%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET919+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n011.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 00:23:09 EDT 2022 % Result : Theorem 173.52s 130.23s % Output : Proof 182.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET919+1 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n011.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 : Sat Jul 9 18:41:55 EDT 2022 % 0.13/0.34 % CPUTime : % 0.51/0.62 ____ _ % 0.51/0.62 ___ / __ \_____(_)___ ________ __________ % 0.51/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.51/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.51/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.51/0.62 % 0.51/0.62 A Theorem Prover for First-Order Logic % 0.51/0.62 (ePrincess v.1.0) % 0.51/0.62 % 0.51/0.62 (c) Philipp Rümmer, 2009-2015 % 0.51/0.62 (c) Peter Backeman, 2014-2015 % 0.51/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.51/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.51/0.62 Bug reports to peter@backeman.se % 0.51/0.62 % 0.51/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.51/0.62 % 0.51/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.74/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.48/0.97 Prover 0: Preprocessing ... % 1.96/1.17 Prover 0: Warning: ignoring some quantifiers % 2.02/1.19 Prover 0: Constructing countermodel ... % 2.78/1.44 Prover 0: gave up % 2.78/1.44 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.04/1.46 Prover 1: Preprocessing ... % 3.15/1.52 Prover 1: Warning: ignoring some quantifiers % 3.32/1.53 Prover 1: Constructing countermodel ... % 3.96/1.75 Prover 1: gave up % 3.96/1.75 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.96/1.76 Prover 2: Preprocessing ... % 4.53/1.82 Prover 2: Warning: ignoring some quantifiers % 4.53/1.82 Prover 2: Constructing countermodel ... % 5.05/1.95 Prover 2: gave up % 5.05/1.95 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 5.05/1.96 Prover 3: Preprocessing ... % 5.05/1.98 Prover 3: Warning: ignoring some quantifiers % 5.05/1.98 Prover 3: Constructing countermodel ... % 5.36/2.05 Prover 3: gave up % 5.36/2.05 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 5.36/2.06 Prover 4: Preprocessing ... % 5.92/2.11 Prover 4: Warning: ignoring some quantifiers % 5.92/2.12 Prover 4: Constructing countermodel ... % 7.41/2.48 Prover 4: gave up % 7.41/2.48 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 7.41/2.49 Prover 5: Preprocessing ... % 7.58/2.52 Prover 5: Warning: ignoring some quantifiers % 7.58/2.52 Prover 5: Constructing countermodel ... % 8.33/2.67 Prover 5: gave up % 8.33/2.67 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 8.33/2.68 Prover 6: Preprocessing ... % 8.33/2.71 Prover 6: Warning: ignoring some quantifiers % 8.33/2.71 Prover 6: Constructing countermodel ... % 8.75/2.80 Prover 6: gave up % 8.75/2.80 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 8.75/2.81 Prover 7: Preprocessing ... % 8.98/2.83 Prover 7: Proving ... % 33.02/13.23 Prover 8: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 33.19/13.25 Prover 8: Preprocessing ... % 33.19/13.29 Prover 8: Proving ... % 54.24/31.66 Prover 9: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=completeFrugal % 54.32/31.68 Prover 9: Preprocessing ... % 54.44/31.72 Prover 9: Proving ... % 87.41/52.64 Prover 9: stopped % 87.65/52.84 Prover 10: Options: -triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 87.65/52.85 Prover 10: Preprocessing ... % 87.65/52.87 Prover 10: Warning: ignoring some quantifiers % 87.65/52.88 Prover 10: Constructing countermodel ... % 87.85/52.93 Prover 10: gave up % 87.85/52.93 Prover 11: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 87.85/52.94 Prover 11: Preprocessing ... % 87.85/52.95 Prover 11: Warning: ignoring some quantifiers % 87.85/52.95 Prover 11: Constructing countermodel ... % 88.27/52.98 Prover 11: gave up % 88.39/53.00 Prover 12: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 88.39/53.00 Prover 12: Preprocessing ... % 88.39/53.02 Prover 12: Proving ... % 92.57/56.10 Prover 12: stopped % 92.78/56.30 Prover 13: Options: -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 92.78/56.31 Prover 13: Preprocessing ... % 92.78/56.34 Prover 13: Warning: ignoring some quantifiers % 92.78/56.34 Prover 13: Constructing countermodel ... % 93.27/56.46 Prover 13: gave up % 93.27/56.46 Prover 14: Options: -triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 93.27/56.47 Prover 14: Preprocessing ... % 93.27/56.48 Prover 14: Warning: ignoring some quantifiers % 93.27/56.48 Prover 14: Constructing countermodel ... % 93.51/56.51 Prover 14: gave up % 93.51/56.51 Prover 15: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 93.51/56.52 Prover 15: Preprocessing ... % 93.51/56.54 Prover 15: Proving ... % 159.58/118.36 Prover 15: stopped % 159.80/118.56 Prover 16: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 159.80/118.57 Prover 16: Preprocessing ... % 159.80/118.60 Prover 16: Proving ... % 173.52/130.23 Prover 7: proved (20182ms) % 173.52/130.23 Prover 8: stopped % 173.52/130.23 Prover 16: stopped % 173.52/130.23 % 173.52/130.23 % SZS status Theorem for theBenchmark % 173.52/130.23 % 173.52/130.23 Generating proof ... found it (size 115) % 181.71/134.83 % 181.71/134.83 % SZS output start Proof for theBenchmark % 181.71/134.83 Assumed formulas after preprocessing and simplification: % 181.71/134.83 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v3) | (in(v4, v1) & in(v4, v0)))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v1) & in(v3, v0))) & ! [v3] : ( ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : ((v4 = v1 | v4 = v0 | in(v4, v3)) & ( ~ in(v4, v3) | ( ~ (v4 = v1) & ~ (v4 = v0)))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ( ! [v3] : (v3 = v1 | v3 = v0 | ~ in(v3, v2)) & ! [v3] : (in(v3, v2) | ( ~ (v3 = v1) & ~ (v3 = v0))))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ! [v2] : (v2 = v1 | ? [v3] : (( ~ (v3 = v0) | ~ in(v0, v2)) & (v3 = v0 | in(v3, v2))))) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | (in(v0, v1) & ! [v2] : (v2 = v0 | ~ in(v2, v1)))) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v4) & singleton(v0) = v5 & set_intersection2(v3, v1) = v4 & unordered_pair(v0, v2) = v3 & in(v0, v1) & (v2 = v0 | ~ in(v2, v1))) & ? [v0] : ~ empty(v0) & ? [v0] : empty(v0) % 181.71/134.86 | Applying alpha-rule on (0) yields: % 181.71/134.86 | (1) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ( ! [v3] : (v3 = v1 | v3 = v0 | ~ in(v3, v2)) & ! [v3] : (in(v3, v2) | ( ~ (v3 = v1) & ~ (v3 = v0))))) % 181.71/134.86 | (2) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v4) & singleton(v0) = v5 & set_intersection2(v3, v1) = v4 & unordered_pair(v0, v2) = v3 & in(v0, v1) & (v2 = v0 | ~ in(v2, v1))) % 181.71/134.86 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 181.71/134.86 | (4) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 181.71/134.86 | (5) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ! [v2] : (v2 = v1 | ? [v3] : (( ~ (v3 = v0) | ~ in(v0, v2)) & (v3 = v0 | in(v3, v2))))) % 181.71/134.86 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 181.71/134.86 | (7) ? [v0] : empty(v0) % 181.71/134.86 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 181.71/134.86 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v1) & in(v3, v0))) & ! [v3] : ( ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)))) % 181.71/134.86 | (10) ? [v0] : ~ empty(v0) % 181.71/134.86 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 181.71/134.86 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v3) | (in(v4, v1) & in(v4, v0)))))) % 181.71/134.86 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 181.71/134.86 | (14) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | (in(v0, v1) & ! [v2] : (v2 = v0 | ~ in(v2, v1)))) % 181.71/134.86 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : ((v4 = v1 | v4 = v0 | in(v4, v3)) & ( ~ in(v4, v3) | ( ~ (v4 = v1) & ~ (v4 = v0)))))) % 181.71/134.86 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 181.71/134.86 | % 181.71/134.86 | Instantiating (2) with all_5_0_2, all_5_1_3, all_5_2_4, all_5_3_5, all_5_4_6, all_5_5_7 yields: % 181.71/134.86 | (17) ~ (all_5_0_2 = all_5_1_3) & singleton(all_5_5_7) = all_5_0_2 & set_intersection2(all_5_2_4, all_5_4_6) = all_5_1_3 & unordered_pair(all_5_5_7, all_5_3_5) = all_5_2_4 & in(all_5_5_7, all_5_4_6) & (all_5_3_5 = all_5_5_7 | ~ in(all_5_3_5, all_5_4_6)) % 181.71/134.86 | % 181.71/134.86 | Applying alpha-rule on (17) yields: % 181.71/134.86 | (18) singleton(all_5_5_7) = all_5_0_2 % 181.71/134.86 | (19) all_5_3_5 = all_5_5_7 | ~ in(all_5_3_5, all_5_4_6) % 181.71/134.86 | (20) unordered_pair(all_5_5_7, all_5_3_5) = all_5_2_4 % 181.71/134.86 | (21) set_intersection2(all_5_2_4, all_5_4_6) = all_5_1_3 % 181.71/134.86 | (22) ~ (all_5_0_2 = all_5_1_3) % 181.71/134.86 | (23) in(all_5_5_7, all_5_4_6) % 181.71/134.86 | % 182.14/134.87 | Instantiating formula (5) with all_5_0_2, all_5_5_7 and discharging atoms singleton(all_5_5_7) = all_5_0_2, yields: % 182.14/134.87 | (24) ! [v0] : (v0 = all_5_0_2 | ? [v1] : (( ~ (v1 = all_5_5_7) | ~ in(all_5_5_7, v0)) & (v1 = all_5_5_7 | in(v1, v0)))) % 182.14/134.87 | % 182.14/134.87 | Instantiating formula (14) with all_5_0_2, all_5_5_7 and discharging atoms singleton(all_5_5_7) = all_5_0_2, yields: % 182.14/134.87 | (25) in(all_5_5_7, all_5_0_2) & ! [v0] : (v0 = all_5_5_7 | ~ in(v0, all_5_0_2)) % 182.14/134.87 | % 182.14/134.87 | Applying alpha-rule on (25) yields: % 182.14/134.87 | (26) in(all_5_5_7, all_5_0_2) % 182.14/134.87 | (27) ! [v0] : (v0 = all_5_5_7 | ~ in(v0, all_5_0_2)) % 182.14/134.87 | % 182.14/134.87 | Instantiating formula (6) with all_5_1_3, all_5_4_6, all_5_2_4 and discharging atoms set_intersection2(all_5_2_4, all_5_4_6) = all_5_1_3, yields: % 182.14/134.87 | (28) set_intersection2(all_5_4_6, all_5_2_4) = all_5_1_3 % 182.14/134.87 | % 182.14/134.87 | Instantiating formula (9) with all_5_1_3, all_5_4_6, all_5_2_4 and discharging atoms set_intersection2(all_5_2_4, all_5_4_6) = all_5_1_3, yields: % 182.14/134.87 | (29) ! [v0] : ( ~ in(v0, all_5_1_3) | (in(v0, all_5_2_4) & in(v0, all_5_4_6))) & ! [v0] : ( ~ in(v0, all_5_2_4) | ~ in(v0, all_5_4_6) | in(v0, all_5_1_3)) % 182.14/134.87 | % 182.14/134.87 | Applying alpha-rule on (29) yields: % 182.14/134.87 | (30) ! [v0] : ( ~ in(v0, all_5_1_3) | (in(v0, all_5_2_4) & in(v0, all_5_4_6))) % 182.14/134.87 | (31) ! [v0] : ( ~ in(v0, all_5_2_4) | ~ in(v0, all_5_4_6) | in(v0, all_5_1_3)) % 182.14/134.87 | % 182.14/134.87 | Instantiating formula (13) with all_5_2_4, all_5_3_5, all_5_5_7 and discharging atoms unordered_pair(all_5_5_7, all_5_3_5) = all_5_2_4, yields: % 182.14/134.87 | (32) unordered_pair(all_5_3_5, all_5_5_7) = all_5_2_4 % 182.14/134.87 | % 182.14/134.87 | Instantiating formula (12) with all_5_1_3, all_5_2_4, all_5_4_6 and discharging atoms set_intersection2(all_5_4_6, all_5_2_4) = all_5_1_3, yields: % 182.14/134.87 | (33) ! [v0] : (v0 = all_5_1_3 | ? [v1] : (( ~ in(v1, v0) | ~ in(v1, all_5_2_4) | ~ in(v1, all_5_4_6)) & (in(v1, v0) | (in(v1, all_5_2_4) & in(v1, all_5_4_6))))) % 182.14/134.87 | % 182.14/134.87 | Instantiating formula (1) with all_5_2_4, all_5_5_7, all_5_3_5 and discharging atoms unordered_pair(all_5_3_5, all_5_5_7) = all_5_2_4, yields: % 182.14/134.87 | (34) ! [v0] : (v0 = all_5_3_5 | v0 = all_5_5_7 | ~ in(v0, all_5_2_4)) & ! [v0] : (in(v0, all_5_2_4) | ( ~ (v0 = all_5_3_5) & ~ (v0 = all_5_5_7))) % 182.14/134.87 | % 182.14/134.87 | Applying alpha-rule on (34) yields: % 182.14/134.87 | (35) ! [v0] : (v0 = all_5_3_5 | v0 = all_5_5_7 | ~ in(v0, all_5_2_4)) % 182.14/134.87 | (36) ! [v0] : (in(v0, all_5_2_4) | ( ~ (v0 = all_5_3_5) & ~ (v0 = all_5_5_7))) % 182.14/134.87 | % 182.14/134.87 | Instantiating formula (31) with all_5_5_7 and discharging atoms in(all_5_5_7, all_5_4_6), yields: % 182.14/134.87 | (37) ~ in(all_5_5_7, all_5_2_4) | in(all_5_5_7, all_5_1_3) % 182.14/134.87 | % 182.14/134.87 +-Applying beta-rule and splitting (19), into two cases. % 182.14/134.87 |-Branch one: % 182.14/134.87 | (38) ~ in(all_5_3_5, all_5_4_6) % 182.14/134.87 | % 182.14/134.87 +-Applying beta-rule and splitting (37), into two cases. % 182.14/134.87 |-Branch one: % 182.14/134.87 | (39) ~ in(all_5_5_7, all_5_2_4) % 182.14/134.87 | % 182.14/134.87 | Introducing new symbol ex_54_0_10 defined by: % 182.14/134.87 | (40) ex_54_0_10 = all_5_5_7 % 182.14/134.87 | % 182.14/134.87 | Instantiating formula (36) with ex_54_0_10 yields: % 182.14/134.87 | (41) in(ex_54_0_10, all_5_2_4) | ( ~ (ex_54_0_10 = all_5_3_5) & ~ (ex_54_0_10 = all_5_5_7)) % 182.14/134.87 | % 182.14/134.87 +-Applying beta-rule and splitting (41), into two cases. % 182.14/134.87 |-Branch one: % 182.14/134.87 | (42) in(ex_54_0_10, all_5_2_4) % 182.14/134.87 | % 182.14/134.87 | From (40) and (42) follows: % 182.14/134.87 | (43) in(all_5_5_7, all_5_2_4) % 182.14/134.87 | % 182.14/134.87 | Using (43) and (39) yields: % 182.14/134.87 | (44) $false % 182.14/134.87 | % 182.14/134.87 |-The branch is then unsatisfiable % 182.14/134.87 |-Branch two: % 182.14/134.87 | (45) ~ (ex_54_0_10 = all_5_3_5) & ~ (ex_54_0_10 = all_5_5_7) % 182.14/134.87 | % 182.14/134.87 | Applying alpha-rule on (45) yields: % 182.14/134.87 | (46) ~ (ex_54_0_10 = all_5_3_5) % 182.14/134.87 | (47) ~ (ex_54_0_10 = all_5_5_7) % 182.14/134.87 | % 182.14/134.87 | Equations (40) can reduce 47 to: % 182.14/134.87 | (48) $false % 182.14/134.87 | % 182.14/134.87 |-The branch is then unsatisfiable % 182.14/134.87 |-Branch two: % 182.14/134.87 | (43) in(all_5_5_7, all_5_2_4) % 182.14/134.87 | (50) in(all_5_5_7, all_5_1_3) % 182.14/134.87 | % 182.14/134.87 | Introducing new symbol ex_50_0_13 defined by: % 182.14/134.87 | (51) ex_50_0_13 = all_5_0_2 % 182.14/134.87 | % 182.14/134.87 | Instantiating formula (33) with ex_50_0_13 yields: % 182.14/134.87 | (52) ex_50_0_13 = all_5_1_3 | ? [v0] : (( ~ in(v0, ex_50_0_13) | ~ in(v0, all_5_2_4) | ~ in(v0, all_5_4_6)) & (in(v0, ex_50_0_13) | (in(v0, all_5_2_4) & in(v0, all_5_4_6)))) % 182.14/134.87 | % 182.14/134.87 +-Applying beta-rule and splitting (52), into two cases. % 182.14/134.87 |-Branch one: % 182.14/134.87 | (53) ex_50_0_13 = all_5_1_3 % 182.14/134.87 | % 182.14/134.87 | Combining equations (51,53) yields a new equation: % 182.14/134.87 | (54) all_5_0_2 = all_5_1_3 % 182.14/134.87 | % 182.14/134.87 | Simplifying 54 yields: % 182.14/134.87 | (55) all_5_0_2 = all_5_1_3 % 182.14/134.87 | % 182.14/134.87 | Equations (55) can reduce 22 to: % 182.14/134.87 | (48) $false % 182.14/134.87 | % 182.14/134.87 |-The branch is then unsatisfiable % 182.14/134.87 |-Branch two: % 182.14/134.87 | (57) ? [v0] : (( ~ in(v0, ex_50_0_13) | ~ in(v0, all_5_2_4) | ~ in(v0, all_5_4_6)) & (in(v0, ex_50_0_13) | (in(v0, all_5_2_4) & in(v0, all_5_4_6)))) % 182.14/134.87 | % 182.14/134.87 | Instantiating (57) with all_53_0_14 yields: % 182.14/134.87 | (58) ( ~ in(all_53_0_14, ex_50_0_13) | ~ in(all_53_0_14, all_5_2_4) | ~ in(all_53_0_14, all_5_4_6)) & (in(all_53_0_14, ex_50_0_13) | (in(all_53_0_14, all_5_2_4) & in(all_53_0_14, all_5_4_6))) % 182.14/134.87 | % 182.14/134.87 | Applying alpha-rule on (58) yields: % 182.14/134.87 | (59) ~ in(all_53_0_14, ex_50_0_13) | ~ in(all_53_0_14, all_5_2_4) | ~ in(all_53_0_14, all_5_4_6) % 182.14/134.87 | (60) in(all_53_0_14, ex_50_0_13) | (in(all_53_0_14, all_5_2_4) & in(all_53_0_14, all_5_4_6)) % 182.14/134.88 | % 182.14/134.88 +-Applying beta-rule and splitting (59), into two cases. % 182.14/134.88 |-Branch one: % 182.14/134.88 | (61) ~ in(all_53_0_14, ex_50_0_13) % 182.14/134.88 | % 182.14/134.88 +-Applying beta-rule and splitting (60), into two cases. % 182.14/134.88 |-Branch one: % 182.14/134.88 | (62) in(all_53_0_14, ex_50_0_13) % 182.14/134.88 | % 182.14/134.88 | Using (62) and (61) yields: % 182.14/134.88 | (44) $false % 182.14/134.88 | % 182.14/134.88 |-The branch is then unsatisfiable % 182.14/134.88 |-Branch two: % 182.14/134.88 | (64) in(all_53_0_14, all_5_2_4) & in(all_53_0_14, all_5_4_6) % 182.14/134.88 | % 182.14/134.88 | Applying alpha-rule on (64) yields: % 182.14/134.88 | (65) in(all_53_0_14, all_5_2_4) % 182.14/134.88 | (66) in(all_53_0_14, all_5_4_6) % 182.14/134.88 | % 182.14/134.88 | Instantiating formula (35) with all_53_0_14 and discharging atoms in(all_53_0_14, all_5_2_4), yields: % 182.14/134.88 | (67) all_53_0_14 = all_5_3_5 | all_53_0_14 = all_5_5_7 % 182.14/134.88 | % 182.14/134.88 | Instantiating formula (27) with all_53_0_14 yields: % 182.14/134.88 | (68) all_53_0_14 = all_5_5_7 | ~ in(all_53_0_14, all_5_0_2) % 182.14/134.88 | % 182.14/134.88 +-Applying beta-rule and splitting (68), into two cases. % 182.14/134.88 |-Branch one: % 182.14/134.88 | (69) ~ in(all_53_0_14, all_5_0_2) % 182.14/134.88 | % 182.14/134.88 +-Applying beta-rule and splitting (67), into two cases. % 182.14/134.88 |-Branch one: % 182.14/134.88 | (70) all_53_0_14 = all_5_3_5 % 182.14/134.88 | % 182.14/134.88 | From (70) and (66) follows: % 182.14/134.88 | (71) in(all_5_3_5, all_5_4_6) % 182.14/134.88 | % 182.14/134.88 | Using (71) and (38) yields: % 182.14/134.88 | (44) $false % 182.14/134.88 | % 182.14/134.88 |-The branch is then unsatisfiable % 182.14/134.88 |-Branch two: % 182.14/134.88 | (73) all_53_0_14 = all_5_5_7 % 182.14/134.88 | % 182.14/134.88 | From (73) and (69) follows: % 182.14/134.88 | (74) ~ in(all_5_5_7, all_5_0_2) % 182.14/134.88 | % 182.14/134.88 | Using (26) and (74) yields: % 182.14/134.88 | (44) $false % 182.14/134.88 | % 182.14/134.88 |-The branch is then unsatisfiable % 182.14/134.88 |-Branch two: % 182.14/134.88 | (73) all_53_0_14 = all_5_5_7 % 182.14/134.88 | % 182.14/134.88 | From (73) and (61) follows: % 182.14/134.88 | (77) ~ in(all_5_5_7, ex_50_0_13) % 182.14/134.88 | % 182.14/134.88 | From (51) and (77) follows: % 182.14/134.88 | (74) ~ in(all_5_5_7, all_5_0_2) % 182.14/134.88 | % 182.14/134.88 | Using (26) and (74) yields: % 182.14/134.88 | (44) $false % 182.14/134.88 | % 182.14/134.88 |-The branch is then unsatisfiable % 182.14/134.88 |-Branch two: % 182.14/134.88 | (62) in(all_53_0_14, ex_50_0_13) % 182.14/134.88 | (81) ~ in(all_53_0_14, all_5_2_4) | ~ in(all_53_0_14, all_5_4_6) % 182.14/134.88 | % 182.14/134.88 | Instantiating formula (27) with all_53_0_14 yields: % 182.14/134.88 | (68) all_53_0_14 = all_5_5_7 | ~ in(all_53_0_14, all_5_0_2) % 182.14/134.88 | % 182.14/134.88 +-Applying beta-rule and splitting (81), into two cases. % 182.14/134.88 |-Branch one: % 182.14/134.88 | (83) ~ in(all_53_0_14, all_5_2_4) % 182.14/134.88 | % 182.14/134.88 +-Applying beta-rule and splitting (68), into two cases. % 182.14/134.88 |-Branch one: % 182.14/134.88 | (69) ~ in(all_53_0_14, all_5_0_2) % 182.14/134.88 | % 182.14/134.88 | From (51) and (62) follows: % 182.14/134.88 | (85) in(all_53_0_14, all_5_0_2) % 182.14/134.88 | % 182.14/134.88 | Using (85) and (69) yields: % 182.14/134.88 | (44) $false % 182.14/134.88 | % 182.14/134.88 |-The branch is then unsatisfiable % 182.14/134.88 |-Branch two: % 182.14/134.88 | (73) all_53_0_14 = all_5_5_7 % 182.14/134.88 | % 182.14/134.88 | From (73) and (83) follows: % 182.14/134.88 | (39) ~ in(all_5_5_7, all_5_2_4) % 182.14/134.88 | % 182.14/134.88 | Using (43) and (39) yields: % 182.14/134.88 | (44) $false % 182.14/134.88 | % 182.14/134.88 |-The branch is then unsatisfiable % 182.14/134.88 |-Branch two: % 182.14/134.88 | (90) ~ in(all_53_0_14, all_5_4_6) % 182.14/134.88 | % 182.14/134.88 +-Applying beta-rule and splitting (68), into two cases. % 182.14/134.88 |-Branch one: % 182.14/134.88 | (69) ~ in(all_53_0_14, all_5_0_2) % 182.14/134.88 | % 182.14/134.88 | From (51) and (62) follows: % 182.14/134.88 | (85) in(all_53_0_14, all_5_0_2) % 182.14/134.88 | % 182.14/134.88 | Using (85) and (69) yields: % 182.14/134.88 | (44) $false % 182.14/134.88 | % 182.14/134.88 |-The branch is then unsatisfiable % 182.14/134.88 |-Branch two: % 182.14/134.88 | (73) all_53_0_14 = all_5_5_7 % 182.14/134.88 | % 182.14/134.88 | From (73) and (90) follows: % 182.14/134.88 | (95) ~ in(all_5_5_7, all_5_4_6) % 182.14/134.88 | % 182.14/134.88 | Using (23) and (95) yields: % 182.14/134.88 | (44) $false % 182.14/134.88 | % 182.14/134.88 |-The branch is then unsatisfiable % 182.14/134.88 |-Branch two: % 182.14/134.88 | (97) all_5_3_5 = all_5_5_7 % 182.14/134.88 | % 182.14/134.88 +-Applying beta-rule and splitting (37), into two cases. % 182.14/134.88 |-Branch one: % 182.14/134.88 | (39) ~ in(all_5_5_7, all_5_2_4) % 182.14/134.88 | % 182.14/134.88 | Introducing new symbol ex_44_0_29 defined by: % 182.14/134.88 | (99) ex_44_0_29 = all_5_5_7 % 182.14/134.88 | % 182.14/134.88 | Instantiating formula (36) with ex_44_0_29 yields: % 182.14/134.88 | (100) in(ex_44_0_29, all_5_2_4) | ( ~ (ex_44_0_29 = all_5_3_5) & ~ (ex_44_0_29 = all_5_5_7)) % 182.14/134.88 | % 182.14/134.88 +-Applying beta-rule and splitting (100), into two cases. % 182.14/134.88 |-Branch one: % 182.14/134.88 | (101) in(ex_44_0_29, all_5_2_4) % 182.14/134.88 | % 182.14/134.88 | From (99) and (101) follows: % 182.14/134.88 | (43) in(all_5_5_7, all_5_2_4) % 182.14/134.88 | % 182.14/134.88 | Using (43) and (39) yields: % 182.14/134.88 | (44) $false % 182.14/134.88 | % 182.14/134.88 |-The branch is then unsatisfiable % 182.14/134.88 |-Branch two: % 182.14/134.88 | (104) ~ (ex_44_0_29 = all_5_3_5) & ~ (ex_44_0_29 = all_5_5_7) % 182.14/134.88 | % 182.14/134.88 | Applying alpha-rule on (104) yields: % 182.14/134.88 | (105) ~ (ex_44_0_29 = all_5_3_5) % 182.14/134.88 | (106) ~ (ex_44_0_29 = all_5_5_7) % 182.14/134.88 | % 182.14/134.88 | Equations (99) can reduce 106 to: % 182.14/134.88 | (48) $false % 182.14/134.88 | % 182.14/134.88 |-The branch is then unsatisfiable % 182.14/134.88 |-Branch two: % 182.14/134.88 | (50) in(all_5_5_7, all_5_1_3) % 182.14/134.88 | % 182.14/134.88 | Introducing new symbol ex_55_0_32 defined by: % 182.14/134.88 | (109) ex_55_0_32 = all_5_1_3 % 182.14/134.88 | % 182.14/134.88 | Instantiating formula (24) with ex_55_0_32 yields: % 182.14/134.88 | (110) ex_55_0_32 = all_5_0_2 | ? [v0] : (( ~ (v0 = all_5_5_7) | ~ in(all_5_5_7, ex_55_0_32)) & (v0 = all_5_5_7 | in(v0, ex_55_0_32))) % 182.14/134.88 | % 182.14/134.88 +-Applying beta-rule and splitting (110), into two cases. % 182.14/134.88 |-Branch one: % 182.14/134.88 | (111) ex_55_0_32 = all_5_0_2 % 182.14/134.88 | % 182.14/134.88 | Combining equations (111,109) yields a new equation: % 182.14/134.88 | (54) all_5_0_2 = all_5_1_3 % 182.14/134.88 | % 182.14/134.88 | Simplifying 54 yields: % 182.14/134.88 | (55) all_5_0_2 = all_5_1_3 % 182.14/134.88 | % 182.14/134.88 | Equations (55) can reduce 22 to: % 182.14/134.88 | (48) $false % 182.14/134.88 | % 182.14/134.88 |-The branch is then unsatisfiable % 182.14/134.88 |-Branch two: % 182.14/134.88 | (115) ? [v0] : (( ~ (v0 = all_5_5_7) | ~ in(all_5_5_7, ex_55_0_32)) & (v0 = all_5_5_7 | in(v0, ex_55_0_32))) % 182.14/134.88 | % 182.14/134.88 | Instantiating (115) with all_58_0_33 yields: % 182.14/134.88 | (116) ( ~ (all_58_0_33 = all_5_5_7) | ~ in(all_5_5_7, ex_55_0_32)) & (all_58_0_33 = all_5_5_7 | in(all_58_0_33, ex_55_0_32)) % 182.14/134.88 | % 182.14/134.88 | Applying alpha-rule on (116) yields: % 182.14/134.88 | (117) ~ (all_58_0_33 = all_5_5_7) | ~ in(all_5_5_7, ex_55_0_32) % 182.14/134.88 | (118) all_58_0_33 = all_5_5_7 | in(all_58_0_33, ex_55_0_32) % 182.14/134.88 | % 182.14/134.88 +-Applying beta-rule and splitting (118), into two cases. % 182.14/134.88 |-Branch one: % 182.14/134.88 | (119) in(all_58_0_33, ex_55_0_32) % 182.14/134.88 | % 182.14/134.88 | Instantiating formula (35) with all_58_0_33 yields: % 182.14/134.88 | (120) all_58_0_33 = all_5_3_5 | all_58_0_33 = all_5_5_7 | ~ in(all_58_0_33, all_5_2_4) % 182.14/134.88 | % 182.14/134.88 | Instantiating formula (30) with all_58_0_33 yields: % 182.14/134.88 | (121) ~ in(all_58_0_33, all_5_1_3) | (in(all_58_0_33, all_5_2_4) & in(all_58_0_33, all_5_4_6)) % 182.14/134.88 | % 182.14/134.88 +-Applying beta-rule and splitting (117), into two cases. % 182.14/134.88 |-Branch one: % 182.14/134.88 | (122) ~ in(all_5_5_7, ex_55_0_32) % 182.14/134.88 | % 182.14/134.89 | From (109) and (122) follows: % 182.14/134.89 | (123) ~ in(all_5_5_7, all_5_1_3) % 182.14/134.89 | % 182.14/134.89 | Using (50) and (123) yields: % 182.14/134.89 | (44) $false % 182.14/134.89 | % 182.14/134.89 |-The branch is then unsatisfiable % 182.14/134.89 |-Branch two: % 182.14/134.89 | (125) ~ (all_58_0_33 = all_5_5_7) % 182.14/134.89 | % 182.14/134.89 +-Applying beta-rule and splitting (120), into two cases. % 182.14/134.89 |-Branch one: % 182.14/134.89 | (126) ~ in(all_58_0_33, all_5_2_4) % 182.14/134.89 | % 182.14/134.89 +-Applying beta-rule and splitting (121), into two cases. % 182.14/134.89 |-Branch one: % 182.14/134.89 | (127) ~ in(all_58_0_33, all_5_1_3) % 182.14/134.89 | % 182.14/134.89 | From (109) and (119) follows: % 182.14/134.89 | (128) in(all_58_0_33, all_5_1_3) % 182.14/134.89 | % 182.14/134.89 | Using (128) and (127) yields: % 182.14/134.89 | (44) $false % 182.14/134.89 | % 182.14/134.89 |-The branch is then unsatisfiable % 182.14/134.89 |-Branch two: % 182.14/134.89 | (130) in(all_58_0_33, all_5_2_4) & in(all_58_0_33, all_5_4_6) % 182.14/134.89 | % 182.14/134.89 | Applying alpha-rule on (130) yields: % 182.14/134.89 | (131) in(all_58_0_33, all_5_2_4) % 182.14/134.89 | (132) in(all_58_0_33, all_5_4_6) % 182.14/134.89 | % 182.14/134.89 | Using (131) and (126) yields: % 182.14/134.89 | (44) $false % 182.14/134.89 | % 182.14/134.89 |-The branch is then unsatisfiable % 182.14/134.89 |-Branch two: % 182.14/134.89 | (134) all_58_0_33 = all_5_3_5 | all_58_0_33 = all_5_5_7 % 182.14/134.89 | % 182.14/134.89 +-Applying beta-rule and splitting (134), into two cases. % 182.14/134.89 |-Branch one: % 182.14/134.89 | (135) all_58_0_33 = all_5_3_5 % 182.14/134.89 | % 182.14/134.89 | Combining equations (97,135) yields a new equation: % 182.14/134.89 | (136) all_58_0_33 = all_5_5_7 % 182.14/134.89 | % 182.14/134.89 | Equations (136) can reduce 125 to: % 182.14/134.89 | (48) $false % 182.14/134.89 | % 182.14/134.89 |-The branch is then unsatisfiable % 182.14/134.89 |-Branch two: % 182.14/134.89 | (136) all_58_0_33 = all_5_5_7 % 182.14/134.89 | % 182.14/134.89 | Equations (136) can reduce 125 to: % 182.14/134.89 | (48) $false % 182.14/134.89 | % 182.14/134.89 |-The branch is then unsatisfiable % 182.14/134.89 |-Branch two: % 182.14/134.89 | (136) all_58_0_33 = all_5_5_7 % 182.14/134.89 | % 182.14/134.89 +-Applying beta-rule and splitting (117), into two cases. % 182.14/134.89 |-Branch one: % 182.14/134.89 | (122) ~ in(all_5_5_7, ex_55_0_32) % 182.14/134.89 | % 182.14/134.89 | From (109) and (122) follows: % 182.14/134.89 | (123) ~ in(all_5_5_7, all_5_1_3) % 182.14/134.89 | % 182.14/134.89 | Using (50) and (123) yields: % 182.14/134.89 | (44) $false % 182.14/134.89 | % 182.14/134.89 |-The branch is then unsatisfiable % 182.14/134.89 |-Branch two: % 182.14/134.89 | (125) ~ (all_58_0_33 = all_5_5_7) % 182.14/134.89 | % 182.14/134.89 | Equations (136) can reduce 125 to: % 182.14/134.89 | (48) $false % 182.14/134.89 | % 182.14/134.89 |-The branch is then unsatisfiable % 182.14/134.89 % SZS output end Proof for theBenchmark % 182.14/134.89 % 182.14/134.89 134254ms %------------------------------------------------------------------------------