%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET887+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n024.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 00:22:56 EDT 2022 % Result : Theorem 72.58s 34.70s % Output : Proof 74.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET887+1 : TPTP v8.1.0. Released v3.2.0. % 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n024.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 16:48:43 EDT 2022 % 0.12/0.34 % CPUTime : % 0.59/0.58 ____ _ % 0.59/0.58 ___ / __ \_____(_)___ ________ __________ % 0.59/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.59/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.59/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.59/0.58 % 0.59/0.58 A Theorem Prover for First-Order Logic % 0.59/0.59 (ePrincess v.1.0) % 0.59/0.59 % 0.59/0.59 (c) Philipp Rümmer, 2009-2015 % 0.59/0.59 (c) Peter Backeman, 2014-2015 % 0.59/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.59/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.59/0.59 Bug reports to peter@backeman.se % 0.59/0.59 % 0.59/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.59/0.59 % 0.59/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.75/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.50/0.95 Prover 0: Preprocessing ... % 1.85/1.13 Prover 0: Warning: ignoring some quantifiers % 1.85/1.15 Prover 0: Constructing countermodel ... % 21.46/5.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 21.46/5.97 Prover 1: Preprocessing ... % 21.85/6.05 Prover 1: Warning: ignoring some quantifiers % 21.85/6.06 Prover 1: Constructing countermodel ... % 22.24/6.15 Prover 1: gave up % 22.24/6.15 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 22.24/6.16 Prover 2: Preprocessing ... % 22.78/6.21 Prover 2: Warning: ignoring some quantifiers % 22.83/6.21 Prover 2: Constructing countermodel ... % 22.83/6.27 Prover 2: gave up % 22.83/6.27 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 22.83/6.28 Prover 3: Preprocessing ... % 22.83/6.31 Prover 3: Warning: ignoring some quantifiers % 22.83/6.31 Prover 3: Constructing countermodel ... % 23.34/6.34 Prover 3: gave up % 23.34/6.34 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 23.34/6.36 Prover 4: Preprocessing ... % 23.34/6.40 Prover 4: Warning: ignoring some quantifiers % 23.34/6.40 Prover 4: Constructing countermodel ... % 23.76/6.49 Prover 4: gave up % 23.76/6.49 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 24.16/6.50 Prover 5: Preprocessing ... % 24.16/6.53 Prover 5: Warning: ignoring some quantifiers % 24.16/6.53 Prover 5: Constructing countermodel ... % 24.16/6.57 Prover 5: gave up % 24.16/6.57 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 24.16/6.58 Prover 6: Preprocessing ... % 24.54/6.60 Prover 6: Warning: ignoring some quantifiers % 24.54/6.60 Prover 6: Constructing countermodel ... % 24.54/6.64 Prover 6: gave up % 24.54/6.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 24.54/6.65 Prover 7: Preprocessing ... % 24.54/6.67 Prover 7: Proving ... % 46.77/15.60 Prover 8: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 46.77/15.62 Prover 8: Preprocessing ... % 47.07/15.66 Prover 8: Proving ... % 71.13/34.24 Prover 0: stopped % 71.72/34.44 Prover 9: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=completeFrugal % 71.72/34.45 Prover 9: Preprocessing ... % 71.99/34.49 Prover 9: Proving ... % 72.58/34.70 Prover 9: proved (261ms) % 72.58/34.70 Prover 8: stopped % 72.58/34.70 Prover 7: stopped % 72.58/34.70 % 72.58/34.70 % SZS status Theorem for theBenchmark % 72.58/34.70 % 72.58/34.70 Generating proof ... found it (size 43) % 74.18/35.08 % 74.18/35.08 % SZS output start Proof for theBenchmark % 74.18/35.08 Assumed formulas after preprocessing and simplification: % 74.18/35.08 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v4 = v1) & ~ (v3 = v1) & unordered_pair(v3, v4) = v6 & unordered_pair(v1, v2) = v5 & subset(v5, v6) & empty(v8) & empty(v0) & ~ empty(v7) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v9 | v11 = v9 | ~ (unordered_pair(v11, v12) = v13) | ~ (unordered_pair(v9, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | v12 = v9 | ~ (unordered_pair(v9, v10) = v11) | ~ in(v12, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | v9 = v0 | ~ (unordered_pair(v10, v11) = v12) | ~ subset(v9, v12) | ? [v13] : ? [v14] : (singleton(v11) = v14 & singleton(v10) = v13 & (v14 = v9 | v13 = v9))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (singleton(v9) = v12) | ~ (unordered_pair(v10, v11) = v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (unordered_pair(v12, v11) = v10) | ~ (unordered_pair(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (singleton(v10) = v12) | ~ (singleton(v9) = v11) | ! [v13] : (v13 = v12 | v13 = v11 | v13 = v0 | ? [v14] : (unordered_pair(v9, v10) = v14 & (v14 = v13 | ~ subset(v13, v14))))) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (singleton(v11) = v10) | ~ (singleton(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v10, v9) = v11) | unordered_pair(v9, v10) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | unordered_pair(v10, v9) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | in(v10, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | in(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | ! [v12] : (v12 = v11 | ? [v13] : ((v13 = v10 | v13 = v9 | in(v13, v12)) & ( ~ in(v13, v12) | ( ~ (v13 = v10) & ~ (v13 = v9)))))) & ! [v9] : ! [v10] : ( ~ in(v10, v9) | ~ in(v9, v10)) & ! [v9] : (v9 = v0 | ? [v10] : in(v10, v9)) & ! [v9] : ~ in(v9, v0) & ! [v9] : subset(v9, v9) & ! [v9] : ! [v10] : ! [v11] : ? [v12] : ? [v13] : ? [v14] : (singleton(v11) = v13 & singleton(v10) = v12 & unordered_pair(v10, v11) = v14 & (subset(v9, v14) | ( ~ (v14 = v9) & ~ (v13 = v9) & ~ (v12 = v9) & ~ (v9 = v0))))) % 74.18/35.10 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 yields: % 74.18/35.10 | (1) ~ (all_0_4_4 = all_0_7_7) & ~ (all_0_5_5 = all_0_7_7) & unordered_pair(all_0_5_5, all_0_4_4) = all_0_2_2 & unordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3 & subset(all_0_3_3, all_0_2_2) & empty(all_0_0_0) & empty(all_0_8_8) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = all_0_8_8 | ~ (unordered_pair(v1, v2) = v3) | ~ subset(v0, v3) | ? [v4] : ? [v5] : (singleton(v2) = v5 & singleton(v1) = v4 & (v5 = v0 | v4 = v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ! [v4] : (v4 = v3 | v4 = v2 | v4 = all_0_8_8 | ? [v5] : (unordered_pair(v0, v1) = v5 & (v5 = v4 | ~ subset(v4, v5))))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(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] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : (v0 = all_0_8_8 | ? [v1] : in(v1, v0)) & ! [v0] : ~ in(v0, all_0_8_8) & ! [v0] : subset(v0, v0) & ! [v0] : ! [v1] : ! [v2] : ? [v3] : ? [v4] : ? [v5] : (singleton(v2) = v4 & singleton(v1) = v3 & unordered_pair(v1, v2) = v5 & (subset(v0, v5) | ( ~ (v5 = v0) & ~ (v4 = v0) & ~ (v3 = v0) & ~ (v0 = all_0_8_8)))) % 74.18/35.11 | % 74.18/35.11 | Applying alpha-rule on (1) yields: % 74.18/35.11 | (2) ! [v0] : ~ in(v0, all_0_8_8) % 74.18/35.11 | (3) empty(all_0_0_0) % 74.18/35.11 | (4) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 74.18/35.11 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) % 74.18/35.11 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) % 74.18/35.11 | (7) ! [v0] : (v0 = all_0_8_8 | ? [v1] : in(v1, v0)) % 74.18/35.11 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 74.18/35.11 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) % 74.18/35.11 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 74.18/35.11 | (11) ! [v0] : subset(v0, v0) % 74.18/35.11 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) % 74.18/35.11 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 74.18/35.11 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 74.18/35.11 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 74.18/35.11 | (16) ~ empty(all_0_1_1) % 74.18/35.11 | (17) unordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3 % 74.18/35.11 | (18) ! [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)))))) % 74.18/35.11 | (19) unordered_pair(all_0_5_5, all_0_4_4) = all_0_2_2 % 74.18/35.11 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = all_0_8_8 | ~ (unordered_pair(v1, v2) = v3) | ~ subset(v0, v3) | ? [v4] : ? [v5] : (singleton(v2) = v5 & singleton(v1) = v4 & (v5 = v0 | v4 = v0))) % 74.18/35.11 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ! [v4] : (v4 = v3 | v4 = v2 | v4 = all_0_8_8 | ? [v5] : (unordered_pair(v0, v1) = v5 & (v5 = v4 | ~ subset(v4, v5))))) % 74.18/35.11 | (22) ~ (all_0_4_4 = all_0_7_7) % 74.18/35.11 | (23) subset(all_0_3_3, all_0_2_2) % 74.18/35.11 | (24) empty(all_0_8_8) % 74.18/35.11 | (25) ! [v0] : ! [v1] : ! [v2] : ? [v3] : ? [v4] : ? [v5] : (singleton(v2) = v4 & singleton(v1) = v3 & unordered_pair(v1, v2) = v5 & (subset(v0, v5) | ( ~ (v5 = v0) & ~ (v4 = v0) & ~ (v3 = v0) & ~ (v0 = all_0_8_8)))) % 74.18/35.11 | (26) ~ (all_0_5_5 = all_0_7_7) % 74.18/35.11 | % 74.18/35.11 | Instantiating formula (6) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms unordered_pair(all_0_5_5, all_0_4_4) = all_0_2_2, yields: % 74.18/35.11 | (27) in(all_0_4_4, all_0_2_2) % 74.18/35.11 | % 74.18/35.11 | Instantiating formula (5) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms unordered_pair(all_0_5_5, all_0_4_4) = all_0_2_2, yields: % 74.18/35.11 | (28) in(all_0_5_5, all_0_2_2) % 74.18/35.11 | % 74.18/35.11 | Instantiating formula (5) with all_0_3_3, all_0_6_6, all_0_7_7 and discharging atoms unordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3, yields: % 74.18/35.11 | (29) in(all_0_7_7, all_0_3_3) % 74.18/35.11 | % 74.18/35.11 | Instantiating formula (20) with all_0_2_2, all_0_4_4, all_0_5_5, all_0_3_3 and discharging atoms unordered_pair(all_0_5_5, all_0_4_4) = all_0_2_2, subset(all_0_3_3, all_0_2_2), yields: % 74.18/35.11 | (30) all_0_2_2 = all_0_3_3 | all_0_3_3 = all_0_8_8 | ? [v0] : ? [v1] : (singleton(all_0_4_4) = v1 & singleton(all_0_5_5) = v0 & (v1 = all_0_3_3 | v0 = all_0_3_3)) % 74.18/35.11 | % 74.18/35.11 +-Applying beta-rule and splitting (30), into two cases. % 74.18/35.11 |-Branch one: % 74.18/35.11 | (31) all_0_2_2 = all_0_3_3 % 74.18/35.11 | % 74.18/35.11 | From (31) and (19) follows: % 74.18/35.12 | (32) unordered_pair(all_0_5_5, all_0_4_4) = all_0_3_3 % 74.18/35.12 | % 74.18/35.12 | From (31) and (27) follows: % 74.18/35.12 | (33) in(all_0_4_4, all_0_3_3) % 74.18/35.12 | % 74.18/35.12 | From (31) and (28) follows: % 74.18/35.12 | (34) in(all_0_5_5, all_0_3_3) % 74.18/35.12 | % 74.18/35.12 | Instantiating formula (9) with all_0_7_7, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms unordered_pair(all_0_5_5, all_0_4_4) = all_0_3_3, in(all_0_7_7, all_0_3_3), yields: % 74.18/35.12 | (35) all_0_4_4 = all_0_7_7 | all_0_5_5 = all_0_7_7 % 74.18/35.12 | % 74.18/35.12 | Instantiating formula (9) with all_0_4_4, all_0_3_3, all_0_6_6, all_0_7_7 and discharging atoms unordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3, in(all_0_4_4, all_0_3_3), yields: % 74.18/35.12 | (36) all_0_4_4 = all_0_6_6 | all_0_4_4 = all_0_7_7 % 74.18/35.12 | % 74.18/35.12 | Instantiating formula (9) with all_0_5_5, all_0_3_3, all_0_6_6, all_0_7_7 and discharging atoms unordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3, in(all_0_5_5, all_0_3_3), yields: % 74.18/35.12 | (37) all_0_5_5 = all_0_6_6 | all_0_5_5 = all_0_7_7 % 74.18/35.12 | % 74.18/35.12 +-Applying beta-rule and splitting (37), into two cases. % 74.18/35.12 |-Branch one: % 74.18/35.12 | (38) all_0_5_5 = all_0_6_6 % 74.18/35.12 | % 74.18/35.12 +-Applying beta-rule and splitting (36), into two cases. % 74.18/35.12 |-Branch one: % 74.18/35.12 | (39) all_0_4_4 = all_0_6_6 % 74.18/35.12 | % 74.18/35.12 | Equations (39) can reduce 22 to: % 74.18/35.12 | (40) ~ (all_0_6_6 = all_0_7_7) % 74.18/35.12 | % 74.18/35.12 +-Applying beta-rule and splitting (35), into two cases. % 74.18/35.12 |-Branch one: % 74.18/35.12 | (41) all_0_4_4 = all_0_7_7 % 74.18/35.12 | % 74.18/35.12 | Combining equations (39,41) yields a new equation: % 74.18/35.12 | (42) all_0_6_6 = all_0_7_7 % 74.18/35.12 | % 74.18/35.12 | Simplifying 42 yields: % 74.18/35.12 | (43) all_0_6_6 = all_0_7_7 % 74.18/35.12 | % 74.18/35.12 | Equations (43) can reduce 40 to: % 74.18/35.12 | (44) $false % 74.18/35.12 | % 74.18/35.12 |-The branch is then unsatisfiable % 74.18/35.12 |-Branch two: % 74.18/35.12 | (45) all_0_5_5 = all_0_7_7 % 74.18/35.12 | % 74.18/35.12 | Combining equations (45,38) yields a new equation: % 74.18/35.12 | (43) all_0_6_6 = all_0_7_7 % 74.18/35.12 | % 74.18/35.12 | Equations (43) can reduce 40 to: % 74.18/35.12 | (44) $false % 74.18/35.12 | % 74.18/35.12 |-The branch is then unsatisfiable % 74.18/35.12 |-Branch two: % 74.18/35.12 | (41) all_0_4_4 = all_0_7_7 % 74.18/35.12 | % 74.18/35.12 | Equations (41) can reduce 22 to: % 74.18/35.12 | (44) $false % 74.18/35.12 | % 74.18/35.12 |-The branch is then unsatisfiable % 74.18/35.12 |-Branch two: % 74.18/35.12 | (45) all_0_5_5 = all_0_7_7 % 74.18/35.12 | % 74.18/35.12 | Equations (45) can reduce 26 to: % 74.18/35.12 | (44) $false % 74.18/35.12 | % 74.18/35.12 |-The branch is then unsatisfiable % 74.18/35.12 |-Branch two: % 74.18/35.12 | (52) all_0_3_3 = all_0_8_8 | ? [v0] : ? [v1] : (singleton(all_0_4_4) = v1 & singleton(all_0_5_5) = v0 & (v1 = all_0_3_3 | v0 = all_0_3_3)) % 74.18/35.12 | % 74.18/35.12 +-Applying beta-rule and splitting (52), into two cases. % 74.18/35.12 |-Branch one: % 74.18/35.12 | (53) all_0_3_3 = all_0_8_8 % 74.18/35.12 | % 74.18/35.12 | From (53) and (29) follows: % 74.18/35.12 | (54) in(all_0_7_7, all_0_8_8) % 74.18/35.12 | % 74.18/35.12 | Instantiating formula (2) with all_0_7_7 and discharging atoms in(all_0_7_7, all_0_8_8), yields: % 74.18/35.12 | (55) $false % 74.18/35.12 | % 74.18/35.12 |-The branch is then unsatisfiable % 74.18/35.12 |-Branch two: % 74.18/35.12 | (56) ? [v0] : ? [v1] : (singleton(all_0_4_4) = v1 & singleton(all_0_5_5) = v0 & (v1 = all_0_3_3 | v0 = all_0_3_3)) % 74.18/35.12 | % 74.18/35.12 | Instantiating (56) with all_23_0_9, all_23_1_10 yields: % 74.18/35.12 | (57) singleton(all_0_4_4) = all_23_0_9 & singleton(all_0_5_5) = all_23_1_10 & (all_23_0_9 = all_0_3_3 | all_23_1_10 = all_0_3_3) % 74.18/35.12 | % 74.18/35.12 | Applying alpha-rule on (57) yields: % 74.18/35.12 | (58) singleton(all_0_4_4) = all_23_0_9 % 74.18/35.12 | (59) singleton(all_0_5_5) = all_23_1_10 % 74.18/35.12 | (60) all_23_0_9 = all_0_3_3 | all_23_1_10 = all_0_3_3 % 74.18/35.12 | % 74.18/35.12 +-Applying beta-rule and splitting (60), into two cases. % 74.18/35.12 |-Branch one: % 74.18/35.12 | (61) all_23_0_9 = all_0_3_3 % 74.18/35.12 | % 74.18/35.12 | From (61) and (58) follows: % 74.18/35.12 | (62) singleton(all_0_4_4) = all_0_3_3 % 74.18/35.12 | % 74.18/35.12 | Instantiating formula (10) with all_0_3_3, all_0_6_6, all_0_7_7, all_0_4_4 and discharging atoms singleton(all_0_4_4) = all_0_3_3, unordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3, yields: % 74.18/35.12 | (41) all_0_4_4 = all_0_7_7 % 74.18/35.12 | % 74.18/35.12 | Equations (41) can reduce 22 to: % 74.18/35.12 | (44) $false % 74.18/35.12 | % 74.18/35.12 |-The branch is then unsatisfiable % 74.18/35.12 |-Branch two: % 74.18/35.12 | (65) all_23_1_10 = all_0_3_3 % 74.18/35.12 | % 74.18/35.12 | From (65) and (59) follows: % 74.18/35.12 | (66) singleton(all_0_5_5) = all_0_3_3 % 74.18/35.12 | % 74.18/35.12 | Instantiating formula (10) with all_0_3_3, all_0_6_6, all_0_7_7, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_3_3, unordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3, yields: % 74.18/35.12 | (45) all_0_5_5 = all_0_7_7 % 74.18/35.12 | % 74.18/35.12 | Equations (45) can reduce 26 to: % 74.18/35.12 | (44) $false % 74.18/35.12 | % 74.18/35.12 |-The branch is then unsatisfiable % 74.18/35.12 % SZS output end Proof for theBenchmark % 74.18/35.12 % 74.18/35.12 34520ms %------------------------------------------------------------------------------