%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KRS129+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n022.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 02:56:39 EDT 2022 % Result : Theorem 4.46s 1.73s % Output : Proof 6.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : KRS129+1 : TPTP v8.1.0. Released v3.1.0. % 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n022.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Tue Jun 7 15:44:20 EDT 2022 % 0.13/0.33 % CPUTime : % 0.19/0.58 ____ _ % 0.19/0.58 ___ / __ \_____(_)___ ________ __________ % 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.58 % 0.19/0.58 A Theorem Prover for First-Order Logic % 0.19/0.58 (ePrincess v.1.0) % 0.19/0.58 % 0.19/0.58 (c) Philipp Rümmer, 2009-2015 % 0.19/0.58 (c) Peter Backeman, 2014-2015 % 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.58 Bug reports to peter@backeman.se % 0.19/0.58 % 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.58 % 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.76/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.56/0.96 Prover 0: Preprocessing ... % 2.00/1.11 Prover 0: Warning: ignoring some quantifiers % 2.00/1.12 Prover 0: Constructing countermodel ... % 2.37/1.24 Prover 0: gave up % 2.37/1.24 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.37/1.28 Prover 1: Preprocessing ... % 3.01/1.42 Prover 1: Constructing countermodel ... % 3.60/1.53 Prover 1: gave up % 3.60/1.53 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.67/1.55 Prover 2: Preprocessing ... % 4.06/1.63 Prover 2: Warning: ignoring some quantifiers % 4.06/1.64 Prover 2: Constructing countermodel ... % 4.46/1.73 Prover 2: proved (202ms) % 4.46/1.73 % 4.46/1.73 No countermodel exists, formula is valid % 4.46/1.73 % SZS status Theorem for theBenchmark % 4.46/1.73 % 4.46/1.73 Generating proof ... Warning: ignoring some quantifiers % 5.50/1.99 found it (size 55) % 5.50/1.99 % 5.50/1.99 % SZS output start Proof for theBenchmark % 5.50/1.99 Assumed formulas after preprocessing and simplification: % 5.50/1.99 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (rhasEuroMP(iUK, iKinnock) = 0 & cPerson(iKinnock) = 0 & cEuropeanCountry(iPT) = 0 & cEuropeanCountry(iNL) = 0 & cEuropeanCountry(iUK) = 0 & cEuropeanCountry(iES) = 0 & cEuropeanCountry(iFR) = 0 & cEuropeanCountry(iBE) = 0 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (risEuroMPFrom(v7, v6) = v5) | ~ (risEuroMPFrom(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (rhasEuroMP(v7, v6) = v5) | ~ (rhasEuroMP(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (risEuroMPFrom(v5, v4) = v6) | ~ (risEuroMPFrom(v5, v4) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (risEuroMPFrom(v4, v5) = v6) | ~ (risEuroMPFrom(v4, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (risEuroMPFrom(v4, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & rhasEuroMP(v5, v4) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (rhasEuroMP(v5, v4) = v6) | ~ (rhasEuroMP(v5, v4) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (rhasEuroMP(v5, v4) = v6) | ? [v7] : ( ~ (v7 = 0) & risEuroMPFrom(v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (rhasEuroMP(v4, v5) = v6) | ~ (rhasEuroMP(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 | ~ (cPerson(v6) = v5) | ~ (cPerson(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (cEuropeanCountry(v6) = v5) | ~ (cEuropeanCountry(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (cEuroMP(v6) = v5) | ~ (cEuroMP(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (cEUCountry(v6) = v5) | ~ (cEUCountry(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (risEuroMPFrom(v4, v6) = 0) | ~ (cEuroMP(v4) = v5) | ? [v7] : ( ~ (v7 = 0) & cowlThing(v6) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (cowlThing(v6) = 0) | ~ (cEuroMP(v4) = v5) | ? [v7] : ( ~ (v7 = 0) & risEuroMPFrom(v4, v6) = v7)) & ! [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 | ~ (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 | ~ (cPerson(v4) = v5) | ~ (cPerson(v4) = 0)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (cEuropeanCountry(v4) = v5) | ~ (cEuropeanCountry(v4) = 0)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (cEuroMP(v4) = v5) | ~ (cEuroMP(v4) = 0)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (cEUCountry(v4) = v5) | ~ (cEUCountry(v4) = 0)) & ! [v4] : ! [v5] : ( ~ (risEuroMPFrom(v4, v5) = 0) | rhasEuroMP(v5, v4) = 0) & ! [v4] : ! [v5] : ( ~ (rhasEuroMP(v5, v4) = 0) | risEuroMPFrom(v4, v5) = 0) & ! [v4] : ! [v5] : ( ~ (rhasEuroMP(v4, v5) = 0) | cEUCountry(v4) = 0) & ! [v4] : (v4 = iPT | v4 = iNL | v4 = iUK | v4 = iES | v4 = iFR | v4 = iBE | ~ (cEUCountry(v4) = 0)) & ! [v4] : (v4 = 0 | ~ (cEUCountry(iPT) = v4)) & ! [v4] : (v4 = 0 | ~ (cEUCountry(iNL) = v4)) & ! [v4] : (v4 = 0 | ~ (cEUCountry(iUK) = v4)) & ! [v4] : (v4 = 0 | ~ (cEUCountry(iES) = v4)) & ! [v4] : (v4 = 0 | ~ (cEUCountry(iFR) = v4)) & ! [v4] : (v4 = 0 | ~ (cEUCountry(iBE) = v4)) & ! [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] : ~ (cowlNothing(v4) = 0) & ! [v4] : ( ~ (cEuroMP(v4) = 0) | ? [v5] : (risEuroMPFrom(v4, v5) = 0 & cowlThing(v5) = 0)) & ? [v4] : ? [v5] : ? [v6] : risEuroMPFrom(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : rhasEuroMP(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] : cPerson(v4) = v5 & ? [v4] : ? [v5] : cEuropeanCountry(v4) = v5 & ? [v4] : ? [v5] : cEuroMP(v4) = v5 & ? [v4] : ? [v5] : cEUCountry(v4) = v5 & ((v3 = 0 & cowlNothing(v1) = 0) | ( ~ (v2 = 0) & cowlThing(v1) = v2) | ( ~ (v0 = 0) & cEuroMP(iKinnock) = v0) | (xsd_string(v1) = v2 & xsd_integer(v1) = v3 & ((v3 = 0 & v2 = 0) | ( ~ (v3 = 0) & ~ (v2 = 0)))))) % 5.86/2.03 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 5.86/2.03 | (1) rhasEuroMP(iUK, iKinnock) = 0 & cPerson(iKinnock) = 0 & cEuropeanCountry(iPT) = 0 & cEuropeanCountry(iNL) = 0 & cEuropeanCountry(iUK) = 0 & cEuropeanCountry(iES) = 0 & cEuropeanCountry(iFR) = 0 & cEuropeanCountry(iBE) = 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 = iPT | v0 = iNL | v0 = iUK | v0 = iES | v0 = iFR | v0 = iBE | ~ (cEUCountry(v0) = 0)) & ! [v0] : (v0 = 0 | ~ (cEUCountry(iPT) = v0)) & ! [v0] : (v0 = 0 | ~ (cEUCountry(iNL) = v0)) & ! [v0] : (v0 = 0 | ~ (cEUCountry(iUK) = v0)) & ! [v0] : (v0 = 0 | ~ (cEUCountry(iES) = v0)) & ! [v0] : (v0 = 0 | ~ (cEUCountry(iFR) = v0)) & ! [v0] : (v0 = 0 | ~ (cEUCountry(iBE) = 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 & ((all_0_0_0 = 0 & cowlNothing(all_0_2_2) = 0) | ( ~ (all_0_1_1 = 0) & cowlThing(all_0_2_2) = all_0_1_1) | ( ~ (all_0_3_3 = 0) & cEuroMP(iKinnock) = all_0_3_3) | (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0))))) % 5.86/2.04 | % 5.86/2.04 | Applying alpha-rule on (1) yields: % 5.86/2.05 | (2) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rhasEuroMP(v0, v1) = v2) | ~ (rhasEuroMP(v0, v1) = 0)) % 5.86/2.05 | (3) ! [v0] : ( ~ (xsd_integer(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_string(v0) = v1)) % 5.86/2.05 | (4) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) % 5.86/2.05 | (5) cPerson(iKinnock) = 0 % 5.86/2.05 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rhasEuroMP(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & risEuroMPFrom(v0, v1) = v3)) % 5.86/2.05 | (7) ! [v0] : ~ (cowlNothing(v0) = 0) % 5.86/2.05 | (8) cEuropeanCountry(iES) = 0 % 5.86/2.05 | (9) ! [v0] : ! [v1] : (v1 = 0 | ~ (cEuropeanCountry(v0) = v1) | ~ (cEuropeanCountry(v0) = 0)) % 5.86/2.05 | (10) ? [v0] : ? [v1] : ? [v2] : rhasEuroMP(v1, v0) = v2 % 5.86/2.05 | (11) ! [v0] : (v0 = 0 | ~ (cEUCountry(iES) = v0)) % 5.86/2.05 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cEuroMP(v2) = v1) | ~ (cEuroMP(v2) = v0)) % 5.86/2.05 | (13) rhasEuroMP(iUK, iKinnock) = 0 % 5.86/2.05 | (14) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ (cowlThing(v0) = 0)) % 5.86/2.05 | (15) ! [v0] : (v0 = 0 | ~ (cEUCountry(iNL) = v0)) % 5.86/2.05 | (16) ? [v0] : ? [v1] : cEuropeanCountry(v0) = v1 % 5.86/2.05 | (17) ? [v0] : ? [v1] : ? [v2] : risEuroMPFrom(v1, v0) = v2 % 5.86/2.05 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 5.86/2.05 | (19) ! [v0] : ! [v1] : (v1 = 0 | ~ (cEUCountry(v0) = v1) | ~ (cEUCountry(v0) = 0)) % 5.86/2.05 | (20) ? [v0] : ? [v1] : cowlNothing(v0) = v1 % 5.86/2.05 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cowlThing(v2) = 0) | ~ (cEuroMP(v0) = v1) | ? [v3] : ( ~ (v3 = 0) & risEuroMPFrom(v0, v2) = v3)) % 5.86/2.05 | (22) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (risEuroMPFrom(v0, v1) = v2) | ~ (risEuroMPFrom(v0, v1) = 0)) % 5.86/2.05 | (23) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlNothing(v0) = v1) | ~ (cowlNothing(v0) = 0)) % 5.86/2.05 | (24) ! [v0] : ! [v1] : (v1 = 0 | ~ (cPerson(v0) = v1) | ~ (cPerson(v0) = 0)) % 5.86/2.05 | (25) ! [v0] : ( ~ (cEuroMP(v0) = 0) | ? [v1] : (risEuroMPFrom(v0, v1) = 0 & cowlThing(v1) = 0)) % 5.86/2.05 | (26) ! [v0] : ! [v1] : ( ~ (rhasEuroMP(v1, v0) = 0) | risEuroMPFrom(v0, v1) = 0) % 5.86/2.05 | (27) ! [v0] : ! [v1] : ( ~ (risEuroMPFrom(v0, v1) = 0) | rhasEuroMP(v1, v0) = 0) % 5.86/2.05 | (28) (all_0_0_0 = 0 & cowlNothing(all_0_2_2) = 0) | ( ~ (all_0_1_1 = 0) & cowlThing(all_0_2_2) = all_0_1_1) | ( ~ (all_0_3_3 = 0) & cEuroMP(iKinnock) = all_0_3_3) | (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)))) % 5.86/2.05 | (29) ! [v0] : (v0 = 0 | ~ (cEUCountry(iBE) = v0)) % 5.86/2.05 | (30) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) % 5.86/2.05 | (31) ? [v0] : ? [v1] : xsd_integer(v0) = v1 % 5.86/2.05 | (32) cEuropeanCountry(iUK) = 0 % 5.86/2.05 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cEUCountry(v2) = v1) | ~ (cEUCountry(v2) = v0)) % 5.86/2.05 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (risEuroMPFrom(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & rhasEuroMP(v1, v0) = v3)) % 5.86/2.05 | (35) ! [v0] : ! [v1] : (v1 = 0 | ~ (cEuroMP(v0) = v1) | ~ (cEuroMP(v0) = 0)) % 5.86/2.05 | (36) cEuropeanCountry(iPT) = 0 % 5.86/2.05 | (37) ? [v0] : ? [v1] : cPerson(v0) = v1 % 5.86/2.05 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rhasEuroMP(v3, v2) = v1) | ~ (rhasEuroMP(v3, v2) = v0)) % 5.86/2.06 | (39) ? [v0] : ? [v1] : cEuroMP(v0) = v1 % 5.86/2.06 | (40) ! [v0] : (v0 = iPT | v0 = iNL | v0 = iUK | v0 = iES | v0 = iFR | v0 = iBE | ~ (cEUCountry(v0) = 0)) % 5.86/2.06 | (41) ! [v0] : (v0 = 0 | ~ (cEUCountry(iUK) = v0)) % 5.86/2.06 | (42) cEuropeanCountry(iNL) = 0 % 5.86/2.06 | (43) cEuropeanCountry(iBE) = 0 % 5.86/2.06 | (44) ! [v0] : (v0 = 0 | ~ (cEUCountry(iFR) = v0)) % 5.86/2.06 | (45) cEuropeanCountry(iFR) = 0 % 5.86/2.06 | (46) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cEuropeanCountry(v2) = v1) | ~ (cEuropeanCountry(v2) = v0)) % 5.86/2.06 | (47) ? [v0] : ? [v1] : cEUCountry(v0) = v1 % 5.86/2.06 | (48) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ (xsd_integer(v0) = 0)) % 5.86/2.06 | (49) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (risEuroMPFrom(v0, v2) = 0) | ~ (cEuroMP(v0) = v1) | ? [v3] : ( ~ (v3 = 0) & cowlThing(v2) = v3)) % 5.86/2.06 | (50) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ (xsd_string(v0) = 0)) % 5.86/2.06 | (51) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | xsd_string(v0) = 0) % 5.86/2.06 | (52) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) % 5.86/2.06 | (53) ! [v0] : (v0 = 0 | ~ (cEUCountry(iPT) = v0)) % 5.86/2.06 | (54) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) % 5.86/2.06 | (55) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) % 5.86/2.06 | (56) ? [v0] : ? [v1] : cowlThing(v0) = v1 % 5.86/2.06 | (57) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cPerson(v2) = v1) | ~ (cPerson(v2) = v0)) % 5.86/2.06 | (58) ! [v0] : ! [v1] : ( ~ (rhasEuroMP(v0, v1) = 0) | cEUCountry(v0) = 0) % 5.86/2.06 | (59) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rhasEuroMP(v1, v0) = v2) | ~ (rhasEuroMP(v1, v0) = 0)) % 5.86/2.06 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (risEuroMPFrom(v3, v2) = v1) | ~ (risEuroMPFrom(v3, v2) = v0)) % 5.86/2.06 | (61) ? [v0] : ? [v1] : xsd_string(v0) = v1 % 5.86/2.06 | (62) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) % 5.86/2.06 | (63) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (risEuroMPFrom(v1, v0) = v2) | ~ (risEuroMPFrom(v1, v0) = 0)) % 5.86/2.06 | % 5.86/2.06 | Instantiating (56) with all_19_0_22, all_19_1_23 yields: % 5.86/2.06 | (64) cowlThing(all_19_1_23) = all_19_0_22 % 5.86/2.06 | % 5.86/2.06 | Instantiating formula (30) with all_19_0_22, all_19_1_23 and discharging atoms cowlThing(all_19_1_23) = all_19_0_22, yields: % 5.86/2.06 | (65) all_19_0_22 = 0 % 5.86/2.06 | % 5.86/2.06 | From (65) and (64) follows: % 5.86/2.06 | (66) cowlThing(all_19_1_23) = 0 % 5.86/2.06 | % 5.86/2.06 | Instantiating formula (26) with iUK, iKinnock and discharging atoms rhasEuroMP(iUK, iKinnock) = 0, yields: % 5.86/2.07 | (67) risEuroMPFrom(iKinnock, iUK) = 0 % 5.86/2.07 | % 5.86/2.07 +-Applying beta-rule and splitting (28), into two cases. % 5.86/2.07 |-Branch one: % 5.86/2.07 | (68) (all_0_0_0 = 0 & cowlNothing(all_0_2_2) = 0) | ( ~ (all_0_1_1 = 0) & cowlThing(all_0_2_2) = all_0_1_1) | ( ~ (all_0_3_3 = 0) & cEuroMP(iKinnock) = all_0_3_3) % 5.86/2.07 | % 5.86/2.07 +-Applying beta-rule and splitting (68), into two cases. % 5.86/2.07 |-Branch one: % 5.86/2.07 | (69) (all_0_0_0 = 0 & cowlNothing(all_0_2_2) = 0) | ( ~ (all_0_1_1 = 0) & cowlThing(all_0_2_2) = all_0_1_1) % 5.86/2.07 | % 5.86/2.07 +-Applying beta-rule and splitting (69), into two cases. % 5.86/2.07 |-Branch one: % 5.86/2.07 | (70) all_0_0_0 = 0 & cowlNothing(all_0_2_2) = 0 % 5.86/2.07 | % 5.86/2.07 | Applying alpha-rule on (70) yields: % 5.86/2.07 | (71) all_0_0_0 = 0 % 5.86/2.07 | (72) cowlNothing(all_0_2_2) = 0 % 5.86/2.07 | % 5.86/2.07 | Instantiating formula (7) with all_0_2_2 and discharging atoms cowlNothing(all_0_2_2) = 0, yields: % 5.86/2.07 | (73) $false % 5.86/2.07 | % 5.86/2.07 |-The branch is then unsatisfiable % 5.86/2.07 |-Branch two: % 5.86/2.07 | (74) ~ (all_0_1_1 = 0) & cowlThing(all_0_2_2) = all_0_1_1 % 5.86/2.07 | % 5.86/2.07 | Applying alpha-rule on (74) yields: % 5.86/2.07 | (75) ~ (all_0_1_1 = 0) % 5.86/2.07 | (76) cowlThing(all_0_2_2) = all_0_1_1 % 5.86/2.07 | % 5.86/2.07 | Instantiating formula (30) with all_0_1_1, all_0_2_2 and discharging atoms cowlThing(all_0_2_2) = all_0_1_1, yields: % 5.86/2.07 | (77) all_0_1_1 = 0 % 5.86/2.07 | % 5.86/2.07 | Equations (77) can reduce 75 to: % 5.86/2.07 | (78) $false % 5.86/2.07 | % 5.86/2.07 |-The branch is then unsatisfiable % 5.86/2.07 |-Branch two: % 5.86/2.07 | (79) ~ (all_0_3_3 = 0) & cEuroMP(iKinnock) = all_0_3_3 % 5.86/2.07 | % 5.86/2.07 | Applying alpha-rule on (79) yields: % 5.86/2.07 | (80) ~ (all_0_3_3 = 0) % 5.86/2.07 | (81) cEuroMP(iKinnock) = all_0_3_3 % 5.86/2.07 | % 5.86/2.07 | Instantiating formula (49) with iUK, all_0_3_3, iKinnock and discharging atoms risEuroMPFrom(iKinnock, iUK) = 0, cEuroMP(iKinnock) = all_0_3_3, yields: % 5.86/2.07 | (82) all_0_3_3 = 0 | ? [v0] : ( ~ (v0 = 0) & cowlThing(iUK) = v0) % 5.86/2.07 | % 5.86/2.07 | Instantiating formula (21) with all_19_1_23, all_0_3_3, iKinnock and discharging atoms cowlThing(all_19_1_23) = 0, cEuroMP(iKinnock) = all_0_3_3, yields: % 5.86/2.07 | (83) all_0_3_3 = 0 | ? [v0] : ( ~ (v0 = 0) & risEuroMPFrom(iKinnock, all_19_1_23) = v0) % 5.86/2.07 | % 5.86/2.07 +-Applying beta-rule and splitting (83), into two cases. % 5.86/2.07 |-Branch one: % 5.86/2.07 | (84) all_0_3_3 = 0 % 5.86/2.07 | % 5.86/2.07 | Equations (84) can reduce 80 to: % 5.86/2.07 | (78) $false % 5.86/2.07 | % 5.86/2.07 |-The branch is then unsatisfiable % 5.86/2.07 |-Branch two: % 5.86/2.07 | (80) ~ (all_0_3_3 = 0) % 5.86/2.07 | (87) ? [v0] : ( ~ (v0 = 0) & risEuroMPFrom(iKinnock, all_19_1_23) = v0) % 5.86/2.07 | % 5.86/2.07 +-Applying beta-rule and splitting (82), into two cases. % 5.86/2.07 |-Branch one: % 5.86/2.07 | (84) all_0_3_3 = 0 % 5.86/2.07 | % 5.86/2.07 | Equations (84) can reduce 80 to: % 5.86/2.07 | (78) $false % 5.86/2.07 | % 5.86/2.07 |-The branch is then unsatisfiable % 5.86/2.07 |-Branch two: % 5.86/2.07 | (80) ~ (all_0_3_3 = 0) % 5.86/2.07 | (91) ? [v0] : ( ~ (v0 = 0) & cowlThing(iUK) = v0) % 5.86/2.07 | % 5.86/2.07 | Instantiating (91) with all_53_0_27 yields: % 5.86/2.07 | (92) ~ (all_53_0_27 = 0) & cowlThing(iUK) = all_53_0_27 % 5.86/2.07 | % 5.86/2.07 | Applying alpha-rule on (92) yields: % 5.86/2.07 | (93) ~ (all_53_0_27 = 0) % 5.86/2.07 | (94) cowlThing(iUK) = all_53_0_27 % 5.86/2.07 | % 5.86/2.07 | Instantiating formula (30) with all_53_0_27, iUK and discharging atoms cowlThing(iUK) = all_53_0_27, yields: % 5.86/2.07 | (95) all_53_0_27 = 0 % 5.86/2.07 | % 5.86/2.07 | Equations (95) can reduce 93 to: % 5.86/2.07 | (78) $false % 5.86/2.07 | % 5.86/2.07 |-The branch is then unsatisfiable % 5.86/2.08 |-Branch two: % 5.86/2.08 | (97) xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0))) % 5.86/2.08 | % 5.86/2.08 | Applying alpha-rule on (97) yields: % 5.86/2.08 | (98) xsd_string(all_0_2_2) = all_0_1_1 % 5.86/2.08 | (99) xsd_integer(all_0_2_2) = all_0_0_0 % 5.86/2.08 | (100) (all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)) % 5.86/2.08 | % 5.86/2.08 | Instantiating formula (51) with all_0_0_0, all_0_2_2 and discharging atoms xsd_integer(all_0_2_2) = all_0_0_0, yields: % 5.86/2.08 | (101) all_0_0_0 = 0 | xsd_string(all_0_2_2) = 0 % 5.86/2.08 | % 5.86/2.08 +-Applying beta-rule and splitting (101), into two cases. % 5.86/2.08 |-Branch one: % 5.86/2.08 | (102) xsd_string(all_0_2_2) = 0 % 5.86/2.08 | % 5.86/2.08 | Instantiating formula (62) with all_0_2_2, 0, all_0_1_1 and discharging atoms xsd_string(all_0_2_2) = all_0_1_1, xsd_string(all_0_2_2) = 0, yields: % 5.86/2.08 | (77) all_0_1_1 = 0 % 5.86/2.08 | % 5.86/2.08 | From (77) and (98) follows: % 5.86/2.08 | (102) xsd_string(all_0_2_2) = 0 % 5.86/2.08 | % 5.86/2.08 +-Applying beta-rule and splitting (100), into two cases. % 5.86/2.08 |-Branch one: % 5.86/2.08 | (105) all_0_0_0 = 0 & all_0_1_1 = 0 % 5.86/2.08 | % 5.86/2.08 | Applying alpha-rule on (105) yields: % 5.86/2.08 | (71) all_0_0_0 = 0 % 6.17/2.08 | (77) all_0_1_1 = 0 % 6.17/2.08 | % 6.17/2.08 | From (71) and (99) follows: % 6.17/2.08 | (108) xsd_integer(all_0_2_2) = 0 % 6.17/2.08 | % 6.17/2.08 | Instantiating formula (3) with all_0_2_2 and discharging atoms xsd_integer(all_0_2_2) = 0, yields: % 6.17/2.08 | (109) ? [v0] : ( ~ (v0 = 0) & xsd_string(all_0_2_2) = v0) % 6.17/2.08 | % 6.17/2.08 | Instantiating (109) with all_60_0_28 yields: % 6.17/2.08 | (110) ~ (all_60_0_28 = 0) & xsd_string(all_0_2_2) = all_60_0_28 % 6.17/2.08 | % 6.17/2.08 | Applying alpha-rule on (110) yields: % 6.17/2.08 | (111) ~ (all_60_0_28 = 0) % 6.18/2.08 | (112) xsd_string(all_0_2_2) = all_60_0_28 % 6.18/2.08 | % 6.18/2.08 | Instantiating formula (50) with all_60_0_28, all_0_2_2 and discharging atoms xsd_string(all_0_2_2) = all_60_0_28, xsd_string(all_0_2_2) = 0, yields: % 6.18/2.08 | (113) all_60_0_28 = 0 % 6.18/2.08 | % 6.18/2.08 | Equations (113) can reduce 111 to: % 6.18/2.08 | (78) $false % 6.18/2.08 | % 6.18/2.08 |-The branch is then unsatisfiable % 6.18/2.08 |-Branch two: % 6.18/2.08 | (115) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) % 6.18/2.08 | % 6.18/2.08 | Applying alpha-rule on (115) yields: % 6.18/2.08 | (116) ~ (all_0_0_0 = 0) % 6.18/2.08 | (75) ~ (all_0_1_1 = 0) % 6.18/2.08 | % 6.18/2.08 | Equations (77) can reduce 75 to: % 6.18/2.08 | (78) $false % 6.18/2.08 | % 6.18/2.08 |-The branch is then unsatisfiable % 6.18/2.08 |-Branch two: % 6.18/2.08 | (119) ~ (xsd_string(all_0_2_2) = 0) % 6.18/2.08 | (71) all_0_0_0 = 0 % 6.18/2.08 | % 6.18/2.08 +-Applying beta-rule and splitting (100), into two cases. % 6.18/2.08 |-Branch one: % 6.18/2.08 | (105) all_0_0_0 = 0 & all_0_1_1 = 0 % 6.18/2.08 | % 6.18/2.08 | Applying alpha-rule on (105) yields: % 6.18/2.08 | (71) all_0_0_0 = 0 % 6.18/2.08 | (77) all_0_1_1 = 0 % 6.18/2.08 | % 6.18/2.08 | From (77) and (98) follows: % 6.18/2.08 | (102) xsd_string(all_0_2_2) = 0 % 6.18/2.08 | % 6.18/2.08 | Using (102) and (119) yields: % 6.18/2.08 | (73) $false % 6.18/2.08 | % 6.18/2.08 |-The branch is then unsatisfiable % 6.18/2.08 |-Branch two: % 6.18/2.08 | (115) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) % 6.18/2.08 | % 6.18/2.08 | Applying alpha-rule on (115) yields: % 6.18/2.08 | (116) ~ (all_0_0_0 = 0) % 6.18/2.08 | (75) ~ (all_0_1_1 = 0) % 6.18/2.08 | % 6.18/2.08 | Equations (71) can reduce 116 to: % 6.18/2.08 | (78) $false % 6.18/2.08 | % 6.18/2.08 |-The branch is then unsatisfiable % 6.18/2.09 % SZS output end Proof for theBenchmark % 6.18/2.09 % 6.18/2.09 1495ms %------------------------------------------------------------------------------