%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KRS145+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n028.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 3.29s 1.50s % Output : Proof 4.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : KRS145+1 : TPTP v8.1.0. Released v3.1.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n028.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 13:53:30 EDT 2022 % 0.12/0.34 % CPUTime : % 0.61/0.59 ____ _ % 0.61/0.59 ___ / __ \_____(_)___ ________ __________ % 0.61/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.61/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.61/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.61/0.59 % 0.61/0.59 A Theorem Prover for First-Order Logic % 0.61/0.60 (ePrincess v.1.0) % 0.61/0.60 % 0.61/0.60 (c) Philipp Rümmer, 2009-2015 % 0.61/0.60 (c) Peter Backeman, 2014-2015 % 0.61/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.61/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.61/0.60 Bug reports to peter@backeman.se % 0.61/0.60 % 0.61/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.61/0.60 % 0.61/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.76/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.58/0.96 Prover 0: Preprocessing ... % 1.78/1.07 Prover 0: Warning: ignoring some quantifiers % 1.92/1.09 Prover 0: Constructing countermodel ... % 2.16/1.18 Prover 0: gave up % 2.16/1.18 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.22/1.20 Prover 1: Preprocessing ... % 2.67/1.32 Prover 1: Constructing countermodel ... % 3.29/1.50 Prover 1: proved (319ms) % 3.29/1.50 % 3.29/1.50 No countermodel exists, formula is valid % 3.29/1.50 % SZS status Theorem for theBenchmark % 3.29/1.50 % 3.29/1.50 Generating proof ... found it (size 53) % 4.64/1.81 % 4.64/1.81 % SZS output start Proof for theBenchmark % 4.64/1.81 Assumed formulas after preprocessing and simplification: % 4.64/1.81 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | v11 = v9 | v10 = v9 | ~ (rp(v8, v11) = 0) | ~ (rp(v8, v10) = 0) | ~ (rp(v8, v9) = 0) | ~ (cc(v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (rp(v11, v10) = v9) | ~ (rp(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (rp(v9, v8) = v10) | ~ (rp(v9, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (rp(v8, v9) = v10) | ~ (rp(v8, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (xsd_string(v10) = v9) | ~ (xsd_string(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (xsd_integer(v10) = v9) | ~ (xsd_integer(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (cowlThing(v10) = v9) | ~ (cowlThing(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (cowlNothing(v10) = v9) | ~ (cowlNothing(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (cc(v10) = v9) | ~ (cc(v10) = v8)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (xsd_string(v8) = v9) | ~ (xsd_string(v8) = 0)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (xsd_string(v8) = v9) | xsd_integer(v8) = 0) & ! [v8] : ! [v9] : (v9 = 0 | ~ (xsd_integer(v8) = v9) | ~ (xsd_integer(v8) = 0)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (cowlThing(v8) = v9) | ~ (cowlThing(v8) = 0)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (cowlThing(v8) = v9)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (cowlNothing(v8) = v9) | ~ (cowlNothing(v8) = 0)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (cc(v8) = v9) | ~ (cc(v8) = 0)) & ! [v8] : ( ~ (xsd_string(v8) = 0) | ? [v9] : ( ~ (v9 = 0) & xsd_integer(v8) = v9)) & ! [v8] : ~ (cowlNothing(v8) = 0) & ! [v8] : ( ~ (cc(v8) = 0) | ? [v9] : ? [v10] : ( ~ (v10 = v9) & rp(v8, v10) = 0 & rp(v8, v9) = 0)) & ((v1 = 0 & cc(v0) = 0 & ( ! [v8] : ! [v9] : (v9 = v8 | ~ (rp(v0, v9) = 0) | ~ (rp(v0, v8) = 0)) | (v7 = 0 & v6 = 0 & v5 = 0 & ~ (v4 = v3) & ~ (v4 = v2) & ~ (v3 = v2) & rp(v0, v4) = 0 & rp(v0, v3) = 0 & rp(v0, v2) = 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)))) % 4.73/1.84 | 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, all_0_7_7 yields: % 4.73/1.84 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | v2 = v1 | ~ (rp(v0, v3) = 0) | ~ (rp(v0, v2) = 0) | ~ (rp(v0, v1) = 0) | ~ (cc(v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0)) & ! [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] : ? [v2] : ( ~ (v2 = v1) & rp(v0, v2) = 0 & rp(v0, v1) = 0)) & ((all_0_6_6 = 0 & cc(all_0_7_7) = 0 & ( ! [v0] : ! [v1] : (v1 = v0 | ~ (rp(all_0_7_7, v1) = 0) | ~ (rp(all_0_7_7, v0) = 0)) | (all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_2_2 = 0 & ~ (all_0_3_3 = all_0_4_4) & ~ (all_0_3_3 = all_0_5_5) & ~ (all_0_4_4 = all_0_5_5) & rp(all_0_7_7, all_0_3_3) = 0 & rp(all_0_7_7, all_0_4_4) = 0 & rp(all_0_7_7, all_0_5_5) = 0))) | (xsd_string(all_0_7_7) = all_0_6_6 & xsd_integer(all_0_7_7) = all_0_5_5 & ((all_0_5_5 = 0 & all_0_6_6 = 0) | ( ~ (all_0_5_5 = 0) & ~ (all_0_6_6 = 0)))) | (cowlThing(all_0_7_7) = all_0_6_6 & cowlNothing(all_0_7_7) = all_0_5_5 & ( ~ (all_0_6_6 = 0) | all_0_5_5 = 0))) % 4.73/1.85 | % 4.73/1.85 | Applying alpha-rule on (1) yields: % 4.73/1.85 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cc(v2) = v1) | ~ (cc(v2) = v0)) % 4.73/1.85 | (3) ! [v0] : ~ (cowlNothing(v0) = 0) % 4.73/1.85 | (4) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ (cowlThing(v0) = 0)) % 4.73/1.85 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0)) % 4.73/1.85 | (6) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) % 4.73/1.85 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) % 4.73/1.85 | (8) ! [v0] : ! [v1] : (v1 = 0 | ~ (cc(v0) = v1) | ~ (cc(v0) = 0)) % 4.73/1.85 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v0, v1) = v2) | ~ (rp(v0, v1) = 0)) % 4.73/1.85 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | v2 = v1 | ~ (rp(v0, v3) = 0) | ~ (rp(v0, v2) = 0) | ~ (rp(v0, v1) = 0) | ~ (cc(v0) = 0)) % 4.73/1.85 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 4.73/1.85 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ (xsd_integer(v0) = 0)) % 4.73/1.85 | (13) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlNothing(v0) = v1) | ~ (cowlNothing(v0) = 0)) % 4.73/1.85 | (14) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) % 4.73/1.85 | (15) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ (xsd_string(v0) = 0)) % 4.73/1.85 | (16) (all_0_6_6 = 0 & cc(all_0_7_7) = 0 & ( ! [v0] : ! [v1] : (v1 = v0 | ~ (rp(all_0_7_7, v1) = 0) | ~ (rp(all_0_7_7, v0) = 0)) | (all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_2_2 = 0 & ~ (all_0_3_3 = all_0_4_4) & ~ (all_0_3_3 = all_0_5_5) & ~ (all_0_4_4 = all_0_5_5) & rp(all_0_7_7, all_0_3_3) = 0 & rp(all_0_7_7, all_0_4_4) = 0 & rp(all_0_7_7, all_0_5_5) = 0))) | (xsd_string(all_0_7_7) = all_0_6_6 & xsd_integer(all_0_7_7) = all_0_5_5 & ((all_0_5_5 = 0 & all_0_6_6 = 0) | ( ~ (all_0_5_5 = 0) & ~ (all_0_6_6 = 0)))) | (cowlThing(all_0_7_7) = all_0_6_6 & cowlNothing(all_0_7_7) = all_0_5_5 & ( ~ (all_0_6_6 = 0) | all_0_5_5 = 0)) % 4.73/1.85 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v1, v0) = v2) | ~ (rp(v1, v0) = 0)) % 4.73/1.85 | (18) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) % 4.73/1.85 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) % 4.73/1.85 | (20) ! [v0] : ( ~ (cc(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = v1) & rp(v0, v2) = 0 & rp(v0, v1) = 0)) % 4.73/1.85 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) % 4.73/1.85 | % 4.73/1.85 +-Applying beta-rule and splitting (16), into two cases. % 4.73/1.85 |-Branch one: % 4.73/1.85 | (22) (all_0_6_6 = 0 & cc(all_0_7_7) = 0 & ( ! [v0] : ! [v1] : (v1 = v0 | ~ (rp(all_0_7_7, v1) = 0) | ~ (rp(all_0_7_7, v0) = 0)) | (all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_2_2 = 0 & ~ (all_0_3_3 = all_0_4_4) & ~ (all_0_3_3 = all_0_5_5) & ~ (all_0_4_4 = all_0_5_5) & rp(all_0_7_7, all_0_3_3) = 0 & rp(all_0_7_7, all_0_4_4) = 0 & rp(all_0_7_7, all_0_5_5) = 0))) | (xsd_string(all_0_7_7) = all_0_6_6 & xsd_integer(all_0_7_7) = all_0_5_5 & ((all_0_5_5 = 0 & all_0_6_6 = 0) | ( ~ (all_0_5_5 = 0) & ~ (all_0_6_6 = 0)))) % 4.73/1.86 | % 4.73/1.86 +-Applying beta-rule and splitting (22), into two cases. % 4.73/1.86 |-Branch one: % 4.73/1.86 | (23) all_0_6_6 = 0 & cc(all_0_7_7) = 0 & ( ! [v0] : ! [v1] : (v1 = v0 | ~ (rp(all_0_7_7, v1) = 0) | ~ (rp(all_0_7_7, v0) = 0)) | (all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_2_2 = 0 & ~ (all_0_3_3 = all_0_4_4) & ~ (all_0_3_3 = all_0_5_5) & ~ (all_0_4_4 = all_0_5_5) & rp(all_0_7_7, all_0_3_3) = 0 & rp(all_0_7_7, all_0_4_4) = 0 & rp(all_0_7_7, all_0_5_5) = 0)) % 4.73/1.86 | % 4.73/1.86 | Applying alpha-rule on (23) yields: % 4.73/1.86 | (24) all_0_6_6 = 0 % 4.73/1.86 | (25) cc(all_0_7_7) = 0 % 4.73/1.86 | (26) ! [v0] : ! [v1] : (v1 = v0 | ~ (rp(all_0_7_7, v1) = 0) | ~ (rp(all_0_7_7, v0) = 0)) | (all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_2_2 = 0 & ~ (all_0_3_3 = all_0_4_4) & ~ (all_0_3_3 = all_0_5_5) & ~ (all_0_4_4 = all_0_5_5) & rp(all_0_7_7, all_0_3_3) = 0 & rp(all_0_7_7, all_0_4_4) = 0 & rp(all_0_7_7, all_0_5_5) = 0) % 4.73/1.86 | % 4.73/1.86 | Instantiating formula (20) with all_0_7_7 and discharging atoms cc(all_0_7_7) = 0, yields: % 4.73/1.86 | (27) ? [v0] : ? [v1] : ( ~ (v1 = v0) & rp(all_0_7_7, v1) = 0 & rp(all_0_7_7, v0) = 0) % 4.73/1.86 | % 4.73/1.86 | Instantiating (27) with all_11_0_8, all_11_1_9 yields: % 4.73/1.86 | (28) ~ (all_11_0_8 = all_11_1_9) & rp(all_0_7_7, all_11_0_8) = 0 & rp(all_0_7_7, all_11_1_9) = 0 % 4.73/1.86 | % 4.73/1.86 | Applying alpha-rule on (28) yields: % 4.73/1.86 | (29) ~ (all_11_0_8 = all_11_1_9) % 4.73/1.86 | (30) rp(all_0_7_7, all_11_0_8) = 0 % 4.73/1.86 | (31) rp(all_0_7_7, all_11_1_9) = 0 % 4.73/1.86 | % 4.73/1.86 +-Applying beta-rule and splitting (26), into two cases. % 4.73/1.86 |-Branch one: % 4.73/1.86 | (32) ! [v0] : ! [v1] : (v1 = v0 | ~ (rp(all_0_7_7, v1) = 0) | ~ (rp(all_0_7_7, v0) = 0)) % 4.73/1.86 | % 4.73/1.86 | Instantiating formula (32) with all_11_1_9, all_11_0_8 and discharging atoms rp(all_0_7_7, all_11_0_8) = 0, rp(all_0_7_7, all_11_1_9) = 0, yields: % 4.73/1.86 | (33) all_11_0_8 = all_11_1_9 % 4.73/1.86 | % 4.73/1.86 | Equations (33) can reduce 29 to: % 4.73/1.86 | (34) $false % 4.73/1.86 | % 4.73/1.86 |-The branch is then unsatisfiable % 4.73/1.86 |-Branch two: % 4.73/1.86 | (35) all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_2_2 = 0 & ~ (all_0_3_3 = all_0_4_4) & ~ (all_0_3_3 = all_0_5_5) & ~ (all_0_4_4 = all_0_5_5) & rp(all_0_7_7, all_0_3_3) = 0 & rp(all_0_7_7, all_0_4_4) = 0 & rp(all_0_7_7, all_0_5_5) = 0 % 4.73/1.86 | % 4.73/1.86 | Applying alpha-rule on (35) yields: % 4.73/1.86 | (36) rp(all_0_7_7, all_0_5_5) = 0 % 4.73/1.86 | (37) rp(all_0_7_7, all_0_3_3) = 0 % 4.73/1.86 | (38) rp(all_0_7_7, all_0_4_4) = 0 % 4.73/1.86 | (39) ~ (all_0_3_3 = all_0_4_4) % 4.73/1.86 | (40) ~ (all_0_4_4 = all_0_5_5) % 4.73/1.86 | (41) all_0_2_2 = 0 % 4.73/1.86 | (42) all_0_0_0 = 0 % 4.73/1.86 | (43) all_0_1_1 = 0 % 4.73/1.86 | (44) ~ (all_0_3_3 = all_0_5_5) % 4.73/1.86 | % 4.73/1.86 | Instantiating formula (10) with all_0_5_5, all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms rp(all_0_7_7, all_0_3_3) = 0, rp(all_0_7_7, all_0_4_4) = 0, rp(all_0_7_7, all_0_5_5) = 0, cc(all_0_7_7) = 0, yields: % 4.73/1.86 | (45) all_0_3_3 = all_0_4_4 | all_0_3_3 = all_0_5_5 | all_0_4_4 = all_0_5_5 % 4.73/1.86 | % 4.73/1.87 +-Applying beta-rule and splitting (45), into two cases. % 4.73/1.87 |-Branch one: % 4.73/1.87 | (46) all_0_3_3 = all_0_4_4 % 4.73/1.87 | % 4.73/1.87 | Equations (46) can reduce 39 to: % 4.73/1.87 | (34) $false % 4.73/1.87 | % 4.73/1.87 |-The branch is then unsatisfiable % 4.73/1.87 |-Branch two: % 4.73/1.87 | (39) ~ (all_0_3_3 = all_0_4_4) % 4.73/1.87 | (49) all_0_3_3 = all_0_5_5 | all_0_4_4 = all_0_5_5 % 4.73/1.87 | % 4.73/1.87 +-Applying beta-rule and splitting (49), into two cases. % 4.73/1.87 |-Branch one: % 4.73/1.87 | (50) all_0_3_3 = all_0_5_5 % 4.73/1.87 | % 4.73/1.87 | Equations (50) can reduce 44 to: % 4.73/1.87 | (34) $false % 4.73/1.87 | % 4.73/1.87 |-The branch is then unsatisfiable % 4.73/1.87 |-Branch two: % 4.73/1.87 | (44) ~ (all_0_3_3 = all_0_5_5) % 4.73/1.87 | (53) all_0_4_4 = all_0_5_5 % 4.73/1.87 | % 4.73/1.87 | Equations (53) can reduce 40 to: % 4.73/1.87 | (34) $false % 4.73/1.87 | % 4.73/1.87 |-The branch is then unsatisfiable % 4.73/1.87 |-Branch two: % 4.73/1.87 | (55) xsd_string(all_0_7_7) = all_0_6_6 & xsd_integer(all_0_7_7) = all_0_5_5 & ((all_0_5_5 = 0 & all_0_6_6 = 0) | ( ~ (all_0_5_5 = 0) & ~ (all_0_6_6 = 0))) % 4.73/1.87 | % 4.73/1.87 | Applying alpha-rule on (55) yields: % 4.73/1.87 | (56) xsd_string(all_0_7_7) = all_0_6_6 % 4.73/1.87 | (57) xsd_integer(all_0_7_7) = all_0_5_5 % 4.73/1.87 | (58) (all_0_5_5 = 0 & all_0_6_6 = 0) | ( ~ (all_0_5_5 = 0) & ~ (all_0_6_6 = 0)) % 4.73/1.87 | % 4.73/1.87 | Instantiating formula (6) with all_0_7_7 yields: % 4.73/1.87 | (59) ~ (xsd_string(all_0_7_7) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_7_7) = v0) % 4.73/1.87 | % 4.73/1.87 | Instantiating formula (18) with all_0_6_6, all_0_7_7 and discharging atoms xsd_string(all_0_7_7) = all_0_6_6, yields: % 4.73/1.87 | (60) all_0_6_6 = 0 | xsd_integer(all_0_7_7) = 0 % 4.73/1.87 | % 4.73/1.87 +-Applying beta-rule and splitting (58), into two cases. % 4.73/1.87 |-Branch one: % 4.73/1.87 | (61) all_0_5_5 = 0 & all_0_6_6 = 0 % 4.73/1.87 | % 4.73/1.87 | Applying alpha-rule on (61) yields: % 4.73/1.87 | (62) all_0_5_5 = 0 % 4.73/1.87 | (24) all_0_6_6 = 0 % 4.73/1.87 | % 4.73/1.87 | From (24) and (56) follows: % 4.73/1.87 | (64) xsd_string(all_0_7_7) = 0 % 4.73/1.87 | % 4.73/1.87 | From (62) and (57) follows: % 4.73/1.87 | (65) xsd_integer(all_0_7_7) = 0 % 4.73/1.87 | % 4.73/1.87 +-Applying beta-rule and splitting (59), into two cases. % 4.73/1.87 |-Branch one: % 4.73/1.87 | (66) ~ (xsd_string(all_0_7_7) = 0) % 4.73/1.87 | % 4.73/1.87 | Using (64) and (66) yields: % 4.73/1.87 | (67) $false % 4.73/1.87 | % 4.73/1.87 |-The branch is then unsatisfiable % 4.73/1.87 |-Branch two: % 4.73/1.87 | (64) xsd_string(all_0_7_7) = 0 % 4.73/1.87 | (69) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_7_7) = v0) % 4.73/1.87 | % 4.73/1.87 | Instantiating (69) with all_17_0_10 yields: % 4.73/1.87 | (70) ~ (all_17_0_10 = 0) & xsd_integer(all_0_7_7) = all_17_0_10 % 4.73/1.87 | % 4.73/1.87 | Applying alpha-rule on (70) yields: % 4.73/1.87 | (71) ~ (all_17_0_10 = 0) % 4.73/1.87 | (72) xsd_integer(all_0_7_7) = all_17_0_10 % 4.73/1.87 | % 4.73/1.87 | Instantiating formula (11) with all_0_7_7, 0, all_17_0_10 and discharging atoms xsd_integer(all_0_7_7) = all_17_0_10, xsd_integer(all_0_7_7) = 0, yields: % 4.73/1.87 | (73) all_17_0_10 = 0 % 4.73/1.87 | % 4.73/1.87 | Equations (73) can reduce 71 to: % 4.73/1.87 | (34) $false % 4.73/1.87 | % 4.73/1.87 |-The branch is then unsatisfiable % 4.73/1.87 |-Branch two: % 4.73/1.87 | (75) ~ (all_0_5_5 = 0) & ~ (all_0_6_6 = 0) % 4.73/1.87 | % 4.73/1.87 | Applying alpha-rule on (75) yields: % 4.73/1.87 | (76) ~ (all_0_5_5 = 0) % 4.73/1.87 | (77) ~ (all_0_6_6 = 0) % 4.73/1.87 | % 4.73/1.87 +-Applying beta-rule and splitting (60), into two cases. % 4.73/1.87 |-Branch one: % 4.73/1.87 | (65) xsd_integer(all_0_7_7) = 0 % 4.73/1.87 | % 4.73/1.87 | Instantiating formula (11) with all_0_7_7, 0, all_0_5_5 and discharging atoms xsd_integer(all_0_7_7) = all_0_5_5, xsd_integer(all_0_7_7) = 0, yields: % 4.73/1.87 | (62) all_0_5_5 = 0 % 4.73/1.87 | % 4.73/1.87 | Equations (62) can reduce 76 to: % 4.73/1.87 | (34) $false % 4.73/1.87 | % 4.73/1.87 |-The branch is then unsatisfiable % 4.73/1.87 |-Branch two: % 4.73/1.87 | (81) ~ (xsd_integer(all_0_7_7) = 0) % 4.73/1.87 | (24) all_0_6_6 = 0 % 4.73/1.87 | % 4.73/1.87 | Equations (24) can reduce 77 to: % 4.73/1.87 | (34) $false % 4.73/1.87 | % 4.73/1.87 |-The branch is then unsatisfiable % 4.73/1.87 |-Branch two: % 4.73/1.87 | (84) cowlThing(all_0_7_7) = all_0_6_6 & cowlNothing(all_0_7_7) = all_0_5_5 & ( ~ (all_0_6_6 = 0) | all_0_5_5 = 0) % 4.73/1.87 | % 4.73/1.88 | Applying alpha-rule on (84) yields: % 4.73/1.88 | (85) cowlThing(all_0_7_7) = all_0_6_6 % 4.73/1.88 | (86) cowlNothing(all_0_7_7) = all_0_5_5 % 4.73/1.88 | (87) ~ (all_0_6_6 = 0) | all_0_5_5 = 0 % 4.73/1.88 | % 4.73/1.88 | Instantiating formula (14) with all_0_6_6, all_0_7_7 and discharging atoms cowlThing(all_0_7_7) = all_0_6_6, yields: % 4.73/1.88 | (24) all_0_6_6 = 0 % 4.73/1.88 | % 4.73/1.88 | Instantiating formula (3) with all_0_7_7 yields: % 4.73/1.88 | (89) ~ (cowlNothing(all_0_7_7) = 0) % 4.73/1.88 | % 4.73/1.88 +-Applying beta-rule and splitting (87), into two cases. % 4.73/1.88 |-Branch one: % 4.73/1.88 | (77) ~ (all_0_6_6 = 0) % 4.73/1.88 | % 4.73/1.88 | Equations (24) can reduce 77 to: % 4.73/1.88 | (34) $false % 4.73/1.88 | % 4.73/1.88 |-The branch is then unsatisfiable % 4.73/1.88 |-Branch two: % 4.73/1.88 | (24) all_0_6_6 = 0 % 4.73/1.88 | (62) all_0_5_5 = 0 % 4.73/1.88 | % 4.73/1.88 | From (62) and (86) follows: % 4.73/1.88 | (94) cowlNothing(all_0_7_7) = 0 % 4.73/1.88 | % 4.73/1.88 | Using (94) and (89) yields: % 4.73/1.88 | (67) $false % 4.73/1.88 | % 4.73/1.88 |-The branch is then unsatisfiable % 4.73/1.88 % SZS output end Proof for theBenchmark % 4.73/1.88 % 4.73/1.88 1271ms %------------------------------------------------------------------------------