%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KRS171+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n025.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 2.32s 1.31s % Output : Proof 3.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : KRS171+1 : TPTP v8.1.0. Released v3.1.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n025.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 16:55:34 EDT 2022 % 0.12/0.34 % CPUTime : % 0.67/0.62 ____ _ % 0.67/0.62 ___ / __ \_____(_)___ ________ __________ % 0.67/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.67/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.67/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.67/0.62 % 0.67/0.62 A Theorem Prover for First-Order Logic % 0.67/0.63 (ePrincess v.1.0) % 0.67/0.63 % 0.67/0.63 (c) Philipp Rümmer, 2009-2015 % 0.67/0.63 (c) Peter Backeman, 2014-2015 % 0.67/0.63 (contributions by Angelo Brillout, Peter Baumgartner) % 0.67/0.63 Free software under GNU Lesser General Public License (LGPL). % 0.67/0.63 Bug reports to peter@backeman.se % 0.67/0.63 % 0.67/0.63 For more information, visit http://user.uu.se/~petba168/breu/ % 0.67/0.63 % 0.67/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.74/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.38/0.96 Prover 0: Preprocessing ... % 1.45/1.02 Prover 0: Warning: ignoring some quantifiers % 1.62/1.04 Prover 0: Constructing countermodel ... % 1.72/1.14 Prover 0: gave up % 1.72/1.14 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.95/1.17 Prover 1: Preprocessing ... % 2.32/1.25 Prover 1: Constructing countermodel ... % 2.32/1.31 Prover 1: proved (168ms) % 2.32/1.31 % 2.32/1.31 No countermodel exists, formula is valid % 2.32/1.31 % SZS status Theorem for theBenchmark % 2.32/1.31 % 2.32/1.31 Generating proof ... found it (size 69) % 3.17/1.55 % 3.17/1.55 % SZS output start Proof for theBenchmark % 3.17/1.55 Assumed formulas after preprocessing and simplification: % 3.17/1.55 | (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) & ((rhasLeader(v0, v1) = v2 & rhasHead(v0, v1) = v3 & ((v3 = 0 & ~ (v2 = 0)) | (v2 = 0 & ~ (v3 = 0)))) | (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)))) % 3.17/1.59 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 3.17/1.59 | (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) & ((rhasLeader(all_0_3_3, all_0_2_2) = all_0_1_1 & rhasHead(all_0_3_3, all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_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))) % 3.17/1.59 | % 3.17/1.59 | Applying alpha-rule on (1) yields: % 3.17/1.59 | (2) ! [v0] : ~ (cowlNothing(v0) = 0) % 3.17/1.59 | (3) (rhasLeader(all_0_3_3, all_0_2_2) = all_0_1_1 & rhasHead(all_0_3_3, all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_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)) % 3.17/1.60 | (4) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) % 3.17/1.60 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rhasLeader(v3, v2) = v1) | ~ (rhasLeader(v3, v2) = v0)) % 3.17/1.60 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rhasHead(v3, v2) = v1) | ~ (rhasHead(v3, v2) = v0)) % 3.17/1.60 | (7) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) % 3.17/1.60 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) % 3.17/1.60 | (9) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) % 3.17/1.60 | (10) ! [v0] : ! [v1] : ( ~ (rhasLeader(v0, v1) = 0) | rhasHead(v0, v1) = 0) % 3.17/1.60 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 3.17/1.60 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) % 3.17/1.60 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) % 3.17/1.60 | (14) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rhasLeader(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & rhasHead(v0, v1) = v3)) % 3.17/1.60 | % 3.17/1.60 +-Applying beta-rule and splitting (3), into two cases. % 3.17/1.60 |-Branch one: % 3.17/1.60 | (15) (rhasLeader(all_0_3_3, all_0_2_2) = all_0_1_1 & rhasHead(all_0_3_3, all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_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)))) % 3.17/1.60 | % 3.17/1.60 +-Applying beta-rule and splitting (15), into two cases. % 3.17/1.60 |-Branch one: % 3.17/1.60 | (16) rhasLeader(all_0_3_3, all_0_2_2) = all_0_1_1 & rhasHead(all_0_3_3, all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0))) % 3.17/1.60 | % 3.17/1.60 | Applying alpha-rule on (16) yields: % 3.17/1.60 | (17) rhasLeader(all_0_3_3, all_0_2_2) = all_0_1_1 % 3.17/1.60 | (18) rhasHead(all_0_3_3, all_0_2_2) = all_0_0_0 % 3.17/1.60 | (19) (all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)) % 3.17/1.60 | % 3.17/1.60 | Instantiating formula (10) with all_0_2_2, all_0_3_3 yields: % 3.17/1.60 | (20) ~ (rhasLeader(all_0_3_3, all_0_2_2) = 0) | rhasHead(all_0_3_3, all_0_2_2) = 0 % 3.17/1.60 | % 3.17/1.60 | Instantiating formula (14) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms rhasLeader(all_0_3_3, all_0_2_2) = all_0_1_1, yields: % 3.17/1.60 | (21) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & rhasHead(all_0_3_3, all_0_2_2) = v0) % 3.17/1.60 | % 3.17/1.60 +-Applying beta-rule and splitting (20), into two cases. % 3.17/1.60 |-Branch one: % 3.17/1.60 | (22) ~ (rhasLeader(all_0_3_3, all_0_2_2) = 0) % 3.17/1.60 | % 3.17/1.60 | Using (17) and (22) yields: % 3.17/1.60 | (23) ~ (all_0_1_1 = 0) % 3.17/1.61 | % 3.17/1.61 +-Applying beta-rule and splitting (19), into two cases. % 3.17/1.61 |-Branch one: % 3.17/1.61 | (24) all_0_0_0 = 0 & ~ (all_0_1_1 = 0) % 3.17/1.61 | % 3.17/1.61 | Applying alpha-rule on (24) yields: % 3.17/1.61 | (25) all_0_0_0 = 0 % 3.17/1.61 | (23) ~ (all_0_1_1 = 0) % 3.17/1.61 | % 3.17/1.61 | From (25) and (18) follows: % 3.17/1.61 | (27) rhasHead(all_0_3_3, all_0_2_2) = 0 % 3.17/1.61 | % 3.17/1.61 +-Applying beta-rule and splitting (21), into two cases. % 3.17/1.61 |-Branch one: % 3.17/1.61 | (28) all_0_1_1 = 0 % 3.17/1.61 | % 3.17/1.61 | Equations (28) can reduce 23 to: % 3.17/1.61 | (29) $false % 3.17/1.61 | % 3.17/1.61 |-The branch is then unsatisfiable % 3.17/1.61 |-Branch two: % 3.17/1.61 | (23) ~ (all_0_1_1 = 0) % 3.17/1.61 | (31) ? [v0] : ( ~ (v0 = 0) & rhasHead(all_0_3_3, all_0_2_2) = v0) % 3.17/1.61 | % 3.17/1.61 | Instantiating (31) with all_25_0_4 yields: % 3.17/1.61 | (32) ~ (all_25_0_4 = 0) & rhasHead(all_0_3_3, all_0_2_2) = all_25_0_4 % 3.17/1.61 | % 3.17/1.61 | Applying alpha-rule on (32) yields: % 3.17/1.61 | (33) ~ (all_25_0_4 = 0) % 3.17/1.61 | (34) rhasHead(all_0_3_3, all_0_2_2) = all_25_0_4 % 3.17/1.61 | % 3.17/1.61 | Instantiating formula (6) with all_0_3_3, all_0_2_2, 0, all_25_0_4 and discharging atoms rhasHead(all_0_3_3, all_0_2_2) = all_25_0_4, rhasHead(all_0_3_3, all_0_2_2) = 0, yields: % 3.17/1.61 | (35) all_25_0_4 = 0 % 3.17/1.61 | % 3.17/1.61 | Equations (35) can reduce 33 to: % 3.17/1.61 | (29) $false % 3.17/1.61 | % 3.17/1.61 |-The branch is then unsatisfiable % 3.17/1.61 |-Branch two: % 3.17/1.61 | (37) all_0_1_1 = 0 & ~ (all_0_0_0 = 0) % 3.17/1.61 | % 3.17/1.61 | Applying alpha-rule on (37) yields: % 3.17/1.61 | (28) all_0_1_1 = 0 % 3.17/1.61 | (39) ~ (all_0_0_0 = 0) % 3.17/1.61 | % 3.17/1.61 | Equations (28) can reduce 23 to: % 3.17/1.61 | (29) $false % 3.17/1.61 | % 3.17/1.61 |-The branch is then unsatisfiable % 3.17/1.61 |-Branch two: % 3.17/1.61 | (41) rhasLeader(all_0_3_3, all_0_2_2) = 0 % 3.17/1.61 | (27) rhasHead(all_0_3_3, all_0_2_2) = 0 % 3.17/1.61 | % 3.17/1.61 | Instantiating formula (5) with all_0_3_3, all_0_2_2, 0, all_0_1_1 and discharging atoms rhasLeader(all_0_3_3, all_0_2_2) = all_0_1_1, rhasLeader(all_0_3_3, all_0_2_2) = 0, yields: % 3.17/1.61 | (28) all_0_1_1 = 0 % 3.17/1.61 | % 3.17/1.61 | Instantiating formula (6) 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: % 3.17/1.61 | (25) all_0_0_0 = 0 % 3.17/1.61 | % 3.17/1.61 +-Applying beta-rule and splitting (19), into two cases. % 3.17/1.61 |-Branch one: % 3.17/1.61 | (24) all_0_0_0 = 0 & ~ (all_0_1_1 = 0) % 3.17/1.61 | % 3.17/1.61 | Applying alpha-rule on (24) yields: % 3.17/1.61 | (25) all_0_0_0 = 0 % 3.17/1.61 | (23) ~ (all_0_1_1 = 0) % 3.17/1.61 | % 3.17/1.61 | Equations (28) can reduce 23 to: % 3.17/1.61 | (29) $false % 3.17/1.61 | % 3.17/1.61 |-The branch is then unsatisfiable % 3.17/1.61 |-Branch two: % 3.17/1.61 | (37) all_0_1_1 = 0 & ~ (all_0_0_0 = 0) % 3.17/1.61 | % 3.17/1.61 | Applying alpha-rule on (37) yields: % 3.17/1.61 | (28) all_0_1_1 = 0 % 3.17/1.61 | (39) ~ (all_0_0_0 = 0) % 3.17/1.61 | % 3.17/1.61 | Equations (25) can reduce 39 to: % 3.17/1.61 | (29) $false % 3.17/1.61 | % 3.17/1.61 |-The branch is then unsatisfiable % 3.17/1.61 |-Branch two: % 3.17/1.61 | (53) 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))) % 3.17/1.61 | % 3.17/1.61 | Applying alpha-rule on (53) yields: % 3.17/1.61 | (54) xsd_string(all_0_3_3) = all_0_2_2 % 3.17/1.61 | (55) xsd_integer(all_0_3_3) = all_0_1_1 % 3.17/1.61 | (56) (all_0_1_1 = 0 & all_0_2_2 = 0) | ( ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0)) % 3.17/1.61 | % 3.17/1.61 | Instantiating formula (7) with all_0_3_3 yields: % 3.17/1.61 | (57) ~ (xsd_string(all_0_3_3) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_3_3) = v0) % 3.17/1.61 | % 3.17/1.61 | Instantiating formula (4) with all_0_2_2, all_0_3_3 and discharging atoms xsd_string(all_0_3_3) = all_0_2_2, yields: % 3.17/1.61 | (58) all_0_2_2 = 0 | xsd_integer(all_0_3_3) = 0 % 3.17/1.61 | % 3.17/1.61 +-Applying beta-rule and splitting (58), into two cases. % 3.17/1.61 |-Branch one: % 3.17/1.61 | (59) xsd_integer(all_0_3_3) = 0 % 3.17/1.61 | % 3.17/1.61 | 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: % 3.17/1.62 | (28) all_0_1_1 = 0 % 3.17/1.62 | % 3.17/1.62 | From (28) and (55) follows: % 3.17/1.62 | (59) xsd_integer(all_0_3_3) = 0 % 3.17/1.62 | % 3.17/1.62 +-Applying beta-rule and splitting (57), into two cases. % 3.17/1.62 |-Branch one: % 3.17/1.62 | (62) ~ (xsd_string(all_0_3_3) = 0) % 3.17/1.62 | % 3.17/1.62 +-Applying beta-rule and splitting (56), into two cases. % 3.17/1.62 |-Branch one: % 3.17/1.62 | (63) all_0_1_1 = 0 & all_0_2_2 = 0 % 3.17/1.62 | % 3.17/1.62 | Applying alpha-rule on (63) yields: % 3.17/1.62 | (28) all_0_1_1 = 0 % 3.17/1.62 | (65) all_0_2_2 = 0 % 3.17/1.62 | % 3.17/1.62 | From (65) and (54) follows: % 3.17/1.62 | (66) xsd_string(all_0_3_3) = 0 % 3.17/1.62 | % 3.17/1.62 | Using (66) and (62) yields: % 3.17/1.62 | (67) $false % 3.17/1.62 | % 3.17/1.62 |-The branch is then unsatisfiable % 3.17/1.62 |-Branch two: % 3.17/1.62 | (68) ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0) % 3.17/1.62 | % 3.17/1.62 | Applying alpha-rule on (68) yields: % 3.17/1.62 | (23) ~ (all_0_1_1 = 0) % 3.17/1.62 | (70) ~ (all_0_2_2 = 0) % 3.17/1.62 | % 3.17/1.62 | Equations (28) can reduce 23 to: % 3.17/1.62 | (29) $false % 3.17/1.62 | % 3.17/1.62 |-The branch is then unsatisfiable % 3.17/1.62 |-Branch two: % 3.17/1.62 | (66) xsd_string(all_0_3_3) = 0 % 3.17/1.62 | (73) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_3_3) = v0) % 3.17/1.62 | % 3.17/1.62 | Instantiating (73) with all_21_0_5 yields: % 3.17/1.62 | (74) ~ (all_21_0_5 = 0) & xsd_integer(all_0_3_3) = all_21_0_5 % 3.17/1.62 | % 3.17/1.62 | Applying alpha-rule on (74) yields: % 3.17/1.62 | (75) ~ (all_21_0_5 = 0) % 3.17/1.62 | (76) xsd_integer(all_0_3_3) = all_21_0_5 % 3.17/1.62 | % 3.17/1.62 | 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: % 3.17/1.62 | (77) all_21_0_5 = 0 % 3.17/1.62 | % 3.17/1.62 | Equations (77) can reduce 75 to: % 3.17/1.62 | (29) $false % 3.17/1.62 | % 3.17/1.62 |-The branch is then unsatisfiable % 3.17/1.62 |-Branch two: % 3.17/1.62 | (79) ~ (xsd_integer(all_0_3_3) = 0) % 3.17/1.62 | (65) all_0_2_2 = 0 % 3.17/1.62 | % 3.17/1.62 +-Applying beta-rule and splitting (56), into two cases. % 3.17/1.62 |-Branch one: % 3.17/1.62 | (63) all_0_1_1 = 0 & all_0_2_2 = 0 % 3.17/1.62 | % 3.17/1.62 | Applying alpha-rule on (63) yields: % 3.17/1.62 | (28) all_0_1_1 = 0 % 3.17/1.62 | (65) all_0_2_2 = 0 % 3.17/1.62 | % 3.17/1.62 | From (28) and (55) follows: % 3.17/1.62 | (59) xsd_integer(all_0_3_3) = 0 % 3.17/1.62 | % 3.17/1.62 | Using (59) and (79) yields: % 3.17/1.62 | (67) $false % 3.17/1.62 | % 3.17/1.62 |-The branch is then unsatisfiable % 3.17/1.62 |-Branch two: % 3.17/1.62 | (68) ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0) % 3.17/1.62 | % 3.17/1.62 | Applying alpha-rule on (68) yields: % 3.17/1.62 | (23) ~ (all_0_1_1 = 0) % 3.17/1.62 | (70) ~ (all_0_2_2 = 0) % 3.17/1.62 | % 3.17/1.62 | Equations (65) can reduce 70 to: % 3.17/1.62 | (29) $false % 3.17/1.62 | % 3.17/1.62 |-The branch is then unsatisfiable % 3.17/1.62 |-Branch two: % 3.17/1.62 | (90) 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) % 3.17/1.62 | % 3.17/1.62 | Applying alpha-rule on (90) yields: % 3.17/1.62 | (91) cowlNothing(all_0_3_3) = all_0_1_1 % 3.17/1.62 | (92) cowlThing(all_0_3_3) = all_0_2_2 % 3.17/1.62 | (93) ~ (all_0_2_2 = 0) | all_0_1_1 = 0 % 3.17/1.62 | % 3.17/1.62 | Instantiating formula (2) with all_0_3_3 yields: % 3.17/1.62 | (94) ~ (cowlNothing(all_0_3_3) = 0) % 3.17/1.62 | % 3.17/1.62 | Instantiating formula (9) with all_0_2_2, all_0_3_3 and discharging atoms cowlThing(all_0_3_3) = all_0_2_2, yields: % 3.17/1.62 | (65) all_0_2_2 = 0 % 3.17/1.62 | % 3.17/1.63 +-Applying beta-rule and splitting (93), into two cases. % 3.17/1.63 |-Branch one: % 3.17/1.63 | (70) ~ (all_0_2_2 = 0) % 3.17/1.63 | % 3.17/1.63 | Equations (65) can reduce 70 to: % 3.17/1.63 | (29) $false % 3.17/1.63 | % 3.17/1.63 |-The branch is then unsatisfiable % 3.17/1.63 |-Branch two: % 3.17/1.63 | (65) all_0_2_2 = 0 % 3.17/1.63 | (28) all_0_1_1 = 0 % 3.17/1.63 | % 3.17/1.63 | From (28) and (91) follows: % 3.17/1.63 | (100) cowlNothing(all_0_3_3) = 0 % 3.17/1.63 | % 3.17/1.63 | Using (100) and (94) yields: % 3.17/1.63 | (67) $false % 3.17/1.63 | % 3.17/1.63 |-The branch is then unsatisfiable % 3.17/1.63 % SZS output end Proof for theBenchmark % 3.17/1.63 % 3.17/1.63 985ms %------------------------------------------------------------------------------