%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET986+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n007.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 00:23:37 EDT 2022 % Result : Theorem 33.16s 9.46s % Output : Proof 75.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET986+1 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n007.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 19:43:46 EDT 2022 % 0.13/0.34 % CPUTime : % 0.59/0.60 ____ _ % 0.59/0.60 ___ / __ \_____(_)___ ________ __________ % 0.59/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.59/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.59/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.59/0.60 % 0.59/0.60 A Theorem Prover for First-Order Logic % 0.59/0.61 (ePrincess v.1.0) % 0.59/0.61 % 0.59/0.61 (c) Philipp Rümmer, 2009-2015 % 0.59/0.61 (c) Peter Backeman, 2014-2015 % 0.59/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.59/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.59/0.61 Bug reports to peter@backeman.se % 0.59/0.61 % 0.59/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.59/0.61 % 0.59/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.69/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.45/0.93 Prover 0: Preprocessing ... % 1.87/1.15 Prover 0: Warning: ignoring some quantifiers % 2.11/1.17 Prover 0: Constructing countermodel ... % 3.15/1.47 Prover 0: gave up % 3.15/1.47 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.15/1.49 Prover 1: Preprocessing ... % 3.37/1.59 Prover 1: Warning: ignoring some quantifiers % 3.37/1.59 Prover 1: Constructing countermodel ... % 4.66/1.82 Prover 1: gave up % 4.66/1.82 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.75/1.83 Prover 2: Preprocessing ... % 5.21/1.92 Prover 2: Warning: ignoring some quantifiers % 5.21/1.93 Prover 2: Constructing countermodel ... % 6.10/2.14 Prover 2: gave up % 6.10/2.14 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 6.10/2.15 Prover 3: Preprocessing ... % 6.10/2.18 Prover 3: Warning: ignoring some quantifiers % 6.10/2.19 Prover 3: Constructing countermodel ... % 6.58/2.26 Prover 3: gave up % 6.58/2.26 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 6.58/2.28 Prover 4: Preprocessing ... % 7.31/2.39 Prover 4: Warning: ignoring some quantifiers % 7.31/2.39 Prover 4: Constructing countermodel ... % 11.66/3.44 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 11.74/3.46 Prover 5: Preprocessing ... % 12.06/3.55 Prover 5: Warning: ignoring some quantifiers % 12.06/3.55 Prover 5: Constructing countermodel ... % 17.25/4.85 Prover 5: gave up % 17.25/4.85 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 17.54/4.87 Prover 6: Preprocessing ... % 17.70/4.90 Prover 6: Warning: ignoring some quantifiers % 17.70/4.91 Prover 6: Constructing countermodel ... % 17.84/4.99 Prover 6: gave up % 17.84/4.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 17.84/5.00 Prover 7: Preprocessing ... % 17.84/5.02 Prover 7: Proving ... % 33.16/9.46 Prover 7: proved (4472ms) % 33.16/9.46 Prover 4: stopped % 33.16/9.46 % 33.16/9.46 % SZS status Theorem for theBenchmark % 33.16/9.46 % 33.16/9.46 Generating proof ... found it (size 38) % 75.05/37.29 % 75.05/37.29 % SZS output start Proof for theBenchmark % 75.05/37.29 Assumed formulas after preprocessing and simplification: % 75.05/37.29 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ in(v0, v1) | in(v0, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ in(v0, v4) | ( ~ (v2 = v0) & in(v0, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(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_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(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_union2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v3] : (in(v3, v2) | ( ~ in(v3, v1) & ~ in(v3, v0))))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(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] : ( ~ 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] : subset(v0, v0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = v1) & set_difference(v1, v2) = v3 & singleton(v0) = v2 & set_union2(v3, v2) = v4 & in(v0, v1)) & ? [v0] : ~ empty(v0) & ? [v0] : empty(v0) % 75.19/37.32 | Applying alpha-rule on (0) yields: % 75.19/37.32 | (1) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v3] : (in(v3, v2) | ( ~ in(v3, v1) & ~ in(v3, v0))))) % 75.19/37.32 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 75.19/37.32 | (3) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 75.19/37.32 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ in(v0, v4) | ( ~ (v2 = v0) & in(v0, v1))) % 75.19/37.32 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 75.19/37.32 | (6) ! [v0] : subset(v0, v0) % 75.19/37.32 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 75.19/37.32 | (8) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | (in(v0, v1) & ! [v2] : (v2 = v0 | ~ in(v2, v1)))) % 75.19/37.32 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ in(v0, v1) | in(v0, v4)) % 75.19/37.32 | (10) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = v1) & set_difference(v1, v2) = v3 & singleton(v0) = v2 & set_union2(v3, v2) = v4 & in(v0, v1)) % 75.19/37.32 | (11) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 75.19/37.32 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 75.19/37.32 | (13) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ in(v2, v0) | in(v2, v1))) % 75.19/37.33 | (14) ! [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)))) % 75.19/37.33 | (15) ? [v0] : empty(v0) % 75.19/37.33 | (16) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ! [v2] : (v2 = v1 | ? [v3] : (( ~ (v3 = v0) | ~ in(v0, v2)) & (v3 = v0 | in(v3, v2))))) % 75.19/37.33 | (17) ! [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)))))) % 75.19/37.33 | (18) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 75.19/37.33 | (19) ? [v0] : ~ empty(v0) % 75.19/37.33 | (20) ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) % 75.19/37.33 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 75.19/37.33 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 75.19/37.33 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(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))))) % 75.19/37.33 | % 75.19/37.33 | Instantiating (10) with all_3_0_1, all_3_1_2, all_3_2_3, all_3_3_4, all_3_4_5 yields: % 75.19/37.33 | (24) ~ (all_3_0_1 = all_3_3_4) & set_difference(all_3_3_4, all_3_2_3) = all_3_1_2 & singleton(all_3_4_5) = all_3_2_3 & set_union2(all_3_1_2, all_3_2_3) = all_3_0_1 & in(all_3_4_5, all_3_3_4) % 75.19/37.33 | % 75.19/37.33 | Applying alpha-rule on (24) yields: % 75.19/37.33 | (25) singleton(all_3_4_5) = all_3_2_3 % 75.19/37.33 | (26) ~ (all_3_0_1 = all_3_3_4) % 75.19/37.33 | (27) in(all_3_4_5, all_3_3_4) % 75.19/37.33 | (28) set_union2(all_3_1_2, all_3_2_3) = all_3_0_1 % 75.19/37.33 | (29) set_difference(all_3_3_4, all_3_2_3) = all_3_1_2 % 75.19/37.33 | % 75.19/37.33 | Instantiating formula (14) with all_3_1_2, all_3_2_3, all_3_3_4 and discharging atoms set_difference(all_3_3_4, all_3_2_3) = all_3_1_2, yields: % 75.19/37.33 | (30) ! [v0] : ( ~ in(v0, all_3_1_2) | (in(v0, all_3_3_4) & ~ in(v0, all_3_2_3))) & ! [v0] : ( ~ in(v0, all_3_3_4) | in(v0, all_3_1_2) | in(v0, all_3_2_3)) % 75.19/37.33 | % 75.19/37.33 | Applying alpha-rule on (30) yields: % 75.19/37.33 | (31) ! [v0] : ( ~ in(v0, all_3_1_2) | (in(v0, all_3_3_4) & ~ in(v0, all_3_2_3))) % 75.19/37.33 | (32) ! [v0] : ( ~ in(v0, all_3_3_4) | in(v0, all_3_1_2) | in(v0, all_3_2_3)) % 75.19/37.33 | % 75.19/37.33 | Instantiating formula (8) with all_3_2_3, all_3_4_5 and discharging atoms singleton(all_3_4_5) = all_3_2_3, yields: % 75.19/37.33 | (33) in(all_3_4_5, all_3_2_3) & ! [v0] : (v0 = all_3_4_5 | ~ in(v0, all_3_2_3)) % 75.19/37.33 | % 75.19/37.33 | Applying alpha-rule on (33) yields: % 75.19/37.33 | (34) in(all_3_4_5, all_3_2_3) % 75.19/37.33 | (35) ! [v0] : (v0 = all_3_4_5 | ~ in(v0, all_3_2_3)) % 75.19/37.33 | % 75.19/37.33 | Instantiating formula (7) with all_3_0_1, all_3_2_3, all_3_1_2 and discharging atoms set_union2(all_3_1_2, all_3_2_3) = all_3_0_1, yields: % 75.19/37.33 | (36) set_union2(all_3_2_3, all_3_1_2) = all_3_0_1 % 75.19/37.33 | % 75.19/37.33 | Instantiating formula (23) with all_3_0_1, all_3_1_2, all_3_2_3 and discharging atoms set_union2(all_3_2_3, all_3_1_2) = all_3_0_1, yields: % 75.19/37.33 | (37) ! [v0] : (v0 = all_3_0_1 | ? [v1] : (( ~ in(v1, v0) | ( ~ in(v1, all_3_1_2) & ~ in(v1, all_3_2_3))) & (in(v1, v0) | in(v1, all_3_1_2) | in(v1, all_3_2_3)))) % 75.19/37.34 | % 75.19/37.34 | Introducing new symbol ex_85_0_20 defined by: % 75.19/37.34 | (38) ex_85_0_20 = all_3_3_4 % 75.19/37.34 | % 75.19/37.34 | Instantiating formula (37) with ex_85_0_20 yields: % 75.19/37.34 | (39) ex_85_0_20 = all_3_0_1 | ? [v0] : (( ~ in(v0, ex_85_0_20) | ( ~ in(v0, all_3_1_2) & ~ in(v0, all_3_2_3))) & (in(v0, ex_85_0_20) | in(v0, all_3_1_2) | in(v0, all_3_2_3))) % 75.19/37.34 | % 75.19/37.34 +-Applying beta-rule and splitting (39), into two cases. % 75.19/37.34 |-Branch one: % 75.19/37.34 | (40) ex_85_0_20 = all_3_0_1 % 75.19/37.34 | % 75.19/37.34 | Combining equations (40,38) yields a new equation: % 75.19/37.34 | (41) all_3_0_1 = all_3_3_4 % 75.19/37.34 | % 75.19/37.34 | Simplifying 41 yields: % 75.19/37.34 | (42) all_3_0_1 = all_3_3_4 % 75.19/37.34 | % 75.19/37.34 | Equations (42) can reduce 26 to: % 75.19/37.34 | (43) $false % 75.19/37.34 | % 75.19/37.34 |-The branch is then unsatisfiable % 75.19/37.34 |-Branch two: % 75.19/37.34 | (44) ? [v0] : (( ~ in(v0, ex_85_0_20) | ( ~ in(v0, all_3_1_2) & ~ in(v0, all_3_2_3))) & (in(v0, ex_85_0_20) | in(v0, all_3_1_2) | in(v0, all_3_2_3))) % 75.19/37.34 | % 75.19/37.34 | Instantiating (44) with all_88_0_23 yields: % 75.36/37.34 | (45) ( ~ in(all_88_0_23, ex_85_0_20) | ( ~ in(all_88_0_23, all_3_1_2) & ~ in(all_88_0_23, all_3_2_3))) & (in(all_88_0_23, ex_85_0_20) | in(all_88_0_23, all_3_1_2) | in(all_88_0_23, all_3_2_3)) % 75.36/37.34 | % 75.36/37.34 | Applying alpha-rule on (45) yields: % 75.36/37.34 | (46) ~ in(all_88_0_23, ex_85_0_20) | ( ~ in(all_88_0_23, all_3_1_2) & ~ in(all_88_0_23, all_3_2_3)) % 75.36/37.34 | (47) in(all_88_0_23, ex_85_0_20) | in(all_88_0_23, all_3_1_2) | in(all_88_0_23, all_3_2_3) % 75.36/37.34 | % 75.36/37.34 +-Applying beta-rule and splitting (47), into two cases. % 75.36/37.34 |-Branch one: % 75.36/37.34 | (48) in(all_88_0_23, ex_85_0_20) % 75.36/37.34 | % 75.36/37.34 +-Applying beta-rule and splitting (46), into two cases. % 75.36/37.34 |-Branch one: % 75.36/37.34 | (49) ~ in(all_88_0_23, ex_85_0_20) % 75.36/37.34 | % 75.36/37.34 | Using (48) and (49) yields: % 75.36/37.34 | (50) $false % 75.36/37.34 | % 75.36/37.34 |-The branch is then unsatisfiable % 75.36/37.34 |-Branch two: % 75.36/37.34 | (51) ~ in(all_88_0_23, all_3_1_2) & ~ in(all_88_0_23, all_3_2_3) % 75.36/37.34 | % 75.36/37.34 | Applying alpha-rule on (51) yields: % 75.36/37.34 | (52) ~ in(all_88_0_23, all_3_1_2) % 75.36/37.34 | (53) ~ in(all_88_0_23, all_3_2_3) % 75.36/37.34 | % 75.36/37.34 | Instantiating formula (32) with all_88_0_23 and discharging atoms ~ in(all_88_0_23, all_3_1_2), ~ in(all_88_0_23, all_3_2_3), yields: % 75.36/37.34 | (54) ~ in(all_88_0_23, all_3_3_4) % 75.36/37.34 | % 75.36/37.34 | From (38) and (48) follows: % 75.36/37.34 | (55) in(all_88_0_23, all_3_3_4) % 75.36/37.34 | % 75.36/37.34 | Using (55) and (54) yields: % 75.36/37.34 | (50) $false % 75.36/37.34 | % 75.36/37.34 |-The branch is then unsatisfiable % 75.36/37.34 |-Branch two: % 75.36/37.34 | (49) ~ in(all_88_0_23, ex_85_0_20) % 75.36/37.34 | (58) in(all_88_0_23, all_3_1_2) | in(all_88_0_23, all_3_2_3) % 75.36/37.34 | % 75.36/37.34 +-Applying beta-rule and splitting (58), into two cases. % 75.36/37.34 |-Branch one: % 75.36/37.34 | (59) in(all_88_0_23, all_3_1_2) % 75.36/37.34 | % 75.36/37.34 | Instantiating formula (4) with all_3_1_2, all_3_2_3, all_3_4_5, all_3_3_4, all_88_0_23 and discharging atoms set_difference(all_3_3_4, all_3_2_3) = all_3_1_2, singleton(all_3_4_5) = all_3_2_3, in(all_88_0_23, all_3_1_2), yields: % 75.36/37.34 | (60) ~ (all_88_0_23 = all_3_4_5) & in(all_88_0_23, all_3_3_4) % 75.36/37.34 | % 75.36/37.34 | Applying alpha-rule on (60) yields: % 75.36/37.34 | (61) ~ (all_88_0_23 = all_3_4_5) % 75.36/37.34 | (55) in(all_88_0_23, all_3_3_4) % 75.36/37.34 | % 75.36/37.34 | From (38) and (49) follows: % 75.36/37.34 | (54) ~ in(all_88_0_23, all_3_3_4) % 75.36/37.34 | % 75.36/37.34 | Using (55) and (54) yields: % 75.36/37.34 | (50) $false % 75.36/37.34 | % 75.36/37.34 |-The branch is then unsatisfiable % 75.36/37.34 |-Branch two: % 75.36/37.34 | (65) in(all_88_0_23, all_3_2_3) % 75.36/37.34 | % 75.36/37.34 | Instantiating formula (35) with all_88_0_23 and discharging atoms in(all_88_0_23, all_3_2_3), yields: % 75.36/37.34 | (66) all_88_0_23 = all_3_4_5 % 75.36/37.34 | % 75.36/37.34 | From (66) and (49) follows: % 75.36/37.34 | (67) ~ in(all_3_4_5, ex_85_0_20) % 75.36/37.34 | % 75.36/37.34 | From (38) and (67) follows: % 75.36/37.34 | (68) ~ in(all_3_4_5, all_3_3_4) % 75.36/37.34 | % 75.36/37.34 | Using (27) and (68) yields: % 75.36/37.34 | (50) $false % 75.36/37.34 | % 75.36/37.34 |-The branch is then unsatisfiable % 75.36/37.35 % SZS output end Proof for theBenchmark % 75.36/37.35 % 75.36/37.35 36726ms %------------------------------------------------------------------------------