%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET587+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n021.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 : Tue Jul 19 00:20:29 EDT 2022 % Result : Theorem 11.57s 3.64s % Output : Proof 14.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SET587+3 : TPTP v8.1.0. Released v2.2.0. % 0.04/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n021.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 : Sat Jul 9 18:22:51 EDT 2022 % 0.12/0.34 % CPUTime : % 0.53/0.58 ____ _ % 0.53/0.58 ___ / __ \_____(_)___ ________ __________ % 0.53/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.53/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.53/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.53/0.58 % 0.53/0.58 A Theorem Prover for First-Order Logic % 0.53/0.59 (ePrincess v.1.0) % 0.53/0.59 % 0.53/0.59 (c) Philipp Rümmer, 2009-2015 % 0.53/0.59 (c) Peter Backeman, 2014-2015 % 0.53/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.53/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.53/0.59 Bug reports to peter@backeman.se % 0.53/0.59 % 0.53/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.53/0.59 % 0.53/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.41/0.89 Prover 0: Preprocessing ... % 1.66/1.02 Prover 0: Warning: ignoring some quantifiers % 1.82/1.04 Prover 0: Constructing countermodel ... % 2.18/1.16 Prover 0: gave up % 2.18/1.17 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.27/1.18 Prover 1: Preprocessing ... % 2.50/1.26 Prover 1: Warning: ignoring some quantifiers % 2.50/1.27 Prover 1: Constructing countermodel ... % 2.50/1.31 Prover 1: gave up % 2.50/1.32 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.70/1.34 Prover 2: Preprocessing ... % 3.21/1.44 Prover 2: Warning: ignoring some quantifiers % 3.21/1.45 Prover 2: Constructing countermodel ... % 3.36/1.50 Prover 2: gave up % 3.36/1.51 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.36/1.52 Prover 3: Preprocessing ... % 3.62/1.54 Prover 3: Warning: ignoring some quantifiers % 3.62/1.54 Prover 3: Constructing countermodel ... % 3.71/1.57 Prover 3: gave up % 3.71/1.57 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 3.71/1.59 Prover 4: Preprocessing ... % 4.03/1.65 Prover 4: Warning: ignoring some quantifiers % 4.03/1.66 Prover 4: Constructing countermodel ... % 5.46/2.00 Prover 4: gave up % 5.46/2.00 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 5.46/2.00 Prover 5: Preprocessing ... % 5.46/2.04 Prover 5: Warning: ignoring some quantifiers % 5.46/2.04 Prover 5: Constructing countermodel ... % 5.83/2.07 Prover 5: gave up % 5.83/2.07 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 5.83/2.08 Prover 6: Preprocessing ... % 5.93/2.10 Prover 6: Warning: ignoring some quantifiers % 5.93/2.10 Prover 6: Constructing countermodel ... % 6.11/2.12 Prover 6: gave up % 6.11/2.12 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 6.11/2.13 Prover 7: Preprocessing ... % 6.11/2.14 Prover 7: Proving ... % 11.57/3.64 Prover 7: proved (1520ms) % 11.57/3.64 % 11.57/3.64 % SZS status Theorem for theBenchmark % 11.57/3.64 % 11.57/3.64 Generating proof ... found it (size 62) % 14.44/4.43 % 14.44/4.43 % SZS output start Proof for theBenchmark % 14.44/4.43 Assumed formulas after preprocessing and simplification: % 14.44/4.43 | (0) ? [v0] : ( ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (difference(v4, v3) = v2) | ~ (difference(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v2) = v4) | ~ member(v3, v4) | (member(v3, v1) & ~ member(v3, v2))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v2) = v4) | ~ member(v3, v1) | member(v3, v4) | member(v3, v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ subset(v2, v1) | ~ subset(v1, v2)) & ! [v1] : ! [v2] : (v2 = v1 | ? [v3] : (( ~ member(v3, v2) | ~ member(v3, v1)) & (member(v3, v2) | member(v3, v1)))) & ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ! [v3] : ( ~ member(v3, v1) | member(v3, v2))) & ! [v1] : ! [v2] : (subset(v1, v2) | ? [v3] : (member(v3, v1) & ~ member(v3, v2))) & ! [v1] : ( ~ empty(v1) | ! [v2] : ~ member(v2, v1)) & ! [v1] : ~ member(v1, v0) & ! [v1] : (empty(v1) | ? [v2] : member(v2, v1)) & ! [v1] : subset(v1, v1) & ? [v1] : ? [v2] : ? [v3] : (difference(v1, v2) = v3 & ((v3 = v0 & ~ subset(v1, v2)) | ( ~ (v3 = v0) & subset(v1, v2))))) % 14.73/4.45 | Instantiating (0) with all_0_0_0 yields: % 14.73/4.45 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | (member(v2, v0) & ~ member(v2, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ member(v2, v0) | member(v2, v1))) & ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) & ! [v0] : ( ~ empty(v0) | ! [v1] : ~ member(v1, v0)) & ! [v0] : ~ member(v0, all_0_0_0) & ! [v0] : (empty(v0) | ? [v1] : member(v1, v0)) & ! [v0] : subset(v0, v0) & ? [v0] : ? [v1] : ? [v2] : (difference(v0, v1) = v2 & ((v2 = all_0_0_0 & ~ subset(v0, v1)) | ( ~ (v2 = all_0_0_0) & subset(v0, v1)))) % 14.73/4.45 | % 14.73/4.45 | Applying alpha-rule on (1) yields: % 14.73/4.45 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1)) % 14.73/4.45 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | (member(v2, v0) & ~ member(v2, v1))) % 14.73/4.45 | (4) ? [v0] : ? [v1] : ? [v2] : (difference(v0, v1) = v2 & ((v2 = all_0_0_0 & ~ subset(v0, v1)) | ( ~ (v2 = all_0_0_0) & subset(v0, v1)))) % 14.73/4.45 | (5) ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) % 14.73/4.46 | (6) ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) % 14.73/4.46 | (7) ! [v0] : ~ member(v0, all_0_0_0) % 14.73/4.46 | (8) ! [v0] : ( ~ empty(v0) | ! [v1] : ~ member(v1, v0)) % 14.73/4.46 | (9) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ member(v2, v0) | member(v2, v1))) % 14.73/4.46 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 14.73/4.46 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 14.84/4.46 | (12) ! [v0] : subset(v0, v0) % 14.84/4.46 | (13) ! [v0] : (empty(v0) | ? [v1] : member(v1, v0)) % 14.84/4.46 | % 14.84/4.46 | Instantiating (4) with all_2_0_1, all_2_1_2, all_2_2_3 yields: % 14.84/4.46 | (14) difference(all_2_2_3, all_2_1_2) = all_2_0_1 & ((all_2_0_1 = all_0_0_0 & ~ subset(all_2_2_3, all_2_1_2)) | ( ~ (all_2_0_1 = all_0_0_0) & subset(all_2_2_3, all_2_1_2))) % 14.84/4.46 | % 14.84/4.46 | Applying alpha-rule on (14) yields: % 14.84/4.46 | (15) difference(all_2_2_3, all_2_1_2) = all_2_0_1 % 14.84/4.46 | (16) (all_2_0_1 = all_0_0_0 & ~ subset(all_2_2_3, all_2_1_2)) | ( ~ (all_2_0_1 = all_0_0_0) & subset(all_2_2_3, all_2_1_2)) % 14.84/4.46 | % 14.84/4.46 +-Applying beta-rule and splitting (16), into two cases. % 14.84/4.46 |-Branch one: % 14.84/4.46 | (17) all_2_0_1 = all_0_0_0 & ~ subset(all_2_2_3, all_2_1_2) % 14.84/4.46 | % 14.84/4.46 | Applying alpha-rule on (17) yields: % 14.84/4.46 | (18) all_2_0_1 = all_0_0_0 % 14.84/4.46 | (19) ~ subset(all_2_2_3, all_2_1_2) % 14.84/4.46 | % 14.84/4.46 | From (18) and (15) follows: % 14.84/4.46 | (20) difference(all_2_2_3, all_2_1_2) = all_0_0_0 % 14.84/4.46 | % 14.84/4.46 | Introducing new symbol ex_26_1_8 defined by: % 14.84/4.46 | (21) ex_26_1_8 = all_2_2_3 % 14.84/4.46 | % 14.84/4.46 | Introducing new symbol ex_26_0_7 defined by: % 14.84/4.46 | (22) ex_26_0_7 = all_2_1_2 % 14.84/4.46 | % 14.84/4.46 | Instantiating formula (5) with ex_26_0_7, ex_26_1_8 yields: % 14.84/4.46 | (23) subset(ex_26_1_8, ex_26_0_7) | ? [v0] : (member(v0, ex_26_1_8) & ~ member(v0, ex_26_0_7)) % 14.84/4.46 | % 14.84/4.46 +-Applying beta-rule and splitting (23), into two cases. % 14.84/4.46 |-Branch one: % 14.84/4.46 | (24) subset(ex_26_1_8, ex_26_0_7) % 14.84/4.46 | % 14.84/4.46 | From (21)(22) and (24) follows: % 14.84/4.46 | (25) subset(all_2_2_3, all_2_1_2) % 14.84/4.46 | % 14.84/4.46 | Using (25) and (19) yields: % 14.84/4.46 | (26) $false % 14.84/4.46 | % 14.84/4.46 |-The branch is then unsatisfiable % 14.84/4.46 |-Branch two: % 14.84/4.46 | (27) ? [v0] : (member(v0, ex_26_1_8) & ~ member(v0, ex_26_0_7)) % 14.84/4.46 | % 14.84/4.46 | Instantiating (27) with all_28_0_9 yields: % 14.84/4.46 | (28) member(all_28_0_9, ex_26_1_8) & ~ member(all_28_0_9, ex_26_0_7) % 14.84/4.46 | % 14.84/4.46 | Applying alpha-rule on (28) yields: % 14.84/4.46 | (29) member(all_28_0_9, ex_26_1_8) % 14.84/4.46 | (30) ~ member(all_28_0_9, ex_26_0_7) % 14.84/4.46 | % 14.84/4.46 | Instantiating formula (7) with all_28_0_9 yields: % 14.84/4.46 | (31) ~ member(all_28_0_9, all_0_0_0) % 14.84/4.46 | % 14.84/4.46 | Instantiating formula (2) with all_0_0_0, all_28_0_9, all_2_1_2, all_2_2_3 and discharging atoms difference(all_2_2_3, all_2_1_2) = all_0_0_0, ~ member(all_28_0_9, all_0_0_0), yields: % 14.84/4.47 | (32) ~ member(all_28_0_9, all_2_2_3) | member(all_28_0_9, all_2_1_2) % 14.84/4.47 | % 14.84/4.47 +-Applying beta-rule and splitting (32), into two cases. % 14.84/4.47 |-Branch one: % 14.84/4.47 | (33) ~ member(all_28_0_9, all_2_2_3) % 14.84/4.47 | % 14.84/4.47 | From (21) and (29) follows: % 14.84/4.47 | (34) member(all_28_0_9, all_2_2_3) % 14.84/4.47 | % 14.84/4.47 | Using (34) and (33) yields: % 14.84/4.47 | (26) $false % 14.84/4.47 | % 14.84/4.47 |-The branch is then unsatisfiable % 14.84/4.47 |-Branch two: % 14.84/4.47 | (36) member(all_28_0_9, all_2_1_2) % 14.84/4.47 | % 14.84/4.47 | From (22) and (30) follows: % 14.84/4.47 | (37) ~ member(all_28_0_9, all_2_1_2) % 14.84/4.47 | % 14.84/4.47 | Using (36) and (37) yields: % 14.84/4.47 | (26) $false % 14.84/4.47 | % 14.84/4.47 |-The branch is then unsatisfiable % 14.84/4.47 |-Branch two: % 14.84/4.47 | (39) ~ (all_2_0_1 = all_0_0_0) & subset(all_2_2_3, all_2_1_2) % 14.84/4.47 | % 14.84/4.47 | Applying alpha-rule on (39) yields: % 14.84/4.47 | (40) ~ (all_2_0_1 = all_0_0_0) % 14.84/4.47 | (25) subset(all_2_2_3, all_2_1_2) % 14.84/4.47 | % 14.84/4.47 | Instantiating formula (9) with all_2_1_2, all_2_2_3 and discharging atoms subset(all_2_2_3, all_2_1_2), yields: % 14.84/4.47 | (42) ! [v0] : ( ~ member(v0, all_2_2_3) | member(v0, all_2_1_2)) % 14.84/4.47 | % 14.84/4.47 | Introducing new symbol ex_19_1_11 defined by: % 14.84/4.47 | (43) ex_19_1_11 = all_2_0_1 % 14.84/4.47 | % 14.84/4.47 | Introducing new symbol ex_19_0_10 defined by: % 14.84/4.47 | (44) ex_19_0_10 = all_0_0_0 % 14.84/4.47 | % 14.84/4.47 | Instantiating formula (6) with ex_19_0_10, ex_19_1_11 yields: % 14.84/4.47 | (45) ex_19_0_10 = ex_19_1_11 | ? [v0] : (( ~ member(v0, ex_19_0_10) | ~ member(v0, ex_19_1_11)) & (member(v0, ex_19_0_10) | member(v0, ex_19_1_11))) % 14.84/4.47 | % 14.84/4.47 +-Applying beta-rule and splitting (45), into two cases. % 14.84/4.47 |-Branch one: % 14.84/4.47 | (46) ex_19_0_10 = ex_19_1_11 % 14.84/4.47 | % 14.84/4.47 | Combining equations (44,46) yields a new equation: % 14.84/4.47 | (47) ex_19_1_11 = all_0_0_0 % 14.84/4.47 | % 14.84/4.47 | Combining equations (47,43) yields a new equation: % 14.84/4.47 | (18) all_2_0_1 = all_0_0_0 % 14.84/4.47 | % 14.84/4.47 | Equations (18) can reduce 40 to: % 14.84/4.47 | (49) $false % 14.84/4.47 | % 14.84/4.47 |-The branch is then unsatisfiable % 14.84/4.47 |-Branch two: % 14.84/4.47 | (50) ? [v0] : (( ~ member(v0, ex_19_0_10) | ~ member(v0, ex_19_1_11)) & (member(v0, ex_19_0_10) | member(v0, ex_19_1_11))) % 14.84/4.47 | % 14.84/4.47 | Instantiating (50) with all_22_0_12 yields: % 14.84/4.47 | (51) ( ~ member(all_22_0_12, ex_19_0_10) | ~ member(all_22_0_12, ex_19_1_11)) & (member(all_22_0_12, ex_19_0_10) | member(all_22_0_12, ex_19_1_11)) % 14.84/4.47 | % 14.84/4.47 | Applying alpha-rule on (51) yields: % 14.84/4.47 | (52) ~ member(all_22_0_12, ex_19_0_10) | ~ member(all_22_0_12, ex_19_1_11) % 14.84/4.47 | (53) member(all_22_0_12, ex_19_0_10) | member(all_22_0_12, ex_19_1_11) % 14.84/4.47 | % 14.84/4.47 +-Applying beta-rule and splitting (52), into two cases. % 14.84/4.47 |-Branch one: % 14.84/4.47 | (54) ~ member(all_22_0_12, ex_19_0_10) % 14.84/4.47 | % 14.84/4.47 +-Applying beta-rule and splitting (53), into two cases. % 14.84/4.47 |-Branch one: % 14.84/4.47 | (55) member(all_22_0_12, ex_19_0_10) % 14.84/4.47 | % 14.84/4.47 | Using (55) and (54) yields: % 14.84/4.47 | (26) $false % 14.84/4.47 | % 14.84/4.47 |-The branch is then unsatisfiable % 14.84/4.47 |-Branch two: % 14.84/4.47 | (57) member(all_22_0_12, ex_19_1_11) % 14.84/4.47 | % 14.84/4.47 | Instantiating formula (3) with all_2_0_1, all_22_0_12, all_2_1_2, all_2_2_3 and discharging atoms difference(all_2_2_3, all_2_1_2) = all_2_0_1, yields: % 14.84/4.47 | (58) ~ member(all_22_0_12, all_2_0_1) | (member(all_22_0_12, all_2_2_3) & ~ member(all_22_0_12, all_2_1_2)) % 14.84/4.47 | % 14.84/4.47 | Instantiating formula (42) with all_22_0_12 yields: % 14.84/4.47 | (59) ~ member(all_22_0_12, all_2_2_3) | member(all_22_0_12, all_2_1_2) % 14.84/4.47 | % 14.84/4.47 +-Applying beta-rule and splitting (59), into two cases. % 14.84/4.47 |-Branch one: % 14.84/4.47 | (60) ~ member(all_22_0_12, all_2_2_3) % 14.84/4.47 | % 14.84/4.47 +-Applying beta-rule and splitting (58), into two cases. % 14.84/4.47 |-Branch one: % 14.84/4.47 | (61) ~ member(all_22_0_12, all_2_0_1) % 14.84/4.47 | % 14.84/4.47 | From (43) and (57) follows: % 14.84/4.47 | (62) member(all_22_0_12, all_2_0_1) % 14.84/4.47 | % 14.84/4.47 | Using (62) and (61) yields: % 14.84/4.47 | (26) $false % 14.84/4.47 | % 14.84/4.47 |-The branch is then unsatisfiable % 14.84/4.47 |-Branch two: % 14.84/4.48 | (64) member(all_22_0_12, all_2_2_3) & ~ member(all_22_0_12, all_2_1_2) % 14.84/4.48 | % 14.84/4.48 | Applying alpha-rule on (64) yields: % 14.84/4.48 | (65) member(all_22_0_12, all_2_2_3) % 14.84/4.48 | (66) ~ member(all_22_0_12, all_2_1_2) % 14.84/4.48 | % 14.84/4.48 | Using (65) and (60) yields: % 14.84/4.48 | (26) $false % 14.84/4.48 | % 14.84/4.48 |-The branch is then unsatisfiable % 14.84/4.48 |-Branch two: % 14.84/4.48 | (68) member(all_22_0_12, all_2_1_2) % 14.84/4.48 | % 14.84/4.48 +-Applying beta-rule and splitting (58), into two cases. % 14.84/4.48 |-Branch one: % 14.84/4.48 | (61) ~ member(all_22_0_12, all_2_0_1) % 14.84/4.48 | % 14.84/4.48 | From (43) and (57) follows: % 14.84/4.48 | (62) member(all_22_0_12, all_2_0_1) % 14.84/4.48 | % 14.84/4.48 | Using (62) and (61) yields: % 14.84/4.48 | (26) $false % 14.84/4.48 | % 14.84/4.48 |-The branch is then unsatisfiable % 14.84/4.48 |-Branch two: % 14.84/4.48 | (64) member(all_22_0_12, all_2_2_3) & ~ member(all_22_0_12, all_2_1_2) % 14.84/4.48 | % 14.84/4.48 | Applying alpha-rule on (64) yields: % 14.84/4.48 | (65) member(all_22_0_12, all_2_2_3) % 14.84/4.48 | (66) ~ member(all_22_0_12, all_2_1_2) % 14.84/4.48 | % 14.84/4.48 | Using (68) and (66) yields: % 14.84/4.48 | (26) $false % 14.84/4.48 | % 14.84/4.48 |-The branch is then unsatisfiable % 14.84/4.48 |-Branch two: % 14.84/4.48 | (55) member(all_22_0_12, ex_19_0_10) % 14.84/4.48 | (77) ~ member(all_22_0_12, ex_19_1_11) % 14.84/4.48 | % 14.84/4.48 | Instantiating formula (7) with all_22_0_12 yields: % 14.84/4.48 | (78) ~ member(all_22_0_12, all_0_0_0) % 14.84/4.48 | % 14.84/4.48 | From (44) and (55) follows: % 14.84/4.48 | (79) member(all_22_0_12, all_0_0_0) % 14.84/4.48 | % 14.84/4.48 | Using (79) and (78) yields: % 14.84/4.48 | (26) $false % 14.84/4.48 | % 14.84/4.48 |-The branch is then unsatisfiable % 14.84/4.48 % SZS output end Proof for theBenchmark % 14.84/4.48 % 14.84/4.48 3883ms %------------------------------------------------------------------------------