TSTP Solution File: KRS137+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KRS137+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n021.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 2.61s 1.27s
% Output : Proof 3.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS137+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n021.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 15:55:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.50/0.59 ____ _
% 0.50/0.59 ___ / __ \_____(_)___ ________ __________
% 0.50/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.59
% 0.50/0.59 A Theorem Prover for First-Order Logic
% 0.50/0.60 (ePrincess v.1.0)
% 0.50/0.60
% 0.50/0.60 (c) Philipp Rümmer, 2009-2015
% 0.50/0.60 (c) Peter Backeman, 2014-2015
% 0.50/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.60 Bug reports to peter@backeman.se
% 0.50/0.60
% 0.50/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.60
% 0.50/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.32/0.89 Prover 0: Preprocessing ...
% 1.50/0.97 Prover 0: Warning: ignoring some quantifiers
% 1.50/0.98 Prover 0: Constructing countermodel ...
% 1.93/1.09 Prover 0: gave up
% 1.93/1.09 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.93/1.10 Prover 1: Preprocessing ...
% 2.32/1.19 Prover 1: Constructing countermodel ...
% 2.61/1.27 Prover 1: proved (179ms)
% 2.61/1.27
% 2.61/1.27 No countermodel exists, formula is valid
% 2.61/1.27 % SZS status Theorem for theBenchmark
% 2.61/1.27
% 2.61/1.27 Generating proof ... found it (size 65)
% 3.21/1.52
% 3.21/1.52 % SZS output start Proof for theBenchmark
% 3.21/1.52 Assumed formulas after preprocessing and simplification:
% 3.21/1.52 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (cCar(icar) = 0 & cCar(iauto) = v0 & cAutomobile(icar) = v1 & cAutomobile(iauto) = 0 & cowlThing(icar) = 0 & cowlThing(iauto) = 0 & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cCar(v7) = v6) | ~ (cCar(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cAutomobile(v7) = v6) | ~ (cAutomobile(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (xsd_string(v7) = v6) | ~ (xsd_string(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (xsd_integer(v7) = v6) | ~ (xsd_integer(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cowlNothing(v7) = v6) | ~ (cowlNothing(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cowlThing(v7) = v6) | ~ (cowlThing(v7) = v5)) & ! [v5] : ! [v6] : (v6 = 0 | ~ (cCar(v5) = v6) | ? [v7] : ( ~ (v7 = 0) & cAutomobile(v5) = v7)) & ! [v5] : ! [v6] : (v6 = 0 | ~ (xsd_string(v5) = v6) | xsd_integer(v5) = 0) & ! [v5] : ! [v6] : (v6 = 0 | ~ (cowlThing(v5) = v6)) & ! [v5] : ( ~ (cCar(v5) = 0) | cAutomobile(v5) = 0) & ! [v5] : ( ~ (xsd_string(v5) = 0) | ? [v6] : ( ~ (v6 = 0) & xsd_integer(v5) = v6)) & ! [v5] : ~ (cowlNothing(v5) = 0) & ( ~ (v1 = 0) | ~ (v0 = 0) | (xsd_string(v2) = v3 & xsd_integer(v2) = v4 & ((v4 = 0 & v3 = 0) | ( ~ (v4 = 0) & ~ (v3 = 0)))) | (cowlNothing(v2) = v4 & cowlThing(v2) = v3 & ( ~ (v3 = 0) | v4 = 0))))
% 3.42/1.55 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 3.42/1.55 | (1) cCar(icar) = 0 & cCar(iauto) = all_0_4_4 & cAutomobile(icar) = all_0_3_3 & cAutomobile(iauto) = 0 & cowlThing(icar) = 0 & cowlThing(iauto) = 0 & ! [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_3_3 = 0) | ~ (all_0_4_4 = 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)))
% 3.42/1.56 |
% 3.42/1.56 | Applying alpha-rule on (1) yields:
% 3.42/1.56 | (2) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 3.42/1.56 | (3) cowlThing(iauto) = 0
% 3.42/1.56 | (4) cCar(iauto) = all_0_4_4
% 3.42/1.56 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0)
% 3.42/1.56 | (6) ! [v0] : ( ~ (cCar(v0) = 0) | cAutomobile(v0) = 0)
% 3.42/1.56 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0))
% 3.42/1.56 | (8) cAutomobile(icar) = all_0_3_3
% 3.42/1.56 | (9) ! [v0] : ~ (cowlNothing(v0) = 0)
% 3.42/1.56 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1))
% 3.42/1.56 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0))
% 3.42/1.57 | (12) cAutomobile(iauto) = 0
% 3.42/1.57 | (13) ! [v0] : ! [v1] : (v1 = 0 | ~ (cCar(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & cAutomobile(v0) = v2))
% 3.51/1.57 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cAutomobile(v2) = v1) | ~ (cAutomobile(v2) = v0))
% 3.51/1.57 | (15) ~ (all_0_3_3 = 0) | ~ (all_0_4_4 = 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))
% 3.51/1.57 | (16) cCar(icar) = 0
% 3.51/1.57 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0))
% 3.51/1.57 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cCar(v2) = v1) | ~ (cCar(v2) = v0))
% 3.51/1.57 | (19) cowlThing(icar) = 0
% 3.51/1.57 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0))
% 3.51/1.57 |
% 3.51/1.57 | Instantiating formula (18) with iauto, all_0_4_4, 0 and discharging atoms cCar(iauto) = all_0_4_4, yields:
% 3.51/1.57 | (21) all_0_4_4 = 0 | ~ (cCar(iauto) = 0)
% 3.51/1.57 |
% 3.51/1.57 | Instantiating formula (14) with iauto, 0, all_0_3_3 and discharging atoms cAutomobile(iauto) = 0, yields:
% 3.51/1.57 | (22) all_0_3_3 = 0 | ~ (cAutomobile(iauto) = all_0_3_3)
% 3.51/1.57 |
% 3.51/1.57 | Instantiating formula (6) with icar and discharging atoms cCar(icar) = 0, yields:
% 3.51/1.57 | (23) cAutomobile(icar) = 0
% 3.51/1.57 |
% 3.51/1.57 | Instantiating formula (13) with all_0_4_4, iauto and discharging atoms cCar(iauto) = all_0_4_4, yields:
% 3.51/1.57 | (24) all_0_4_4 = 0 | ? [v0] : ( ~ (v0 = 0) & cAutomobile(iauto) = v0)
% 3.51/1.57 |
% 3.51/1.57 +-Applying beta-rule and splitting (24), into two cases.
% 3.51/1.57 |-Branch one:
% 3.51/1.57 | (25) all_0_4_4 = 0
% 3.51/1.57 |
% 3.51/1.57 | From (25) and (4) follows:
% 3.51/1.57 | (26) cCar(iauto) = 0
% 3.51/1.57 |
% 3.51/1.57 | Instantiating formula (14) with icar, 0, all_0_3_3 and discharging atoms cAutomobile(icar) = all_0_3_3, cAutomobile(icar) = 0, yields:
% 3.51/1.57 | (27) all_0_3_3 = 0
% 3.51/1.57 |
% 3.51/1.57 +-Applying beta-rule and splitting (21), into two cases.
% 3.51/1.57 |-Branch one:
% 3.51/1.57 | (28) ~ (cCar(iauto) = 0)
% 3.51/1.57 |
% 3.51/1.57 | Using (26) and (28) yields:
% 3.51/1.57 | (29) $false
% 3.51/1.57 |
% 3.51/1.57 |-The branch is then unsatisfiable
% 3.51/1.57 |-Branch two:
% 3.51/1.57 | (26) cCar(iauto) = 0
% 3.51/1.57 | (25) all_0_4_4 = 0
% 3.51/1.57 |
% 3.51/1.57 +-Applying beta-rule and splitting (22), into two cases.
% 3.51/1.57 |-Branch one:
% 3.51/1.57 | (32) ~ (cAutomobile(iauto) = all_0_3_3)
% 3.51/1.57 |
% 3.51/1.57 | From (27) and (32) follows:
% 3.51/1.57 | (33) ~ (cAutomobile(iauto) = 0)
% 3.51/1.58 |
% 3.51/1.58 | Using (12) and (33) yields:
% 3.51/1.58 | (29) $false
% 3.51/1.58 |
% 3.51/1.58 |-The branch is then unsatisfiable
% 3.51/1.58 |-Branch two:
% 3.51/1.58 | (35) cAutomobile(iauto) = all_0_3_3
% 3.51/1.58 | (27) all_0_3_3 = 0
% 3.51/1.58 |
% 3.51/1.58 +-Applying beta-rule and splitting (15), into two cases.
% 3.51/1.58 |-Branch one:
% 3.51/1.58 | (37) ~ (all_0_3_3 = 0)
% 3.51/1.58 |
% 3.51/1.58 | Equations (27) can reduce 37 to:
% 3.51/1.58 | (38) $false
% 3.51/1.58 |
% 3.51/1.58 |-The branch is then unsatisfiable
% 3.51/1.58 |-Branch two:
% 3.51/1.58 | (27) all_0_3_3 = 0
% 3.51/1.58 | (40) ~ (all_0_4_4 = 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))
% 3.51/1.58 |
% 3.51/1.58 +-Applying beta-rule and splitting (40), into two cases.
% 3.51/1.58 |-Branch one:
% 3.51/1.58 | (41) ~ (all_0_4_4 = 0)
% 3.51/1.58 |
% 3.51/1.58 | Equations (25) can reduce 41 to:
% 3.51/1.58 | (38) $false
% 3.51/1.58 |
% 3.51/1.58 |-The branch is then unsatisfiable
% 3.51/1.58 |-Branch two:
% 3.51/1.58 | (25) all_0_4_4 = 0
% 3.51/1.58 | (44) (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))
% 3.51/1.58 |
% 3.51/1.58 +-Applying beta-rule and splitting (44), into two cases.
% 3.51/1.58 |-Branch one:
% 3.51/1.58 | (45) 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)))
% 3.51/1.58 |
% 3.51/1.58 | Applying alpha-rule on (45) yields:
% 3.51/1.58 | (46) xsd_string(all_0_2_2) = all_0_1_1
% 3.51/1.58 | (47) xsd_integer(all_0_2_2) = all_0_0_0
% 3.51/1.58 | (48) (all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0))
% 3.51/1.58 |
% 3.51/1.58 | Instantiating formula (2) with all_0_2_2 yields:
% 3.51/1.58 | (49) ~ (xsd_string(all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0)
% 3.51/1.58 |
% 3.51/1.58 | Instantiating formula (5) with all_0_1_1, all_0_2_2 and discharging atoms xsd_string(all_0_2_2) = all_0_1_1, yields:
% 3.51/1.58 | (50) all_0_1_1 = 0 | xsd_integer(all_0_2_2) = 0
% 3.51/1.58 |
% 3.51/1.58 +-Applying beta-rule and splitting (50), into two cases.
% 3.51/1.58 |-Branch one:
% 3.51/1.58 | (51) xsd_integer(all_0_2_2) = 0
% 3.51/1.58 |
% 3.51/1.58 | Instantiating formula (7) 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:
% 3.51/1.58 | (52) all_0_0_0 = 0
% 3.51/1.58 |
% 3.51/1.58 | From (52) and (47) follows:
% 3.51/1.58 | (51) xsd_integer(all_0_2_2) = 0
% 3.51/1.58 |
% 3.51/1.58 +-Applying beta-rule and splitting (49), into two cases.
% 3.51/1.58 |-Branch one:
% 3.51/1.58 | (54) ~ (xsd_string(all_0_2_2) = 0)
% 3.51/1.58 |
% 3.51/1.58 +-Applying beta-rule and splitting (48), into two cases.
% 3.51/1.58 |-Branch one:
% 3.51/1.58 | (55) all_0_0_0 = 0 & all_0_1_1 = 0
% 3.51/1.58 |
% 3.51/1.58 | Applying alpha-rule on (55) yields:
% 3.51/1.58 | (52) all_0_0_0 = 0
% 3.51/1.58 | (57) all_0_1_1 = 0
% 3.51/1.58 |
% 3.51/1.58 | From (57) and (46) follows:
% 3.51/1.58 | (58) xsd_string(all_0_2_2) = 0
% 3.51/1.58 |
% 3.51/1.58 | Using (58) and (54) yields:
% 3.51/1.58 | (29) $false
% 3.51/1.58 |
% 3.51/1.58 |-The branch is then unsatisfiable
% 3.51/1.58 |-Branch two:
% 3.51/1.58 | (60) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)
% 3.51/1.58 |
% 3.51/1.58 | Applying alpha-rule on (60) yields:
% 3.51/1.58 | (61) ~ (all_0_0_0 = 0)
% 3.51/1.58 | (62) ~ (all_0_1_1 = 0)
% 3.51/1.58 |
% 3.51/1.58 | Equations (52) can reduce 61 to:
% 3.51/1.58 | (38) $false
% 3.51/1.58 |
% 3.51/1.58 |-The branch is then unsatisfiable
% 3.51/1.58 |-Branch two:
% 3.51/1.58 | (58) xsd_string(all_0_2_2) = 0
% 3.51/1.58 | (65) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0)
% 3.51/1.58 |
% 3.51/1.58 | Instantiating (65) with all_67_0_5 yields:
% 3.51/1.58 | (66) ~ (all_67_0_5 = 0) & xsd_integer(all_0_2_2) = all_67_0_5
% 3.51/1.58 |
% 3.51/1.58 | Applying alpha-rule on (66) yields:
% 3.51/1.58 | (67) ~ (all_67_0_5 = 0)
% 3.51/1.58 | (68) xsd_integer(all_0_2_2) = all_67_0_5
% 3.51/1.59 |
% 3.51/1.59 | Instantiating formula (7) with all_0_2_2, all_67_0_5, 0 and discharging atoms xsd_integer(all_0_2_2) = all_67_0_5, xsd_integer(all_0_2_2) = 0, yields:
% 3.51/1.59 | (69) all_67_0_5 = 0
% 3.51/1.59 |
% 3.51/1.59 | Equations (69) can reduce 67 to:
% 3.51/1.59 | (38) $false
% 3.51/1.59 |
% 3.51/1.59 |-The branch is then unsatisfiable
% 3.51/1.59 |-Branch two:
% 3.51/1.59 | (71) ~ (xsd_integer(all_0_2_2) = 0)
% 3.51/1.59 | (57) all_0_1_1 = 0
% 3.51/1.59 |
% 3.51/1.59 +-Applying beta-rule and splitting (48), into two cases.
% 3.51/1.59 |-Branch one:
% 3.51/1.59 | (55) all_0_0_0 = 0 & all_0_1_1 = 0
% 3.51/1.59 |
% 3.51/1.59 | Applying alpha-rule on (55) yields:
% 3.51/1.59 | (52) all_0_0_0 = 0
% 3.51/1.59 | (57) all_0_1_1 = 0
% 3.51/1.59 |
% 3.51/1.59 | From (52) and (47) follows:
% 3.51/1.59 | (51) xsd_integer(all_0_2_2) = 0
% 3.51/1.59 |
% 3.51/1.59 | Using (51) and (71) yields:
% 3.51/1.59 | (29) $false
% 3.51/1.59 |
% 3.51/1.59 |-The branch is then unsatisfiable
% 3.51/1.59 |-Branch two:
% 3.51/1.59 | (60) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)
% 3.51/1.59 |
% 3.51/1.59 | Applying alpha-rule on (60) yields:
% 3.51/1.59 | (61) ~ (all_0_0_0 = 0)
% 3.51/1.59 | (62) ~ (all_0_1_1 = 0)
% 3.51/1.59 |
% 3.51/1.59 | Equations (57) can reduce 62 to:
% 3.51/1.59 | (38) $false
% 3.51/1.59 |
% 3.51/1.59 |-The branch is then unsatisfiable
% 3.51/1.59 |-Branch two:
% 3.51/1.59 | (82) 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)
% 3.51/1.59 |
% 3.51/1.59 | Applying alpha-rule on (82) yields:
% 3.51/1.59 | (83) cowlNothing(all_0_2_2) = all_0_0_0
% 3.51/1.59 | (84) cowlThing(all_0_2_2) = all_0_1_1
% 3.51/1.59 | (85) ~ (all_0_1_1 = 0) | all_0_0_0 = 0
% 3.51/1.59 |
% 3.51/1.59 | Instantiating formula (9) with all_0_2_2 yields:
% 3.51/1.59 | (86) ~ (cowlNothing(all_0_2_2) = 0)
% 3.51/1.59 |
% 3.51/1.59 | Instantiating formula (10) with all_0_1_1, all_0_2_2 and discharging atoms cowlThing(all_0_2_2) = all_0_1_1, yields:
% 3.51/1.59 | (57) all_0_1_1 = 0
% 3.51/1.59 |
% 3.51/1.59 +-Applying beta-rule and splitting (85), into two cases.
% 3.51/1.59 |-Branch one:
% 3.51/1.59 | (62) ~ (all_0_1_1 = 0)
% 3.51/1.59 |
% 3.51/1.59 | Equations (57) can reduce 62 to:
% 3.51/1.59 | (38) $false
% 3.51/1.59 |
% 3.51/1.59 |-The branch is then unsatisfiable
% 3.51/1.59 |-Branch two:
% 3.51/1.59 | (57) all_0_1_1 = 0
% 3.51/1.59 | (52) all_0_0_0 = 0
% 3.51/1.59 |
% 3.51/1.59 | From (52) and (83) follows:
% 3.51/1.59 | (92) cowlNothing(all_0_2_2) = 0
% 3.51/1.59 |
% 3.51/1.59 | Using (92) and (86) yields:
% 3.51/1.59 | (29) $false
% 3.51/1.59 |
% 3.51/1.59 |-The branch is then unsatisfiable
% 3.51/1.59 |-Branch two:
% 3.51/1.59 | (41) ~ (all_0_4_4 = 0)
% 3.51/1.59 | (95) ? [v0] : ( ~ (v0 = 0) & cAutomobile(iauto) = v0)
% 3.51/1.59 |
% 3.51/1.59 | Instantiating (95) with all_13_0_7 yields:
% 3.51/1.59 | (96) ~ (all_13_0_7 = 0) & cAutomobile(iauto) = all_13_0_7
% 3.51/1.59 |
% 3.51/1.59 | Applying alpha-rule on (96) yields:
% 3.51/1.59 | (97) ~ (all_13_0_7 = 0)
% 3.51/1.59 | (98) cAutomobile(iauto) = all_13_0_7
% 3.51/1.59 |
% 3.51/1.59 | Instantiating formula (14) with iauto, all_13_0_7, 0 and discharging atoms cAutomobile(iauto) = all_13_0_7, cAutomobile(iauto) = 0, yields:
% 3.51/1.59 | (99) all_13_0_7 = 0
% 3.51/1.59 |
% 3.51/1.59 | Equations (99) can reduce 97 to:
% 3.51/1.59 | (38) $false
% 3.51/1.59 |
% 3.51/1.59 |-The branch is then unsatisfiable
% 3.51/1.59 % SZS output end Proof for theBenchmark
% 3.51/1.59
% 3.51/1.59 988ms
%------------------------------------------------------------------------------