%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU138+1 : TPTP v8.1.0. Released v3.3.0. % 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 08:46:52 EDT 2022 % Result : Theorem 20.82s 6.11s % Output : Proof 24.99s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : SEU138+1 : TPTP v8.1.0. Released v3.3.0. % 0.08/0.15 % Command : ePrincess-casc -timeout=%d %s % 0.15/0.37 % Computer : n020.cluster.edu % 0.15/0.37 % Model : x86_64 x86_64 % 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.37 % Memory : 8042.1875MB % 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.37 % CPULimit : 300 % 0.15/0.37 % WCLimit : 600 % 0.15/0.37 % DateTime : Sun Jun 19 07:31:18 EDT 2022 % 0.15/0.37 % CPUTime : % 0.57/0.62 ____ _ % 0.57/0.62 ___ / __ \_____(_)___ ________ __________ % 0.57/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.57/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.57/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.57/0.62 % 0.57/0.62 A Theorem Prover for First-Order Logic % 0.57/0.63 (ePrincess v.1.0) % 0.57/0.63 % 0.57/0.63 (c) Philipp Rümmer, 2009-2015 % 0.57/0.63 (c) Peter Backeman, 2014-2015 % 0.57/0.63 (contributions by Angelo Brillout, Peter Baumgartner) % 0.57/0.63 Free software under GNU Lesser General Public License (LGPL). % 0.57/0.63 Bug reports to peter@backeman.se % 0.57/0.63 % 0.57/0.63 For more information, visit http://user.uu.se/~petba168/breu/ % 0.57/0.63 % 0.57/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.66/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.46/0.96 Prover 0: Preprocessing ... % 1.84/1.15 Prover 0: Warning: ignoring some quantifiers % 1.84/1.17 Prover 0: Constructing countermodel ... % 2.75/1.39 Prover 0: gave up % 2.75/1.40 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.75/1.42 Prover 1: Preprocessing ... % 3.21/1.50 Prover 1: Warning: ignoring some quantifiers % 3.21/1.51 Prover 1: Constructing countermodel ... % 3.47/1.61 Prover 1: gave up % 3.47/1.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.81/1.62 Prover 2: Preprocessing ... % 4.16/1.72 Prover 2: Warning: ignoring some quantifiers % 4.16/1.72 Prover 2: Constructing countermodel ... % 4.80/1.84 Prover 2: gave up % 4.80/1.84 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.80/1.86 Prover 3: Preprocessing ... % 4.80/1.89 Prover 3: Warning: ignoring some quantifiers % 4.80/1.89 Prover 3: Constructing countermodel ... % 5.15/1.97 Prover 3: gave up % 5.15/1.97 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 5.47/1.98 Prover 4: Preprocessing ... % 5.91/2.09 Prover 4: Warning: ignoring some quantifiers % 6.01/2.09 Prover 4: Constructing countermodel ... % 10.36/3.18 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 10.36/3.20 Prover 5: Preprocessing ... % 10.75/3.28 Prover 5: Warning: ignoring some quantifiers % 10.75/3.28 Prover 5: Constructing countermodel ... % 11.41/3.38 Prover 5: gave up % 11.41/3.38 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 11.41/3.39 Prover 6: Preprocessing ... % 11.65/3.44 Prover 6: Warning: ignoring some quantifiers % 11.73/3.44 Prover 6: Constructing countermodel ... % 11.73/3.50 Prover 6: gave up % 11.73/3.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 11.73/3.51 Prover 7: Preprocessing ... % 12.07/3.54 Prover 7: Proving ... % 20.82/6.11 Prover 7: proved (2605ms) % 20.82/6.11 Prover 4: stopped % 20.82/6.11 % 20.82/6.11 % SZS status Theorem for theBenchmark % 20.82/6.11 % 20.82/6.11 Generating proof ... found it (size 53) % 24.99/7.38 % 24.99/7.38 % SZS output start Proof for theBenchmark % 24.99/7.38 Assumed formulas after preprocessing and simplification: % 24.99/7.38 | (0) ? [v0] : (empty(v0) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (set_difference(v4, v3) = v2) | ~ (set_difference(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (set_intersection2(v4, v3) = v2) | ~ (set_intersection2(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v2) = v3) | ! [v4] : (v4 = v3 | ? [v5] : (( ~ in(v5, v4) | ~ in(v5, v1) | in(v5, v2)) & (in(v5, v4) | (in(v5, v1) & ~ in(v5, v2)))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v2) = v3) | ( ! [v4] : ( ~ in(v4, v3) | (in(v4, v1) & ~ in(v4, v2))) & ! [v4] : ( ~ in(v4, v1) | in(v4, v3) | in(v4, v2)))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | set_intersection2(v2, v1) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ! [v4] : (v4 = v3 | ? [v5] : (( ~ in(v5, v4) | ~ in(v5, v2) | ~ in(v5, v1)) & (in(v5, v4) | (in(v5, v2) & in(v5, v1)))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ( ! [v4] : ( ~ in(v4, v3) | (in(v4, v2) & in(v4, v1))) & ! [v4] : ( ~ in(v4, v2) | ~ in(v4, v1) | in(v4, v3)))) & ! [v1] : ! [v2] : (v2 = v1 | ~ (set_difference(v1, v0) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (set_intersection2(v1, v1) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ empty(v2) | ~ empty(v1)) & ! [v1] : ! [v2] : (v2 = v1 | ~ subset(v2, v1) | ~ subset(v1, v2)) & ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2)) & ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v1, v0) = v2)) & ! [v1] : ! [v2] : ( ~ empty(v2) | ~ in(v1, v2)) & ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ! [v3] : ( ~ in(v3, v1) | in(v3, v2))) & ! [v1] : ! [v2] : ( ~ in(v2, v1) | ~ in(v1, v2)) & ! [v1] : ! [v2] : (subset(v1, v2) | ? [v3] : (in(v3, v1) & ~ in(v3, v2))) & ! [v1] : (v1 = v0 | ~ empty(v1)) & ! [v1] : subset(v1, v1) & ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v4) & set_difference(v1, v3) = v4 & set_difference(v1, v2) = v3 & set_intersection2(v1, v2) = v5) & ? [v1] : ~ empty(v1) & ? [v1] : empty(v1)) % 24.99/7.41 | Instantiating (0) with all_0_0_0 yields: % 24.99/7.41 | (1) empty(all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v0) | in(v4, v1)) & (in(v4, v3) | (in(v4, v0) & ~ in(v4, v1)))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v0) & ~ in(v3, v1))) & ! [v3] : ( ~ in(v3, v0) | in(v3, v2) | in(v3, v1)))) & ! [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] : (v1 = v0 | ~ (set_difference(v0, all_0_0_0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (set_difference(all_0_0_0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (set_intersection2(v0, all_0_0_0) = v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ in(v2, v0) | in(v2, v1))) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) & ! [v0] : (v0 = all_0_0_0 | ~ empty(v0)) & ! [v0] : subset(v0, v0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = v3) & set_difference(v0, v2) = v3 & set_difference(v0, v1) = v2 & set_intersection2(v0, v1) = v4) & ? [v0] : ~ empty(v0) & ? [v0] : empty(v0) % 24.99/7.42 | % 24.99/7.42 | Applying alpha-rule on (1) yields: % 24.99/7.42 | (2) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 24.99/7.42 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 24.99/7.42 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 24.99/7.42 | (5) empty(all_0_0_0) % 24.99/7.42 | (6) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 24.99/7.42 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v0) | in(v4, v1)) & (in(v4, v3) | (in(v4, v0) & ~ in(v4, v1)))))) % 24.99/7.42 | (8) ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (set_intersection2(v0, all_0_0_0) = v1)) % 24.99/7.42 | (9) ? [v0] : ~ empty(v0) % 24.99/7.42 | (10) ! [v0] : subset(v0, v0) % 24.99/7.42 | (11) ! [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)))) % 24.99/7.42 | (12) ? [v0] : empty(v0) % 24.99/7.42 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 24.99/7.42 | (14) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = v3) & set_difference(v0, v2) = v3 & set_difference(v0, v1) = v2 & set_intersection2(v0, v1) = v4) % 24.99/7.42 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, all_0_0_0) = v1)) % 24.99/7.42 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 24.99/7.42 | (17) ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (set_difference(all_0_0_0, v0) = v1)) % 24.99/7.42 | (18) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ in(v2, v0) | in(v2, v1))) % 24.99/7.42 | (19) ! [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)))))) % 24.99/7.42 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 24.99/7.42 | (21) ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) % 24.99/7.42 | (22) ! [v0] : (v0 = all_0_0_0 | ~ empty(v0)) % 24.99/7.42 | (23) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 24.99/7.42 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v0) & ~ in(v3, v1))) & ! [v3] : ( ~ in(v3, v0) | in(v3, v2) | in(v3, v1)))) % 24.99/7.42 | % 24.99/7.42 | Instantiating (14) with all_5_0_2, all_5_1_3, all_5_2_4, all_5_3_5, all_5_4_6 yields: % 24.99/7.42 | (25) ~ (all_5_0_2 = all_5_1_3) & set_difference(all_5_4_6, all_5_2_4) = all_5_1_3 & set_difference(all_5_4_6, all_5_3_5) = all_5_2_4 & set_intersection2(all_5_4_6, all_5_3_5) = all_5_0_2 % 24.99/7.42 | % 24.99/7.42 | Applying alpha-rule on (25) yields: % 24.99/7.42 | (26) ~ (all_5_0_2 = all_5_1_3) % 24.99/7.42 | (27) set_difference(all_5_4_6, all_5_2_4) = all_5_1_3 % 24.99/7.42 | (28) set_difference(all_5_4_6, all_5_3_5) = all_5_2_4 % 24.99/7.42 | (29) set_intersection2(all_5_4_6, all_5_3_5) = all_5_0_2 % 24.99/7.42 | % 24.99/7.42 | Instantiating formula (7) with all_5_1_3, all_5_2_4, all_5_4_6 and discharging atoms set_difference(all_5_4_6, all_5_2_4) = all_5_1_3, yields: % 24.99/7.43 | (30) ! [v0] : (v0 = all_5_1_3 | ? [v1] : (( ~ in(v1, v0) | ~ in(v1, all_5_4_6) | in(v1, all_5_2_4)) & (in(v1, v0) | (in(v1, all_5_4_6) & ~ in(v1, all_5_2_4))))) % 24.99/7.43 | % 24.99/7.43 | Instantiating formula (24) with all_5_2_4, all_5_3_5, all_5_4_6 and discharging atoms set_difference(all_5_4_6, all_5_3_5) = all_5_2_4, yields: % 24.99/7.43 | (31) ! [v0] : ( ~ in(v0, all_5_2_4) | (in(v0, all_5_4_6) & ~ in(v0, all_5_3_5))) & ! [v0] : ( ~ in(v0, all_5_4_6) | in(v0, all_5_2_4) | in(v0, all_5_3_5)) % 24.99/7.43 | % 24.99/7.43 | Applying alpha-rule on (31) yields: % 24.99/7.43 | (32) ! [v0] : ( ~ in(v0, all_5_2_4) | (in(v0, all_5_4_6) & ~ in(v0, all_5_3_5))) % 24.99/7.43 | (33) ! [v0] : ( ~ in(v0, all_5_4_6) | in(v0, all_5_2_4) | in(v0, all_5_3_5)) % 24.99/7.43 | % 24.99/7.43 | Instantiating formula (13) with all_5_0_2, all_5_3_5, all_5_4_6 and discharging atoms set_intersection2(all_5_4_6, all_5_3_5) = all_5_0_2, yields: % 24.99/7.43 | (34) set_intersection2(all_5_3_5, all_5_4_6) = all_5_0_2 % 24.99/7.43 | % 24.99/7.43 | Instantiating formula (11) with all_5_0_2, all_5_4_6, all_5_3_5 and discharging atoms set_intersection2(all_5_3_5, all_5_4_6) = all_5_0_2, yields: % 24.99/7.43 | (35) ! [v0] : ( ~ in(v0, all_5_0_2) | (in(v0, all_5_3_5) & in(v0, all_5_4_6))) & ! [v0] : ( ~ in(v0, all_5_3_5) | ~ in(v0, all_5_4_6) | in(v0, all_5_0_2)) % 24.99/7.43 | % 24.99/7.43 | Applying alpha-rule on (35) yields: % 24.99/7.43 | (36) ! [v0] : ( ~ in(v0, all_5_0_2) | (in(v0, all_5_3_5) & in(v0, all_5_4_6))) % 24.99/7.43 | (37) ! [v0] : ( ~ in(v0, all_5_3_5) | ~ in(v0, all_5_4_6) | in(v0, all_5_0_2)) % 24.99/7.43 | % 24.99/7.43 | Introducing new symbol ex_58_0_14 defined by: % 24.99/7.43 | (38) ex_58_0_14 = all_5_0_2 % 24.99/7.43 | % 24.99/7.43 | Instantiating formula (30) with ex_58_0_14 yields: % 24.99/7.43 | (39) ex_58_0_14 = all_5_1_3 | ? [v0] : (( ~ in(v0, ex_58_0_14) | ~ in(v0, all_5_4_6) | in(v0, all_5_2_4)) & (in(v0, ex_58_0_14) | (in(v0, all_5_4_6) & ~ in(v0, all_5_2_4)))) % 24.99/7.43 | % 24.99/7.43 +-Applying beta-rule and splitting (39), into two cases. % 24.99/7.43 |-Branch one: % 24.99/7.43 | (40) ex_58_0_14 = all_5_1_3 % 24.99/7.43 | % 24.99/7.43 | Combining equations (38,40) yields a new equation: % 24.99/7.43 | (41) all_5_0_2 = all_5_1_3 % 24.99/7.43 | % 24.99/7.43 | Simplifying 41 yields: % 24.99/7.43 | (42) all_5_0_2 = all_5_1_3 % 24.99/7.43 | % 24.99/7.43 | Equations (42) can reduce 26 to: % 24.99/7.43 | (43) $false % 24.99/7.43 | % 24.99/7.43 |-The branch is then unsatisfiable % 24.99/7.43 |-Branch two: % 24.99/7.43 | (44) ? [v0] : (( ~ in(v0, ex_58_0_14) | ~ in(v0, all_5_4_6) | in(v0, all_5_2_4)) & (in(v0, ex_58_0_14) | (in(v0, all_5_4_6) & ~ in(v0, all_5_2_4)))) % 24.99/7.43 | % 24.99/7.43 | Instantiating (44) with all_61_0_15 yields: % 24.99/7.43 | (45) ( ~ in(all_61_0_15, ex_58_0_14) | ~ in(all_61_0_15, all_5_4_6) | in(all_61_0_15, all_5_2_4)) & (in(all_61_0_15, ex_58_0_14) | (in(all_61_0_15, all_5_4_6) & ~ in(all_61_0_15, all_5_2_4))) % 24.99/7.43 | % 24.99/7.43 | Applying alpha-rule on (45) yields: % 24.99/7.43 | (46) ~ in(all_61_0_15, ex_58_0_14) | ~ in(all_61_0_15, all_5_4_6) | in(all_61_0_15, all_5_2_4) % 24.99/7.43 | (47) in(all_61_0_15, ex_58_0_14) | (in(all_61_0_15, all_5_4_6) & ~ in(all_61_0_15, all_5_2_4)) % 24.99/7.43 | % 24.99/7.43 +-Applying beta-rule and splitting (46), into two cases. % 24.99/7.43 |-Branch one: % 24.99/7.43 | (48) ~ in(all_61_0_15, ex_58_0_14) % 24.99/7.43 | % 24.99/7.43 +-Applying beta-rule and splitting (47), into two cases. % 24.99/7.43 |-Branch one: % 24.99/7.43 | (49) in(all_61_0_15, ex_58_0_14) % 24.99/7.43 | % 24.99/7.43 | Using (49) and (48) yields: % 24.99/7.43 | (50) $false % 24.99/7.43 | % 24.99/7.43 |-The branch is then unsatisfiable % 24.99/7.43 |-Branch two: % 24.99/7.43 | (51) in(all_61_0_15, all_5_4_6) & ~ in(all_61_0_15, all_5_2_4) % 24.99/7.43 | % 24.99/7.43 | Applying alpha-rule on (51) yields: % 24.99/7.43 | (52) in(all_61_0_15, all_5_4_6) % 24.99/7.43 | (53) ~ in(all_61_0_15, all_5_2_4) % 24.99/7.43 | % 24.99/7.43 | Instantiating formula (37) with all_61_0_15 and discharging atoms in(all_61_0_15, all_5_4_6), yields: % 24.99/7.43 | (54) ~ in(all_61_0_15, all_5_3_5) | in(all_61_0_15, all_5_0_2) % 24.99/7.43 | % 24.99/7.43 | Instantiating formula (33) with all_61_0_15 and discharging atoms in(all_61_0_15, all_5_4_6), ~ in(all_61_0_15, all_5_2_4), yields: % 24.99/7.43 | (55) in(all_61_0_15, all_5_3_5) % 24.99/7.43 | % 24.99/7.43 +-Applying beta-rule and splitting (54), into two cases. % 24.99/7.43 |-Branch one: % 24.99/7.43 | (56) ~ in(all_61_0_15, all_5_3_5) % 24.99/7.43 | % 24.99/7.43 | Using (55) and (56) yields: % 24.99/7.43 | (50) $false % 24.99/7.43 | % 24.99/7.43 |-The branch is then unsatisfiable % 24.99/7.43 |-Branch two: % 24.99/7.43 | (58) in(all_61_0_15, all_5_0_2) % 24.99/7.43 | % 24.99/7.43 | From (38) and (48) follows: % 24.99/7.43 | (59) ~ in(all_61_0_15, all_5_0_2) % 24.99/7.43 | % 24.99/7.43 | Using (58) and (59) yields: % 24.99/7.43 | (50) $false % 24.99/7.43 | % 24.99/7.43 |-The branch is then unsatisfiable % 24.99/7.43 |-Branch two: % 24.99/7.43 | (49) in(all_61_0_15, ex_58_0_14) % 24.99/7.43 | (62) ~ in(all_61_0_15, all_5_4_6) | in(all_61_0_15, all_5_2_4) % 24.99/7.44 | % 24.99/7.44 | Instantiating formula (36) with all_61_0_15 yields: % 24.99/7.44 | (63) ~ in(all_61_0_15, all_5_0_2) | (in(all_61_0_15, all_5_3_5) & in(all_61_0_15, all_5_4_6)) % 24.99/7.44 | % 24.99/7.44 | Instantiating formula (32) with all_61_0_15 yields: % 24.99/7.44 | (64) ~ in(all_61_0_15, all_5_2_4) | (in(all_61_0_15, all_5_4_6) & ~ in(all_61_0_15, all_5_3_5)) % 24.99/7.44 | % 24.99/7.44 +-Applying beta-rule and splitting (62), into two cases. % 24.99/7.44 |-Branch one: % 24.99/7.44 | (65) ~ in(all_61_0_15, all_5_4_6) % 24.99/7.44 | % 24.99/7.44 +-Applying beta-rule and splitting (63), into two cases. % 24.99/7.44 |-Branch one: % 24.99/7.44 | (59) ~ in(all_61_0_15, all_5_0_2) % 24.99/7.44 | % 24.99/7.44 | From (38) and (49) follows: % 24.99/7.44 | (58) in(all_61_0_15, all_5_0_2) % 24.99/7.44 | % 24.99/7.44 | Using (58) and (59) yields: % 24.99/7.44 | (50) $false % 24.99/7.44 | % 24.99/7.44 |-The branch is then unsatisfiable % 24.99/7.44 |-Branch two: % 24.99/7.44 | (69) in(all_61_0_15, all_5_3_5) & in(all_61_0_15, all_5_4_6) % 24.99/7.44 | % 24.99/7.44 | Applying alpha-rule on (69) yields: % 24.99/7.44 | (55) in(all_61_0_15, all_5_3_5) % 24.99/7.44 | (52) in(all_61_0_15, all_5_4_6) % 24.99/7.44 | % 24.99/7.44 | Using (52) and (65) yields: % 24.99/7.44 | (50) $false % 24.99/7.44 | % 24.99/7.44 |-The branch is then unsatisfiable % 24.99/7.44 |-Branch two: % 24.99/7.44 | (73) in(all_61_0_15, all_5_2_4) % 24.99/7.44 | % 24.99/7.44 +-Applying beta-rule and splitting (64), into two cases. % 24.99/7.44 |-Branch one: % 24.99/7.44 | (53) ~ in(all_61_0_15, all_5_2_4) % 24.99/7.44 | % 24.99/7.44 | Using (73) and (53) yields: % 24.99/7.44 | (50) $false % 24.99/7.44 | % 24.99/7.44 |-The branch is then unsatisfiable % 24.99/7.44 |-Branch two: % 24.99/7.44 | (76) in(all_61_0_15, all_5_4_6) & ~ in(all_61_0_15, all_5_3_5) % 24.99/7.44 | % 24.99/7.44 | Applying alpha-rule on (76) yields: % 24.99/7.44 | (52) in(all_61_0_15, all_5_4_6) % 24.99/7.44 | (56) ~ in(all_61_0_15, all_5_3_5) % 24.99/7.44 | % 24.99/7.44 +-Applying beta-rule and splitting (63), into two cases. % 24.99/7.44 |-Branch one: % 24.99/7.44 | (59) ~ in(all_61_0_15, all_5_0_2) % 24.99/7.44 | % 24.99/7.44 | From (38) and (49) follows: % 24.99/7.44 | (58) in(all_61_0_15, all_5_0_2) % 24.99/7.44 | % 24.99/7.44 | Using (58) and (59) yields: % 24.99/7.44 | (50) $false % 24.99/7.44 | % 24.99/7.44 |-The branch is then unsatisfiable % 24.99/7.44 |-Branch two: % 24.99/7.44 | (69) in(all_61_0_15, all_5_3_5) & in(all_61_0_15, all_5_4_6) % 24.99/7.44 | % 24.99/7.44 | Applying alpha-rule on (69) yields: % 24.99/7.44 | (55) in(all_61_0_15, all_5_3_5) % 24.99/7.44 | (52) in(all_61_0_15, all_5_4_6) % 24.99/7.44 | % 24.99/7.44 | Using (55) and (56) yields: % 24.99/7.44 | (50) $false % 24.99/7.44 | % 24.99/7.44 |-The branch is then unsatisfiable % 24.99/7.44 % SZS output end Proof for theBenchmark % 24.99/7.44 % 24.99/7.44 6802ms %------------------------------------------------------------------------------