TSTP Solution File: KRS170+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KRS170+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 02:56:47 EDT 2022
% Result : Theorem 1.79s 1.04s
% Output : Proof 2.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : KRS170+1 : TPTP v8.1.0. Released v3.1.0.
% 0.05/0.09 % Command : ePrincess-casc -timeout=%d %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Tue Jun 7 15:00:05 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.13/0.45 ____ _
% 0.13/0.45 ___ / __ \_____(_)___ ________ __________
% 0.13/0.45 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.13/0.45 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.13/0.45 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.13/0.45
% 0.13/0.45 A Theorem Prover for First-Order Logic
% 0.13/0.45 (ePrincess v.1.0)
% 0.13/0.45
% 0.13/0.45 (c) Philipp Rümmer, 2009-2015
% 0.13/0.45 (c) Peter Backeman, 2014-2015
% 0.13/0.45 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.13/0.45 Free software under GNU Lesser General Public License (LGPL).
% 0.13/0.45 Bug reports to peter@backeman.se
% 0.13/0.45
% 0.13/0.45 For more information, visit http://user.uu.se/~petba168/breu/
% 0.13/0.45
% 0.13/0.46 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.13/0.50 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 0.90/0.71 Prover 0: Preprocessing ...
% 1.10/0.77 Prover 0: Warning: ignoring some quantifiers
% 1.10/0.79 Prover 0: Constructing countermodel ...
% 1.33/0.88 Prover 0: gave up
% 1.33/0.88 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.33/0.90 Prover 1: Preprocessing ...
% 1.63/0.98 Prover 1: Constructing countermodel ...
% 1.79/1.04 Prover 1: proved (156ms)
% 1.79/1.04
% 1.79/1.04 No countermodel exists, formula is valid
% 1.79/1.04 % SZS status Theorem for theBenchmark
% 1.79/1.04
% 1.79/1.04 Generating proof ... found it (size 57)
% 2.20/1.21
% 2.20/1.21 % SZS output start Proof for theBenchmark
% 2.20/1.21 Assumed formulas after preprocessing and simplification:
% 2.20/1.21 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (rhasLeader(v7, v6) = v5) | ~ (rhasLeader(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (rhasHead(v7, v6) = v5) | ~ (rhasHead(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (rhasLeader(v4, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & rhasHead(v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (xsd_string(v6) = v5) | ~ (xsd_string(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (xsd_integer(v6) = v5) | ~ (xsd_integer(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (cowlNothing(v6) = v5) | ~ (cowlNothing(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (cowlThing(v6) = v5) | ~ (cowlThing(v6) = v4)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (xsd_string(v4) = v5) | xsd_integer(v4) = 0) & ! [v4] : ! [v5] : (v5 = 0 | ~ (cowlThing(v4) = v5)) & ! [v4] : ! [v5] : ( ~ (rhasLeader(v4, v5) = 0) | rhasHead(v4, v5) = 0) & ! [v4] : ( ~ (xsd_string(v4) = 0) | ? [v5] : ( ~ (v5 = 0) & xsd_integer(v4) = v5)) & ! [v4] : ~ (cowlNothing(v4) = 0) & ((v2 = 0 & ~ (v3 = 0) & rhasLeader(v0, v1) = v3 & rhasHead(v0, v1) = 0) | (v2 = 0 & ~ (v3 = 0) & rhasLeader(v0, v1) = 0 & rhasHead(v0, v1) = v3) | (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))))
% 2.38/1.25 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 2.38/1.25 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rhasLeader(v3, v2) = v1) | ~ (rhasLeader(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rhasHead(v3, v2) = v1) | ~ (rhasHead(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rhasLeader(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & rhasHead(v0, v1) = v3)) & ! [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 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (rhasLeader(v0, v1) = 0) | rhasHead(v0, v1) = 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) & rhasLeader(all_0_3_3, all_0_2_2) = all_0_0_0 & rhasHead(all_0_3_3, all_0_2_2) = 0) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & rhasLeader(all_0_3_3, all_0_2_2) = 0 & rhasHead(all_0_3_3, all_0_2_2) = all_0_0_0) | (xsd_string(all_0_3_3) = all_0_2_2 & xsd_integer(all_0_3_3) = all_0_1_1 & ((all_0_1_1 = 0 & all_0_2_2 = 0) | ( ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0)))) | (cowlNothing(all_0_3_3) = all_0_1_1 & cowlThing(all_0_3_3) = all_0_2_2 & ( ~ (all_0_2_2 = 0) | all_0_1_1 = 0)))
% 2.47/1.25 |
% 2.47/1.25 | Applying alpha-rule on (1) yields:
% 2.47/1.25 | (2) ! [v0] : ! [v1] : ( ~ (rhasLeader(v0, v1) = 0) | rhasHead(v0, v1) = 0)
% 2.47/1.25 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rhasLeader(v3, v2) = v1) | ~ (rhasLeader(v3, v2) = v0))
% 2.47/1.25 | (4) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1))
% 2.47/1.25 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0)
% 2.47/1.25 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0))
% 2.47/1.25 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rhasLeader(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & rhasHead(v0, v1) = v3))
% 2.47/1.26 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rhasHead(v3, v2) = v1) | ~ (rhasHead(v3, v2) = v0))
% 2.47/1.26 | (9) (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & rhasLeader(all_0_3_3, all_0_2_2) = all_0_0_0 & rhasHead(all_0_3_3, all_0_2_2) = 0) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & rhasLeader(all_0_3_3, all_0_2_2) = 0 & rhasHead(all_0_3_3, all_0_2_2) = all_0_0_0) | (xsd_string(all_0_3_3) = all_0_2_2 & xsd_integer(all_0_3_3) = all_0_1_1 & ((all_0_1_1 = 0 & all_0_2_2 = 0) | ( ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0)))) | (cowlNothing(all_0_3_3) = all_0_1_1 & cowlThing(all_0_3_3) = all_0_2_2 & ( ~ (all_0_2_2 = 0) | all_0_1_1 = 0))
% 2.47/1.26 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0))
% 2.47/1.26 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0))
% 2.47/1.26 | (12) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 2.47/1.26 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0))
% 2.47/1.26 | (14) ! [v0] : ~ (cowlNothing(v0) = 0)
% 2.47/1.26 |
% 2.47/1.26 +-Applying beta-rule and splitting (9), into two cases.
% 2.47/1.26 |-Branch one:
% 2.47/1.26 | (15) (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & rhasLeader(all_0_3_3, all_0_2_2) = all_0_0_0 & rhasHead(all_0_3_3, all_0_2_2) = 0) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & rhasLeader(all_0_3_3, all_0_2_2) = 0 & rhasHead(all_0_3_3, all_0_2_2) = all_0_0_0) | (xsd_string(all_0_3_3) = all_0_2_2 & xsd_integer(all_0_3_3) = all_0_1_1 & ((all_0_1_1 = 0 & all_0_2_2 = 0) | ( ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0))))
% 2.47/1.26 |
% 2.47/1.26 +-Applying beta-rule and splitting (15), into two cases.
% 2.47/1.26 |-Branch one:
% 2.47/1.26 | (16) (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & rhasLeader(all_0_3_3, all_0_2_2) = all_0_0_0 & rhasHead(all_0_3_3, all_0_2_2) = 0) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & rhasLeader(all_0_3_3, all_0_2_2) = 0 & rhasHead(all_0_3_3, all_0_2_2) = all_0_0_0)
% 2.47/1.26 |
% 2.47/1.26 +-Applying beta-rule and splitting (16), into two cases.
% 2.47/1.26 |-Branch one:
% 2.47/1.26 | (17) all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & rhasLeader(all_0_3_3, all_0_2_2) = all_0_0_0 & rhasHead(all_0_3_3, all_0_2_2) = 0
% 2.47/1.26 |
% 2.47/1.26 | Applying alpha-rule on (17) yields:
% 2.47/1.26 | (18) all_0_1_1 = 0
% 2.47/1.26 | (19) ~ (all_0_0_0 = 0)
% 2.47/1.26 | (20) rhasLeader(all_0_3_3, all_0_2_2) = all_0_0_0
% 2.47/1.26 | (21) rhasHead(all_0_3_3, all_0_2_2) = 0
% 2.47/1.26 |
% 2.47/1.26 | Instantiating formula (7) with all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms rhasLeader(all_0_3_3, all_0_2_2) = all_0_0_0, yields:
% 2.47/1.26 | (22) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & rhasHead(all_0_3_3, all_0_2_2) = v0)
% 2.47/1.26 |
% 2.47/1.26 +-Applying beta-rule and splitting (22), into two cases.
% 2.47/1.26 |-Branch one:
% 2.47/1.26 | (23) all_0_0_0 = 0
% 2.47/1.26 |
% 2.47/1.26 | Equations (23) can reduce 19 to:
% 2.47/1.26 | (24) $false
% 2.47/1.26 |
% 2.47/1.26 |-The branch is then unsatisfiable
% 2.47/1.26 |-Branch two:
% 2.47/1.26 | (19) ~ (all_0_0_0 = 0)
% 2.47/1.26 | (26) ? [v0] : ( ~ (v0 = 0) & rhasHead(all_0_3_3, all_0_2_2) = v0)
% 2.47/1.26 |
% 2.47/1.26 | Instantiating (26) with all_13_0_4 yields:
% 2.47/1.26 | (27) ~ (all_13_0_4 = 0) & rhasHead(all_0_3_3, all_0_2_2) = all_13_0_4
% 2.47/1.26 |
% 2.47/1.26 | Applying alpha-rule on (27) yields:
% 2.47/1.26 | (28) ~ (all_13_0_4 = 0)
% 2.47/1.26 | (29) rhasHead(all_0_3_3, all_0_2_2) = all_13_0_4
% 2.47/1.26 |
% 2.47/1.26 | Instantiating formula (8) with all_0_3_3, all_0_2_2, all_13_0_4, 0 and discharging atoms rhasHead(all_0_3_3, all_0_2_2) = all_13_0_4, rhasHead(all_0_3_3, all_0_2_2) = 0, yields:
% 2.47/1.27 | (30) all_13_0_4 = 0
% 2.47/1.27 |
% 2.47/1.27 | Equations (30) can reduce 28 to:
% 2.47/1.27 | (24) $false
% 2.47/1.27 |
% 2.47/1.27 |-The branch is then unsatisfiable
% 2.47/1.27 |-Branch two:
% 2.47/1.27 | (32) all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & rhasLeader(all_0_3_3, all_0_2_2) = 0 & rhasHead(all_0_3_3, all_0_2_2) = all_0_0_0
% 2.47/1.27 |
% 2.47/1.27 | Applying alpha-rule on (32) yields:
% 2.47/1.27 | (18) all_0_1_1 = 0
% 2.47/1.27 | (19) ~ (all_0_0_0 = 0)
% 2.47/1.27 | (35) rhasLeader(all_0_3_3, all_0_2_2) = 0
% 2.47/1.27 | (36) rhasHead(all_0_3_3, all_0_2_2) = all_0_0_0
% 2.47/1.27 |
% 2.47/1.27 | Instantiating formula (2) with all_0_2_2, all_0_3_3 and discharging atoms rhasLeader(all_0_3_3, all_0_2_2) = 0, yields:
% 2.47/1.27 | (21) rhasHead(all_0_3_3, all_0_2_2) = 0
% 2.47/1.27 |
% 2.47/1.27 | Instantiating formula (8) with all_0_3_3, all_0_2_2, 0, all_0_0_0 and discharging atoms rhasHead(all_0_3_3, all_0_2_2) = all_0_0_0, rhasHead(all_0_3_3, all_0_2_2) = 0, yields:
% 2.47/1.27 | (23) all_0_0_0 = 0
% 2.47/1.27 |
% 2.47/1.27 | Equations (23) can reduce 19 to:
% 2.47/1.27 | (24) $false
% 2.47/1.27 |
% 2.47/1.27 |-The branch is then unsatisfiable
% 2.47/1.27 |-Branch two:
% 2.47/1.27 | (40) xsd_string(all_0_3_3) = all_0_2_2 & xsd_integer(all_0_3_3) = all_0_1_1 & ((all_0_1_1 = 0 & all_0_2_2 = 0) | ( ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0)))
% 2.47/1.27 |
% 2.47/1.27 | Applying alpha-rule on (40) yields:
% 2.47/1.27 | (41) xsd_string(all_0_3_3) = all_0_2_2
% 2.47/1.27 | (42) xsd_integer(all_0_3_3) = all_0_1_1
% 2.47/1.27 | (43) (all_0_1_1 = 0 & all_0_2_2 = 0) | ( ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0))
% 2.47/1.27 |
% 2.47/1.27 | Instantiating formula (12) with all_0_3_3 yields:
% 2.47/1.27 | (44) ~ (xsd_string(all_0_3_3) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_3_3) = v0)
% 2.47/1.27 |
% 2.47/1.27 | Instantiating formula (5) with all_0_2_2, all_0_3_3 and discharging atoms xsd_string(all_0_3_3) = all_0_2_2, yields:
% 2.47/1.27 | (45) all_0_2_2 = 0 | xsd_integer(all_0_3_3) = 0
% 2.47/1.27 |
% 2.47/1.27 +-Applying beta-rule and splitting (45), into two cases.
% 2.47/1.27 |-Branch one:
% 2.47/1.27 | (46) xsd_integer(all_0_3_3) = 0
% 2.47/1.27 |
% 2.47/1.27 | Instantiating formula (11) with all_0_3_3, 0, all_0_1_1 and discharging atoms xsd_integer(all_0_3_3) = all_0_1_1, xsd_integer(all_0_3_3) = 0, yields:
% 2.47/1.27 | (18) all_0_1_1 = 0
% 2.47/1.27 |
% 2.47/1.27 | From (18) and (42) follows:
% 2.47/1.27 | (46) xsd_integer(all_0_3_3) = 0
% 2.47/1.27 |
% 2.47/1.27 +-Applying beta-rule and splitting (44), into two cases.
% 2.47/1.27 |-Branch one:
% 2.47/1.27 | (49) ~ (xsd_string(all_0_3_3) = 0)
% 2.47/1.27 |
% 2.47/1.27 +-Applying beta-rule and splitting (43), into two cases.
% 2.47/1.27 |-Branch one:
% 2.47/1.27 | (50) all_0_1_1 = 0 & all_0_2_2 = 0
% 2.47/1.27 |
% 2.47/1.27 | Applying alpha-rule on (50) yields:
% 2.47/1.27 | (18) all_0_1_1 = 0
% 2.47/1.27 | (52) all_0_2_2 = 0
% 2.47/1.27 |
% 2.47/1.27 | From (52) and (41) follows:
% 2.47/1.27 | (53) xsd_string(all_0_3_3) = 0
% 2.47/1.27 |
% 2.47/1.27 | Using (53) and (49) yields:
% 2.47/1.27 | (54) $false
% 2.47/1.27 |
% 2.47/1.27 |-The branch is then unsatisfiable
% 2.47/1.27 |-Branch two:
% 2.47/1.27 | (55) ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0)
% 2.47/1.27 |
% 2.47/1.27 | Applying alpha-rule on (55) yields:
% 2.47/1.27 | (56) ~ (all_0_1_1 = 0)
% 2.47/1.27 | (57) ~ (all_0_2_2 = 0)
% 2.47/1.27 |
% 2.47/1.27 | Equations (18) can reduce 56 to:
% 2.47/1.27 | (24) $false
% 2.47/1.27 |
% 2.47/1.27 |-The branch is then unsatisfiable
% 2.47/1.27 |-Branch two:
% 2.47/1.27 | (53) xsd_string(all_0_3_3) = 0
% 2.47/1.27 | (60) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_3_3) = v0)
% 2.47/1.27 |
% 2.47/1.27 | Instantiating (60) with all_21_0_5 yields:
% 2.47/1.27 | (61) ~ (all_21_0_5 = 0) & xsd_integer(all_0_3_3) = all_21_0_5
% 2.47/1.27 |
% 2.47/1.27 | Applying alpha-rule on (61) yields:
% 2.47/1.27 | (62) ~ (all_21_0_5 = 0)
% 2.47/1.27 | (63) xsd_integer(all_0_3_3) = all_21_0_5
% 2.47/1.27 |
% 2.47/1.27 | Instantiating formula (11) with all_0_3_3, all_21_0_5, 0 and discharging atoms xsd_integer(all_0_3_3) = all_21_0_5, xsd_integer(all_0_3_3) = 0, yields:
% 2.47/1.27 | (64) all_21_0_5 = 0
% 2.47/1.28 |
% 2.47/1.28 | Equations (64) can reduce 62 to:
% 2.47/1.28 | (24) $false
% 2.47/1.28 |
% 2.47/1.28 |-The branch is then unsatisfiable
% 2.47/1.28 |-Branch two:
% 2.47/1.28 | (66) ~ (xsd_integer(all_0_3_3) = 0)
% 2.47/1.28 | (52) all_0_2_2 = 0
% 2.47/1.28 |
% 2.47/1.28 +-Applying beta-rule and splitting (43), into two cases.
% 2.47/1.28 |-Branch one:
% 2.47/1.28 | (50) all_0_1_1 = 0 & all_0_2_2 = 0
% 2.47/1.28 |
% 2.47/1.28 | Applying alpha-rule on (50) yields:
% 2.47/1.28 | (18) all_0_1_1 = 0
% 2.47/1.28 | (52) all_0_2_2 = 0
% 2.47/1.28 |
% 2.47/1.28 | From (18) and (42) follows:
% 2.47/1.28 | (46) xsd_integer(all_0_3_3) = 0
% 2.47/1.28 |
% 2.47/1.28 | Using (46) and (66) yields:
% 2.47/1.28 | (54) $false
% 2.47/1.28 |
% 2.47/1.28 |-The branch is then unsatisfiable
% 2.47/1.28 |-Branch two:
% 2.47/1.28 | (55) ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0)
% 2.47/1.28 |
% 2.47/1.28 | Applying alpha-rule on (55) yields:
% 2.47/1.28 | (56) ~ (all_0_1_1 = 0)
% 2.47/1.28 | (57) ~ (all_0_2_2 = 0)
% 2.47/1.28 |
% 2.47/1.28 | Equations (52) can reduce 57 to:
% 2.47/1.28 | (24) $false
% 2.47/1.28 |
% 2.47/1.28 |-The branch is then unsatisfiable
% 2.47/1.28 |-Branch two:
% 2.47/1.28 | (77) cowlNothing(all_0_3_3) = all_0_1_1 & cowlThing(all_0_3_3) = all_0_2_2 & ( ~ (all_0_2_2 = 0) | all_0_1_1 = 0)
% 2.47/1.28 |
% 2.47/1.28 | Applying alpha-rule on (77) yields:
% 2.47/1.28 | (78) cowlNothing(all_0_3_3) = all_0_1_1
% 2.47/1.28 | (79) cowlThing(all_0_3_3) = all_0_2_2
% 2.47/1.28 | (80) ~ (all_0_2_2 = 0) | all_0_1_1 = 0
% 2.47/1.28 |
% 2.47/1.28 | Instantiating formula (14) with all_0_3_3 yields:
% 2.47/1.28 | (81) ~ (cowlNothing(all_0_3_3) = 0)
% 2.47/1.28 |
% 2.47/1.28 | Instantiating formula (4) with all_0_2_2, all_0_3_3 and discharging atoms cowlThing(all_0_3_3) = all_0_2_2, yields:
% 2.47/1.28 | (52) all_0_2_2 = 0
% 2.47/1.28 |
% 2.47/1.28 +-Applying beta-rule and splitting (80), into two cases.
% 2.47/1.28 |-Branch one:
% 2.47/1.28 | (57) ~ (all_0_2_2 = 0)
% 2.47/1.28 |
% 2.47/1.28 | Equations (52) can reduce 57 to:
% 2.47/1.28 | (24) $false
% 2.47/1.28 |
% 2.47/1.28 |-The branch is then unsatisfiable
% 2.47/1.28 |-Branch two:
% 2.47/1.28 | (52) all_0_2_2 = 0
% 2.47/1.28 | (18) all_0_1_1 = 0
% 2.47/1.28 |
% 2.47/1.28 | From (18) and (78) follows:
% 2.47/1.28 | (87) cowlNothing(all_0_3_3) = 0
% 2.47/1.28 |
% 2.47/1.28 | Using (87) and (81) yields:
% 2.47/1.28 | (54) $false
% 2.47/1.28 |
% 2.47/1.28 |-The branch is then unsatisfiable
% 2.47/1.28 % SZS output end Proof for theBenchmark
% 2.47/1.28
% 2.47/1.28 817ms
%------------------------------------------------------------------------------