% 7.66/2.48
% 7.66/2.48 Generating proof ... found it (size 51)
% 10.35/3.10
% 10.35/3.10 % SZS output start Proof for theBenchmark
% 10.35/3.10 Assumed formulas after preprocessing and simplification:
% 10.35/3.10 | (0) ? [v0] : ? [v1] : ( ~ (v1 = xS) & sdtmndt0(v0, xx) = v1 & sdtpldt0(xS, xx) = v0 & isFinite0(slcrc0) & aElement0(xx) & aSet0(xS) & aSet0(slcrc0) & ~ isCountable0(slcrc0) & ~ 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 = slcrc0 | ~ aSet0(v2) | ? [v3] : aElementOf0(v3, v2)) & ! [v2] : ( ~ isCountable0(v2) | ~ isFinite0(v2) | ~ aSet0(v2)) & ! [v2] : ~ aElementOf0(v2, slcrc0) & ! [v2] : ( ~ aSet0(v2) | aSubsetOf0(v2, v2)))
% 10.35/3.14 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 10.35/3.14 | (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) & aElement0(xx) & aSet0(xS) & aSet0(slcrc0) & ~ isCountable0(slcrc0) & ~ 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 = slcrc0 | ~ aSet0(v0) | ? [v1] : aElementOf0(v1, v0)) & ! [v0] : ( ~ isCountable0(v0) | ~ isFinite0(v0) | ~ aSet0(v0)) & ! [v0] : ~ aElementOf0(v0, slcrc0) & ! [v0] : ( ~ aSet0(v0) | aSubsetOf0(v0, v0))
% 10.35/3.15 |
% 10.35/3.15 | Applying alpha-rule on (1) yields:
% 10.35/3.15 | (2) ! [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))))))
% 10.35/3.15 | (3) ~ (all_0_0_0 = xS)
% 10.35/3.15 | (4) aSet0(slcrc0)
% 10.35/3.15 | (5) ! [v0] : ! [v1] : ( ~ aSubsetOf0(v1, v0) | ~ isFinite0(v0) | ~ aSet0(v0) | isFinite0(v1))
% 10.35/3.15 | (6) aSet0(xS)
% 10.35/3.15 | (7) ! [v0] : ( ~ aSet0(v0) | aSubsetOf0(v0, v0))
% 10.35/3.15 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ aSubsetOf0(v1, v0) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v1) | ~ aSet0(v0))
% 10.35/3.15 | (9) ! [v0] : ! [v1] : ( ~ aElementOf0(v1, v0) | ~ aSet0(v0) | aElement0(v1))
% 10.35/3.15 | (10) ! [v0] : ! [v1] : ( ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1))
% 10.35/3.15 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2))
% 10.35/3.15 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (sdtmndt0(v0, v1) = v2) | ~ (sdtpldt0(v2, v1) = v3) | ~ aElementOf0(v1, v0) | ~ aSet0(v0))
% 10.35/3.15 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ aSubsetOf0(v1, v2) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v2) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v0, v2))
% 10.35/3.15 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 10.35/3.16 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 10.35/3.16 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v1, v2))
% 10.35/3.16 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElement0(v3))
% 10.35/3.16 | (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)))))
% 10.35/3.16 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2))
% 10.35/3.16 | (20) sdtpldt0(xS, xx) = all_0_1_1
% 10.35/3.16 | (21) ~ isCountable0(slcrc0)
% 10.35/3.16 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2))
% 10.35/3.16 | (23) ! [v0] : ( ~ isCountable0(v0) | ~ isFinite0(v0) | ~ aSet0(v0))
% 10.35/3.16 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElement0(v3))
% 10.35/3.16 | (25) isFinite0(slcrc0)
% 10.35/3.16 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2))
% 10.35/3.16 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v1, v2) | ~ aElement0(v1) | ~ aSet0(v0))
% 10.35/3.16 | (28) sdtmndt0(all_0_1_1, xx) = all_0_0_0
% 10.35/3.16 | (29) ! [v0] : ~ aElementOf0(v0, slcrc0)
% 10.35/3.16 | (30) ! [v0] : (v0 = slcrc0 | ~ aSet0(v0) | ? [v1] : aElementOf0(v1, v0))
% 10.35/3.16 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0))
% 10.35/3.16 | (32) aElement0(xx)
% 10.35/3.16 | (33) ~ aElementOf0(xx, xS)
% 10.35/3.16 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | aElementOf0(v2, v0))
% 10.35/3.16 | (35) ! [v0] : ! [v1] : ( ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2] : (aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 10.35/3.16 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0))
% 10.35/3.16 |
% 10.35/3.16 | Instantiating formula (16) with all_0_1_1, xx, xS and discharging atoms sdtpldt0(xS, xx) = all_0_1_1, aElement0(xx), aSet0(xS), yields:
% 10.35/3.16 | (37) aElementOf0(xx, all_0_1_1)
% 10.35/3.16 |
% 10.35/3.16 | Instantiating formula (22) with all_0_1_1, xx, xS and discharging atoms sdtpldt0(xS, xx) = all_0_1_1, aElement0(xx), aSet0(xS), yields:
% 10.35/3.16 | (38) aSet0(all_0_1_1)
% 10.35/3.16 |
% 10.35/3.16 | Instantiating formula (18) with all_0_1_1, 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), yields:
% 10.35/3.16 | (39) all_0_0_0 = all_0_1_1 | ? [v0] : (aElementOf0(v0, all_0_1_1) & (v0 = xx | ~ aElement0(v0)))
% 10.35/3.16 |
% 10.35/3.16 | Instantiating formula (18) 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:
% 10.35/3.16 | (40) 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))))
% 10.35/3.16 |
% 10.35/3.16 | Instantiating formula (26) with 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), yields:
% 10.35/3.16 | (41) aSet0(all_0_0_0)
% 10.35/3.16 |
% 10.35/3.16 | Instantiating formula (35) with all_0_1_1, xS and discharging atoms aSet0(all_0_1_1), aSet0(xS), yields:
% 10.35/3.16 | (42) aSubsetOf0(all_0_1_1, xS) | ? [v0] : (aElementOf0(v0, all_0_1_1) & ~ aElementOf0(v0, xS))
% 10.35/3.16 |
% 10.35/3.16 +-Applying beta-rule and splitting (40), into two cases.
% 10.35/3.16 |-Branch one:
% 10.35/3.16 | (43) all_0_0_0 = xS
% 10.35/3.16 |
% 10.35/3.16 | Equations (43) can reduce 3 to:
% 10.35/3.16 | (44) $false
% 10.35/3.16 |
% 10.35/3.16 |-The branch is then unsatisfiable
% 10.35/3.16 |-Branch two:
% 10.35/3.16 | (3) ~ (all_0_0_0 = xS)
% 10.35/3.16 | (46) ? [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))))
% 10.35/3.17 |
% 10.35/3.17 | Instantiating (46) with all_19_0_2 yields:
% 10.35/3.17 | (47) (all_19_0_2 = xx | ~ aElementOf0(all_19_0_2, all_0_1_1) | ~ aElementOf0(all_19_0_2, xS) | ~ aElement0(all_19_0_2)) & (aElementOf0(all_19_0_2, xS) | ( ~ (all_19_0_2 = xx) & aElementOf0(all_19_0_2, all_0_1_1) & aElement0(all_19_0_2)))
% 10.35/3.17 |
% 10.35/3.17 | Applying alpha-rule on (47) yields:
% 10.35/3.17 | (48) all_19_0_2 = xx | ~ aElementOf0(all_19_0_2, all_0_1_1) | ~ aElementOf0(all_19_0_2, xS) | ~ aElement0(all_19_0_2)
% 10.81/3.17 | (49) aElementOf0(all_19_0_2, xS) | ( ~ (all_19_0_2 = xx) & aElementOf0(all_19_0_2, all_0_1_1) & aElement0(all_19_0_2))
% 10.81/3.17 |
% 10.81/3.17 +-Applying beta-rule and splitting (42), into two cases.
% 10.81/3.17 |-Branch one:
% 10.81/3.17 | (50) aSubsetOf0(all_0_1_1, xS)
% 10.81/3.17 |
% 10.81/3.17 | Instantiating formula (34) 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:
% 10.81/3.17 | (51) $false
% 10.81/3.17 |
% 10.81/3.17 |-The branch is then unsatisfiable
% 10.81/3.17 |-Branch two:
% 10.81/3.17 | (52) ~ aSubsetOf0(all_0_1_1, xS)
% 10.81/3.17 | (53) ? [v0] : (aElementOf0(v0, all_0_1_1) & ~ aElementOf0(v0, xS))
% 10.81/3.17 |
% 10.81/3.17 | Instantiating (53) with all_138_0_47 yields:
% 10.81/3.17 | (54) aElementOf0(all_138_0_47, all_0_1_1) & ~ aElementOf0(all_138_0_47, xS)
% 10.81/3.17 |
% 10.81/3.17 | Applying alpha-rule on (54) yields:
% 10.81/3.17 | (55) aElementOf0(all_138_0_47, all_0_1_1)
% 10.81/3.17 | (56) ~ aElementOf0(all_138_0_47, xS)
% 10.81/3.17 |
% 10.81/3.17 +-Applying beta-rule and splitting (39), into two cases.
% 10.81/3.17 |-Branch one:
% 10.81/3.17 | (57) all_0_0_0 = all_0_1_1
% 10.81/3.17 |
% 10.81/3.17 | From (57) and (28) follows:
% 10.81/3.17 | (58) sdtmndt0(all_0_1_1, xx) = all_0_1_1
% 10.81/3.17 |
% 10.81/3.17 | From (57) and (41) follows:
% 10.81/3.17 | (38) aSet0(all_0_1_1)
% 10.81/3.17 |
% 10.81/3.17 | Instantiating formula (27) with all_0_1_1, xx, all_0_1_1 and discharging atoms sdtmndt0(all_0_1_1, xx) = all_0_1_1, aElementOf0(xx, all_0_1_1), aElement0(xx), aSet0(all_0_1_1), yields:
% 10.81/3.17 | (51) $false
% 10.81/3.17 |
% 10.81/3.17 |-The branch is then unsatisfiable
% 10.81/3.17 |-Branch two:
% 10.81/3.17 | (61) ~ (all_0_0_0 = all_0_1_1)
% 10.81/3.17 | (62) ? [v0] : (aElementOf0(v0, all_0_1_1) & (v0 = xx | ~ aElement0(v0)))
% 10.81/3.17 |
% 10.81/3.17 | Instantiating (62) with all_159_0_54 yields:
% 10.81/3.17 | (63) aElementOf0(all_159_0_54, all_0_1_1) & (all_159_0_54 = xx | ~ aElement0(all_159_0_54))
% 10.81/3.17 |
% 10.81/3.17 | Applying alpha-rule on (63) yields:
% 10.81/3.17 | (64) aElementOf0(all_159_0_54, all_0_1_1)
% 10.81/3.17 | (65) all_159_0_54 = xx | ~ aElement0(all_159_0_54)
% 10.81/3.17 |
% 10.81/3.17 +-Applying beta-rule and splitting (49), into two cases.
% 10.81/3.17 |-Branch one:
% 10.81/3.17 | (66) aElementOf0(all_19_0_2, xS)
% 10.81/3.17 |
% 10.81/3.17 +-Applying beta-rule and splitting (48), into two cases.
% 10.81/3.17 |-Branch one:
% 10.81/3.17 | (67) ~ aElementOf0(all_19_0_2, all_0_1_1)
% 10.81/3.17 |
% 10.81/3.17 | Instantiating formula (9) with all_159_0_54, all_0_1_1 and discharging atoms aElementOf0(all_159_0_54, all_0_1_1), aSet0(all_0_1_1), yields:
% 10.81/3.17 | (68) aElement0(all_159_0_54)
% 10.81/3.17 |
% 10.81/3.17 | Instantiating formula (9) with all_19_0_2, xS and discharging atoms aElementOf0(all_19_0_2, xS), aSet0(xS), yields:
% 10.81/3.17 | (69) aElement0(all_19_0_2)
% 10.81/3.17 |
% 10.81/3.17 +-Applying beta-rule and splitting (65), into two cases.
% 10.81/3.17 |-Branch one:
% 10.81/3.17 | (70) ~ aElement0(all_159_0_54)
% 10.81/3.17 |
% 10.81/3.17 | Using (68) and (70) yields:
% 10.81/3.17 | (51) $false
% 10.81/3.17 |
% 10.81/3.17 |-The branch is then unsatisfiable
% 10.81/3.17 |-Branch two:
% 10.81/3.17 | (68) aElement0(all_159_0_54)
% 10.81/3.17 | (73) all_159_0_54 = xx
% 10.81/3.17 |
% 10.81/3.17 | From (73) and (68) follows:
% 10.81/3.17 | (32) aElement0(xx)
% 10.81/3.17 |
% 10.81/3.17 | Instantiating formula (11) with all_19_0_2, all_0_1_1, xx, xS and discharging atoms sdtpldt0(xS, xx) = all_0_1_1, aElementOf0(all_19_0_2, xS), aElement0(all_19_0_2), aElement0(xx), aSet0(xS), ~ aElementOf0(all_19_0_2, all_0_1_1), yields:
% 10.81/3.17 | (51) $false
% 10.81/3.17 |
% 10.81/3.17 |-The branch is then unsatisfiable
% 10.81/3.17 |-Branch two:
% 10.81/3.17 | (76) aElementOf0(all_19_0_2, all_0_1_1)
% 10.81/3.17 | (77) all_19_0_2 = xx | ~ aElementOf0(all_19_0_2, xS) | ~ aElement0(all_19_0_2)
% 10.81/3.17 |
% 10.81/3.17 | Instantiating formula (36) with all_138_0_47, all_0_1_1, xx, xS and discharging atoms sdtpldt0(xS, xx) = all_0_1_1, aElementOf0(all_138_0_47, all_0_1_1), aElement0(xx), aSet0(xS), ~ aElementOf0(all_138_0_47, xS), yields:
% 10.81/3.17 | (78) all_138_0_47 = xx
% 10.81/3.17 |
% 10.81/3.17 | Instantiating formula (9) with all_19_0_2, xS and discharging atoms aElementOf0(all_19_0_2, xS), aSet0(xS), yields:
% 10.81/3.17 | (69) aElement0(all_19_0_2)
% 10.81/3.17 |
% 10.81/3.17 | From (78) and (56) follows:
% 10.81/3.17 | (33) ~ aElementOf0(xx, xS)
% 10.81/3.17 |
% 10.81/3.17 +-Applying beta-rule and splitting (77), into two cases.
% 10.81/3.17 |-Branch one:
% 10.81/3.17 | (81) ~ aElementOf0(all_19_0_2, xS)
% 10.81/3.17 |
% 10.81/3.17 | Using (66) and (81) yields:
% 10.81/3.17 | (51) $false
% 10.81/3.17 |
% 10.81/3.17 |-The branch is then unsatisfiable
% 10.81/3.17 |-Branch two:
% 10.81/3.17 | (66) aElementOf0(all_19_0_2, xS)
% 10.81/3.17 | (84) all_19_0_2 = xx | ~ aElement0(all_19_0_2)
% 10.81/3.17 |
% 10.81/3.17 +-Applying beta-rule and splitting (84), into two cases.
% 10.81/3.17 |-Branch one:
% 10.81/3.17 | (85) ~ aElement0(all_19_0_2)
% 10.81/3.17 |
% 10.81/3.17 | Using (69) and (85) yields:
% 10.81/3.18 | (51) $false
% 10.81/3.18 |
% 10.81/3.18 |-The branch is then unsatisfiable
% 10.81/3.18 |-Branch two:
% 10.81/3.18 | (69) aElement0(all_19_0_2)
% 10.81/3.18 | (88) all_19_0_2 = xx
% 10.81/3.18 |
% 10.81/3.18 | From (88) and (66) follows:
% 10.81/3.18 | (89) aElementOf0(xx, xS)
% 10.81/3.18 |
% 10.81/3.18 | Using (89) and (33) yields:
% 10.81/3.18 | (51) $false
% 10.81/3.18 |
% 10.81/3.18 |-The branch is then unsatisfiable
% 10.81/3.18 |-Branch two:
% 10.81/3.18 | (81) ~ aElementOf0(all_19_0_2, xS)
% 10.81/3.18 | (92) ~ (all_19_0_2 = xx) & aElementOf0(all_19_0_2, all_0_1_1) & aElement0(all_19_0_2)
% 10.81/3.18 |
% 10.81/3.18 | Applying alpha-rule on (92) yields:
% 10.81/3.18 | (93) ~ (all_19_0_2 = xx)
% 10.81/3.18 | (76) aElementOf0(all_19_0_2, all_0_1_1)
% 10.81/3.18 | (69) aElement0(all_19_0_2)
% 10.81/3.18 |
% 10.81/3.18 | Instantiating formula (36) with all_19_0_2, all_0_1_1, xx, xS and discharging atoms sdtpldt0(xS, xx) = all_0_1_1, aElementOf0(all_19_0_2, all_0_1_1), aElement0(xx), aSet0(xS), ~ aElementOf0(all_19_0_2, xS), yields:
% 10.81/3.18 | (88) all_19_0_2 = xx
% 10.81/3.18 |
% 10.81/3.18 | Equations (88) can reduce 93 to:
% 10.81/3.18 | (44) $false
% 10.81/3.18 |
% 10.81/3.18 |-The branch is then unsatisfiable
% 10.81/3.18 % SZS output end Proof for theBenchmark
% 10.81/3.18
% 10.81/3.18 2591ms
%------------------------------------------------------------------------------