TSTP Solution File: KRS140+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KRS140+1 : TPTP v8.1.0. Released v3.1.0.
% 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 : Sun Jul 17 02:56:40 EDT 2022
% Result : Theorem 2.63s 1.39s
% Output : Proof 4.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KRS140+1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n026.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 : Tue Jun 7 15:20:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ____ _
% 0.19/0.60 ___ / __ \_____(_)___ ________ __________
% 0.19/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic
% 0.19/0.60 (ePrincess v.1.0)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2015
% 0.19/0.60 (c) Peter Backeman, 2014-2015
% 0.19/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.60 Bug reports to peter@backeman.se
% 0.19/0.60
% 0.19/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.47/0.93 Prover 0: Preprocessing ...
% 1.72/1.03 Prover 0: Warning: ignoring some quantifiers
% 1.72/1.05 Prover 0: Constructing countermodel ...
% 1.81/1.15 Prover 0: gave up
% 1.81/1.15 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.81/1.18 Prover 1: Preprocessing ...
% 2.37/1.28 Prover 1: Constructing countermodel ...
% 2.63/1.39 Prover 1: proved (239ms)
% 2.63/1.39
% 2.63/1.39 No countermodel exists, formula is valid
% 2.63/1.39 % SZS status Theorem for theBenchmark
% 2.63/1.39
% 2.63/1.39 Generating proof ... found it (size 87)
% 3.81/1.66
% 3.81/1.66 % SZS output start Proof for theBenchmark
% 3.81/1.66 Assumed formulas after preprocessing and simplification:
% 3.81/1.66 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (rsymProp(ib, ib) = 0 & rsymProp(ia, ia) = 0 & cowlThing(ib) = 0 & cowlThing(ia) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (rsymProp(v9, v8) = v7) | ~ (rsymProp(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (rsymProp(v7, v6) = v8) | ~ (rsymProp(v7, v6) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (rsymProp(v6, v7) = v8) | ~ (rsymProp(v6, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (xsd_string(v8) = v7) | ~ (xsd_string(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (xsd_integer(v8) = v7) | ~ (xsd_integer(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (cowlThing(v8) = v7) | ~ (cowlThing(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (cowlNothing(v8) = v7) | ~ (cowlNothing(v8) = v6)) & ! [v6] : ! [v7] : (v7 = ib | v7 = ia | ~ (rsymProp(v6, v7) = 0)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (xsd_string(v6) = v7) | ~ (xsd_string(v6) = 0)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (xsd_string(v6) = v7) | xsd_integer(v6) = 0) & ! [v6] : ! [v7] : (v7 = 0 | ~ (xsd_integer(v6) = v7) | ~ (xsd_integer(v6) = 0)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (cowlThing(v6) = v7) | ~ (cowlThing(v6) = 0)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (cowlThing(v6) = v7)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (cowlNothing(v6) = v7) | ~ (cowlNothing(v6) = 0)) & ! [v6] : ! [v7] : ( ~ (rsymProp(v6, v7) = 0) | rsymProp(v7, v6) = 0) & ! [v6] : ( ~ (xsd_string(v6) = 0) | ? [v7] : ( ~ (v7 = 0) & xsd_integer(v6) = v7)) & ! [v6] : ~ (cowlNothing(v6) = 0) & ( ! [v6] : ( ~ (rsymProp(ia, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & cowlThing(v6) = v7)) | (v4 = 0 & v3 = 0 & ~ (v5 = 0) & rsymProp(v1, v2) = 0 & rsymProp(v0, v2) = v5 & rsymProp(v0, v1) = 0) | (xsd_string(v0) = v1 & xsd_integer(v0) = v2 & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & ~ (v1 = 0)))) | (cowlThing(v0) = v1 & cowlNothing(v0) = v2 & ( ~ (v1 = 0) | v2 = 0))))
% 3.81/1.69 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 3.81/1.69 | (1) rsymProp(ib, ib) = 0 & rsymProp(ia, ia) = 0 & cowlThing(ib) = 0 & cowlThing(ia) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rsymProp(v3, v2) = v1) | ~ (rsymProp(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rsymProp(v1, v0) = v2) | ~ (rsymProp(v1, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rsymProp(v0, v1) = v2) | ~ (rsymProp(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0] : ! [v1] : (v1 = ib | v1 = ia | ~ (rsymProp(v0, v1) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ (xsd_string(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ (xsd_integer(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ (cowlThing(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlNothing(v0) = v1) | ~ (cowlNothing(v0) = 0)) & ! [v0] : ! [v1] : ( ~ (rsymProp(v0, v1) = 0) | rsymProp(v1, v0) = 0) & ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) & ! [v0] : ~ (cowlNothing(v0) = 0) & ( ! [v0] : ( ~ (rsymProp(ia, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & cowlThing(v0) = v1)) | (all_0_1_1 = 0 & all_0_2_2 = 0 & ~ (all_0_0_0 = 0) & rsymProp(all_0_4_4, all_0_3_3) = 0 & rsymProp(all_0_5_5, all_0_3_3) = all_0_0_0 & rsymProp(all_0_5_5, all_0_4_4) = 0) | (xsd_string(all_0_5_5) = all_0_4_4 & xsd_integer(all_0_5_5) = all_0_3_3 & ((all_0_3_3 = 0 & all_0_4_4 = 0) | ( ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0)))) | (cowlThing(all_0_5_5) = all_0_4_4 & cowlNothing(all_0_5_5) = all_0_3_3 & ( ~ (all_0_4_4 = 0) | all_0_3_3 = 0)))
% 4.06/1.70 |
% 4.06/1.70 | Applying alpha-rule on (1) yields:
% 4.06/1.70 | (2) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ (cowlThing(v0) = 0))
% 4.06/1.70 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rsymProp(v0, v1) = v2) | ~ (rsymProp(v0, v1) = 0))
% 4.06/1.70 | (4) rsymProp(ib, ib) = 0
% 4.06/1.70 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0)
% 4.06/1.70 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0))
% 4.06/1.70 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rsymProp(v3, v2) = v1) | ~ (rsymProp(v3, v2) = v0))
% 4.06/1.71 | (8) ! [v0] : ~ (cowlNothing(v0) = 0)
% 4.06/1.71 | (9) ! [v0] : ! [v1] : ( ~ (rsymProp(v0, v1) = 0) | rsymProp(v1, v0) = 0)
% 4.06/1.71 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ (xsd_integer(v0) = 0))
% 4.06/1.71 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0))
% 4.06/1.71 | (12) ! [v0] : ( ~ (rsymProp(ia, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & cowlThing(v0) = v1)) | (all_0_1_1 = 0 & all_0_2_2 = 0 & ~ (all_0_0_0 = 0) & rsymProp(all_0_4_4, all_0_3_3) = 0 & rsymProp(all_0_5_5, all_0_3_3) = all_0_0_0 & rsymProp(all_0_5_5, all_0_4_4) = 0) | (xsd_string(all_0_5_5) = all_0_4_4 & xsd_integer(all_0_5_5) = all_0_3_3 & ((all_0_3_3 = 0 & all_0_4_4 = 0) | ( ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0)))) | (cowlThing(all_0_5_5) = all_0_4_4 & cowlNothing(all_0_5_5) = all_0_3_3 & ( ~ (all_0_4_4 = 0) | all_0_3_3 = 0))
% 4.06/1.71 | (13) cowlThing(ib) = 0
% 4.06/1.71 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0))
% 4.06/1.71 | (15) cowlThing(ia) = 0
% 4.06/1.71 | (16) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlNothing(v0) = v1) | ~ (cowlNothing(v0) = 0))
% 4.06/1.71 | (17) ! [v0] : ! [v1] : (v1 = ib | v1 = ia | ~ (rsymProp(v0, v1) = 0))
% 4.06/1.71 | (18) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ (xsd_string(v0) = 0))
% 4.06/1.71 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rsymProp(v1, v0) = v2) | ~ (rsymProp(v1, v0) = 0))
% 4.06/1.71 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0))
% 4.06/1.71 | (21) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 4.06/1.71 | (22) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1))
% 4.06/1.71 | (23) rsymProp(ia, ia) = 0
% 4.06/1.71 |
% 4.06/1.71 +-Applying beta-rule and splitting (12), into two cases.
% 4.06/1.71 |-Branch one:
% 4.06/1.71 | (24) ! [v0] : ( ~ (rsymProp(ia, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & cowlThing(v0) = v1)) | (all_0_1_1 = 0 & all_0_2_2 = 0 & ~ (all_0_0_0 = 0) & rsymProp(all_0_4_4, all_0_3_3) = 0 & rsymProp(all_0_5_5, all_0_3_3) = all_0_0_0 & rsymProp(all_0_5_5, all_0_4_4) = 0) | (xsd_string(all_0_5_5) = all_0_4_4 & xsd_integer(all_0_5_5) = all_0_3_3 & ((all_0_3_3 = 0 & all_0_4_4 = 0) | ( ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0))))
% 4.06/1.71 |
% 4.06/1.71 +-Applying beta-rule and splitting (24), into two cases.
% 4.06/1.71 |-Branch one:
% 4.06/1.71 | (25) ! [v0] : ( ~ (rsymProp(ia, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & cowlThing(v0) = v1)) | (all_0_1_1 = 0 & all_0_2_2 = 0 & ~ (all_0_0_0 = 0) & rsymProp(all_0_4_4, all_0_3_3) = 0 & rsymProp(all_0_5_5, all_0_3_3) = all_0_0_0 & rsymProp(all_0_5_5, all_0_4_4) = 0)
% 4.06/1.71 |
% 4.06/1.71 +-Applying beta-rule and splitting (25), into two cases.
% 4.06/1.71 |-Branch one:
% 4.06/1.71 | (26) ! [v0] : ( ~ (rsymProp(ia, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & cowlThing(v0) = v1))
% 4.06/1.71 |
% 4.06/1.71 | Instantiating formula (26) with ia and discharging atoms rsymProp(ia, ia) = 0, yields:
% 4.06/1.71 | (27) ? [v0] : ( ~ (v0 = 0) & cowlThing(ia) = v0)
% 4.06/1.71 |
% 4.06/1.71 | Instantiating (27) with all_10_0_6 yields:
% 4.06/1.71 | (28) ~ (all_10_0_6 = 0) & cowlThing(ia) = all_10_0_6
% 4.06/1.71 |
% 4.06/1.71 | Applying alpha-rule on (28) yields:
% 4.06/1.71 | (29) ~ (all_10_0_6 = 0)
% 4.06/1.71 | (30) cowlThing(ia) = all_10_0_6
% 4.06/1.71 |
% 4.06/1.72 | Instantiating formula (22) with all_10_0_6, ia and discharging atoms cowlThing(ia) = all_10_0_6, yields:
% 4.06/1.72 | (31) all_10_0_6 = 0
% 4.06/1.72 |
% 4.06/1.72 | Equations (31) can reduce 29 to:
% 4.06/1.72 | (32) $false
% 4.06/1.72 |
% 4.06/1.72 |-The branch is then unsatisfiable
% 4.06/1.72 |-Branch two:
% 4.06/1.72 | (33) all_0_1_1 = 0 & all_0_2_2 = 0 & ~ (all_0_0_0 = 0) & rsymProp(all_0_4_4, all_0_3_3) = 0 & rsymProp(all_0_5_5, all_0_3_3) = all_0_0_0 & rsymProp(all_0_5_5, all_0_4_4) = 0
% 4.06/1.72 |
% 4.06/1.72 | Applying alpha-rule on (33) yields:
% 4.06/1.72 | (34) rsymProp(all_0_4_4, all_0_3_3) = 0
% 4.06/1.72 | (35) rsymProp(all_0_5_5, all_0_3_3) = all_0_0_0
% 4.06/1.72 | (36) rsymProp(all_0_5_5, all_0_4_4) = 0
% 4.06/1.72 | (37) all_0_2_2 = 0
% 4.06/1.72 | (38) ~ (all_0_0_0 = 0)
% 4.06/1.72 | (39) all_0_1_1 = 0
% 4.06/1.72 |
% 4.06/1.72 | Instantiating formula (17) with all_0_3_3, all_0_4_4 and discharging atoms rsymProp(all_0_4_4, all_0_3_3) = 0, yields:
% 4.06/1.72 | (40) all_0_3_3 = ib | all_0_3_3 = ia
% 4.06/1.72 |
% 4.06/1.72 | Instantiating formula (19) with all_0_0_0, all_0_5_5, all_0_3_3 and discharging atoms rsymProp(all_0_5_5, all_0_3_3) = all_0_0_0, yields:
% 4.06/1.72 | (41) all_0_0_0 = 0 | ~ (rsymProp(all_0_5_5, all_0_3_3) = 0)
% 4.06/1.72 |
% 4.06/1.72 | Instantiating formula (7) with all_0_5_5, all_0_4_4, 0, all_0_0_0 and discharging atoms rsymProp(all_0_5_5, all_0_4_4) = 0, yields:
% 4.06/1.72 | (42) all_0_0_0 = 0 | ~ (rsymProp(all_0_5_5, all_0_4_4) = all_0_0_0)
% 4.06/1.72 |
% 4.06/1.72 | Instantiating formula (9) with all_0_3_3, all_0_4_4 and discharging atoms rsymProp(all_0_4_4, all_0_3_3) = 0, yields:
% 4.06/1.72 | (43) rsymProp(all_0_3_3, all_0_4_4) = 0
% 4.06/1.72 |
% 4.06/1.72 | Instantiating formula (9) with all_0_4_4, all_0_5_5 and discharging atoms rsymProp(all_0_5_5, all_0_4_4) = 0, yields:
% 4.06/1.72 | (44) rsymProp(all_0_4_4, all_0_5_5) = 0
% 4.06/1.72 |
% 4.06/1.72 | Instantiating formula (17) with all_0_4_4, all_0_3_3 and discharging atoms rsymProp(all_0_3_3, all_0_4_4) = 0, yields:
% 4.06/1.72 | (45) all_0_4_4 = ib | all_0_4_4 = ia
% 4.06/1.72 |
% 4.06/1.72 | Instantiating formula (17) with all_0_5_5, all_0_4_4 and discharging atoms rsymProp(all_0_4_4, all_0_5_5) = 0, yields:
% 4.06/1.72 | (46) all_0_5_5 = ib | all_0_5_5 = ia
% 4.06/1.72 |
% 4.06/1.72 +-Applying beta-rule and splitting (42), into two cases.
% 4.06/1.72 |-Branch one:
% 4.06/1.72 | (47) ~ (rsymProp(all_0_5_5, all_0_4_4) = all_0_0_0)
% 4.06/1.72 |
% 4.06/1.72 | Using (35) and (47) yields:
% 4.06/1.72 | (48) ~ (all_0_3_3 = all_0_4_4)
% 4.06/1.72 |
% 4.06/1.72 +-Applying beta-rule and splitting (41), into two cases.
% 4.06/1.72 |-Branch one:
% 4.06/1.72 | (49) ~ (rsymProp(all_0_5_5, all_0_3_3) = 0)
% 4.06/1.72 |
% 4.06/1.72 | Using (34) and (49) yields:
% 4.06/1.72 | (50) ~ (all_0_4_4 = all_0_5_5)
% 4.06/1.72 |
% 4.06/1.72 +-Applying beta-rule and splitting (40), into two cases.
% 4.06/1.72 |-Branch one:
% 4.06/1.72 | (51) all_0_3_3 = ia
% 4.06/1.72 |
% 4.06/1.72 | Equations (51) can reduce 48 to:
% 4.06/1.72 | (52) ~ (all_0_4_4 = ia)
% 4.06/1.72 |
% 4.06/1.72 | Simplifying 52 yields:
% 4.06/1.72 | (53) ~ (all_0_4_4 = ia)
% 4.06/1.72 |
% 4.06/1.72 | From (51) and (49) follows:
% 4.06/1.72 | (54) ~ (rsymProp(all_0_5_5, ia) = 0)
% 4.06/1.72 |
% 4.06/1.72 +-Applying beta-rule and splitting (45), into two cases.
% 4.06/1.72 |-Branch one:
% 4.06/1.72 | (55) all_0_4_4 = ia
% 4.06/1.72 |
% 4.06/1.72 | Equations (55) can reduce 53 to:
% 4.06/1.72 | (32) $false
% 4.06/1.72 |
% 4.06/1.72 |-The branch is then unsatisfiable
% 4.06/1.72 |-Branch two:
% 4.06/1.72 | (53) ~ (all_0_4_4 = ia)
% 4.06/1.72 | (58) all_0_4_4 = ib
% 4.06/1.72 |
% 4.06/1.72 | Equations (58) can reduce 50 to:
% 4.06/1.72 | (59) ~ (all_0_5_5 = ib)
% 4.06/1.72 |
% 4.06/1.72 | Simplifying 59 yields:
% 4.06/1.72 | (60) ~ (all_0_5_5 = ib)
% 4.06/1.72 |
% 4.06/1.72 +-Applying beta-rule and splitting (46), into two cases.
% 4.06/1.72 |-Branch one:
% 4.06/1.72 | (61) all_0_5_5 = ia
% 4.06/1.72 |
% 4.06/1.72 | From (61) and (54) follows:
% 4.06/1.73 | (62) ~ (rsymProp(ia, ia) = 0)
% 4.06/1.73 |
% 4.06/1.73 | Using (23) and (62) yields:
% 4.06/1.73 | (63) $false
% 4.06/1.73 |
% 4.06/1.73 |-The branch is then unsatisfiable
% 4.06/1.73 |-Branch two:
% 4.06/1.73 | (64) ~ (all_0_5_5 = ia)
% 4.06/1.73 | (65) all_0_5_5 = ib
% 4.06/1.73 |
% 4.06/1.73 | Equations (65) can reduce 60 to:
% 4.06/1.73 | (32) $false
% 4.06/1.73 |
% 4.06/1.73 |-The branch is then unsatisfiable
% 4.06/1.73 |-Branch two:
% 4.06/1.73 | (67) ~ (all_0_3_3 = ia)
% 4.06/1.73 | (68) all_0_3_3 = ib
% 4.06/1.73 |
% 4.06/1.73 | Equations (68) can reduce 48 to:
% 4.06/1.73 | (69) ~ (all_0_4_4 = ib)
% 4.06/1.73 |
% 4.06/1.73 | Simplifying 69 yields:
% 4.06/1.73 | (70) ~ (all_0_4_4 = ib)
% 4.06/1.73 |
% 4.06/1.73 | From (68) and (49) follows:
% 4.06/1.73 | (71) ~ (rsymProp(all_0_5_5, ib) = 0)
% 4.06/1.73 |
% 4.06/1.73 +-Applying beta-rule and splitting (45), into two cases.
% 4.06/1.73 |-Branch one:
% 4.06/1.73 | (55) all_0_4_4 = ia
% 4.06/1.73 |
% 4.06/1.73 | Equations (55) can reduce 50 to:
% 4.06/1.73 | (73) ~ (all_0_5_5 = ia)
% 4.06/1.73 |
% 4.06/1.73 | Simplifying 73 yields:
% 4.06/1.73 | (64) ~ (all_0_5_5 = ia)
% 4.06/1.73 |
% 4.06/1.73 +-Applying beta-rule and splitting (46), into two cases.
% 4.06/1.73 |-Branch one:
% 4.06/1.73 | (61) all_0_5_5 = ia
% 4.06/1.73 |
% 4.06/1.73 | Equations (61) can reduce 64 to:
% 4.06/1.73 | (32) $false
% 4.06/1.73 |
% 4.06/1.73 |-The branch is then unsatisfiable
% 4.06/1.73 |-Branch two:
% 4.06/1.73 | (64) ~ (all_0_5_5 = ia)
% 4.06/1.73 | (65) all_0_5_5 = ib
% 4.06/1.73 |
% 4.06/1.73 | From (65) and (71) follows:
% 4.06/1.73 | (79) ~ (rsymProp(ib, ib) = 0)
% 4.06/1.73 |
% 4.06/1.73 | Using (4) and (79) yields:
% 4.06/1.73 | (63) $false
% 4.06/1.73 |
% 4.06/1.73 |-The branch is then unsatisfiable
% 4.06/1.73 |-Branch two:
% 4.06/1.73 | (53) ~ (all_0_4_4 = ia)
% 4.06/1.73 | (58) all_0_4_4 = ib
% 4.06/1.73 |
% 4.06/1.73 | Equations (58) can reduce 70 to:
% 4.06/1.73 | (32) $false
% 4.06/1.73 |
% 4.06/1.73 |-The branch is then unsatisfiable
% 4.06/1.73 |-Branch two:
% 4.06/1.73 | (84) rsymProp(all_0_5_5, all_0_3_3) = 0
% 4.06/1.73 | (85) all_0_0_0 = 0
% 4.06/1.73 |
% 4.06/1.73 | Equations (85) can reduce 38 to:
% 4.06/1.73 | (32) $false
% 4.06/1.73 |
% 4.06/1.73 |-The branch is then unsatisfiable
% 4.06/1.73 |-Branch two:
% 4.06/1.73 | (87) rsymProp(all_0_5_5, all_0_4_4) = all_0_0_0
% 4.06/1.73 | (85) all_0_0_0 = 0
% 4.06/1.73 |
% 4.06/1.73 | Equations (85) can reduce 38 to:
% 4.06/1.73 | (32) $false
% 4.06/1.73 |
% 4.06/1.73 |-The branch is then unsatisfiable
% 4.06/1.73 |-Branch two:
% 4.06/1.73 | (90) xsd_string(all_0_5_5) = all_0_4_4 & xsd_integer(all_0_5_5) = all_0_3_3 & ((all_0_3_3 = 0 & all_0_4_4 = 0) | ( ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0)))
% 4.06/1.73 |
% 4.06/1.73 | Applying alpha-rule on (90) yields:
% 4.06/1.73 | (91) xsd_string(all_0_5_5) = all_0_4_4
% 4.06/1.73 | (92) xsd_integer(all_0_5_5) = all_0_3_3
% 4.06/1.73 | (93) (all_0_3_3 = 0 & all_0_4_4 = 0) | ( ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0))
% 4.06/1.73 |
% 4.06/1.73 | Instantiating formula (21) with all_0_5_5 yields:
% 4.06/1.73 | (94) ~ (xsd_string(all_0_5_5) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_5_5) = v0)
% 4.06/1.73 |
% 4.06/1.73 | Instantiating formula (5) with all_0_4_4, all_0_5_5 and discharging atoms xsd_string(all_0_5_5) = all_0_4_4, yields:
% 4.06/1.73 | (95) all_0_4_4 = 0 | xsd_integer(all_0_5_5) = 0
% 4.06/1.73 |
% 4.06/1.73 +-Applying beta-rule and splitting (93), into two cases.
% 4.06/1.73 |-Branch one:
% 4.06/1.73 | (96) all_0_3_3 = 0 & all_0_4_4 = 0
% 4.06/1.73 |
% 4.06/1.73 | Applying alpha-rule on (96) yields:
% 4.06/1.73 | (97) all_0_3_3 = 0
% 4.06/1.73 | (98) all_0_4_4 = 0
% 4.06/1.73 |
% 4.06/1.73 | From (98) and (91) follows:
% 4.06/1.73 | (99) xsd_string(all_0_5_5) = 0
% 4.06/1.73 |
% 4.06/1.73 | From (97) and (92) follows:
% 4.06/1.73 | (100) xsd_integer(all_0_5_5) = 0
% 4.06/1.74 |
% 4.06/1.74 +-Applying beta-rule and splitting (94), into two cases.
% 4.06/1.74 |-Branch one:
% 4.06/1.74 | (101) ~ (xsd_string(all_0_5_5) = 0)
% 4.06/1.74 |
% 4.06/1.74 | Using (99) and (101) yields:
% 4.06/1.74 | (63) $false
% 4.06/1.74 |
% 4.06/1.74 |-The branch is then unsatisfiable
% 4.06/1.74 |-Branch two:
% 4.06/1.74 | (99) xsd_string(all_0_5_5) = 0
% 4.06/1.74 | (104) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_5_5) = v0)
% 4.06/1.74 |
% 4.06/1.74 | Instantiating (104) with all_21_0_7 yields:
% 4.06/1.74 | (105) ~ (all_21_0_7 = 0) & xsd_integer(all_0_5_5) = all_21_0_7
% 4.06/1.74 |
% 4.06/1.74 | Applying alpha-rule on (105) yields:
% 4.06/1.74 | (106) ~ (all_21_0_7 = 0)
% 4.06/1.74 | (107) xsd_integer(all_0_5_5) = all_21_0_7
% 4.06/1.74 |
% 4.06/1.74 | Instantiating formula (11) with all_0_5_5, 0, all_21_0_7 and discharging atoms xsd_integer(all_0_5_5) = all_21_0_7, xsd_integer(all_0_5_5) = 0, yields:
% 4.06/1.74 | (108) all_21_0_7 = 0
% 4.06/1.74 |
% 4.06/1.74 | Equations (108) can reduce 106 to:
% 4.06/1.74 | (32) $false
% 4.06/1.74 |
% 4.06/1.74 |-The branch is then unsatisfiable
% 4.06/1.74 |-Branch two:
% 4.06/1.74 | (110) ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0)
% 4.06/1.74 |
% 4.06/1.74 | Applying alpha-rule on (110) yields:
% 4.06/1.74 | (111) ~ (all_0_3_3 = 0)
% 4.06/1.74 | (112) ~ (all_0_4_4 = 0)
% 4.06/1.74 |
% 4.06/1.74 +-Applying beta-rule and splitting (95), into two cases.
% 4.06/1.74 |-Branch one:
% 4.06/1.74 | (100) xsd_integer(all_0_5_5) = 0
% 4.06/1.74 |
% 4.06/1.74 | Instantiating formula (11) with all_0_5_5, 0, all_0_3_3 and discharging atoms xsd_integer(all_0_5_5) = all_0_3_3, xsd_integer(all_0_5_5) = 0, yields:
% 4.06/1.74 | (97) all_0_3_3 = 0
% 4.06/1.74 |
% 4.06/1.74 | Equations (97) can reduce 111 to:
% 4.06/1.74 | (32) $false
% 4.06/1.74 |
% 4.06/1.74 |-The branch is then unsatisfiable
% 4.06/1.74 |-Branch two:
% 4.06/1.74 | (116) ~ (xsd_integer(all_0_5_5) = 0)
% 4.06/1.74 | (98) all_0_4_4 = 0
% 4.06/1.74 |
% 4.06/1.74 | Equations (98) can reduce 112 to:
% 4.06/1.74 | (32) $false
% 4.06/1.74 |
% 4.06/1.74 |-The branch is then unsatisfiable
% 4.06/1.74 |-Branch two:
% 4.06/1.74 | (119) cowlThing(all_0_5_5) = all_0_4_4 & cowlNothing(all_0_5_5) = all_0_3_3 & ( ~ (all_0_4_4 = 0) | all_0_3_3 = 0)
% 4.06/1.74 |
% 4.06/1.74 | Applying alpha-rule on (119) yields:
% 4.06/1.74 | (120) cowlThing(all_0_5_5) = all_0_4_4
% 4.06/1.74 | (121) cowlNothing(all_0_5_5) = all_0_3_3
% 4.06/1.74 | (122) ~ (all_0_4_4 = 0) | all_0_3_3 = 0
% 4.06/1.74 |
% 4.06/1.74 | Instantiating formula (22) with all_0_4_4, all_0_5_5 and discharging atoms cowlThing(all_0_5_5) = all_0_4_4, yields:
% 4.06/1.74 | (98) all_0_4_4 = 0
% 4.06/1.74 |
% 4.06/1.74 | Instantiating formula (8) with all_0_5_5 yields:
% 4.06/1.74 | (124) ~ (cowlNothing(all_0_5_5) = 0)
% 4.06/1.74 |
% 4.06/1.74 +-Applying beta-rule and splitting (122), into two cases.
% 4.06/1.74 |-Branch one:
% 4.06/1.74 | (112) ~ (all_0_4_4 = 0)
% 4.06/1.74 |
% 4.06/1.74 | Equations (98) can reduce 112 to:
% 4.06/1.74 | (32) $false
% 4.06/1.74 |
% 4.06/1.74 |-The branch is then unsatisfiable
% 4.06/1.74 |-Branch two:
% 4.06/1.74 | (98) all_0_4_4 = 0
% 4.06/1.74 | (97) all_0_3_3 = 0
% 4.06/1.74 |
% 4.06/1.74 | From (97) and (121) follows:
% 4.06/1.74 | (129) cowlNothing(all_0_5_5) = 0
% 4.06/1.74 |
% 4.06/1.74 | Using (129) and (124) yields:
% 4.06/1.74 | (63) $false
% 4.06/1.74 |
% 4.06/1.74 |-The branch is then unsatisfiable
% 4.06/1.74 % SZS output end Proof for theBenchmark
% 4.06/1.74
% 4.06/1.74 1136ms
%------------------------------------------------------------------------------