TSTP Solution File: KRS104+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KRS104+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n023.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 02:56:34 EDT 2022
% Result : Unsatisfiable 24.78s 6.97s
% Output : Proof 33.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS104+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 7 09:35:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.59/0.59 ____ _
% 0.59/0.59 ___ / __ \_____(_)___ ________ __________
% 0.59/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.59
% 0.59/0.59 A Theorem Prover for First-Order Logic
% 0.59/0.59 (ePrincess v.1.0)
% 0.59/0.59
% 0.59/0.59 (c) Philipp Rümmer, 2009-2015
% 0.59/0.59 (c) Peter Backeman, 2014-2015
% 0.59/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.59 Bug reports to peter@backeman.se
% 0.59/0.59
% 0.59/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.59
% 0.59/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.51/0.93 Prover 0: Preprocessing ...
% 2.02/1.09 Prover 0: Warning: ignoring some quantifiers
% 2.02/1.11 Prover 0: Constructing countermodel ...
% 2.83/1.35 Prover 0: gave up
% 2.83/1.35 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.08/1.40 Prover 1: Preprocessing ...
% 3.89/1.60 Prover 1: Constructing countermodel ...
% 3.89/1.62 Prover 1: gave up
% 3.89/1.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.06/1.64 Prover 2: Preprocessing ...
% 4.51/1.79 Prover 2: Warning: ignoring some quantifiers
% 4.80/1.82 Prover 2: Constructing countermodel ...
% 5.08/1.94 Prover 2: gave up
% 5.08/1.94 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.08/1.96 Prover 3: Preprocessing ...
% 5.53/1.97 Prover 3: Warning: ignoring some quantifiers
% 5.53/1.98 Prover 3: Constructing countermodel ...
% 5.78/2.04 Prover 3: gave up
% 5.78/2.04 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 5.78/2.06 Prover 4: Preprocessing ...
% 6.24/2.19 Prover 4: Warning: ignoring some quantifiers
% 6.24/2.20 Prover 4: Constructing countermodel ...
% 10.95/3.24 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 10.95/3.26 Prover 5: Preprocessing ...
% 11.53/3.37 Prover 5: Constructing countermodel ...
% 11.53/3.39 Prover 5: gave up
% 11.53/3.39 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 11.53/3.41 Prover 6: Preprocessing ...
% 11.88/3.49 Prover 6: Warning: ignoring some quantifiers
% 11.88/3.49 Prover 6: Constructing countermodel ...
% 11.88/3.53 Prover 6: gave up
% 11.88/3.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 12.28/3.54 Prover 7: Preprocessing ...
% 12.28/3.56 Prover 7: Proving ...
% 24.70/6.97 Prover 7: proved (3439ms)
% 24.78/6.97 Prover 4: stopped
% 24.78/6.97
% 24.78/6.97 % SZS status Unsatisfiable for theBenchmark
% 24.78/6.97
% 24.78/6.97 Generating proof ... found it (size 84)
% 33.13/9.61
% 33.13/9.61 % SZS output start Proof for theBenchmark
% 33.13/9.61 Assumed formulas after preprocessing and simplification:
% 33.13/9.61 | (0) ? [v0] : (cUnsatisfiable(v0) & ! [v1] : ( ~ ca_Cx8xcomp(v1) | ? [v2] : ra_Px8(v1, v2)) & ! [v1] : ( ~ ca_Cx8xcomp(v1) | (cc(v1) & cb(v1))) & ! [v1] : ( ~ ca_Cx7xcomp(v1) | ! [v2] : ~ ra_Px7(v1, v2)) & ! [v1] : ( ~ ca_Cx7xcomp(v1) | (cc(v1) & ca(v1))) & ! [v1] : ( ~ ca_Cx6xcomp(v1) | ? [v2] : ra_Px6(v1, v2)) & ! [v1] : ( ~ ca_Cx6xcomp(v1) | (cb(v1) & ca(v1))) & ! [v1] : ( ~ ca_Cx1xcomp(v1) | ! [v2] : ~ ra_Px1(v1, v2)) & ! [v1] : ( ~ cc(v1) | ~ cb(v1) | ca_Cx8xcomp(v1)) & ! [v1] : ( ~ cc(v1) | ~ ca(v1) | ca_Cx7xcomp(v1)) & ! [v1] : ( ~ cc(v1) | ? [v2] : ra_Px2(v1, v2)) & ! [v1] : ( ~ cbxcomp(v1) | ~ ccxcomp(v1) | ca_Cx1(v1)) & ! [v1] : ( ~ cbxcomp(v1) | ! [v2] : ~ ra_Px3(v1, v2)) & ! [v1] : ( ~ ccxcomp(v1) | ! [v2] : ~ ra_Px2(v1, v2)) & ! [v1] : ( ~ cb(v1) | ~ ca(v1) | ca_Cx6xcomp(v1)) & ! [v1] : ( ~ cb(v1) | ccxcomp(v1)) & ! [v1] : ( ~ cb(v1) | ? [v2] : ra_Px3(v1, v2)) & ! [v1] : ( ~ ca_Cx1(v1) | ? [v2] : ra_Px1(v1, v2)) & ! [v1] : ( ~ ca_Cx1(v1) | (cbxcomp(v1) & ccxcomp(v1))) & ! [v1] : ( ~ ca(v1) | ca_Cx1(v1)) & ! [v1] : ( ~ ca_Cx6(v1) | ~ ca_Cx8(v1) | ~ ca_Cx7(v1) | cUnsatisfiablexcomp(v1)) & ! [v1] : ( ~ ca_Cx6(v1) | ! [v2] : ~ ra_Px6(v1, v2)) & ! [v1] : ( ~ ca_Cx8(v1) | ! [v2] : ~ ra_Px8(v1, v2)) & ! [v1] : ( ~ ca_Cx7(v1) | ? [v2] : ra_Px7(v1, v2)) & ! [v1] : ( ~ cUnsatisfiablexcomp(v1) | ? [v2] : ra_Px5(v1, v2)) & ! [v1] : ( ~ cUnsatisfiablexcomp(v1) | (ca_Cx6(v1) & ca_Cx8(v1) & ca_Cx7(v1))) & ! [v1] : ( ~ cUnsatisfiable(v1) | ! [v2] : ~ ra_Px5(v1, v2)) & ! [v1] : ( ~ xsd_integer(v1) | ~ xsd_string(v1)) & ! [v1] : ~ cowlNothing(v1) & ! [v1] : (ca_Cx8xcomp(v1) | ! [v2] : ~ ra_Px8(v1, v2)) & ! [v1] : (ca_Cx7xcomp(v1) | ? [v2] : ra_Px7(v1, v2)) & ! [v1] : (ca_Cx6xcomp(v1) | ! [v2] : ~ ra_Px6(v1, v2)) & ! [v1] : (ca_Cx1xcomp(v1) | ? [v2] : ra_Px1(v1, v2)) & ! [v1] : (cc(v1) | ! [v2] : ~ ra_Px2(v1, v2)) & ! [v1] : (cbxcomp(v1) | ? [v2] : ra_Px3(v1, v2)) & ! [v1] : (ccxcomp(v1) | ? [v2] : ra_Px2(v1, v2)) & ! [v1] : (cb(v1) | ! [v2] : ~ ra_Px3(v1, v2)) & ! [v1] : (ca_Cx1(v1) | ! [v2] : ~ ra_Px1(v1, v2)) & ! [v1] : (ca_Cx6(v1) | ? [v2] : ra_Px6(v1, v2)) & ! [v1] : (ca_Cx8(v1) | ? [v2] : ra_Px8(v1, v2)) & ! [v1] : (ca_Cx7(v1) | ! [v2] : ~ ra_Px7(v1, v2)) & ! [v1] : (cUnsatisfiablexcomp(v1) | ! [v2] : ~ ra_Px5(v1, v2)) & ! [v1] : (cUnsatisfiable(v1) | ? [v2] : ra_Px5(v1, v2)) & ! [v1] : (xsd_integer(v1) | xsd_string(v1)) & ! [v1] : cowlThing(v1))
% 33.13/9.62 | Instantiating (0) with all_0_0_0 yields:
% 33.13/9.62 | (1) cUnsatisfiable(all_0_0_0) & ! [v0] : ( ~ ca_Cx8xcomp(v0) | ? [v1] : ra_Px8(v0, v1)) & ! [v0] : ( ~ ca_Cx8xcomp(v0) | (cc(v0) & cb(v0))) & ! [v0] : ( ~ ca_Cx7xcomp(v0) | ! [v1] : ~ ra_Px7(v0, v1)) & ! [v0] : ( ~ ca_Cx7xcomp(v0) | (cc(v0) & ca(v0))) & ! [v0] : ( ~ ca_Cx6xcomp(v0) | ? [v1] : ra_Px6(v0, v1)) & ! [v0] : ( ~ ca_Cx6xcomp(v0) | (cb(v0) & ca(v0))) & ! [v0] : ( ~ ca_Cx1xcomp(v0) | ! [v1] : ~ ra_Px1(v0, v1)) & ! [v0] : ( ~ cc(v0) | ~ cb(v0) | ca_Cx8xcomp(v0)) & ! [v0] : ( ~ cc(v0) | ~ ca(v0) | ca_Cx7xcomp(v0)) & ! [v0] : ( ~ cc(v0) | ? [v1] : ra_Px2(v0, v1)) & ! [v0] : ( ~ cbxcomp(v0) | ~ ccxcomp(v0) | ca_Cx1(v0)) & ! [v0] : ( ~ cbxcomp(v0) | ! [v1] : ~ ra_Px3(v0, v1)) & ! [v0] : ( ~ ccxcomp(v0) | ! [v1] : ~ ra_Px2(v0, v1)) & ! [v0] : ( ~ cb(v0) | ~ ca(v0) | ca_Cx6xcomp(v0)) & ! [v0] : ( ~ cb(v0) | ccxcomp(v0)) & ! [v0] : ( ~ cb(v0) | ? [v1] : ra_Px3(v0, v1)) & ! [v0] : ( ~ ca_Cx1(v0) | ? [v1] : ra_Px1(v0, v1)) & ! [v0] : ( ~ ca_Cx1(v0) | (cbxcomp(v0) & ccxcomp(v0))) & ! [v0] : ( ~ ca(v0) | ca_Cx1(v0)) & ! [v0] : ( ~ ca_Cx6(v0) | ~ ca_Cx8(v0) | ~ ca_Cx7(v0) | cUnsatisfiablexcomp(v0)) & ! [v0] : ( ~ ca_Cx6(v0) | ! [v1] : ~ ra_Px6(v0, v1)) & ! [v0] : ( ~ ca_Cx8(v0) | ! [v1] : ~ ra_Px8(v0, v1)) & ! [v0] : ( ~ ca_Cx7(v0) | ? [v1] : ra_Px7(v0, v1)) & ! [v0] : ( ~ cUnsatisfiablexcomp(v0) | ? [v1] : ra_Px5(v0, v1)) & ! [v0] : ( ~ cUnsatisfiablexcomp(v0) | (ca_Cx6(v0) & ca_Cx8(v0) & ca_Cx7(v0))) & ! [v0] : ( ~ cUnsatisfiable(v0) | ! [v1] : ~ ra_Px5(v0, v1)) & ! [v0] : ( ~ xsd_integer(v0) | ~ xsd_string(v0)) & ! [v0] : ~ cowlNothing(v0) & ! [v0] : (ca_Cx8xcomp(v0) | ! [v1] : ~ ra_Px8(v0, v1)) & ! [v0] : (ca_Cx7xcomp(v0) | ? [v1] : ra_Px7(v0, v1)) & ! [v0] : (ca_Cx6xcomp(v0) | ! [v1] : ~ ra_Px6(v0, v1)) & ! [v0] : (ca_Cx1xcomp(v0) | ? [v1] : ra_Px1(v0, v1)) & ! [v0] : (cc(v0) | ! [v1] : ~ ra_Px2(v0, v1)) & ! [v0] : (cbxcomp(v0) | ? [v1] : ra_Px3(v0, v1)) & ! [v0] : (ccxcomp(v0) | ? [v1] : ra_Px2(v0, v1)) & ! [v0] : (cb(v0) | ! [v1] : ~ ra_Px3(v0, v1)) & ! [v0] : (ca_Cx1(v0) | ! [v1] : ~ ra_Px1(v0, v1)) & ! [v0] : (ca_Cx6(v0) | ? [v1] : ra_Px6(v0, v1)) & ! [v0] : (ca_Cx8(v0) | ? [v1] : ra_Px8(v0, v1)) & ! [v0] : (ca_Cx7(v0) | ! [v1] : ~ ra_Px7(v0, v1)) & ! [v0] : (cUnsatisfiablexcomp(v0) | ! [v1] : ~ ra_Px5(v0, v1)) & ! [v0] : (cUnsatisfiable(v0) | ? [v1] : ra_Px5(v0, v1)) & ! [v0] : (xsd_integer(v0) | xsd_string(v0)) & ! [v0] : cowlThing(v0)
% 33.13/9.62 |
% 33.13/9.62 | Applying alpha-rule on (1) yields:
% 33.13/9.62 | (2) ! [v0] : (cUnsatisfiable(v0) | ? [v1] : ra_Px5(v0, v1))
% 33.13/9.62 | (3) ! [v0] : ( ~ cb(v0) | ccxcomp(v0))
% 33.13/9.62 | (4) ! [v0] : (ca_Cx8xcomp(v0) | ! [v1] : ~ ra_Px8(v0, v1))
% 33.13/9.63 | (5) ! [v0] : (ccxcomp(v0) | ? [v1] : ra_Px2(v0, v1))
% 33.13/9.63 | (6) ! [v0] : (ca_Cx6xcomp(v0) | ! [v1] : ~ ra_Px6(v0, v1))
% 33.13/9.63 | (7) ! [v0] : (cb(v0) | ! [v1] : ~ ra_Px3(v0, v1))
% 33.13/9.63 | (8) ! [v0] : ( ~ cc(v0) | ~ cb(v0) | ca_Cx8xcomp(v0))
% 33.13/9.63 | (9) ! [v0] : ( ~ xsd_integer(v0) | ~ xsd_string(v0))
% 33.13/9.63 | (10) ! [v0] : ( ~ cUnsatisfiablexcomp(v0) | ? [v1] : ra_Px5(v0, v1))
% 33.13/9.63 | (11) ! [v0] : ( ~ ca_Cx1(v0) | ? [v1] : ra_Px1(v0, v1))
% 33.13/9.63 | (12) ! [v0] : ( ~ ca_Cx7xcomp(v0) | ! [v1] : ~ ra_Px7(v0, v1))
% 33.13/9.63 | (13) ! [v0] : (ca_Cx1xcomp(v0) | ? [v1] : ra_Px1(v0, v1))
% 33.13/9.63 | (14) ! [v0] : (ca_Cx6(v0) | ? [v1] : ra_Px6(v0, v1))
% 33.13/9.63 | (15) ! [v0] : ( ~ ca_Cx7xcomp(v0) | (cc(v0) & ca(v0)))
% 33.13/9.63 | (16) ! [v0] : ( ~ ca_Cx8(v0) | ! [v1] : ~ ra_Px8(v0, v1))
% 33.13/9.63 | (17) ! [v0] : ( ~ ca(v0) | ca_Cx1(v0))
% 33.13/9.63 | (18) ! [v0] : ( ~ cb(v0) | ? [v1] : ra_Px3(v0, v1))
% 33.13/9.63 | (19) ! [v0] : ( ~ cbxcomp(v0) | ! [v1] : ~ ra_Px3(v0, v1))
% 33.13/9.63 | (20) ! [v0] : (ca_Cx7xcomp(v0) | ? [v1] : ra_Px7(v0, v1))
% 33.13/9.63 | (21) ! [v0] : (ca_Cx8(v0) | ? [v1] : ra_Px8(v0, v1))
% 33.13/9.63 | (22) cUnsatisfiable(all_0_0_0)
% 33.13/9.63 | (23) ! [v0] : (ca_Cx1(v0) | ! [v1] : ~ ra_Px1(v0, v1))
% 33.13/9.63 | (24) ! [v0] : ( ~ ca_Cx1(v0) | (cbxcomp(v0) & ccxcomp(v0)))
% 33.13/9.63 | (25) ! [v0] : ( ~ ca_Cx8xcomp(v0) | (cc(v0) & cb(v0)))
% 33.13/9.63 | (26) ! [v0] : ( ~ cc(v0) | ~ ca(v0) | ca_Cx7xcomp(v0))
% 33.13/9.63 | (27) ! [v0] : ( ~ ca_Cx6xcomp(v0) | (cb(v0) & ca(v0)))
% 33.13/9.63 | (28) ! [v0] : ( ~ ca_Cx6xcomp(v0) | ? [v1] : ra_Px6(v0, v1))
% 33.13/9.63 | (29) ! [v0] : ~ cowlNothing(v0)
% 33.13/9.63 | (30) ! [v0] : ( ~ ccxcomp(v0) | ! [v1] : ~ ra_Px2(v0, v1))
% 33.13/9.63 | (31) ! [v0] : (ca_Cx7(v0) | ! [v1] : ~ ra_Px7(v0, v1))
% 33.13/9.63 | (32) ! [v0] : ( ~ ca_Cx1xcomp(v0) | ! [v1] : ~ ra_Px1(v0, v1))
% 33.13/9.63 | (33) ! [v0] : ( ~ cUnsatisfiablexcomp(v0) | (ca_Cx6(v0) & ca_Cx8(v0) & ca_Cx7(v0)))
% 33.13/9.63 | (34) ! [v0] : (xsd_integer(v0) | xsd_string(v0))
% 33.13/9.63 | (35) ! [v0] : ( ~ cUnsatisfiable(v0) | ! [v1] : ~ ra_Px5(v0, v1))
% 33.13/9.63 | (36) ! [v0] : ( ~ cc(v0) | ? [v1] : ra_Px2(v0, v1))
% 33.13/9.63 | (37) ! [v0] : ( ~ ca_Cx7(v0) | ? [v1] : ra_Px7(v0, v1))
% 33.13/9.63 | (38) ! [v0] : (cbxcomp(v0) | ? [v1] : ra_Px3(v0, v1))
% 33.13/9.63 | (39) ! [v0] : ( ~ cbxcomp(v0) | ~ ccxcomp(v0) | ca_Cx1(v0))
% 33.13/9.63 | (40) ! [v0] : cowlThing(v0)
% 33.13/9.63 | (41) ! [v0] : ( ~ ca_Cx6(v0) | ~ ca_Cx8(v0) | ~ ca_Cx7(v0) | cUnsatisfiablexcomp(v0))
% 33.13/9.63 | (42) ! [v0] : ( ~ ca_Cx8xcomp(v0) | ? [v1] : ra_Px8(v0, v1))
% 33.13/9.63 | (43) ! [v0] : (cUnsatisfiablexcomp(v0) | ! [v1] : ~ ra_Px5(v0, v1))
% 33.13/9.63 | (44) ! [v0] : ( ~ cb(v0) | ~ ca(v0) | ca_Cx6xcomp(v0))
% 33.13/9.63 | (45) ! [v0] : ( ~ ca_Cx6(v0) | ! [v1] : ~ ra_Px6(v0, v1))
% 33.13/9.63 | (46) ! [v0] : (cc(v0) | ! [v1] : ~ ra_Px2(v0, v1))
% 33.13/9.63 |
% 33.13/9.63 | Instantiating formula (35) with all_0_0_0 and discharging atoms cUnsatisfiable(all_0_0_0), yields:
% 33.13/9.63 | (47) ! [v0] : ~ ra_Px5(all_0_0_0, v0)
% 33.13/9.63 |
% 33.13/9.63 | Introducing new symbol ex_11_0_1 defined by:
% 33.13/9.63 | (48) ex_11_0_1 = all_0_0_0
% 33.13/9.63 |
% 33.13/9.63 | Instantiating formula (4) with ex_11_0_1 yields:
% 33.13/9.63 | (49) ca_Cx8xcomp(ex_11_0_1) | ! [v0] : ~ ra_Px8(ex_11_0_1, v0)
% 33.13/9.63 |
% 33.13/9.63 +-Applying beta-rule and splitting (49), into two cases.
% 33.13/9.63 |-Branch one:
% 33.13/9.63 | (50) ca_Cx8xcomp(ex_11_0_1)
% 33.13/9.63 |
% 33.13/9.63 | Instantiating formula (25) with ex_11_0_1 and discharging atoms ca_Cx8xcomp(ex_11_0_1), yields:
% 33.13/9.63 | (51) cc(ex_11_0_1) & cb(ex_11_0_1)
% 33.13/9.63 |
% 33.13/9.63 | Applying alpha-rule on (51) yields:
% 33.13/9.63 | (52) cc(ex_11_0_1)
% 33.13/9.63 | (53) cb(ex_11_0_1)
% 33.13/9.63 |
% 33.13/9.63 | Instantiating formula (36) with ex_11_0_1 and discharging atoms cc(ex_11_0_1), yields:
% 33.13/9.63 | (54) ? [v0] : ra_Px2(ex_11_0_1, v0)
% 33.13/9.63 |
% 33.13/9.63 | Instantiating formula (3) with ex_11_0_1 and discharging atoms cb(ex_11_0_1), yields:
% 33.13/9.63 | (55) ccxcomp(ex_11_0_1)
% 33.13/9.63 |
% 33.13/9.63 | Instantiating (54) with all_28_0_3 yields:
% 33.13/9.63 | (56) ra_Px2(ex_11_0_1, all_28_0_3)
% 33.13/9.63 |
% 33.13/9.63 | Instantiating formula (30) with ex_11_0_1 and discharging atoms ccxcomp(ex_11_0_1), yields:
% 33.13/9.63 | (57) ! [v0] : ~ ra_Px2(ex_11_0_1, v0)
% 33.13/9.63 |
% 33.13/9.63 | Instantiating formula (57) with all_28_0_3 and discharging atoms ra_Px2(ex_11_0_1, all_28_0_3), yields:
% 33.13/9.63 | (58) $false
% 33.13/9.63 |
% 33.13/9.63 |-The branch is then unsatisfiable
% 33.13/9.63 |-Branch two:
% 33.13/9.63 | (59) ! [v0] : ~ ra_Px8(ex_11_0_1, v0)
% 33.13/9.64 |
% 33.13/9.64 | Introducing new symbol ex_16_0_5 defined by:
% 33.13/9.64 | (60) ex_16_0_5 = all_0_0_0
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (20) with ex_16_0_5 yields:
% 33.13/9.64 | (61) ca_Cx7xcomp(ex_16_0_5) | ? [v0] : ra_Px7(ex_16_0_5, v0)
% 33.13/9.64 |
% 33.13/9.64 +-Applying beta-rule and splitting (61), into two cases.
% 33.13/9.64 |-Branch one:
% 33.13/9.64 | (62) ca_Cx7xcomp(ex_16_0_5)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (15) with ex_16_0_5 and discharging atoms ca_Cx7xcomp(ex_16_0_5), yields:
% 33.13/9.64 | (63) cc(ex_16_0_5) & ca(ex_16_0_5)
% 33.13/9.64 |
% 33.13/9.64 | Applying alpha-rule on (63) yields:
% 33.13/9.64 | (64) cc(ex_16_0_5)
% 33.13/9.64 | (65) ca(ex_16_0_5)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (36) with ex_16_0_5 and discharging atoms cc(ex_16_0_5), yields:
% 33.13/9.64 | (66) ? [v0] : ra_Px2(ex_16_0_5, v0)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (17) with ex_16_0_5 and discharging atoms ca(ex_16_0_5), yields:
% 33.13/9.64 | (67) ca_Cx1(ex_16_0_5)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating (66) with all_32_0_7 yields:
% 33.13/9.64 | (68) ra_Px2(ex_16_0_5, all_32_0_7)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (24) with ex_16_0_5 and discharging atoms ca_Cx1(ex_16_0_5), yields:
% 33.13/9.64 | (69) cbxcomp(ex_16_0_5) & ccxcomp(ex_16_0_5)
% 33.13/9.64 |
% 33.13/9.64 | Applying alpha-rule on (69) yields:
% 33.13/9.64 | (70) cbxcomp(ex_16_0_5)
% 33.13/9.64 | (71) ccxcomp(ex_16_0_5)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (30) with ex_16_0_5 and discharging atoms ccxcomp(ex_16_0_5), yields:
% 33.13/9.64 | (72) ! [v0] : ~ ra_Px2(ex_16_0_5, v0)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (72) with all_32_0_7 and discharging atoms ra_Px2(ex_16_0_5, all_32_0_7), yields:
% 33.13/9.64 | (58) $false
% 33.13/9.64 |
% 33.13/9.64 |-The branch is then unsatisfiable
% 33.13/9.64 |-Branch two:
% 33.13/9.64 | (74) ? [v0] : ra_Px7(ex_16_0_5, v0)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating (74) with all_18_0_6 yields:
% 33.13/9.64 | (75) ra_Px7(ex_16_0_5, all_18_0_6)
% 33.13/9.64 |
% 33.13/9.64 | Introducing new symbol ex_46_0_12 defined by:
% 33.13/9.64 | (76) ex_46_0_12 = all_0_0_0
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (21) with ex_46_0_12 yields:
% 33.13/9.64 | (77) ca_Cx8(ex_46_0_12) | ? [v0] : ra_Px8(ex_46_0_12, v0)
% 33.13/9.64 |
% 33.13/9.64 +-Applying beta-rule and splitting (77), into two cases.
% 33.13/9.64 |-Branch one:
% 33.13/9.64 | (78) ca_Cx8(ex_46_0_12)
% 33.13/9.64 |
% 33.13/9.64 | Introducing new symbol ex_57_0_14 defined by:
% 33.13/9.64 | (79) ex_57_0_14 = all_0_0_0
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (6) with ex_57_0_14 yields:
% 33.13/9.64 | (80) ca_Cx6xcomp(ex_57_0_14) | ! [v0] : ~ ra_Px6(ex_57_0_14, v0)
% 33.13/9.64 |
% 33.13/9.64 +-Applying beta-rule and splitting (80), into two cases.
% 33.13/9.64 |-Branch one:
% 33.13/9.64 | (81) ca_Cx6xcomp(ex_57_0_14)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (27) with ex_57_0_14 and discharging atoms ca_Cx6xcomp(ex_57_0_14), yields:
% 33.13/9.64 | (82) cb(ex_57_0_14) & ca(ex_57_0_14)
% 33.13/9.64 |
% 33.13/9.64 | Applying alpha-rule on (82) yields:
% 33.13/9.64 | (83) cb(ex_57_0_14)
% 33.13/9.64 | (84) ca(ex_57_0_14)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (18) with ex_57_0_14 and discharging atoms cb(ex_57_0_14), yields:
% 33.13/9.64 | (85) ? [v0] : ra_Px3(ex_57_0_14, v0)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (17) with ex_57_0_14 and discharging atoms ca(ex_57_0_14), yields:
% 33.13/9.64 | (86) ca_Cx1(ex_57_0_14)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating (85) with all_74_0_16 yields:
% 33.13/9.64 | (87) ra_Px3(ex_57_0_14, all_74_0_16)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (24) with ex_57_0_14 and discharging atoms ca_Cx1(ex_57_0_14), yields:
% 33.13/9.64 | (88) cbxcomp(ex_57_0_14) & ccxcomp(ex_57_0_14)
% 33.13/9.64 |
% 33.13/9.64 | Applying alpha-rule on (88) yields:
% 33.13/9.64 | (89) cbxcomp(ex_57_0_14)
% 33.13/9.64 | (90) ccxcomp(ex_57_0_14)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (19) with ex_57_0_14 and discharging atoms cbxcomp(ex_57_0_14), yields:
% 33.13/9.64 | (91) ! [v0] : ~ ra_Px3(ex_57_0_14, v0)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (91) with all_74_0_16 and discharging atoms ra_Px3(ex_57_0_14, all_74_0_16), yields:
% 33.13/9.64 | (58) $false
% 33.13/9.64 |
% 33.13/9.64 |-The branch is then unsatisfiable
% 33.13/9.64 |-Branch two:
% 33.13/9.64 | (93) ! [v0] : ~ ra_Px6(ex_57_0_14, v0)
% 33.13/9.64 |
% 33.13/9.64 | Introducing new symbol ex_102_0_23 defined by:
% 33.13/9.64 | (94) ex_102_0_23 = all_0_0_0
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (31) with ex_102_0_23 yields:
% 33.13/9.64 | (95) ca_Cx7(ex_102_0_23) | ! [v0] : ~ ra_Px7(ex_102_0_23, v0)
% 33.13/9.64 |
% 33.13/9.64 +-Applying beta-rule and splitting (95), into two cases.
% 33.13/9.64 |-Branch one:
% 33.13/9.64 | (96) ca_Cx7(ex_102_0_23)
% 33.13/9.64 |
% 33.13/9.64 | Introducing new symbol ex_123_0_27 defined by:
% 33.13/9.64 | (97) ex_123_0_27 = all_0_0_0
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (14) with ex_123_0_27 yields:
% 33.13/9.64 | (98) ca_Cx6(ex_123_0_27) | ? [v0] : ra_Px6(ex_123_0_27, v0)
% 33.13/9.64 |
% 33.13/9.64 +-Applying beta-rule and splitting (98), into two cases.
% 33.13/9.64 |-Branch one:
% 33.13/9.64 | (99) ca_Cx6(ex_123_0_27)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (41) with ex_46_0_12 and discharging atoms ca_Cx8(ex_46_0_12), yields:
% 33.13/9.64 | (100) ~ ca_Cx6(ex_46_0_12) | ~ ca_Cx7(ex_46_0_12) | cUnsatisfiablexcomp(ex_46_0_12)
% 33.13/9.64 |
% 33.13/9.64 +-Applying beta-rule and splitting (100), into two cases.
% 33.13/9.64 |-Branch one:
% 33.13/9.64 | (101) ~ ca_Cx6(ex_46_0_12)
% 33.13/9.64 |
% 33.13/9.64 | From (97) and (99) follows:
% 33.13/9.64 | (102) ca_Cx6(all_0_0_0)
% 33.13/9.64 |
% 33.13/9.64 | From (76) and (101) follows:
% 33.13/9.64 | (103) ~ ca_Cx6(all_0_0_0)
% 33.13/9.64 |
% 33.13/9.64 | Using (102) and (103) yields:
% 33.13/9.64 | (58) $false
% 33.13/9.64 |
% 33.13/9.64 |-The branch is then unsatisfiable
% 33.13/9.64 |-Branch two:
% 33.13/9.64 | (105) ~ ca_Cx7(ex_46_0_12) | cUnsatisfiablexcomp(ex_46_0_12)
% 33.13/9.64 |
% 33.13/9.64 +-Applying beta-rule and splitting (105), into two cases.
% 33.13/9.64 |-Branch one:
% 33.13/9.64 | (106) ~ ca_Cx7(ex_46_0_12)
% 33.13/9.64 |
% 33.13/9.64 | From (94) and (96) follows:
% 33.13/9.64 | (107) ca_Cx7(all_0_0_0)
% 33.13/9.64 |
% 33.13/9.64 | From (76) and (106) follows:
% 33.13/9.64 | (108) ~ ca_Cx7(all_0_0_0)
% 33.13/9.64 |
% 33.13/9.64 | Using (107) and (108) yields:
% 33.13/9.64 | (58) $false
% 33.13/9.64 |
% 33.13/9.64 |-The branch is then unsatisfiable
% 33.13/9.64 |-Branch two:
% 33.13/9.64 | (110) cUnsatisfiablexcomp(ex_46_0_12)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (10) with ex_46_0_12 and discharging atoms cUnsatisfiablexcomp(ex_46_0_12), yields:
% 33.13/9.64 | (111) ? [v0] : ra_Px5(ex_46_0_12, v0)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating (111) with all_143_0_29 yields:
% 33.13/9.64 | (112) ra_Px5(ex_46_0_12, all_143_0_29)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (47) with all_143_0_29 yields:
% 33.13/9.64 | (113) ~ ra_Px5(all_0_0_0, all_143_0_29)
% 33.13/9.64 |
% 33.13/9.64 | From (76) and (112) follows:
% 33.13/9.64 | (114) ra_Px5(all_0_0_0, all_143_0_29)
% 33.13/9.64 |
% 33.13/9.64 | Using (114) and (113) yields:
% 33.13/9.64 | (58) $false
% 33.13/9.64 |
% 33.13/9.64 |-The branch is then unsatisfiable
% 33.13/9.64 |-Branch two:
% 33.13/9.64 | (116) ? [v0] : ra_Px6(ex_123_0_27, v0)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating (116) with all_125_0_28 yields:
% 33.13/9.64 | (117) ra_Px6(ex_123_0_27, all_125_0_28)
% 33.13/9.64 |
% 33.13/9.64 | Instantiating formula (93) with all_125_0_28 yields:
% 33.13/9.65 | (118) ~ ra_Px6(ex_57_0_14, all_125_0_28)
% 33.13/9.65 |
% 33.13/9.65 | From (97) and (117) follows:
% 33.13/9.65 | (119) ra_Px6(all_0_0_0, all_125_0_28)
% 33.13/9.65 |
% 33.13/9.65 | From (79) and (118) follows:
% 33.13/9.65 | (120) ~ ra_Px6(all_0_0_0, all_125_0_28)
% 33.13/9.65 |
% 33.13/9.65 | Using (119) and (120) yields:
% 33.13/9.65 | (58) $false
% 33.13/9.65 |
% 33.13/9.65 |-The branch is then unsatisfiable
% 33.13/9.65 |-Branch two:
% 33.13/9.65 | (122) ! [v0] : ~ ra_Px7(ex_102_0_23, v0)
% 33.13/9.65 |
% 33.13/9.65 | Instantiating formula (122) with all_18_0_6 yields:
% 33.13/9.65 | (123) ~ ra_Px7(ex_102_0_23, all_18_0_6)
% 33.13/9.65 |
% 33.13/9.65 | From (60) and (75) follows:
% 33.13/9.65 | (124) ra_Px7(all_0_0_0, all_18_0_6)
% 33.13/9.65 |
% 33.13/9.65 | From (94) and (123) follows:
% 33.13/9.65 | (125) ~ ra_Px7(all_0_0_0, all_18_0_6)
% 33.13/9.65 |
% 33.13/9.65 | Using (124) and (125) yields:
% 33.13/9.65 | (58) $false
% 33.13/9.65 |
% 33.13/9.65 |-The branch is then unsatisfiable
% 33.13/9.65 |-Branch two:
% 33.13/9.65 | (127) ? [v0] : ra_Px8(ex_46_0_12, v0)
% 33.13/9.65 |
% 33.13/9.65 | Instantiating (127) with all_48_0_13 yields:
% 33.13/9.65 | (128) ra_Px8(ex_46_0_12, all_48_0_13)
% 33.13/9.65 |
% 33.13/9.65 | Instantiating formula (59) with all_48_0_13 yields:
% 33.13/9.65 | (129) ~ ra_Px8(ex_11_0_1, all_48_0_13)
% 33.13/9.65 |
% 33.13/9.65 | From (76) and (128) follows:
% 33.13/9.65 | (130) ra_Px8(all_0_0_0, all_48_0_13)
% 33.13/9.65 |
% 33.13/9.65 | From (48) and (129) follows:
% 33.13/9.65 | (131) ~ ra_Px8(all_0_0_0, all_48_0_13)
% 33.13/9.65 |
% 33.13/9.65 | Using (130) and (131) yields:
% 33.13/9.65 | (58) $false
% 33.13/9.65 |
% 33.13/9.65 |-The branch is then unsatisfiable
% 33.13/9.65 % SZS output end Proof for theBenchmark
% 33.13/9.65
% 33.13/9.65 9047ms
%------------------------------------------------------------------------------