%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KRS164+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n024.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 2.48s 1.25s % Output : Proof 3.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : KRS164+1 : TPTP v8.1.0. Released v3.1.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n024.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 14:15:19 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/sandbox/benchmark/theBenchmark.p ... % 0.49/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.25/0.87 Prover 0: Preprocessing ... % 1.48/0.94 Prover 0: Warning: ignoring some quantifiers % 1.48/0.96 Prover 0: Constructing countermodel ... % 1.85/1.07 Prover 0: gave up % 1.85/1.07 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.90/1.09 Prover 1: Preprocessing ... % 2.25/1.17 Prover 1: Constructing countermodel ... % 2.48/1.25 Prover 1: proved (177ms) % 2.48/1.25 % 2.48/1.25 No countermodel exists, formula is valid % 2.48/1.25 % SZS status Theorem for theBenchmark % 2.48/1.25 % 2.48/1.25 Generating proof ... found it (size 65) % 3.16/1.48 % 3.16/1.48 % SZS output start Proof for theBenchmark % 3.16/1.48 Assumed formulas after preprocessing and simplification: % 3.16/1.48 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (cCar(icar) = 0 & cCar(iauto) = v0 & cAutomobile(icar) = v1 & cAutomobile(iauto) = 0 & cowlThing(icar) = 0 & cowlThing(iauto) = 0 & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cCar(v7) = v6) | ~ (cCar(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cAutomobile(v7) = v6) | ~ (cAutomobile(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (xsd_string(v7) = v6) | ~ (xsd_string(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (xsd_integer(v7) = v6) | ~ (xsd_integer(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cowlNothing(v7) = v6) | ~ (cowlNothing(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (cowlThing(v7) = v6) | ~ (cowlThing(v7) = v5)) & ! [v5] : ! [v6] : (v6 = 0 | ~ (cCar(v5) = v6) | ? [v7] : ( ~ (v7 = 0) & cAutomobile(v5) = v7)) & ! [v5] : ! [v6] : (v6 = 0 | ~ (xsd_string(v5) = v6) | xsd_integer(v5) = 0) & ! [v5] : ! [v6] : (v6 = 0 | ~ (cowlThing(v5) = v6)) & ! [v5] : ( ~ (cCar(v5) = 0) | cAutomobile(v5) = 0) & ! [v5] : ( ~ (xsd_string(v5) = 0) | ? [v6] : ( ~ (v6 = 0) & xsd_integer(v5) = v6)) & ! [v5] : ~ (cowlNothing(v5) = 0) & ( ~ (v1 = 0) | ~ (v0 = 0) | (xsd_string(v2) = v3 & xsd_integer(v2) = v4 & ((v4 = 0 & v3 = 0) | ( ~ (v4 = 0) & ~ (v3 = 0)))) | (cowlNothing(v2) = v4 & cowlThing(v2) = v3 & ( ~ (v3 = 0) | v4 = 0)))) % 3.16/1.51 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 3.16/1.51 | (1) cCar(icar) = 0 & cCar(iauto) = all_0_4_4 & cAutomobile(icar) = all_0_3_3 & cAutomobile(iauto) = 0 & cowlThing(icar) = 0 & cowlThing(iauto) = 0 & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cCar(v2) = v1) | ~ (cCar(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cAutomobile(v2) = v1) | ~ (cAutomobile(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] : (v1 = 0 | ~ (cCar(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & cAutomobile(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) & ! [v0] : ( ~ (cCar(v0) = 0) | cAutomobile(v0) = 0) & ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) & ! [v0] : ~ (cowlNothing(v0) = 0) & ( ~ (all_0_3_3 = 0) | ~ (all_0_4_4 = 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))) % 3.16/1.52 | % 3.16/1.52 | Applying alpha-rule on (1) yields: % 3.16/1.52 | (2) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) % 3.16/1.52 | (3) cowlThing(iauto) = 0 % 3.16/1.52 | (4) cCar(iauto) = all_0_4_4 % 3.16/1.52 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) % 3.16/1.52 | (6) ! [v0] : ( ~ (cCar(v0) = 0) | cAutomobile(v0) = 0) % 3.16/1.52 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 3.16/1.52 | (8) cAutomobile(icar) = all_0_3_3 % 3.16/1.52 | (9) ! [v0] : ~ (cowlNothing(v0) = 0) % 3.16/1.52 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) % 3.16/1.52 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) % 3.16/1.52 | (12) cAutomobile(iauto) = 0 % 3.16/1.53 | (13) ! [v0] : ! [v1] : (v1 = 0 | ~ (cCar(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & cAutomobile(v0) = v2)) % 3.16/1.53 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cAutomobile(v2) = v1) | ~ (cAutomobile(v2) = v0)) % 3.16/1.53 | (15) ~ (all_0_3_3 = 0) | ~ (all_0_4_4 = 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)) % 3.16/1.53 | (16) cCar(icar) = 0 % 3.16/1.53 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) % 3.16/1.53 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cCar(v2) = v1) | ~ (cCar(v2) = v0)) % 3.16/1.53 | (19) cowlThing(icar) = 0 % 3.16/1.53 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) % 3.16/1.53 | % 3.16/1.53 | Instantiating formula (18) with iauto, all_0_4_4, 0 and discharging atoms cCar(iauto) = all_0_4_4, yields: % 3.16/1.53 | (21) all_0_4_4 = 0 | ~ (cCar(iauto) = 0) % 3.16/1.53 | % 3.16/1.53 | Instantiating formula (14) with iauto, 0, all_0_3_3 and discharging atoms cAutomobile(iauto) = 0, yields: % 3.16/1.53 | (22) all_0_3_3 = 0 | ~ (cAutomobile(iauto) = all_0_3_3) % 3.16/1.53 | % 3.16/1.53 | Instantiating formula (6) with icar and discharging atoms cCar(icar) = 0, yields: % 3.16/1.53 | (23) cAutomobile(icar) = 0 % 3.16/1.53 | % 3.39/1.53 | Instantiating formula (13) with all_0_4_4, iauto and discharging atoms cCar(iauto) = all_0_4_4, yields: % 3.39/1.53 | (24) all_0_4_4 = 0 | ? [v0] : ( ~ (v0 = 0) & cAutomobile(iauto) = v0) % 3.39/1.53 | % 3.39/1.53 +-Applying beta-rule and splitting (24), into two cases. % 3.39/1.53 |-Branch one: % 3.39/1.53 | (25) all_0_4_4 = 0 % 3.39/1.53 | % 3.39/1.53 | From (25) and (4) follows: % 3.39/1.53 | (26) cCar(iauto) = 0 % 3.39/1.53 | % 3.39/1.53 | Instantiating formula (14) with icar, 0, all_0_3_3 and discharging atoms cAutomobile(icar) = all_0_3_3, cAutomobile(icar) = 0, yields: % 3.39/1.53 | (27) all_0_3_3 = 0 % 3.39/1.53 | % 3.39/1.53 +-Applying beta-rule and splitting (21), into two cases. % 3.39/1.53 |-Branch one: % 3.39/1.53 | (28) ~ (cCar(iauto) = 0) % 3.39/1.53 | % 3.39/1.53 | Using (26) and (28) yields: % 3.39/1.53 | (29) $false % 3.39/1.53 | % 3.39/1.53 |-The branch is then unsatisfiable % 3.39/1.53 |-Branch two: % 3.39/1.53 | (26) cCar(iauto) = 0 % 3.39/1.53 | (25) all_0_4_4 = 0 % 3.39/1.53 | % 3.39/1.53 +-Applying beta-rule and splitting (22), into two cases. % 3.39/1.53 |-Branch one: % 3.39/1.53 | (32) ~ (cAutomobile(iauto) = all_0_3_3) % 3.39/1.53 | % 3.39/1.53 | From (27) and (32) follows: % 3.39/1.53 | (33) ~ (cAutomobile(iauto) = 0) % 3.39/1.53 | % 3.39/1.53 | Using (12) and (33) yields: % 3.39/1.53 | (29) $false % 3.39/1.53 | % 3.39/1.53 |-The branch is then unsatisfiable % 3.39/1.53 |-Branch two: % 3.39/1.53 | (35) cAutomobile(iauto) = all_0_3_3 % 3.39/1.53 | (27) all_0_3_3 = 0 % 3.39/1.53 | % 3.39/1.53 +-Applying beta-rule and splitting (15), into two cases. % 3.39/1.53 |-Branch one: % 3.39/1.53 | (37) ~ (all_0_3_3 = 0) % 3.39/1.53 | % 3.39/1.54 | Equations (27) can reduce 37 to: % 3.39/1.54 | (38) $false % 3.39/1.54 | % 3.39/1.54 |-The branch is then unsatisfiable % 3.39/1.54 |-Branch two: % 3.39/1.54 | (27) all_0_3_3 = 0 % 3.39/1.54 | (40) ~ (all_0_4_4 = 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)) % 3.39/1.54 | % 3.39/1.54 +-Applying beta-rule and splitting (40), into two cases. % 3.39/1.54 |-Branch one: % 3.39/1.54 | (41) ~ (all_0_4_4 = 0) % 3.39/1.54 | % 3.39/1.54 | Equations (25) can reduce 41 to: % 3.39/1.54 | (38) $false % 3.39/1.54 | % 3.39/1.54 |-The branch is then unsatisfiable % 3.39/1.54 |-Branch two: % 3.39/1.54 | (25) all_0_4_4 = 0 % 3.39/1.54 | (44) (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)) % 3.39/1.54 | % 3.39/1.54 +-Applying beta-rule and splitting (44), into two cases. % 3.39/1.54 |-Branch one: % 3.39/1.54 | (45) 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))) % 3.39/1.54 | % 3.39/1.54 | Applying alpha-rule on (45) yields: % 3.39/1.54 | (46) xsd_string(all_0_2_2) = all_0_1_1 % 3.39/1.54 | (47) xsd_integer(all_0_2_2) = all_0_0_0 % 3.39/1.54 | (48) (all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)) % 3.39/1.54 | % 3.39/1.54 | Instantiating formula (2) with all_0_2_2 yields: % 3.39/1.54 | (49) ~ (xsd_string(all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0) % 3.39/1.54 | % 3.39/1.54 | Instantiating formula (5) with all_0_1_1, all_0_2_2 and discharging atoms xsd_string(all_0_2_2) = all_0_1_1, yields: % 3.39/1.54 | (50) all_0_1_1 = 0 | xsd_integer(all_0_2_2) = 0 % 3.39/1.54 | % 3.39/1.54 +-Applying beta-rule and splitting (50), into two cases. % 3.39/1.54 |-Branch one: % 3.39/1.54 | (51) xsd_integer(all_0_2_2) = 0 % 3.39/1.54 | % 3.39/1.54 | Instantiating formula (7) 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: % 3.39/1.54 | (52) all_0_0_0 = 0 % 3.39/1.54 | % 3.39/1.54 | From (52) and (47) follows: % 3.39/1.54 | (51) xsd_integer(all_0_2_2) = 0 % 3.39/1.54 | % 3.39/1.54 +-Applying beta-rule and splitting (49), into two cases. % 3.39/1.54 |-Branch one: % 3.39/1.54 | (54) ~ (xsd_string(all_0_2_2) = 0) % 3.39/1.54 | % 3.39/1.54 +-Applying beta-rule and splitting (48), into two cases. % 3.39/1.54 |-Branch one: % 3.39/1.54 | (55) all_0_0_0 = 0 & all_0_1_1 = 0 % 3.39/1.54 | % 3.39/1.54 | Applying alpha-rule on (55) yields: % 3.39/1.54 | (52) all_0_0_0 = 0 % 3.39/1.54 | (57) all_0_1_1 = 0 % 3.39/1.54 | % 3.39/1.54 | From (57) and (46) follows: % 3.39/1.54 | (58) xsd_string(all_0_2_2) = 0 % 3.39/1.54 | % 3.39/1.54 | Using (58) and (54) yields: % 3.39/1.54 | (29) $false % 3.39/1.54 | % 3.39/1.54 |-The branch is then unsatisfiable % 3.39/1.54 |-Branch two: % 3.39/1.54 | (60) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) % 3.39/1.54 | % 3.39/1.54 | Applying alpha-rule on (60) yields: % 3.39/1.54 | (61) ~ (all_0_0_0 = 0) % 3.39/1.54 | (62) ~ (all_0_1_1 = 0) % 3.39/1.54 | % 3.39/1.54 | Equations (52) can reduce 61 to: % 3.39/1.54 | (38) $false % 3.39/1.54 | % 3.39/1.54 |-The branch is then unsatisfiable % 3.39/1.54 |-Branch two: % 3.39/1.54 | (58) xsd_string(all_0_2_2) = 0 % 3.39/1.54 | (65) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0) % 3.39/1.54 | % 3.39/1.54 | Instantiating (65) with all_67_0_5 yields: % 3.39/1.54 | (66) ~ (all_67_0_5 = 0) & xsd_integer(all_0_2_2) = all_67_0_5 % 3.39/1.54 | % 3.39/1.54 | Applying alpha-rule on (66) yields: % 3.39/1.54 | (67) ~ (all_67_0_5 = 0) % 3.39/1.54 | (68) xsd_integer(all_0_2_2) = all_67_0_5 % 3.39/1.54 | % 3.39/1.54 | Instantiating formula (7) with all_0_2_2, all_67_0_5, 0 and discharging atoms xsd_integer(all_0_2_2) = all_67_0_5, xsd_integer(all_0_2_2) = 0, yields: % 3.39/1.54 | (69) all_67_0_5 = 0 % 3.39/1.54 | % 3.39/1.54 | Equations (69) can reduce 67 to: % 3.39/1.54 | (38) $false % 3.39/1.54 | % 3.39/1.54 |-The branch is then unsatisfiable % 3.39/1.54 |-Branch two: % 3.39/1.54 | (71) ~ (xsd_integer(all_0_2_2) = 0) % 3.39/1.54 | (57) all_0_1_1 = 0 % 3.39/1.55 | % 3.39/1.55 +-Applying beta-rule and splitting (48), into two cases. % 3.39/1.55 |-Branch one: % 3.39/1.55 | (55) all_0_0_0 = 0 & all_0_1_1 = 0 % 3.39/1.55 | % 3.39/1.55 | Applying alpha-rule on (55) yields: % 3.39/1.55 | (52) all_0_0_0 = 0 % 3.39/1.55 | (57) all_0_1_1 = 0 % 3.39/1.55 | % 3.39/1.55 | From (52) and (47) follows: % 3.39/1.55 | (51) xsd_integer(all_0_2_2) = 0 % 3.39/1.55 | % 3.39/1.55 | Using (51) and (71) yields: % 3.39/1.55 | (29) $false % 3.39/1.55 | % 3.39/1.55 |-The branch is then unsatisfiable % 3.39/1.55 |-Branch two: % 3.39/1.55 | (60) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) % 3.39/1.55 | % 3.39/1.55 | Applying alpha-rule on (60) yields: % 3.39/1.55 | (61) ~ (all_0_0_0 = 0) % 3.39/1.55 | (62) ~ (all_0_1_1 = 0) % 3.39/1.55 | % 3.39/1.55 | Equations (57) can reduce 62 to: % 3.39/1.55 | (38) $false % 3.39/1.55 | % 3.39/1.55 |-The branch is then unsatisfiable % 3.39/1.55 |-Branch two: % 3.39/1.55 | (82) 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) % 3.39/1.55 | % 3.39/1.55 | Applying alpha-rule on (82) yields: % 3.39/1.55 | (83) cowlNothing(all_0_2_2) = all_0_0_0 % 3.39/1.55 | (84) cowlThing(all_0_2_2) = all_0_1_1 % 3.39/1.55 | (85) ~ (all_0_1_1 = 0) | all_0_0_0 = 0 % 3.39/1.55 | % 3.39/1.55 | Instantiating formula (9) with all_0_2_2 yields: % 3.39/1.55 | (86) ~ (cowlNothing(all_0_2_2) = 0) % 3.39/1.55 | % 3.39/1.55 | Instantiating formula (10) with all_0_1_1, all_0_2_2 and discharging atoms cowlThing(all_0_2_2) = all_0_1_1, yields: % 3.39/1.55 | (57) all_0_1_1 = 0 % 3.39/1.55 | % 3.39/1.55 +-Applying beta-rule and splitting (85), into two cases. % 3.39/1.55 |-Branch one: % 3.39/1.55 | (62) ~ (all_0_1_1 = 0) % 3.39/1.55 | % 3.39/1.55 | Equations (57) can reduce 62 to: % 3.39/1.55 | (38) $false % 3.39/1.55 | % 3.39/1.55 |-The branch is then unsatisfiable % 3.39/1.55 |-Branch two: % 3.39/1.55 | (57) all_0_1_1 = 0 % 3.39/1.55 | (52) all_0_0_0 = 0 % 3.39/1.55 | % 3.39/1.55 | From (52) and (83) follows: % 3.39/1.55 | (92) cowlNothing(all_0_2_2) = 0 % 3.39/1.55 | % 3.39/1.55 | Using (92) and (86) yields: % 3.39/1.55 | (29) $false % 3.39/1.55 | % 3.39/1.55 |-The branch is then unsatisfiable % 3.39/1.55 |-Branch two: % 3.39/1.55 | (41) ~ (all_0_4_4 = 0) % 3.39/1.55 | (95) ? [v0] : ( ~ (v0 = 0) & cAutomobile(iauto) = v0) % 3.39/1.55 | % 3.39/1.55 | Instantiating (95) with all_13_0_7 yields: % 3.39/1.55 | (96) ~ (all_13_0_7 = 0) & cAutomobile(iauto) = all_13_0_7 % 3.39/1.55 | % 3.39/1.55 | Applying alpha-rule on (96) yields: % 3.39/1.55 | (97) ~ (all_13_0_7 = 0) % 3.39/1.55 | (98) cAutomobile(iauto) = all_13_0_7 % 3.39/1.55 | % 3.39/1.55 | Instantiating formula (14) with iauto, all_13_0_7, 0 and discharging atoms cAutomobile(iauto) = all_13_0_7, cAutomobile(iauto) = 0, yields: % 3.39/1.55 | (99) all_13_0_7 = 0 % 3.39/1.55 | % 3.39/1.55 | Equations (99) can reduce 97 to: % 3.39/1.55 | (38) $false % 3.39/1.55 | % 3.39/1.55 |-The branch is then unsatisfiable % 3.39/1.55 % SZS output end Proof for theBenchmark % 3.39/1.55 % 3.39/1.55 972ms %------------------------------------------------------------------------------