%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KRS160+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 02:56:45 EDT 2022 % Result : Theorem 3.93s 1.58s % Output : Proof 5.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : KRS160+1 : TPTP v8.1.0. Released v3.1.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.11/0.33 % Computer : n029.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 600 % 0.11/0.33 % DateTime : Tue Jun 7 08:39:50 EDT 2022 % 0.11/0.33 % CPUTime : % 0.51/0.58 ____ _ % 0.51/0.58 ___ / __ \_____(_)___ ________ __________ % 0.51/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.51/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.51/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.51/0.58 % 0.51/0.58 A Theorem Prover for First-Order Logic % 0.51/0.58 (ePrincess v.1.0) % 0.51/0.58 % 0.51/0.58 (c) Philipp Rümmer, 2009-2015 % 0.51/0.58 (c) Peter Backeman, 2014-2015 % 0.51/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.51/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.51/0.58 Bug reports to peter@backeman.se % 0.51/0.58 % 0.51/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.51/0.58 % 0.51/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.77/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.47/0.92 Prover 0: Preprocessing ... % 1.94/1.07 Prover 0: Warning: ignoring some quantifiers % 2.03/1.09 Prover 0: Constructing countermodel ... % 2.62/1.31 Prover 0: gave up % 2.62/1.31 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.88/1.34 Prover 1: Preprocessing ... % 3.52/1.49 Prover 1: Constructing countermodel ... % 3.93/1.58 Prover 1: proved (269ms) % 3.93/1.58 % 3.93/1.58 No countermodel exists, formula is valid % 3.93/1.58 % SZS status Theorem for theBenchmark % 3.93/1.58 % 3.93/1.58 Generating proof ... found it (size 56) % 5.14/1.85 % 5.14/1.85 % SZS output start Proof for theBenchmark % 5.14/1.85 Assumed formulas after preprocessing and simplification: % 5.14/1.85 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (cTEST(iV21080) = 0 & cC8xcomp(iV21080) = 0 & cC6xcomp(iV21081) = 0 & cC12(iV21080) = v0 & rR1(iV21080, iV21081) = 0 & cC4(iV21081) = 0 & cC10(iV21081) = v1 & cC2(iV21081) = 0 & cowlThing(iV21081) = 0 & cowlThing(iV21080) = 0 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (ra_Px2(v8, v7) = v6) | ~ (ra_Px2(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (ra_Px4(v8, v7) = v6) | ~ (ra_Px4(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (ra_Px1(v8, v7) = v6) | ~ (ra_Px1(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (rR1(v8, v7) = v6) | ~ (rR1(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cTEST(v7) = v6) | ~ (cTEST(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cC8xcomp(v7) = v6) | ~ (cC8xcomp(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cC8(v7) = v6) | ~ (cC8(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cC6xcomp(v7) = v6) | ~ (cC6xcomp(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cC6(v7) = v6) | ~ (cC6(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cC2xcomp(v7) = v6) | ~ (cC2xcomp(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cC12(v7) = v6) | ~ (cC12(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cC4(v7) = v6) | ~ (cC4(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cC10(v7) = v6) | ~ (cC10(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cC2(v7) = v6) | ~ (cC2(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (xsd_string(v7) = v6) | ~ (xsd_string(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (xsd_integer(v7) = v6) | ~ (xsd_integer(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cowlNothing(v7) = v6) | ~ (cowlNothing(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cowlThing(v7) = v6) | ~ (cowlThing(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | ~ (cC8(v5) = v6) | ~ (ra_Px2(v5, v7) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | ~ (cC8(v5) = v6) | ~ (rR1(v5, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & cC6(v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | ~ (cC6xcomp(v5) = v6) | ~ (ra_Px4(v5, v7) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | ~ (cC2xcomp(v5) = v6) | ~ (ra_Px1(v5, v7) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | ~ (cC12(v5) = v6) | ~ (cC10(v7) = 0) | ? [v8] : ( ~ (v8 = 0) & rR1(v5, v7) = v8)) & ! [v5] : ! [v6] : (v6 = 0 | ~ (cTEST(v5) = v6) | ? [v7] : ? [v8] : (cC8xcomp(v5) = v7 & cC12(v5) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v5] : ! [v6] : (v6 = 0 | ~ (cC8xcomp(v5) = v6) | ? [v7] : ra_Px2(v5, v7) = 0) & ! [v5] : ! [v6] : (v6 = 0 | ~ (cC6(v5) = v6) | ? [v7] : ra_Px4(v5, v7) = 0) & ! [v5] : ! [v6] : (v6 = 0 | ~ (cC2(v5) = v6) | ? [v7] : ra_Px1(v5, v7) = 0) & ! [v5] : ! [v6] : (v6 = 0 | ~ (xsd_string(v5) = v6) | xsd_integer(v5) = 0) & ! [v5] : ! [v6] : (v6 = 0 | ~ (cowlThing(v5) = v6)) & ! [v5] : ! [v6] : ( ~ (cC8xcomp(v5) = 0) | ~ (ra_Px2(v5, v6) = 0)) & ! [v5] : ! [v6] : ( ~ (ra_Px4(v5, v6) = 0) | ~ (cC6(v5) = 0)) & ! [v5] : ! [v6] : ( ~ (cC2xcomp(v5) = v6) | ? [v7] : ? [v8] : (cC6(v5) = v7 & cC4(v5) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0)))) & ! [v5] : ! [v6] : ( ~ (ra_Px1(v5, v6) = 0) | ~ (cC2(v5) = 0)) & ! [v5] : ! [v6] : ( ~ (cC4(v5) = v6) | ? [v7] : ? [v8] : (cC10(v5) = v7 & cC2(v5) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0)))) & ! [v5] : ( ~ (cTEST(v5) = 0) | (cC8xcomp(v5) = 0 & cC12(v5) = 0)) & ! [v5] : ( ~ (cC8(v5) = 0) | ? [v6] : ra_Px2(v5, v6) = 0) & ! [v5] : ( ~ (cC8(v5) = 0) | ? [v6] : (cC6(v6) = 0 & rR1(v5, v6) = 0)) & ! [v5] : ( ~ (cC6xcomp(v5) = 0) | ? [v6] : ra_Px4(v5, v6) = 0) & ! [v5] : ( ~ (cC2xcomp(v5) = 0) | ? [v6] : ? [v7] : (cC6(v5) = v7 & cC4(v5) = v6 & ( ~ (v6 = 0) | v7 = 0))) & ! [v5] : ( ~ (cC2xcomp(v5) = 0) | ? [v6] : ra_Px1(v5, v6) = 0) & ! [v5] : ( ~ (cC12(v5) = 0) | ? [v6] : (rR1(v5, v6) = 0 & cC10(v6) = 0)) & ! [v5] : ( ~ (rR1(iV21080, v5) = 0) | cC6xcomp(v5) = 0) & ! [v5] : ( ~ (cC4(v5) = 0) | ? [v6] : ? [v7] : (cC10(v5) = v7 & cC2(v5) = v6 & ( ~ (v6 = 0) | v7 = 0))) & ! [v5] : ( ~ (xsd_string(v5) = 0) | ? [v6] : ( ~ (v6 = 0) & xsd_integer(v5) = v6)) & ! [v5] : ~ (cowlNothing(v5) = 0) & ( ~ (v1 = 0) | ~ (v0 = 0) | (xsd_string(v2) = v3 & xsd_integer(v2) = v4 & ((v4 = 0 & v3 = 0) | ( ~ (v4 = 0) & ~ (v3 = 0)))) | (cowlNothing(v2) = v4 & cowlThing(v2) = v3 & ( ~ (v3 = 0) | v4 = 0)))) % 5.14/1.89 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 5.14/1.89 | (1) cTEST(iV21080) = 0 & cC8xcomp(iV21080) = 0 & cC6xcomp(iV21081) = 0 & cC12(iV21080) = all_0_4_4 & rR1(iV21080, iV21081) = 0 & cC4(iV21081) = 0 & cC10(iV21081) = all_0_3_3 & cC2(iV21081) = 0 & cowlThing(iV21081) = 0 & cowlThing(iV21080) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ra_Px2(v3, v2) = v1) | ~ (ra_Px2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ra_Px4(v3, v2) = v1) | ~ (ra_Px4(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ra_Px1(v3, v2) = v1) | ~ (ra_Px1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rR1(v3, v2) = v1) | ~ (rR1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cTEST(v2) = v1) | ~ (cTEST(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC8xcomp(v2) = v1) | ~ (cC8xcomp(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC8(v2) = v1) | ~ (cC8(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC6xcomp(v2) = v1) | ~ (cC6xcomp(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC6(v2) = v1) | ~ (cC6(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC2xcomp(v2) = v1) | ~ (cC2xcomp(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC12(v2) = v1) | ~ (cC12(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC4(v2) = v1) | ~ (cC4(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC10(v2) = v1) | ~ (cC10(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC2(v2) = v1) | ~ (cC2(v2) = v0)) & ! [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 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cC8(v0) = v1) | ~ (ra_Px2(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cC8(v0) = v1) | ~ (rR1(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & cC6(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cC6xcomp(v0) = v1) | ~ (ra_Px4(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cC2xcomp(v0) = v1) | ~ (ra_Px1(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cC12(v0) = v1) | ~ (cC10(v2) = 0) | ? [v3] : ( ~ (v3 = 0) & rR1(v0, v2) = v3)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cTEST(v0) = v1) | ? [v2] : ? [v3] : (cC8xcomp(v0) = v2 & cC12(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cC8xcomp(v0) = v1) | ? [v2] : ra_Px2(v0, v2) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cC6(v0) = v1) | ? [v2] : ra_Px4(v0, v2) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cC2(v0) = v1) | ? [v2] : ra_Px1(v0, v2) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (cC8xcomp(v0) = 0) | ~ (ra_Px2(v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (ra_Px4(v0, v1) = 0) | ~ (cC6(v0) = 0)) & ! [v0] : ! [v1] : ( ~ (cC2xcomp(v0) = v1) | ? [v2] : ? [v3] : (cC6(v0) = v2 & cC4(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0] : ! [v1] : ( ~ (ra_Px1(v0, v1) = 0) | ~ (cC2(v0) = 0)) & ! [v0] : ! [v1] : ( ~ (cC4(v0) = v1) | ? [v2] : ? [v3] : (cC10(v0) = v2 & cC2(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0] : ( ~ (cTEST(v0) = 0) | (cC8xcomp(v0) = 0 & cC12(v0) = 0)) & ! [v0] : ( ~ (cC8(v0) = 0) | ? [v1] : ra_Px2(v0, v1) = 0) & ! [v0] : ( ~ (cC8(v0) = 0) | ? [v1] : (cC6(v1) = 0 & rR1(v0, v1) = 0)) & ! [v0] : ( ~ (cC6xcomp(v0) = 0) | ? [v1] : ra_Px4(v0, v1) = 0) & ! [v0] : ( ~ (cC2xcomp(v0) = 0) | ? [v1] : ? [v2] : (cC6(v0) = v2 & cC4(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))) & ! [v0] : ( ~ (cC2xcomp(v0) = 0) | ? [v1] : ra_Px1(v0, v1) = 0) & ! [v0] : ( ~ (cC12(v0) = 0) | ? [v1] : (rR1(v0, v1) = 0 & cC10(v1) = 0)) & ! [v0] : ( ~ (rR1(iV21080, v0) = 0) | cC6xcomp(v0) = 0) & ! [v0] : ( ~ (cC4(v0) = 0) | ? [v1] : ? [v2] : (cC10(v0) = v2 & cC2(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))) & ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) & ! [v0] : ~ (cowlNothing(v0) = 0) & ( ~ (all_0_3_3 = 0) | ~ (all_0_4_4 = 0) | (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)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0))) % 5.14/1.91 | % 5.14/1.91 | Applying alpha-rule on (1) yields: % 5.14/1.91 | (2) ! [v0] : ! [v1] : ( ~ (cC2xcomp(v0) = v1) | ? [v2] : ? [v3] : (cC6(v0) = v2 & cC4(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) % 5.14/1.91 | (3) cowlThing(iV21081) = 0 % 5.14/1.91 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) % 5.14/1.91 | (5) ! [v0] : ( ~ (cC2xcomp(v0) = 0) | ? [v1] : ra_Px1(v0, v1) = 0) % 5.14/1.91 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cTEST(v2) = v1) | ~ (cTEST(v2) = v0)) % 5.14/1.91 | (7) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) % 5.14/1.91 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 5.14/1.91 | (9) cC2(iV21081) = 0 % 5.14/1.91 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC6xcomp(v2) = v1) | ~ (cC6xcomp(v2) = v0)) % 5.14/1.91 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cC8(v0) = v1) | ~ (ra_Px2(v0, v2) = 0)) % 5.14/1.91 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cC6xcomp(v0) = v1) | ~ (ra_Px4(v0, v2) = 0)) % 5.14/1.91 | (13) ! [v0] : ( ~ (cTEST(v0) = 0) | (cC8xcomp(v0) = 0 & cC12(v0) = 0)) % 5.14/1.91 | (14) ! [v0] : ! [v1] : ( ~ (ra_Px4(v0, v1) = 0) | ~ (cC6(v0) = 0)) % 5.14/1.91 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) % 5.14/1.91 | (16) ! [v0] : ! [v1] : ( ~ (ra_Px1(v0, v1) = 0) | ~ (cC2(v0) = 0)) % 5.14/1.91 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) % 5.14/1.91 | (18) cC4(iV21081) = 0 % 5.14/1.91 | (19) cC12(iV21080) = all_0_4_4 % 5.14/1.91 | (20) ! [v0] : ~ (cowlNothing(v0) = 0) % 5.14/1.91 | (21) cowlThing(iV21080) = 0 % 5.14/1.91 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rR1(v3, v2) = v1) | ~ (rR1(v3, v2) = v0)) % 5.14/1.91 | (23) ! [v0] : ( ~ (cC6xcomp(v0) = 0) | ? [v1] : ra_Px4(v0, v1) = 0) % 5.14/1.91 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ra_Px2(v3, v2) = v1) | ~ (ra_Px2(v3, v2) = v0)) % 5.14/1.91 | (25) ! [v0] : ( ~ (cC8(v0) = 0) | ? [v1] : ra_Px2(v0, v1) = 0) % 5.14/1.91 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC10(v2) = v1) | ~ (cC10(v2) = v0)) % 5.14/1.91 | (27) ! [v0] : ( ~ (cC4(v0) = 0) | ? [v1] : ? [v2] : (cC10(v0) = v2 & cC2(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))) % 5.14/1.91 | (28) ! [v0] : ! [v1] : ( ~ (cC4(v0) = v1) | ? [v2] : ? [v3] : (cC10(v0) = v2 & cC2(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) % 5.14/1.91 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ra_Px1(v3, v2) = v1) | ~ (ra_Px1(v3, v2) = v0)) % 5.14/1.91 | (30) cC8xcomp(iV21080) = 0 % 5.14/1.91 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC8(v2) = v1) | ~ (cC8(v2) = v0)) % 5.14/1.91 | (32) ! [v0] : ( ~ (rR1(iV21080, v0) = 0) | cC6xcomp(v0) = 0) % 5.14/1.91 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC2xcomp(v2) = v1) | ~ (cC2xcomp(v2) = v0)) % 5.14/1.91 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC12(v2) = v1) | ~ (cC12(v2) = v0)) % 5.14/1.91 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cC12(v0) = v1) | ~ (cC10(v2) = 0) | ? [v3] : ( ~ (v3 = 0) & rR1(v0, v2) = v3)) % 5.14/1.91 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC6(v2) = v1) | ~ (cC6(v2) = v0)) % 5.14/1.92 | (37) cC6xcomp(iV21081) = 0 % 5.14/1.92 | (38) ! [v0] : ! [v1] : (v1 = 0 | ~ (cTEST(v0) = v1) | ? [v2] : ? [v3] : (cC8xcomp(v0) = v2 & cC12(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 5.14/1.92 | (39) ! [v0] : ! [v1] : (v1 = 0 | ~ (cC8xcomp(v0) = v1) | ? [v2] : ra_Px2(v0, v2) = 0) % 5.14/1.92 | (40) ! [v0] : ! [v1] : (v1 = 0 | ~ (cC2(v0) = v1) | ? [v2] : ra_Px1(v0, v2) = 0) % 5.14/1.92 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC8xcomp(v2) = v1) | ~ (cC8xcomp(v2) = v0)) % 5.14/1.92 | (42) ! [v0] : ! [v1] : ( ~ (cC8xcomp(v0) = 0) | ~ (ra_Px2(v0, v1) = 0)) % 5.14/1.92 | (43) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) % 5.14/1.92 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC2(v2) = v1) | ~ (cC2(v2) = v0)) % 5.14/1.92 | (45) cC10(iV21081) = all_0_3_3 % 5.14/1.92 | (46) ! [v0] : ! [v1] : (v1 = 0 | ~ (cC6(v0) = v1) | ? [v2] : ra_Px4(v0, v2) = 0) % 5.14/1.92 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ra_Px4(v3, v2) = v1) | ~ (ra_Px4(v3, v2) = v0)) % 5.14/1.92 | (48) ! [v0] : ( ~ (cC2xcomp(v0) = 0) | ? [v1] : ? [v2] : (cC6(v0) = v2 & cC4(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))) % 5.14/1.92 | (49) ! [v0] : ( ~ (cC8(v0) = 0) | ? [v1] : (cC6(v1) = 0 & rR1(v0, v1) = 0)) % 5.14/1.92 | (50) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC4(v2) = v1) | ~ (cC4(v2) = v0)) % 5.14/1.92 | (51) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cC8(v0) = v1) | ~ (rR1(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & cC6(v2) = v3)) % 5.14/1.92 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cC2xcomp(v0) = v1) | ~ (ra_Px1(v0, v2) = 0)) % 5.14/1.92 | (53) ~ (all_0_3_3 = 0) | ~ (all_0_4_4 = 0) | (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)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)) % 5.14/1.92 | (54) ! [v0] : ( ~ (cC12(v0) = 0) | ? [v1] : (rR1(v0, v1) = 0 & cC10(v1) = 0)) % 5.14/1.92 | (55) cTEST(iV21080) = 0 % 5.14/1.92 | (56) rR1(iV21080, iV21081) = 0 % 5.14/1.92 | (57) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) % 5.14/1.92 | % 5.14/1.92 | Instantiating formula (13) with iV21080 and discharging atoms cTEST(iV21080) = 0, yields: % 5.14/1.92 | (58) cC8xcomp(iV21080) = 0 & cC12(iV21080) = 0 % 5.14/1.92 | % 5.14/1.92 | Applying alpha-rule on (58) yields: % 5.14/1.92 | (30) cC8xcomp(iV21080) = 0 % 5.14/1.92 | (60) cC12(iV21080) = 0 % 5.14/1.92 | % 5.14/1.92 | Instantiating formula (54) with iV21080 yields: % 5.14/1.92 | (61) ~ (cC12(iV21080) = 0) | ? [v0] : (rR1(iV21080, v0) = 0 & cC10(v0) = 0) % 5.14/1.92 | % 5.14/1.92 | Instantiating formula (27) with iV21081 and discharging atoms cC4(iV21081) = 0, yields: % 5.14/1.92 | (62) ? [v0] : ? [v1] : (cC10(iV21081) = v1 & cC2(iV21081) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 5.14/1.92 | % 5.14/1.92 | Instantiating (62) with all_9_0_5, all_9_1_6 yields: % 5.14/1.92 | (63) cC10(iV21081) = all_9_0_5 & cC2(iV21081) = all_9_1_6 & ( ~ (all_9_1_6 = 0) | all_9_0_5 = 0) % 5.14/1.92 | % 5.14/1.92 | Applying alpha-rule on (63) yields: % 5.14/1.92 | (64) cC10(iV21081) = all_9_0_5 % 5.14/1.92 | (65) cC2(iV21081) = all_9_1_6 % 5.14/1.92 | (66) ~ (all_9_1_6 = 0) | all_9_0_5 = 0 % 5.14/1.92 | % 5.14/1.92 +-Applying beta-rule and splitting (61), into two cases. % 5.14/1.92 |-Branch one: % 5.14/1.92 | (67) ~ (cC12(iV21080) = 0) % 5.14/1.92 | % 5.14/1.93 | Using (60) and (67) yields: % 5.14/1.93 | (68) $false % 5.14/1.93 | % 5.14/1.93 |-The branch is then unsatisfiable % 5.14/1.93 |-Branch two: % 5.14/1.93 | (60) cC12(iV21080) = 0 % 5.14/1.93 | (70) ? [v0] : (rR1(iV21080, v0) = 0 & cC10(v0) = 0) % 5.14/1.93 | % 5.14/1.93 | Instantiating formula (34) with iV21080, 0, all_0_4_4 and discharging atoms cC12(iV21080) = all_0_4_4, cC12(iV21080) = 0, yields: % 5.14/1.93 | (71) all_0_4_4 = 0 % 5.14/1.93 | % 5.14/1.93 | Instantiating formula (26) with iV21081, all_9_0_5, all_0_3_3 and discharging atoms cC10(iV21081) = all_9_0_5, cC10(iV21081) = all_0_3_3, yields: % 5.14/1.93 | (72) all_9_0_5 = all_0_3_3 % 5.14/1.93 | % 5.14/1.93 | Instantiating formula (44) with iV21081, all_9_1_6, 0 and discharging atoms cC2(iV21081) = all_9_1_6, cC2(iV21081) = 0, yields: % 5.14/1.93 | (73) all_9_1_6 = 0 % 5.14/1.93 | % 5.14/1.93 +-Applying beta-rule and splitting (66), into two cases. % 5.14/1.93 |-Branch one: % 5.14/1.93 | (74) ~ (all_9_1_6 = 0) % 5.14/1.93 | % 5.14/1.93 | Equations (73) can reduce 74 to: % 5.14/1.93 | (75) $false % 5.14/1.93 | % 5.14/1.93 |-The branch is then unsatisfiable % 5.14/1.93 |-Branch two: % 5.14/1.93 | (73) all_9_1_6 = 0 % 5.14/1.93 | (77) all_9_0_5 = 0 % 5.14/1.93 | % 5.14/1.93 | Combining equations (77,72) yields a new equation: % 5.14/1.93 | (78) all_0_3_3 = 0 % 5.14/1.93 | % 5.14/1.93 +-Applying beta-rule and splitting (53), into two cases. % 5.14/1.93 |-Branch one: % 5.14/1.93 | (79) ~ (all_0_3_3 = 0) % 5.14/1.93 | % 5.46/1.93 | Equations (78) can reduce 79 to: % 5.46/1.93 | (75) $false % 5.46/1.93 | % 5.46/1.93 |-The branch is then unsatisfiable % 5.46/1.93 |-Branch two: % 5.46/1.93 | (78) all_0_3_3 = 0 % 5.46/1.93 | (82) ~ (all_0_4_4 = 0) | (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)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)) % 5.46/1.93 | % 5.46/1.93 +-Applying beta-rule and splitting (82), into two cases. % 5.46/1.93 |-Branch one: % 5.46/1.93 | (83) ~ (all_0_4_4 = 0) % 5.46/1.93 | % 5.46/1.93 | Equations (71) can reduce 83 to: % 5.46/1.93 | (75) $false % 5.46/1.93 | % 5.46/1.93 |-The branch is then unsatisfiable % 5.46/1.93 |-Branch two: % 5.46/1.93 | (71) all_0_4_4 = 0 % 5.46/1.93 | (86) (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)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)) % 5.46/1.93 | % 5.46/1.93 +-Applying beta-rule and splitting (86), into two cases. % 5.46/1.93 |-Branch one: % 5.46/1.93 | (87) 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))) % 5.46/1.93 | % 5.46/1.93 | Applying alpha-rule on (87) yields: % 5.46/1.93 | (88) xsd_string(all_0_2_2) = all_0_1_1 % 5.46/1.93 | (89) xsd_integer(all_0_2_2) = all_0_0_0 % 5.46/1.93 | (90) (all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)) % 5.46/1.93 | % 5.46/1.93 | Instantiating formula (57) with all_0_2_2 yields: % 5.46/1.93 | (91) ~ (xsd_string(all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0) % 5.46/1.93 | % 5.46/1.93 | Instantiating formula (43) with all_0_1_1, all_0_2_2 and discharging atoms xsd_string(all_0_2_2) = all_0_1_1, yields: % 5.46/1.93 | (92) all_0_1_1 = 0 | xsd_integer(all_0_2_2) = 0 % 5.46/1.93 | % 5.46/1.93 +-Applying beta-rule and splitting (90), into two cases. % 5.46/1.93 |-Branch one: % 5.46/1.93 | (93) all_0_0_0 = 0 & all_0_1_1 = 0 % 5.46/1.93 | % 5.46/1.93 | Applying alpha-rule on (93) yields: % 5.46/1.93 | (94) all_0_0_0 = 0 % 5.46/1.93 | (95) all_0_1_1 = 0 % 5.46/1.93 | % 5.46/1.93 | From (95) and (88) follows: % 5.46/1.93 | (96) xsd_string(all_0_2_2) = 0 % 5.46/1.93 | % 5.46/1.93 | From (94) and (89) follows: % 5.46/1.93 | (97) xsd_integer(all_0_2_2) = 0 % 5.46/1.93 | % 5.46/1.93 +-Applying beta-rule and splitting (91), into two cases. % 5.46/1.93 |-Branch one: % 5.46/1.93 | (98) ~ (xsd_string(all_0_2_2) = 0) % 5.46/1.93 | % 5.46/1.94 | Using (96) and (98) yields: % 5.46/1.94 | (68) $false % 5.46/1.94 | % 5.46/1.94 |-The branch is then unsatisfiable % 5.46/1.94 |-Branch two: % 5.46/1.94 | (96) xsd_string(all_0_2_2) = 0 % 5.46/1.94 | (101) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0) % 5.46/1.94 | % 5.46/1.94 | Instantiating (101) with all_86_0_10 yields: % 5.46/1.94 | (102) ~ (all_86_0_10 = 0) & xsd_integer(all_0_2_2) = all_86_0_10 % 5.46/1.94 | % 5.46/1.94 | Applying alpha-rule on (102) yields: % 5.46/1.94 | (103) ~ (all_86_0_10 = 0) % 5.46/1.94 | (104) xsd_integer(all_0_2_2) = all_86_0_10 % 5.46/1.94 | % 5.46/1.94 | Instantiating formula (8) with all_0_2_2, 0, all_86_0_10 and discharging atoms xsd_integer(all_0_2_2) = all_86_0_10, xsd_integer(all_0_2_2) = 0, yields: % 5.46/1.94 | (105) all_86_0_10 = 0 % 5.46/1.94 | % 5.46/1.94 | Equations (105) can reduce 103 to: % 5.46/1.94 | (75) $false % 5.46/1.94 | % 5.46/1.94 |-The branch is then unsatisfiable % 5.46/1.94 |-Branch two: % 5.46/1.94 | (107) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) % 5.46/1.94 | % 5.46/1.94 | Applying alpha-rule on (107) yields: % 5.46/1.94 | (108) ~ (all_0_0_0 = 0) % 5.46/1.94 | (109) ~ (all_0_1_1 = 0) % 5.46/1.94 | % 5.46/1.94 +-Applying beta-rule and splitting (92), into two cases. % 5.46/1.94 |-Branch one: % 5.46/1.94 | (97) xsd_integer(all_0_2_2) = 0 % 5.46/1.94 | % 5.46/1.94 | Instantiating formula (8) with all_0_2_2, 0, all_0_0_0 and discharging atoms xsd_integer(all_0_2_2) = all_0_0_0, xsd_integer(all_0_2_2) = 0, yields: % 5.46/1.94 | (94) all_0_0_0 = 0 % 5.46/1.94 | % 5.46/1.94 | Equations (94) can reduce 108 to: % 5.46/1.94 | (75) $false % 5.46/1.94 | % 5.46/1.94 |-The branch is then unsatisfiable % 5.46/1.94 |-Branch two: % 5.46/1.94 | (113) ~ (xsd_integer(all_0_2_2) = 0) % 5.46/1.94 | (95) all_0_1_1 = 0 % 5.46/1.94 | % 5.46/1.94 | Equations (95) can reduce 109 to: % 5.46/1.94 | (75) $false % 5.46/1.94 | % 5.46/1.94 |-The branch is then unsatisfiable % 5.46/1.94 |-Branch two: % 5.46/1.94 | (116) cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0) % 5.46/1.94 | % 5.46/1.94 | Applying alpha-rule on (116) yields: % 5.46/1.94 | (117) cowlNothing(all_0_2_2) = all_0_0_0 % 5.46/1.94 | (118) cowlThing(all_0_2_2) = all_0_1_1 % 5.46/1.94 | (119) ~ (all_0_1_1 = 0) | all_0_0_0 = 0 % 5.46/1.94 | % 5.46/1.94 | Instantiating formula (20) with all_0_2_2 yields: % 5.46/1.94 | (120) ~ (cowlNothing(all_0_2_2) = 0) % 5.46/1.94 | % 5.46/1.94 | Instantiating formula (7) with all_0_1_1, all_0_2_2 and discharging atoms cowlThing(all_0_2_2) = all_0_1_1, yields: % 5.46/1.94 | (95) all_0_1_1 = 0 % 5.46/1.94 | % 5.46/1.94 +-Applying beta-rule and splitting (119), into two cases. % 5.46/1.94 |-Branch one: % 5.46/1.94 | (109) ~ (all_0_1_1 = 0) % 5.46/1.94 | % 5.46/1.94 | Equations (95) can reduce 109 to: % 5.46/1.94 | (75) $false % 5.46/1.94 | % 5.46/1.94 |-The branch is then unsatisfiable % 5.46/1.94 |-Branch two: % 5.46/1.94 | (95) all_0_1_1 = 0 % 5.46/1.94 | (94) all_0_0_0 = 0 % 5.46/1.94 | % 5.46/1.94 | From (94) and (117) follows: % 5.46/1.94 | (126) cowlNothing(all_0_2_2) = 0 % 5.46/1.94 | % 5.46/1.94 | Using (126) and (120) yields: % 5.46/1.94 | (68) $false % 5.46/1.94 | % 5.46/1.94 |-The branch is then unsatisfiable % 5.46/1.94 % SZS output end Proof for theBenchmark % 5.46/1.94 % 5.46/1.94 1348ms %------------------------------------------------------------------------------