TSTP Solution File: KRS165+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KRS165+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 02:56:46 EDT 2022
% Result : Theorem 2.33s 1.21s
% Output : Proof 3.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : KRS165+1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.32 % Computer : n026.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Tue Jun 7 19:42:31 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.18/0.57 ____ _
% 0.18/0.57 ___ / __ \_____(_)___ ________ __________
% 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.57
% 0.18/0.57 A Theorem Prover for First-Order Logic
% 0.18/0.57 (ePrincess v.1.0)
% 0.18/0.57
% 0.18/0.57 (c) Philipp Rümmer, 2009-2015
% 0.18/0.57 (c) Peter Backeman, 2014-2015
% 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.57 Bug reports to peter@backeman.se
% 0.18/0.57
% 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.57
% 0.18/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.37/0.86 Prover 0: Preprocessing ...
% 1.49/0.92 Prover 0: Warning: ignoring some quantifiers
% 1.55/0.94 Prover 0: Constructing countermodel ...
% 1.75/1.04 Prover 0: gave up
% 1.75/1.04 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.75/1.06 Prover 1: Preprocessing ...
% 2.03/1.14 Prover 1: Constructing countermodel ...
% 2.33/1.21 Prover 1: proved (161ms)
% 2.33/1.21
% 2.33/1.21 No countermodel exists, formula is valid
% 2.33/1.21 % SZS status Theorem for theBenchmark
% 2.33/1.21
% 2.33/1.21 Generating proof ... found it (size 57)
% 2.88/1.43
% 2.88/1.43 % SZS output start Proof for theBenchmark
% 2.88/1.43 Assumed formulas after preprocessing and simplification:
% 2.88/1.43 | (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) & ((v1 = 0 & ~ (v2 = 0) & cCar(v0) = v2 & cAutomobile(v0) = 0) | (v1 = 0 & ~ (v2 = 0) & cCar(v0) = 0 & cAutomobile(v0) = v2) | (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))))
% 3.17/1.46 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 3.17/1.46 | (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) & ((all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & cCar(all_0_2_2) = all_0_0_0 & cAutomobile(all_0_2_2) = 0) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & cCar(all_0_2_2) = 0 & cAutomobile(all_0_2_2) = all_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)))
% 3.17/1.47 |
% 3.17/1.47 | Applying alpha-rule on (1) yields:
% 3.17/1.47 | (2) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0)
% 3.17/1.47 | (3) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1))
% 3.17/1.47 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0))
% 3.17/1.47 | (5) ! [v0] : ( ~ (cCar(v0) = 0) | cAutomobile(v0) = 0)
% 3.17/1.47 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (cCar(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & cAutomobile(v0) = v2))
% 3.17/1.47 | (7) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 3.17/1.47 | (8) (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & cCar(all_0_2_2) = all_0_0_0 & cAutomobile(all_0_2_2) = 0) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & cCar(all_0_2_2) = 0 & cAutomobile(all_0_2_2) = all_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))
% 3.17/1.47 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0))
% 3.17/1.47 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cAutomobile(v2) = v1) | ~ (cAutomobile(v2) = v0))
% 3.17/1.47 | (11) ! [v0] : ~ (cowlNothing(v0) = 0)
% 3.17/1.47 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0))
% 3.17/1.47 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cCar(v2) = v1) | ~ (cCar(v2) = v0))
% 3.17/1.47 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0))
% 3.17/1.48 |
% 3.17/1.48 +-Applying beta-rule and splitting (8), into two cases.
% 3.17/1.48 |-Branch one:
% 3.17/1.48 | (15) (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & cCar(all_0_2_2) = all_0_0_0 & cAutomobile(all_0_2_2) = 0) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & cCar(all_0_2_2) = 0 & cAutomobile(all_0_2_2) = all_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))))
% 3.17/1.48 |
% 3.17/1.48 +-Applying beta-rule and splitting (15), into two cases.
% 3.17/1.48 |-Branch one:
% 3.17/1.48 | (16) (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & cCar(all_0_2_2) = all_0_0_0 & cAutomobile(all_0_2_2) = 0) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & cCar(all_0_2_2) = 0 & cAutomobile(all_0_2_2) = all_0_0_0)
% 3.17/1.48 |
% 3.17/1.48 +-Applying beta-rule and splitting (16), into two cases.
% 3.17/1.48 |-Branch one:
% 3.17/1.48 | (17) all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & cCar(all_0_2_2) = all_0_0_0 & cAutomobile(all_0_2_2) = 0
% 3.17/1.48 |
% 3.17/1.48 | Applying alpha-rule on (17) yields:
% 3.17/1.48 | (18) all_0_1_1 = 0
% 3.17/1.48 | (19) ~ (all_0_0_0 = 0)
% 3.17/1.48 | (20) cCar(all_0_2_2) = all_0_0_0
% 3.17/1.48 | (21) cAutomobile(all_0_2_2) = 0
% 3.17/1.48 |
% 3.17/1.48 | Instantiating formula (6) with all_0_0_0, all_0_2_2 and discharging atoms cCar(all_0_2_2) = all_0_0_0, yields:
% 3.17/1.48 | (22) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & cAutomobile(all_0_2_2) = v0)
% 3.17/1.48 |
% 3.17/1.48 +-Applying beta-rule and splitting (22), into two cases.
% 3.17/1.48 |-Branch one:
% 3.17/1.48 | (23) all_0_0_0 = 0
% 3.17/1.48 |
% 3.17/1.48 | Equations (23) can reduce 19 to:
% 3.17/1.48 | (24) $false
% 3.17/1.48 |
% 3.17/1.48 |-The branch is then unsatisfiable
% 3.17/1.48 |-Branch two:
% 3.17/1.48 | (19) ~ (all_0_0_0 = 0)
% 3.17/1.48 | (26) ? [v0] : ( ~ (v0 = 0) & cAutomobile(all_0_2_2) = v0)
% 3.17/1.48 |
% 3.17/1.48 | Instantiating (26) with all_13_0_3 yields:
% 3.17/1.48 | (27) ~ (all_13_0_3 = 0) & cAutomobile(all_0_2_2) = all_13_0_3
% 3.17/1.48 |
% 3.17/1.48 | Applying alpha-rule on (27) yields:
% 3.17/1.48 | (28) ~ (all_13_0_3 = 0)
% 3.17/1.48 | (29) cAutomobile(all_0_2_2) = all_13_0_3
% 3.17/1.48 |
% 3.17/1.48 | Instantiating formula (10) with all_0_2_2, all_13_0_3, 0 and discharging atoms cAutomobile(all_0_2_2) = all_13_0_3, cAutomobile(all_0_2_2) = 0, yields:
% 3.17/1.48 | (30) all_13_0_3 = 0
% 3.17/1.48 |
% 3.17/1.48 | Equations (30) can reduce 28 to:
% 3.17/1.48 | (24) $false
% 3.17/1.48 |
% 3.17/1.48 |-The branch is then unsatisfiable
% 3.17/1.48 |-Branch two:
% 3.17/1.48 | (32) all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & cCar(all_0_2_2) = 0 & cAutomobile(all_0_2_2) = all_0_0_0
% 3.17/1.48 |
% 3.17/1.48 | Applying alpha-rule on (32) yields:
% 3.17/1.48 | (18) all_0_1_1 = 0
% 3.17/1.48 | (19) ~ (all_0_0_0 = 0)
% 3.17/1.48 | (35) cCar(all_0_2_2) = 0
% 3.17/1.48 | (36) cAutomobile(all_0_2_2) = all_0_0_0
% 3.17/1.48 |
% 3.17/1.48 | Instantiating formula (5) with all_0_2_2 and discharging atoms cCar(all_0_2_2) = 0, yields:
% 3.17/1.48 | (21) cAutomobile(all_0_2_2) = 0
% 3.17/1.48 |
% 3.17/1.48 | Instantiating formula (10) 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:
% 3.17/1.48 | (23) all_0_0_0 = 0
% 3.27/1.48 |
% 3.27/1.48 | Equations (23) can reduce 19 to:
% 3.27/1.48 | (24) $false
% 3.27/1.48 |
% 3.27/1.48 |-The branch is then unsatisfiable
% 3.27/1.48 |-Branch two:
% 3.27/1.48 | (40) 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)))
% 3.27/1.49 |
% 3.27/1.49 | Applying alpha-rule on (40) yields:
% 3.27/1.49 | (41) xsd_string(all_0_2_2) = all_0_1_1
% 3.27/1.49 | (42) xsd_integer(all_0_2_2) = all_0_0_0
% 3.27/1.49 | (43) (all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0))
% 3.27/1.49 |
% 3.27/1.49 | Instantiating formula (7) with all_0_2_2 yields:
% 3.27/1.49 | (44) ~ (xsd_string(all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0)
% 3.27/1.49 |
% 3.27/1.49 | Instantiating formula (2) with all_0_1_1, all_0_2_2 and discharging atoms xsd_string(all_0_2_2) = all_0_1_1, yields:
% 3.27/1.49 | (45) all_0_1_1 = 0 | xsd_integer(all_0_2_2) = 0
% 3.27/1.49 |
% 3.27/1.49 +-Applying beta-rule and splitting (45), into two cases.
% 3.27/1.49 |-Branch one:
% 3.27/1.49 | (46) xsd_integer(all_0_2_2) = 0
% 3.27/1.49 |
% 3.27/1.49 | Instantiating formula (14) 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:
% 3.27/1.49 | (23) all_0_0_0 = 0
% 3.27/1.49 |
% 3.27/1.49 | From (23) and (42) follows:
% 3.27/1.49 | (46) xsd_integer(all_0_2_2) = 0
% 3.27/1.49 |
% 3.27/1.49 +-Applying beta-rule and splitting (44), into two cases.
% 3.27/1.49 |-Branch one:
% 3.27/1.49 | (49) ~ (xsd_string(all_0_2_2) = 0)
% 3.27/1.49 |
% 3.27/1.49 +-Applying beta-rule and splitting (43), into two cases.
% 3.27/1.49 |-Branch one:
% 3.27/1.49 | (50) all_0_0_0 = 0 & all_0_1_1 = 0
% 3.27/1.49 |
% 3.27/1.49 | Applying alpha-rule on (50) yields:
% 3.27/1.49 | (23) all_0_0_0 = 0
% 3.27/1.49 | (18) all_0_1_1 = 0
% 3.27/1.49 |
% 3.27/1.49 | From (18) and (41) follows:
% 3.27/1.49 | (53) xsd_string(all_0_2_2) = 0
% 3.27/1.49 |
% 3.27/1.49 | Using (53) and (49) yields:
% 3.27/1.49 | (54) $false
% 3.27/1.49 |
% 3.27/1.49 |-The branch is then unsatisfiable
% 3.27/1.49 |-Branch two:
% 3.27/1.49 | (55) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)
% 3.27/1.49 |
% 3.27/1.49 | Applying alpha-rule on (55) yields:
% 3.27/1.49 | (19) ~ (all_0_0_0 = 0)
% 3.27/1.49 | (57) ~ (all_0_1_1 = 0)
% 3.27/1.49 |
% 3.27/1.49 | Equations (23) can reduce 19 to:
% 3.27/1.49 | (24) $false
% 3.27/1.49 |
% 3.27/1.49 |-The branch is then unsatisfiable
% 3.27/1.49 |-Branch two:
% 3.27/1.49 | (53) xsd_string(all_0_2_2) = 0
% 3.27/1.49 | (60) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0)
% 3.27/1.49 |
% 3.27/1.49 | Instantiating (60) with all_21_0_4 yields:
% 3.27/1.49 | (61) ~ (all_21_0_4 = 0) & xsd_integer(all_0_2_2) = all_21_0_4
% 3.27/1.49 |
% 3.27/1.49 | Applying alpha-rule on (61) yields:
% 3.27/1.49 | (62) ~ (all_21_0_4 = 0)
% 3.27/1.49 | (63) xsd_integer(all_0_2_2) = all_21_0_4
% 3.27/1.49 |
% 3.27/1.49 | Instantiating formula (14) 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:
% 3.27/1.49 | (64) all_21_0_4 = 0
% 3.27/1.49 |
% 3.27/1.49 | Equations (64) can reduce 62 to:
% 3.27/1.49 | (24) $false
% 3.27/1.49 |
% 3.27/1.49 |-The branch is then unsatisfiable
% 3.27/1.49 |-Branch two:
% 3.27/1.49 | (66) ~ (xsd_integer(all_0_2_2) = 0)
% 3.27/1.49 | (18) all_0_1_1 = 0
% 3.27/1.49 |
% 3.27/1.49 +-Applying beta-rule and splitting (43), into two cases.
% 3.27/1.49 |-Branch one:
% 3.27/1.49 | (50) all_0_0_0 = 0 & all_0_1_1 = 0
% 3.27/1.49 |
% 3.27/1.49 | Applying alpha-rule on (50) yields:
% 3.27/1.49 | (23) all_0_0_0 = 0
% 3.27/1.49 | (18) all_0_1_1 = 0
% 3.27/1.49 |
% 3.27/1.49 | From (23) and (42) follows:
% 3.27/1.49 | (46) xsd_integer(all_0_2_2) = 0
% 3.27/1.49 |
% 3.27/1.49 | Using (46) and (66) yields:
% 3.27/1.49 | (54) $false
% 3.27/1.49 |
% 3.27/1.49 |-The branch is then unsatisfiable
% 3.27/1.49 |-Branch two:
% 3.27/1.49 | (55) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)
% 3.27/1.49 |
% 3.27/1.49 | Applying alpha-rule on (55) yields:
% 3.27/1.49 | (19) ~ (all_0_0_0 = 0)
% 3.27/1.50 | (57) ~ (all_0_1_1 = 0)
% 3.27/1.50 |
% 3.27/1.50 | Equations (18) can reduce 57 to:
% 3.27/1.50 | (24) $false
% 3.27/1.50 |
% 3.27/1.50 |-The branch is then unsatisfiable
% 3.27/1.50 |-Branch two:
% 3.27/1.50 | (77) 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)
% 3.27/1.50 |
% 3.27/1.50 | Applying alpha-rule on (77) yields:
% 3.27/1.50 | (78) cowlNothing(all_0_2_2) = all_0_0_0
% 3.27/1.50 | (79) cowlThing(all_0_2_2) = all_0_1_1
% 3.27/1.50 | (80) ~ (all_0_1_1 = 0) | all_0_0_0 = 0
% 3.27/1.50 |
% 3.27/1.50 | Instantiating formula (11) with all_0_2_2 yields:
% 3.27/1.50 | (81) ~ (cowlNothing(all_0_2_2) = 0)
% 3.27/1.50 |
% 3.27/1.50 | Instantiating formula (3) with all_0_1_1, all_0_2_2 and discharging atoms cowlThing(all_0_2_2) = all_0_1_1, yields:
% 3.27/1.50 | (18) all_0_1_1 = 0
% 3.27/1.50 |
% 3.27/1.50 +-Applying beta-rule and splitting (80), into two cases.
% 3.27/1.50 |-Branch one:
% 3.27/1.50 | (57) ~ (all_0_1_1 = 0)
% 3.27/1.50 |
% 3.27/1.50 | Equations (18) can reduce 57 to:
% 3.27/1.50 | (24) $false
% 3.27/1.50 |
% 3.27/1.50 |-The branch is then unsatisfiable
% 3.27/1.50 |-Branch two:
% 3.27/1.50 | (18) all_0_1_1 = 0
% 3.27/1.50 | (23) all_0_0_0 = 0
% 3.27/1.50 |
% 3.27/1.50 | From (23) and (78) follows:
% 3.27/1.50 | (87) cowlNothing(all_0_2_2) = 0
% 3.27/1.50 |
% 3.27/1.50 | Using (87) and (81) yields:
% 3.27/1.50 | (54) $false
% 3.27/1.50 |
% 3.27/1.50 |-The branch is then unsatisfiable
% 3.27/1.50 % SZS output end Proof for theBenchmark
% 3.27/1.50
% 3.27/1.50 916ms
%------------------------------------------------------------------------------