TSTP Solution File: KRS174+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KRS174+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 02:56:47 EDT 2022
% Result : Theorem 2.76s 1.35s
% Output : Proof 4.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KRS174+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.32 % Computer : n021.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Tue Jun 7 12:31:36 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.54/0.57 ____ _
% 0.54/0.57 ___ / __ \_____(_)___ ________ __________
% 0.54/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.57
% 0.54/0.57 A Theorem Prover for First-Order Logic
% 0.54/0.57 (ePrincess v.1.0)
% 0.54/0.57
% 0.54/0.57 (c) Philipp Rümmer, 2009-2015
% 0.54/0.57 (c) Peter Backeman, 2014-2015
% 0.54/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.57 Bug reports to peter@backeman.se
% 0.54/0.57
% 0.54/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.57
% 0.54/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.60/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.43/0.90 Prover 0: Preprocessing ...
% 1.65/1.02 Prover 0: Warning: ignoring some quantifiers
% 1.81/1.03 Prover 0: Constructing countermodel ...
% 1.92/1.13 Prover 0: gave up
% 1.92/1.13 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.92/1.15 Prover 1: Preprocessing ...
% 2.54/1.25 Prover 1: Constructing countermodel ...
% 2.76/1.35 Prover 1: proved (225ms)
% 2.76/1.35
% 2.76/1.35 No countermodel exists, formula is valid
% 2.76/1.35 % SZS status Theorem for theBenchmark
% 2.76/1.35
% 2.76/1.35 Generating proof ... found it (size 108)
% 4.04/1.62
% 4.04/1.62 % SZS output start Proof for theBenchmark
% 4.04/1.62 Assumed formulas after preprocessing and simplification:
% 4.04/1.62 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (cowlThing(ib) = 0 & cowlThing(ia) = 0 & ! [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 | ~ (cowlThing(v6) = v5) | ~ (cowlThing(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (cowlNothing(v6) = v5) | ~ (cowlNothing(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (cB(v6) = v5) | ~ (cB(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (cA_and_B(v6) = v5) | ~ (cA_and_B(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (cA(v6) = v5) | ~ (cA(v6) = v4)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (xsd_string(v4) = v5) | ~ (xsd_string(v4) = 0)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (xsd_string(v4) = v5) | xsd_integer(v4) = 0) & ! [v4] : ! [v5] : (v5 = 0 | ~ (xsd_integer(v4) = v5) | ~ (xsd_integer(v4) = 0)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (cowlThing(v4) = v5) | ~ (cowlThing(v4) = 0)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (cowlThing(v4) = v5)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (cowlNothing(v4) = v5) | ~ (cowlNothing(v4) = 0)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (cB(v4) = v5) | ~ (cB(v4) = 0)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (cA_and_B(v4) = v5) | ~ (cA_and_B(v4) = 0)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (cA(v4) = v5) | ~ (cA(v4) = 0)) & ! [v4] : (v4 = ib | v4 = ia | ~ (cA_and_B(v4) = 0)) & ! [v4] : (v4 = ib | ~ (cB(v4) = 0)) & ! [v4] : (v4 = ia | ~ (cA(v4) = 0)) & ! [v4] : (v4 = 0 | ~ (cB(ib) = v4)) & ! [v4] : (v4 = 0 | ~ (cA_and_B(ib) = v4)) & ! [v4] : (v4 = 0 | ~ (cA_and_B(ia) = v4)) & ! [v4] : (v4 = 0 | ~ (cA(ia) = v4)) & ! [v4] : ( ~ (xsd_string(v4) = 0) | ? [v5] : ( ~ (v5 = 0) & xsd_integer(v4) = v5)) & ! [v4] : ~ (cowlNothing(v4) = 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)) | (cB(v0) = v2 & cA_and_B(v0) = v1 & cA(v0) = v3 & ((v1 = 0 & ~ (v3 = 0) & ~ (v2 = 0)) | ( ~ (v1 = 0) & (v3 = 0 | v2 = 0))))))
% 4.04/1.66 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 4.04/1.66 | (1) cowlThing(ib) = 0 & cowlThing(ia) = 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] : ! [v2] : (v1 = v0 | ~ (cB(v2) = v1) | ~ (cB(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cA_and_B(v2) = v1) | ~ (cA_and_B(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cA(v2) = v1) | ~ (cA(v2) = v0)) & ! [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] : (v1 = 0 | ~ (cB(v0) = v1) | ~ (cB(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cA_and_B(v0) = v1) | ~ (cA_and_B(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cA(v0) = v1) | ~ (cA(v0) = 0)) & ! [v0] : (v0 = ib | v0 = ia | ~ (cA_and_B(v0) = 0)) & ! [v0] : (v0 = ib | ~ (cB(v0) = 0)) & ! [v0] : (v0 = ia | ~ (cA(v0) = 0)) & ! [v0] : (v0 = 0 | ~ (cB(ib) = v0)) & ! [v0] : (v0 = 0 | ~ (cA_and_B(ib) = v0)) & ! [v0] : (v0 = 0 | ~ (cA_and_B(ia) = v0)) & ! [v0] : (v0 = 0 | ~ (cA(ia) = v0)) & ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) & ! [v0] : ~ (cowlNothing(v0) = 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)))) | (cowlThing(all_0_3_3) = all_0_2_2 & cowlNothing(all_0_3_3) = all_0_1_1 & ( ~ (all_0_2_2 = 0) | all_0_1_1 = 0)) | (cB(all_0_3_3) = all_0_1_1 & cA_and_B(all_0_3_3) = all_0_2_2 & cA(all_0_3_3) = all_0_0_0 & ((all_0_2_2 = 0 & ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)) | ( ~ (all_0_2_2 = 0) & (all_0_0_0 = 0 | all_0_1_1 = 0)))))
% 4.04/1.67 |
% 4.04/1.67 | Applying alpha-rule on (1) yields:
% 4.04/1.67 | (2) ! [v0] : ! [v1] : (v1 = 0 | ~ (cB(v0) = v1) | ~ (cB(v0) = 0))
% 4.04/1.67 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cA_and_B(v2) = v1) | ~ (cA_and_B(v2) = v0))
% 4.04/1.67 | (4) ! [v0] : (v0 = ib | v0 = ia | ~ (cA_and_B(v0) = 0))
% 4.04/1.67 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ (xsd_string(v0) = 0))
% 4.04/1.67 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cA(v2) = v1) | ~ (cA(v2) = v0))
% 4.04/1.67 | (7) ! [v0] : ! [v1] : (v1 = 0 | ~ (cA(v0) = v1) | ~ (cA(v0) = 0))
% 4.04/1.67 | (8) ! [v0] : ~ (cowlNothing(v0) = 0)
% 4.04/1.67 | (9) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0)
% 4.04/1.67 | (10) ! [v0] : (v0 = 0 | ~ (cA_and_B(ia) = v0))
% 4.04/1.67 | (11) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ (cowlThing(v0) = 0))
% 4.04/1.67 | (12) ! [v0] : (v0 = ia | ~ (cA(v0) = 0))
% 4.04/1.67 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cB(v2) = v1) | ~ (cB(v2) = v0))
% 4.04/1.67 | (14) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1))
% 4.04/1.67 | (15) ! [v0] : ! [v1] : (v1 = 0 | ~ (cA_and_B(v0) = v1) | ~ (cA_and_B(v0) = 0))
% 4.04/1.67 | (16) (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)))) | (cowlThing(all_0_3_3) = all_0_2_2 & cowlNothing(all_0_3_3) = all_0_1_1 & ( ~ (all_0_2_2 = 0) | all_0_1_1 = 0)) | (cB(all_0_3_3) = all_0_1_1 & cA_and_B(all_0_3_3) = all_0_2_2 & cA(all_0_3_3) = all_0_0_0 & ((all_0_2_2 = 0 & ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)) | ( ~ (all_0_2_2 = 0) & (all_0_0_0 = 0 | all_0_1_1 = 0))))
% 4.04/1.67 | (17) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ (xsd_integer(v0) = 0))
% 4.04/1.67 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0))
% 4.04/1.67 | (19) ! [v0] : (v0 = 0 | ~ (cA_and_B(ib) = v0))
% 4.04/1.67 | (20) ! [v0] : (v0 = 0 | ~ (cB(ib) = v0))
% 4.04/1.67 | (21) cowlThing(ia) = 0
% 4.04/1.67 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0))
% 4.04/1.67 | (23) ! [v0] : (v0 = ib | ~ (cB(v0) = 0))
% 4.04/1.67 | (24) cowlThing(ib) = 0
% 4.04/1.67 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0))
% 4.04/1.68 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0))
% 4.04/1.68 | (27) ! [v0] : (v0 = 0 | ~ (cA(ia) = v0))
% 4.04/1.68 | (28) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlNothing(v0) = v1) | ~ (cowlNothing(v0) = 0))
% 4.04/1.68 | (29) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 4.04/1.68 |
% 4.04/1.68 +-Applying beta-rule and splitting (16), into two cases.
% 4.04/1.68 |-Branch one:
% 4.04/1.68 | (30) (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)))) | (cowlThing(all_0_3_3) = all_0_2_2 & cowlNothing(all_0_3_3) = all_0_1_1 & ( ~ (all_0_2_2 = 0) | all_0_1_1 = 0))
% 4.04/1.68 |
% 4.04/1.68 +-Applying beta-rule and splitting (30), into two cases.
% 4.04/1.68 |-Branch one:
% 4.04/1.68 | (31) 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)))
% 4.04/1.68 |
% 4.04/1.68 | Applying alpha-rule on (31) yields:
% 4.04/1.68 | (32) xsd_string(all_0_3_3) = all_0_2_2
% 4.04/1.68 | (33) xsd_integer(all_0_3_3) = all_0_1_1
% 4.04/1.68 | (34) (all_0_1_1 = 0 & all_0_2_2 = 0) | ( ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0))
% 4.04/1.68 |
% 4.04/1.68 | Instantiating formula (29) with all_0_3_3 yields:
% 4.04/1.68 | (35) ~ (xsd_string(all_0_3_3) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_3_3) = v0)
% 4.04/1.68 |
% 4.04/1.68 | Instantiating formula (9) with all_0_2_2, all_0_3_3 and discharging atoms xsd_string(all_0_3_3) = all_0_2_2, yields:
% 4.04/1.68 | (36) all_0_2_2 = 0 | xsd_integer(all_0_3_3) = 0
% 4.25/1.68 |
% 4.25/1.68 +-Applying beta-rule and splitting (36), into two cases.
% 4.25/1.68 |-Branch one:
% 4.25/1.68 | (37) xsd_integer(all_0_3_3) = 0
% 4.25/1.68 |
% 4.25/1.68 | Instantiating formula (22) 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:
% 4.25/1.68 | (38) all_0_1_1 = 0
% 4.25/1.68 |
% 4.25/1.68 | From (38) and (33) follows:
% 4.25/1.68 | (37) xsd_integer(all_0_3_3) = 0
% 4.25/1.68 |
% 4.25/1.68 +-Applying beta-rule and splitting (35), into two cases.
% 4.25/1.68 |-Branch one:
% 4.25/1.68 | (40) ~ (xsd_string(all_0_3_3) = 0)
% 4.25/1.68 |
% 4.25/1.68 +-Applying beta-rule and splitting (34), into two cases.
% 4.25/1.68 |-Branch one:
% 4.25/1.68 | (41) all_0_1_1 = 0 & all_0_2_2 = 0
% 4.25/1.68 |
% 4.25/1.68 | Applying alpha-rule on (41) yields:
% 4.25/1.68 | (38) all_0_1_1 = 0
% 4.25/1.68 | (43) all_0_2_2 = 0
% 4.25/1.68 |
% 4.25/1.68 | From (43) and (32) follows:
% 4.25/1.68 | (44) xsd_string(all_0_3_3) = 0
% 4.25/1.68 |
% 4.25/1.68 | Using (44) and (40) yields:
% 4.25/1.68 | (45) $false
% 4.25/1.68 |
% 4.25/1.68 |-The branch is then unsatisfiable
% 4.25/1.68 |-Branch two:
% 4.25/1.68 | (46) ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0)
% 4.25/1.68 |
% 4.25/1.68 | Applying alpha-rule on (46) yields:
% 4.25/1.68 | (47) ~ (all_0_1_1 = 0)
% 4.25/1.68 | (48) ~ (all_0_2_2 = 0)
% 4.25/1.68 |
% 4.25/1.68 | Equations (38) can reduce 47 to:
% 4.25/1.68 | (49) $false
% 4.25/1.68 |
% 4.25/1.68 |-The branch is then unsatisfiable
% 4.25/1.68 |-Branch two:
% 4.25/1.68 | (44) xsd_string(all_0_3_3) = 0
% 4.25/1.68 | (51) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_3_3) = v0)
% 4.25/1.68 |
% 4.25/1.68 | Instantiating (51) with all_25_0_4 yields:
% 4.25/1.68 | (52) ~ (all_25_0_4 = 0) & xsd_integer(all_0_3_3) = all_25_0_4
% 4.25/1.68 |
% 4.25/1.68 | Applying alpha-rule on (52) yields:
% 4.25/1.68 | (53) ~ (all_25_0_4 = 0)
% 4.25/1.68 | (54) xsd_integer(all_0_3_3) = all_25_0_4
% 4.25/1.69 |
% 4.25/1.69 | Instantiating formula (17) with all_25_0_4, all_0_3_3 and discharging atoms xsd_integer(all_0_3_3) = all_25_0_4, xsd_integer(all_0_3_3) = 0, yields:
% 4.25/1.69 | (55) all_25_0_4 = 0
% 4.25/1.69 |
% 4.25/1.69 | Equations (55) can reduce 53 to:
% 4.25/1.69 | (49) $false
% 4.25/1.69 |
% 4.25/1.69 |-The branch is then unsatisfiable
% 4.25/1.69 |-Branch two:
% 4.25/1.69 | (57) ~ (xsd_integer(all_0_3_3) = 0)
% 4.25/1.69 | (43) all_0_2_2 = 0
% 4.25/1.69 |
% 4.25/1.69 +-Applying beta-rule and splitting (34), into two cases.
% 4.25/1.69 |-Branch one:
% 4.25/1.69 | (41) all_0_1_1 = 0 & all_0_2_2 = 0
% 4.25/1.69 |
% 4.25/1.69 | Applying alpha-rule on (41) yields:
% 4.25/1.69 | (38) all_0_1_1 = 0
% 4.25/1.69 | (43) all_0_2_2 = 0
% 4.25/1.69 |
% 4.25/1.69 | From (38) and (33) follows:
% 4.25/1.69 | (37) xsd_integer(all_0_3_3) = 0
% 4.25/1.69 |
% 4.25/1.69 | Using (37) and (57) yields:
% 4.25/1.69 | (45) $false
% 4.25/1.69 |
% 4.25/1.69 |-The branch is then unsatisfiable
% 4.25/1.69 |-Branch two:
% 4.25/1.69 | (46) ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0)
% 4.25/1.69 |
% 4.25/1.69 | Applying alpha-rule on (46) yields:
% 4.25/1.69 | (47) ~ (all_0_1_1 = 0)
% 4.25/1.69 | (48) ~ (all_0_2_2 = 0)
% 4.25/1.69 |
% 4.25/1.69 | Equations (43) can reduce 48 to:
% 4.25/1.69 | (49) $false
% 4.25/1.69 |
% 4.25/1.69 |-The branch is then unsatisfiable
% 4.25/1.69 |-Branch two:
% 4.25/1.69 | (68) cowlThing(all_0_3_3) = all_0_2_2 & cowlNothing(all_0_3_3) = all_0_1_1 & ( ~ (all_0_2_2 = 0) | all_0_1_1 = 0)
% 4.25/1.69 |
% 4.25/1.69 | Applying alpha-rule on (68) yields:
% 4.25/1.69 | (69) cowlThing(all_0_3_3) = all_0_2_2
% 4.25/1.69 | (70) cowlNothing(all_0_3_3) = all_0_1_1
% 4.25/1.69 | (71) ~ (all_0_2_2 = 0) | all_0_1_1 = 0
% 4.25/1.69 |
% 4.25/1.69 | Instantiating formula (14) with all_0_2_2, all_0_3_3 and discharging atoms cowlThing(all_0_3_3) = all_0_2_2, yields:
% 4.25/1.69 | (43) all_0_2_2 = 0
% 4.25/1.69 |
% 4.25/1.69 | Instantiating formula (8) with all_0_3_3 yields:
% 4.25/1.69 | (73) ~ (cowlNothing(all_0_3_3) = 0)
% 4.25/1.69 |
% 4.25/1.69 +-Applying beta-rule and splitting (71), into two cases.
% 4.25/1.69 |-Branch one:
% 4.25/1.69 | (48) ~ (all_0_2_2 = 0)
% 4.25/1.69 |
% 4.25/1.69 | Equations (43) can reduce 48 to:
% 4.25/1.69 | (49) $false
% 4.25/1.69 |
% 4.25/1.69 |-The branch is then unsatisfiable
% 4.25/1.69 |-Branch two:
% 4.25/1.69 | (43) all_0_2_2 = 0
% 4.25/1.69 | (38) all_0_1_1 = 0
% 4.25/1.69 |
% 4.25/1.69 | From (38) and (70) follows:
% 4.25/1.69 | (78) cowlNothing(all_0_3_3) = 0
% 4.25/1.69 |
% 4.25/1.69 | Using (78) and (73) yields:
% 4.25/1.69 | (45) $false
% 4.25/1.69 |
% 4.25/1.69 |-The branch is then unsatisfiable
% 4.25/1.69 |-Branch two:
% 4.25/1.69 | (80) cB(all_0_3_3) = all_0_1_1 & cA_and_B(all_0_3_3) = all_0_2_2 & cA(all_0_3_3) = all_0_0_0 & ((all_0_2_2 = 0 & ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)) | ( ~ (all_0_2_2 = 0) & (all_0_0_0 = 0 | all_0_1_1 = 0)))
% 4.25/1.69 |
% 4.25/1.69 | Applying alpha-rule on (80) yields:
% 4.25/1.69 | (81) cB(all_0_3_3) = all_0_1_1
% 4.25/1.69 | (82) cA_and_B(all_0_3_3) = all_0_2_2
% 4.25/1.69 | (83) cA(all_0_3_3) = all_0_0_0
% 4.25/1.69 | (84) (all_0_2_2 = 0 & ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)) | ( ~ (all_0_2_2 = 0) & (all_0_0_0 = 0 | all_0_1_1 = 0))
% 4.25/1.69 |
% 4.25/1.69 | Instantiating formula (23) with all_0_3_3 yields:
% 4.25/1.69 | (85) all_0_3_3 = ib | ~ (cB(all_0_3_3) = 0)
% 4.25/1.69 |
% 4.25/1.69 | Instantiating formula (20) with all_0_1_1 yields:
% 4.25/1.69 | (86) all_0_1_1 = 0 | ~ (cB(ib) = all_0_1_1)
% 4.25/1.69 |
% 4.25/1.69 | Instantiating formula (4) with all_0_3_3 yields:
% 4.25/1.69 | (87) all_0_3_3 = ib | all_0_3_3 = ia | ~ (cA_and_B(all_0_3_3) = 0)
% 4.25/1.69 |
% 4.25/1.69 | Instantiating formula (19) with all_0_2_2 yields:
% 4.25/1.69 | (88) all_0_2_2 = 0 | ~ (cA_and_B(ib) = all_0_2_2)
% 4.25/1.69 |
% 4.25/1.69 | Instantiating formula (10) with all_0_2_2 yields:
% 4.25/1.69 | (89) all_0_2_2 = 0 | ~ (cA_and_B(ia) = all_0_2_2)
% 4.25/1.69 |
% 4.25/1.69 | Instantiating formula (12) with all_0_3_3 yields:
% 4.25/1.69 | (90) all_0_3_3 = ia | ~ (cA(all_0_3_3) = 0)
% 4.25/1.69 |
% 4.25/1.69 | Instantiating formula (27) with all_0_0_0 yields:
% 4.25/1.69 | (91) all_0_0_0 = 0 | ~ (cA(ia) = all_0_0_0)
% 4.25/1.69 |
% 4.25/1.69 +-Applying beta-rule and splitting (90), into two cases.
% 4.25/1.69 |-Branch one:
% 4.25/1.69 | (92) ~ (cA(all_0_3_3) = 0)
% 4.25/1.69 |
% 4.25/1.69 | Using (83) and (92) yields:
% 4.25/1.69 | (93) ~ (all_0_0_0 = 0)
% 4.25/1.69 |
% 4.25/1.69 +-Applying beta-rule and splitting (91), into two cases.
% 4.25/1.69 |-Branch one:
% 4.25/1.69 | (94) ~ (cA(ia) = all_0_0_0)
% 4.25/1.70 |
% 4.25/1.70 | Using (83) and (94) yields:
% 4.25/1.70 | (95) ~ (all_0_3_3 = ia)
% 4.25/1.70 |
% 4.25/1.70 +-Applying beta-rule and splitting (86), into two cases.
% 4.25/1.70 |-Branch one:
% 4.25/1.70 | (96) ~ (cB(ib) = all_0_1_1)
% 4.25/1.70 |
% 4.25/1.70 | Using (81) and (96) yields:
% 4.25/1.70 | (97) ~ (all_0_3_3 = ib)
% 4.25/1.70 |
% 4.25/1.70 +-Applying beta-rule and splitting (87), into two cases.
% 4.25/1.70 |-Branch one:
% 4.25/1.70 | (98) ~ (cA_and_B(all_0_3_3) = 0)
% 4.25/1.70 |
% 4.25/1.70 +-Applying beta-rule and splitting (85), into two cases.
% 4.25/1.70 |-Branch one:
% 4.25/1.70 | (99) ~ (cB(all_0_3_3) = 0)
% 4.25/1.70 |
% 4.25/1.70 | Using (81) and (99) yields:
% 4.25/1.70 | (47) ~ (all_0_1_1 = 0)
% 4.25/1.70 |
% 4.25/1.70 | Using (82) and (98) yields:
% 4.25/1.70 | (48) ~ (all_0_2_2 = 0)
% 4.25/1.70 |
% 4.25/1.70 +-Applying beta-rule and splitting (84), into two cases.
% 4.25/1.70 |-Branch one:
% 4.25/1.70 | (102) all_0_2_2 = 0 & ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)
% 4.25/1.70 |
% 4.25/1.70 | Applying alpha-rule on (102) yields:
% 4.25/1.70 | (43) all_0_2_2 = 0
% 4.25/1.70 | (93) ~ (all_0_0_0 = 0)
% 4.25/1.70 | (47) ~ (all_0_1_1 = 0)
% 4.25/1.70 |
% 4.25/1.70 | Equations (43) can reduce 48 to:
% 4.25/1.70 | (49) $false
% 4.25/1.70 |
% 4.25/1.70 |-The branch is then unsatisfiable
% 4.25/1.70 |-Branch two:
% 4.25/1.70 | (107) ~ (all_0_2_2 = 0) & (all_0_0_0 = 0 | all_0_1_1 = 0)
% 4.25/1.70 |
% 4.25/1.70 | Applying alpha-rule on (107) yields:
% 4.25/1.70 | (48) ~ (all_0_2_2 = 0)
% 4.25/1.70 | (109) all_0_0_0 = 0 | all_0_1_1 = 0
% 4.25/1.70 |
% 4.25/1.70 +-Applying beta-rule and splitting (109), into two cases.
% 4.25/1.70 |-Branch one:
% 4.25/1.70 | (110) all_0_0_0 = 0
% 4.25/1.70 |
% 4.25/1.70 | Equations (110) can reduce 93 to:
% 4.25/1.70 | (49) $false
% 4.25/1.70 |
% 4.25/1.70 |-The branch is then unsatisfiable
% 4.25/1.70 |-Branch two:
% 4.25/1.70 | (93) ~ (all_0_0_0 = 0)
% 4.25/1.70 | (38) all_0_1_1 = 0
% 4.25/1.70 |
% 4.25/1.70 | Equations (38) can reduce 47 to:
% 4.25/1.70 | (49) $false
% 4.25/1.70 |
% 4.25/1.70 |-The branch is then unsatisfiable
% 4.25/1.70 |-Branch two:
% 4.25/1.70 | (115) cB(all_0_3_3) = 0
% 4.25/1.70 | (116) all_0_3_3 = ib
% 4.25/1.70 |
% 4.25/1.70 | Equations (116) can reduce 97 to:
% 4.25/1.70 | (49) $false
% 4.25/1.70 |
% 4.25/1.70 |-The branch is then unsatisfiable
% 4.25/1.70 |-Branch two:
% 4.25/1.70 | (118) cA_and_B(all_0_3_3) = 0
% 4.25/1.70 | (119) all_0_3_3 = ib | all_0_3_3 = ia
% 4.25/1.70 |
% 4.25/1.70 +-Applying beta-rule and splitting (119), into two cases.
% 4.25/1.70 |-Branch one:
% 4.25/1.70 | (116) all_0_3_3 = ib
% 4.25/1.70 |
% 4.25/1.70 | Equations (116) can reduce 97 to:
% 4.25/1.70 | (49) $false
% 4.25/1.70 |
% 4.25/1.70 |-The branch is then unsatisfiable
% 4.25/1.70 |-Branch two:
% 4.25/1.70 | (97) ~ (all_0_3_3 = ib)
% 4.25/1.70 | (123) all_0_3_3 = ia
% 4.25/1.70 |
% 4.25/1.70 | Equations (123) can reduce 95 to:
% 4.25/1.70 | (49) $false
% 4.25/1.70 |
% 4.25/1.70 |-The branch is then unsatisfiable
% 4.25/1.70 |-Branch two:
% 4.25/1.70 | (125) cB(ib) = all_0_1_1
% 4.25/1.70 | (38) all_0_1_1 = 0
% 4.25/1.70 |
% 4.25/1.70 | From (38) and (81) follows:
% 4.25/1.70 | (115) cB(all_0_3_3) = 0
% 4.25/1.70 |
% 4.25/1.70 +-Applying beta-rule and splitting (84), into two cases.
% 4.25/1.70 |-Branch one:
% 4.25/1.70 | (102) all_0_2_2 = 0 & ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)
% 4.25/1.70 |
% 4.25/1.70 | Applying alpha-rule on (102) yields:
% 4.25/1.70 | (43) all_0_2_2 = 0
% 4.25/1.70 | (93) ~ (all_0_0_0 = 0)
% 4.25/1.70 | (47) ~ (all_0_1_1 = 0)
% 4.25/1.70 |
% 4.25/1.70 | Equations (38) can reduce 47 to:
% 4.25/1.70 | (49) $false
% 4.25/1.70 |
% 4.25/1.70 |-The branch is then unsatisfiable
% 4.25/1.70 |-Branch two:
% 4.25/1.70 | (107) ~ (all_0_2_2 = 0) & (all_0_0_0 = 0 | all_0_1_1 = 0)
% 4.25/1.70 |
% 4.25/1.70 | Applying alpha-rule on (107) yields:
% 4.25/1.70 | (48) ~ (all_0_2_2 = 0)
% 4.25/1.70 | (109) all_0_0_0 = 0 | all_0_1_1 = 0
% 4.25/1.70 |
% 4.25/1.70 +-Applying beta-rule and splitting (88), into two cases.
% 4.25/1.70 |-Branch one:
% 4.25/1.70 | (136) ~ (cA_and_B(ib) = all_0_2_2)
% 4.25/1.71 |
% 4.25/1.71 +-Applying beta-rule and splitting (85), into two cases.
% 4.25/1.71 |-Branch one:
% 4.25/1.71 | (99) ~ (cB(all_0_3_3) = 0)
% 4.25/1.71 |
% 4.25/1.71 | Using (115) and (99) yields:
% 4.25/1.71 | (45) $false
% 4.25/1.71 |
% 4.25/1.71 |-The branch is then unsatisfiable
% 4.25/1.71 |-Branch two:
% 4.25/1.71 | (115) cB(all_0_3_3) = 0
% 4.25/1.71 | (116) all_0_3_3 = ib
% 4.25/1.71 |
% 4.25/1.71 | From (116) and (82) follows:
% 4.25/1.71 | (141) cA_and_B(ib) = all_0_2_2
% 4.25/1.71 |
% 4.25/1.71 | Using (141) and (136) yields:
% 4.25/1.71 | (45) $false
% 4.25/1.71 |
% 4.25/1.71 |-The branch is then unsatisfiable
% 4.25/1.71 |-Branch two:
% 4.25/1.71 | (141) cA_and_B(ib) = all_0_2_2
% 4.25/1.71 | (43) all_0_2_2 = 0
% 4.25/1.71 |
% 4.25/1.71 | Equations (43) can reduce 48 to:
% 4.25/1.71 | (49) $false
% 4.25/1.71 |
% 4.25/1.71 |-The branch is then unsatisfiable
% 4.25/1.71 |-Branch two:
% 4.25/1.71 | (146) cA(ia) = all_0_0_0
% 4.25/1.71 | (110) all_0_0_0 = 0
% 4.25/1.71 |
% 4.25/1.71 | Equations (110) can reduce 93 to:
% 4.25/1.71 | (49) $false
% 4.25/1.71 |
% 4.25/1.71 |-The branch is then unsatisfiable
% 4.25/1.71 |-Branch two:
% 4.25/1.71 | (149) cA(all_0_3_3) = 0
% 4.25/1.71 | (123) all_0_3_3 = ia
% 4.25/1.71 |
% 4.25/1.71 | From (123) and (82) follows:
% 4.25/1.71 | (151) cA_and_B(ia) = all_0_2_2
% 4.25/1.71 |
% 4.25/1.71 | From (123) and (83) follows:
% 4.25/1.71 | (146) cA(ia) = all_0_0_0
% 4.25/1.71 |
% 4.25/1.71 +-Applying beta-rule and splitting (91), into two cases.
% 4.25/1.71 |-Branch one:
% 4.25/1.71 | (94) ~ (cA(ia) = all_0_0_0)
% 4.25/1.71 |
% 4.25/1.71 | Using (146) and (94) yields:
% 4.25/1.71 | (45) $false
% 4.25/1.71 |
% 4.25/1.71 |-The branch is then unsatisfiable
% 4.25/1.71 |-Branch two:
% 4.25/1.71 | (146) cA(ia) = all_0_0_0
% 4.25/1.71 | (110) all_0_0_0 = 0
% 4.25/1.71 |
% 4.25/1.71 +-Applying beta-rule and splitting (89), into two cases.
% 4.25/1.71 |-Branch one:
% 4.25/1.71 | (157) ~ (cA_and_B(ia) = all_0_2_2)
% 4.25/1.71 |
% 4.25/1.71 | Using (151) and (157) yields:
% 4.25/1.71 | (45) $false
% 4.25/1.71 |
% 4.25/1.71 |-The branch is then unsatisfiable
% 4.25/1.71 |-Branch two:
% 4.25/1.71 | (151) cA_and_B(ia) = all_0_2_2
% 4.25/1.71 | (43) all_0_2_2 = 0
% 4.25/1.71 |
% 4.25/1.71 +-Applying beta-rule and splitting (84), into two cases.
% 4.25/1.71 |-Branch one:
% 4.25/1.71 | (102) all_0_2_2 = 0 & ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)
% 4.25/1.71 |
% 4.25/1.71 | Applying alpha-rule on (102) yields:
% 4.25/1.71 | (43) all_0_2_2 = 0
% 4.25/1.71 | (93) ~ (all_0_0_0 = 0)
% 4.25/1.71 | (47) ~ (all_0_1_1 = 0)
% 4.25/1.71 |
% 4.25/1.71 | Equations (110) can reduce 93 to:
% 4.25/1.71 | (49) $false
% 4.25/1.71 |
% 4.25/1.71 |-The branch is then unsatisfiable
% 4.25/1.71 |-Branch two:
% 4.25/1.71 | (107) ~ (all_0_2_2 = 0) & (all_0_0_0 = 0 | all_0_1_1 = 0)
% 4.25/1.71 |
% 4.25/1.71 | Applying alpha-rule on (107) yields:
% 4.25/1.71 | (48) ~ (all_0_2_2 = 0)
% 4.25/1.71 | (109) all_0_0_0 = 0 | all_0_1_1 = 0
% 4.25/1.71 |
% 4.25/1.71 | Equations (43) can reduce 48 to:
% 4.25/1.71 | (49) $false
% 4.25/1.71 |
% 4.25/1.71 |-The branch is then unsatisfiable
% 4.25/1.71 % SZS output end Proof for theBenchmark
% 4.25/1.71
% 4.25/1.71 1132ms
%------------------------------------------------------------------------------