%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KRS152+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 02:56:43 EDT 2022 % Result : Theorem 3.26s 1.37s % Output : Proof 4.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : KRS152+1 : TPTP v8.1.0. Released v3.1.0. % 0.03/0.12 % 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 09:28:08 EDT 2022 % 0.12/0.33 % CPUTime : % 0.54/0.58 ____ _ % 0.54/0.58 ___ / __ \_____(_)___ ________ __________ % 0.54/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.54/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.54/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.54/0.58 % 0.54/0.58 A Theorem Prover for First-Order Logic % 0.54/0.58 (ePrincess v.1.0) % 0.54/0.58 % 0.54/0.58 (c) Philipp Rümmer, 2009-2015 % 0.54/0.58 (c) Peter Backeman, 2014-2015 % 0.54/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.54/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.54/0.58 Bug reports to peter@backeman.se % 0.54/0.58 % 0.54/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.54/0.58 % 0.54/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.54/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.46/0.87 Prover 0: Preprocessing ... % 1.74/0.98 Prover 0: Warning: ignoring some quantifiers % 1.74/0.99 Prover 0: Constructing countermodel ... % 2.07/1.13 Prover 0: gave up % 2.07/1.13 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.34/1.15 Prover 1: Preprocessing ... % 2.81/1.27 Prover 1: Constructing countermodel ... % 3.26/1.37 Prover 1: proved (238ms) % 3.26/1.37 % 3.26/1.37 No countermodel exists, formula is valid % 3.26/1.37 % SZS status Theorem for theBenchmark % 3.26/1.37 % 3.26/1.37 Generating proof ... found it (size 57) % 4.11/1.66 % 4.11/1.66 % SZS output start Proof for theBenchmark % 4.11/1.66 Assumed formulas after preprocessing and simplification: % 4.11/1.66 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v1 = 0) & ~ (v0 = 0) & cTEST(iV21080) = 0 & cC8(iV21080) = v0 & cC6(iV21081) = v1 & cC12(iV21080) = v2 & rR1(iV21080, iV21081) = 0 & cC4(iV21081) = 0 & cC10(iV21081) = v3 & cC2(iV21081) = 0 & cowlThing(iV21081) = 0 & cowlThing(iV21080) = 0 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (rR1(v10, v9) = v8) | ~ (rR1(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (cTEST(v9) = v8) | ~ (cTEST(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (cC8(v9) = v8) | ~ (cC8(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (cC6(v9) = v8) | ~ (cC6(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (cC12(v9) = v8) | ~ (cC12(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (cC4(v9) = v8) | ~ (cC4(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (cC10(v9) = v8) | ~ (cC10(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (cC2(v9) = v8) | ~ (cC2(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (xsd_string(v9) = v8) | ~ (xsd_string(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (xsd_integer(v9) = v8) | ~ (xsd_integer(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (cowlNothing(v9) = v8) | ~ (cowlNothing(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (cowlThing(v9) = v8) | ~ (cowlThing(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (cC8(v7) = v8) | ~ (rR1(v7, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & cC6(v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (cC12(v7) = v8) | ~ (cC10(v9) = 0) | ? [v10] : ( ~ (v10 = 0) & rR1(v7, v9) = v10)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (cTEST(v7) = v8) | ? [v9] : ? [v10] : (cC8(v7) = v10 & cC12(v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v7] : ! [v8] : (v8 = 0 | ~ (xsd_string(v7) = v8) | xsd_integer(v7) = 0) & ! [v7] : ! [v8] : (v8 = 0 | ~ (cowlThing(v7) = v8)) & ! [v7] : ! [v8] : ( ~ (cC4(v7) = v8) | ? [v9] : ? [v10] : (cC6(v7) = v9 & cC2(v7) = v10 & ( ~ (v9 = 0) | (v8 = 0 & ~ (v10 = 0))))) & ! [v7] : ! [v8] : ( ~ (cC4(v7) = v8) | ? [v9] : ? [v10] : (cC10(v7) = v9 & cC2(v7) = v10 & ( ~ (v9 = 0) | (v10 = 0 & v8 = 0)))) & ! [v7] : ( ~ (cTEST(v7) = 0) | ? [v8] : ( ~ (v8 = 0) & cC8(v7) = v8 & cC12(v7) = 0)) & ! [v7] : ( ~ (cC8(v7) = 0) | ? [v8] : (cC6(v8) = 0 & rR1(v7, v8) = 0)) & ! [v7] : ( ~ (cC12(v7) = 0) | ? [v8] : (rR1(v7, v8) = 0 & cC10(v8) = 0)) & ! [v7] : ( ~ (rR1(iV21080, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & cC6(v7) = v8)) & ! [v7] : ( ~ (cC4(v7) = 0) | ? [v8] : ? [v9] : (cC6(v7) = v9 & cC2(v7) = v8 & (v9 = 0 | v8 = 0))) & ! [v7] : ( ~ (cC4(v7) = 0) | ? [v8] : ? [v9] : (cC10(v7) = v9 & cC2(v7) = v8 & ( ~ (v8 = 0) | v9 = 0))) & ! [v7] : ( ~ (xsd_string(v7) = 0) | ? [v8] : ( ~ (v8 = 0) & xsd_integer(v7) = v8)) & ! [v7] : ~ (cowlNothing(v7) = 0) & ( ~ (v3 = 0) | ~ (v2 = 0) | (xsd_string(v4) = v5 & xsd_integer(v4) = v6 & ((v6 = 0 & v5 = 0) | ( ~ (v6 = 0) & ~ (v5 = 0)))) | (cowlNothing(v4) = v6 & cowlThing(v4) = v5 & ( ~ (v5 = 0) | v6 = 0)))) % 4.27/1.70 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields: % 4.27/1.70 | (1) ~ (all_0_5_5 = 0) & ~ (all_0_6_6 = 0) & cTEST(iV21080) = 0 & cC8(iV21080) = all_0_6_6 & cC6(iV21081) = all_0_5_5 & 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 | ~ (rR1(v3, v2) = v1) | ~ (rR1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cTEST(v2) = v1) | ~ (cTEST(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC8(v2) = v1) | ~ (cC8(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC6(v2) = v1) | ~ (cC6(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) | ~ (rR1(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & cC6(v2) = v3)) & ! [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] : (cC8(v0) = v3 & cC12(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (cC4(v0) = v1) | ? [v2] : ? [v3] : (cC6(v0) = v2 & cC2(v0) = v3 & ( ~ (v2 = 0) | (v1 = 0 & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ( ~ (cC4(v0) = v1) | ? [v2] : ? [v3] : (cC10(v0) = v2 & cC2(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0] : ( ~ (cTEST(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & cC8(v0) = v1 & cC12(v0) = 0)) & ! [v0] : ( ~ (cC8(v0) = 0) | ? [v1] : (cC6(v1) = 0 & rR1(v0, v1) = 0)) & ! [v0] : ( ~ (cC12(v0) = 0) | ? [v1] : (rR1(v0, v1) = 0 & cC10(v1) = 0)) & ! [v0] : ( ~ (rR1(iV21080, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & cC6(v0) = v1)) & ! [v0] : ( ~ (cC4(v0) = 0) | ? [v1] : ? [v2] : (cC6(v0) = v2 & cC2(v0) = v1 & (v2 = 0 | v1 = 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))) % 4.27/1.72 | % 4.27/1.72 | Applying alpha-rule on (1) yields: % 4.27/1.72 | (2) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) % 4.27/1.72 | (3) cC4(iV21081) = 0 % 4.27/1.72 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) % 4.27/1.72 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rR1(v3, v2) = v1) | ~ (rR1(v3, v2) = v0)) % 4.27/1.72 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC4(v2) = v1) | ~ (cC4(v2) = v0)) % 4.27/1.72 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) % 4.27/1.72 | (8) ! [v0] : ( ~ (cTEST(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & cC8(v0) = v1 & cC12(v0) = 0)) % 4.27/1.72 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC10(v2) = v1) | ~ (cC10(v2) = v0)) % 4.27/1.72 | (10) ! [v0] : ~ (cowlNothing(v0) = 0) % 4.27/1.72 | (11) ! [v0] : ( ~ (rR1(iV21080, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & cC6(v0) = v1)) % 4.27/1.72 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) % 4.27/1.72 | (13) cC2(iV21081) = 0 % 4.27/1.72 | (14) cC8(iV21080) = all_0_6_6 % 4.27/1.72 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC2(v2) = v1) | ~ (cC2(v2) = v0)) % 4.27/1.72 | (16) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) % 4.27/1.72 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC6(v2) = v1) | ~ (cC6(v2) = v0)) % 4.27/1.72 | (18) cC6(iV21081) = all_0_5_5 % 4.27/1.72 | (19) cowlThing(iV21080) = 0 % 4.27/1.72 | (20) ! [v0] : ( ~ (cC8(v0) = 0) | ? [v1] : (cC6(v1) = 0 & rR1(v0, v1) = 0)) % 4.27/1.72 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 4.27/1.72 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cTEST(v2) = v1) | ~ (cTEST(v2) = v0)) % 4.27/1.72 | (23) ~ (all_0_5_5 = 0) % 4.27/1.72 | (24) cC12(iV21080) = all_0_4_4 % 4.27/1.72 | (25) ~ (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)) % 4.27/1.72 | (26) ! [v0] : ( ~ (cC4(v0) = 0) | ? [v1] : ? [v2] : (cC6(v0) = v2 & cC2(v0) = v1 & (v2 = 0 | v1 = 0))) % 4.27/1.72 | (27) ! [v0] : ! [v1] : ( ~ (cC4(v0) = v1) | ? [v2] : ? [v3] : (cC6(v0) = v2 & cC2(v0) = v3 & ( ~ (v2 = 0) | (v1 = 0 & ~ (v3 = 0))))) % 4.27/1.72 | (28) cowlThing(iV21081) = 0 % 4.27/1.72 | (29) ! [v0] : ( ~ (cC12(v0) = 0) | ? [v1] : (rR1(v0, v1) = 0 & cC10(v1) = 0)) % 4.27/1.72 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC12(v2) = v1) | ~ (cC12(v2) = v0)) % 4.27/1.72 | (31) rR1(iV21080, iV21081) = 0 % 4.27/1.73 | (32) ! [v0] : ( ~ (cC4(v0) = 0) | ? [v1] : ? [v2] : (cC10(v0) = v2 & cC2(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))) % 4.27/1.73 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cC12(v0) = v1) | ~ (cC10(v2) = 0) | ? [v3] : ( ~ (v3 = 0) & rR1(v0, v2) = v3)) % 4.27/1.73 | (34) ~ (all_0_6_6 = 0) % 4.27/1.73 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) % 4.27/1.73 | (36) ! [v0] : ! [v1] : (v1 = 0 | ~ (cTEST(v0) = v1) | ? [v2] : ? [v3] : (cC8(v0) = v3 & cC12(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 4.27/1.73 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC8(v2) = v1) | ~ (cC8(v2) = v0)) % 4.27/1.73 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cC8(v0) = v1) | ~ (rR1(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & cC6(v2) = v3)) % 4.27/1.73 | (39) ! [v0] : ! [v1] : ( ~ (cC4(v0) = v1) | ? [v2] : ? [v3] : (cC10(v0) = v2 & cC2(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) % 4.27/1.73 | (40) cTEST(iV21080) = 0 % 4.27/1.73 | (41) cC10(iV21081) = all_0_3_3 % 4.27/1.73 | % 4.27/1.73 | Instantiating formula (8) with iV21080 and discharging atoms cTEST(iV21080) = 0, yields: % 4.27/1.73 | (42) ? [v0] : ( ~ (v0 = 0) & cC8(iV21080) = v0 & cC12(iV21080) = 0) % 4.27/1.73 | % 4.27/1.73 | Instantiating formula (29) with iV21080 yields: % 4.27/1.73 | (43) ~ (cC12(iV21080) = 0) | ? [v0] : (rR1(iV21080, v0) = 0 & cC10(v0) = 0) % 4.27/1.73 | % 4.27/1.73 | Instantiating formula (32) with iV21081 and discharging atoms cC4(iV21081) = 0, yields: % 4.27/1.73 | (44) ? [v0] : ? [v1] : (cC10(iV21081) = v1 & cC2(iV21081) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 4.27/1.73 | % 4.27/1.73 | Instantiating (44) with all_8_0_7, all_8_1_8 yields: % 4.27/1.73 | (45) cC10(iV21081) = all_8_0_7 & cC2(iV21081) = all_8_1_8 & ( ~ (all_8_1_8 = 0) | all_8_0_7 = 0) % 4.27/1.73 | % 4.27/1.73 | Applying alpha-rule on (45) yields: % 4.27/1.73 | (46) cC10(iV21081) = all_8_0_7 % 4.27/1.73 | (47) cC2(iV21081) = all_8_1_8 % 4.27/1.73 | (48) ~ (all_8_1_8 = 0) | all_8_0_7 = 0 % 4.27/1.73 | % 4.27/1.73 | Instantiating (42) with all_10_0_9 yields: % 4.27/1.73 | (49) ~ (all_10_0_9 = 0) & cC8(iV21080) = all_10_0_9 & cC12(iV21080) = 0 % 4.27/1.73 | % 4.27/1.73 | Applying alpha-rule on (49) yields: % 4.27/1.73 | (50) ~ (all_10_0_9 = 0) % 4.27/1.73 | (51) cC8(iV21080) = all_10_0_9 % 4.27/1.73 | (52) cC12(iV21080) = 0 % 4.27/1.73 | % 4.27/1.73 +-Applying beta-rule and splitting (43), into two cases. % 4.27/1.73 |-Branch one: % 4.27/1.73 | (53) ~ (cC12(iV21080) = 0) % 4.27/1.73 | % 4.27/1.73 | Using (52) and (53) yields: % 4.27/1.73 | (54) $false % 4.27/1.73 | % 4.27/1.73 |-The branch is then unsatisfiable % 4.27/1.73 |-Branch two: % 4.27/1.73 | (52) cC12(iV21080) = 0 % 4.27/1.73 | (56) ? [v0] : (rR1(iV21080, v0) = 0 & cC10(v0) = 0) % 4.27/1.73 | % 4.27/1.73 | Instantiating formula (30) with iV21080, 0, all_0_4_4 and discharging atoms cC12(iV21080) = all_0_4_4, cC12(iV21080) = 0, yields: % 4.27/1.74 | (57) all_0_4_4 = 0 % 4.27/1.74 | % 4.27/1.74 | Instantiating formula (9) with iV21081, all_8_0_7, all_0_3_3 and discharging atoms cC10(iV21081) = all_8_0_7, cC10(iV21081) = all_0_3_3, yields: % 4.27/1.74 | (58) all_8_0_7 = all_0_3_3 % 4.27/1.74 | % 4.27/1.74 | Instantiating formula (15) with iV21081, all_8_1_8, 0 and discharging atoms cC2(iV21081) = all_8_1_8, cC2(iV21081) = 0, yields: % 4.27/1.74 | (59) all_8_1_8 = 0 % 4.27/1.74 | % 4.27/1.74 +-Applying beta-rule and splitting (48), into two cases. % 4.27/1.74 |-Branch one: % 4.27/1.74 | (60) ~ (all_8_1_8 = 0) % 4.27/1.74 | % 4.27/1.74 | Equations (59) can reduce 60 to: % 4.27/1.74 | (61) $false % 4.27/1.74 | % 4.27/1.74 |-The branch is then unsatisfiable % 4.27/1.74 |-Branch two: % 4.27/1.74 | (59) all_8_1_8 = 0 % 4.27/1.74 | (63) all_8_0_7 = 0 % 4.27/1.74 | % 4.27/1.74 | Combining equations (63,58) yields a new equation: % 4.27/1.74 | (64) all_0_3_3 = 0 % 4.27/1.74 | % 4.27/1.74 +-Applying beta-rule and splitting (25), into two cases. % 4.27/1.74 |-Branch one: % 4.27/1.74 | (65) ~ (all_0_3_3 = 0) % 4.27/1.74 | % 4.27/1.74 | Equations (64) can reduce 65 to: % 4.27/1.74 | (61) $false % 4.27/1.74 | % 4.27/1.74 |-The branch is then unsatisfiable % 4.27/1.74 |-Branch two: % 4.27/1.74 | (64) all_0_3_3 = 0 % 4.27/1.74 | (68) ~ (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)) % 4.27/1.74 | % 4.27/1.74 +-Applying beta-rule and splitting (68), into two cases. % 4.27/1.74 |-Branch one: % 4.27/1.74 | (69) ~ (all_0_4_4 = 0) % 4.27/1.74 | % 4.27/1.74 | Equations (57) can reduce 69 to: % 4.27/1.74 | (61) $false % 4.27/1.74 | % 4.27/1.74 |-The branch is then unsatisfiable % 4.27/1.74 |-Branch two: % 4.27/1.74 | (57) all_0_4_4 = 0 % 4.27/1.74 | (72) (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)) % 4.27/1.74 | % 4.27/1.74 +-Applying beta-rule and splitting (72), into two cases. % 4.27/1.74 |-Branch one: % 4.27/1.74 | (73) 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))) % 4.27/1.74 | % 4.27/1.74 | Applying alpha-rule on (73) yields: % 4.27/1.74 | (74) xsd_string(all_0_2_2) = all_0_1_1 % 4.27/1.74 | (75) xsd_integer(all_0_2_2) = all_0_0_0 % 4.27/1.74 | (76) (all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)) % 4.27/1.74 | % 4.27/1.74 | Instantiating formula (16) with all_0_2_2 yields: % 4.27/1.74 | (77) ~ (xsd_string(all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0) % 4.27/1.74 | % 4.27/1.74 | Instantiating formula (12) with all_0_1_1, all_0_2_2 and discharging atoms xsd_string(all_0_2_2) = all_0_1_1, yields: % 4.27/1.74 | (78) all_0_1_1 = 0 | xsd_integer(all_0_2_2) = 0 % 4.27/1.74 | % 4.27/1.74 +-Applying beta-rule and splitting (76), into two cases. % 4.27/1.74 |-Branch one: % 4.27/1.74 | (79) all_0_0_0 = 0 & all_0_1_1 = 0 % 4.27/1.74 | % 4.27/1.74 | Applying alpha-rule on (79) yields: % 4.27/1.74 | (80) all_0_0_0 = 0 % 4.27/1.74 | (81) all_0_1_1 = 0 % 4.27/1.74 | % 4.27/1.74 | From (81) and (74) follows: % 4.27/1.74 | (82) xsd_string(all_0_2_2) = 0 % 4.27/1.74 | % 4.27/1.74 | From (80) and (75) follows: % 4.27/1.74 | (83) xsd_integer(all_0_2_2) = 0 % 4.27/1.74 | % 4.27/1.74 +-Applying beta-rule and splitting (77), into two cases. % 4.27/1.74 |-Branch one: % 4.27/1.74 | (84) ~ (xsd_string(all_0_2_2) = 0) % 4.27/1.74 | % 4.27/1.74 | Using (82) and (84) yields: % 4.27/1.74 | (54) $false % 4.27/1.74 | % 4.27/1.74 |-The branch is then unsatisfiable % 4.27/1.74 |-Branch two: % 4.27/1.74 | (82) xsd_string(all_0_2_2) = 0 % 4.27/1.75 | (87) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0) % 4.27/1.75 | % 4.27/1.75 | Instantiating (87) with all_90_0_12 yields: % 4.27/1.75 | (88) ~ (all_90_0_12 = 0) & xsd_integer(all_0_2_2) = all_90_0_12 % 4.27/1.75 | % 4.27/1.75 | Applying alpha-rule on (88) yields: % 4.27/1.75 | (89) ~ (all_90_0_12 = 0) % 4.27/1.75 | (90) xsd_integer(all_0_2_2) = all_90_0_12 % 4.27/1.75 | % 4.27/1.75 | Instantiating formula (21) with all_0_2_2, 0, all_90_0_12 and discharging atoms xsd_integer(all_0_2_2) = all_90_0_12, xsd_integer(all_0_2_2) = 0, yields: % 4.27/1.75 | (91) all_90_0_12 = 0 % 4.27/1.75 | % 4.27/1.75 | Equations (91) can reduce 89 to: % 4.27/1.75 | (61) $false % 4.27/1.75 | % 4.27/1.75 |-The branch is then unsatisfiable % 4.27/1.75 |-Branch two: % 4.27/1.75 | (93) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) % 4.27/1.75 | % 4.27/1.75 | Applying alpha-rule on (93) yields: % 4.27/1.75 | (94) ~ (all_0_0_0 = 0) % 4.27/1.75 | (95) ~ (all_0_1_1 = 0) % 4.27/1.75 | % 4.27/1.75 +-Applying beta-rule and splitting (78), into two cases. % 4.27/1.75 |-Branch one: % 4.27/1.75 | (83) xsd_integer(all_0_2_2) = 0 % 4.27/1.75 | % 4.27/1.75 | Instantiating formula (21) 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: % 4.27/1.75 | (80) all_0_0_0 = 0 % 4.27/1.75 | % 4.27/1.75 | Equations (80) can reduce 94 to: % 4.27/1.75 | (61) $false % 4.27/1.75 | % 4.27/1.75 |-The branch is then unsatisfiable % 4.27/1.75 |-Branch two: % 4.27/1.75 | (99) ~ (xsd_integer(all_0_2_2) = 0) % 4.27/1.75 | (81) all_0_1_1 = 0 % 4.27/1.75 | % 4.27/1.75 | Equations (81) can reduce 95 to: % 4.27/1.75 | (61) $false % 4.27/1.75 | % 4.27/1.75 |-The branch is then unsatisfiable % 4.27/1.75 |-Branch two: % 4.27/1.75 | (102) 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) % 4.27/1.75 | % 4.27/1.75 | Applying alpha-rule on (102) yields: % 4.27/1.75 | (103) cowlNothing(all_0_2_2) = all_0_0_0 % 4.27/1.75 | (104) cowlThing(all_0_2_2) = all_0_1_1 % 4.27/1.75 | (105) ~ (all_0_1_1 = 0) | all_0_0_0 = 0 % 4.27/1.75 | % 4.27/1.75 | Instantiating formula (10) with all_0_2_2 yields: % 4.27/1.75 | (106) ~ (cowlNothing(all_0_2_2) = 0) % 4.27/1.75 | % 4.27/1.75 | Instantiating formula (2) with all_0_1_1, all_0_2_2 and discharging atoms cowlThing(all_0_2_2) = all_0_1_1, yields: % 4.27/1.75 | (81) all_0_1_1 = 0 % 4.27/1.75 | % 4.27/1.75 +-Applying beta-rule and splitting (105), into two cases. % 4.27/1.75 |-Branch one: % 4.27/1.75 | (95) ~ (all_0_1_1 = 0) % 4.27/1.75 | % 4.27/1.75 | Equations (81) can reduce 95 to: % 4.27/1.75 | (61) $false % 4.27/1.75 | % 4.27/1.75 |-The branch is then unsatisfiable % 4.27/1.75 |-Branch two: % 4.27/1.75 | (81) all_0_1_1 = 0 % 4.27/1.75 | (80) all_0_0_0 = 0 % 4.27/1.75 | % 4.27/1.75 | From (80) and (103) follows: % 4.27/1.75 | (112) cowlNothing(all_0_2_2) = 0 % 4.27/1.75 | % 4.27/1.75 | Using (112) and (106) yields: % 4.27/1.75 | (54) $false % 4.27/1.75 | % 4.27/1.75 |-The branch is then unsatisfiable % 4.27/1.75 % SZS output end Proof for theBenchmark % 4.27/1.75 % 4.27/1.75 1166ms %------------------------------------------------------------------------------