%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KRS144+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n021.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 2.91s 1.37s % Output : Proof 4.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : KRS144+1 : TPTP v8.1.0. Released v3.1.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n021.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Tue Jun 7 10:48:06 EDT 2022 % 0.12/0.33 % CPUTime : % 0.49/0.57 ____ _ % 0.49/0.57 ___ / __ \_____(_)___ ________ __________ % 0.49/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.49/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.49/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.49/0.57 % 0.49/0.57 A Theorem Prover for First-Order Logic % 0.49/0.57 (ePrincess v.1.0) % 0.49/0.57 % 0.49/0.57 (c) Philipp Rümmer, 2009-2015 % 0.49/0.57 (c) Peter Backeman, 2014-2015 % 0.49/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.49/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.49/0.57 Bug reports to peter@backeman.se % 0.49/0.57 % 0.49/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.49/0.57 % 0.49/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.49/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.30/0.91 Prover 0: Preprocessing ... % 1.71/1.02 Prover 0: Warning: ignoring some quantifiers % 1.71/1.03 Prover 0: Constructing countermodel ... % 2.05/1.12 Prover 0: gave up % 2.05/1.12 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.05/1.15 Prover 1: Preprocessing ... % 2.49/1.26 Prover 1: Constructing countermodel ... % 2.91/1.37 Prover 1: proved (252ms) % 2.91/1.37 % 2.91/1.37 No countermodel exists, formula is valid % 2.91/1.37 % SZS status Theorem for theBenchmark % 2.91/1.37 % 2.91/1.37 Generating proof ... found it (size 53) % 3.75/1.64 % 3.75/1.64 % SZS output start Proof for theBenchmark % 3.75/1.64 Assumed formulas after preprocessing and simplification: % 3.75/1.64 | (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)) & ((v7 = 0 & v6 = 0 & v5 = 0 & v1 = 0 & ~ (v4 = v3) & ~ (v4 = v2) & ~ (v3 = v2) & rp(v0, v4) = 0 & rp(v0, v3) = 0 & rp(v0, v2) = 0 & cc(v0) = 0) | (v1 = 0 & cc(v0) = 0 & ! [v8] : ! [v9] : (v9 = v8 | ~ (rp(v0, v9) = 0) | ~ (rp(v0, v8) = 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)))) % 4.08/1.67 | 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: % 4.08/1.67 | (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_0_0 = 0 & all_0_1_1 = 0 & all_0_2_2 = 0 & all_0_6_6 = 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 & cc(all_0_7_7) = 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))) | (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))) % 4.19/1.68 | % 4.19/1.68 | Applying alpha-rule on (1) yields: % 4.19/1.68 | (2) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) % 4.19/1.68 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 4.19/1.68 | (4) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) % 4.19/1.68 | (5) ! [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)) % 4.19/1.68 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ (xsd_integer(v0) = 0)) % 4.19/1.68 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) % 4.19/1.68 | (8) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) % 4.19/1.68 | (9) (all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_2_2 = 0 & all_0_6_6 = 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 & cc(all_0_7_7) = 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))) | (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)) % 4.19/1.68 | (10) ! [v0] : ( ~ (cc(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = v1) & rp(v0, v2) = 0 & rp(v0, v1) = 0)) % 4.19/1.69 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) % 4.19/1.69 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0)) % 4.19/1.69 | (13) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ (xsd_string(v0) = 0)) % 4.19/1.69 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) % 4.19/1.69 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cc(v2) = v1) | ~ (cc(v2) = v0)) % 4.19/1.69 | (16) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ (cowlThing(v0) = 0)) % 4.19/1.69 | (17) ! [v0] : ! [v1] : (v1 = 0 | ~ (cc(v0) = v1) | ~ (cc(v0) = 0)) % 4.19/1.69 | (18) ! [v0] : ~ (cowlNothing(v0) = 0) % 4.19/1.69 | (19) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlNothing(v0) = v1) | ~ (cowlNothing(v0) = 0)) % 4.19/1.69 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v0, v1) = v2) | ~ (rp(v0, v1) = 0)) % 4.19/1.69 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v1, v0) = v2) | ~ (rp(v1, v0) = 0)) % 4.19/1.69 | % 4.19/1.69 +-Applying beta-rule and splitting (9), into two cases. % 4.19/1.69 |-Branch one: % 4.19/1.69 | (22) (all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_2_2 = 0 & all_0_6_6 = 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 & cc(all_0_7_7) = 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))) | (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)))) % 4.19/1.69 | % 4.19/1.69 +-Applying beta-rule and splitting (22), into two cases. % 4.19/1.69 |-Branch one: % 4.19/1.69 | (23) (all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_2_2 = 0 & all_0_6_6 = 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 & cc(all_0_7_7) = 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))) % 4.19/1.69 | % 4.19/1.69 +-Applying beta-rule and splitting (23), into two cases. % 4.19/1.69 |-Branch one: % 4.19/1.69 | (24) all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_2_2 = 0 & all_0_6_6 = 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 & cc(all_0_7_7) = 0 % 4.19/1.69 | % 4.19/1.69 | Applying alpha-rule on (24) yields: % 4.19/1.69 | (25) all_0_1_1 = 0 % 4.19/1.69 | (26) rp(all_0_7_7, all_0_4_4) = 0 % 4.19/1.69 | (27) rp(all_0_7_7, all_0_3_3) = 0 % 4.19/1.69 | (28) ~ (all_0_3_3 = all_0_5_5) % 4.19/1.69 | (29) all_0_6_6 = 0 % 4.19/1.69 | (30) rp(all_0_7_7, all_0_5_5) = 0 % 4.19/1.69 | (31) all_0_0_0 = 0 % 4.19/1.69 | (32) ~ (all_0_4_4 = all_0_5_5) % 4.19/1.69 | (33) all_0_2_2 = 0 % 4.19/1.69 | (34) ~ (all_0_3_3 = all_0_4_4) % 4.19/1.69 | (35) cc(all_0_7_7) = 0 % 4.19/1.69 | % 4.19/1.69 | Instantiating formula (5) with all_0_3_3, all_0_4_4, all_0_5_5, 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: % 4.19/1.69 | (36) all_0_3_3 = all_0_4_4 | all_0_3_3 = all_0_5_5 | all_0_4_4 = all_0_5_5 % 4.19/1.69 | % 4.19/1.70 +-Applying beta-rule and splitting (36), into two cases. % 4.19/1.70 |-Branch one: % 4.19/1.70 | (37) all_0_3_3 = all_0_4_4 % 4.19/1.70 | % 4.19/1.70 | Equations (37) can reduce 34 to: % 4.19/1.70 | (38) $false % 4.19/1.70 | % 4.19/1.70 |-The branch is then unsatisfiable % 4.19/1.70 |-Branch two: % 4.19/1.70 | (34) ~ (all_0_3_3 = all_0_4_4) % 4.19/1.70 | (40) all_0_3_3 = all_0_5_5 | all_0_4_4 = all_0_5_5 % 4.19/1.70 | % 4.19/1.70 +-Applying beta-rule and splitting (40), into two cases. % 4.19/1.70 |-Branch one: % 4.19/1.70 | (41) all_0_3_3 = all_0_5_5 % 4.19/1.70 | % 4.19/1.70 | Equations (41) can reduce 28 to: % 4.19/1.70 | (38) $false % 4.19/1.70 | % 4.19/1.70 |-The branch is then unsatisfiable % 4.19/1.70 |-Branch two: % 4.19/1.70 | (28) ~ (all_0_3_3 = all_0_5_5) % 4.19/1.70 | (44) all_0_4_4 = all_0_5_5 % 4.19/1.70 | % 4.19/1.70 | Equations (44) can reduce 32 to: % 4.19/1.70 | (38) $false % 4.19/1.70 | % 4.19/1.70 |-The branch is then unsatisfiable % 4.19/1.70 |-Branch two: % 4.19/1.70 | (46) 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)) % 4.19/1.70 | % 4.19/1.70 | Applying alpha-rule on (46) yields: % 4.19/1.70 | (29) all_0_6_6 = 0 % 4.19/1.70 | (35) cc(all_0_7_7) = 0 % 4.19/1.70 | (49) ! [v0] : ! [v1] : (v1 = v0 | ~ (rp(all_0_7_7, v1) = 0) | ~ (rp(all_0_7_7, v0) = 0)) % 4.19/1.70 | % 4.19/1.70 | Instantiating formula (10) with all_0_7_7 and discharging atoms cc(all_0_7_7) = 0, yields: % 4.19/1.70 | (50) ? [v0] : ? [v1] : ( ~ (v1 = v0) & rp(all_0_7_7, v1) = 0 & rp(all_0_7_7, v0) = 0) % 4.19/1.70 | % 4.19/1.70 | Instantiating (50) with all_12_0_10, all_12_1_11 yields: % 4.19/1.70 | (51) ~ (all_12_0_10 = all_12_1_11) & rp(all_0_7_7, all_12_0_10) = 0 & rp(all_0_7_7, all_12_1_11) = 0 % 4.19/1.70 | % 4.19/1.70 | Applying alpha-rule on (51) yields: % 4.19/1.70 | (52) ~ (all_12_0_10 = all_12_1_11) % 4.19/1.70 | (53) rp(all_0_7_7, all_12_0_10) = 0 % 4.19/1.70 | (54) rp(all_0_7_7, all_12_1_11) = 0 % 4.19/1.70 | % 4.19/1.70 | Instantiating formula (49) with all_12_1_11, all_12_0_10 and discharging atoms rp(all_0_7_7, all_12_0_10) = 0, rp(all_0_7_7, all_12_1_11) = 0, yields: % 4.19/1.70 | (55) all_12_0_10 = all_12_1_11 % 4.19/1.70 | % 4.19/1.70 | Equations (55) can reduce 52 to: % 4.19/1.70 | (38) $false % 4.19/1.70 | % 4.19/1.70 |-The branch is then unsatisfiable % 4.19/1.70 |-Branch two: % 4.19/1.70 | (57) 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))) % 4.19/1.70 | % 4.19/1.70 | Applying alpha-rule on (57) yields: % 4.19/1.70 | (58) xsd_string(all_0_7_7) = all_0_6_6 % 4.19/1.70 | (59) xsd_integer(all_0_7_7) = all_0_5_5 % 4.19/1.70 | (60) (all_0_5_5 = 0 & all_0_6_6 = 0) | ( ~ (all_0_5_5 = 0) & ~ (all_0_6_6 = 0)) % 4.19/1.70 | % 4.19/1.70 | Instantiating formula (4) with all_0_7_7 yields: % 4.19/1.70 | (61) ~ (xsd_string(all_0_7_7) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_7_7) = v0) % 4.19/1.70 | % 4.19/1.70 | Instantiating formula (8) with all_0_6_6, all_0_7_7 and discharging atoms xsd_string(all_0_7_7) = all_0_6_6, yields: % 4.19/1.70 | (62) all_0_6_6 = 0 | xsd_integer(all_0_7_7) = 0 % 4.19/1.70 | % 4.19/1.70 +-Applying beta-rule and splitting (60), into two cases. % 4.19/1.70 |-Branch one: % 4.19/1.70 | (63) all_0_5_5 = 0 & all_0_6_6 = 0 % 4.19/1.70 | % 4.19/1.70 | Applying alpha-rule on (63) yields: % 4.19/1.70 | (64) all_0_5_5 = 0 % 4.19/1.70 | (29) all_0_6_6 = 0 % 4.19/1.70 | % 4.19/1.70 | From (29) and (58) follows: % 4.19/1.71 | (66) xsd_string(all_0_7_7) = 0 % 4.19/1.71 | % 4.19/1.71 | From (64) and (59) follows: % 4.19/1.71 | (67) xsd_integer(all_0_7_7) = 0 % 4.19/1.71 | % 4.19/1.71 +-Applying beta-rule and splitting (61), into two cases. % 4.19/1.71 |-Branch one: % 4.19/1.71 | (68) ~ (xsd_string(all_0_7_7) = 0) % 4.19/1.71 | % 4.19/1.71 | Using (66) and (68) yields: % 4.19/1.71 | (69) $false % 4.19/1.71 | % 4.19/1.71 |-The branch is then unsatisfiable % 4.19/1.71 |-Branch two: % 4.19/1.71 | (66) xsd_string(all_0_7_7) = 0 % 4.19/1.71 | (71) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_7_7) = v0) % 4.19/1.71 | % 4.19/1.71 | Instantiating (71) with all_17_0_12 yields: % 4.19/1.71 | (72) ~ (all_17_0_12 = 0) & xsd_integer(all_0_7_7) = all_17_0_12 % 4.19/1.71 | % 4.19/1.71 | Applying alpha-rule on (72) yields: % 4.19/1.71 | (73) ~ (all_17_0_12 = 0) % 4.19/1.71 | (74) xsd_integer(all_0_7_7) = all_17_0_12 % 4.19/1.71 | % 4.19/1.71 | Instantiating formula (3) with all_0_7_7, 0, all_17_0_12 and discharging atoms xsd_integer(all_0_7_7) = all_17_0_12, xsd_integer(all_0_7_7) = 0, yields: % 4.19/1.71 | (75) all_17_0_12 = 0 % 4.19/1.71 | % 4.19/1.71 | Equations (75) can reduce 73 to: % 4.19/1.71 | (38) $false % 4.19/1.71 | % 4.19/1.71 |-The branch is then unsatisfiable % 4.19/1.71 |-Branch two: % 4.19/1.71 | (77) ~ (all_0_5_5 = 0) & ~ (all_0_6_6 = 0) % 4.19/1.71 | % 4.19/1.71 | Applying alpha-rule on (77) yields: % 4.19/1.71 | (78) ~ (all_0_5_5 = 0) % 4.19/1.71 | (79) ~ (all_0_6_6 = 0) % 4.19/1.71 | % 4.19/1.71 +-Applying beta-rule and splitting (62), into two cases. % 4.19/1.71 |-Branch one: % 4.19/1.71 | (67) xsd_integer(all_0_7_7) = 0 % 4.19/1.71 | % 4.19/1.71 | Instantiating formula (3) 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: % 4.19/1.71 | (64) all_0_5_5 = 0 % 4.19/1.71 | % 4.19/1.71 | Equations (64) can reduce 78 to: % 4.19/1.71 | (38) $false % 4.19/1.71 | % 4.19/1.71 |-The branch is then unsatisfiable % 4.19/1.71 |-Branch two: % 4.19/1.71 | (83) ~ (xsd_integer(all_0_7_7) = 0) % 4.19/1.71 | (29) all_0_6_6 = 0 % 4.19/1.71 | % 4.19/1.71 | Equations (29) can reduce 79 to: % 4.19/1.71 | (38) $false % 4.19/1.71 | % 4.19/1.71 |-The branch is then unsatisfiable % 4.19/1.71 |-Branch two: % 4.19/1.71 | (86) 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) % 4.19/1.71 | % 4.19/1.71 | Applying alpha-rule on (86) yields: % 4.19/1.71 | (87) cowlThing(all_0_7_7) = all_0_6_6 % 4.19/1.71 | (88) cowlNothing(all_0_7_7) = all_0_5_5 % 4.19/1.71 | (89) ~ (all_0_6_6 = 0) | all_0_5_5 = 0 % 4.19/1.71 | % 4.19/1.71 | Instantiating formula (2) with all_0_6_6, all_0_7_7 and discharging atoms cowlThing(all_0_7_7) = all_0_6_6, yields: % 4.19/1.71 | (29) all_0_6_6 = 0 % 4.19/1.71 | % 4.19/1.71 | Instantiating formula (18) with all_0_7_7 yields: % 4.19/1.71 | (91) ~ (cowlNothing(all_0_7_7) = 0) % 4.19/1.71 | % 4.19/1.71 +-Applying beta-rule and splitting (89), into two cases. % 4.19/1.71 |-Branch one: % 4.19/1.71 | (79) ~ (all_0_6_6 = 0) % 4.19/1.71 | % 4.19/1.71 | Equations (29) can reduce 79 to: % 4.19/1.71 | (38) $false % 4.19/1.71 | % 4.19/1.71 |-The branch is then unsatisfiable % 4.19/1.71 |-Branch two: % 4.19/1.71 | (29) all_0_6_6 = 0 % 4.19/1.71 | (64) all_0_5_5 = 0 % 4.19/1.71 | % 4.19/1.71 | From (64) and (88) follows: % 4.19/1.71 | (96) cowlNothing(all_0_7_7) = 0 % 4.19/1.71 | % 4.19/1.71 | Using (96) and (91) yields: % 4.19/1.71 | (69) $false % 4.19/1.71 | % 4.19/1.71 |-The branch is then unsatisfiable % 4.19/1.71 % SZS output end Proof for theBenchmark % 4.19/1.71 % 4.19/1.71 1132ms %------------------------------------------------------------------------------