%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KRS131+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n032.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 02:56:39 EDT 2022 % Result : Theorem 2.10s 1.13s % Output : Proof 2.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : KRS131+1 : TPTP v8.1.0. Released v3.1.0. % 0.00/0.09 % Command : ePrincess-casc -timeout=%d %s % 0.09/0.28 % Computer : n032.cluster.edu % 0.09/0.28 % Model : x86_64 x86_64 % 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.28 % Memory : 8042.1875MB % 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.28 % CPULimit : 300 % 0.09/0.28 % WCLimit : 600 % 0.09/0.28 % DateTime : Tue Jun 7 12:32:05 EDT 2022 % 0.09/0.28 % CPUTime : % 0.13/0.46 ____ _ % 0.13/0.46 ___ / __ \_____(_)___ ________ __________ % 0.13/0.46 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.13/0.46 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.13/0.46 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.13/0.46 % 0.13/0.46 A Theorem Prover for First-Order Logic % 0.13/0.46 (ePrincess v.1.0) % 0.13/0.46 % 0.13/0.46 (c) Philipp Rümmer, 2009-2015 % 0.13/0.46 (c) Peter Backeman, 2014-2015 % 0.13/0.46 (contributions by Angelo Brillout, Peter Baumgartner) % 0.13/0.46 Free software under GNU Lesser General Public License (LGPL). % 0.13/0.46 Bug reports to peter@backeman.se % 0.13/0.46 % 0.13/0.46 For more information, visit http://user.uu.se/~petba168/breu/ % 0.13/0.46 % 0.13/0.46 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.13/0.50 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.05/0.73 Prover 0: Preprocessing ... % 1.18/0.81 Prover 0: Warning: ignoring some quantifiers % 1.18/0.83 Prover 0: Constructing countermodel ... % 1.60/0.92 Prover 0: gave up % 1.60/0.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.61/0.94 Prover 1: Preprocessing ... % 1.90/1.03 Prover 1: Constructing countermodel ... % 2.10/1.13 Prover 1: proved (202ms) % 2.10/1.13 % 2.10/1.13 No countermodel exists, formula is valid % 2.10/1.13 % SZS status Theorem for theBenchmark % 2.10/1.13 % 2.10/1.13 Generating proof ... found it (size 79) % 2.91/1.31 % 2.91/1.31 % SZS output start Proof for theBenchmark % 2.91/1.31 Assumed formulas after preprocessing and simplification: % 2.91/1.31 | (0) ? [v0] : ? [v1] : ? [v2] : ( ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (rp(v6, v5) = v4) | ~ (rp(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (rq(v6, v5) = v4) | ~ (rq(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (cnotA(v5) = v4) | ~ (cnotA(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (cNothing(v5) = v4) | ~ (cNothing(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (cA(v5) = v4) | ~ (cA(v5) = v3)) & ! [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 | ~ (cowlNothing(v5) = v4) | ~ (cowlNothing(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (cowlThing(v5) = v4) | ~ (cowlThing(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (cA(v3) = v4) | ~ (rq(v3, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & cowlThing(v5) = v6)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (cnotA(v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & cNothing(v5) = v6 & rq(v3, v5) = 0)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (xsd_string(v3) = v4) | xsd_integer(v3) = 0) & ! [v3] : ! [v4] : (v4 = 0 | ~ (cowlThing(v3) = v4)) & ! [v3] : ! [v4] : ( ~ (cnotA(v3) = 0) | ~ (rq(v3, v4) = 0) | cNothing(v4) = 0) & ! [v3] : ! [v4] : ( ~ (cNothing(v3) = 0) | ~ (rp(v3, v4) = 0)) & ! [v3] : ( ~ (cNothing(v3) = 0) | ? [v4] : rp(v3, v4) = 0) & ! [v3] : ( ~ (cA(v3) = 0) | ? [v4] : (rq(v3, v4) = 0 & cowlThing(v4) = 0)) & ! [v3] : ( ~ (xsd_string(v3) = 0) | ? [v4] : ( ~ (v4 = 0) & xsd_integer(v3) = v4)) & ! [v3] : ~ (cowlNothing(v3) = 0) & ((cnotA(v0) = v1 & cA(v0) = v2 & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) & ~ (v1 = 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)))) % 2.91/1.34 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 2.91/1.34 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rq(v3, v2) = v1) | ~ (rq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cnotA(v2) = v1) | ~ (cnotA(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cNothing(v2) = v1) | ~ (cNothing(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cA(v2) = v1) | ~ (cA(v2) = v0)) & ! [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] : ! [v2] : (v1 = 0 | ~ (cA(v0) = v1) | ~ (rq(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & cowlThing(v2) = v3)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cnotA(v0) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & cNothing(v2) = v3 & rq(v0, v2) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (cnotA(v0) = 0) | ~ (rq(v0, v1) = 0) | cNothing(v1) = 0) & ! [v0] : ! [v1] : ( ~ (cNothing(v0) = 0) | ~ (rp(v0, v1) = 0)) & ! [v0] : ( ~ (cNothing(v0) = 0) | ? [v1] : rp(v0, v1) = 0) & ! [v0] : ( ~ (cA(v0) = 0) | ? [v1] : (rq(v0, v1) = 0 & cowlThing(v1) = 0)) & ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) & ! [v0] : ~ (cowlNothing(v0) = 0) & ((cnotA(all_0_2_2) = all_0_1_1 & cA(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)))) | (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)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0))) % 2.91/1.35 | % 2.91/1.35 | Applying alpha-rule on (1) yields: % 2.91/1.35 | (2) (cnotA(all_0_2_2) = all_0_1_1 & cA(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)))) | (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)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)) % 2.91/1.35 | (3) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) % 2.91/1.35 | (4) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) % 2.91/1.35 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rp(v3, v2) = v1) | ~ (rp(v3, v2) = v0)) % 2.91/1.35 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cnotA(v2) = v1) | ~ (cnotA(v2) = v0)) % 2.91/1.35 | (7) ! [v0] : ! [v1] : ( ~ (cnotA(v0) = 0) | ~ (rq(v0, v1) = 0) | cNothing(v1) = 0) % 2.91/1.35 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cA(v2) = v1) | ~ (cA(v2) = v0)) % 2.91/1.35 | (9) ! [v0] : ! [v1] : (v1 = 0 | ~ (cnotA(v0) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & cNothing(v2) = v3 & rq(v0, v2) = 0)) % 2.91/1.36 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) % 2.91/1.36 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) % 2.91/1.36 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 2.91/1.36 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cNothing(v2) = v1) | ~ (cNothing(v2) = v0)) % 2.91/1.36 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rq(v3, v2) = v1) | ~ (rq(v3, v2) = v0)) % 2.91/1.36 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cA(v0) = v1) | ~ (rq(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & cowlThing(v2) = v3)) % 2.91/1.36 | (16) ! [v0] : ( ~ (cNothing(v0) = 0) | ? [v1] : rp(v0, v1) = 0) % 2.91/1.36 | (17) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) % 2.91/1.36 | (18) ! [v0] : ! [v1] : ( ~ (cNothing(v0) = 0) | ~ (rp(v0, v1) = 0)) % 2.91/1.36 | (19) ! [v0] : ~ (cowlNothing(v0) = 0) % 2.91/1.36 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) % 2.91/1.36 | (21) ! [v0] : ( ~ (cA(v0) = 0) | ? [v1] : (rq(v0, v1) = 0 & cowlThing(v1) = 0)) % 2.91/1.36 | % 2.91/1.36 +-Applying beta-rule and splitting (2), into two cases. % 2.91/1.36 |-Branch one: % 2.91/1.36 | (22) (cnotA(all_0_2_2) = all_0_1_1 & cA(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)))) | (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)))) % 2.91/1.36 | % 2.91/1.36 +-Applying beta-rule and splitting (22), into two cases. % 2.91/1.36 |-Branch one: % 2.91/1.36 | (23) cnotA(all_0_2_2) = all_0_1_1 & cA(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))) % 2.91/1.36 | % 2.91/1.36 | Applying alpha-rule on (23) yields: % 2.91/1.36 | (24) cnotA(all_0_2_2) = all_0_1_1 % 2.91/1.36 | (25) cA(all_0_2_2) = all_0_0_0 % 2.91/1.36 | (26) (all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)) % 2.91/1.36 | % 2.91/1.36 | Instantiating formula (9) with all_0_1_1, all_0_2_2 and discharging atoms cnotA(all_0_2_2) = all_0_1_1, yields: % 2.91/1.36 | (27) all_0_1_1 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & cNothing(v0) = v1 & rq(all_0_2_2, v0) = 0) % 2.91/1.36 | % 2.91/1.36 | Instantiating formula (21) with all_0_2_2 yields: % 2.91/1.36 | (28) ~ (cA(all_0_2_2) = 0) | ? [v0] : (rq(all_0_2_2, v0) = 0 & cowlThing(v0) = 0) % 2.91/1.36 | % 2.91/1.36 +-Applying beta-rule and splitting (28), into two cases. % 2.91/1.36 |-Branch one: % 2.91/1.36 | (29) ~ (cA(all_0_2_2) = 0) % 2.91/1.36 | % 2.91/1.36 | Using (25) and (29) yields: % 2.91/1.36 | (30) ~ (all_0_0_0 = 0) % 2.91/1.36 | % 2.91/1.36 +-Applying beta-rule and splitting (26), into two cases. % 2.91/1.36 |-Branch one: % 2.91/1.36 | (31) all_0_0_0 = 0 & all_0_1_1 = 0 % 2.91/1.36 | % 2.91/1.36 | Applying alpha-rule on (31) yields: % 2.91/1.36 | (32) all_0_0_0 = 0 % 2.91/1.36 | (33) all_0_1_1 = 0 % 2.91/1.36 | % 2.91/1.36 | Equations (32) can reduce 30 to: % 2.91/1.36 | (34) $false % 2.91/1.36 | % 2.91/1.36 |-The branch is then unsatisfiable % 2.91/1.36 |-Branch two: % 2.91/1.36 | (35) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) % 2.91/1.36 | % 2.91/1.36 | Applying alpha-rule on (35) yields: % 2.91/1.36 | (30) ~ (all_0_0_0 = 0) % 2.91/1.36 | (37) ~ (all_0_1_1 = 0) % 2.91/1.36 | % 2.91/1.36 +-Applying beta-rule and splitting (27), into two cases. % 2.91/1.36 |-Branch one: % 2.91/1.36 | (33) all_0_1_1 = 0 % 2.91/1.36 | % 2.91/1.36 | Equations (33) can reduce 37 to: % 2.91/1.36 | (34) $false % 2.91/1.36 | % 2.91/1.36 |-The branch is then unsatisfiable % 2.91/1.36 |-Branch two: % 2.91/1.36 | (37) ~ (all_0_1_1 = 0) % 2.91/1.36 | (41) ? [v0] : ? [v1] : ( ~ (v1 = 0) & cNothing(v0) = v1 & rq(all_0_2_2, v0) = 0) % 2.91/1.37 | % 2.91/1.37 | Instantiating (41) with all_25_0_3, all_25_1_4 yields: % 2.91/1.37 | (42) ~ (all_25_0_3 = 0) & cNothing(all_25_1_4) = all_25_0_3 & rq(all_0_2_2, all_25_1_4) = 0 % 2.91/1.37 | % 2.91/1.37 | Applying alpha-rule on (42) yields: % 2.91/1.37 | (43) ~ (all_25_0_3 = 0) % 2.91/1.37 | (44) cNothing(all_25_1_4) = all_25_0_3 % 2.91/1.37 | (45) rq(all_0_2_2, all_25_1_4) = 0 % 2.91/1.37 | % 2.91/1.37 | Instantiating formula (15) with all_25_1_4, all_0_0_0, all_0_2_2 and discharging atoms cA(all_0_2_2) = all_0_0_0, rq(all_0_2_2, all_25_1_4) = 0, yields: % 2.91/1.37 | (46) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & cowlThing(all_25_1_4) = v0) % 2.91/1.37 | % 2.91/1.37 +-Applying beta-rule and splitting (46), into two cases. % 2.91/1.37 |-Branch one: % 2.91/1.37 | (32) all_0_0_0 = 0 % 2.91/1.37 | % 2.91/1.37 | Equations (32) can reduce 30 to: % 2.91/1.37 | (34) $false % 2.91/1.37 | % 2.91/1.37 |-The branch is then unsatisfiable % 2.91/1.37 |-Branch two: % 2.91/1.37 | (30) ~ (all_0_0_0 = 0) % 2.91/1.37 | (50) ? [v0] : ( ~ (v0 = 0) & cowlThing(all_25_1_4) = v0) % 2.91/1.37 | % 2.91/1.37 | Instantiating (50) with all_34_0_5 yields: % 2.91/1.37 | (51) ~ (all_34_0_5 = 0) & cowlThing(all_25_1_4) = all_34_0_5 % 2.91/1.37 | % 2.91/1.37 | Applying alpha-rule on (51) yields: % 2.91/1.37 | (52) ~ (all_34_0_5 = 0) % 2.91/1.37 | (53) cowlThing(all_25_1_4) = all_34_0_5 % 2.91/1.37 | % 2.91/1.37 | Instantiating formula (4) with all_34_0_5, all_25_1_4 and discharging atoms cowlThing(all_25_1_4) = all_34_0_5, yields: % 2.91/1.37 | (54) all_34_0_5 = 0 % 2.91/1.37 | % 2.91/1.37 | Equations (54) can reduce 52 to: % 2.91/1.37 | (34) $false % 2.91/1.37 | % 2.91/1.37 |-The branch is then unsatisfiable % 2.91/1.37 |-Branch two: % 2.91/1.37 | (56) cA(all_0_2_2) = 0 % 2.91/1.37 | (57) ? [v0] : (rq(all_0_2_2, v0) = 0 & cowlThing(v0) = 0) % 2.91/1.37 | % 2.91/1.37 | Instantiating (57) with all_13_0_6 yields: % 2.91/1.37 | (58) rq(all_0_2_2, all_13_0_6) = 0 & cowlThing(all_13_0_6) = 0 % 2.91/1.37 | % 2.91/1.37 | Applying alpha-rule on (58) yields: % 2.91/1.37 | (59) rq(all_0_2_2, all_13_0_6) = 0 % 2.91/1.37 | (60) cowlThing(all_13_0_6) = 0 % 2.91/1.37 | % 2.91/1.37 | Instantiating formula (8) with all_0_2_2, 0, all_0_0_0 and discharging atoms cA(all_0_2_2) = all_0_0_0, cA(all_0_2_2) = 0, yields: % 2.91/1.37 | (32) all_0_0_0 = 0 % 2.91/1.37 | % 2.91/1.37 +-Applying beta-rule and splitting (26), into two cases. % 2.91/1.37 |-Branch one: % 2.91/1.37 | (31) all_0_0_0 = 0 & all_0_1_1 = 0 % 2.91/1.37 | % 2.91/1.37 | Applying alpha-rule on (31) yields: % 2.91/1.37 | (32) all_0_0_0 = 0 % 2.91/1.37 | (33) all_0_1_1 = 0 % 2.91/1.37 | % 2.91/1.37 | From (33) and (24) follows: % 2.91/1.37 | (65) cnotA(all_0_2_2) = 0 % 2.91/1.37 | % 2.91/1.37 | Instantiating formula (7) with all_13_0_6, all_0_2_2 and discharging atoms cnotA(all_0_2_2) = 0, rq(all_0_2_2, all_13_0_6) = 0, yields: % 2.91/1.37 | (66) cNothing(all_13_0_6) = 0 % 2.91/1.37 | % 2.91/1.37 | Instantiating formula (16) with all_13_0_6 and discharging atoms cNothing(all_13_0_6) = 0, yields: % 2.91/1.37 | (67) ? [v0] : rp(all_13_0_6, v0) = 0 % 2.91/1.37 | % 2.91/1.37 | Instantiating (67) with all_34_0_7 yields: % 2.91/1.37 | (68) rp(all_13_0_6, all_34_0_7) = 0 % 2.91/1.37 | % 2.91/1.37 | Instantiating formula (18) with all_34_0_7, all_13_0_6 and discharging atoms cNothing(all_13_0_6) = 0, rp(all_13_0_6, all_34_0_7) = 0, yields: % 2.91/1.37 | (69) $false % 2.91/1.37 | % 2.91/1.37 |-The branch is then unsatisfiable % 2.91/1.37 |-Branch two: % 2.91/1.37 | (35) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) % 2.91/1.37 | % 2.91/1.37 | Applying alpha-rule on (35) yields: % 2.91/1.37 | (30) ~ (all_0_0_0 = 0) % 2.91/1.37 | (37) ~ (all_0_1_1 = 0) % 2.91/1.37 | % 2.91/1.37 | Equations (32) can reduce 30 to: % 2.91/1.37 | (34) $false % 2.91/1.37 | % 2.91/1.37 |-The branch is then unsatisfiable % 2.91/1.37 |-Branch two: % 2.91/1.37 | (74) 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))) % 2.91/1.37 | % 2.91/1.37 | Applying alpha-rule on (74) yields: % 2.91/1.37 | (75) xsd_string(all_0_2_2) = all_0_1_1 % 2.91/1.37 | (76) xsd_integer(all_0_2_2) = all_0_0_0 % 2.91/1.37 | (26) (all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)) % 2.91/1.37 | % 2.91/1.37 | Instantiating formula (17) with all_0_2_2 yields: % 2.91/1.37 | (78) ~ (xsd_string(all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0) % 2.91/1.37 | % 2.91/1.37 | Instantiating formula (3) with all_0_1_1, all_0_2_2 and discharging atoms xsd_string(all_0_2_2) = all_0_1_1, yields: % 2.91/1.37 | (79) all_0_1_1 = 0 | xsd_integer(all_0_2_2) = 0 % 2.91/1.37 | % 2.91/1.37 +-Applying beta-rule and splitting (79), into two cases. % 2.91/1.37 |-Branch one: % 2.91/1.37 | (80) xsd_integer(all_0_2_2) = 0 % 2.91/1.37 | % 2.91/1.37 | Instantiating formula (12) 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: % 2.91/1.38 | (32) all_0_0_0 = 0 % 2.91/1.38 | % 2.91/1.38 | From (32) and (76) follows: % 2.91/1.38 | (80) xsd_integer(all_0_2_2) = 0 % 2.91/1.38 | % 2.91/1.38 +-Applying beta-rule and splitting (78), into two cases. % 2.91/1.38 |-Branch one: % 2.91/1.38 | (83) ~ (xsd_string(all_0_2_2) = 0) % 2.91/1.38 | % 2.91/1.38 +-Applying beta-rule and splitting (26), into two cases. % 2.91/1.38 |-Branch one: % 2.91/1.38 | (31) all_0_0_0 = 0 & all_0_1_1 = 0 % 2.91/1.38 | % 2.91/1.38 | Applying alpha-rule on (31) yields: % 2.91/1.38 | (32) all_0_0_0 = 0 % 2.91/1.38 | (33) all_0_1_1 = 0 % 2.91/1.38 | % 2.91/1.38 | From (33) and (75) follows: % 2.91/1.38 | (87) xsd_string(all_0_2_2) = 0 % 2.91/1.38 | % 2.91/1.38 | Using (87) and (83) yields: % 2.91/1.38 | (69) $false % 2.91/1.38 | % 2.91/1.38 |-The branch is then unsatisfiable % 2.91/1.38 |-Branch two: % 2.91/1.38 | (35) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) % 2.91/1.38 | % 2.91/1.38 | Applying alpha-rule on (35) yields: % 2.91/1.38 | (30) ~ (all_0_0_0 = 0) % 2.91/1.38 | (37) ~ (all_0_1_1 = 0) % 2.91/1.38 | % 2.91/1.38 | Equations (32) can reduce 30 to: % 2.91/1.38 | (34) $false % 2.91/1.38 | % 2.91/1.38 |-The branch is then unsatisfiable % 2.91/1.38 |-Branch two: % 2.91/1.38 | (87) xsd_string(all_0_2_2) = 0 % 2.91/1.38 | (94) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0) % 2.91/1.38 | % 2.91/1.38 | Instantiating (94) with all_21_0_8 yields: % 2.91/1.38 | (95) ~ (all_21_0_8 = 0) & xsd_integer(all_0_2_2) = all_21_0_8 % 2.91/1.38 | % 2.91/1.38 | Applying alpha-rule on (95) yields: % 2.91/1.38 | (96) ~ (all_21_0_8 = 0) % 2.91/1.38 | (97) xsd_integer(all_0_2_2) = all_21_0_8 % 2.91/1.38 | % 2.91/1.38 | Instantiating formula (12) with all_0_2_2, all_21_0_8, 0 and discharging atoms xsd_integer(all_0_2_2) = all_21_0_8, xsd_integer(all_0_2_2) = 0, yields: % 2.91/1.38 | (98) all_21_0_8 = 0 % 2.91/1.38 | % 2.91/1.38 | Equations (98) can reduce 96 to: % 2.91/1.38 | (34) $false % 2.91/1.38 | % 2.91/1.38 |-The branch is then unsatisfiable % 2.91/1.38 |-Branch two: % 2.91/1.38 | (100) ~ (xsd_integer(all_0_2_2) = 0) % 2.91/1.38 | (33) all_0_1_1 = 0 % 2.91/1.38 | % 2.91/1.38 +-Applying beta-rule and splitting (26), into two cases. % 2.91/1.38 |-Branch one: % 2.91/1.38 | (31) all_0_0_0 = 0 & all_0_1_1 = 0 % 2.91/1.38 | % 2.91/1.38 | Applying alpha-rule on (31) yields: % 2.91/1.38 | (32) all_0_0_0 = 0 % 2.91/1.38 | (33) all_0_1_1 = 0 % 2.91/1.38 | % 2.91/1.38 | From (32) and (76) follows: % 2.91/1.38 | (80) xsd_integer(all_0_2_2) = 0 % 2.91/1.38 | % 2.91/1.38 | Using (80) and (100) yields: % 2.91/1.38 | (69) $false % 2.91/1.38 | % 2.91/1.38 |-The branch is then unsatisfiable % 2.91/1.38 |-Branch two: % 2.91/1.38 | (35) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) % 2.91/1.38 | % 2.91/1.38 | Applying alpha-rule on (35) yields: % 2.91/1.38 | (30) ~ (all_0_0_0 = 0) % 2.91/1.38 | (37) ~ (all_0_1_1 = 0) % 2.91/1.38 | % 2.91/1.38 | Equations (33) can reduce 37 to: % 2.91/1.38 | (34) $false % 2.91/1.38 | % 2.91/1.38 |-The branch is then unsatisfiable % 2.91/1.38 |-Branch two: % 2.91/1.38 | (111) cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0) % 2.91/1.38 | % 2.91/1.38 | Applying alpha-rule on (111) yields: % 2.91/1.38 | (112) cowlNothing(all_0_2_2) = all_0_0_0 % 2.91/1.38 | (113) cowlThing(all_0_2_2) = all_0_1_1 % 2.91/1.38 | (114) ~ (all_0_1_1 = 0) | all_0_0_0 = 0 % 2.91/1.38 | % 2.91/1.38 | Instantiating formula (19) with all_0_2_2 yields: % 2.91/1.38 | (115) ~ (cowlNothing(all_0_2_2) = 0) % 2.91/1.38 | % 2.91/1.38 | Instantiating formula (4) with all_0_1_1, all_0_2_2 and discharging atoms cowlThing(all_0_2_2) = all_0_1_1, yields: % 2.91/1.38 | (33) all_0_1_1 = 0 % 2.91/1.38 | % 2.91/1.38 +-Applying beta-rule and splitting (114), into two cases. % 2.91/1.38 |-Branch one: % 2.91/1.38 | (37) ~ (all_0_1_1 = 0) % 2.91/1.38 | % 2.91/1.38 | Equations (33) can reduce 37 to: % 2.91/1.38 | (34) $false % 2.91/1.38 | % 2.91/1.38 |-The branch is then unsatisfiable % 2.91/1.38 |-Branch two: % 2.91/1.38 | (33) all_0_1_1 = 0 % 2.91/1.38 | (32) all_0_0_0 = 0 % 2.91/1.38 | % 2.91/1.38 | From (32) and (112) follows: % 2.91/1.38 | (121) cowlNothing(all_0_2_2) = 0 % 2.91/1.38 | % 2.91/1.38 | Using (121) and (115) yields: % 2.91/1.38 | (69) $false % 2.91/1.38 | % 2.91/1.38 |-The branch is then unsatisfiable % 2.91/1.38 % SZS output end Proof for theBenchmark % 2.91/1.38 % 2.91/1.38 918ms %------------------------------------------------------------------------------