TSTP Solution File: KRS063+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KRS063+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 02:56:27 EDT 2022
% Result : Unsatisfiable 4.65s 1.79s
% Output : Proof 5.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS063+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n029.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 14:35:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.52/0.59 ____ _
% 0.52/0.59 ___ / __ \_____(_)___ ________ __________
% 0.52/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.52/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.52/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.52/0.59
% 0.52/0.59 A Theorem Prover for First-Order Logic
% 0.52/0.59 (ePrincess v.1.0)
% 0.52/0.59
% 0.52/0.59 (c) Philipp Rümmer, 2009-2015
% 0.52/0.59 (c) Peter Backeman, 2014-2015
% 0.52/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.52/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.52/0.59 Bug reports to peter@backeman.se
% 0.52/0.59
% 0.52/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.52/0.59
% 0.52/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.54/0.96 Prover 0: Preprocessing ...
% 1.92/1.09 Prover 0: Warning: ignoring some quantifiers
% 1.92/1.10 Prover 0: Constructing countermodel ...
% 2.21/1.21 Prover 0: gave up
% 2.21/1.22 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.53/1.26 Prover 1: Preprocessing ...
% 2.90/1.44 Prover 1: Constructing countermodel ...
% 3.69/1.56 Prover 1: gave up
% 3.69/1.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.69/1.59 Prover 2: Preprocessing ...
% 4.22/1.70 Prover 2: Warning: ignoring some quantifiers
% 4.22/1.70 Prover 2: Constructing countermodel ...
% 4.65/1.79 Prover 2: proved (229ms)
% 4.65/1.79
% 4.65/1.79 No countermodel exists, formula is valid
% 4.65/1.79 % SZS status Unsatisfiable for theBenchmark
% 4.65/1.79
% 4.65/1.79 Generating proof ... Warning: ignoring some quantifiers
% 5.54/1.97 found it (size 19)
% 5.54/1.97
% 5.54/1.97 % SZS output start Proof for theBenchmark
% 5.54/1.97 Assumed formulas after preprocessing and simplification:
% 5.54/1.98 | (0) ? [v0] : ( ~ (v0 = 0) & rhasEuroMP(iUK, iKinnock) = 0 & cPerson(iKinnock) = 0 & cEuropeanCountry(iUK) = 0 & cEuropeanCountry(iFR) = 0 & cEuropeanCountry(iES) = 0 & cEuropeanCountry(iNL) = 0 & cEuropeanCountry(iBE) = 0 & cEuropeanCountry(iPT) = 0 & cEuroMP(iKinnock) = v0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (risEuroMPFrom(v4, v3) = v2) | ~ (risEuroMPFrom(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (rhasEuroMP(v4, v3) = v2) | ~ (rhasEuroMP(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (risEuroMPFrom(v2, v1) = v3) | ~ (risEuroMPFrom(v2, v1) = 0)) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (risEuroMPFrom(v1, v2) = v3) | ~ (risEuroMPFrom(v1, v2) = 0)) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (risEuroMPFrom(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & rhasEuroMP(v2, v1) = v4)) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (rhasEuroMP(v2, v1) = v3) | ~ (rhasEuroMP(v2, v1) = 0)) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (rhasEuroMP(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & risEuroMPFrom(v1, v2) = v4)) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (rhasEuroMP(v1, v2) = v3) | ~ (rhasEuroMP(v1, v2) = 0)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (xsd_string(v3) = v2) | ~ (xsd_string(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (xsd_integer(v3) = v2) | ~ (xsd_integer(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (cowlThing(v3) = v2) | ~ (cowlThing(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (cowlNothing(v3) = v2) | ~ (cowlNothing(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (cPerson(v3) = v2) | ~ (cPerson(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (cEuropeanCountry(v3) = v2) | ~ (cEuropeanCountry(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (cEuroMP(v3) = v2) | ~ (cEuroMP(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (cEUCountry(v3) = v2) | ~ (cEUCountry(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (risEuroMPFrom(v1, v3) = 0) | ~ (cEuroMP(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & cowlThing(v3) = v4)) & ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (cowlThing(v3) = 0) | ~ (cEuroMP(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & risEuroMPFrom(v1, v3) = v4)) & ! [v1] : ! [v2] : (v2 = 0 | ~ (xsd_string(v1) = v2) | ~ (xsd_string(v1) = 0)) & ! [v1] : ! [v2] : (v2 = 0 | ~ (xsd_string(v1) = v2) | xsd_integer(v1) = 0) & ! [v1] : ! [v2] : (v2 = 0 | ~ (xsd_integer(v1) = v2) | ~ (xsd_integer(v1) = 0)) & ! [v1] : ! [v2] : (v2 = 0 | ~ (xsd_integer(v1) = v2) | xsd_string(v1) = 0) & ! [v1] : ! [v2] : (v2 = 0 | ~ (cowlThing(v1) = v2) | ~ (cowlThing(v1) = 0)) & ! [v1] : ! [v2] : (v2 = 0 | ~ (cowlThing(v1) = v2)) & ! [v1] : ! [v2] : (v2 = 0 | ~ (cowlNothing(v1) = v2) | ~ (cowlNothing(v1) = 0)) & ! [v1] : ! [v2] : (v2 = 0 | ~ (cPerson(v1) = v2) | ~ (cPerson(v1) = 0)) & ! [v1] : ! [v2] : (v2 = 0 | ~ (cEuropeanCountry(v1) = v2) | ~ (cEuropeanCountry(v1) = 0)) & ! [v1] : ! [v2] : (v2 = 0 | ~ (cEuroMP(v1) = v2) | ~ (cEuroMP(v1) = 0)) & ! [v1] : ! [v2] : (v2 = 0 | ~ (cEUCountry(v1) = v2) | ~ (cEUCountry(v1) = 0)) & ! [v1] : ! [v2] : ( ~ (risEuroMPFrom(v1, v2) = 0) | rhasEuroMP(v2, v1) = 0) & ! [v1] : ! [v2] : ( ~ (rhasEuroMP(v2, v1) = 0) | risEuroMPFrom(v1, v2) = 0) & ! [v1] : ! [v2] : ( ~ (rhasEuroMP(v1, v2) = 0) | cEUCountry(v1) = 0) & ! [v1] : (v1 = iUK | v1 = iFR | v1 = iES | v1 = iNL | v1 = iBE | v1 = iPT | ~ (cEUCountry(v1) = 0)) & ! [v1] : (v1 = 0 | ~ (cEUCountry(iUK) = v1)) & ! [v1] : (v1 = 0 | ~ (cEUCountry(iFR) = v1)) & ! [v1] : (v1 = 0 | ~ (cEUCountry(iES) = v1)) & ! [v1] : (v1 = 0 | ~ (cEUCountry(iNL) = v1)) & ! [v1] : (v1 = 0 | ~ (cEUCountry(iBE) = v1)) & ! [v1] : (v1 = 0 | ~ (cEUCountry(iPT) = v1)) & ! [v1] : ( ~ (xsd_string(v1) = 0) | ? [v2] : ( ~ (v2 = 0) & xsd_integer(v1) = v2)) & ! [v1] : ( ~ (xsd_integer(v1) = 0) | ? [v2] : ( ~ (v2 = 0) & xsd_string(v1) = v2)) & ! [v1] : ~ (cowlNothing(v1) = 0) & ! [v1] : ( ~ (cEuroMP(v1) = 0) | ? [v2] : (risEuroMPFrom(v1, v2) = 0 & cowlThing(v2) = 0)) & ? [v1] : ? [v2] : ? [v3] : risEuroMPFrom(v2, v1) = v3 & ? [v1] : ? [v2] : ? [v3] : rhasEuroMP(v2, v1) = v3 & ? [v1] : ? [v2] : xsd_string(v1) = v2 & ? [v1] : ? [v2] : xsd_integer(v1) = v2 & ? [v1] : ? [v2] : cowlThing(v1) = v2 & ? [v1] : ? [v2] : cowlNothing(v1) = v2 & ? [v1] : ? [v2] : cPerson(v1) = v2 & ? [v1] : ? [v2] : cEuropeanCountry(v1) = v2 & ? [v1] : ? [v2] : cEuroMP(v1) = v2 & ? [v1] : ? [v2] : cEUCountry(v1) = v2)
% 5.54/2.01 | Instantiating (0) with all_0_0_0 yields:
% 5.54/2.01 | (1) ~ (all_0_0_0 = 0) & rhasEuroMP(iUK, iKinnock) = 0 & cPerson(iKinnock) = 0 & cEuropeanCountry(iUK) = 0 & cEuropeanCountry(iFR) = 0 & cEuropeanCountry(iES) = 0 & cEuropeanCountry(iNL) = 0 & cEuropeanCountry(iBE) = 0 & cEuropeanCountry(iPT) = 0 & cEuroMP(iKinnock) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (risEuroMPFrom(v3, v2) = v1) | ~ (risEuroMPFrom(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rhasEuroMP(v3, v2) = v1) | ~ (rhasEuroMP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (risEuroMPFrom(v1, v0) = v2) | ~ (risEuroMPFrom(v1, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (risEuroMPFrom(v0, v1) = v2) | ~ (risEuroMPFrom(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (risEuroMPFrom(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & rhasEuroMP(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rhasEuroMP(v1, v0) = v2) | ~ (rhasEuroMP(v1, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rhasEuroMP(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & risEuroMPFrom(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rhasEuroMP(v0, v1) = v2) | ~ (rhasEuroMP(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 | ~ (cPerson(v2) = v1) | ~ (cPerson(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cEuropeanCountry(v2) = v1) | ~ (cEuropeanCountry(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cEuroMP(v2) = v1) | ~ (cEuroMP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cEUCountry(v2) = v1) | ~ (cEUCountry(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (risEuroMPFrom(v0, v2) = 0) | ~ (cEuroMP(v0) = v1) | ? [v3] : ( ~ (v3 = 0) & cowlThing(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cowlThing(v2) = 0) | ~ (cEuroMP(v0) = v1) | ? [v3] : ( ~ (v3 = 0) & risEuroMPFrom(v0, v2) = v3)) & ! [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 | ~ (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 | ~ (cPerson(v0) = v1) | ~ (cPerson(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cEuropeanCountry(v0) = v1) | ~ (cEuropeanCountry(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cEuroMP(v0) = v1) | ~ (cEuroMP(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cEUCountry(v0) = v1) | ~ (cEUCountry(v0) = 0)) & ! [v0] : ! [v1] : ( ~ (risEuroMPFrom(v0, v1) = 0) | rhasEuroMP(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (rhasEuroMP(v1, v0) = 0) | risEuroMPFrom(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (rhasEuroMP(v0, v1) = 0) | cEUCountry(v0) = 0) & ! [v0] : (v0 = iUK | v0 = iFR | v0 = iES | v0 = iNL | v0 = iBE | v0 = iPT | ~ (cEUCountry(v0) = 0)) & ! [v0] : (v0 = 0 | ~ (cEUCountry(iUK) = v0)) & ! [v0] : (v0 = 0 | ~ (cEUCountry(iFR) = v0)) & ! [v0] : (v0 = 0 | ~ (cEUCountry(iES) = v0)) & ! [v0] : (v0 = 0 | ~ (cEUCountry(iNL) = v0)) & ! [v0] : (v0 = 0 | ~ (cEUCountry(iBE) = v0)) & ! [v0] : (v0 = 0 | ~ (cEUCountry(iPT) = v0)) & ! [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] : ~ (cowlNothing(v0) = 0) & ! [v0] : ( ~ (cEuroMP(v0) = 0) | ? [v1] : (risEuroMPFrom(v0, v1) = 0 & cowlThing(v1) = 0)) & ? [v0] : ? [v1] : ? [v2] : risEuroMPFrom(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : rhasEuroMP(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] : cPerson(v0) = v1 & ? [v0] : ? [v1] : cEuropeanCountry(v0) = v1 & ? [v0] : ? [v1] : cEuroMP(v0) = v1 & ? [v0] : ? [v1] : cEUCountry(v0) = v1
% 5.54/2.02 |
% 5.54/2.02 | Applying alpha-rule on (1) yields:
% 5.54/2.02 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0))
% 5.54/2.02 | (3) rhasEuroMP(iUK, iKinnock) = 0
% 5.54/2.02 | (4) cEuroMP(iKinnock) = all_0_0_0
% 5.54/2.02 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | xsd_string(v0) = 0)
% 5.54/2.02 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0)
% 5.54/2.02 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cEUCountry(v2) = v1) | ~ (cEUCountry(v2) = v0))
% 5.54/2.02 | (8) ? [v0] : ? [v1] : cEUCountry(v0) = v1
% 5.54/2.02 | (9) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1))
% 5.54/2.02 | (10) cPerson(iKinnock) = 0
% 5.54/2.02 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (risEuroMPFrom(v1, v0) = v2) | ~ (risEuroMPFrom(v1, v0) = 0))
% 5.54/2.02 | (12) ! [v0] : (v0 = 0 | ~ (cEUCountry(iUK) = v0))
% 5.54/2.02 | (13) ? [v0] : ? [v1] : xsd_integer(v0) = v1
% 5.54/2.02 | (14) ? [v0] : ? [v1] : ? [v2] : rhasEuroMP(v1, v0) = v2
% 5.54/2.02 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0))
% 5.54/2.02 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rhasEuroMP(v0, v1) = v2) | ~ (rhasEuroMP(v0, v1) = 0))
% 5.54/2.02 | (17) ! [v0] : ! [v1] : (v1 = 0 | ~ (cEUCountry(v0) = v1) | ~ (cEUCountry(v0) = 0))
% 5.54/2.02 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cEuroMP(v2) = v1) | ~ (cEuroMP(v2) = v0))
% 5.54/2.02 | (19) ? [v0] : ? [v1] : cEuropeanCountry(v0) = v1
% 5.54/2.02 | (20) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ (xsd_integer(v0) = 0))
% 5.54/2.02 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (risEuroMPFrom(v0, v2) = 0) | ~ (cEuroMP(v0) = v1) | ? [v3] : ( ~ (v3 = 0) & cowlThing(v2) = v3))
% 5.54/2.02 | (22) cEuropeanCountry(iES) = 0
% 5.54/2.02 | (23) ! [v0] : ~ (cowlNothing(v0) = 0)
% 5.54/2.02 | (24) ? [v0] : ? [v1] : cEuroMP(v0) = v1
% 5.54/2.02 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rhasEuroMP(v3, v2) = v1) | ~ (rhasEuroMP(v3, v2) = v0))
% 5.54/2.02 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rhasEuroMP(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & risEuroMPFrom(v0, v1) = v3))
% 5.54/2.02 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cEuropeanCountry(v2) = v1) | ~ (cEuropeanCountry(v2) = v0))
% 5.54/2.02 | (28) ! [v0] : (v0 = 0 | ~ (cEUCountry(iES) = v0))
% 5.54/2.02 | (29) ! [v0] : ! [v1] : (v1 = 0 | ~ (cEuroMP(v0) = v1) | ~ (cEuroMP(v0) = 0))
% 5.54/2.03 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0))
% 5.54/2.03 | (31) ! [v0] : ( ~ (cEuroMP(v0) = 0) | ? [v1] : (risEuroMPFrom(v0, v1) = 0 & cowlThing(v1) = 0))
% 5.54/2.03 | (32) ? [v0] : ? [v1] : cPerson(v0) = v1
% 5.54/2.03 | (33) ~ (all_0_0_0 = 0)
% 5.54/2.03 | (34) ! [v0] : ! [v1] : (v1 = 0 | ~ (cPerson(v0) = v1) | ~ (cPerson(v0) = 0))
% 5.54/2.03 | (35) cEuropeanCountry(iPT) = 0
% 5.54/2.03 | (36) ? [v0] : ? [v1] : ? [v2] : risEuroMPFrom(v1, v0) = v2
% 5.54/2.03 | (37) cEuropeanCountry(iUK) = 0
% 5.54/2.03 | (38) ? [v0] : ? [v1] : cowlThing(v0) = v1
% 5.54/2.03 | (39) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ (xsd_string(v0) = 0))
% 5.54/2.03 | (40) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rhasEuroMP(v1, v0) = v2) | ~ (rhasEuroMP(v1, v0) = 0))
% 5.54/2.03 | (41) ! [v0] : (v0 = 0 | ~ (cEUCountry(iBE) = v0))
% 5.54/2.03 | (42) cEuropeanCountry(iFR) = 0
% 5.54/2.03 | (43) ? [v0] : ? [v1] : xsd_string(v0) = v1
% 5.54/2.03 | (44) ! [v0] : (v0 = 0 | ~ (cEUCountry(iNL) = v0))
% 5.54/2.03 | (45) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (risEuroMPFrom(v0, v1) = v2) | ~ (risEuroMPFrom(v0, v1) = 0))
% 5.54/2.03 | (46) ! [v0] : ! [v1] : ( ~ (rhasEuroMP(v0, v1) = 0) | cEUCountry(v0) = 0)
% 5.54/2.03 | (47) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ (cowlThing(v0) = 0))
% 5.54/2.03 | (48) ! [v0] : (v0 = 0 | ~ (cEUCountry(iFR) = v0))
% 5.54/2.03 | (49) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (risEuroMPFrom(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & rhasEuroMP(v1, v0) = v3))
% 5.54/2.03 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (risEuroMPFrom(v3, v2) = v1) | ~ (risEuroMPFrom(v3, v2) = v0))
% 5.54/2.03 | (51) ! [v0] : ! [v1] : (v1 = 0 | ~ (cEuropeanCountry(v0) = v1) | ~ (cEuropeanCountry(v0) = 0))
% 5.54/2.03 | (52) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlNothing(v0) = v1) | ~ (cowlNothing(v0) = 0))
% 5.54/2.03 | (53) ! [v0] : ! [v1] : ( ~ (rhasEuroMP(v1, v0) = 0) | risEuroMPFrom(v0, v1) = 0)
% 5.54/2.03 | (54) ! [v0] : ! [v1] : ( ~ (risEuroMPFrom(v0, v1) = 0) | rhasEuroMP(v1, v0) = 0)
% 5.54/2.03 | (55) ? [v0] : ? [v1] : cowlNothing(v0) = v1
% 5.54/2.03 | (56) cEuropeanCountry(iNL) = 0
% 5.54/2.03 | (57) ! [v0] : (v0 = 0 | ~ (cEUCountry(iPT) = v0))
% 5.54/2.03 | (58) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0))
% 5.54/2.03 | (59) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cowlThing(v2) = 0) | ~ (cEuroMP(v0) = v1) | ? [v3] : ( ~ (v3 = 0) & risEuroMPFrom(v0, v2) = v3))
% 5.54/2.03 | (60) ! [v0] : (v0 = iUK | v0 = iFR | v0 = iES | v0 = iNL | v0 = iBE | v0 = iPT | ~ (cEUCountry(v0) = 0))
% 5.54/2.03 | (61) ! [v0] : ( ~ (xsd_integer(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_string(v0) = v1))
% 5.54/2.03 | (62) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 5.54/2.03 | (63) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cPerson(v2) = v1) | ~ (cPerson(v2) = v0))
% 5.54/2.03 | (64) cEuropeanCountry(iBE) = 0
% 5.54/2.03 |
% 5.54/2.03 | Instantiating (38) with all_11_0_9, all_11_1_10 yields:
% 5.54/2.03 | (65) cowlThing(all_11_1_10) = all_11_0_9
% 5.54/2.03 |
% 5.54/2.03 | Instantiating formula (9) with all_11_0_9, all_11_1_10 and discharging atoms cowlThing(all_11_1_10) = all_11_0_9, yields:
% 5.54/2.03 | (66) all_11_0_9 = 0
% 5.54/2.03 |
% 5.54/2.03 | From (66) and (65) follows:
% 5.54/2.03 | (67) cowlThing(all_11_1_10) = 0
% 5.54/2.04 |
% 5.54/2.04 | Instantiating formula (53) with iUK, iKinnock and discharging atoms rhasEuroMP(iUK, iKinnock) = 0, yields:
% 5.54/2.04 | (68) risEuroMPFrom(iKinnock, iUK) = 0
% 5.54/2.04 |
% 5.54/2.04 | Instantiating formula (59) with all_11_1_10, all_0_0_0, iKinnock and discharging atoms cowlThing(all_11_1_10) = 0, cEuroMP(iKinnock) = all_0_0_0, yields:
% 5.54/2.04 | (69) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & risEuroMPFrom(iKinnock, all_11_1_10) = v0)
% 5.54/2.04 |
% 5.54/2.04 +-Applying beta-rule and splitting (69), into two cases.
% 5.54/2.04 |-Branch one:
% 5.54/2.04 | (70) all_0_0_0 = 0
% 5.54/2.04 |
% 5.54/2.04 | Equations (70) can reduce 33 to:
% 5.54/2.04 | (71) $false
% 5.54/2.04 |
% 5.54/2.04 |-The branch is then unsatisfiable
% 5.54/2.04 |-Branch two:
% 5.54/2.04 | (33) ~ (all_0_0_0 = 0)
% 5.54/2.04 | (73) ? [v0] : ( ~ (v0 = 0) & risEuroMPFrom(iKinnock, all_11_1_10) = v0)
% 5.54/2.04 |
% 5.54/2.04 | Instantiating formula (21) with iUK, all_0_0_0, iKinnock and discharging atoms risEuroMPFrom(iKinnock, iUK) = 0, cEuroMP(iKinnock) = all_0_0_0, yields:
% 5.54/2.04 | (74) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & cowlThing(iUK) = v0)
% 5.54/2.04 |
% 5.54/2.04 +-Applying beta-rule and splitting (74), into two cases.
% 5.54/2.04 |-Branch one:
% 5.54/2.04 | (70) all_0_0_0 = 0
% 5.54/2.04 |
% 5.54/2.04 | Equations (70) can reduce 33 to:
% 5.54/2.04 | (71) $false
% 5.54/2.04 |
% 5.54/2.04 |-The branch is then unsatisfiable
% 5.54/2.04 |-Branch two:
% 5.54/2.04 | (33) ~ (all_0_0_0 = 0)
% 5.54/2.04 | (78) ? [v0] : ( ~ (v0 = 0) & cowlThing(iUK) = v0)
% 5.54/2.04 |
% 5.54/2.04 | Instantiating (78) with all_46_0_24 yields:
% 5.54/2.04 | (79) ~ (all_46_0_24 = 0) & cowlThing(iUK) = all_46_0_24
% 5.54/2.04 |
% 5.54/2.04 | Applying alpha-rule on (79) yields:
% 5.54/2.04 | (80) ~ (all_46_0_24 = 0)
% 5.54/2.04 | (81) cowlThing(iUK) = all_46_0_24
% 5.54/2.04 |
% 5.54/2.04 | Instantiating formula (9) with all_46_0_24, iUK and discharging atoms cowlThing(iUK) = all_46_0_24, yields:
% 5.54/2.04 | (82) all_46_0_24 = 0
% 5.54/2.04 |
% 5.54/2.04 | Equations (82) can reduce 80 to:
% 5.54/2.04 | (71) $false
% 5.54/2.04 |
% 5.54/2.04 |-The branch is then unsatisfiable
% 5.54/2.04 % SZS output end Proof for theBenchmark
% 5.54/2.04
% 5.54/2.04 1444ms
%------------------------------------------------------------------------------