%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KRS142+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n022.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 02:56:41 EDT 2022 % Result : Theorem 2.75s 1.41s % Output : Proof 3.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : KRS142+1 : TPTP v8.1.0. Released v3.1.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n022.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Tue Jun 7 06:51:50 EDT 2022 % 0.13/0.34 % CPUTime : % 0.65/0.64 ____ _ % 0.65/0.64 ___ / __ \_____(_)___ ________ __________ % 0.65/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.65/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.65/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.65/0.64 % 0.65/0.64 A Theorem Prover for First-Order Logic % 0.65/0.64 (ePrincess v.1.0) % 0.65/0.64 % 0.65/0.64 (c) Philipp Rümmer, 2009-2015 % 0.65/0.64 (c) Peter Backeman, 2014-2015 % 0.65/0.64 (contributions by Angelo Brillout, Peter Baumgartner) % 0.65/0.64 Free software under GNU Lesser General Public License (LGPL). % 0.65/0.64 Bug reports to peter@backeman.se % 0.65/0.64 % 0.65/0.64 For more information, visit http://user.uu.se/~petba168/breu/ % 0.65/0.64 % 0.65/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.65/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.49/0.97 Prover 0: Preprocessing ... % 1.83/1.08 Prover 0: Warning: ignoring some quantifiers % 1.85/1.09 Prover 0: Constructing countermodel ... % 2.01/1.19 Prover 0: gave up % 2.01/1.19 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.01/1.21 Prover 1: Preprocessing ... % 2.46/1.32 Prover 1: Constructing countermodel ... % 2.75/1.41 Prover 1: proved (226ms) % 2.75/1.41 % 2.75/1.41 No countermodel exists, formula is valid % 2.75/1.41 % SZS status Theorem for theBenchmark % 2.75/1.41 % 2.75/1.41 Generating proof ... found it (size 45) % 3.48/1.66 % 3.48/1.66 % SZS output start Proof for theBenchmark % 3.48/1.66 Assumed formulas after preprocessing and simplification: % 3.48/1.66 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (rp(v9, v8) = v7) | ~ (rp(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ (rp(v6, v8) = 0) | ~ (rp(v6, v7) = 0) | ~ (cc(v6) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (rp(v7, v6) = v8) | ~ (rp(v7, v6) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (rp(v6, v7) = v8) | ~ (rp(v6, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (xsd_string(v8) = v7) | ~ (xsd_string(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (xsd_integer(v8) = v7) | ~ (xsd_integer(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (cowlThing(v8) = v7) | ~ (cowlThing(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (cowlNothing(v8) = v7) | ~ (cowlNothing(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (cc(v8) = v7) | ~ (cc(v8) = v6)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (xsd_string(v6) = v7) | ~ (xsd_string(v6) = 0)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (xsd_string(v6) = v7) | xsd_integer(v6) = 0) & ! [v6] : ! [v7] : (v7 = 0 | ~ (xsd_integer(v6) = v7) | ~ (xsd_integer(v6) = 0)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (cowlThing(v6) = v7) | ~ (cowlThing(v6) = 0)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (cowlThing(v6) = v7)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (cowlNothing(v6) = v7) | ~ (cowlNothing(v6) = 0)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (cc(v6) = v7) | ~ (cc(v6) = 0)) & ! [v6] : ( ~ (xsd_string(v6) = 0) | ? [v7] : ( ~ (v7 = 0) & xsd_integer(v6) = v7)) & ! [v6] : ~ (cowlNothing(v6) = 0) & ! [v6] : ( ~ (cc(v6) = 0) | ? [v7] : rp(v6, v7) = 0) & ((v5 = 0 & v4 = 0 & v1 = 0 & ~ (v3 = v2) & rp(v0, v3) = 0 & rp(v0, v2) = 0 & cc(v0) = 0) | (v1 = 0 & cc(v0) = 0 & ! [v6] : ~ (rp(v0, v6) = 0)) | (xsd_string(v0) = v1 & xsd_integer(v0) = v2 & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & ~ (v1 = 0)))) | (cowlThing(v0) = v1 & cowlNothing(v0) = v2 & ( ~ (v1 = 0) | v2 = 0)))) % 3.96/1.69 | 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 yields: % 3.96/1.69 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (rp(v0, v2) = 0) | ~ (rp(v0, v1) = 0) | ~ (cc(v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v1, v0) = v2) | ~ (rp(v1, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v0, v1) = v2) | ~ (rp(v0, v1) = 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 | ~ (cc(v2) = v1) | ~ (cc(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 | ~ (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 | ~ (cc(v0) = v1) | ~ (cc(v0) = 0)) & ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) & ! [v0] : ~ (cowlNothing(v0) = 0) & ! [v0] : ( ~ (cc(v0) = 0) | ? [v1] : rp(v0, v1) = 0) & ((all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_4_4 = 0 & ~ (all_0_2_2 = all_0_3_3) & rp(all_0_5_5, all_0_2_2) = 0 & rp(all_0_5_5, all_0_3_3) = 0 & cc(all_0_5_5) = 0) | (all_0_4_4 = 0 & cc(all_0_5_5) = 0 & ! [v0] : ~ (rp(all_0_5_5, v0) = 0)) | (xsd_string(all_0_5_5) = all_0_4_4 & xsd_integer(all_0_5_5) = all_0_3_3 & ((all_0_3_3 = 0 & all_0_4_4 = 0) | ( ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0)))) | (cowlThing(all_0_5_5) = all_0_4_4 & cowlNothing(all_0_5_5) = all_0_3_3 & ( ~ (all_0_4_4 = 0) | all_0_3_3 = 0))) % 3.96/1.70 | % 3.96/1.70 | Applying alpha-rule on (1) yields: % 3.96/1.70 | (2) ! [v0] : ~ (cowlNothing(v0) = 0) % 3.96/1.70 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) % 3.96/1.70 | (4) ! [v0] : ( ~ (cc(v0) = 0) | ? [v1] : rp(v0, v1) = 0) % 3.96/1.70 | (5) (all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_4_4 = 0 & ~ (all_0_2_2 = all_0_3_3) & rp(all_0_5_5, all_0_2_2) = 0 & rp(all_0_5_5, all_0_3_3) = 0 & cc(all_0_5_5) = 0) | (all_0_4_4 = 0 & cc(all_0_5_5) = 0 & ! [v0] : ~ (rp(all_0_5_5, v0) = 0)) | (xsd_string(all_0_5_5) = all_0_4_4 & xsd_integer(all_0_5_5) = all_0_3_3 & ((all_0_3_3 = 0 & all_0_4_4 = 0) | ( ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0)))) | (cowlThing(all_0_5_5) = all_0_4_4 & cowlNothing(all_0_5_5) = all_0_3_3 & ( ~ (all_0_4_4 = 0) | all_0_3_3 = 0)) % 3.96/1.70 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) % 3.96/1.70 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 3.96/1.70 | (8) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) % 3.96/1.70 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v0, v1) = v2) | ~ (rp(v0, v1) = 0)) % 3.96/1.70 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ (xsd_string(v0) = 0)) % 3.96/1.71 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0)) % 3.96/1.71 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (cc(v0) = v1) | ~ (cc(v0) = 0)) % 3.96/1.71 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cc(v2) = v1) | ~ (cc(v2) = v0)) % 3.96/1.71 | (14) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) % 3.96/1.71 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v1, v0) = v2) | ~ (rp(v1, v0) = 0)) % 3.96/1.71 | (16) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ (cowlThing(v0) = 0)) % 3.96/1.71 | (17) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlNothing(v0) = v1) | ~ (cowlNothing(v0) = 0)) % 3.96/1.71 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) % 3.96/1.71 | (19) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) % 3.96/1.71 | (20) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ (xsd_integer(v0) = 0)) % 3.96/1.71 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (rp(v0, v2) = 0) | ~ (rp(v0, v1) = 0) | ~ (cc(v0) = 0)) % 3.96/1.71 | % 3.96/1.71 +-Applying beta-rule and splitting (5), into two cases. % 3.96/1.71 |-Branch one: % 3.96/1.71 | (22) (all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_4_4 = 0 & ~ (all_0_2_2 = all_0_3_3) & rp(all_0_5_5, all_0_2_2) = 0 & rp(all_0_5_5, all_0_3_3) = 0 & cc(all_0_5_5) = 0) | (all_0_4_4 = 0 & cc(all_0_5_5) = 0 & ! [v0] : ~ (rp(all_0_5_5, v0) = 0)) | (xsd_string(all_0_5_5) = all_0_4_4 & xsd_integer(all_0_5_5) = all_0_3_3 & ((all_0_3_3 = 0 & all_0_4_4 = 0) | ( ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0)))) % 3.96/1.71 | % 3.96/1.71 +-Applying beta-rule and splitting (22), into two cases. % 3.96/1.71 |-Branch one: % 3.96/1.71 | (23) (all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_4_4 = 0 & ~ (all_0_2_2 = all_0_3_3) & rp(all_0_5_5, all_0_2_2) = 0 & rp(all_0_5_5, all_0_3_3) = 0 & cc(all_0_5_5) = 0) | (all_0_4_4 = 0 & cc(all_0_5_5) = 0 & ! [v0] : ~ (rp(all_0_5_5, v0) = 0)) % 3.96/1.71 | % 3.96/1.71 +-Applying beta-rule and splitting (23), into two cases. % 3.96/1.71 |-Branch one: % 3.96/1.71 | (24) all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_4_4 = 0 & ~ (all_0_2_2 = all_0_3_3) & rp(all_0_5_5, all_0_2_2) = 0 & rp(all_0_5_5, all_0_3_3) = 0 & cc(all_0_5_5) = 0 % 3.96/1.71 | % 3.96/1.71 | Applying alpha-rule on (24) yields: % 3.96/1.71 | (25) all_0_4_4 = 0 % 3.96/1.71 | (26) rp(all_0_5_5, all_0_2_2) = 0 % 3.96/1.71 | (27) rp(all_0_5_5, all_0_3_3) = 0 % 3.96/1.71 | (28) cc(all_0_5_5) = 0 % 3.96/1.71 | (29) ~ (all_0_2_2 = all_0_3_3) % 3.96/1.71 | (30) all_0_0_0 = 0 % 3.96/1.71 | (31) all_0_1_1 = 0 % 3.96/1.71 | % 3.96/1.71 | Instantiating formula (21) with all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms rp(all_0_5_5, all_0_2_2) = 0, rp(all_0_5_5, all_0_3_3) = 0, cc(all_0_5_5) = 0, yields: % 3.96/1.71 | (32) all_0_2_2 = all_0_3_3 % 3.96/1.71 | % 3.96/1.71 | Equations (32) can reduce 29 to: % 3.96/1.71 | (33) $false % 3.96/1.72 | % 3.96/1.72 |-The branch is then unsatisfiable % 3.96/1.72 |-Branch two: % 3.96/1.72 | (34) all_0_4_4 = 0 & cc(all_0_5_5) = 0 & ! [v0] : ~ (rp(all_0_5_5, v0) = 0) % 3.96/1.72 | % 3.96/1.72 | Applying alpha-rule on (34) yields: % 3.96/1.72 | (25) all_0_4_4 = 0 % 3.96/1.72 | (28) cc(all_0_5_5) = 0 % 3.96/1.72 | (37) ! [v0] : ~ (rp(all_0_5_5, v0) = 0) % 3.96/1.72 | % 3.96/1.72 | Instantiating formula (4) with all_0_5_5 and discharging atoms cc(all_0_5_5) = 0, yields: % 3.96/1.72 | (38) ? [v0] : rp(all_0_5_5, v0) = 0 % 3.96/1.72 | % 3.96/1.72 | Instantiating (38) with all_12_0_6 yields: % 3.96/1.72 | (39) rp(all_0_5_5, all_12_0_6) = 0 % 3.96/1.72 | % 3.96/1.72 | Instantiating formula (37) with all_12_0_6 and discharging atoms rp(all_0_5_5, all_12_0_6) = 0, yields: % 3.96/1.72 | (40) $false % 3.96/1.72 | % 3.96/1.72 |-The branch is then unsatisfiable % 3.96/1.72 |-Branch two: % 3.96/1.72 | (41) xsd_string(all_0_5_5) = all_0_4_4 & xsd_integer(all_0_5_5) = all_0_3_3 & ((all_0_3_3 = 0 & all_0_4_4 = 0) | ( ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0))) % 3.96/1.72 | % 3.96/1.72 | Applying alpha-rule on (41) yields: % 3.96/1.72 | (42) xsd_string(all_0_5_5) = all_0_4_4 % 3.96/1.72 | (43) xsd_integer(all_0_5_5) = all_0_3_3 % 3.96/1.72 | (44) (all_0_3_3 = 0 & all_0_4_4 = 0) | ( ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0)) % 3.96/1.72 | % 3.96/1.72 | Instantiating formula (14) with all_0_5_5 yields: % 3.96/1.72 | (45) ~ (xsd_string(all_0_5_5) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_5_5) = v0) % 3.96/1.72 | % 3.96/1.72 | Instantiating formula (19) with all_0_4_4, all_0_5_5 and discharging atoms xsd_string(all_0_5_5) = all_0_4_4, yields: % 3.96/1.72 | (46) all_0_4_4 = 0 | xsd_integer(all_0_5_5) = 0 % 3.96/1.72 | % 3.96/1.72 +-Applying beta-rule and splitting (44), into two cases. % 3.96/1.72 |-Branch one: % 3.96/1.72 | (47) all_0_3_3 = 0 & all_0_4_4 = 0 % 3.96/1.72 | % 3.96/1.72 | Applying alpha-rule on (47) yields: % 3.96/1.72 | (48) all_0_3_3 = 0 % 3.96/1.72 | (25) all_0_4_4 = 0 % 3.96/1.72 | % 3.96/1.72 | From (25) and (42) follows: % 3.96/1.72 | (50) xsd_string(all_0_5_5) = 0 % 3.96/1.72 | % 3.96/1.72 | From (48) and (43) follows: % 3.96/1.72 | (51) xsd_integer(all_0_5_5) = 0 % 3.96/1.72 | % 3.96/1.72 +-Applying beta-rule and splitting (45), into two cases. % 3.96/1.72 |-Branch one: % 3.96/1.72 | (52) ~ (xsd_string(all_0_5_5) = 0) % 3.96/1.72 | % 3.96/1.72 | Using (50) and (52) yields: % 3.96/1.72 | (40) $false % 3.96/1.72 | % 3.96/1.72 |-The branch is then unsatisfiable % 3.96/1.72 |-Branch two: % 3.96/1.72 | (50) xsd_string(all_0_5_5) = 0 % 3.96/1.72 | (55) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_5_5) = v0) % 3.96/1.72 | % 3.96/1.72 | Instantiating (55) with all_17_0_7 yields: % 3.96/1.72 | (56) ~ (all_17_0_7 = 0) & xsd_integer(all_0_5_5) = all_17_0_7 % 3.96/1.72 | % 3.96/1.72 | Applying alpha-rule on (56) yields: % 3.96/1.72 | (57) ~ (all_17_0_7 = 0) % 3.96/1.72 | (58) xsd_integer(all_0_5_5) = all_17_0_7 % 3.96/1.72 | % 3.96/1.72 | Instantiating formula (7) with all_0_5_5, 0, all_17_0_7 and discharging atoms xsd_integer(all_0_5_5) = all_17_0_7, xsd_integer(all_0_5_5) = 0, yields: % 3.96/1.72 | (59) all_17_0_7 = 0 % 3.96/1.72 | % 3.96/1.72 | Equations (59) can reduce 57 to: % 3.96/1.72 | (33) $false % 3.96/1.72 | % 3.96/1.72 |-The branch is then unsatisfiable % 3.96/1.72 |-Branch two: % 3.96/1.72 | (61) ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = 0) % 3.96/1.72 | % 3.96/1.72 | Applying alpha-rule on (61) yields: % 3.96/1.72 | (62) ~ (all_0_3_3 = 0) % 3.96/1.72 | (63) ~ (all_0_4_4 = 0) % 3.96/1.73 | % 3.96/1.73 +-Applying beta-rule and splitting (46), into two cases. % 3.96/1.73 |-Branch one: % 3.96/1.73 | (51) xsd_integer(all_0_5_5) = 0 % 3.96/1.73 | % 3.96/1.73 | Instantiating formula (7) with all_0_5_5, 0, all_0_3_3 and discharging atoms xsd_integer(all_0_5_5) = all_0_3_3, xsd_integer(all_0_5_5) = 0, yields: % 3.96/1.73 | (48) all_0_3_3 = 0 % 3.96/1.73 | % 3.96/1.73 | Equations (48) can reduce 62 to: % 3.96/1.73 | (33) $false % 3.96/1.73 | % 3.96/1.73 |-The branch is then unsatisfiable % 3.96/1.73 |-Branch two: % 3.96/1.73 | (67) ~ (xsd_integer(all_0_5_5) = 0) % 3.96/1.73 | (25) all_0_4_4 = 0 % 3.96/1.73 | % 3.96/1.73 | Equations (25) can reduce 63 to: % 3.96/1.73 | (33) $false % 3.96/1.73 | % 3.96/1.73 |-The branch is then unsatisfiable % 3.96/1.73 |-Branch two: % 3.96/1.73 | (70) cowlThing(all_0_5_5) = all_0_4_4 & cowlNothing(all_0_5_5) = all_0_3_3 & ( ~ (all_0_4_4 = 0) | all_0_3_3 = 0) % 3.96/1.73 | % 3.96/1.73 | Applying alpha-rule on (70) yields: % 3.96/1.73 | (71) cowlThing(all_0_5_5) = all_0_4_4 % 3.96/1.73 | (72) cowlNothing(all_0_5_5) = all_0_3_3 % 3.96/1.73 | (73) ~ (all_0_4_4 = 0) | all_0_3_3 = 0 % 3.96/1.73 | % 3.96/1.73 | Instantiating formula (8) with all_0_4_4, all_0_5_5 and discharging atoms cowlThing(all_0_5_5) = all_0_4_4, yields: % 3.96/1.73 | (25) all_0_4_4 = 0 % 3.96/1.73 | % 3.96/1.73 | Instantiating formula (2) with all_0_5_5 yields: % 3.96/1.73 | (75) ~ (cowlNothing(all_0_5_5) = 0) % 3.96/1.73 | % 3.96/1.73 +-Applying beta-rule and splitting (73), into two cases. % 3.96/1.73 |-Branch one: % 3.96/1.73 | (63) ~ (all_0_4_4 = 0) % 3.96/1.73 | % 3.96/1.73 | Equations (25) can reduce 63 to: % 3.96/1.73 | (33) $false % 3.96/1.73 | % 3.96/1.73 |-The branch is then unsatisfiable % 3.96/1.73 |-Branch two: % 3.96/1.73 | (25) all_0_4_4 = 0 % 3.96/1.73 | (48) all_0_3_3 = 0 % 3.96/1.73 | % 3.96/1.73 | From (48) and (72) follows: % 3.96/1.73 | (80) cowlNothing(all_0_5_5) = 0 % 3.96/1.73 | % 3.96/1.73 | Using (80) and (75) yields: % 3.96/1.73 | (40) $false % 3.96/1.73 | % 3.96/1.73 |-The branch is then unsatisfiable % 3.96/1.73 % SZS output end Proof for theBenchmark % 3.96/1.73 % 3.96/1.73 1083ms %------------------------------------------------------------------------------