TSTP Solution File: KRS166+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KRS166+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n032.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 02:56:46 EDT 2022
% Result : Theorem 1.90s 1.04s
% Output : Proof 2.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : KRS166+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.10 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.29 % Computer : n032.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.30 % WCLimit : 600
% 0.11/0.30 % DateTime : Tue Jun 7 19:20:36 EDT 2022
% 0.11/0.30 % CPUTime :
% 0.14/0.49 ____ _
% 0.14/0.49 ___ / __ \_____(_)___ ________ __________
% 0.14/0.49 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.14/0.49 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.14/0.49 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.14/0.49
% 0.14/0.49 A Theorem Prover for First-Order Logic
% 0.14/0.49 (ePrincess v.1.0)
% 0.14/0.49
% 0.14/0.49 (c) Philipp Rümmer, 2009-2015
% 0.14/0.49 (c) Peter Backeman, 2014-2015
% 0.14/0.49 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.14/0.49 Free software under GNU Lesser General Public License (LGPL).
% 0.14/0.49 Bug reports to peter@backeman.se
% 0.14/0.49
% 0.14/0.49 For more information, visit http://user.uu.se/~petba168/breu/
% 0.14/0.49
% 0.14/0.49 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.14/0.54 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.01/0.74 Prover 0: Preprocessing ...
% 1.13/0.79 Prover 0: Warning: ignoring some quantifiers
% 1.13/0.81 Prover 0: Constructing countermodel ...
% 1.43/0.89 Prover 0: gave up
% 1.43/0.89 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.43/0.91 Prover 1: Preprocessing ...
% 1.71/0.98 Prover 1: Constructing countermodel ...
% 1.90/1.04 Prover 1: proved (147ms)
% 1.90/1.04
% 1.90/1.04 No countermodel exists, formula is valid
% 1.90/1.04 % SZS status Theorem for theBenchmark
% 1.90/1.04
% 1.90/1.04 Generating proof ... found it (size 69)
% 2.50/1.23
% 2.50/1.23 % SZS output start Proof for theBenchmark
% 2.50/1.23 Assumed formulas after preprocessing and simplification:
% 2.50/1.23 | (0) ? [v0] : ? [v1] : ? [v2] : ( ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (cCar(v5) = v4) | ~ (cCar(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (cAutomobile(v5) = v4) | ~ (cAutomobile(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (xsd_string(v5) = v4) | ~ (xsd_string(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (xsd_integer(v5) = v4) | ~ (xsd_integer(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (cowlNothing(v5) = v4) | ~ (cowlNothing(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (cowlThing(v5) = v4) | ~ (cowlThing(v5) = v3)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (cCar(v3) = v4) | ? [v5] : ( ~ (v5 = 0) & cAutomobile(v3) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (xsd_string(v3) = v4) | xsd_integer(v3) = 0) & ! [v3] : ! [v4] : (v4 = 0 | ~ (cowlThing(v3) = v4)) & ! [v3] : ( ~ (cCar(v3) = 0) | cAutomobile(v3) = 0) & ! [v3] : ( ~ (xsd_string(v3) = 0) | ? [v4] : ( ~ (v4 = 0) & xsd_integer(v3) = v4)) & ! [v3] : ~ (cowlNothing(v3) = 0) & ((cCar(v0) = v1 & cAutomobile(v0) = v2 & ((v2 = 0 & ~ (v1 = 0)) | (v1 = 0 & ~ (v2 = 0)))) | (xsd_string(v0) = v1 & xsd_integer(v0) = v2 & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & ~ (v1 = 0)))) | (cowlNothing(v0) = v2 & cowlThing(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))))
% 2.51/1.26 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 2.51/1.26 | (1) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cCar(v2) = v1) | ~ (cCar(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cAutomobile(v2) = v1) | ~ (cAutomobile(v2) = v0)) & ! [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 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cCar(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & cAutomobile(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) & ! [v0] : ( ~ (cCar(v0) = 0) | cAutomobile(v0) = 0) & ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) & ! [v0] : ~ (cowlNothing(v0) = 0) & ((cCar(all_0_2_2) = all_0_1_1 & cAutomobile(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)))) | (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)))
% 2.51/1.27 |
% 2.51/1.27 | Applying alpha-rule on (1) yields:
% 2.51/1.27 | (2) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 2.51/1.27 | (3) ! [v0] : ( ~ (cCar(v0) = 0) | cAutomobile(v0) = 0)
% 2.51/1.27 | (4) ! [v0] : ~ (cowlNothing(v0) = 0)
% 2.51/1.27 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0))
% 2.51/1.27 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1))
% 2.51/1.27 | (7) ! [v0] : ! [v1] : (v1 = 0 | ~ (cCar(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & cAutomobile(v0) = v2))
% 2.51/1.27 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cAutomobile(v2) = v1) | ~ (cAutomobile(v2) = v0))
% 2.51/1.27 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cCar(v2) = v1) | ~ (cCar(v2) = v0))
% 2.51/1.27 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0))
% 2.51/1.27 | (11) (cCar(all_0_2_2) = all_0_1_1 & cAutomobile(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)))) | (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0))
% 2.51/1.28 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0)
% 2.51/1.28 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0))
% 2.51/1.28 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0))
% 2.51/1.28 |
% 2.51/1.28 +-Applying beta-rule and splitting (11), into two cases.
% 2.51/1.28 |-Branch one:
% 2.51/1.28 | (15) (cCar(all_0_2_2) = all_0_1_1 & cAutomobile(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)))) | (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0))))
% 2.51/1.28 |
% 2.51/1.28 +-Applying beta-rule and splitting (15), into two cases.
% 2.51/1.28 |-Branch one:
% 2.51/1.28 | (16) cCar(all_0_2_2) = all_0_1_1 & cAutomobile(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)))
% 2.51/1.28 |
% 2.51/1.28 | Applying alpha-rule on (16) yields:
% 2.51/1.28 | (17) cCar(all_0_2_2) = all_0_1_1
% 2.51/1.28 | (18) cAutomobile(all_0_2_2) = all_0_0_0
% 2.51/1.28 | (19) (all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0))
% 2.51/1.28 |
% 2.51/1.28 | Instantiating formula (3) with all_0_2_2 yields:
% 2.51/1.28 | (20) ~ (cCar(all_0_2_2) = 0) | cAutomobile(all_0_2_2) = 0
% 2.51/1.28 |
% 2.51/1.28 | Instantiating formula (7) with all_0_1_1, all_0_2_2 and discharging atoms cCar(all_0_2_2) = all_0_1_1, yields:
% 2.51/1.28 | (21) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & cAutomobile(all_0_2_2) = v0)
% 2.51/1.28 |
% 2.51/1.28 +-Applying beta-rule and splitting (20), into two cases.
% 2.51/1.28 |-Branch one:
% 2.51/1.28 | (22) ~ (cCar(all_0_2_2) = 0)
% 2.51/1.28 |
% 2.51/1.28 | Using (17) and (22) yields:
% 2.51/1.28 | (23) ~ (all_0_1_1 = 0)
% 2.51/1.28 |
% 2.51/1.28 +-Applying beta-rule and splitting (19), into two cases.
% 2.51/1.28 |-Branch one:
% 2.51/1.28 | (24) all_0_0_0 = 0 & ~ (all_0_1_1 = 0)
% 2.51/1.28 |
% 2.51/1.28 | Applying alpha-rule on (24) yields:
% 2.51/1.28 | (25) all_0_0_0 = 0
% 2.51/1.28 | (23) ~ (all_0_1_1 = 0)
% 2.51/1.28 |
% 2.51/1.28 | From (25) and (18) follows:
% 2.51/1.28 | (27) cAutomobile(all_0_2_2) = 0
% 2.51/1.28 |
% 2.51/1.28 +-Applying beta-rule and splitting (21), into two cases.
% 2.51/1.28 |-Branch one:
% 2.51/1.28 | (28) all_0_1_1 = 0
% 2.51/1.28 |
% 2.51/1.28 | Equations (28) can reduce 23 to:
% 2.51/1.28 | (29) $false
% 2.51/1.28 |
% 2.51/1.28 |-The branch is then unsatisfiable
% 2.51/1.28 |-Branch two:
% 2.51/1.28 | (23) ~ (all_0_1_1 = 0)
% 2.51/1.28 | (31) ? [v0] : ( ~ (v0 = 0) & cAutomobile(all_0_2_2) = v0)
% 2.51/1.28 |
% 2.51/1.28 | Instantiating (31) with all_25_0_3 yields:
% 2.51/1.28 | (32) ~ (all_25_0_3 = 0) & cAutomobile(all_0_2_2) = all_25_0_3
% 2.51/1.28 |
% 2.51/1.28 | Applying alpha-rule on (32) yields:
% 2.51/1.28 | (33) ~ (all_25_0_3 = 0)
% 2.51/1.28 | (34) cAutomobile(all_0_2_2) = all_25_0_3
% 2.51/1.28 |
% 2.51/1.28 | Instantiating formula (8) with all_0_2_2, 0, all_25_0_3 and discharging atoms cAutomobile(all_0_2_2) = all_25_0_3, cAutomobile(all_0_2_2) = 0, yields:
% 2.51/1.28 | (35) all_25_0_3 = 0
% 2.51/1.29 |
% 2.51/1.29 | Equations (35) can reduce 33 to:
% 2.51/1.29 | (29) $false
% 2.51/1.29 |
% 2.51/1.29 |-The branch is then unsatisfiable
% 2.51/1.29 |-Branch two:
% 2.51/1.29 | (37) all_0_1_1 = 0 & ~ (all_0_0_0 = 0)
% 2.51/1.29 |
% 2.51/1.29 | Applying alpha-rule on (37) yields:
% 2.51/1.29 | (28) all_0_1_1 = 0
% 2.51/1.29 | (39) ~ (all_0_0_0 = 0)
% 2.51/1.29 |
% 2.51/1.29 | Equations (28) can reduce 23 to:
% 2.51/1.29 | (29) $false
% 2.51/1.29 |
% 2.51/1.29 |-The branch is then unsatisfiable
% 2.51/1.29 |-Branch two:
% 2.51/1.29 | (41) cCar(all_0_2_2) = 0
% 2.51/1.29 | (27) cAutomobile(all_0_2_2) = 0
% 2.51/1.29 |
% 2.51/1.29 | Instantiating formula (9) with all_0_2_2, 0, all_0_1_1 and discharging atoms cCar(all_0_2_2) = all_0_1_1, cCar(all_0_2_2) = 0, yields:
% 2.51/1.29 | (28) all_0_1_1 = 0
% 2.51/1.29 |
% 2.51/1.29 | Instantiating formula (8) with all_0_2_2, 0, all_0_0_0 and discharging atoms cAutomobile(all_0_2_2) = all_0_0_0, cAutomobile(all_0_2_2) = 0, yields:
% 2.51/1.29 | (25) all_0_0_0 = 0
% 2.51/1.29 |
% 2.51/1.29 +-Applying beta-rule and splitting (19), into two cases.
% 2.51/1.29 |-Branch one:
% 2.51/1.29 | (24) all_0_0_0 = 0 & ~ (all_0_1_1 = 0)
% 2.51/1.29 |
% 2.51/1.29 | Applying alpha-rule on (24) yields:
% 2.51/1.29 | (25) all_0_0_0 = 0
% 2.51/1.29 | (23) ~ (all_0_1_1 = 0)
% 2.51/1.29 |
% 2.51/1.29 | Equations (28) can reduce 23 to:
% 2.51/1.29 | (29) $false
% 2.51/1.29 |
% 2.51/1.29 |-The branch is then unsatisfiable
% 2.51/1.29 |-Branch two:
% 2.51/1.29 | (37) all_0_1_1 = 0 & ~ (all_0_0_0 = 0)
% 2.51/1.29 |
% 2.51/1.29 | Applying alpha-rule on (37) yields:
% 2.51/1.29 | (28) all_0_1_1 = 0
% 2.51/1.29 | (39) ~ (all_0_0_0 = 0)
% 2.51/1.29 |
% 2.51/1.29 | Equations (25) can reduce 39 to:
% 2.51/1.29 | (29) $false
% 2.51/1.29 |
% 2.51/1.29 |-The branch is then unsatisfiable
% 2.51/1.29 |-Branch two:
% 2.51/1.29 | (53) xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)))
% 2.51/1.29 |
% 2.51/1.29 | Applying alpha-rule on (53) yields:
% 2.51/1.29 | (54) xsd_string(all_0_2_2) = all_0_1_1
% 2.51/1.29 | (55) xsd_integer(all_0_2_2) = all_0_0_0
% 2.51/1.29 | (56) (all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0))
% 2.51/1.29 |
% 2.51/1.29 | Instantiating formula (2) with all_0_2_2 yields:
% 2.51/1.29 | (57) ~ (xsd_string(all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0)
% 2.51/1.29 |
% 2.51/1.29 | Instantiating formula (12) with all_0_1_1, all_0_2_2 and discharging atoms xsd_string(all_0_2_2) = all_0_1_1, yields:
% 2.51/1.29 | (58) all_0_1_1 = 0 | xsd_integer(all_0_2_2) = 0
% 2.51/1.29 |
% 2.51/1.29 +-Applying beta-rule and splitting (58), into two cases.
% 2.51/1.29 |-Branch one:
% 2.51/1.29 | (59) xsd_integer(all_0_2_2) = 0
% 2.51/1.29 |
% 2.51/1.29 | Instantiating formula (5) with all_0_2_2, 0, all_0_0_0 and discharging atoms xsd_integer(all_0_2_2) = all_0_0_0, xsd_integer(all_0_2_2) = 0, yields:
% 2.51/1.29 | (25) all_0_0_0 = 0
% 2.51/1.29 |
% 2.51/1.29 | From (25) and (55) follows:
% 2.51/1.29 | (59) xsd_integer(all_0_2_2) = 0
% 2.51/1.29 |
% 2.51/1.29 +-Applying beta-rule and splitting (57), into two cases.
% 2.51/1.29 |-Branch one:
% 2.51/1.29 | (62) ~ (xsd_string(all_0_2_2) = 0)
% 2.51/1.29 |
% 2.51/1.29 +-Applying beta-rule and splitting (56), into two cases.
% 2.51/1.29 |-Branch one:
% 2.51/1.29 | (63) all_0_0_0 = 0 & all_0_1_1 = 0
% 2.51/1.29 |
% 2.51/1.29 | Applying alpha-rule on (63) yields:
% 2.51/1.29 | (25) all_0_0_0 = 0
% 2.51/1.29 | (28) all_0_1_1 = 0
% 2.51/1.29 |
% 2.51/1.29 | From (28) and (54) follows:
% 2.51/1.29 | (66) xsd_string(all_0_2_2) = 0
% 2.51/1.29 |
% 2.51/1.29 | Using (66) and (62) yields:
% 2.51/1.29 | (67) $false
% 2.51/1.29 |
% 2.51/1.29 |-The branch is then unsatisfiable
% 2.51/1.29 |-Branch two:
% 2.51/1.29 | (68) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)
% 2.51/1.29 |
% 2.51/1.29 | Applying alpha-rule on (68) yields:
% 2.51/1.29 | (39) ~ (all_0_0_0 = 0)
% 2.51/1.29 | (23) ~ (all_0_1_1 = 0)
% 2.51/1.29 |
% 2.51/1.29 | Equations (25) can reduce 39 to:
% 2.51/1.29 | (29) $false
% 2.51/1.29 |
% 2.51/1.29 |-The branch is then unsatisfiable
% 2.51/1.29 |-Branch two:
% 2.51/1.29 | (66) xsd_string(all_0_2_2) = 0
% 2.51/1.29 | (73) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0)
% 2.51/1.29 |
% 2.51/1.29 | Instantiating (73) with all_21_0_4 yields:
% 2.51/1.29 | (74) ~ (all_21_0_4 = 0) & xsd_integer(all_0_2_2) = all_21_0_4
% 2.51/1.29 |
% 2.51/1.29 | Applying alpha-rule on (74) yields:
% 2.51/1.30 | (75) ~ (all_21_0_4 = 0)
% 2.51/1.30 | (76) xsd_integer(all_0_2_2) = all_21_0_4
% 2.51/1.30 |
% 2.51/1.30 | Instantiating formula (5) with all_0_2_2, all_21_0_4, 0 and discharging atoms xsd_integer(all_0_2_2) = all_21_0_4, xsd_integer(all_0_2_2) = 0, yields:
% 2.51/1.30 | (77) all_21_0_4 = 0
% 2.51/1.30 |
% 2.51/1.30 | Equations (77) can reduce 75 to:
% 2.51/1.30 | (29) $false
% 2.51/1.30 |
% 2.51/1.30 |-The branch is then unsatisfiable
% 2.51/1.30 |-Branch two:
% 2.51/1.30 | (79) ~ (xsd_integer(all_0_2_2) = 0)
% 2.51/1.30 | (28) all_0_1_1 = 0
% 2.51/1.30 |
% 2.51/1.30 +-Applying beta-rule and splitting (56), into two cases.
% 2.51/1.30 |-Branch one:
% 2.51/1.30 | (63) all_0_0_0 = 0 & all_0_1_1 = 0
% 2.51/1.30 |
% 2.51/1.30 | Applying alpha-rule on (63) yields:
% 2.51/1.30 | (25) all_0_0_0 = 0
% 2.51/1.30 | (28) all_0_1_1 = 0
% 2.51/1.30 |
% 2.51/1.30 | From (25) and (55) follows:
% 2.51/1.30 | (59) xsd_integer(all_0_2_2) = 0
% 2.51/1.30 |
% 2.51/1.30 | Using (59) and (79) yields:
% 2.51/1.30 | (67) $false
% 2.51/1.30 |
% 2.51/1.30 |-The branch is then unsatisfiable
% 2.51/1.30 |-Branch two:
% 2.51/1.30 | (68) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)
% 2.51/1.30 |
% 2.51/1.30 | Applying alpha-rule on (68) yields:
% 2.51/1.30 | (39) ~ (all_0_0_0 = 0)
% 2.51/1.30 | (23) ~ (all_0_1_1 = 0)
% 2.51/1.30 |
% 2.51/1.30 | Equations (28) can reduce 23 to:
% 2.51/1.30 | (29) $false
% 2.51/1.30 |
% 2.51/1.30 |-The branch is then unsatisfiable
% 2.51/1.30 |-Branch two:
% 2.51/1.30 | (90) cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)
% 2.51/1.30 |
% 2.51/1.30 | Applying alpha-rule on (90) yields:
% 2.51/1.30 | (91) cowlNothing(all_0_2_2) = all_0_0_0
% 2.51/1.30 | (92) cowlThing(all_0_2_2) = all_0_1_1
% 2.51/1.30 | (93) ~ (all_0_1_1 = 0) | all_0_0_0 = 0
% 2.51/1.30 |
% 2.51/1.30 | Instantiating formula (4) with all_0_2_2 yields:
% 2.51/1.30 | (94) ~ (cowlNothing(all_0_2_2) = 0)
% 2.51/1.30 |
% 2.51/1.30 | Instantiating formula (6) with all_0_1_1, all_0_2_2 and discharging atoms cowlThing(all_0_2_2) = all_0_1_1, yields:
% 2.51/1.30 | (28) all_0_1_1 = 0
% 2.51/1.30 |
% 2.51/1.30 +-Applying beta-rule and splitting (93), into two cases.
% 2.51/1.30 |-Branch one:
% 2.51/1.30 | (23) ~ (all_0_1_1 = 0)
% 2.51/1.30 |
% 2.51/1.30 | Equations (28) can reduce 23 to:
% 2.51/1.30 | (29) $false
% 2.51/1.30 |
% 2.51/1.30 |-The branch is then unsatisfiable
% 2.51/1.30 |-Branch two:
% 2.51/1.30 | (28) all_0_1_1 = 0
% 2.51/1.30 | (25) all_0_0_0 = 0
% 2.51/1.30 |
% 2.51/1.30 | From (25) and (91) follows:
% 2.51/1.30 | (100) cowlNothing(all_0_2_2) = 0
% 2.51/1.30 |
% 2.51/1.30 | Using (100) and (94) yields:
% 2.51/1.30 | (67) $false
% 2.51/1.30 |
% 2.51/1.30 |-The branch is then unsatisfiable
% 2.51/1.30 % SZS output end Proof for theBenchmark
% 2.51/1.30
% 2.51/1.30 799ms
%------------------------------------------------------------------------------