%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KRS175+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n020.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 02:56:48 EDT 2022 % Result : Theorem 3.63s 1.59s % Output : Proof 5.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : KRS175+1 : TPTP v8.1.0. Released v3.1.0. % 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n020.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Tue Jun 7 10:29:51 EDT 2022 % 0.12/0.35 % CPUTime : % 0.56/0.59 ____ _ % 0.56/0.59 ___ / __ \_____(_)___ ________ __________ % 0.56/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.56/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.56/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.56/0.59 % 0.56/0.59 A Theorem Prover for First-Order Logic % 0.56/0.59 (ePrincess v.1.0) % 0.56/0.59 % 0.56/0.59 (c) Philipp Rümmer, 2009-2015 % 0.56/0.59 (c) Peter Backeman, 2014-2015 % 0.56/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.56/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.56/0.59 Bug reports to peter@backeman.se % 0.56/0.59 % 0.56/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.56/0.59 % 0.56/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.52/0.95 Prover 0: Preprocessing ... % 1.73/1.06 Prover 0: Warning: ignoring some quantifiers % 1.89/1.08 Prover 0: Constructing countermodel ... % 2.11/1.18 Prover 0: gave up % 2.11/1.18 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.26/1.21 Prover 1: Preprocessing ... % 2.63/1.32 Prover 1: Constructing countermodel ... % 2.81/1.40 Prover 1: gave up % 2.81/1.40 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.81/1.42 Prover 2: Preprocessing ... % 3.39/1.50 Prover 2: Warning: ignoring some quantifiers % 3.39/1.51 Prover 2: Constructing countermodel ... % 3.63/1.59 Prover 2: proved (183ms) % 3.63/1.59 % 3.63/1.59 No countermodel exists, formula is valid % 3.63/1.59 % SZS status Theorem for theBenchmark % 3.63/1.59 % 3.63/1.59 Generating proof ... Warning: ignoring some quantifiers % 4.85/1.85 found it (size 68) % 4.85/1.85 % 4.85/1.85 % SZS output start Proof for theBenchmark % 4.85/1.85 Assumed formulas after preprocessing and simplification: % 4.85/1.85 | (0) ? [v0] : ? [v1] : ? [v2] : (cowlThing(ib) = 0 & cowlThing(ia) = 0 & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (xsd_string(v5) = v4) | ~ (xsd_string(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (xsd_integer(v5) = v4) | ~ (xsd_integer(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (cowlThing(v5) = v4) | ~ (cowlThing(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (cowlNothing(v5) = v4) | ~ (cowlNothing(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (cB(v5) = v4) | ~ (cB(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (cA_and_B(v5) = v4) | ~ (cA_and_B(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (cA(v5) = v4) | ~ (cA(v5) = v3)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (xsd_string(v3) = v4) | ~ (xsd_string(v3) = 0)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (xsd_string(v3) = v4) | xsd_integer(v3) = 0) & ! [v3] : ! [v4] : (v4 = 0 | ~ (xsd_integer(v3) = v4) | ~ (xsd_integer(v3) = 0)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (xsd_integer(v3) = v4) | xsd_string(v3) = 0) & ! [v3] : ! [v4] : (v4 = 0 | ~ (cowlThing(v3) = v4) | ~ (cowlThing(v3) = 0)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (cowlThing(v3) = v4)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (cowlNothing(v3) = v4) | ~ (cowlNothing(v3) = 0)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (cB(v3) = v4) | ~ (cB(v3) = 0)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (cB(v3) = v4) | ? [v5] : ((v5 = 0 & cA(v3) = 0) | ( ~ (v5 = 0) & cA_and_B(v3) = v5))) & ! [v3] : ! [v4] : (v4 = 0 | ~ (cA_and_B(v3) = v4) | ~ (cA_and_B(v3) = 0)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (cA_and_B(v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & cB(v3) = v6 & cA(v3) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (cA(v3) = v4) | ~ (cA(v3) = 0)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (cA(v3) = v4) | ? [v5] : ((v5 = 0 & cB(v3) = 0) | ( ~ (v5 = 0) & cA_and_B(v3) = v5))) & ! [v3] : ! [v4] : ( ~ (cB(v3) = v4) | ? [v5] : ((v5 = 0 & cA_and_B(v3) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & cA(v3) = v5))) & ! [v3] : ! [v4] : ( ~ (cA(v3) = v4) | ? [v5] : ((v5 = 0 & cA_and_B(v3) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & cB(v3) = v5))) & ! [v3] : (v3 = ib | ~ (cB(v3) = 0)) & ! [v3] : (v3 = ia | ~ (cA(v3) = 0)) & ! [v3] : (v3 = 0 | ~ (cB(ib) = v3)) & ! [v3] : (v3 = 0 | ~ (cA(ia) = v3)) & ! [v3] : ( ~ (xsd_string(v3) = 0) | ? [v4] : ( ~ (v4 = 0) & xsd_integer(v3) = v4)) & ! [v3] : ( ~ (xsd_integer(v3) = 0) | ? [v4] : ( ~ (v4 = 0) & xsd_string(v3) = v4)) & ! [v3] : ~ (cowlNothing(v3) = 0) & ! [v3] : ( ~ (cA_and_B(v3) = 0) | ? [v4] : ((v4 = 0 & cB(v3) = 0) | (v4 = 0 & cA(v3) = 0))) & ? [v3] : ? [v4] : xsd_string(v3) = v4 & ? [v3] : ? [v4] : xsd_integer(v3) = v4 & ? [v3] : ? [v4] : cowlThing(v3) = v4 & ? [v3] : ? [v4] : cowlNothing(v3) = v4 & ? [v3] : ? [v4] : cB(v3) = v4 & ? [v3] : ? [v4] : cA_and_B(v3) = v4 & ? [v3] : ? [v4] : cA(v3) = v4 & ((v2 = 0 & cowlNothing(v0) = 0) | ( ~ (v1 = 0) & cowlThing(v0) = v1) | (xsd_string(v0) = v1 & xsd_integer(v0) = v2 & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & ~ (v1 = 0)))) | (cA_and_B(v0) = v1 & ((v1 = 0 & ~ (v0 = ib) & ~ (v0 = ia)) | ( ~ (v1 = 0) & (v0 = ib | v0 = ia)))))) % 4.85/1.89 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 4.85/1.89 | (1) cowlThing(ib) = 0 & cowlThing(ia) = 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 | ~ (cB(v2) = v1) | ~ (cB(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cA_and_B(v2) = v1) | ~ (cA_and_B(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cA(v2) = v1) | ~ (cA(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ (xsd_string(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ (xsd_integer(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | xsd_string(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (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 | ~ (cB(v0) = v1) | ~ (cB(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cB(v0) = v1) | ? [v2] : ((v2 = 0 & cA(v0) = 0) | ( ~ (v2 = 0) & cA_and_B(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cA_and_B(v0) = v1) | ~ (cA_and_B(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cA_and_B(v0) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & ~ (v2 = 0) & cB(v0) = v3 & cA(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cA(v0) = v1) | ~ (cA(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cA(v0) = v1) | ? [v2] : ((v2 = 0 & cB(v0) = 0) | ( ~ (v2 = 0) & cA_and_B(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (cB(v0) = v1) | ? [v2] : ((v2 = 0 & cA_and_B(v0) = 0) | ( ~ (v2 = 0) & ~ (v1 = 0) & cA(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (cA(v0) = v1) | ? [v2] : ((v2 = 0 & cA_and_B(v0) = 0) | ( ~ (v2 = 0) & ~ (v1 = 0) & cB(v0) = v2))) & ! [v0] : (v0 = ib | ~ (cB(v0) = 0)) & ! [v0] : (v0 = ia | ~ (cA(v0) = 0)) & ! [v0] : (v0 = 0 | ~ (cB(ib) = v0)) & ! [v0] : (v0 = 0 | ~ (cA(ia) = 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] : ( ~ (cA_and_B(v0) = 0) | ? [v1] : ((v1 = 0 & cB(v0) = 0) | (v1 = 0 & cA(v0) = 0))) & ? [v0] : ? [v1] : xsd_string(v0) = v1 & ? [v0] : ? [v1] : xsd_integer(v0) = v1 & ? [v0] : ? [v1] : cowlThing(v0) = v1 & ? [v0] : ? [v1] : cowlNothing(v0) = v1 & ? [v0] : ? [v1] : cB(v0) = v1 & ? [v0] : ? [v1] : cA_and_B(v0) = v1 & ? [v0] : ? [v1] : cA(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) | (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)))) | (cA_and_B(all_0_2_2) = all_0_1_1 & ((all_0_1_1 = 0 & ~ (all_0_2_2 = ib) & ~ (all_0_2_2 = ia)) | ( ~ (all_0_1_1 = 0) & (all_0_2_2 = ib | all_0_2_2 = ia))))) % 4.85/1.89 | % 4.85/1.89 | Applying alpha-rule on (1) yields: % 4.85/1.90 | (2) ! [v0] : ! [v1] : (v1 = 0 | ~ (cA(v0) = v1) | ~ (cA(v0) = 0)) % 4.85/1.90 | (3) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ (cowlThing(v0) = 0)) % 4.85/1.90 | (4) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | xsd_string(v0) = 0) % 4.85/1.90 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) % 4.85/1.90 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) % 4.85/1.90 | (7) ! [v0] : ! [v1] : (v1 = 0 | ~ (cB(v0) = v1) | ? [v2] : ((v2 = 0 & cA(v0) = 0) | ( ~ (v2 = 0) & cA_and_B(v0) = v2))) % 4.85/1.90 | (8) ! [v0] : ! [v1] : (v1 = 0 | ~ (cA_and_B(v0) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & ~ (v2 = 0) & cB(v0) = v3 & cA(v0) = v2)) % 4.85/1.90 | (9) ! [v0] : ( ~ (xsd_integer(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_string(v0) = v1)) % 4.85/1.90 | (10) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) % 4.85/1.90 | (11) cowlThing(ib) = 0 % 4.85/1.90 | (12) ? [v0] : ? [v1] : cowlThing(v0) = v1 % 4.85/1.90 | (13) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) % 4.85/1.90 | (14) ! [v0] : ! [v1] : (v1 = 0 | ~ (cB(v0) = v1) | ~ (cB(v0) = 0)) % 4.85/1.90 | (15) ? [v0] : ? [v1] : xsd_string(v0) = v1 % 4.85/1.90 | (16) ! [v0] : ! [v1] : ( ~ (cA(v0) = v1) | ? [v2] : ((v2 = 0 & cA_and_B(v0) = 0) | ( ~ (v2 = 0) & ~ (v1 = 0) & cB(v0) = v2))) % 4.85/1.90 | (17) ! [v0] : ! [v1] : ( ~ (cB(v0) = v1) | ? [v2] : ((v2 = 0 & cA_and_B(v0) = 0) | ( ~ (v2 = 0) & ~ (v1 = 0) & cA(v0) = v2))) % 4.85/1.90 | (18) ! [v0] : (v0 = 0 | ~ (cA(ia) = v0)) % 4.85/1.90 | (19) (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) | (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)))) | (cA_and_B(all_0_2_2) = all_0_1_1 & ((all_0_1_1 = 0 & ~ (all_0_2_2 = ib) & ~ (all_0_2_2 = ia)) | ( ~ (all_0_1_1 = 0) & (all_0_2_2 = ib | all_0_2_2 = ia)))) % 5.16/1.90 | (20) ! [v0] : ! [v1] : (v1 = 0 | ~ (cA(v0) = v1) | ? [v2] : ((v2 = 0 & cB(v0) = 0) | ( ~ (v2 = 0) & cA_and_B(v0) = v2))) % 5.16/1.90 | (21) ! [v0] : (v0 = ia | ~ (cA(v0) = 0)) % 5.16/1.90 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 5.16/1.90 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cA(v2) = v1) | ~ (cA(v2) = v0)) % 5.16/1.90 | (24) ? [v0] : ? [v1] : cowlNothing(v0) = v1 % 5.16/1.90 | (25) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlNothing(v0) = v1) | ~ (cowlNothing(v0) = 0)) % 5.16/1.90 | (26) ? [v0] : ? [v1] : cB(v0) = v1 % 5.16/1.90 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) % 5.16/1.90 | (28) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ (xsd_string(v0) = 0)) % 5.16/1.90 | (29) ! [v0] : ( ~ (cA_and_B(v0) = 0) | ? [v1] : ((v1 = 0 & cB(v0) = 0) | (v1 = 0 & cA(v0) = 0))) % 5.16/1.90 | (30) ! [v0] : ~ (cowlNothing(v0) = 0) % 5.16/1.91 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) % 5.16/1.91 | (32) ! [v0] : (v0 = ib | ~ (cB(v0) = 0)) % 5.16/1.91 | (33) ? [v0] : ? [v1] : cA(v0) = v1 % 5.16/1.91 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cA_and_B(v2) = v1) | ~ (cA_and_B(v2) = v0)) % 5.16/1.91 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cB(v2) = v1) | ~ (cB(v2) = v0)) % 5.16/1.91 | (36) cowlThing(ia) = 0 % 5.16/1.91 | (37) ! [v0] : (v0 = 0 | ~ (cB(ib) = v0)) % 5.16/1.91 | (38) ! [v0] : ! [v1] : (v1 = 0 | ~ (cA_and_B(v0) = v1) | ~ (cA_and_B(v0) = 0)) % 5.16/1.91 | (39) ? [v0] : ? [v1] : cA_and_B(v0) = v1 % 5.16/1.91 | (40) ? [v0] : ? [v1] : xsd_integer(v0) = v1 % 5.16/1.91 | (41) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ (xsd_integer(v0) = 0)) % 5.16/1.91 | % 5.16/1.91 +-Applying beta-rule and splitting (19), into two cases. % 5.16/1.91 |-Branch one: % 5.16/1.91 | (42) (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) | (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)))) % 5.16/1.91 | % 5.16/1.91 +-Applying beta-rule and splitting (42), into two cases. % 5.16/1.91 |-Branch one: % 5.16/1.91 | (43) (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) % 5.16/1.91 | % 5.16/1.91 +-Applying beta-rule and splitting (43), into two cases. % 5.16/1.91 |-Branch one: % 5.16/1.91 | (44) all_0_0_0 = 0 & cowlNothing(all_0_2_2) = 0 % 5.16/1.91 | % 5.16/1.91 | Applying alpha-rule on (44) yields: % 5.16/1.91 | (45) all_0_0_0 = 0 % 5.16/1.91 | (46) cowlNothing(all_0_2_2) = 0 % 5.16/1.91 | % 5.16/1.91 | Instantiating formula (30) with all_0_2_2 and discharging atoms cowlNothing(all_0_2_2) = 0, yields: % 5.16/1.91 | (47) $false % 5.16/1.91 | % 5.16/1.91 |-The branch is then unsatisfiable % 5.16/1.91 |-Branch two: % 5.16/1.91 | (48) ~ (all_0_1_1 = 0) & cowlThing(all_0_2_2) = all_0_1_1 % 5.16/1.91 | % 5.16/1.91 | Applying alpha-rule on (48) yields: % 5.16/1.91 | (49) ~ (all_0_1_1 = 0) % 5.16/1.91 | (50) cowlThing(all_0_2_2) = all_0_1_1 % 5.16/1.91 | % 5.16/1.91 | Instantiating formula (13) with all_0_1_1, all_0_2_2 and discharging atoms cowlThing(all_0_2_2) = all_0_1_1, yields: % 5.16/1.91 | (51) all_0_1_1 = 0 % 5.16/1.91 | % 5.16/1.91 | Equations (51) can reduce 49 to: % 5.16/1.91 | (52) $false % 5.16/1.91 | % 5.16/1.91 |-The branch is then unsatisfiable % 5.16/1.91 |-Branch two: % 5.16/1.91 | (53) 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))) % 5.16/1.91 | % 5.16/1.91 | Applying alpha-rule on (53) yields: % 5.16/1.91 | (54) xsd_string(all_0_2_2) = all_0_1_1 % 5.16/1.91 | (55) xsd_integer(all_0_2_2) = all_0_0_0 % 5.16/1.91 | (56) (all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)) % 5.16/1.91 | % 5.16/1.91 | Instantiating formula (4) with all_0_0_0, all_0_2_2 and discharging atoms xsd_integer(all_0_2_2) = all_0_0_0, yields: % 5.16/1.91 | (57) all_0_0_0 = 0 | xsd_string(all_0_2_2) = 0 % 5.16/1.91 | % 5.16/1.91 +-Applying beta-rule and splitting (57), into two cases. % 5.16/1.91 |-Branch one: % 5.16/1.91 | (58) xsd_string(all_0_2_2) = 0 % 5.16/1.91 | % 5.16/1.91 | Instantiating formula (6) 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: % 5.16/1.91 | (51) all_0_1_1 = 0 % 5.16/1.91 | % 5.16/1.91 | From (51) and (54) follows: % 5.16/1.92 | (58) xsd_string(all_0_2_2) = 0 % 5.16/1.92 | % 5.16/1.92 +-Applying beta-rule and splitting (56), into two cases. % 5.16/1.92 |-Branch one: % 5.16/1.92 | (61) all_0_0_0 = 0 & all_0_1_1 = 0 % 5.16/1.92 | % 5.16/1.92 | Applying alpha-rule on (61) yields: % 5.16/1.92 | (45) all_0_0_0 = 0 % 5.16/1.92 | (51) all_0_1_1 = 0 % 5.16/1.92 | % 5.16/1.92 | From (45) and (55) follows: % 5.16/1.92 | (64) xsd_integer(all_0_2_2) = 0 % 5.16/1.92 | % 5.16/1.92 | Instantiating formula (9) with all_0_2_2 and discharging atoms xsd_integer(all_0_2_2) = 0, yields: % 5.16/1.92 | (65) ? [v0] : ( ~ (v0 = 0) & xsd_string(all_0_2_2) = v0) % 5.16/1.92 | % 5.16/1.92 | Instantiating (65) with all_48_0_17 yields: % 5.16/1.92 | (66) ~ (all_48_0_17 = 0) & xsd_string(all_0_2_2) = all_48_0_17 % 5.16/1.92 | % 5.16/1.92 | Applying alpha-rule on (66) yields: % 5.16/1.92 | (67) ~ (all_48_0_17 = 0) % 5.16/1.92 | (68) xsd_string(all_0_2_2) = all_48_0_17 % 5.16/1.92 | % 5.16/1.92 | Instantiating formula (28) with all_48_0_17, all_0_2_2 and discharging atoms xsd_string(all_0_2_2) = all_48_0_17, xsd_string(all_0_2_2) = 0, yields: % 5.16/1.92 | (69) all_48_0_17 = 0 % 5.16/1.92 | % 5.16/1.92 | Equations (69) can reduce 67 to: % 5.16/1.92 | (52) $false % 5.16/1.92 | % 5.16/1.92 |-The branch is then unsatisfiable % 5.16/1.92 |-Branch two: % 5.16/1.92 | (71) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) % 5.16/1.92 | % 5.16/1.92 | Applying alpha-rule on (71) yields: % 5.16/1.92 | (72) ~ (all_0_0_0 = 0) % 5.16/1.92 | (49) ~ (all_0_1_1 = 0) % 5.16/1.92 | % 5.16/1.92 | Equations (51) can reduce 49 to: % 5.16/1.92 | (52) $false % 5.16/1.92 | % 5.16/1.92 |-The branch is then unsatisfiable % 5.16/1.92 |-Branch two: % 5.16/1.92 | (75) ~ (xsd_string(all_0_2_2) = 0) % 5.16/1.92 | (45) all_0_0_0 = 0 % 5.16/1.92 | % 5.16/1.92 +-Applying beta-rule and splitting (56), into two cases. % 5.16/1.92 |-Branch one: % 5.16/1.92 | (61) all_0_0_0 = 0 & all_0_1_1 = 0 % 5.16/1.92 | % 5.16/1.92 | Applying alpha-rule on (61) yields: % 5.16/1.92 | (45) all_0_0_0 = 0 % 5.16/1.92 | (51) all_0_1_1 = 0 % 5.16/1.92 | % 5.16/1.92 | From (51) and (54) follows: % 5.16/1.92 | (58) xsd_string(all_0_2_2) = 0 % 5.16/1.92 | % 5.16/1.92 | Using (58) and (75) yields: % 5.16/1.92 | (47) $false % 5.16/1.92 | % 5.16/1.92 |-The branch is then unsatisfiable % 5.16/1.92 |-Branch two: % 5.16/1.92 | (71) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) % 5.16/1.92 | % 5.16/1.92 | Applying alpha-rule on (71) yields: % 5.16/1.92 | (72) ~ (all_0_0_0 = 0) % 5.16/1.92 | (49) ~ (all_0_1_1 = 0) % 5.16/1.92 | % 5.16/1.92 | Equations (45) can reduce 72 to: % 5.16/1.92 | (52) $false % 5.16/1.92 | % 5.16/1.92 |-The branch is then unsatisfiable % 5.16/1.92 |-Branch two: % 5.16/1.92 | (86) cA_and_B(all_0_2_2) = all_0_1_1 & ((all_0_1_1 = 0 & ~ (all_0_2_2 = ib) & ~ (all_0_2_2 = ia)) | ( ~ (all_0_1_1 = 0) & (all_0_2_2 = ib | all_0_2_2 = ia))) % 5.16/1.92 | % 5.16/1.92 | Applying alpha-rule on (86) yields: % 5.16/1.92 | (87) cA_and_B(all_0_2_2) = all_0_1_1 % 5.16/1.92 | (88) (all_0_1_1 = 0 & ~ (all_0_2_2 = ib) & ~ (all_0_2_2 = ia)) | ( ~ (all_0_1_1 = 0) & (all_0_2_2 = ib | all_0_2_2 = ia)) % 5.16/1.92 | % 5.16/1.92 | Instantiating formula (8) with all_0_1_1, all_0_2_2 and discharging atoms cA_and_B(all_0_2_2) = all_0_1_1, yields: % 5.16/1.92 | (89) all_0_1_1 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & cB(all_0_2_2) = v1 & cA(all_0_2_2) = v0) % 5.16/1.92 | % 5.16/1.92 +-Applying beta-rule and splitting (88), into two cases. % 5.16/1.92 |-Branch one: % 5.16/1.92 | (90) all_0_1_1 = 0 & ~ (all_0_2_2 = ib) & ~ (all_0_2_2 = ia) % 5.16/1.92 | % 5.16/1.92 | Applying alpha-rule on (90) yields: % 5.16/1.92 | (51) all_0_1_1 = 0 % 5.16/1.92 | (92) ~ (all_0_2_2 = ib) % 5.16/1.92 | (93) ~ (all_0_2_2 = ia) % 5.16/1.92 | % 5.16/1.92 | From (51) and (87) follows: % 5.16/1.92 | (94) cA_and_B(all_0_2_2) = 0 % 5.16/1.92 | % 5.16/1.92 | Instantiating formula (29) with all_0_2_2 and discharging atoms cA_and_B(all_0_2_2) = 0, yields: % 5.16/1.92 | (95) ? [v0] : ((v0 = 0 & cB(all_0_2_2) = 0) | (v0 = 0 & cA(all_0_2_2) = 0)) % 5.16/1.92 | % 5.16/1.92 | Instantiating (95) with all_40_0_19 yields: % 5.16/1.92 | (96) (all_40_0_19 = 0 & cB(all_0_2_2) = 0) | (all_40_0_19 = 0 & cA(all_0_2_2) = 0) % 5.16/1.92 | % 5.16/1.92 +-Applying beta-rule and splitting (96), into two cases. % 5.16/1.92 |-Branch one: % 5.16/1.93 | (97) all_40_0_19 = 0 & cB(all_0_2_2) = 0 % 5.16/1.93 | % 5.16/1.93 | Applying alpha-rule on (97) yields: % 5.16/1.93 | (98) all_40_0_19 = 0 % 5.16/1.93 | (99) cB(all_0_2_2) = 0 % 5.16/1.93 | % 5.16/1.93 | Instantiating formula (32) with all_0_2_2 and discharging atoms cB(all_0_2_2) = 0, yields: % 5.16/1.93 | (100) all_0_2_2 = ib % 5.16/1.93 | % 5.16/1.93 | Equations (100) can reduce 92 to: % 5.16/1.93 | (52) $false % 5.16/1.93 | % 5.16/1.93 |-The branch is then unsatisfiable % 5.16/1.93 |-Branch two: % 5.16/1.93 | (102) all_40_0_19 = 0 & cA(all_0_2_2) = 0 % 5.16/1.93 | % 5.16/1.93 | Applying alpha-rule on (102) yields: % 5.16/1.93 | (98) all_40_0_19 = 0 % 5.16/1.93 | (104) cA(all_0_2_2) = 0 % 5.16/1.93 | % 5.16/1.93 | Instantiating formula (21) with all_0_2_2 and discharging atoms cA(all_0_2_2) = 0, yields: % 5.16/1.93 | (105) all_0_2_2 = ia % 5.16/1.93 | % 5.16/1.93 | Equations (105) can reduce 93 to: % 5.16/1.93 | (52) $false % 5.16/1.93 | % 5.16/1.93 |-The branch is then unsatisfiable % 5.16/1.93 |-Branch two: % 5.16/1.93 | (107) ~ (all_0_1_1 = 0) & (all_0_2_2 = ib | all_0_2_2 = ia) % 5.16/1.93 | % 5.16/1.93 | Applying alpha-rule on (107) yields: % 5.16/1.93 | (49) ~ (all_0_1_1 = 0) % 5.16/1.93 | (109) all_0_2_2 = ib | all_0_2_2 = ia % 5.16/1.93 | % 5.16/1.93 +-Applying beta-rule and splitting (89), into two cases. % 5.16/1.93 |-Branch one: % 5.16/1.93 | (51) all_0_1_1 = 0 % 5.16/1.93 | % 5.16/1.93 | Equations (51) can reduce 49 to: % 5.16/1.93 | (52) $false % 5.16/1.93 | % 5.16/1.93 |-The branch is then unsatisfiable % 5.16/1.93 |-Branch two: % 5.16/1.93 | (49) ~ (all_0_1_1 = 0) % 5.16/1.93 | (113) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & cB(all_0_2_2) = v1 & cA(all_0_2_2) = v0) % 5.16/1.93 | % 5.16/1.93 | Instantiating (113) with all_39_0_20, all_39_1_21 yields: % 5.16/1.93 | (114) ~ (all_39_0_20 = 0) & ~ (all_39_1_21 = 0) & cB(all_0_2_2) = all_39_0_20 & cA(all_0_2_2) = all_39_1_21 % 5.16/1.93 | % 5.16/1.93 | Applying alpha-rule on (114) yields: % 5.16/1.93 | (115) ~ (all_39_0_20 = 0) % 5.16/1.93 | (116) ~ (all_39_1_21 = 0) % 5.16/1.93 | (117) cB(all_0_2_2) = all_39_0_20 % 5.16/1.93 | (118) cA(all_0_2_2) = all_39_1_21 % 5.16/1.93 | % 5.16/1.93 +-Applying beta-rule and splitting (109), into two cases. % 5.16/1.93 |-Branch one: % 5.16/1.93 | (100) all_0_2_2 = ib % 5.16/1.93 | % 5.16/1.93 | From (100) and (117) follows: % 5.16/1.93 | (120) cB(ib) = all_39_0_20 % 5.16/1.93 | % 5.16/1.93 | Instantiating formula (37) with all_39_0_20 and discharging atoms cB(ib) = all_39_0_20, yields: % 5.16/1.93 | (121) all_39_0_20 = 0 % 5.16/1.93 | % 5.16/1.93 | Equations (121) can reduce 115 to: % 5.16/1.93 | (52) $false % 5.16/1.93 | % 5.16/1.93 |-The branch is then unsatisfiable % 5.16/1.93 |-Branch two: % 5.16/1.93 | (92) ~ (all_0_2_2 = ib) % 5.16/1.93 | (105) all_0_2_2 = ia % 5.16/1.93 | % 5.16/1.93 | From (105) and (118) follows: % 5.16/1.93 | (125) cA(ia) = all_39_1_21 % 5.16/1.93 | % 5.16/1.93 | Instantiating formula (18) with all_39_1_21 and discharging atoms cA(ia) = all_39_1_21, yields: % 5.16/1.93 | (126) all_39_1_21 = 0 % 5.16/1.93 | % 5.16/1.93 | Equations (126) can reduce 116 to: % 5.16/1.93 | (52) $false % 5.16/1.93 | % 5.16/1.93 |-The branch is then unsatisfiable % 5.16/1.93 % SZS output end Proof for theBenchmark % 5.16/1.93 % 5.16/1.93 1330ms %------------------------------------------------------------------------------