TSTP Solution File: KRS172+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KRS172+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 02:56:47 EDT 2022
% Result : Theorem 3.89s 1.66s
% Output : Proof 5.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KRS172+1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 7 09:06:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.60/0.61 ____ _
% 0.60/0.61 ___ / __ \_____(_)___ ________ __________
% 0.60/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.60/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.60/0.61
% 0.60/0.61 A Theorem Prover for First-Order Logic
% 0.60/0.61 (ePrincess v.1.0)
% 0.60/0.61
% 0.60/0.61 (c) Philipp Rümmer, 2009-2015
% 0.60/0.61 (c) Peter Backeman, 2014-2015
% 0.60/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.60/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.60/0.61 Bug reports to peter@backeman.se
% 0.60/0.61
% 0.60/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.60/0.61
% 0.60/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.58/0.98 Prover 0: Preprocessing ...
% 1.71/1.10 Prover 0: Warning: ignoring some quantifiers
% 1.71/1.12 Prover 0: Constructing countermodel ...
% 2.16/1.21 Prover 0: gave up
% 2.16/1.21 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.16/1.24 Prover 1: Preprocessing ...
% 2.69/1.37 Prover 1: Constructing countermodel ...
% 2.99/1.47 Prover 1: gave up
% 2.99/1.47 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.23/1.49 Prover 2: Preprocessing ...
% 3.23/1.57 Prover 2: Warning: ignoring some quantifiers
% 3.64/1.57 Prover 2: Constructing countermodel ...
% 3.89/1.65 Prover 2: proved (188ms)
% 3.89/1.66
% 3.89/1.66 No countermodel exists, formula is valid
% 3.89/1.66 % SZS status Theorem for theBenchmark
% 3.89/1.66
% 3.89/1.66 Generating proof ... Warning: ignoring some quantifiers
% 5.17/1.91 found it (size 53)
% 5.17/1.91
% 5.17/1.91 % SZS output start Proof for theBenchmark
% 5.17/1.91 Assumed formulas after preprocessing and simplification:
% 5.17/1.92 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (cowlThing(iv) = 0 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (rq(v7, v6) = v5) | ~ (rq(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (rp(v7, v6) = v5) | ~ (rp(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (rq(v4, v6) = 0) | ~ (rq(v4, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (rp(v4, v6) = 0) | ~ (rp(v4, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (rq(v5, v4) = v6) | ~ (rq(v5, v4) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (rq(v4, v5) = v6) | ~ (rq(v4, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (rp(v5, v4) = v6) | ~ (rp(v5, v4) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (rp(v4, v5) = v6) | ~ (rp(v4, v5) = 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 | ~ (cd(v6) = v5) | ~ (cd(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 | ~ (xsd_integer(v4) = v5) | xsd_string(v4) = 0) & ! [v4] : ! [v5] : (v5 = 0 | ~ (rq(v4, iv) = v5) | ? [v6] : ( ~ (v6 = 0) & cd(v4) = v6)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (rp(v4, iv) = v5) | ? [v6] : ( ~ (v6 = 0) & cd(v4) = v6)) & ! [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 | ~ (cd(v4) = v5) | ~ (cd(v4) = 0)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (cd(v4) = v5) | ? [v6] : ( ~ (v6 = 0) & rq(v4, iv) = v6)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (cd(v4) = v5) | ? [v6] : ( ~ (v6 = 0) & rp(v4, iv) = v6)) & ! [v4] : ! [v5] : ( ~ (rq(v4, v5) = 0) | cd(v4) = 0) & ! [v4] : ! [v5] : ( ~ (rp(v4, v5) = 0) | cd(v4) = 0) & ! [v4] : ( ~ (xsd_string(v4) = 0) | ? [v5] : ( ~ (v5 = 0) & xsd_integer(v4) = v5)) & ! [v4] : ( ~ (xsd_integer(v4) = 0) | ? [v5] : ( ~ (v5 = 0) & xsd_string(v4) = v5)) & ! [v4] : ( ~ (rq(v4, iv) = 0) | cd(v4) = 0) & ! [v4] : ( ~ (rp(v4, iv) = 0) | cd(v4) = 0) & ! [v4] : ~ (cowlNothing(v4) = 0) & ! [v4] : ( ~ (cd(v4) = 0) | rq(v4, iv) = 0) & ! [v4] : ( ~ (cd(v4) = 0) | rp(v4, iv) = 0) & ? [v4] : ? [v5] : ? [v6] : rq(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : rp(v5, v4) = v6 & ? [v4] : ? [v5] : xsd_string(v4) = v5 & ? [v4] : ? [v5] : xsd_integer(v4) = v5 & ? [v4] : ? [v5] : cowlThing(v4) = v5 & ? [v4] : ? [v5] : cowlNothing(v4) = v5 & ? [v4] : ? [v5] : cd(v4) = v5 & ((v2 = 0 & cowlNothing(v0) = 0) | ( ~ (v1 = 0) & cowlThing(v0) = v1) | (xsd_string(v0) = v1 & xsd_integer(v0) = v2 & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & ~ (v1 = 0)))) | (rq(v0, v1) = v2 & rp(v0, v1) = v3 & ((v3 = 0 & ~ (v2 = 0)) | (v2 = 0 & ~ (v3 = 0))))))
% 5.17/1.95 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 5.17/1.95 | (1) cowlThing(iv) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rq(v3, v2) = v1) | ~ (rq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (rq(v0, v2) = 0) | ~ (rq(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (rp(v0, v2) = 0) | ~ (rp(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rq(v1, v0) = v2) | ~ (rq(v1, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rq(v0, v1) = v2) | ~ (rq(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v1, v0) = v2) | ~ (rp(v1, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v0, v1) = v2) | ~ (rp(v0, v1) = 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 | ~ (cd(v2) = v1) | ~ (cd(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 | ~ (xsd_integer(v0) = v1) | xsd_string(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (rq(v0, iv) = v1) | ? [v2] : ( ~ (v2 = 0) & cd(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (rp(v0, iv) = v1) | ? [v2] : ( ~ (v2 = 0) & cd(v0) = v2)) & ! [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 | ~ (cd(v0) = v1) | ~ (cd(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cd(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & rq(v0, iv) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cd(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & rp(v0, iv) = v2)) & ! [v0] : ! [v1] : ( ~ (rq(v0, v1) = 0) | cd(v0) = 0) & ! [v0] : ! [v1] : ( ~ (rp(v0, v1) = 0) | cd(v0) = 0) & ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) & ! [v0] : ( ~ (xsd_integer(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_string(v0) = v1)) & ! [v0] : ( ~ (rq(v0, iv) = 0) | cd(v0) = 0) & ! [v0] : ( ~ (rp(v0, iv) = 0) | cd(v0) = 0) & ! [v0] : ~ (cowlNothing(v0) = 0) & ! [v0] : ( ~ (cd(v0) = 0) | rq(v0, iv) = 0) & ! [v0] : ( ~ (cd(v0) = 0) | rp(v0, iv) = 0) & ? [v0] : ? [v1] : ? [v2] : rq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : rp(v1, v0) = v2 & ? [v0] : ? [v1] : xsd_string(v0) = v1 & ? [v0] : ? [v1] : xsd_integer(v0) = v1 & ? [v0] : ? [v1] : cowlThing(v0) = v1 & ? [v0] : ? [v1] : cowlNothing(v0) = v1 & ? [v0] : ? [v1] : cd(v0) = v1 & ((all_0_1_1 = 0 & cowlNothing(all_0_3_3) = 0) | ( ~ (all_0_2_2 = 0) & cowlThing(all_0_3_3) = all_0_2_2) | (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)))) | (rq(all_0_3_3, all_0_2_2) = all_0_1_1 & rp(all_0_3_3, all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)))))
% 5.17/1.96 |
% 5.17/1.96 | Applying alpha-rule on (1) yields:
% 5.17/1.96 | (2) (all_0_1_1 = 0 & cowlNothing(all_0_3_3) = 0) | ( ~ (all_0_2_2 = 0) & cowlThing(all_0_3_3) = all_0_2_2) | (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)))) | (rq(all_0_3_3, all_0_2_2) = all_0_1_1 & rp(all_0_3_3, all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0))))
% 5.17/1.96 | (3) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | xsd_string(v0) = 0)
% 5.17/1.96 | (4) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0)
% 5.17/1.96 | (5) ? [v0] : ? [v1] : cd(v0) = v1
% 5.17/1.96 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0))
% 5.17/1.96 | (7) ? [v0] : ? [v1] : cowlThing(v0) = v1
% 5.17/1.96 | (8) ? [v0] : ? [v1] : xsd_string(v0) = v1
% 5.17/1.96 | (9) ! [v0] : ( ~ (cd(v0) = 0) | rp(v0, iv) = 0)
% 5.17/1.96 | (10) ! [v0] : ( ~ (rp(v0, iv) = 0) | cd(v0) = 0)
% 5.17/1.96 | (11) ? [v0] : ? [v1] : xsd_integer(v0) = v1
% 5.17/1.97 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v0, v1) = v2) | ~ (rp(v0, v1) = 0))
% 5.17/1.97 | (13) ? [v0] : ? [v1] : ? [v2] : rq(v1, v0) = v2
% 5.17/1.97 | (14) ? [v0] : ? [v1] : ? [v2] : rp(v1, v0) = v2
% 5.17/1.97 | (15) ! [v0] : ! [v1] : ( ~ (rp(v0, v1) = 0) | cd(v0) = 0)
% 5.17/1.97 | (16) ! [v0] : ( ~ (cd(v0) = 0) | rq(v0, iv) = 0)
% 5.17/1.97 | (17) ! [v0] : ( ~ (rq(v0, iv) = 0) | cd(v0) = 0)
% 5.17/1.97 | (18) ! [v0] : ! [v1] : (v1 = 0 | ~ (rq(v0, iv) = v1) | ? [v2] : ( ~ (v2 = 0) & cd(v0) = v2))
% 5.17/1.97 | (19) ! [v0] : ! [v1] : (v1 = 0 | ~ (cd(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & rp(v0, iv) = v2))
% 5.17/1.97 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v1, v0) = v2) | ~ (rp(v1, v0) = 0))
% 5.17/1.97 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (rq(v0, v2) = 0) | ~ (rq(v0, v1) = 0))
% 5.17/1.97 | (22) ! [v0] : ! [v1] : (v1 = 0 | ~ (cd(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & rq(v0, iv) = v2))
% 5.17/1.97 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rq(v3, v2) = v1) | ~ (rq(v3, v2) = v0))
% 5.17/1.97 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0))
% 5.17/1.97 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cd(v2) = v1) | ~ (cd(v2) = v0))
% 5.17/1.97 | (26) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1))
% 5.17/1.97 | (27) ! [v0] : ( ~ (xsd_integer(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_string(v0) = v1))
% 5.17/1.97 | (28) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 5.17/1.97 | (29) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ (xsd_integer(v0) = 0))
% 5.17/1.97 | (30) ! [v0] : ! [v1] : ( ~ (rq(v0, v1) = 0) | cd(v0) = 0)
% 5.17/1.97 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0))
% 5.17/1.97 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0))
% 5.17/1.97 | (33) ! [v0] : ~ (cowlNothing(v0) = 0)
% 5.17/1.97 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rq(v0, v1) = v2) | ~ (rq(v0, v1) = 0))
% 5.17/1.97 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0))
% 5.17/1.97 | (36) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rq(v1, v0) = v2) | ~ (rq(v1, v0) = 0))
% 5.17/1.97 | (37) ! [v0] : ! [v1] : (v1 = 0 | ~ (rp(v0, iv) = v1) | ? [v2] : ( ~ (v2 = 0) & cd(v0) = v2))
% 5.17/1.97 | (38) ? [v0] : ? [v1] : cowlNothing(v0) = v1
% 5.17/1.97 | (39) cowlThing(iv) = 0
% 5.17/1.97 | (40) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ (xsd_string(v0) = 0))
% 5.17/1.97 | (41) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlNothing(v0) = v1) | ~ (cowlNothing(v0) = 0))
% 5.17/1.97 | (42) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (rp(v0, v2) = 0) | ~ (rp(v0, v1) = 0))
% 5.17/1.98 | (43) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ (cowlThing(v0) = 0))
% 5.17/1.98 | (44) ! [v0] : ! [v1] : (v1 = 0 | ~ (cd(v0) = v1) | ~ (cd(v0) = 0))
% 5.17/1.98 |
% 5.17/1.98 +-Applying beta-rule and splitting (2), into two cases.
% 5.17/1.98 |-Branch one:
% 5.17/1.98 | (45) (all_0_1_1 = 0 & cowlNothing(all_0_3_3) = 0) | ( ~ (all_0_2_2 = 0) & cowlThing(all_0_3_3) = all_0_2_2) | (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))))
% 5.17/1.98 |
% 5.17/1.98 +-Applying beta-rule and splitting (45), into two cases.
% 5.17/1.98 |-Branch one:
% 5.17/1.98 | (46) (all_0_1_1 = 0 & cowlNothing(all_0_3_3) = 0) | ( ~ (all_0_2_2 = 0) & cowlThing(all_0_3_3) = all_0_2_2)
% 5.17/1.98 |
% 5.17/1.98 +-Applying beta-rule and splitting (46), into two cases.
% 5.17/1.98 |-Branch one:
% 5.17/1.98 | (47) all_0_1_1 = 0 & cowlNothing(all_0_3_3) = 0
% 5.17/1.98 |
% 5.17/1.98 | Applying alpha-rule on (47) yields:
% 5.17/1.98 | (48) all_0_1_1 = 0
% 5.17/1.98 | (49) cowlNothing(all_0_3_3) = 0
% 5.17/1.98 |
% 5.17/1.98 | Instantiating formula (33) with all_0_3_3 and discharging atoms cowlNothing(all_0_3_3) = 0, yields:
% 5.17/1.98 | (50) $false
% 5.17/1.98 |
% 5.17/1.98 |-The branch is then unsatisfiable
% 5.17/1.98 |-Branch two:
% 5.17/1.98 | (51) ~ (all_0_2_2 = 0) & cowlThing(all_0_3_3) = all_0_2_2
% 5.17/1.98 |
% 5.17/1.98 | Applying alpha-rule on (51) yields:
% 5.17/1.98 | (52) ~ (all_0_2_2 = 0)
% 5.17/1.98 | (53) cowlThing(all_0_3_3) = all_0_2_2
% 5.17/1.98 |
% 5.17/1.98 | Instantiating formula (26) with all_0_2_2, all_0_3_3 and discharging atoms cowlThing(all_0_3_3) = all_0_2_2, yields:
% 5.17/1.98 | (54) all_0_2_2 = 0
% 5.17/1.98 |
% 5.17/1.98 | Equations (54) can reduce 52 to:
% 5.17/1.98 | (55) $false
% 5.17/1.98 |
% 5.17/1.98 |-The branch is then unsatisfiable
% 5.17/1.98 |-Branch two:
% 5.17/1.98 | (56) 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)))
% 5.17/1.98 |
% 5.17/1.98 | Applying alpha-rule on (56) yields:
% 5.17/1.98 | (57) xsd_string(all_0_3_3) = all_0_2_2
% 5.17/1.98 | (58) xsd_integer(all_0_3_3) = all_0_1_1
% 5.17/1.98 | (59) (all_0_1_1 = 0 & all_0_2_2 = 0) | ( ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0))
% 5.17/1.98 |
% 5.17/1.98 | Instantiating formula (3) with all_0_1_1, all_0_3_3 and discharging atoms xsd_integer(all_0_3_3) = all_0_1_1, yields:
% 5.17/1.98 | (60) all_0_1_1 = 0 | xsd_string(all_0_3_3) = 0
% 5.17/1.98 |
% 5.17/1.98 +-Applying beta-rule and splitting (59), into two cases.
% 5.17/1.98 |-Branch one:
% 5.17/1.98 | (61) all_0_1_1 = 0 & all_0_2_2 = 0
% 5.17/1.98 |
% 5.17/1.98 | Applying alpha-rule on (61) yields:
% 5.17/1.98 | (48) all_0_1_1 = 0
% 5.17/1.98 | (54) all_0_2_2 = 0
% 5.17/1.98 |
% 5.17/1.98 | From (54) and (57) follows:
% 5.17/1.98 | (64) xsd_string(all_0_3_3) = 0
% 5.17/1.98 |
% 5.17/1.98 | From (48) and (58) follows:
% 5.17/1.98 | (65) xsd_integer(all_0_3_3) = 0
% 5.17/1.98 |
% 5.17/1.98 | Instantiating formula (27) with all_0_3_3 and discharging atoms xsd_integer(all_0_3_3) = 0, yields:
% 5.17/1.98 | (66) ? [v0] : ( ~ (v0 = 0) & xsd_string(all_0_3_3) = v0)
% 5.17/1.99 |
% 5.17/1.99 | Instantiating (66) with all_40_0_20 yields:
% 5.17/1.99 | (67) ~ (all_40_0_20 = 0) & xsd_string(all_0_3_3) = all_40_0_20
% 5.17/1.99 |
% 5.17/1.99 | Applying alpha-rule on (67) yields:
% 5.17/1.99 | (68) ~ (all_40_0_20 = 0)
% 5.17/1.99 | (69) xsd_string(all_0_3_3) = all_40_0_20
% 5.17/1.99 |
% 5.17/1.99 | Instantiating formula (40) with all_40_0_20, all_0_3_3 and discharging atoms xsd_string(all_0_3_3) = all_40_0_20, xsd_string(all_0_3_3) = 0, yields:
% 5.17/1.99 | (70) all_40_0_20 = 0
% 5.17/1.99 |
% 5.17/1.99 | Equations (70) can reduce 68 to:
% 5.17/1.99 | (55) $false
% 5.17/1.99 |
% 5.17/1.99 |-The branch is then unsatisfiable
% 5.17/1.99 |-Branch two:
% 5.17/1.99 | (72) ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0)
% 5.17/1.99 |
% 5.17/1.99 | Applying alpha-rule on (72) yields:
% 5.17/1.99 | (73) ~ (all_0_1_1 = 0)
% 5.17/1.99 | (52) ~ (all_0_2_2 = 0)
% 5.17/1.99 |
% 5.17/1.99 +-Applying beta-rule and splitting (60), into two cases.
% 5.17/1.99 |-Branch one:
% 5.17/1.99 | (64) xsd_string(all_0_3_3) = 0
% 5.17/1.99 |
% 5.17/1.99 | Instantiating formula (35) with all_0_3_3, 0, all_0_2_2 and discharging atoms xsd_string(all_0_3_3) = all_0_2_2, xsd_string(all_0_3_3) = 0, yields:
% 5.17/1.99 | (54) all_0_2_2 = 0
% 5.17/1.99 |
% 5.17/1.99 | Equations (54) can reduce 52 to:
% 5.17/1.99 | (55) $false
% 5.17/1.99 |
% 5.17/1.99 |-The branch is then unsatisfiable
% 5.17/1.99 |-Branch two:
% 5.17/1.99 | (78) ~ (xsd_string(all_0_3_3) = 0)
% 5.17/1.99 | (48) all_0_1_1 = 0
% 5.17/1.99 |
% 5.17/1.99 | Equations (48) can reduce 73 to:
% 5.17/1.99 | (55) $false
% 5.17/1.99 |
% 5.17/1.99 |-The branch is then unsatisfiable
% 5.17/1.99 |-Branch two:
% 5.17/1.99 | (81) rq(all_0_3_3, all_0_2_2) = all_0_1_1 & rp(all_0_3_3, all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)))
% 5.17/1.99 |
% 5.17/1.99 | Applying alpha-rule on (81) yields:
% 5.17/1.99 | (82) rq(all_0_3_3, all_0_2_2) = all_0_1_1
% 5.17/1.99 | (83) rp(all_0_3_3, all_0_2_2) = all_0_0_0
% 5.17/1.99 | (84) (all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0))
% 5.17/1.99 |
% 5.17/1.99 +-Applying beta-rule and splitting (84), into two cases.
% 5.17/1.99 |-Branch one:
% 5.17/1.99 | (85) all_0_0_0 = 0 & ~ (all_0_1_1 = 0)
% 5.17/1.99 |
% 5.17/1.99 | Applying alpha-rule on (85) yields:
% 5.17/1.99 | (86) all_0_0_0 = 0
% 5.17/1.99 | (73) ~ (all_0_1_1 = 0)
% 5.17/1.99 |
% 5.17/1.99 | From (86) and (83) follows:
% 5.17/1.99 | (88) rp(all_0_3_3, all_0_2_2) = 0
% 5.17/1.99 |
% 5.17/1.99 | Instantiating formula (15) with all_0_2_2, all_0_3_3 and discharging atoms rp(all_0_3_3, all_0_2_2) = 0, yields:
% 5.17/1.99 | (89) cd(all_0_3_3) = 0
% 5.17/1.99 |
% 5.17/1.99 | Instantiating formula (16) with all_0_3_3 and discharging atoms cd(all_0_3_3) = 0, yields:
% 5.17/1.99 | (90) rq(all_0_3_3, iv) = 0
% 5.17/1.99 |
% 5.17/1.99 | Instantiating formula (9) with all_0_3_3 and discharging atoms cd(all_0_3_3) = 0, yields:
% 5.17/1.99 | (91) rp(all_0_3_3, iv) = 0
% 5.17/1.99 |
% 5.17/1.99 | Instantiating formula (42) with iv, all_0_2_2, all_0_3_3 and discharging atoms rp(all_0_3_3, all_0_2_2) = 0, rp(all_0_3_3, iv) = 0, yields:
% 5.17/1.99 | (92) all_0_2_2 = iv
% 5.17/1.99 |
% 5.17/1.99 | From (92) and (82) follows:
% 5.17/1.99 | (93) rq(all_0_3_3, iv) = all_0_1_1
% 5.17/1.99 |
% 5.17/1.99 | Instantiating formula (36) with all_0_1_1, all_0_3_3, iv and discharging atoms rq(all_0_3_3, iv) = all_0_1_1, rq(all_0_3_3, iv) = 0, yields:
% 5.17/1.99 | (48) all_0_1_1 = 0
% 5.17/1.99 |
% 5.17/1.99 | Equations (48) can reduce 73 to:
% 5.17/1.99 | (55) $false
% 5.17/1.99 |
% 5.17/1.99 |-The branch is then unsatisfiable
% 5.17/1.99 |-Branch two:
% 5.17/1.99 | (96) all_0_1_1 = 0 & ~ (all_0_0_0 = 0)
% 5.17/1.99 |
% 5.17/1.99 | Applying alpha-rule on (96) yields:
% 5.17/1.99 | (48) all_0_1_1 = 0
% 5.17/1.99 | (98) ~ (all_0_0_0 = 0)
% 5.17/1.99 |
% 5.17/1.99 | From (48) and (82) follows:
% 5.17/1.99 | (99) rq(all_0_3_3, all_0_2_2) = 0
% 5.17/1.99 |
% 5.17/1.99 | Instantiating formula (30) with all_0_2_2, all_0_3_3 and discharging atoms rq(all_0_3_3, all_0_2_2) = 0, yields:
% 5.17/1.99 | (89) cd(all_0_3_3) = 0
% 5.17/1.99 |
% 5.17/2.00 | Instantiating formula (16) with all_0_3_3 and discharging atoms cd(all_0_3_3) = 0, yields:
% 5.17/2.00 | (90) rq(all_0_3_3, iv) = 0
% 5.17/2.00 |
% 5.17/2.00 | Instantiating formula (9) with all_0_3_3 and discharging atoms cd(all_0_3_3) = 0, yields:
% 5.17/2.00 | (91) rp(all_0_3_3, iv) = 0
% 5.17/2.00 |
% 5.17/2.00 | Instantiating formula (21) with iv, all_0_2_2, all_0_3_3 and discharging atoms rq(all_0_3_3, all_0_2_2) = 0, rq(all_0_3_3, iv) = 0, yields:
% 5.17/2.00 | (92) all_0_2_2 = iv
% 5.17/2.00 |
% 5.17/2.00 | From (92) and (83) follows:
% 5.17/2.00 | (104) rp(all_0_3_3, iv) = all_0_0_0
% 5.17/2.00 |
% 5.17/2.00 | Instantiating formula (20) with all_0_0_0, all_0_3_3, iv and discharging atoms rp(all_0_3_3, iv) = all_0_0_0, rp(all_0_3_3, iv) = 0, yields:
% 5.17/2.00 | (86) all_0_0_0 = 0
% 5.17/2.00 |
% 5.17/2.00 | Equations (86) can reduce 98 to:
% 5.17/2.00 | (55) $false
% 5.17/2.00 |
% 5.17/2.00 |-The branch is then unsatisfiable
% 5.17/2.00 % SZS output end Proof for theBenchmark
% 5.17/2.00
% 5.17/2.00 1368ms
%------------------------------------------------------------------------------