%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET577+3 : TPTP v8.1.0. Released v2.2.0. % 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 : Tue Jul 19 00:20:23 EDT 2022 % Result : Theorem 32.81s 14.14s % Output : Proof 53.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET577+3 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n020.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sun Jul 10 01:59:58 EDT 2022 % 0.12/0.34 % CPUTime : % 0.64/0.63 ____ _ % 0.64/0.63 ___ / __ \_____(_)___ ________ __________ % 0.64/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.64/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.64/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.64/0.63 % 0.64/0.63 A Theorem Prover for First-Order Logic % 0.64/0.63 (ePrincess v.1.0) % 0.64/0.63 % 0.64/0.63 (c) Philipp Rümmer, 2009-2015 % 0.64/0.63 (c) Peter Backeman, 2014-2015 % 0.64/0.63 (contributions by Angelo Brillout, Peter Baumgartner) % 0.64/0.63 Free software under GNU Lesser General Public License (LGPL). % 0.64/0.63 Bug reports to peter@backeman.se % 0.64/0.63 % 0.64/0.63 For more information, visit http://user.uu.se/~petba168/breu/ % 0.64/0.63 % 0.64/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.76/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.39/0.97 Prover 0: Preprocessing ... % 1.73/1.12 Prover 0: Warning: ignoring some quantifiers % 1.88/1.14 Prover 0: Constructing countermodel ... % 2.25/1.26 Prover 0: gave up % 2.25/1.26 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.33/1.27 Prover 1: Preprocessing ... % 2.61/1.34 Prover 1: Warning: ignoring some quantifiers % 2.61/1.35 Prover 1: Constructing countermodel ... % 2.72/1.38 Prover 1: gave up % 2.72/1.38 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.72/1.39 Prover 2: Preprocessing ... % 3.03/1.46 Prover 2: Warning: ignoring some quantifiers % 3.03/1.47 Prover 2: Constructing countermodel ... % 3.20/1.50 Prover 2: gave up % 3.20/1.51 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.20/1.52 Prover 3: Preprocessing ... % 3.47/1.53 Prover 3: Warning: ignoring some quantifiers % 3.47/1.54 Prover 3: Constructing countermodel ... % 3.61/1.56 Prover 3: gave up % 3.61/1.56 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 3.61/1.57 Prover 4: Preprocessing ... % 3.99/1.64 Prover 4: Warning: ignoring some quantifiers % 3.99/1.65 Prover 4: Constructing countermodel ... % 5.51/2.01 Prover 4: gave up % 5.51/2.01 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 5.51/2.02 Prover 5: Preprocessing ... % 5.92/2.08 Prover 5: Warning: ignoring some quantifiers % 5.92/2.09 Prover 5: Constructing countermodel ... % 6.12/2.12 Prover 5: gave up % 6.12/2.13 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 6.12/2.14 Prover 6: Preprocessing ... % 6.30/2.17 Prover 6: Warning: ignoring some quantifiers % 6.30/2.17 Prover 6: Constructing countermodel ... % 6.30/2.19 Prover 6: gave up % 6.30/2.20 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 6.30/2.20 Prover 7: Preprocessing ... % 6.30/2.22 Prover 7: Proving ... % 29.98/12.92 Prover 8: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 29.98/12.94 Prover 8: Preprocessing ... % 30.15/12.97 Prover 8: Proving ... % 32.81/14.13 Prover 8: proved (1214ms) % 32.81/14.14 Prover 7: stopped % 32.81/14.14 % 32.81/14.14 % SZS status Theorem for theBenchmark % 32.81/14.14 % 32.81/14.14 Generating proof ... found it (size 74) % 52.84/27.09 % 52.84/27.09 % SZS output start Proof for theBenchmark % 52.84/27.09 Assumed formulas after preprocessing and simplification: % 52.84/27.09 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ? [v5] : (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (member(v2, v1) = v4 & member(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ! [v2] : ( ~ (member(v2, v0) = 0) | member(v2, v1) = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v0) & union(v1, v2) = v3 & ! [v4] : ! [v5] : (v5 = 0 | ~ (member(v4, v0) = v5) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & ~ (v6 = 0) & member(v4, v2) = v7 & member(v4, v1) = v6)) & ! [v4] : ( ~ (member(v4, v0) = 0) | ? [v5] : ? [v6] : (member(v4, v2) = v6 & member(v4, v1) = v5 & (v6 = 0 | v5 = 0)))) % 52.84/27.11 | Applying alpha-rule on (0) yields: % 52.84/27.11 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 52.84/27.11 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 52.84/27.11 | (3) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v0) & union(v1, v2) = v3 & ! [v4] : ! [v5] : (v5 = 0 | ~ (member(v4, v0) = v5) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & ~ (v6 = 0) & member(v4, v2) = v7 & member(v4, v1) = v6)) & ! [v4] : ( ~ (member(v4, v0) = 0) | ? [v5] : ? [v6] : (member(v4, v2) = v6 & member(v4, v1) = v5 & (v6 = 0 | v5 = 0)))) % 53.13/27.11 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 53.13/27.11 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 53.13/27.12 | (6) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ! [v2] : ( ~ (member(v2, v0) = 0) | member(v2, v1) = 0)) % 53.13/27.12 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) % 53.13/27.12 | (8) ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (member(v2, v1) = v4 & member(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) % 53.13/27.12 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = v5)) % 53.13/27.12 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) % 53.13/27.12 | (11) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 53.13/27.12 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ? [v5] : (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0))) % 53.13/27.12 | % 53.13/27.12 | Instantiating (3) with all_1_0_0, all_1_1_1, all_1_2_2, all_1_3_3 yields: % 53.13/27.12 | (13) ~ (all_1_0_0 = all_1_3_3) & union(all_1_2_2, all_1_1_1) = all_1_0_0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (member(v0, all_1_3_3) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & ~ (v2 = 0) & member(v0, all_1_1_1) = v3 & member(v0, all_1_2_2) = v2)) & ! [v0] : ( ~ (member(v0, all_1_3_3) = 0) | ? [v1] : ? [v2] : (member(v0, all_1_1_1) = v2 & member(v0, all_1_2_2) = v1 & (v2 = 0 | v1 = 0))) % 53.13/27.12 | % 53.13/27.12 | Applying alpha-rule on (13) yields: % 53.13/27.12 | (14) ~ (all_1_0_0 = all_1_3_3) % 53.13/27.12 | (15) union(all_1_2_2, all_1_1_1) = all_1_0_0 % 53.13/27.12 | (16) ! [v0] : ! [v1] : (v1 = 0 | ~ (member(v0, all_1_3_3) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & ~ (v2 = 0) & member(v0, all_1_1_1) = v3 & member(v0, all_1_2_2) = v2)) % 53.13/27.12 | (17) ! [v0] : ( ~ (member(v0, all_1_3_3) = 0) | ? [v1] : ? [v2] : (member(v0, all_1_1_1) = v2 & member(v0, all_1_2_2) = v1 & (v2 = 0 | v1 = 0))) % 53.13/27.12 | % 53.13/27.12 | Instantiating formula (7) with all_1_0_0, all_1_1_1, all_1_2_2 and discharging atoms union(all_1_2_2, all_1_1_1) = all_1_0_0, yields: % 53.13/27.12 | (18) union(all_1_1_1, all_1_2_2) = all_1_0_0 % 53.13/27.12 | % 53.13/27.12 | Introducing new symbol ex_16_1_5 defined by: % 53.13/27.12 | (19) ex_16_1_5 = all_1_3_3 % 53.13/27.12 | % 53.13/27.12 | Introducing new symbol ex_16_0_4 defined by: % 53.13/27.12 | (20) ex_16_0_4 = all_1_0_0 % 53.13/27.12 | % 53.13/27.12 | Instantiating formula (8) with ex_16_0_4, ex_16_1_5 yields: % 53.13/27.12 | (21) ex_16_0_4 = ex_16_1_5 | ? [v0] : ? [v1] : ? [v2] : (member(v0, ex_16_0_4) = v2 & member(v0, ex_16_1_5) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0)) % 53.13/27.12 | % 53.13/27.12 +-Applying beta-rule and splitting (21), into two cases. % 53.13/27.12 |-Branch one: % 53.13/27.12 | (22) ex_16_0_4 = ex_16_1_5 % 53.13/27.12 | % 53.13/27.12 | Combining equations (20,22) yields a new equation: % 53.13/27.12 | (23) ex_16_1_5 = all_1_0_0 % 53.13/27.12 | % 53.13/27.12 | Combining equations (23,19) yields a new equation: % 53.13/27.12 | (24) all_1_0_0 = all_1_3_3 % 53.13/27.12 | % 53.13/27.12 | Simplifying 24 yields: % 53.13/27.12 | (25) all_1_0_0 = all_1_3_3 % 53.13/27.12 | % 53.13/27.12 | Equations (25) can reduce 14 to: % 53.13/27.12 | (26) $false % 53.13/27.12 | % 53.13/27.12 |-The branch is then unsatisfiable % 53.13/27.12 |-Branch two: % 53.13/27.12 | (27) ? [v0] : ? [v1] : ? [v2] : (member(v0, ex_16_0_4) = v2 & member(v0, ex_16_1_5) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0)) % 53.13/27.12 | % 53.13/27.12 | Instantiating (27) with all_19_0_6, all_19_1_7, all_19_2_8 yields: % 53.13/27.12 | (28) member(all_19_2_8, ex_16_0_4) = all_19_0_6 & member(all_19_2_8, ex_16_1_5) = all_19_1_7 & ( ~ (all_19_0_6 = 0) | ~ (all_19_1_7 = 0)) & (all_19_0_6 = 0 | all_19_1_7 = 0) % 53.13/27.13 | % 53.13/27.13 | Applying alpha-rule on (28) yields: % 53.13/27.13 | (29) member(all_19_2_8, ex_16_0_4) = all_19_0_6 % 53.13/27.13 | (30) member(all_19_2_8, ex_16_1_5) = all_19_1_7 % 53.13/27.13 | (31) ~ (all_19_0_6 = 0) | ~ (all_19_1_7 = 0) % 53.13/27.13 | (32) all_19_0_6 = 0 | all_19_1_7 = 0 % 53.13/27.13 | % 53.13/27.13 | Instantiating formula (9) with all_19_0_6, all_1_0_0, all_19_2_8, all_1_2_2, all_1_1_1 and discharging atoms union(all_1_1_1, all_1_2_2) = all_1_0_0, yields: % 53.13/27.13 | (33) all_19_0_6 = 0 | ~ (member(all_19_2_8, all_1_0_0) = all_19_0_6) | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_19_2_8, all_1_1_1) = v0 & member(all_19_2_8, all_1_2_2) = v1) % 53.13/27.13 | % 53.13/27.13 | Instantiating formula (16) with all_19_1_7, all_19_2_8 yields: % 53.13/27.13 | (34) all_19_1_7 = 0 | ~ (member(all_19_2_8, all_1_3_3) = all_19_1_7) | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_19_2_8, all_1_1_1) = v1 & member(all_19_2_8, all_1_2_2) = v0) % 53.13/27.13 | % 53.13/27.13 +-Applying beta-rule and splitting (31), into two cases. % 53.13/27.13 |-Branch one: % 53.13/27.13 | (35) ~ (all_19_0_6 = 0) % 53.13/27.13 | % 53.13/27.13 +-Applying beta-rule and splitting (32), into two cases. % 53.13/27.13 |-Branch one: % 53.13/27.13 | (36) all_19_0_6 = 0 % 53.13/27.13 | % 53.13/27.13 | Equations (36) can reduce 35 to: % 53.13/27.13 | (26) $false % 53.13/27.13 | % 53.13/27.13 |-The branch is then unsatisfiable % 53.13/27.13 |-Branch two: % 53.13/27.13 | (38) all_19_1_7 = 0 % 53.13/27.13 | % 53.13/27.13 | From (38) and (30) follows: % 53.13/27.13 | (39) member(all_19_2_8, ex_16_1_5) = 0 % 53.13/27.13 | % 53.13/27.13 | Instantiating formula (17) with all_19_2_8 yields: % 53.13/27.13 | (40) ~ (member(all_19_2_8, all_1_3_3) = 0) | ? [v0] : ? [v1] : (member(all_19_2_8, all_1_1_1) = v1 & member(all_19_2_8, all_1_2_2) = v0 & (v1 = 0 | v0 = 0)) % 53.13/27.13 | % 53.13/27.13 +-Applying beta-rule and splitting (33), into two cases. % 53.13/27.13 |-Branch one: % 53.13/27.13 | (41) ~ (member(all_19_2_8, all_1_0_0) = all_19_0_6) % 53.13/27.13 | % 53.13/27.13 | From (20) and (29) follows: % 53.13/27.13 | (42) member(all_19_2_8, all_1_0_0) = all_19_0_6 % 53.13/27.13 | % 53.13/27.13 | Using (42) and (41) yields: % 53.13/27.13 | (43) $false % 53.13/27.13 | % 53.13/27.13 |-The branch is then unsatisfiable % 53.13/27.13 |-Branch two: % 53.13/27.13 | (44) all_19_0_6 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_19_2_8, all_1_1_1) = v0 & member(all_19_2_8, all_1_2_2) = v1) % 53.13/27.13 | % 53.13/27.13 +-Applying beta-rule and splitting (44), into two cases. % 53.13/27.13 |-Branch one: % 53.13/27.13 | (36) all_19_0_6 = 0 % 53.13/27.13 | % 53.13/27.13 | Equations (36) can reduce 35 to: % 53.13/27.13 | (26) $false % 53.13/27.13 | % 53.13/27.13 |-The branch is then unsatisfiable % 53.13/27.13 |-Branch two: % 53.13/27.13 | (47) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_19_2_8, all_1_1_1) = v0 & member(all_19_2_8, all_1_2_2) = v1) % 53.13/27.13 | % 53.13/27.13 | Instantiating (47) with all_44_0_122, all_44_1_123 yields: % 53.13/27.13 | (48) ~ (all_44_0_122 = 0) & ~ (all_44_1_123 = 0) & member(all_19_2_8, all_1_1_1) = all_44_1_123 & member(all_19_2_8, all_1_2_2) = all_44_0_122 % 53.13/27.13 | % 53.13/27.13 | Applying alpha-rule on (48) yields: % 53.13/27.13 | (49) ~ (all_44_0_122 = 0) % 53.13/27.13 | (50) ~ (all_44_1_123 = 0) % 53.13/27.13 | (51) member(all_19_2_8, all_1_1_1) = all_44_1_123 % 53.13/27.13 | (52) member(all_19_2_8, all_1_2_2) = all_44_0_122 % 53.13/27.13 | % 53.13/27.13 +-Applying beta-rule and splitting (40), into two cases. % 53.13/27.13 |-Branch one: % 53.13/27.13 | (53) ~ (member(all_19_2_8, all_1_3_3) = 0) % 53.13/27.13 | % 53.13/27.13 | From (19) and (39) follows: % 53.13/27.13 | (54) member(all_19_2_8, all_1_3_3) = 0 % 53.13/27.13 | % 53.13/27.13 | Using (54) and (53) yields: % 53.13/27.13 | (43) $false % 53.13/27.13 | % 53.13/27.13 |-The branch is then unsatisfiable % 53.13/27.13 |-Branch two: % 53.13/27.13 | (56) ? [v0] : ? [v1] : (member(all_19_2_8, all_1_1_1) = v1 & member(all_19_2_8, all_1_2_2) = v0 & (v1 = 0 | v0 = 0)) % 53.13/27.13 | % 53.13/27.13 | Instantiating (56) with all_53_0_130, all_53_1_131 yields: % 53.13/27.13 | (57) member(all_19_2_8, all_1_1_1) = all_53_0_130 & member(all_19_2_8, all_1_2_2) = all_53_1_131 & (all_53_0_130 = 0 | all_53_1_131 = 0) % 53.13/27.13 | % 53.13/27.13 | Applying alpha-rule on (57) yields: % 53.13/27.13 | (58) member(all_19_2_8, all_1_1_1) = all_53_0_130 % 53.13/27.13 | (59) member(all_19_2_8, all_1_2_2) = all_53_1_131 % 53.13/27.13 | (60) all_53_0_130 = 0 | all_53_1_131 = 0 % 53.13/27.13 | % 53.13/27.13 | Instantiating formula (2) with all_19_2_8, all_1_1_1, all_44_1_123, all_53_0_130 and discharging atoms member(all_19_2_8, all_1_1_1) = all_53_0_130, member(all_19_2_8, all_1_1_1) = all_44_1_123, yields: % 53.13/27.13 | (61) all_53_0_130 = all_44_1_123 % 53.13/27.13 | % 53.13/27.13 | Instantiating formula (2) with all_19_2_8, all_1_2_2, all_44_0_122, all_53_1_131 and discharging atoms member(all_19_2_8, all_1_2_2) = all_53_1_131, member(all_19_2_8, all_1_2_2) = all_44_0_122, yields: % 53.13/27.13 | (62) all_53_1_131 = all_44_0_122 % 53.13/27.13 | % 53.13/27.13 +-Applying beta-rule and splitting (60), into two cases. % 53.13/27.13 |-Branch one: % 53.13/27.13 | (63) all_53_0_130 = 0 % 53.13/27.13 | % 53.13/27.13 | Combining equations (63,61) yields a new equation: % 53.13/27.13 | (64) all_44_1_123 = 0 % 53.13/27.13 | % 53.13/27.13 | Equations (64) can reduce 50 to: % 53.13/27.13 | (26) $false % 53.13/27.13 | % 53.13/27.13 |-The branch is then unsatisfiable % 53.13/27.13 |-Branch two: % 53.13/27.13 | (66) all_53_1_131 = 0 % 53.13/27.13 | % 53.13/27.13 | Combining equations (62,66) yields a new equation: % 53.13/27.13 | (67) all_44_0_122 = 0 % 53.13/27.13 | % 53.13/27.13 | Simplifying 67 yields: % 53.13/27.13 | (68) all_44_0_122 = 0 % 53.13/27.13 | % 53.13/27.13 | Equations (68) can reduce 49 to: % 53.13/27.13 | (26) $false % 53.13/27.13 | % 53.13/27.13 |-The branch is then unsatisfiable % 53.13/27.13 |-Branch two: % 53.13/27.13 | (36) all_19_0_6 = 0 % 53.13/27.13 | (71) ~ (all_19_1_7 = 0) % 53.13/27.13 | % 53.13/27.13 | From (36) and (29) follows: % 53.13/27.13 | (72) member(all_19_2_8, ex_16_0_4) = 0 % 53.13/27.13 | % 53.13/27.13 | Instantiating formula (12) with all_1_0_0, all_19_2_8, all_1_1_1, all_1_2_2 and discharging atoms union(all_1_2_2, all_1_1_1) = all_1_0_0, yields: % 53.13/27.13 | (73) ~ (member(all_19_2_8, all_1_0_0) = 0) | ? [v0] : ? [v1] : (member(all_19_2_8, all_1_1_1) = v1 & member(all_19_2_8, all_1_2_2) = v0 & (v1 = 0 | v0 = 0)) % 53.13/27.13 | % 53.13/27.13 +-Applying beta-rule and splitting (34), into two cases. % 53.13/27.13 |-Branch one: % 53.13/27.13 | (74) ~ (member(all_19_2_8, all_1_3_3) = all_19_1_7) % 53.13/27.14 | % 53.13/27.14 | From (19) and (30) follows: % 53.13/27.14 | (75) member(all_19_2_8, all_1_3_3) = all_19_1_7 % 53.13/27.14 | % 53.13/27.14 | Using (75) and (74) yields: % 53.13/27.14 | (43) $false % 53.13/27.14 | % 53.13/27.14 |-The branch is then unsatisfiable % 53.13/27.14 |-Branch two: % 53.13/27.14 | (77) all_19_1_7 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_19_2_8, all_1_1_1) = v1 & member(all_19_2_8, all_1_2_2) = v0) % 53.13/27.14 | % 53.13/27.14 +-Applying beta-rule and splitting (73), into two cases. % 53.13/27.14 |-Branch one: % 53.13/27.14 | (78) ~ (member(all_19_2_8, all_1_0_0) = 0) % 53.13/27.14 | % 53.13/27.14 | From (20) and (72) follows: % 53.13/27.14 | (79) member(all_19_2_8, all_1_0_0) = 0 % 53.13/27.14 | % 53.13/27.14 | Using (79) and (78) yields: % 53.13/27.14 | (43) $false % 53.13/27.14 | % 53.13/27.14 |-The branch is then unsatisfiable % 53.13/27.14 |-Branch two: % 53.13/27.14 | (56) ? [v0] : ? [v1] : (member(all_19_2_8, all_1_1_1) = v1 & member(all_19_2_8, all_1_2_2) = v0 & (v1 = 0 | v0 = 0)) % 53.13/27.14 | % 53.13/27.14 | Instantiating (56) with all_42_0_41, all_42_1_42 yields: % 53.13/27.14 | (82) member(all_19_2_8, all_1_1_1) = all_42_0_41 & member(all_19_2_8, all_1_2_2) = all_42_1_42 & (all_42_0_41 = 0 | all_42_1_42 = 0) % 53.13/27.14 | % 53.13/27.14 | Applying alpha-rule on (82) yields: % 53.13/27.14 | (83) member(all_19_2_8, all_1_1_1) = all_42_0_41 % 53.13/27.14 | (84) member(all_19_2_8, all_1_2_2) = all_42_1_42 % 53.13/27.14 | (85) all_42_0_41 = 0 | all_42_1_42 = 0 % 53.13/27.14 | % 53.13/27.14 +-Applying beta-rule and splitting (77), into two cases. % 53.13/27.14 |-Branch one: % 53.13/27.14 | (38) all_19_1_7 = 0 % 53.13/27.14 | % 53.13/27.14 | Equations (38) can reduce 71 to: % 53.13/27.14 | (26) $false % 53.13/27.14 | % 53.13/27.14 |-The branch is then unsatisfiable % 53.13/27.14 |-Branch two: % 53.13/27.14 | (88) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_19_2_8, all_1_1_1) = v1 & member(all_19_2_8, all_1_2_2) = v0) % 53.13/27.14 | % 53.13/27.14 | Instantiating (88) with all_48_0_43, all_48_1_44 yields: % 53.13/27.14 | (89) ~ (all_48_0_43 = 0) & ~ (all_48_1_44 = 0) & member(all_19_2_8, all_1_1_1) = all_48_0_43 & member(all_19_2_8, all_1_2_2) = all_48_1_44 % 53.13/27.14 | % 53.13/27.14 | Applying alpha-rule on (89) yields: % 53.13/27.14 | (90) ~ (all_48_0_43 = 0) % 53.13/27.14 | (91) ~ (all_48_1_44 = 0) % 53.13/27.14 | (92) member(all_19_2_8, all_1_1_1) = all_48_0_43 % 53.13/27.14 | (93) member(all_19_2_8, all_1_2_2) = all_48_1_44 % 53.13/27.14 | % 53.13/27.14 | Instantiating formula (2) with all_19_2_8, all_1_1_1, all_42_0_41, all_48_0_43 and discharging atoms member(all_19_2_8, all_1_1_1) = all_48_0_43, member(all_19_2_8, all_1_1_1) = all_42_0_41, yields: % 53.13/27.14 | (94) all_48_0_43 = all_42_0_41 % 53.13/27.14 | % 53.13/27.14 | Instantiating formula (2) with all_19_2_8, all_1_2_2, all_42_1_42, all_48_1_44 and discharging atoms member(all_19_2_8, all_1_2_2) = all_48_1_44, member(all_19_2_8, all_1_2_2) = all_42_1_42, yields: % 53.13/27.14 | (95) all_48_1_44 = all_42_1_42 % 53.13/27.14 | % 53.13/27.14 | Equations (94) can reduce 90 to: % 53.13/27.14 | (96) ~ (all_42_0_41 = 0) % 53.13/27.14 | % 53.13/27.14 | Equations (95) can reduce 91 to: % 53.13/27.14 | (97) ~ (all_42_1_42 = 0) % 53.13/27.14 | % 53.13/27.14 +-Applying beta-rule and splitting (85), into two cases. % 53.13/27.14 |-Branch one: % 53.13/27.14 | (98) all_42_0_41 = 0 % 53.13/27.14 | % 53.13/27.14 | Equations (98) can reduce 96 to: % 53.13/27.14 | (26) $false % 53.13/27.14 | % 53.13/27.14 |-The branch is then unsatisfiable % 53.13/27.14 |-Branch two: % 53.13/27.14 | (100) all_42_1_42 = 0 % 53.13/27.14 | % 53.13/27.14 | Equations (100) can reduce 97 to: % 53.13/27.14 | (26) $false % 53.13/27.14 | % 53.13/27.14 |-The branch is then unsatisfiable % 53.13/27.14 % SZS output end Proof for theBenchmark % 53.13/27.14 % 53.13/27.14 26497ms %------------------------------------------------------------------------------