%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KRS167+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n029.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 02:56:46 EDT 2022 % Result : Theorem 3.17s 1.50s % Output : Proof 4.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : KRS167+1 : TPTP v8.1.0. Released v3.1.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n029.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 07:19:05 EDT 2022 % 0.12/0.33 % CPUTime : % 0.68/0.64 ____ _ % 0.68/0.64 ___ / __ \_____(_)___ ________ __________ % 0.68/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.68/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.68/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.68/0.64 % 0.68/0.64 A Theorem Prover for First-Order Logic % 0.68/0.64 (ePrincess v.1.0) % 0.68/0.64 % 0.68/0.64 (c) Philipp Rümmer, 2009-2015 % 0.68/0.64 (c) Peter Backeman, 2014-2015 % 0.68/0.64 (contributions by Angelo Brillout, Peter Baumgartner) % 0.68/0.64 Free software under GNU Lesser General Public License (LGPL). % 0.68/0.64 Bug reports to peter@backeman.se % 0.68/0.64 % 0.68/0.64 For more information, visit http://user.uu.se/~petba168/breu/ % 0.68/0.64 % 0.68/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.85/0.71 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.63/1.01 Prover 0: Preprocessing ... % 1.82/1.12 Prover 0: Warning: ignoring some quantifiers % 1.82/1.14 Prover 0: Constructing countermodel ... % 2.13/1.23 Prover 0: gave up % 2.13/1.23 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.23/1.25 Prover 1: Preprocessing ... % 2.65/1.37 Prover 1: Constructing countermodel ... % 3.17/1.50 Prover 1: proved (268ms) % 3.17/1.50 % 3.17/1.50 No countermodel exists, formula is valid % 3.17/1.50 % SZS status Theorem for theBenchmark % 3.17/1.50 % 3.17/1.50 Generating proof ... found it (size 82) % 4.44/1.79 % 4.44/1.79 % SZS output start Proof for theBenchmark % 4.44/1.79 Assumed formulas after preprocessing and simplification: % 4.44/1.79 | (0) ? [v0] : ? [v1] : ? [v2] : ( ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (rp(v6, v5) = v4) | ~ (rp(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (rp(v3, v5) = 0) | ~ (rp(v3, v4) = 0) | ~ (cc2(v3) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (rp(v3, v5) = 0) | ~ (rp(v3, v4) = 0) | ~ (cc1(v3) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (rp(v4, v3) = v5) | ~ (rp(v4, v3) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (rp(v3, v4) = v5) | ~ (rp(v3, v4) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (xsd_string(v5) = v4) | ~ (xsd_string(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (xsd_integer(v5) = v4) | ~ (xsd_integer(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (cowlThing(v5) = v4) | ~ (cowlThing(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (cowlNothing(v5) = v4) | ~ (cowlNothing(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (cc2(v5) = v4) | ~ (cc2(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (cc1(v5) = v4) | ~ (cc1(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (rp(v3, v5) = 0) | ~ (cc2(v3) = v4) | ? [v6] : ? [v7] : ( ~ (v7 = v6) & rp(v3, v7) = 0 & rp(v3, v6) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (rp(v3, v5) = 0) | ~ (cc1(v3) = v4) | ? [v6] : ? [v7] : ( ~ (v7 = v6) & rp(v3, v7) = 0 & rp(v3, v6) = 0)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (xsd_string(v3) = v4) | ~ (xsd_string(v3) = 0)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (xsd_string(v3) = v4) | xsd_integer(v3) = 0) & ! [v3] : ! [v4] : (v4 = 0 | ~ (xsd_integer(v3) = v4) | ~ (xsd_integer(v3) = 0)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (cowlThing(v3) = v4) | ~ (cowlThing(v3) = 0)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (cowlThing(v3) = v4)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (cowlNothing(v3) = v4) | ~ (cowlNothing(v3) = 0)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (cc2(v3) = v4) | ~ (cc2(v3) = 0)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (cc1(v3) = v4) | ~ (cc1(v3) = 0)) & ! [v3] : ( ~ (xsd_string(v3) = 0) | ? [v4] : ( ~ (v4 = 0) & xsd_integer(v3) = v4)) & ! [v3] : ~ (cowlNothing(v3) = 0) & ! [v3] : ( ~ (cc2(v3) = 0) | ? [v4] : rp(v3, v4) = 0) & ! [v3] : ( ~ (cc1(v3) = 0) | ? [v4] : rp(v3, v4) = 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)) | (cc2(v0) = v2 & cc1(v0) = v1 & ((v2 = 0 & ~ (v1 = 0)) | (v1 = 0 & ~ (v2 = 0)))))) % 4.55/1.82 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 4.55/1.82 | (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) | ~ (cc2(v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (rp(v0, v2) = 0) | ~ (rp(v0, v1) = 0) | ~ (cc1(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 | ~ (cc2(v2) = v1) | ~ (cc2(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cc1(v2) = v1) | ~ (cc1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (rp(v0, v2) = 0) | ~ (cc2(v0) = v1) | ? [v3] : ? [v4] : ( ~ (v4 = v3) & rp(v0, v4) = 0 & rp(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (rp(v0, v2) = 0) | ~ (cc1(v0) = v1) | ? [v3] : ? [v4] : ( ~ (v4 = v3) & rp(v0, v4) = 0 & rp(v0, v3) = 0)) & ! [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 | ~ (cc2(v0) = v1) | ~ (cc2(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cc1(v0) = v1) | ~ (cc1(v0) = 0)) & ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) & ! [v0] : ~ (cowlNothing(v0) = 0) & ! [v0] : ( ~ (cc2(v0) = 0) | ? [v1] : rp(v0, v1) = 0) & ! [v0] : ( ~ (cc1(v0) = 0) | ? [v1] : rp(v0, v1) = 0) & ((xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)))) | (cowlThing(all_0_2_2) = all_0_1_1 & cowlNothing(all_0_2_2) = all_0_0_0 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)) | (cc2(all_0_2_2) = all_0_0_0 & cc1(all_0_2_2) = all_0_1_1 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0))))) % 4.55/1.83 | % 4.55/1.83 | Applying alpha-rule on (1) yields: % 4.55/1.83 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (rp(v0, v2) = 0) | ~ (cc1(v0) = v1) | ? [v3] : ? [v4] : ( ~ (v4 = v3) & rp(v0, v4) = 0 & rp(v0, v3) = 0)) % 4.55/1.83 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) % 4.55/1.83 | (4) ! [v0] : ! [v1] : (v1 = 0 | ~ (cc2(v0) = v1) | ~ (cc2(v0) = 0)) % 4.55/1.83 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (rp(v0, v2) = 0) | ~ (rp(v0, v1) = 0) | ~ (cc2(v0) = 0)) % 4.55/1.83 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlNothing(v0) = v1) | ~ (cowlNothing(v0) = 0)) % 4.55/1.83 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) % 4.55/1.83 | (8) (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)))) | (cowlThing(all_0_2_2) = all_0_1_1 & cowlNothing(all_0_2_2) = all_0_0_0 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)) | (cc2(all_0_2_2) = all_0_0_0 & cc1(all_0_2_2) = all_0_1_1 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)))) % 4.55/1.83 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (rp(v0, v2) = 0) | ~ (cc2(v0) = v1) | ? [v3] : ? [v4] : ( ~ (v4 = v3) & rp(v0, v4) = 0 & rp(v0, v3) = 0)) % 4.55/1.83 | (10) ! [v0] : ~ (cowlNothing(v0) = 0) % 4.55/1.83 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v1, v0) = v2) | ~ (rp(v1, v0) = 0)) % 4.55/1.83 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ (xsd_string(v0) = 0)) % 4.55/1.83 | (13) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) % 4.55/1.84 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cc2(v2) = v1) | ~ (cc2(v2) = v0)) % 4.55/1.84 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 4.55/1.84 | (16) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) % 4.55/1.84 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) % 4.55/1.84 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0)) % 4.55/1.84 | (19) ! [v0] : ! [v1] : (v1 = 0 | ~ (cc1(v0) = v1) | ~ (cc1(v0) = 0)) % 4.55/1.84 | (20) ! [v0] : ( ~ (cc1(v0) = 0) | ? [v1] : rp(v0, v1) = 0) % 4.55/1.84 | (21) ! [v0] : ( ~ (cc2(v0) = 0) | ? [v1] : rp(v0, v1) = 0) % 4.55/1.84 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cc1(v2) = v1) | ~ (cc1(v2) = v0)) % 4.55/1.84 | (23) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ (cowlThing(v0) = 0)) % 4.55/1.84 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (rp(v0, v2) = 0) | ~ (rp(v0, v1) = 0) | ~ (cc1(v0) = 0)) % 4.55/1.84 | (25) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) % 4.55/1.84 | (26) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ (xsd_integer(v0) = 0)) % 4.55/1.84 | (27) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rp(v0, v1) = v2) | ~ (rp(v0, v1) = 0)) % 4.55/1.84 | % 4.55/1.84 +-Applying beta-rule and splitting (8), into two cases. % 4.55/1.84 |-Branch one: % 4.55/1.84 | (28) (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)))) | (cowlThing(all_0_2_2) = all_0_1_1 & cowlNothing(all_0_2_2) = all_0_0_0 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)) % 4.55/1.84 | % 4.55/1.84 +-Applying beta-rule and splitting (28), into two cases. % 4.55/1.84 |-Branch one: % 4.55/1.84 | (29) xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0))) % 4.55/1.84 | % 4.55/1.84 | Applying alpha-rule on (29) yields: % 4.55/1.84 | (30) xsd_string(all_0_2_2) = all_0_1_1 % 4.55/1.84 | (31) xsd_integer(all_0_2_2) = all_0_0_0 % 4.55/1.84 | (32) (all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)) % 4.55/1.84 | % 4.55/1.84 | Instantiating formula (25) with all_0_2_2 yields: % 4.55/1.84 | (33) ~ (xsd_string(all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0) % 4.55/1.84 | % 4.55/1.84 | Instantiating formula (13) with all_0_1_1, all_0_2_2 and discharging atoms xsd_string(all_0_2_2) = all_0_1_1, yields: % 4.55/1.84 | (34) all_0_1_1 = 0 | xsd_integer(all_0_2_2) = 0 % 4.55/1.84 | % 4.55/1.84 +-Applying beta-rule and splitting (32), into two cases. % 4.55/1.84 |-Branch one: % 4.55/1.84 | (35) all_0_0_0 = 0 & all_0_1_1 = 0 % 4.55/1.84 | % 4.55/1.84 | Applying alpha-rule on (35) yields: % 4.55/1.84 | (36) all_0_0_0 = 0 % 4.55/1.84 | (37) all_0_1_1 = 0 % 4.55/1.84 | % 4.55/1.84 | From (37) and (30) follows: % 4.55/1.84 | (38) xsd_string(all_0_2_2) = 0 % 4.55/1.84 | % 4.55/1.84 | From (36) and (31) follows: % 4.55/1.84 | (39) xsd_integer(all_0_2_2) = 0 % 4.55/1.84 | % 4.55/1.84 +-Applying beta-rule and splitting (33), into two cases. % 4.55/1.84 |-Branch one: % 4.55/1.84 | (40) ~ (xsd_string(all_0_2_2) = 0) % 4.55/1.84 | % 4.55/1.84 | Using (38) and (40) yields: % 4.55/1.84 | (41) $false % 4.55/1.84 | % 4.55/1.85 |-The branch is then unsatisfiable % 4.55/1.85 |-Branch two: % 4.55/1.85 | (38) xsd_string(all_0_2_2) = 0 % 4.55/1.85 | (43) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0) % 4.55/1.85 | % 4.55/1.85 | Instantiating (43) with all_17_0_3 yields: % 4.55/1.85 | (44) ~ (all_17_0_3 = 0) & xsd_integer(all_0_2_2) = all_17_0_3 % 4.55/1.85 | % 4.55/1.85 | Applying alpha-rule on (44) yields: % 4.55/1.85 | (45) ~ (all_17_0_3 = 0) % 4.55/1.85 | (46) xsd_integer(all_0_2_2) = all_17_0_3 % 4.55/1.85 | % 4.55/1.85 | Instantiating formula (15) with all_0_2_2, 0, all_17_0_3 and discharging atoms xsd_integer(all_0_2_2) = all_17_0_3, xsd_integer(all_0_2_2) = 0, yields: % 4.55/1.85 | (47) all_17_0_3 = 0 % 4.55/1.85 | % 4.55/1.85 | Equations (47) can reduce 45 to: % 4.55/1.85 | (48) $false % 4.55/1.85 | % 4.55/1.85 |-The branch is then unsatisfiable % 4.55/1.85 |-Branch two: % 4.55/1.85 | (49) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) % 4.55/1.85 | % 4.55/1.85 | Applying alpha-rule on (49) yields: % 4.55/1.85 | (50) ~ (all_0_0_0 = 0) % 4.55/1.85 | (51) ~ (all_0_1_1 = 0) % 4.55/1.85 | % 4.55/1.85 +-Applying beta-rule and splitting (34), into two cases. % 4.55/1.85 |-Branch one: % 4.55/1.85 | (39) xsd_integer(all_0_2_2) = 0 % 4.55/1.85 | % 4.55/1.85 | Instantiating formula (15) with all_0_2_2, 0, all_0_0_0 and discharging atoms xsd_integer(all_0_2_2) = all_0_0_0, xsd_integer(all_0_2_2) = 0, yields: % 4.55/1.85 | (36) all_0_0_0 = 0 % 4.55/1.85 | % 4.55/1.85 | Equations (36) can reduce 50 to: % 4.55/1.85 | (48) $false % 4.55/1.85 | % 4.55/1.85 |-The branch is then unsatisfiable % 4.55/1.85 |-Branch two: % 4.55/1.85 | (55) ~ (xsd_integer(all_0_2_2) = 0) % 4.55/1.85 | (37) all_0_1_1 = 0 % 4.55/1.85 | % 4.55/1.85 | Equations (37) can reduce 51 to: % 4.55/1.85 | (48) $false % 4.55/1.85 | % 4.55/1.85 |-The branch is then unsatisfiable % 4.55/1.85 |-Branch two: % 4.55/1.85 | (58) cowlThing(all_0_2_2) = all_0_1_1 & cowlNothing(all_0_2_2) = all_0_0_0 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0) % 4.55/1.85 | % 4.55/1.85 | Applying alpha-rule on (58) yields: % 4.55/1.85 | (59) cowlThing(all_0_2_2) = all_0_1_1 % 4.55/1.85 | (60) cowlNothing(all_0_2_2) = all_0_0_0 % 4.55/1.85 | (61) ~ (all_0_1_1 = 0) | all_0_0_0 = 0 % 4.55/1.85 | % 4.55/1.85 | Instantiating formula (16) with all_0_1_1, all_0_2_2 and discharging atoms cowlThing(all_0_2_2) = all_0_1_1, yields: % 4.55/1.85 | (37) all_0_1_1 = 0 % 4.55/1.85 | % 4.55/1.85 | Instantiating formula (10) with all_0_2_2 yields: % 4.55/1.85 | (63) ~ (cowlNothing(all_0_2_2) = 0) % 4.55/1.85 | % 4.55/1.85 +-Applying beta-rule and splitting (61), into two cases. % 4.55/1.85 |-Branch one: % 4.55/1.85 | (51) ~ (all_0_1_1 = 0) % 4.55/1.85 | % 4.55/1.85 | Equations (37) can reduce 51 to: % 4.55/1.85 | (48) $false % 4.55/1.85 | % 4.55/1.85 |-The branch is then unsatisfiable % 4.55/1.85 |-Branch two: % 4.55/1.85 | (37) all_0_1_1 = 0 % 4.55/1.85 | (36) all_0_0_0 = 0 % 4.55/1.85 | % 4.55/1.85 | From (36) and (60) follows: % 4.55/1.85 | (68) cowlNothing(all_0_2_2) = 0 % 4.55/1.85 | % 4.55/1.85 | Using (68) and (63) yields: % 4.55/1.85 | (41) $false % 4.55/1.85 | % 4.55/1.85 |-The branch is then unsatisfiable % 4.55/1.85 |-Branch two: % 4.55/1.85 | (70) cc2(all_0_2_2) = all_0_0_0 & cc1(all_0_2_2) = all_0_1_1 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0))) % 4.55/1.85 | % 4.55/1.85 | Applying alpha-rule on (70) yields: % 4.55/1.85 | (71) cc2(all_0_2_2) = all_0_0_0 % 4.55/1.85 | (72) cc1(all_0_2_2) = all_0_1_1 % 4.55/1.85 | (73) (all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)) % 4.55/1.85 | % 4.55/1.85 | Instantiating formula (21) with all_0_2_2 yields: % 4.55/1.85 | (74) ~ (cc2(all_0_2_2) = 0) | ? [v0] : rp(all_0_2_2, v0) = 0 % 4.55/1.85 | % 4.55/1.85 | Instantiating formula (20) with all_0_2_2 yields: % 4.55/1.85 | (75) ~ (cc1(all_0_2_2) = 0) | ? [v0] : rp(all_0_2_2, v0) = 0 % 4.55/1.85 | % 4.55/1.85 +-Applying beta-rule and splitting (75), into two cases. % 4.55/1.85 |-Branch one: % 4.55/1.85 | (76) ~ (cc1(all_0_2_2) = 0) % 4.55/1.85 | % 4.55/1.85 | Using (72) and (76) yields: % 4.55/1.85 | (51) ~ (all_0_1_1 = 0) % 4.55/1.85 | % 4.55/1.85 +-Applying beta-rule and splitting (73), into two cases. % 4.55/1.85 |-Branch one: % 4.55/1.85 | (78) all_0_0_0 = 0 & ~ (all_0_1_1 = 0) % 4.55/1.85 | % 4.55/1.85 | Applying alpha-rule on (78) yields: % 4.55/1.85 | (36) all_0_0_0 = 0 % 4.55/1.85 | (51) ~ (all_0_1_1 = 0) % 4.55/1.85 | % 4.55/1.85 | From (36) and (71) follows: % 4.55/1.85 | (81) cc2(all_0_2_2) = 0 % 4.55/1.85 | % 4.55/1.85 +-Applying beta-rule and splitting (74), into two cases. % 4.55/1.85 |-Branch one: % 4.55/1.86 | (82) ~ (cc2(all_0_2_2) = 0) % 4.55/1.86 | % 4.55/1.86 | Using (81) and (82) yields: % 4.55/1.86 | (41) $false % 4.55/1.86 | % 4.55/1.86 |-The branch is then unsatisfiable % 4.55/1.86 |-Branch two: % 4.55/1.86 | (81) cc2(all_0_2_2) = 0 % 4.55/1.86 | (85) ? [v0] : rp(all_0_2_2, v0) = 0 % 4.55/1.86 | % 4.55/1.86 | Instantiating (85) with all_25_0_4 yields: % 4.55/1.86 | (86) rp(all_0_2_2, all_25_0_4) = 0 % 4.55/1.86 | % 4.55/1.86 | Instantiating formula (2) with all_25_0_4, all_0_1_1, all_0_2_2 and discharging atoms rp(all_0_2_2, all_25_0_4) = 0, cc1(all_0_2_2) = all_0_1_1, yields: % 4.55/1.86 | (87) all_0_1_1 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & rp(all_0_2_2, v1) = 0 & rp(all_0_2_2, v0) = 0) % 4.55/1.86 | % 4.55/1.86 +-Applying beta-rule and splitting (87), into two cases. % 4.55/1.86 |-Branch one: % 4.55/1.86 | (37) all_0_1_1 = 0 % 4.55/1.86 | % 4.55/1.86 | Equations (37) can reduce 51 to: % 4.55/1.86 | (48) $false % 4.55/1.86 | % 4.55/1.86 |-The branch is then unsatisfiable % 4.55/1.86 |-Branch two: % 4.55/1.86 | (51) ~ (all_0_1_1 = 0) % 4.55/1.86 | (91) ? [v0] : ? [v1] : ( ~ (v1 = v0) & rp(all_0_2_2, v1) = 0 & rp(all_0_2_2, v0) = 0) % 4.55/1.86 | % 4.55/1.86 | Instantiating (91) with all_34_0_5, all_34_1_6 yields: % 4.55/1.86 | (92) ~ (all_34_0_5 = all_34_1_6) & rp(all_0_2_2, all_34_0_5) = 0 & rp(all_0_2_2, all_34_1_6) = 0 % 4.55/1.86 | % 4.55/1.86 | Applying alpha-rule on (92) yields: % 4.55/1.86 | (93) ~ (all_34_0_5 = all_34_1_6) % 4.55/1.86 | (94) rp(all_0_2_2, all_34_0_5) = 0 % 4.55/1.86 | (95) rp(all_0_2_2, all_34_1_6) = 0 % 4.55/1.86 | % 4.55/1.86 | Instantiating formula (5) with all_34_0_5, all_25_0_4, all_0_2_2 and discharging atoms rp(all_0_2_2, all_34_0_5) = 0, rp(all_0_2_2, all_25_0_4) = 0, cc2(all_0_2_2) = 0, yields: % 4.55/1.86 | (96) all_34_0_5 = all_25_0_4 % 4.55/1.86 | % 4.55/1.86 | Instantiating formula (5) with all_34_1_6, all_34_0_5, all_0_2_2 and discharging atoms rp(all_0_2_2, all_34_0_5) = 0, rp(all_0_2_2, all_34_1_6) = 0, cc2(all_0_2_2) = 0, yields: % 4.55/1.86 | (97) all_34_0_5 = all_34_1_6 % 4.55/1.86 | % 4.55/1.86 | Combining equations (96,97) yields a new equation: % 4.55/1.86 | (98) all_34_1_6 = all_25_0_4 % 4.55/1.86 | % 4.55/1.86 | Combining equations (98,97) yields a new equation: % 4.55/1.86 | (96) all_34_0_5 = all_25_0_4 % 4.55/1.86 | % 4.55/1.86 | Equations (96,98) can reduce 93 to: % 4.55/1.86 | (48) $false % 4.55/1.86 | % 4.55/1.86 |-The branch is then unsatisfiable % 4.55/1.86 |-Branch two: % 4.55/1.86 | (101) all_0_1_1 = 0 & ~ (all_0_0_0 = 0) % 4.55/1.86 | % 4.55/1.86 | Applying alpha-rule on (101) yields: % 4.55/1.86 | (37) all_0_1_1 = 0 % 4.55/1.86 | (50) ~ (all_0_0_0 = 0) % 4.55/1.86 | % 4.55/1.86 | Equations (37) can reduce 51 to: % 4.55/1.86 | (48) $false % 4.55/1.86 | % 4.55/1.86 |-The branch is then unsatisfiable % 4.55/1.86 |-Branch two: % 4.55/1.86 | (105) cc1(all_0_2_2) = 0 % 4.55/1.86 | (85) ? [v0] : rp(all_0_2_2, v0) = 0 % 4.55/1.86 | % 4.55/1.86 | Instantiating (85) with all_13_0_7 yields: % 4.55/1.86 | (107) rp(all_0_2_2, all_13_0_7) = 0 % 4.55/1.86 | % 4.55/1.86 | Instantiating formula (22) with all_0_2_2, 0, all_0_1_1 and discharging atoms cc1(all_0_2_2) = all_0_1_1, cc1(all_0_2_2) = 0, yields: % 4.55/1.86 | (37) all_0_1_1 = 0 % 4.55/1.86 | % 4.55/1.86 | From (37) and (72) follows: % 4.55/1.86 | (105) cc1(all_0_2_2) = 0 % 4.55/1.86 | % 4.55/1.86 +-Applying beta-rule and splitting (73), into two cases. % 4.55/1.86 |-Branch one: % 4.55/1.86 | (78) all_0_0_0 = 0 & ~ (all_0_1_1 = 0) % 4.55/1.86 | % 4.55/1.86 | Applying alpha-rule on (78) yields: % 4.55/1.86 | (36) all_0_0_0 = 0 % 4.55/1.86 | (51) ~ (all_0_1_1 = 0) % 4.55/1.86 | % 4.55/1.86 | Equations (37) can reduce 51 to: % 4.55/1.86 | (48) $false % 4.55/1.86 | % 4.55/1.86 |-The branch is then unsatisfiable % 4.55/1.86 |-Branch two: % 4.55/1.86 | (101) all_0_1_1 = 0 & ~ (all_0_0_0 = 0) % 4.55/1.86 | % 4.55/1.86 | Applying alpha-rule on (101) yields: % 4.55/1.86 | (37) all_0_1_1 = 0 % 4.55/1.87 | (50) ~ (all_0_0_0 = 0) % 4.55/1.87 | % 4.55/1.87 | Instantiating formula (9) with all_13_0_7, all_0_0_0, all_0_2_2 and discharging atoms rp(all_0_2_2, all_13_0_7) = 0, cc2(all_0_2_2) = all_0_0_0, yields: % 4.55/1.87 | (117) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & rp(all_0_2_2, v1) = 0 & rp(all_0_2_2, v0) = 0) % 4.55/1.87 | % 4.55/1.87 +-Applying beta-rule and splitting (117), into two cases. % 4.55/1.87 |-Branch one: % 4.55/1.87 | (36) all_0_0_0 = 0 % 4.55/1.87 | % 4.55/1.87 | Equations (36) can reduce 50 to: % 4.55/1.87 | (48) $false % 4.55/1.87 | % 4.55/1.87 |-The branch is then unsatisfiable % 4.55/1.87 |-Branch two: % 4.55/1.87 | (50) ~ (all_0_0_0 = 0) % 4.55/1.87 | (91) ? [v0] : ? [v1] : ( ~ (v1 = v0) & rp(all_0_2_2, v1) = 0 & rp(all_0_2_2, v0) = 0) % 4.55/1.87 | % 4.55/1.87 | Instantiating (91) with all_30_0_8, all_30_1_9 yields: % 4.55/1.87 | (122) ~ (all_30_0_8 = all_30_1_9) & rp(all_0_2_2, all_30_0_8) = 0 & rp(all_0_2_2, all_30_1_9) = 0 % 4.55/1.87 | % 4.55/1.87 | Applying alpha-rule on (122) yields: % 4.55/1.87 | (123) ~ (all_30_0_8 = all_30_1_9) % 4.55/1.87 | (124) rp(all_0_2_2, all_30_0_8) = 0 % 4.55/1.87 | (125) rp(all_0_2_2, all_30_1_9) = 0 % 4.55/1.87 | % 4.55/1.87 | Instantiating formula (24) with all_30_0_8, all_13_0_7, all_0_2_2 and discharging atoms rp(all_0_2_2, all_30_0_8) = 0, rp(all_0_2_2, all_13_0_7) = 0, cc1(all_0_2_2) = 0, yields: % 4.55/1.87 | (126) all_30_0_8 = all_13_0_7 % 4.55/1.87 | % 4.55/1.87 | Instantiating formula (24) with all_30_1_9, all_30_0_8, all_0_2_2 and discharging atoms rp(all_0_2_2, all_30_0_8) = 0, rp(all_0_2_2, all_30_1_9) = 0, cc1(all_0_2_2) = 0, yields: % 4.55/1.87 | (127) all_30_0_8 = all_30_1_9 % 4.55/1.87 | % 4.55/1.87 | Combining equations (126,127) yields a new equation: % 4.55/1.87 | (128) all_30_1_9 = all_13_0_7 % 4.55/1.87 | % 4.55/1.87 | Combining equations (128,127) yields a new equation: % 4.55/1.87 | (126) all_30_0_8 = all_13_0_7 % 4.55/1.87 | % 4.55/1.87 | Equations (126,128) can reduce 123 to: % 4.55/1.87 | (48) $false % 4.55/1.87 | % 4.55/1.87 |-The branch is then unsatisfiable % 4.55/1.87 % SZS output end Proof for theBenchmark % 4.55/1.87 % 4.55/1.87 1214ms %------------------------------------------------------------------------------