%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET637+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n009.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 00:21:05 EDT 2022 % Result : Theorem 15.89s 4.87s % Output : Proof 43.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET637+3 : TPTP v8.1.0. Released v2.2.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n009.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sun Jul 10 23:37:07 EDT 2022 % 0.13/0.34 % CPUTime : % 0.60/0.59 ____ _ % 0.60/0.59 ___ / __ \_____(_)___ ________ __________ % 0.60/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.60/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.60/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.60/0.59 % 0.60/0.59 A Theorem Prover for First-Order Logic % 0.60/0.59 (ePrincess v.1.0) % 0.60/0.59 % 0.60/0.59 (c) Philipp Rümmer, 2009-2015 % 0.60/0.59 (c) Peter Backeman, 2014-2015 % 0.60/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.60/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.60/0.59 Bug reports to peter@backeman.se % 0.60/0.59 % 0.60/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.60/0.59 % 0.60/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.77/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.45/0.93 Prover 0: Preprocessing ... % 1.75/1.08 Prover 0: Warning: ignoring some quantifiers % 1.91/1.10 Prover 0: Constructing countermodel ... % 2.39/1.23 Prover 0: gave up % 2.39/1.23 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.44/1.25 Prover 1: Preprocessing ... % 2.67/1.32 Prover 1: Warning: ignoring some quantifiers % 2.67/1.33 Prover 1: Constructing countermodel ... % 2.86/1.38 Prover 1: gave up % 2.86/1.38 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.86/1.40 Prover 2: Preprocessing ... % 3.25/1.46 Prover 2: Warning: ignoring some quantifiers % 3.25/1.46 Prover 2: Constructing countermodel ... % 3.58/1.53 Prover 2: gave up % 3.58/1.53 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.65/1.55 Prover 3: Preprocessing ... % 3.65/1.56 Prover 3: Warning: ignoring some quantifiers % 3.65/1.57 Prover 3: Constructing countermodel ... % 3.65/1.59 Prover 3: gave up % 3.65/1.59 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 3.65/1.60 Prover 4: Preprocessing ... % 3.99/1.66 Prover 4: Warning: ignoring some quantifiers % 3.99/1.66 Prover 4: Constructing countermodel ... % 4.83/1.91 Prover 4: gave up % 4.83/1.91 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 5.25/1.92 Prover 5: Preprocessing ... % 5.25/1.96 Prover 5: Warning: ignoring some quantifiers % 5.25/1.96 Prover 5: Constructing countermodel ... % 5.58/2.04 Prover 5: gave up % 5.58/2.04 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 5.58/2.04 Prover 6: Preprocessing ... % 5.93/2.07 Prover 6: Warning: ignoring some quantifiers % 5.93/2.07 Prover 6: Constructing countermodel ... % 6.08/2.11 Prover 6: gave up % 6.08/2.11 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 6.08/2.11 Prover 7: Preprocessing ... % 6.19/2.13 Prover 7: Proving ... % 15.89/4.86 Prover 7: proved (2757ms) % 15.89/4.87 % 15.89/4.87 % SZS status Theorem for theBenchmark % 15.89/4.87 % 15.89/4.87 Generating proof ... found it (size 86) % 43.19/19.55 % 43.19/19.55 % SZS output start Proof for theBenchmark % 43.19/19.55 Assumed formulas after preprocessing and simplification: % 43.19/19.55 | (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 | not_equal(v1, v2)) & ! [v1] : ! [v2] : (v2 = v1 | ? [v3] : (( ~ member(v3, v2) | ~ member(v3, v1)) & (member(v3, v2) | member(v3, v1)))) & ! [v1] : ! [v2] : ( ~ intersect(v1, v2) | intersect(v2, v1)) & ! [v1] : ! [v2] : ( ~ intersect(v1, v2) | ? [v3] : (member(v3, v2) & member(v3, v1))) & ! [v1] : ! [v2] : (intersect(v1, v2) | ! [v3] : ( ~ member(v3, v2) | ~ member(v3, v1))) & ! [v1] : ( ~ empty(v1) | ! [v2] : ~ member(v2, v1)) & ! [v1] : ~ not_equal(v1, v1) & ! [v1] : ~ member(v1, v0) & ! [v1] : (empty(v1) | ? [v2] : member(v2, v1)) & ? [v1] : ? [v2] : ? [v3] : (intersection(v1, v2) = v3 & ((not_equal(v3, v0) & ~ intersect(v1, v2)) | (intersect(v1, v2) & ~ not_equal(v3, v0))))) % 43.19/19.58 | Instantiating (0) with all_0_0_0 yields: % 43.19/19.58 | (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 | not_equal(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) & ! [v0] : ! [v1] : ( ~ intersect(v0, v1) | intersect(v1, v0)) & ! [v0] : ! [v1] : ( ~ intersect(v0, v1) | ? [v2] : (member(v2, v1) & member(v2, v0))) & ! [v0] : ! [v1] : (intersect(v0, v1) | ! [v2] : ( ~ member(v2, v1) | ~ member(v2, v0))) & ! [v0] : ( ~ empty(v0) | ! [v1] : ~ member(v1, v0)) & ! [v0] : ~ not_equal(v0, v0) & ! [v0] : ~ member(v0, all_0_0_0) & ! [v0] : (empty(v0) | ? [v1] : member(v1, v0)) & ? [v0] : ? [v1] : ? [v2] : (intersection(v0, v1) = v2 & ((not_equal(v2, all_0_0_0) & ~ intersect(v0, v1)) | (intersect(v0, v1) & ~ not_equal(v2, all_0_0_0)))) % 43.19/19.58 | % 43.19/19.58 | Applying alpha-rule on (1) yields: % 43.19/19.58 | (2) ! [v0] : ~ not_equal(v0, v0) % 43.19/19.58 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 43.19/19.58 | (4) ! [v0] : ! [v1] : (v1 = v0 | not_equal(v0, v1)) % 43.19/19.58 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) % 43.19/19.58 | (6) ! [v0] : ! [v1] : ( ~ intersect(v0, v1) | ? [v2] : (member(v2, v1) & member(v2, v0))) % 43.19/19.58 | (7) ! [v0] : ! [v1] : (intersect(v0, v1) | ! [v2] : ( ~ member(v2, v1) | ~ member(v2, v0))) % 43.19/19.58 | (8) ! [v0] : (empty(v0) | ? [v1] : member(v1, v0)) % 43.19/19.58 | (9) ! [v0] : ! [v1] : ( ~ intersect(v0, v1) | intersect(v1, v0)) % 43.19/19.58 | (10) ! [v0] : ( ~ empty(v0) | ! [v1] : ~ member(v1, v0)) % 43.19/19.58 | (11) ? [v0] : ? [v1] : ? [v2] : (intersection(v0, v1) = v2 & ((not_equal(v2, all_0_0_0) & ~ intersect(v0, v1)) | (intersect(v0, v1) & ~ not_equal(v2, all_0_0_0)))) % 43.19/19.58 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | (member(v2, v1) & member(v2, v0))) % 43.19/19.58 | (13) ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) % 43.19/19.58 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v1) | ~ member(v2, v0) | member(v2, v3)) % 43.19/19.58 | (15) ! [v0] : ~ member(v0, all_0_0_0) % 43.19/19.58 | % 43.19/19.58 | Instantiating (11) with all_2_0_1, all_2_1_2, all_2_2_3 yields: % 43.19/19.58 | (16) intersection(all_2_2_3, all_2_1_2) = all_2_0_1 & ((not_equal(all_2_0_1, all_0_0_0) & ~ intersect(all_2_2_3, all_2_1_2)) | (intersect(all_2_2_3, all_2_1_2) & ~ not_equal(all_2_0_1, all_0_0_0))) % 43.19/19.58 | % 43.19/19.58 | Applying alpha-rule on (16) yields: % 43.19/19.58 | (17) intersection(all_2_2_3, all_2_1_2) = all_2_0_1 % 43.19/19.58 | (18) (not_equal(all_2_0_1, all_0_0_0) & ~ intersect(all_2_2_3, all_2_1_2)) | (intersect(all_2_2_3, all_2_1_2) & ~ not_equal(all_2_0_1, all_0_0_0)) % 43.19/19.58 | % 43.19/19.59 +-Applying beta-rule and splitting (18), into two cases. % 43.19/19.59 |-Branch one: % 43.19/19.59 | (19) not_equal(all_2_0_1, all_0_0_0) & ~ intersect(all_2_2_3, all_2_1_2) % 43.19/19.59 | % 43.19/19.59 | Applying alpha-rule on (19) yields: % 43.19/19.59 | (20) not_equal(all_2_0_1, all_0_0_0) % 43.19/19.59 | (21) ~ intersect(all_2_2_3, all_2_1_2) % 43.19/19.59 | % 43.19/19.59 | Instantiating formula (2) with all_0_0_0 yields: % 43.19/19.59 | (22) ~ not_equal(all_0_0_0, all_0_0_0) % 43.19/19.59 | % 43.19/19.59 | Introducing new symbol ex_36_1_8 defined by: % 43.19/19.59 | (23) ex_36_1_8 = all_2_1_2 % 43.19/19.59 | % 43.19/19.59 | Introducing new symbol ex_36_0_7 defined by: % 43.19/19.59 | (24) ex_36_0_7 = all_2_2_3 % 43.19/19.59 | % 43.19/19.59 | Instantiating formula (7) with ex_36_0_7, ex_36_1_8 yields: % 43.19/19.59 | (25) intersect(ex_36_1_8, ex_36_0_7) | ! [v0] : ( ~ member(v0, ex_36_0_7) | ~ member(v0, ex_36_1_8)) % 43.19/19.59 | % 43.19/19.59 +-Applying beta-rule and splitting (25), into two cases. % 43.19/19.59 |-Branch one: % 43.19/19.59 | (26) intersect(ex_36_1_8, ex_36_0_7) % 43.19/19.59 | % 43.19/19.59 | Instantiating formula (9) with ex_36_0_7, ex_36_1_8 and discharging atoms intersect(ex_36_1_8, ex_36_0_7), yields: % 43.19/19.59 | (27) intersect(ex_36_0_7, ex_36_1_8) % 43.19/19.59 | % 43.19/19.59 | From (24)(23) and (27) follows: % 43.19/19.59 | (28) intersect(all_2_2_3, all_2_1_2) % 43.19/19.59 | % 43.19/19.59 | Using (28) and (21) yields: % 43.19/19.59 | (29) $false % 43.19/19.59 | % 43.19/19.59 |-The branch is then unsatisfiable % 43.19/19.59 |-Branch two: % 43.19/19.59 | (30) ! [v0] : ( ~ member(v0, ex_36_0_7) | ~ member(v0, ex_36_1_8)) % 43.19/19.59 | % 43.19/19.59 | Introducing new symbol ex_54_0_17 defined by: % 43.19/19.59 | (31) ex_54_0_17 = all_2_0_1 % 43.19/19.59 | % 43.19/19.59 | Instantiating formula (8) with ex_54_0_17 yields: % 43.19/19.59 | (32) empty(ex_54_0_17) | ? [v0] : member(v0, ex_54_0_17) % 43.19/19.59 | % 43.19/19.59 +-Applying beta-rule and splitting (32), into two cases. % 43.19/19.59 |-Branch one: % 43.19/19.59 | (33) empty(ex_54_0_17) % 43.19/19.59 | % 43.19/19.59 | Instantiating formula (10) with ex_54_0_17 and discharging atoms empty(ex_54_0_17), yields: % 43.19/19.59 | (34) ! [v0] : ~ member(v0, ex_54_0_17) % 43.19/19.59 | % 43.19/19.59 | Introducing new symbol ex_65_1_26 defined by: % 43.19/19.59 | (35) ex_65_1_26 = all_2_0_1 % 43.19/19.59 | % 43.19/19.59 | Introducing new symbol ex_65_0_25 defined by: % 43.19/19.59 | (36) ex_65_0_25 = all_0_0_0 % 43.19/19.59 | % 43.19/19.59 | Instantiating formula (13) with ex_65_0_25, ex_65_1_26 yields: % 43.19/19.59 | (37) ex_65_0_25 = ex_65_1_26 | ? [v0] : (( ~ member(v0, ex_65_0_25) | ~ member(v0, ex_65_1_26)) & (member(v0, ex_65_0_25) | member(v0, ex_65_1_26))) % 43.19/19.59 | % 43.19/19.59 +-Applying beta-rule and splitting (37), into two cases. % 43.19/19.59 |-Branch one: % 43.19/19.59 | (38) ex_65_0_25 = ex_65_1_26 % 43.19/19.59 | % 43.19/19.59 | Combining equations (38,36) yields a new equation: % 43.19/19.59 | (39) ex_65_1_26 = all_0_0_0 % 43.19/19.59 | % 43.19/19.59 | Simplifying 39 yields: % 43.19/19.59 | (40) ex_65_1_26 = all_0_0_0 % 43.19/19.59 | % 43.19/19.59 | Combining equations (40,35) yields a new equation: % 43.19/19.59 | (41) all_2_0_1 = all_0_0_0 % 43.19/19.59 | % 43.19/19.59 | From (41) and (20) follows: % 43.19/19.59 | (42) not_equal(all_0_0_0, all_0_0_0) % 43.19/19.59 | % 43.19/19.59 | Using (42) and (22) yields: % 43.19/19.59 | (29) $false % 43.19/19.59 | % 43.19/19.59 |-The branch is then unsatisfiable % 43.19/19.59 |-Branch two: % 43.19/19.59 | (44) ? [v0] : (( ~ member(v0, ex_65_0_25) | ~ member(v0, ex_65_1_26)) & (member(v0, ex_65_0_25) | member(v0, ex_65_1_26))) % 43.19/19.59 | % 43.19/19.59 | Instantiating (44) with all_68_0_31 yields: % 43.19/19.59 | (45) ( ~ member(all_68_0_31, ex_65_0_25) | ~ member(all_68_0_31, ex_65_1_26)) & (member(all_68_0_31, ex_65_0_25) | member(all_68_0_31, ex_65_1_26)) % 43.19/19.59 | % 43.19/19.59 | Applying alpha-rule on (45) yields: % 43.19/19.59 | (46) ~ member(all_68_0_31, ex_65_0_25) | ~ member(all_68_0_31, ex_65_1_26) % 43.19/19.59 | (47) member(all_68_0_31, ex_65_0_25) | member(all_68_0_31, ex_65_1_26) % 43.19/19.59 | % 43.19/19.59 +-Applying beta-rule and splitting (46), into two cases. % 43.19/19.59 |-Branch one: % 43.19/19.59 | (48) ~ member(all_68_0_31, ex_65_0_25) % 43.19/19.59 | % 43.19/19.59 +-Applying beta-rule and splitting (47), into two cases. % 43.19/19.59 |-Branch one: % 43.19/19.59 | (49) member(all_68_0_31, ex_65_0_25) % 43.19/19.59 | % 43.19/19.59 | Using (49) and (48) yields: % 43.19/19.59 | (29) $false % 43.19/19.59 | % 43.19/19.59 |-The branch is then unsatisfiable % 43.19/19.59 |-Branch two: % 43.19/19.59 | (51) member(all_68_0_31, ex_65_1_26) % 43.19/19.59 | % 43.19/19.59 | Instantiating formula (34) with all_68_0_31 yields: % 43.19/19.59 | (52) ~ member(all_68_0_31, ex_54_0_17) % 43.19/19.59 | % 43.19/19.59 | From (35) and (51) follows: % 43.19/19.59 | (53) member(all_68_0_31, all_2_0_1) % 43.19/19.59 | % 43.19/19.59 | From (31) and (52) follows: % 43.19/19.59 | (54) ~ member(all_68_0_31, all_2_0_1) % 43.19/19.59 | % 43.19/19.59 | Using (53) and (54) yields: % 43.19/19.59 | (29) $false % 43.19/19.59 | % 43.19/19.59 |-The branch is then unsatisfiable % 43.19/19.59 |-Branch two: % 43.19/19.59 | (49) member(all_68_0_31, ex_65_0_25) % 43.19/19.59 | (57) ~ member(all_68_0_31, ex_65_1_26) % 43.19/19.59 | % 43.19/19.59 | Instantiating formula (15) with all_68_0_31 yields: % 43.19/19.59 | (58) ~ member(all_68_0_31, all_0_0_0) % 43.19/19.59 | % 43.19/19.59 | From (36) and (49) follows: % 43.19/19.59 | (59) member(all_68_0_31, all_0_0_0) % 43.19/19.59 | % 43.19/19.59 | Using (59) and (58) yields: % 43.19/19.59 | (29) $false % 43.19/19.59 | % 43.19/19.59 |-The branch is then unsatisfiable % 43.19/19.59 |-Branch two: % 43.19/19.59 | (61) ? [v0] : member(v0, ex_54_0_17) % 43.19/19.59 | % 43.19/19.59 | Instantiating (61) with all_56_0_19 yields: % 43.19/19.59 | (62) member(all_56_0_19, ex_54_0_17) % 43.19/19.59 | % 43.19/19.59 | Instantiating formula (30) with all_56_0_19 yields: % 43.19/19.59 | (63) ~ member(all_56_0_19, ex_36_0_7) | ~ member(all_56_0_19, ex_36_1_8) % 43.19/19.59 | % 43.19/19.59 | Instantiating formula (14) with all_2_0_1, all_56_0_19, all_2_2_3, all_2_2_3 yields: % 43.19/19.59 | (64) ~ (intersection(all_2_2_3, all_2_2_3) = all_2_0_1) | ~ member(all_56_0_19, all_2_2_3) | member(all_56_0_19, all_2_0_1) % 43.19/19.59 | % 43.19/19.59 | Instantiating formula (12) with all_2_0_1, all_56_0_19, 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: % 43.19/19.59 | (65) ~ member(all_56_0_19, all_2_0_1) | (member(all_56_0_19, all_2_1_2) & member(all_56_0_19, all_2_2_3)) % 43.19/19.59 | % 43.19/19.59 +-Applying beta-rule and splitting (63), into two cases. % 43.19/19.59 |-Branch one: % 43.19/19.59 | (66) ~ member(all_56_0_19, ex_36_0_7) % 43.19/19.59 | % 43.19/19.59 +-Applying beta-rule and splitting (64), into two cases. % 43.19/19.59 |-Branch one: % 43.19/19.59 | (67) ~ member(all_56_0_19, all_2_2_3) % 43.19/19.60 | % 43.19/19.60 +-Applying beta-rule and splitting (65), into two cases. % 43.19/19.60 |-Branch one: % 43.19/19.60 | (68) ~ member(all_56_0_19, all_2_0_1) % 43.19/19.60 | % 43.19/19.60 | From (31) and (62) follows: % 43.19/19.60 | (69) member(all_56_0_19, all_2_0_1) % 43.19/19.60 | % 43.19/19.60 | Using (69) and (68) yields: % 43.19/19.60 | (29) $false % 43.19/19.60 | % 43.19/19.60 |-The branch is then unsatisfiable % 43.19/19.60 |-Branch two: % 43.19/19.60 | (71) member(all_56_0_19, all_2_1_2) & member(all_56_0_19, all_2_2_3) % 43.19/19.60 | % 43.19/19.60 | Applying alpha-rule on (71) yields: % 43.19/19.60 | (72) member(all_56_0_19, all_2_1_2) % 43.19/19.60 | (73) member(all_56_0_19, all_2_2_3) % 43.19/19.60 | % 43.19/19.60 | Using (73) and (67) yields: % 43.19/19.60 | (29) $false % 43.19/19.60 | % 43.19/19.60 |-The branch is then unsatisfiable % 43.19/19.60 |-Branch two: % 43.19/19.60 | (73) member(all_56_0_19, all_2_2_3) % 43.19/19.60 | (76) ~ (intersection(all_2_2_3, all_2_2_3) = all_2_0_1) | member(all_56_0_19, all_2_0_1) % 43.19/19.60 | % 43.19/19.60 | From (24) and (66) follows: % 43.19/19.60 | (67) ~ member(all_56_0_19, all_2_2_3) % 43.19/19.60 | % 43.19/19.60 | Using (73) and (67) yields: % 43.19/19.60 | (29) $false % 43.19/19.60 | % 43.19/19.60 |-The branch is then unsatisfiable % 43.19/19.60 |-Branch two: % 43.19/19.60 | (79) ~ member(all_56_0_19, ex_36_1_8) % 43.19/19.60 | % 43.19/19.60 +-Applying beta-rule and splitting (65), into two cases. % 43.19/19.60 |-Branch one: % 43.19/19.60 | (68) ~ member(all_56_0_19, all_2_0_1) % 43.19/19.60 | % 43.19/19.60 | From (31) and (62) follows: % 43.19/19.60 | (69) member(all_56_0_19, all_2_0_1) % 43.19/19.60 | % 43.19/19.60 | Using (69) and (68) yields: % 43.19/19.60 | (29) $false % 43.19/19.60 | % 43.19/19.60 |-The branch is then unsatisfiable % 43.19/19.60 |-Branch two: % 43.19/19.60 | (71) member(all_56_0_19, all_2_1_2) & member(all_56_0_19, all_2_2_3) % 43.19/19.60 | % 43.19/19.60 | Applying alpha-rule on (71) yields: % 43.19/19.60 | (72) member(all_56_0_19, all_2_1_2) % 43.19/19.60 | (73) member(all_56_0_19, all_2_2_3) % 43.19/19.60 | % 43.19/19.60 | From (23) and (79) follows: % 43.19/19.60 | (86) ~ member(all_56_0_19, all_2_1_2) % 43.19/19.60 | % 43.19/19.60 | Using (72) and (86) yields: % 43.19/19.60 | (29) $false % 43.19/19.60 | % 43.19/19.60 |-The branch is then unsatisfiable % 43.19/19.60 |-Branch two: % 43.19/19.60 | (88) intersect(all_2_2_3, all_2_1_2) & ~ not_equal(all_2_0_1, all_0_0_0) % 43.19/19.60 | % 43.19/19.60 | Applying alpha-rule on (88) yields: % 43.19/19.60 | (28) intersect(all_2_2_3, all_2_1_2) % 43.19/19.60 | (90) ~ not_equal(all_2_0_1, all_0_0_0) % 43.19/19.60 | % 43.19/19.60 | Instantiating formula (6) with all_2_1_2, all_2_2_3 and discharging atoms intersect(all_2_2_3, all_2_1_2), yields: % 43.19/19.60 | (91) ? [v0] : (member(v0, all_2_1_2) & member(v0, all_2_2_3)) % 43.19/19.60 | % 43.19/19.60 | Instantiating (91) with all_35_0_77 yields: % 43.19/19.60 | (92) member(all_35_0_77, all_2_1_2) & member(all_35_0_77, all_2_2_3) % 43.19/19.60 | % 43.19/19.60 | Applying alpha-rule on (92) yields: % 43.19/19.60 | (93) member(all_35_0_77, all_2_1_2) % 43.19/19.60 | (94) member(all_35_0_77, all_2_2_3) % 43.19/19.60 | % 43.19/19.60 | Instantiating formula (15) with all_35_0_77 yields: % 43.19/19.60 | (95) ~ member(all_35_0_77, all_0_0_0) % 43.19/19.60 | % 43.19/19.60 | Instantiating formula (14) with all_2_0_1, all_35_0_77, all_2_1_2, all_2_2_3 and discharging atoms intersection(all_2_2_3, all_2_1_2) = all_2_0_1, member(all_35_0_77, all_2_1_2), member(all_35_0_77, all_2_2_3), yields: % 43.19/19.60 | (96) member(all_35_0_77, all_2_0_1) % 43.19/19.60 | % 43.19/19.60 | Introducing new symbol ex_89_1_89 defined by: % 43.19/19.60 | (97) ex_89_1_89 = all_2_0_1 % 43.19/19.60 | % 43.19/19.60 | Introducing new symbol ex_89_0_88 defined by: % 43.19/19.60 | (98) ex_89_0_88 = all_0_0_0 % 43.19/19.60 | % 43.19/19.60 | Instantiating formula (4) with ex_89_0_88, ex_89_1_89 yields: % 43.19/19.60 | (99) ex_89_0_88 = ex_89_1_89 | not_equal(ex_89_1_89, ex_89_0_88) % 43.19/19.60 | % 43.19/19.60 +-Applying beta-rule and splitting (99), into two cases. % 43.19/19.60 |-Branch one: % 43.19/19.60 | (100) not_equal(ex_89_1_89, ex_89_0_88) % 43.19/19.60 | % 43.19/19.60 | From (97)(98) and (100) follows: % 43.19/19.60 | (20) not_equal(all_2_0_1, all_0_0_0) % 43.19/19.60 | % 43.19/19.60 | Using (20) and (90) yields: % 43.19/19.60 | (29) $false % 43.19/19.60 | % 43.19/19.60 |-The branch is then unsatisfiable % 43.19/19.60 |-Branch two: % 43.19/19.60 | (103) ex_89_0_88 = ex_89_1_89 % 43.19/19.60 | % 43.19/19.60 | Combining equations (98,103) yields a new equation: % 43.19/19.60 | (104) ex_89_1_89 = all_0_0_0 % 43.19/19.60 | % 43.19/19.60 | Combining equations (104,97) yields a new equation: % 43.19/19.60 | (41) all_2_0_1 = all_0_0_0 % 43.19/19.60 | % 43.19/19.60 | From (41) and (96) follows: % 43.19/19.60 | (106) member(all_35_0_77, all_0_0_0) % 43.19/19.60 | % 43.19/19.60 | Using (106) and (95) yields: % 43.19/19.60 | (29) $false % 43.19/19.60 | % 43.19/19.60 |-The branch is then unsatisfiable % 43.19/19.60 % SZS output end Proof for theBenchmark % 43.19/19.60 % 43.19/19.60 19002ms %------------------------------------------------------------------------------