%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET636+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n025.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 00:21:04 EDT 2022 % Result : Theorem 18.12s 5.24s % Output : Proof 37.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SET636+3 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n025.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 : Mon Jul 11 04:21:02 EDT 2022 % 0.12/0.33 % CPUTime : % 0.54/0.56 ____ _ % 0.54/0.56 ___ / __ \_____(_)___ ________ __________ % 0.54/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.54/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.54/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.54/0.56 % 0.54/0.56 A Theorem Prover for First-Order Logic % 0.54/0.56 (ePrincess v.1.0) % 0.54/0.56 % 0.54/0.56 (c) Philipp Rümmer, 2009-2015 % 0.54/0.56 (c) Peter Backeman, 2014-2015 % 0.54/0.56 (contributions by Angelo Brillout, Peter Baumgartner) % 0.54/0.56 Free software under GNU Lesser General Public License (LGPL). % 0.54/0.56 Bug reports to peter@backeman.se % 0.54/0.56 % 0.54/0.56 For more information, visit http://user.uu.se/~petba168/breu/ % 0.54/0.56 % 0.54/0.56 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.59/0.61 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.38/0.87 Prover 0: Preprocessing ... % 1.87/1.03 Prover 0: Warning: ignoring some quantifiers % 1.87/1.05 Prover 0: Constructing countermodel ... % 2.39/1.19 Prover 0: gave up % 2.39/1.19 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.39/1.21 Prover 1: Preprocessing ... % 2.60/1.30 Prover 1: Warning: ignoring some quantifiers % 2.60/1.30 Prover 1: Constructing countermodel ... % 3.08/1.38 Prover 1: gave up % 3.08/1.38 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.08/1.39 Prover 2: Preprocessing ... % 3.48/1.47 Prover 2: Warning: ignoring some quantifiers % 3.48/1.48 Prover 2: Constructing countermodel ... % 3.89/1.57 Prover 2: gave up % 3.89/1.57 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.89/1.58 Prover 3: Preprocessing ... % 3.89/1.60 Prover 3: Warning: ignoring some quantifiers % 3.89/1.61 Prover 3: Constructing countermodel ... % 4.23/1.64 Prover 3: gave up % 4.23/1.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 4.23/1.65 Prover 4: Preprocessing ... % 4.48/1.71 Prover 4: Warning: ignoring some quantifiers % 4.48/1.72 Prover 4: Constructing countermodel ... % 6.37/2.12 Prover 4: gave up % 6.37/2.12 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 6.37/2.13 Prover 5: Preprocessing ... % 6.49/2.17 Prover 5: Warning: ignoring some quantifiers % 6.49/2.17 Prover 5: Constructing countermodel ... % 6.87/2.25 Prover 5: gave up % 6.87/2.26 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 6.87/2.26 Prover 6: Preprocessing ... % 7.19/2.30 Prover 6: Warning: ignoring some quantifiers % 7.19/2.30 Prover 6: Constructing countermodel ... % 7.19/2.34 Prover 6: gave up % 7.19/2.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 7.19/2.35 Prover 7: Preprocessing ... % 7.19/2.37 Prover 7: Proving ... % 18.12/5.24 Prover 7: proved (2895ms) % 18.12/5.24 % 18.12/5.24 % SZS status Theorem for theBenchmark % 18.12/5.24 % 18.12/5.24 Generating proof ... found it (size 87) % 37.03/12.07 % 37.03/12.07 % SZS output start Proof for theBenchmark % 37.03/12.07 Assumed formulas after preprocessing and simplification: % 37.03/12.07 | (0) ? [v0] : ( ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (intersection(v4, v3) = v2) | ~ (intersection(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v1, v2) = v4) | ~ member(v3, v4) | (member(v3, v2) & member(v3, v1))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v1, v2) = v4) | ~ member(v3, v2) | ~ member(v3, v1) | member(v3, v4)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | intersection(v2, v1) = v3) & ! [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] : ( ~ disjoint(v1, v2) | ~ intersect(v1, v2)) & ! [v1] : ! [v2] : ( ~ intersect(v1, v2) | intersect(v2, v1)) & ! [v1] : ! [v2] : ( ~ intersect(v1, v2) | ? [v3] : (member(v3, v2) & member(v3, v1))) & ! [v1] : ! [v2] : (subset(v1, v2) | ? [v3] : (member(v3, v1) & ~ member(v3, v2))) & ! [v1] : ! [v2] : (disjoint(v1, v2) | intersect(v1, v2)) & ! [v1] : ! [v2] : (intersect(v1, v2) | ! [v3] : ( ~ member(v3, v2) | ~ member(v3, v1))) & ! [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] : (intersection(v1, v2) = v3 & ((v3 = v0 & ~ disjoint(v1, v2)) | ( ~ (v3 = v0) & disjoint(v1, v2))))) % 37.10/12.10 | Instantiating (0) with all_0_0_0 yields: % 37.10/12.10 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | (member(v2, v1) & member(v2, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v1) | ~ member(v2, v0) | member(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) & ! [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] : ( ~ disjoint(v0, v1) | ~ intersect(v0, v1)) & ! [v0] : ! [v1] : ( ~ intersect(v0, v1) | intersect(v1, v0)) & ! [v0] : ! [v1] : ( ~ intersect(v0, v1) | ? [v2] : (member(v2, v1) & member(v2, v0))) & ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) & ! [v0] : ! [v1] : (disjoint(v0, v1) | intersect(v0, v1)) & ! [v0] : ! [v1] : (intersect(v0, v1) | ! [v2] : ( ~ member(v2, v1) | ~ member(v2, v0))) & ! [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] : (intersection(v0, v1) = v2 & ((v2 = all_0_0_0 & ~ disjoint(v0, v1)) | ( ~ (v2 = all_0_0_0) & disjoint(v0, v1)))) % 37.10/12.10 | % 37.10/12.10 | Applying alpha-rule on (1) yields: % 37.10/12.11 | (2) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ member(v2, v0) | member(v2, v1))) % 37.10/12.11 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | (member(v2, v1) & member(v2, v0))) % 37.10/12.11 | (4) ! [v0] : ! [v1] : (disjoint(v0, v1) | intersect(v0, v1)) % 37.10/12.11 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v1) | ~ member(v2, v0) | member(v2, v3)) % 37.10/12.11 | (6) ! [v0] : ! [v1] : ( ~ intersect(v0, v1) | ? [v2] : (member(v2, v1) & member(v2, v0))) % 37.10/12.11 | (7) ! [v0] : ! [v1] : ( ~ intersect(v0, v1) | intersect(v1, v0)) % 37.10/12.11 | (8) ! [v0] : ! [v1] : (intersect(v0, v1) | ! [v2] : ( ~ member(v2, v1) | ~ member(v2, v0))) % 37.10/12.11 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 37.10/12.11 | (10) ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) % 37.10/12.11 | (11) ! [v0] : ( ~ empty(v0) | ! [v1] : ~ member(v1, v0)) % 37.10/12.11 | (12) ? [v0] : ? [v1] : ? [v2] : (intersection(v0, v1) = v2 & ((v2 = all_0_0_0 & ~ disjoint(v0, v1)) | ( ~ (v2 = all_0_0_0) & disjoint(v0, v1)))) % 37.10/12.11 | (13) ! [v0] : ~ member(v0, all_0_0_0) % 37.10/12.11 | (14) ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) % 37.27/12.11 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) % 37.27/12.11 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 37.27/12.11 | (17) ! [v0] : subset(v0, v0) % 37.27/12.11 | (18) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | ~ intersect(v0, v1)) % 37.27/12.11 | (19) ! [v0] : (empty(v0) | ? [v1] : member(v1, v0)) % 37.27/12.11 | % 37.27/12.11 | Instantiating (12) with all_2_0_1, all_2_1_2, all_2_2_3 yields: % 37.27/12.11 | (20) intersection(all_2_2_3, all_2_1_2) = all_2_0_1 & ((all_2_0_1 = all_0_0_0 & ~ disjoint(all_2_2_3, all_2_1_2)) | ( ~ (all_2_0_1 = all_0_0_0) & disjoint(all_2_2_3, all_2_1_2))) % 37.27/12.11 | % 37.27/12.11 | Applying alpha-rule on (20) yields: % 37.27/12.11 | (21) intersection(all_2_2_3, all_2_1_2) = all_2_0_1 % 37.27/12.11 | (22) (all_2_0_1 = all_0_0_0 & ~ disjoint(all_2_2_3, all_2_1_2)) | ( ~ (all_2_0_1 = all_0_0_0) & disjoint(all_2_2_3, all_2_1_2)) % 37.27/12.11 | % 37.27/12.11 +-Applying beta-rule and splitting (22), into two cases. % 37.27/12.11 |-Branch one: % 37.27/12.11 | (23) all_2_0_1 = all_0_0_0 & ~ disjoint(all_2_2_3, all_2_1_2) % 37.27/12.11 | % 37.27/12.11 | Applying alpha-rule on (23) yields: % 37.27/12.11 | (24) all_2_0_1 = all_0_0_0 % 37.27/12.12 | (25) ~ disjoint(all_2_2_3, all_2_1_2) % 37.27/12.12 | % 37.27/12.12 | From (24) and (21) follows: % 37.27/12.12 | (26) intersection(all_2_2_3, all_2_1_2) = all_0_0_0 % 37.27/12.12 | % 37.27/12.12 | Introducing new symbol ex_45_1_12 defined by: % 37.27/12.12 | (27) ex_45_1_12 = all_2_2_3 % 37.27/12.12 | % 37.27/12.12 | Introducing new symbol ex_45_0_11 defined by: % 37.27/12.12 | (28) ex_45_0_11 = all_2_1_2 % 37.27/12.12 | % 37.27/12.12 | Instantiating formula (4) with ex_45_0_11, ex_45_1_12 yields: % 37.27/12.12 | (29) disjoint(ex_45_1_12, ex_45_0_11) | intersect(ex_45_1_12, ex_45_0_11) % 37.27/12.12 | % 37.27/12.12 +-Applying beta-rule and splitting (29), into two cases. % 37.27/12.12 |-Branch one: % 37.27/12.12 | (30) disjoint(ex_45_1_12, ex_45_0_11) % 37.27/12.12 | % 37.27/12.12 | From (27)(28) and (30) follows: % 37.27/12.12 | (31) disjoint(all_2_2_3, all_2_1_2) % 37.27/12.12 | % 37.27/12.12 | Using (31) and (25) yields: % 37.27/12.12 | (32) $false % 37.27/12.12 | % 37.27/12.12 |-The branch is then unsatisfiable % 37.27/12.12 |-Branch two: % 37.27/12.12 | (33) intersect(ex_45_1_12, ex_45_0_11) % 37.27/12.12 | % 37.27/12.12 | Instantiating formula (6) with ex_45_0_11, ex_45_1_12 and discharging atoms intersect(ex_45_1_12, ex_45_0_11), yields: % 37.27/12.12 | (34) ? [v0] : (member(v0, ex_45_0_11) & member(v0, ex_45_1_12)) % 37.27/12.12 | % 37.27/12.12 | Instantiating (34) with all_54_0_13 yields: % 37.27/12.12 | (35) member(all_54_0_13, ex_45_0_11) & member(all_54_0_13, ex_45_1_12) % 37.27/12.12 | % 37.27/12.12 | Applying alpha-rule on (35) yields: % 37.27/12.12 | (36) member(all_54_0_13, ex_45_0_11) % 37.27/12.12 | (37) member(all_54_0_13, ex_45_1_12) % 37.27/12.12 | % 37.27/12.12 | Instantiating formula (13) with all_54_0_13 yields: % 37.27/12.12 | (38) ~ member(all_54_0_13, all_0_0_0) % 37.27/12.12 | % 37.27/12.12 | Instantiating formula (5) with all_0_0_0, all_54_0_13, all_2_1_2, all_2_2_3 and discharging atoms intersection(all_2_2_3, all_2_1_2) = all_0_0_0, ~ member(all_54_0_13, all_0_0_0), yields: % 37.27/12.12 | (39) ~ member(all_54_0_13, all_2_1_2) | ~ member(all_54_0_13, all_2_2_3) % 37.27/12.12 | % 37.27/12.12 +-Applying beta-rule and splitting (39), into two cases. % 37.27/12.12 |-Branch one: % 37.27/12.12 | (40) ~ member(all_54_0_13, all_2_1_2) % 37.27/12.12 | % 37.27/12.12 | From (28) and (36) follows: % 37.27/12.12 | (41) member(all_54_0_13, all_2_1_2) % 37.27/12.12 | % 37.27/12.12 | Using (41) and (40) yields: % 37.27/12.12 | (32) $false % 37.27/12.12 | % 37.27/12.12 |-The branch is then unsatisfiable % 37.27/12.12 |-Branch two: % 37.27/12.12 | (43) ~ member(all_54_0_13, all_2_2_3) % 37.27/12.12 | % 37.27/12.12 | From (27) and (37) follows: % 37.27/12.12 | (44) member(all_54_0_13, all_2_2_3) % 37.27/12.12 | % 37.27/12.12 | Using (44) and (43) yields: % 37.27/12.12 | (32) $false % 37.27/12.12 | % 37.27/12.12 |-The branch is then unsatisfiable % 37.27/12.12 |-Branch two: % 37.27/12.12 | (46) ~ (all_2_0_1 = all_0_0_0) & disjoint(all_2_2_3, all_2_1_2) % 37.27/12.12 | % 37.27/12.12 | Applying alpha-rule on (46) yields: % 37.27/12.12 | (47) ~ (all_2_0_1 = all_0_0_0) % 37.27/12.12 | (31) disjoint(all_2_2_3, all_2_1_2) % 37.27/12.12 | % 37.27/12.12 | Introducing new symbol ex_40_1_23 defined by: % 37.27/12.12 | (49) ex_40_1_23 = all_2_1_2 % 37.27/12.12 | % 37.27/12.12 | Introducing new symbol ex_40_0_22 defined by: % 37.27/12.12 | (50) ex_40_0_22 = all_2_2_3 % 37.27/12.12 | % 37.27/12.12 | Instantiating formula (8) with ex_40_0_22, ex_40_1_23 yields: % 37.27/12.12 | (51) intersect(ex_40_1_23, ex_40_0_22) | ! [v0] : ( ~ member(v0, ex_40_0_22) | ~ member(v0, ex_40_1_23)) % 37.27/12.13 | % 37.27/12.13 +-Applying beta-rule and splitting (51), into two cases. % 37.27/12.13 |-Branch one: % 37.27/12.13 | (52) intersect(ex_40_1_23, ex_40_0_22) % 37.27/12.13 | % 37.27/12.13 | Instantiating formula (18) with all_2_1_2, all_2_2_3 and discharging atoms disjoint(all_2_2_3, all_2_1_2), yields: % 37.27/12.13 | (53) ~ intersect(all_2_2_3, all_2_1_2) % 37.27/12.13 | % 37.27/12.13 | Instantiating formula (7) with ex_40_0_22, ex_40_1_23 and discharging atoms intersect(ex_40_1_23, ex_40_0_22), yields: % 37.27/12.13 | (54) intersect(ex_40_0_22, ex_40_1_23) % 37.27/12.13 | % 37.27/12.13 | From (50)(49) and (54) follows: % 37.27/12.13 | (55) intersect(all_2_2_3, all_2_1_2) % 37.27/12.13 | % 37.27/12.13 | Using (55) and (53) yields: % 37.27/12.13 | (32) $false % 37.27/12.13 | % 37.27/12.13 |-The branch is then unsatisfiable % 37.27/12.13 |-Branch two: % 37.27/12.13 | (57) ! [v0] : ( ~ member(v0, ex_40_0_22) | ~ member(v0, ex_40_1_23)) % 37.27/12.13 | % 37.27/12.13 | Introducing new symbol ex_54_0_32 defined by: % 37.27/12.13 | (58) ex_54_0_32 = all_2_0_1 % 37.27/12.13 | % 37.27/12.13 | Instantiating formula (19) with ex_54_0_32 yields: % 37.27/12.13 | (59) empty(ex_54_0_32) | ? [v0] : member(v0, ex_54_0_32) % 37.27/12.13 | % 37.27/12.13 +-Applying beta-rule and splitting (59), into two cases. % 37.27/12.13 |-Branch one: % 37.27/12.13 | (60) empty(ex_54_0_32) % 37.27/12.13 | % 37.27/12.13 | Instantiating formula (11) with ex_54_0_32 and discharging atoms empty(ex_54_0_32), yields: % 37.27/12.13 | (61) ! [v0] : ~ member(v0, ex_54_0_32) % 37.27/12.13 | % 37.27/12.13 | Introducing new symbol ex_84_1_71 defined by: % 37.27/12.13 | (62) ex_84_1_71 = all_2_0_1 % 37.27/12.13 | % 37.27/12.13 | Introducing new symbol ex_84_0_70 defined by: % 37.27/12.13 | (63) ex_84_0_70 = all_0_0_0 % 37.27/12.13 | % 37.27/12.13 | Instantiating formula (10) with ex_84_0_70, ex_84_1_71 yields: % 37.27/12.13 | (64) ex_84_0_70 = ex_84_1_71 | ? [v0] : (( ~ member(v0, ex_84_0_70) | ~ member(v0, ex_84_1_71)) & (member(v0, ex_84_0_70) | member(v0, ex_84_1_71))) % 37.27/12.13 | % 37.27/12.13 +-Applying beta-rule and splitting (64), into two cases. % 37.27/12.13 |-Branch one: % 37.27/12.13 | (65) ex_84_0_70 = ex_84_1_71 % 37.27/12.13 | % 37.27/12.13 | Combining equations (63,65) yields a new equation: % 37.27/12.13 | (66) ex_84_1_71 = all_0_0_0 % 37.27/12.13 | % 37.27/12.13 | Combining equations (66,62) yields a new equation: % 37.27/12.13 | (24) all_2_0_1 = all_0_0_0 % 37.27/12.13 | % 37.27/12.13 | Equations (24) can reduce 47 to: % 37.27/12.13 | (68) $false % 37.27/12.13 | % 37.27/12.13 |-The branch is then unsatisfiable % 37.27/12.13 |-Branch two: % 37.27/12.13 | (69) ? [v0] : (( ~ member(v0, ex_84_0_70) | ~ member(v0, ex_84_1_71)) & (member(v0, ex_84_0_70) | member(v0, ex_84_1_71))) % 37.27/12.13 | % 37.27/12.13 | Instantiating (69) with all_87_0_76 yields: % 37.27/12.13 | (70) ( ~ member(all_87_0_76, ex_84_0_70) | ~ member(all_87_0_76, ex_84_1_71)) & (member(all_87_0_76, ex_84_0_70) | member(all_87_0_76, ex_84_1_71)) % 37.27/12.13 | % 37.27/12.13 | Applying alpha-rule on (70) yields: % 37.27/12.13 | (71) ~ member(all_87_0_76, ex_84_0_70) | ~ member(all_87_0_76, ex_84_1_71) % 37.27/12.13 | (72) member(all_87_0_76, ex_84_0_70) | member(all_87_0_76, ex_84_1_71) % 37.27/12.13 | % 37.27/12.13 +-Applying beta-rule and splitting (71), into two cases. % 37.27/12.13 |-Branch one: % 37.27/12.13 | (73) ~ member(all_87_0_76, ex_84_0_70) % 37.27/12.14 | % 37.27/12.14 +-Applying beta-rule and splitting (72), into two cases. % 37.27/12.14 |-Branch one: % 37.27/12.14 | (74) member(all_87_0_76, ex_84_0_70) % 37.27/12.14 | % 37.27/12.14 | Using (74) and (73) yields: % 37.27/12.14 | (32) $false % 37.27/12.14 | % 37.27/12.14 |-The branch is then unsatisfiable % 37.27/12.14 |-Branch two: % 37.27/12.14 | (76) member(all_87_0_76, ex_84_1_71) % 37.27/12.14 | % 37.27/12.14 | Instantiating formula (61) with all_87_0_76 yields: % 37.27/12.14 | (77) ~ member(all_87_0_76, ex_54_0_32) % 37.27/12.14 | % 37.27/12.14 | From (62) and (76) follows: % 37.27/12.14 | (78) member(all_87_0_76, all_2_0_1) % 37.27/12.14 | % 37.27/12.14 | From (58) and (77) follows: % 37.27/12.14 | (79) ~ member(all_87_0_76, all_2_0_1) % 37.27/12.14 | % 37.27/12.14 | Using (78) and (79) yields: % 37.27/12.14 | (32) $false % 37.27/12.14 | % 37.27/12.14 |-The branch is then unsatisfiable % 37.27/12.14 |-Branch two: % 37.27/12.14 | (74) member(all_87_0_76, ex_84_0_70) % 37.27/12.14 | (82) ~ member(all_87_0_76, ex_84_1_71) % 37.27/12.14 | % 37.27/12.14 | Instantiating formula (13) with all_87_0_76 yields: % 37.27/12.14 | (83) ~ member(all_87_0_76, all_0_0_0) % 37.27/12.14 | % 37.27/12.14 | From (63) and (74) follows: % 37.27/12.14 | (84) member(all_87_0_76, all_0_0_0) % 37.27/12.14 | % 37.27/12.14 | Using (84) and (83) yields: % 37.27/12.14 | (32) $false % 37.27/12.14 | % 37.27/12.14 |-The branch is then unsatisfiable % 37.27/12.14 |-Branch two: % 37.27/12.14 | (86) ? [v0] : member(v0, ex_54_0_32) % 37.27/12.14 | % 37.27/12.14 | Instantiating (86) with all_56_0_35 yields: % 37.27/12.14 | (87) member(all_56_0_35, ex_54_0_32) % 37.27/12.14 | % 37.27/12.14 | Instantiating formula (57) with all_56_0_35 yields: % 37.27/12.14 | (88) ~ member(all_56_0_35, ex_40_0_22) | ~ member(all_56_0_35, ex_40_1_23) % 37.27/12.14 | % 37.27/12.14 | Instantiating formula (5) with all_2_0_1, all_56_0_35, all_2_2_3, all_2_2_3 yields: % 37.27/12.14 | (89) ~ (intersection(all_2_2_3, all_2_2_3) = all_2_0_1) | ~ member(all_56_0_35, all_2_2_3) | member(all_56_0_35, all_2_0_1) % 37.27/12.14 | % 37.27/12.14 | Instantiating formula (3) with all_2_0_1, all_56_0_35, all_2_1_2, all_2_2_3 and discharging atoms intersection(all_2_2_3, all_2_1_2) = all_2_0_1, yields: % 37.27/12.14 | (90) ~ member(all_56_0_35, all_2_0_1) | (member(all_56_0_35, all_2_1_2) & member(all_56_0_35, all_2_2_3)) % 37.27/12.14 | % 37.27/12.14 +-Applying beta-rule and splitting (88), into two cases. % 37.27/12.14 |-Branch one: % 37.27/12.14 | (91) ~ member(all_56_0_35, ex_40_0_22) % 37.27/12.14 | % 37.27/12.14 +-Applying beta-rule and splitting (89), into two cases. % 37.27/12.14 |-Branch one: % 37.27/12.14 | (92) ~ member(all_56_0_35, all_2_2_3) % 37.27/12.14 | % 37.27/12.14 +-Applying beta-rule and splitting (90), into two cases. % 37.27/12.14 |-Branch one: % 37.27/12.14 | (93) ~ member(all_56_0_35, all_2_0_1) % 37.27/12.14 | % 37.27/12.14 | From (58) and (87) follows: % 37.27/12.14 | (94) member(all_56_0_35, all_2_0_1) % 37.27/12.14 | % 37.27/12.14 | Using (94) and (93) yields: % 37.27/12.14 | (32) $false % 37.27/12.14 | % 37.27/12.14 |-The branch is then unsatisfiable % 37.27/12.14 |-Branch two: % 37.27/12.14 | (96) member(all_56_0_35, all_2_1_2) & member(all_56_0_35, all_2_2_3) % 37.27/12.14 | % 37.27/12.14 | Applying alpha-rule on (96) yields: % 37.27/12.14 | (97) member(all_56_0_35, all_2_1_2) % 37.27/12.14 | (98) member(all_56_0_35, all_2_2_3) % 37.27/12.14 | % 37.27/12.14 | Using (98) and (92) yields: % 37.27/12.14 | (32) $false % 37.27/12.14 | % 37.27/12.14 |-The branch is then unsatisfiable % 37.27/12.14 |-Branch two: % 37.27/12.14 | (98) member(all_56_0_35, all_2_2_3) % 37.27/12.14 | (101) ~ (intersection(all_2_2_3, all_2_2_3) = all_2_0_1) | member(all_56_0_35, all_2_0_1) % 37.27/12.14 | % 37.27/12.14 | From (50) and (91) follows: % 37.27/12.14 | (92) ~ member(all_56_0_35, all_2_2_3) % 37.27/12.14 | % 37.27/12.14 | Using (98) and (92) yields: % 37.27/12.14 | (32) $false % 37.27/12.14 | % 37.27/12.14 |-The branch is then unsatisfiable % 37.27/12.14 |-Branch two: % 37.27/12.14 | (104) ~ member(all_56_0_35, ex_40_1_23) % 37.27/12.14 | % 37.27/12.14 +-Applying beta-rule and splitting (90), into two cases. % 37.27/12.14 |-Branch one: % 37.27/12.14 | (93) ~ member(all_56_0_35, all_2_0_1) % 37.27/12.14 | % 37.27/12.14 | From (58) and (87) follows: % 37.27/12.14 | (94) member(all_56_0_35, all_2_0_1) % 37.27/12.14 | % 37.27/12.14 | Using (94) and (93) yields: % 37.27/12.14 | (32) $false % 37.27/12.14 | % 37.27/12.14 |-The branch is then unsatisfiable % 37.27/12.14 |-Branch two: % 37.27/12.14 | (96) member(all_56_0_35, all_2_1_2) & member(all_56_0_35, all_2_2_3) % 37.27/12.14 | % 37.27/12.14 | Applying alpha-rule on (96) yields: % 37.27/12.14 | (97) member(all_56_0_35, all_2_1_2) % 37.27/12.14 | (98) member(all_56_0_35, all_2_2_3) % 37.27/12.14 | % 37.27/12.14 | From (49) and (104) follows: % 37.27/12.14 | (111) ~ member(all_56_0_35, all_2_1_2) % 37.27/12.15 | % 37.27/12.15 | Using (97) and (111) yields: % 37.27/12.15 | (32) $false % 37.27/12.15 | % 37.27/12.15 |-The branch is then unsatisfiable % 37.42/12.15 % SZS output end Proof for theBenchmark % 37.42/12.15 % 37.42/12.15 11572ms %------------------------------------------------------------------------------