%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KRS165+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n026.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 2.33s 1.21s % Output : Proof 3.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : KRS165+1 : TPTP v8.1.0. Released v3.1.0. % 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.11/0.32 % Computer : n026.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 600 % 0.11/0.32 % DateTime : Tue Jun 7 19:42:31 EDT 2022 % 0.11/0.33 % CPUTime : % 0.18/0.57 ____ _ % 0.18/0.57 ___ / __ \_____(_)___ ________ __________ % 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.57 % 0.18/0.57 A Theorem Prover for First-Order Logic % 0.18/0.57 (ePrincess v.1.0) % 0.18/0.57 % 0.18/0.57 (c) Philipp Rümmer, 2009-2015 % 0.18/0.57 (c) Peter Backeman, 2014-2015 % 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.57 Bug reports to peter@backeman.se % 0.18/0.57 % 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.57 % 0.18/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.70/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.37/0.86 Prover 0: Preprocessing ... % 1.49/0.92 Prover 0: Warning: ignoring some quantifiers % 1.55/0.94 Prover 0: Constructing countermodel ... % 1.75/1.04 Prover 0: gave up % 1.75/1.04 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.75/1.06 Prover 1: Preprocessing ... % 2.03/1.14 Prover 1: Constructing countermodel ... % 2.33/1.21 Prover 1: proved (161ms) % 2.33/1.21 % 2.33/1.21 No countermodel exists, formula is valid % 2.33/1.21 % SZS status Theorem for theBenchmark % 2.33/1.21 % 2.33/1.21 Generating proof ... found it (size 57) % 2.88/1.43 % 2.88/1.43 % SZS output start Proof for theBenchmark % 2.88/1.43 Assumed formulas after preprocessing and simplification: % 2.88/1.43 | (0) ? [v0] : ? [v1] : ? [v2] : ( ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (cCar(v5) = v4) | ~ (cCar(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (cAutomobile(v5) = v4) | ~ (cAutomobile(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] : (v4 = 0 | ~ (cCar(v3) = v4) | ? [v5] : ( ~ (v5 = 0) & cAutomobile(v3) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (xsd_string(v3) = v4) | xsd_integer(v3) = 0) & ! [v3] : ! [v4] : (v4 = 0 | ~ (cowlThing(v3) = v4)) & ! [v3] : ( ~ (cCar(v3) = 0) | cAutomobile(v3) = 0) & ! [v3] : ( ~ (xsd_string(v3) = 0) | ? [v4] : ( ~ (v4 = 0) & xsd_integer(v3) = v4)) & ! [v3] : ~ (cowlNothing(v3) = 0) & ((v1 = 0 & ~ (v2 = 0) & cCar(v0) = v2 & cAutomobile(v0) = 0) | (v1 = 0 & ~ (v2 = 0) & cCar(v0) = 0 & cAutomobile(v0) = v2) | (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)))) % 3.17/1.46 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 3.17/1.46 | (1) ! [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_1_1 = 0 & ~ (all_0_0_0 = 0) & cCar(all_0_2_2) = all_0_0_0 & cAutomobile(all_0_2_2) = 0) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & cCar(all_0_2_2) = 0 & cAutomobile(all_0_2_2) = all_0_0_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))) % 3.17/1.47 | % 3.17/1.47 | Applying alpha-rule on (1) yields: % 3.17/1.47 | (2) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) % 3.17/1.47 | (3) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) % 3.17/1.47 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) % 3.17/1.47 | (5) ! [v0] : ( ~ (cCar(v0) = 0) | cAutomobile(v0) = 0) % 3.17/1.47 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (cCar(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & cAutomobile(v0) = v2)) % 3.17/1.47 | (7) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) % 3.17/1.47 | (8) (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & cCar(all_0_2_2) = all_0_0_0 & cAutomobile(all_0_2_2) = 0) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & cCar(all_0_2_2) = 0 & cAutomobile(all_0_2_2) = all_0_0_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)) % 3.17/1.47 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) % 3.17/1.47 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cAutomobile(v2) = v1) | ~ (cAutomobile(v2) = v0)) % 3.17/1.47 | (11) ! [v0] : ~ (cowlNothing(v0) = 0) % 3.17/1.47 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) % 3.17/1.47 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cCar(v2) = v1) | ~ (cCar(v2) = v0)) % 3.17/1.47 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 3.17/1.48 | % 3.17/1.48 +-Applying beta-rule and splitting (8), into two cases. % 3.17/1.48 |-Branch one: % 3.17/1.48 | (15) (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & cCar(all_0_2_2) = all_0_0_0 & cAutomobile(all_0_2_2) = 0) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & cCar(all_0_2_2) = 0 & cAutomobile(all_0_2_2) = all_0_0_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)))) % 3.17/1.48 | % 3.17/1.48 +-Applying beta-rule and splitting (15), into two cases. % 3.17/1.48 |-Branch one: % 3.17/1.48 | (16) (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & cCar(all_0_2_2) = all_0_0_0 & cAutomobile(all_0_2_2) = 0) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & cCar(all_0_2_2) = 0 & cAutomobile(all_0_2_2) = all_0_0_0) % 3.17/1.48 | % 3.17/1.48 +-Applying beta-rule and splitting (16), into two cases. % 3.17/1.48 |-Branch one: % 3.17/1.48 | (17) all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & cCar(all_0_2_2) = all_0_0_0 & cAutomobile(all_0_2_2) = 0 % 3.17/1.48 | % 3.17/1.48 | Applying alpha-rule on (17) yields: % 3.17/1.48 | (18) all_0_1_1 = 0 % 3.17/1.48 | (19) ~ (all_0_0_0 = 0) % 3.17/1.48 | (20) cCar(all_0_2_2) = all_0_0_0 % 3.17/1.48 | (21) cAutomobile(all_0_2_2) = 0 % 3.17/1.48 | % 3.17/1.48 | Instantiating formula (6) with all_0_0_0, all_0_2_2 and discharging atoms cCar(all_0_2_2) = all_0_0_0, yields: % 3.17/1.48 | (22) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & cAutomobile(all_0_2_2) = v0) % 3.17/1.48 | % 3.17/1.48 +-Applying beta-rule and splitting (22), into two cases. % 3.17/1.48 |-Branch one: % 3.17/1.48 | (23) all_0_0_0 = 0 % 3.17/1.48 | % 3.17/1.48 | Equations (23) can reduce 19 to: % 3.17/1.48 | (24) $false % 3.17/1.48 | % 3.17/1.48 |-The branch is then unsatisfiable % 3.17/1.48 |-Branch two: % 3.17/1.48 | (19) ~ (all_0_0_0 = 0) % 3.17/1.48 | (26) ? [v0] : ( ~ (v0 = 0) & cAutomobile(all_0_2_2) = v0) % 3.17/1.48 | % 3.17/1.48 | Instantiating (26) with all_13_0_3 yields: % 3.17/1.48 | (27) ~ (all_13_0_3 = 0) & cAutomobile(all_0_2_2) = all_13_0_3 % 3.17/1.48 | % 3.17/1.48 | Applying alpha-rule on (27) yields: % 3.17/1.48 | (28) ~ (all_13_0_3 = 0) % 3.17/1.48 | (29) cAutomobile(all_0_2_2) = all_13_0_3 % 3.17/1.48 | % 3.17/1.48 | Instantiating formula (10) with all_0_2_2, all_13_0_3, 0 and discharging atoms cAutomobile(all_0_2_2) = all_13_0_3, cAutomobile(all_0_2_2) = 0, yields: % 3.17/1.48 | (30) all_13_0_3 = 0 % 3.17/1.48 | % 3.17/1.48 | Equations (30) can reduce 28 to: % 3.17/1.48 | (24) $false % 3.17/1.48 | % 3.17/1.48 |-The branch is then unsatisfiable % 3.17/1.48 |-Branch two: % 3.17/1.48 | (32) all_0_1_1 = 0 & ~ (all_0_0_0 = 0) & cCar(all_0_2_2) = 0 & cAutomobile(all_0_2_2) = all_0_0_0 % 3.17/1.48 | % 3.17/1.48 | Applying alpha-rule on (32) yields: % 3.17/1.48 | (18) all_0_1_1 = 0 % 3.17/1.48 | (19) ~ (all_0_0_0 = 0) % 3.17/1.48 | (35) cCar(all_0_2_2) = 0 % 3.17/1.48 | (36) cAutomobile(all_0_2_2) = all_0_0_0 % 3.17/1.48 | % 3.17/1.48 | Instantiating formula (5) with all_0_2_2 and discharging atoms cCar(all_0_2_2) = 0, yields: % 3.17/1.48 | (21) cAutomobile(all_0_2_2) = 0 % 3.17/1.48 | % 3.17/1.48 | Instantiating formula (10) with all_0_2_2, 0, all_0_0_0 and discharging atoms cAutomobile(all_0_2_2) = all_0_0_0, cAutomobile(all_0_2_2) = 0, yields: % 3.17/1.48 | (23) all_0_0_0 = 0 % 3.27/1.48 | % 3.27/1.48 | Equations (23) can reduce 19 to: % 3.27/1.48 | (24) $false % 3.27/1.48 | % 3.27/1.48 |-The branch is then unsatisfiable % 3.27/1.48 |-Branch two: % 3.27/1.48 | (40) 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))) % 3.27/1.49 | % 3.27/1.49 | Applying alpha-rule on (40) yields: % 3.27/1.49 | (41) xsd_string(all_0_2_2) = all_0_1_1 % 3.27/1.49 | (42) xsd_integer(all_0_2_2) = all_0_0_0 % 3.27/1.49 | (43) (all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)) % 3.27/1.49 | % 3.27/1.49 | Instantiating formula (7) with all_0_2_2 yields: % 3.27/1.49 | (44) ~ (xsd_string(all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0) % 3.27/1.49 | % 3.27/1.49 | Instantiating formula (2) with all_0_1_1, all_0_2_2 and discharging atoms xsd_string(all_0_2_2) = all_0_1_1, yields: % 3.27/1.49 | (45) all_0_1_1 = 0 | xsd_integer(all_0_2_2) = 0 % 3.27/1.49 | % 3.27/1.49 +-Applying beta-rule and splitting (45), into two cases. % 3.27/1.49 |-Branch one: % 3.27/1.49 | (46) xsd_integer(all_0_2_2) = 0 % 3.27/1.49 | % 3.27/1.49 | Instantiating formula (14) 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: % 3.27/1.49 | (23) all_0_0_0 = 0 % 3.27/1.49 | % 3.27/1.49 | From (23) and (42) follows: % 3.27/1.49 | (46) xsd_integer(all_0_2_2) = 0 % 3.27/1.49 | % 3.27/1.49 +-Applying beta-rule and splitting (44), into two cases. % 3.27/1.49 |-Branch one: % 3.27/1.49 | (49) ~ (xsd_string(all_0_2_2) = 0) % 3.27/1.49 | % 3.27/1.49 +-Applying beta-rule and splitting (43), into two cases. % 3.27/1.49 |-Branch one: % 3.27/1.49 | (50) all_0_0_0 = 0 & all_0_1_1 = 0 % 3.27/1.49 | % 3.27/1.49 | Applying alpha-rule on (50) yields: % 3.27/1.49 | (23) all_0_0_0 = 0 % 3.27/1.49 | (18) all_0_1_1 = 0 % 3.27/1.49 | % 3.27/1.49 | From (18) and (41) follows: % 3.27/1.49 | (53) xsd_string(all_0_2_2) = 0 % 3.27/1.49 | % 3.27/1.49 | Using (53) and (49) yields: % 3.27/1.49 | (54) $false % 3.27/1.49 | % 3.27/1.49 |-The branch is then unsatisfiable % 3.27/1.49 |-Branch two: % 3.27/1.49 | (55) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) % 3.27/1.49 | % 3.27/1.49 | Applying alpha-rule on (55) yields: % 3.27/1.49 | (19) ~ (all_0_0_0 = 0) % 3.27/1.49 | (57) ~ (all_0_1_1 = 0) % 3.27/1.49 | % 3.27/1.49 | Equations (23) can reduce 19 to: % 3.27/1.49 | (24) $false % 3.27/1.49 | % 3.27/1.49 |-The branch is then unsatisfiable % 3.27/1.49 |-Branch two: % 3.27/1.49 | (53) xsd_string(all_0_2_2) = 0 % 3.27/1.49 | (60) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0) % 3.27/1.49 | % 3.27/1.49 | Instantiating (60) with all_21_0_4 yields: % 3.27/1.49 | (61) ~ (all_21_0_4 = 0) & xsd_integer(all_0_2_2) = all_21_0_4 % 3.27/1.49 | % 3.27/1.49 | Applying alpha-rule on (61) yields: % 3.27/1.49 | (62) ~ (all_21_0_4 = 0) % 3.27/1.49 | (63) xsd_integer(all_0_2_2) = all_21_0_4 % 3.27/1.49 | % 3.27/1.49 | Instantiating formula (14) with all_0_2_2, all_21_0_4, 0 and discharging atoms xsd_integer(all_0_2_2) = all_21_0_4, xsd_integer(all_0_2_2) = 0, yields: % 3.27/1.49 | (64) all_21_0_4 = 0 % 3.27/1.49 | % 3.27/1.49 | Equations (64) can reduce 62 to: % 3.27/1.49 | (24) $false % 3.27/1.49 | % 3.27/1.49 |-The branch is then unsatisfiable % 3.27/1.49 |-Branch two: % 3.27/1.49 | (66) ~ (xsd_integer(all_0_2_2) = 0) % 3.27/1.49 | (18) all_0_1_1 = 0 % 3.27/1.49 | % 3.27/1.49 +-Applying beta-rule and splitting (43), into two cases. % 3.27/1.49 |-Branch one: % 3.27/1.49 | (50) all_0_0_0 = 0 & all_0_1_1 = 0 % 3.27/1.49 | % 3.27/1.49 | Applying alpha-rule on (50) yields: % 3.27/1.49 | (23) all_0_0_0 = 0 % 3.27/1.49 | (18) all_0_1_1 = 0 % 3.27/1.49 | % 3.27/1.49 | From (23) and (42) follows: % 3.27/1.49 | (46) xsd_integer(all_0_2_2) = 0 % 3.27/1.49 | % 3.27/1.49 | Using (46) and (66) yields: % 3.27/1.49 | (54) $false % 3.27/1.49 | % 3.27/1.49 |-The branch is then unsatisfiable % 3.27/1.49 |-Branch two: % 3.27/1.49 | (55) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) % 3.27/1.49 | % 3.27/1.49 | Applying alpha-rule on (55) yields: % 3.27/1.49 | (19) ~ (all_0_0_0 = 0) % 3.27/1.50 | (57) ~ (all_0_1_1 = 0) % 3.27/1.50 | % 3.27/1.50 | Equations (18) can reduce 57 to: % 3.27/1.50 | (24) $false % 3.27/1.50 | % 3.27/1.50 |-The branch is then unsatisfiable % 3.27/1.50 |-Branch two: % 3.27/1.50 | (77) 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) % 3.27/1.50 | % 3.27/1.50 | Applying alpha-rule on (77) yields: % 3.27/1.50 | (78) cowlNothing(all_0_2_2) = all_0_0_0 % 3.27/1.50 | (79) cowlThing(all_0_2_2) = all_0_1_1 % 3.27/1.50 | (80) ~ (all_0_1_1 = 0) | all_0_0_0 = 0 % 3.27/1.50 | % 3.27/1.50 | Instantiating formula (11) with all_0_2_2 yields: % 3.27/1.50 | (81) ~ (cowlNothing(all_0_2_2) = 0) % 3.27/1.50 | % 3.27/1.50 | Instantiating formula (3) with all_0_1_1, all_0_2_2 and discharging atoms cowlThing(all_0_2_2) = all_0_1_1, yields: % 3.27/1.50 | (18) all_0_1_1 = 0 % 3.27/1.50 | % 3.27/1.50 +-Applying beta-rule and splitting (80), into two cases. % 3.27/1.50 |-Branch one: % 3.27/1.50 | (57) ~ (all_0_1_1 = 0) % 3.27/1.50 | % 3.27/1.50 | Equations (18) can reduce 57 to: % 3.27/1.50 | (24) $false % 3.27/1.50 | % 3.27/1.50 |-The branch is then unsatisfiable % 3.27/1.50 |-Branch two: % 3.27/1.50 | (18) all_0_1_1 = 0 % 3.27/1.50 | (23) all_0_0_0 = 0 % 3.27/1.50 | % 3.27/1.50 | From (23) and (78) follows: % 3.27/1.50 | (87) cowlNothing(all_0_2_2) = 0 % 3.27/1.50 | % 3.27/1.50 | Using (87) and (81) yields: % 3.27/1.50 | (54) $false % 3.27/1.50 | % 3.27/1.50 |-The branch is then unsatisfiable % 3.27/1.50 % SZS output end Proof for theBenchmark % 3.27/1.50 % 3.27/1.50 916ms %------------------------------------------------------------------------------