%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KRS170+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n032.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 02:56:47 EDT 2022 % Result : Theorem 1.79s 1.04s % Output : Proof 2.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.09 % Problem : KRS170+1 : TPTP v8.1.0. Released v3.1.0. % 0.05/0.09 % Command : ePrincess-casc -timeout=%d %s % 0.09/0.28 % Computer : n032.cluster.edu % 0.09/0.28 % Model : x86_64 x86_64 % 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.28 % Memory : 8042.1875MB % 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.28 % CPULimit : 300 % 0.09/0.28 % WCLimit : 600 % 0.09/0.28 % DateTime : Tue Jun 7 15:00:05 EDT 2022 % 0.09/0.29 % CPUTime : % 0.13/0.45 ____ _ % 0.13/0.45 ___ / __ \_____(_)___ ________ __________ % 0.13/0.45 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.13/0.45 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.13/0.45 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.13/0.45 % 0.13/0.45 A Theorem Prover for First-Order Logic % 0.13/0.45 (ePrincess v.1.0) % 0.13/0.45 % 0.13/0.45 (c) Philipp Rümmer, 2009-2015 % 0.13/0.45 (c) Peter Backeman, 2014-2015 % 0.13/0.45 (contributions by Angelo Brillout, Peter Baumgartner) % 0.13/0.45 Free software under GNU Lesser General Public License (LGPL). % 0.13/0.45 Bug reports to peter@backeman.se % 0.13/0.45 % 0.13/0.45 For more information, visit http://user.uu.se/~petba168/breu/ % 0.13/0.45 % 0.13/0.46 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.13/0.50 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 0.90/0.71 Prover 0: Preprocessing ... % 1.10/0.77 Prover 0: Warning: ignoring some quantifiers % 1.10/0.79 Prover 0: Constructing countermodel ... % 1.33/0.88 Prover 0: gave up % 1.33/0.88 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.33/0.90 Prover 1: Preprocessing ... % 1.63/0.98 Prover 1: Constructing countermodel ... % 1.79/1.04 Prover 1: proved (156ms) % 1.79/1.04 % 1.79/1.04 No countermodel exists, formula is valid % 1.79/1.04 % SZS status Theorem for theBenchmark % 1.79/1.04 % 1.79/1.04 Generating proof ... found it (size 57) % 2.20/1.21 % 2.20/1.21 % SZS output start Proof for theBenchmark % 2.20/1.21 Assumed formulas after preprocessing and simplification: % 2.20/1.21 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (rhasLeader(v7, v6) = v5) | ~ (rhasLeader(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (rhasHead(v7, v6) = v5) | ~ (rhasHead(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (rhasLeader(v4, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & rhasHead(v4, v5) = v7)) & ! [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 | ~ (cowlNothing(v6) = v5) | ~ (cowlNothing(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (cowlThing(v6) = v5) | ~ (cowlThing(v6) = v4)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (xsd_string(v4) = v5) | xsd_integer(v4) = 0) & ! [v4] : ! [v5] : (v5 = 0 | ~ (cowlThing(v4) = v5)) & ! [v4] : ! [v5] : ( ~ (rhasLeader(v4, v5) = 0) | rhasHead(v4, v5) = 0) & ! [v4] : ( ~ (xsd_string(v4) = 0) | ? [v5] : ( ~ (v5 = 0) & xsd_integer(v4) = v5)) & ! [v4] : ~ (cowlNothing(v4) = 0) & ((v2 = 0 & ~ (v3 = 0) & rhasLeader(v0, v1) = v3 & rhasHead(v0, v1) = 0) | (v2 = 0 & ~ (v3 = 0) & rhasLeader(v0, v1) = 0 & rhasHead(v0, v1) = v3) | (xsd_string(v0) = v1 & xsd_integer(v0) = v2 & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & ~ (v1 = 0)))) | (cowlNothing(v0) = v2 & cowlThing(v0) = v1 & ( ~ (v1 = 0) | v2 = 0)))) % 2.38/1.25 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 2.38/1.25 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rhasLeader(v3, v2) = v1) | ~ (rhasLeader(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rhasHead(v3, v2) = v1) | ~ (rhasHead(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rhasLeader(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & rhasHead(v0, v1) = v3)) & ! [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] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (rhasLeader(v0, v1) = 0) | rhasHead(v0, v1) = 0) & ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) & ! [v0] : ~ (cowlNothing(v0) = 0) & ((all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & rhasLeader(all_0_3_3, all_0_2_2) = all_0_0_0 & rhasHead(all_0_3_3, all_0_2_2) = 0) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & rhasLeader(all_0_3_3, all_0_2_2) = 0 & rhasHead(all_0_3_3, all_0_2_2) = all_0_0_0) | (xsd_string(all_0_3_3) = all_0_2_2 & xsd_integer(all_0_3_3) = all_0_1_1 & ((all_0_1_1 = 0 & all_0_2_2 = 0) | ( ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0)))) | (cowlNothing(all_0_3_3) = all_0_1_1 & cowlThing(all_0_3_3) = all_0_2_2 & ( ~ (all_0_2_2 = 0) | all_0_1_1 = 0))) % 2.47/1.25 | % 2.47/1.25 | Applying alpha-rule on (1) yields: % 2.47/1.25 | (2) ! [v0] : ! [v1] : ( ~ (rhasLeader(v0, v1) = 0) | rhasHead(v0, v1) = 0) % 2.47/1.25 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rhasLeader(v3, v2) = v1) | ~ (rhasLeader(v3, v2) = v0)) % 2.47/1.25 | (4) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) % 2.47/1.25 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) % 2.47/1.25 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) % 2.47/1.25 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rhasLeader(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & rhasHead(v0, v1) = v3)) % 2.47/1.26 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rhasHead(v3, v2) = v1) | ~ (rhasHead(v3, v2) = v0)) % 2.47/1.26 | (9) (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & rhasLeader(all_0_3_3, all_0_2_2) = all_0_0_0 & rhasHead(all_0_3_3, all_0_2_2) = 0) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & rhasLeader(all_0_3_3, all_0_2_2) = 0 & rhasHead(all_0_3_3, all_0_2_2) = all_0_0_0) | (xsd_string(all_0_3_3) = all_0_2_2 & xsd_integer(all_0_3_3) = all_0_1_1 & ((all_0_1_1 = 0 & all_0_2_2 = 0) | ( ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0)))) | (cowlNothing(all_0_3_3) = all_0_1_1 & cowlThing(all_0_3_3) = all_0_2_2 & ( ~ (all_0_2_2 = 0) | all_0_1_1 = 0)) % 2.47/1.26 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) % 2.47/1.26 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 2.47/1.26 | (12) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) % 2.47/1.26 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) % 2.47/1.26 | (14) ! [v0] : ~ (cowlNothing(v0) = 0) % 2.47/1.26 | % 2.47/1.26 +-Applying beta-rule and splitting (9), into two cases. % 2.47/1.26 |-Branch one: % 2.47/1.26 | (15) (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & rhasLeader(all_0_3_3, all_0_2_2) = all_0_0_0 & rhasHead(all_0_3_3, all_0_2_2) = 0) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & rhasLeader(all_0_3_3, all_0_2_2) = 0 & rhasHead(all_0_3_3, all_0_2_2) = all_0_0_0) | (xsd_string(all_0_3_3) = all_0_2_2 & xsd_integer(all_0_3_3) = all_0_1_1 & ((all_0_1_1 = 0 & all_0_2_2 = 0) | ( ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0)))) % 2.47/1.26 | % 2.47/1.26 +-Applying beta-rule and splitting (15), into two cases. % 2.47/1.26 |-Branch one: % 2.47/1.26 | (16) (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & rhasLeader(all_0_3_3, all_0_2_2) = all_0_0_0 & rhasHead(all_0_3_3, all_0_2_2) = 0) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & rhasLeader(all_0_3_3, all_0_2_2) = 0 & rhasHead(all_0_3_3, all_0_2_2) = all_0_0_0) % 2.47/1.26 | % 2.47/1.26 +-Applying beta-rule and splitting (16), into two cases. % 2.47/1.26 |-Branch one: % 2.47/1.26 | (17) all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & rhasLeader(all_0_3_3, all_0_2_2) = all_0_0_0 & rhasHead(all_0_3_3, all_0_2_2) = 0 % 2.47/1.26 | % 2.47/1.26 | Applying alpha-rule on (17) yields: % 2.47/1.26 | (18) all_0_1_1 = 0 % 2.47/1.26 | (19) ~ (all_0_0_0 = 0) % 2.47/1.26 | (20) rhasLeader(all_0_3_3, all_0_2_2) = all_0_0_0 % 2.47/1.26 | (21) rhasHead(all_0_3_3, all_0_2_2) = 0 % 2.47/1.26 | % 2.47/1.26 | Instantiating formula (7) with all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms rhasLeader(all_0_3_3, all_0_2_2) = all_0_0_0, yields: % 2.47/1.26 | (22) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & rhasHead(all_0_3_3, all_0_2_2) = v0) % 2.47/1.26 | % 2.47/1.26 +-Applying beta-rule and splitting (22), into two cases. % 2.47/1.26 |-Branch one: % 2.47/1.26 | (23) all_0_0_0 = 0 % 2.47/1.26 | % 2.47/1.26 | Equations (23) can reduce 19 to: % 2.47/1.26 | (24) $false % 2.47/1.26 | % 2.47/1.26 |-The branch is then unsatisfiable % 2.47/1.26 |-Branch two: % 2.47/1.26 | (19) ~ (all_0_0_0 = 0) % 2.47/1.26 | (26) ? [v0] : ( ~ (v0 = 0) & rhasHead(all_0_3_3, all_0_2_2) = v0) % 2.47/1.26 | % 2.47/1.26 | Instantiating (26) with all_13_0_4 yields: % 2.47/1.26 | (27) ~ (all_13_0_4 = 0) & rhasHead(all_0_3_3, all_0_2_2) = all_13_0_4 % 2.47/1.26 | % 2.47/1.26 | Applying alpha-rule on (27) yields: % 2.47/1.26 | (28) ~ (all_13_0_4 = 0) % 2.47/1.26 | (29) rhasHead(all_0_3_3, all_0_2_2) = all_13_0_4 % 2.47/1.26 | % 2.47/1.26 | Instantiating formula (8) with all_0_3_3, all_0_2_2, all_13_0_4, 0 and discharging atoms rhasHead(all_0_3_3, all_0_2_2) = all_13_0_4, rhasHead(all_0_3_3, all_0_2_2) = 0, yields: % 2.47/1.27 | (30) all_13_0_4 = 0 % 2.47/1.27 | % 2.47/1.27 | Equations (30) can reduce 28 to: % 2.47/1.27 | (24) $false % 2.47/1.27 | % 2.47/1.27 |-The branch is then unsatisfiable % 2.47/1.27 |-Branch two: % 2.47/1.27 | (32) all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & rhasLeader(all_0_3_3, all_0_2_2) = 0 & rhasHead(all_0_3_3, all_0_2_2) = all_0_0_0 % 2.47/1.27 | % 2.47/1.27 | Applying alpha-rule on (32) yields: % 2.47/1.27 | (18) all_0_1_1 = 0 % 2.47/1.27 | (19) ~ (all_0_0_0 = 0) % 2.47/1.27 | (35) rhasLeader(all_0_3_3, all_0_2_2) = 0 % 2.47/1.27 | (36) rhasHead(all_0_3_3, all_0_2_2) = all_0_0_0 % 2.47/1.27 | % 2.47/1.27 | Instantiating formula (2) with all_0_2_2, all_0_3_3 and discharging atoms rhasLeader(all_0_3_3, all_0_2_2) = 0, yields: % 2.47/1.27 | (21) rhasHead(all_0_3_3, all_0_2_2) = 0 % 2.47/1.27 | % 2.47/1.27 | Instantiating formula (8) with all_0_3_3, all_0_2_2, 0, all_0_0_0 and discharging atoms rhasHead(all_0_3_3, all_0_2_2) = all_0_0_0, rhasHead(all_0_3_3, all_0_2_2) = 0, yields: % 2.47/1.27 | (23) all_0_0_0 = 0 % 2.47/1.27 | % 2.47/1.27 | Equations (23) can reduce 19 to: % 2.47/1.27 | (24) $false % 2.47/1.27 | % 2.47/1.27 |-The branch is then unsatisfiable % 2.47/1.27 |-Branch two: % 2.47/1.27 | (40) xsd_string(all_0_3_3) = all_0_2_2 & xsd_integer(all_0_3_3) = all_0_1_1 & ((all_0_1_1 = 0 & all_0_2_2 = 0) | ( ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0))) % 2.47/1.27 | % 2.47/1.27 | Applying alpha-rule on (40) yields: % 2.47/1.27 | (41) xsd_string(all_0_3_3) = all_0_2_2 % 2.47/1.27 | (42) xsd_integer(all_0_3_3) = all_0_1_1 % 2.47/1.27 | (43) (all_0_1_1 = 0 & all_0_2_2 = 0) | ( ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0)) % 2.47/1.27 | % 2.47/1.27 | Instantiating formula (12) with all_0_3_3 yields: % 2.47/1.27 | (44) ~ (xsd_string(all_0_3_3) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_3_3) = v0) % 2.47/1.27 | % 2.47/1.27 | Instantiating formula (5) with all_0_2_2, all_0_3_3 and discharging atoms xsd_string(all_0_3_3) = all_0_2_2, yields: % 2.47/1.27 | (45) all_0_2_2 = 0 | xsd_integer(all_0_3_3) = 0 % 2.47/1.27 | % 2.47/1.27 +-Applying beta-rule and splitting (45), into two cases. % 2.47/1.27 |-Branch one: % 2.47/1.27 | (46) xsd_integer(all_0_3_3) = 0 % 2.47/1.27 | % 2.47/1.27 | Instantiating formula (11) with all_0_3_3, 0, all_0_1_1 and discharging atoms xsd_integer(all_0_3_3) = all_0_1_1, xsd_integer(all_0_3_3) = 0, yields: % 2.47/1.27 | (18) all_0_1_1 = 0 % 2.47/1.27 | % 2.47/1.27 | From (18) and (42) follows: % 2.47/1.27 | (46) xsd_integer(all_0_3_3) = 0 % 2.47/1.27 | % 2.47/1.27 +-Applying beta-rule and splitting (44), into two cases. % 2.47/1.27 |-Branch one: % 2.47/1.27 | (49) ~ (xsd_string(all_0_3_3) = 0) % 2.47/1.27 | % 2.47/1.27 +-Applying beta-rule and splitting (43), into two cases. % 2.47/1.27 |-Branch one: % 2.47/1.27 | (50) all_0_1_1 = 0 & all_0_2_2 = 0 % 2.47/1.27 | % 2.47/1.27 | Applying alpha-rule on (50) yields: % 2.47/1.27 | (18) all_0_1_1 = 0 % 2.47/1.27 | (52) all_0_2_2 = 0 % 2.47/1.27 | % 2.47/1.27 | From (52) and (41) follows: % 2.47/1.27 | (53) xsd_string(all_0_3_3) = 0 % 2.47/1.27 | % 2.47/1.27 | Using (53) and (49) yields: % 2.47/1.27 | (54) $false % 2.47/1.27 | % 2.47/1.27 |-The branch is then unsatisfiable % 2.47/1.27 |-Branch two: % 2.47/1.27 | (55) ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0) % 2.47/1.27 | % 2.47/1.27 | Applying alpha-rule on (55) yields: % 2.47/1.27 | (56) ~ (all_0_1_1 = 0) % 2.47/1.27 | (57) ~ (all_0_2_2 = 0) % 2.47/1.27 | % 2.47/1.27 | Equations (18) can reduce 56 to: % 2.47/1.27 | (24) $false % 2.47/1.27 | % 2.47/1.27 |-The branch is then unsatisfiable % 2.47/1.27 |-Branch two: % 2.47/1.27 | (53) xsd_string(all_0_3_3) = 0 % 2.47/1.27 | (60) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_3_3) = v0) % 2.47/1.27 | % 2.47/1.27 | Instantiating (60) with all_21_0_5 yields: % 2.47/1.27 | (61) ~ (all_21_0_5 = 0) & xsd_integer(all_0_3_3) = all_21_0_5 % 2.47/1.27 | % 2.47/1.27 | Applying alpha-rule on (61) yields: % 2.47/1.27 | (62) ~ (all_21_0_5 = 0) % 2.47/1.27 | (63) xsd_integer(all_0_3_3) = all_21_0_5 % 2.47/1.27 | % 2.47/1.27 | Instantiating formula (11) with all_0_3_3, all_21_0_5, 0 and discharging atoms xsd_integer(all_0_3_3) = all_21_0_5, xsd_integer(all_0_3_3) = 0, yields: % 2.47/1.27 | (64) all_21_0_5 = 0 % 2.47/1.28 | % 2.47/1.28 | Equations (64) can reduce 62 to: % 2.47/1.28 | (24) $false % 2.47/1.28 | % 2.47/1.28 |-The branch is then unsatisfiable % 2.47/1.28 |-Branch two: % 2.47/1.28 | (66) ~ (xsd_integer(all_0_3_3) = 0) % 2.47/1.28 | (52) all_0_2_2 = 0 % 2.47/1.28 | % 2.47/1.28 +-Applying beta-rule and splitting (43), into two cases. % 2.47/1.28 |-Branch one: % 2.47/1.28 | (50) all_0_1_1 = 0 & all_0_2_2 = 0 % 2.47/1.28 | % 2.47/1.28 | Applying alpha-rule on (50) yields: % 2.47/1.28 | (18) all_0_1_1 = 0 % 2.47/1.28 | (52) all_0_2_2 = 0 % 2.47/1.28 | % 2.47/1.28 | From (18) and (42) follows: % 2.47/1.28 | (46) xsd_integer(all_0_3_3) = 0 % 2.47/1.28 | % 2.47/1.28 | Using (46) and (66) yields: % 2.47/1.28 | (54) $false % 2.47/1.28 | % 2.47/1.28 |-The branch is then unsatisfiable % 2.47/1.28 |-Branch two: % 2.47/1.28 | (55) ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0) % 2.47/1.28 | % 2.47/1.28 | Applying alpha-rule on (55) yields: % 2.47/1.28 | (56) ~ (all_0_1_1 = 0) % 2.47/1.28 | (57) ~ (all_0_2_2 = 0) % 2.47/1.28 | % 2.47/1.28 | Equations (52) can reduce 57 to: % 2.47/1.28 | (24) $false % 2.47/1.28 | % 2.47/1.28 |-The branch is then unsatisfiable % 2.47/1.28 |-Branch two: % 2.47/1.28 | (77) cowlNothing(all_0_3_3) = all_0_1_1 & cowlThing(all_0_3_3) = all_0_2_2 & ( ~ (all_0_2_2 = 0) | all_0_1_1 = 0) % 2.47/1.28 | % 2.47/1.28 | Applying alpha-rule on (77) yields: % 2.47/1.28 | (78) cowlNothing(all_0_3_3) = all_0_1_1 % 2.47/1.28 | (79) cowlThing(all_0_3_3) = all_0_2_2 % 2.47/1.28 | (80) ~ (all_0_2_2 = 0) | all_0_1_1 = 0 % 2.47/1.28 | % 2.47/1.28 | Instantiating formula (14) with all_0_3_3 yields: % 2.47/1.28 | (81) ~ (cowlNothing(all_0_3_3) = 0) % 2.47/1.28 | % 2.47/1.28 | Instantiating formula (4) with all_0_2_2, all_0_3_3 and discharging atoms cowlThing(all_0_3_3) = all_0_2_2, yields: % 2.47/1.28 | (52) all_0_2_2 = 0 % 2.47/1.28 | % 2.47/1.28 +-Applying beta-rule and splitting (80), into two cases. % 2.47/1.28 |-Branch one: % 2.47/1.28 | (57) ~ (all_0_2_2 = 0) % 2.47/1.28 | % 2.47/1.28 | Equations (52) can reduce 57 to: % 2.47/1.28 | (24) $false % 2.47/1.28 | % 2.47/1.28 |-The branch is then unsatisfiable % 2.47/1.28 |-Branch two: % 2.47/1.28 | (52) all_0_2_2 = 0 % 2.47/1.28 | (18) all_0_1_1 = 0 % 2.47/1.28 | % 2.47/1.28 | From (18) and (78) follows: % 2.47/1.28 | (87) cowlNothing(all_0_3_3) = 0 % 2.47/1.28 | % 2.47/1.28 | Using (87) and (81) yields: % 2.47/1.28 | (54) $false % 2.47/1.28 | % 2.47/1.28 |-The branch is then unsatisfiable % 2.47/1.28 % SZS output end Proof for theBenchmark % 2.47/1.28 % 2.47/1.28 817ms %------------------------------------------------------------------------------