%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KRS163+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n020.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 02:56:45 EDT 2022 % Result : Theorem 2.61s 1.39s % Output : Proof 3.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.14 % Problem : KRS163+1 : TPTP v8.1.0. Released v3.1.0. % 0.13/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.36 % Computer : n020.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Tue Jun 7 16:33:21 EDT 2022 % 0.14/0.36 % CPUTime : % 0.52/0.62 ____ _ % 0.52/0.62 ___ / __ \_____(_)___ ________ __________ % 0.52/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.52/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.52/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.52/0.62 % 0.52/0.62 A Theorem Prover for First-Order Logic % 0.52/0.62 (ePrincess v.1.0) % 0.52/0.62 % 0.52/0.62 (c) Philipp Rümmer, 2009-2015 % 0.52/0.62 (c) Peter Backeman, 2014-2015 % 0.52/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.52/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.52/0.62 Bug reports to peter@backeman.se % 0.52/0.62 % 0.52/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.52/0.62 % 0.52/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.72/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.51/0.96 Prover 0: Preprocessing ... % 1.66/1.06 Prover 0: Warning: ignoring some quantifiers % 1.66/1.08 Prover 0: Constructing countermodel ... % 2.00/1.18 Prover 0: gave up % 2.00/1.18 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.16/1.20 Prover 1: Preprocessing ... % 2.33/1.30 Prover 1: Constructing countermodel ... % 2.61/1.39 Prover 1: proved (213ms) % 2.61/1.39 % 2.61/1.39 No countermodel exists, formula is valid % 2.61/1.39 % SZS status Theorem for theBenchmark % 2.61/1.39 % 2.61/1.39 Generating proof ... found it (size 51) % 3.76/1.64 % 3.76/1.64 % SZS output start Proof for theBenchmark % 3.76/1.64 Assumed formulas after preprocessing and simplification: % 3.76/1.64 | (0) ? [v0] : ? [v1] : ? [v2] : (cowlThing(ib) = 0 & cowlThing(ia) = 0 & cB(ib) = 0 & cA(ia) = 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 | ~ (cB(v5) = v4) | ~ (cB(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (cA(v5) = v4) | ~ (cA(v5) = v3)) & ! [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 | ~ (cB(v3) = v4) | ~ (cB(v3) = 0)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (cA(v3) = v4) | ~ (cA(v3) = 0)) & ! [v3] : ( ~ (xsd_string(v3) = 0) | ? [v4] : ( ~ (v4 = 0) & xsd_integer(v3) = v4)) & ! [v3] : ~ (cowlNothing(v3) = 0) & ! [v3] : ( ~ (cB(v3) = 0) | ? [v4] : ( ~ (v4 = 0) & cA(v3) = v4)) & (ib = ia | (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)))) % 3.76/1.67 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 3.76/1.67 | (1) cowlThing(ib) = 0 & cowlThing(ia) = 0 & cB(ib) = 0 & cA(ia) = 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 | ~ (cB(v2) = v1) | ~ (cB(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cA(v2) = v1) | ~ (cA(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 | ~ (cB(v0) = v1) | ~ (cB(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cA(v0) = v1) | ~ (cA(v0) = 0)) & ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) & ! [v0] : ~ (cowlNothing(v0) = 0) & ! [v0] : ( ~ (cB(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & cA(v0) = v1)) & (ib = ia | (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))) % 3.76/1.68 | % 3.76/1.68 | Applying alpha-rule on (1) yields: % 3.76/1.68 | (2) cowlThing(ib) = 0 % 3.76/1.68 | (3) ! [v0] : ~ (cowlNothing(v0) = 0) % 3.76/1.68 | (4) cA(ia) = 0 % 3.76/1.68 | (5) cB(ib) = 0 % 3.76/1.68 | (6) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) % 3.76/1.68 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) % 3.76/1.68 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cB(v2) = v1) | ~ (cB(v2) = v0)) % 3.76/1.68 | (9) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) % 3.76/1.69 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) % 3.76/1.69 | (11) cowlThing(ia) = 0 % 3.76/1.69 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | ~ (xsd_string(v0) = 0)) % 3.76/1.69 | (13) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1) | ~ (cowlThing(v0) = 0)) % 3.76/1.69 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) % 3.76/1.69 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) % 3.76/1.69 | (16) ! [v0] : ! [v1] : (v1 = 0 | ~ (cA(v0) = v1) | ~ (cA(v0) = 0)) % 3.76/1.69 | (17) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) % 3.76/1.69 | (18) ib = ia | (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)) % 3.76/1.69 | (19) ! [v0] : ! [v1] : (v1 = 0 | ~ (cB(v0) = v1) | ~ (cB(v0) = 0)) % 3.76/1.69 | (20) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_integer(v0) = v1) | ~ (xsd_integer(v0) = 0)) % 3.76/1.69 | (21) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlNothing(v0) = v1) | ~ (cowlNothing(v0) = 0)) % 3.76/1.69 | (22) ! [v0] : ( ~ (cB(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & cA(v0) = v1)) % 3.76/1.69 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cA(v2) = v1) | ~ (cA(v2) = v0)) % 3.76/1.69 | % 3.76/1.69 | Instantiating formula (22) with ib and discharging atoms cB(ib) = 0, yields: % 3.76/1.69 | (24) ? [v0] : ( ~ (v0 = 0) & cA(ib) = v0) % 3.76/1.69 | % 3.76/1.69 | Instantiating (24) with all_8_0_3 yields: % 3.76/1.69 | (25) ~ (all_8_0_3 = 0) & cA(ib) = all_8_0_3 % 3.76/1.69 | % 3.76/1.69 | Applying alpha-rule on (25) yields: % 3.76/1.69 | (26) ~ (all_8_0_3 = 0) % 3.76/1.69 | (27) cA(ib) = all_8_0_3 % 3.76/1.69 | % 3.76/1.69 | Instantiating formula (16) with all_8_0_3, ia and discharging atoms cA(ia) = 0, yields: % 3.76/1.69 | (28) all_8_0_3 = 0 | ~ (cA(ia) = all_8_0_3) % 3.76/1.69 | % 3.76/1.69 +-Applying beta-rule and splitting (18), into two cases. % 3.76/1.69 |-Branch one: % 3.76/1.69 | (29) ib = ia % 3.76/1.69 | % 3.76/1.69 | From (29) and (27) follows: % 3.76/1.69 | (30) cA(ia) = all_8_0_3 % 3.76/1.69 | % 3.76/1.69 +-Applying beta-rule and splitting (28), into two cases. % 3.76/1.69 |-Branch one: % 3.76/1.69 | (31) ~ (cA(ia) = all_8_0_3) % 3.76/1.69 | % 3.76/1.69 | Using (30) and (31) yields: % 3.76/1.69 | (32) $false % 3.76/1.69 | % 3.76/1.69 |-The branch is then unsatisfiable % 3.76/1.69 |-Branch two: % 3.76/1.69 | (30) cA(ia) = all_8_0_3 % 3.76/1.70 | (34) all_8_0_3 = 0 % 3.76/1.70 | % 3.76/1.70 | Equations (34) can reduce 26 to: % 3.76/1.70 | (35) $false % 3.76/1.70 | % 3.76/1.70 |-The branch is then unsatisfiable % 3.76/1.70 |-Branch two: % 3.76/1.70 | (36) ~ (ib = ia) % 3.76/1.70 | (37) (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)) % 3.76/1.70 | % 3.76/1.70 +-Applying beta-rule and splitting (37), into two cases. % 3.76/1.70 |-Branch one: % 3.76/1.70 | (38) 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))) % 3.76/1.70 | % 3.76/1.70 | Applying alpha-rule on (38) yields: % 3.76/1.70 | (39) xsd_string(all_0_2_2) = all_0_1_1 % 3.76/1.70 | (40) xsd_integer(all_0_2_2) = all_0_0_0 % 3.76/1.70 | (41) (all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)) % 3.76/1.70 | % 3.76/1.70 | Instantiating formula (6) with all_0_2_2 yields: % 3.76/1.70 | (42) ~ (xsd_string(all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0) % 3.76/1.70 | % 3.76/1.70 | Instantiating formula (17) with all_0_1_1, all_0_2_2 and discharging atoms xsd_string(all_0_2_2) = all_0_1_1, yields: % 3.76/1.70 | (43) all_0_1_1 = 0 | xsd_integer(all_0_2_2) = 0 % 3.76/1.70 | % 3.76/1.70 +-Applying beta-rule and splitting (43), into two cases. % 3.76/1.70 |-Branch one: % 3.76/1.70 | (44) xsd_integer(all_0_2_2) = 0 % 3.76/1.70 | % 3.76/1.70 | Instantiating formula (10) 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: % 3.76/1.70 | (45) all_0_0_0 = 0 % 3.76/1.70 | % 3.76/1.70 | From (45) and (40) follows: % 3.76/1.70 | (44) xsd_integer(all_0_2_2) = 0 % 3.76/1.70 | % 3.76/1.70 +-Applying beta-rule and splitting (42), into two cases. % 3.76/1.70 |-Branch one: % 3.76/1.70 | (47) ~ (xsd_string(all_0_2_2) = 0) % 3.76/1.70 | % 3.76/1.70 +-Applying beta-rule and splitting (41), into two cases. % 3.76/1.70 |-Branch one: % 3.76/1.70 | (48) all_0_0_0 = 0 & all_0_1_1 = 0 % 3.76/1.70 | % 3.76/1.70 | Applying alpha-rule on (48) yields: % 3.76/1.70 | (45) all_0_0_0 = 0 % 3.76/1.70 | (50) all_0_1_1 = 0 % 3.76/1.70 | % 3.76/1.70 | From (50) and (39) follows: % 3.76/1.70 | (51) xsd_string(all_0_2_2) = 0 % 3.76/1.70 | % 3.76/1.70 | Using (51) and (47) yields: % 3.76/1.70 | (32) $false % 3.76/1.70 | % 3.76/1.70 |-The branch is then unsatisfiable % 3.76/1.70 |-Branch two: % 3.76/1.70 | (53) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) % 3.76/1.70 | % 3.76/1.70 | Applying alpha-rule on (53) yields: % 3.76/1.70 | (54) ~ (all_0_0_0 = 0) % 3.76/1.70 | (55) ~ (all_0_1_1 = 0) % 3.76/1.70 | % 3.76/1.70 | Equations (45) can reduce 54 to: % 3.76/1.70 | (35) $false % 3.76/1.70 | % 3.76/1.70 |-The branch is then unsatisfiable % 3.76/1.70 |-Branch two: % 3.76/1.70 | (51) xsd_string(all_0_2_2) = 0 % 3.76/1.70 | (58) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0) % 3.76/1.70 | % 3.76/1.70 | Instantiating (58) with all_46_0_4 yields: % 3.76/1.70 | (59) ~ (all_46_0_4 = 0) & xsd_integer(all_0_2_2) = all_46_0_4 % 3.76/1.70 | % 3.76/1.70 | Applying alpha-rule on (59) yields: % 3.76/1.70 | (60) ~ (all_46_0_4 = 0) % 3.76/1.70 | (61) xsd_integer(all_0_2_2) = all_46_0_4 % 3.76/1.70 | % 3.76/1.70 | Instantiating formula (20) with all_46_0_4, all_0_2_2 and discharging atoms xsd_integer(all_0_2_2) = all_46_0_4, xsd_integer(all_0_2_2) = 0, yields: % 3.76/1.70 | (62) all_46_0_4 = 0 % 3.76/1.70 | % 3.76/1.70 | Equations (62) can reduce 60 to: % 3.76/1.70 | (35) $false % 3.76/1.70 | % 3.76/1.70 |-The branch is then unsatisfiable % 3.76/1.70 |-Branch two: % 3.76/1.70 | (64) ~ (xsd_integer(all_0_2_2) = 0) % 3.76/1.70 | (50) all_0_1_1 = 0 % 3.76/1.70 | % 3.76/1.70 +-Applying beta-rule and splitting (41), into two cases. % 3.76/1.70 |-Branch one: % 3.76/1.70 | (48) all_0_0_0 = 0 & all_0_1_1 = 0 % 3.76/1.70 | % 3.76/1.70 | Applying alpha-rule on (48) yields: % 3.76/1.70 | (45) all_0_0_0 = 0 % 3.76/1.70 | (50) all_0_1_1 = 0 % 3.76/1.70 | % 3.76/1.70 | From (45) and (40) follows: % 3.76/1.70 | (44) xsd_integer(all_0_2_2) = 0 % 3.76/1.70 | % 3.76/1.70 | Using (44) and (64) yields: % 3.76/1.70 | (32) $false % 3.76/1.70 | % 3.76/1.70 |-The branch is then unsatisfiable % 3.76/1.70 |-Branch two: % 3.76/1.71 | (53) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) % 3.76/1.71 | % 3.76/1.71 | Applying alpha-rule on (53) yields: % 3.76/1.71 | (54) ~ (all_0_0_0 = 0) % 3.76/1.71 | (55) ~ (all_0_1_1 = 0) % 3.76/1.71 | % 3.76/1.71 | Equations (50) can reduce 55 to: % 3.76/1.71 | (35) $false % 3.76/1.71 | % 3.76/1.71 |-The branch is then unsatisfiable % 3.76/1.71 |-Branch two: % 3.76/1.71 | (75) 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) % 3.76/1.71 | % 3.76/1.71 | Applying alpha-rule on (75) yields: % 3.76/1.71 | (76) cowlThing(all_0_2_2) = all_0_1_1 % 3.76/1.71 | (77) cowlNothing(all_0_2_2) = all_0_0_0 % 3.76/1.71 | (78) ~ (all_0_1_1 = 0) | all_0_0_0 = 0 % 3.76/1.71 | % 3.76/1.71 | Instantiating formula (9) with all_0_1_1, all_0_2_2 and discharging atoms cowlThing(all_0_2_2) = all_0_1_1, yields: % 3.76/1.71 | (50) all_0_1_1 = 0 % 3.76/1.71 | % 3.76/1.71 | Instantiating formula (3) with all_0_2_2 yields: % 3.76/1.71 | (80) ~ (cowlNothing(all_0_2_2) = 0) % 3.76/1.71 | % 3.76/1.71 +-Applying beta-rule and splitting (78), into two cases. % 3.76/1.71 |-Branch one: % 3.76/1.71 | (55) ~ (all_0_1_1 = 0) % 3.76/1.71 | % 3.76/1.71 | Equations (50) can reduce 55 to: % 3.76/1.71 | (35) $false % 3.76/1.71 | % 3.76/1.71 |-The branch is then unsatisfiable % 3.76/1.71 |-Branch two: % 3.76/1.71 | (50) all_0_1_1 = 0 % 3.76/1.71 | (45) all_0_0_0 = 0 % 3.76/1.71 | % 3.76/1.71 | From (45) and (77) follows: % 3.76/1.71 | (85) cowlNothing(all_0_2_2) = 0 % 3.76/1.71 | % 3.76/1.71 | Using (85) and (80) yields: % 3.76/1.71 | (32) $false % 3.76/1.71 | % 3.76/1.71 |-The branch is then unsatisfiable % 3.76/1.71 % SZS output end Proof for theBenchmark % 3.76/1.71 % 3.76/1.71 1076ms %------------------------------------------------------------------------------