%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU162+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n006.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 08:47:09 EDT 2022 % Result : Theorem 2.92s 1.43s % Output : Proof 4.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU162+1 : TPTP v8.1.0. Released v3.3.0. % 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n006.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 : Sun Jun 19 05:06:10 EDT 2022 % 0.13/0.34 % CPUTime : % 0.55/0.57 ____ _ % 0.55/0.57 ___ / __ \_____(_)___ ________ __________ % 0.55/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.55/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.55/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.55/0.57 % 0.55/0.57 A Theorem Prover for First-Order Logic % 0.55/0.57 (ePrincess v.1.0) % 0.55/0.57 % 0.55/0.57 (c) Philipp Rümmer, 2009-2015 % 0.55/0.57 (c) Peter Backeman, 2014-2015 % 0.55/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.55/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.55/0.57 Bug reports to peter@backeman.se % 0.55/0.57 % 0.55/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.55/0.57 % 0.55/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.60/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.32/0.89 Prover 0: Preprocessing ... % 1.48/1.00 Prover 0: Warning: ignoring some quantifiers % 1.62/1.01 Prover 0: Constructing countermodel ... % 1.83/1.16 Prover 0: gave up % 1.83/1.16 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.18/1.17 Prover 1: Preprocessing ... % 2.34/1.23 Prover 1: Constructing countermodel ... % 2.40/1.30 Prover 1: gave up % 2.40/1.30 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.40/1.32 Prover 2: Preprocessing ... % 2.69/1.37 Prover 2: Warning: ignoring some quantifiers % 2.69/1.37 Prover 2: Constructing countermodel ... % 2.92/1.43 Prover 2: proved (125ms) % 2.92/1.43 % 2.92/1.43 No countermodel exists, formula is valid % 2.92/1.43 % SZS status Theorem for theBenchmark % 2.92/1.43 % 2.92/1.43 Generating proof ... Warning: ignoring some quantifiers % 3.82/1.65 found it (size 47) % 3.82/1.65 % 3.82/1.65 % SZS output start Proof for theBenchmark % 3.82/1.65 Assumed formulas after preprocessing and simplification: % 3.82/1.65 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (set_difference(v0, v2) = v3 & singleton(v1) = v2 & in(v1, v0) = v4 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (singleton(v5) = v7) | ~ (disjoint(v7, v6) = v8) | in(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (set_difference(v8, v7) = v6) | ~ (set_difference(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (disjoint(v8, v7) = v6) | ~ (disjoint(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (in(v8, v7) = v6) | ~ (in(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (set_difference(v5, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & disjoint(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (disjoint(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & disjoint(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (disjoint(v5, v6) = v7) | ? [v8] : ( ~ (v8 = v5) & set_difference(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (in(v5, v6) = v7) | ? [v8] : (singleton(v5) = v8 & disjoint(v8, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (singleton(v7) = v6) | ~ (singleton(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (singleton(v5) = v7) | ~ (disjoint(v7, v6) = 0) | ? [v8] : ( ~ (v8 = 0) & in(v5, v6) = v8)) & ! [v5] : ! [v6] : ( ~ (set_difference(v5, v6) = v5) | disjoint(v5, v6) = 0) & ! [v5] : ! [v6] : ( ~ (disjoint(v5, v6) = 0) | set_difference(v5, v6) = v5) & ! [v5] : ! [v6] : ( ~ (disjoint(v5, v6) = 0) | disjoint(v6, v5) = 0) & ! [v5] : ! [v6] : ( ~ (in(v6, v5) = 0) | ? [v7] : ( ~ (v7 = 0) & in(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (in(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & singleton(v5) = v7 & disjoint(v7, v6) = v8)) & ! [v5] : ! [v6] : ( ~ (in(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & in(v6, v5) = v7)) & ? [v5] : ? [v6] : ? [v7] : set_difference(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : disjoint(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : in(v6, v5) = v7 & ? [v5] : ? [v6] : singleton(v5) = v6 & ((v4 = 0 & v3 = v0) | ( ~ (v4 = 0) & ~ (v3 = v0)))) % 3.82/1.69 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 3.82/1.69 | (1) set_difference(all_0_4_4, all_0_2_2) = all_0_1_1 & singleton(all_0_3_3) = all_0_2_2 & in(all_0_3_3, all_0_4_4) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (disjoint(v2, v1) = v3) | in(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : (singleton(v0) = v3 & disjoint(v3, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (disjoint(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & singleton(v0) = v2 & disjoint(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ? [v0] : ? [v1] : ? [v2] : set_difference(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : singleton(v0) = v1 & ((all_0_0_0 = 0 & all_0_1_1 = all_0_4_4) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = all_0_4_4))) % 3.82/1.69 | % 3.82/1.69 | Applying alpha-rule on (1) yields: % 3.82/1.69 | (2) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) % 3.82/1.69 | (3) ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2 % 3.82/1.69 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) % 3.82/1.70 | (5) (all_0_0_0 = 0 & all_0_1_1 = all_0_4_4) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = all_0_4_4)) % 3.82/1.70 | (6) in(all_0_3_3, all_0_4_4) = all_0_0_0 % 3.82/1.70 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : (singleton(v0) = v3 & disjoint(v3, v1) = 0)) % 3.82/1.70 | (8) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 % 3.82/1.70 | (9) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 3.82/1.70 | (10) ? [v0] : ? [v1] : ? [v2] : set_difference(v1, v0) = v2 % 3.82/1.70 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 3.82/1.70 | (12) ? [v0] : ? [v1] : singleton(v0) = v1 % 3.82/1.70 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3)) % 3.82/1.70 | (14) singleton(all_0_3_3) = all_0_2_2 % 3.82/1.70 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 3.82/1.70 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) % 3.82/1.70 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (disjoint(v2, v1) = v3) | in(v0, v1) = 0) % 3.82/1.70 | (18) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 3.82/1.70 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (disjoint(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 3.82/1.70 | (20) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0) % 3.82/1.70 | (21) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1) = 0) % 3.82/1.70 | (22) set_difference(all_0_4_4, all_0_2_2) = all_0_1_1 % 3.82/1.70 | (23) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & singleton(v0) = v2 & disjoint(v2, v1) = v3)) % 3.82/1.70 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 3.82/1.70 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 3.82/1.70 | % 3.82/1.70 | Instantiating formula (16) with all_0_1_1, all_0_2_2, all_0_4_4 and discharging atoms set_difference(all_0_4_4, all_0_2_2) = all_0_1_1, yields: % 3.82/1.70 | (26) all_0_1_1 = all_0_4_4 | ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_4_4, all_0_2_2) = v0) % 3.82/1.70 | % 3.82/1.70 | Instantiating formula (7) with all_0_0_0, all_0_4_4, all_0_3_3 and discharging atoms in(all_0_3_3, all_0_4_4) = all_0_0_0, yields: % 3.82/1.70 | (27) all_0_0_0 = 0 | ? [v0] : (singleton(all_0_3_3) = v0 & disjoint(v0, all_0_4_4) = 0) % 3.82/1.70 | % 3.82/1.70 +-Applying beta-rule and splitting (5), into two cases. % 3.82/1.70 |-Branch one: % 3.82/1.70 | (28) all_0_0_0 = 0 & all_0_1_1 = all_0_4_4 % 3.82/1.70 | % 3.82/1.70 | Applying alpha-rule on (28) yields: % 3.82/1.70 | (29) all_0_0_0 = 0 % 3.82/1.70 | (30) all_0_1_1 = all_0_4_4 % 3.82/1.71 | % 4.14/1.71 | From (30) and (22) follows: % 4.14/1.71 | (31) set_difference(all_0_4_4, all_0_2_2) = all_0_4_4 % 4.14/1.71 | % 4.14/1.71 | From (29) and (6) follows: % 4.14/1.71 | (32) in(all_0_3_3, all_0_4_4) = 0 % 4.14/1.71 | % 4.14/1.71 | Instantiating formula (21) with all_0_2_2, all_0_4_4 and discharging atoms set_difference(all_0_4_4, all_0_2_2) = all_0_4_4, yields: % 4.14/1.71 | (33) disjoint(all_0_4_4, all_0_2_2) = 0 % 4.14/1.71 | % 4.14/1.71 | Instantiating formula (23) with all_0_4_4, all_0_3_3 and discharging atoms in(all_0_3_3, all_0_4_4) = 0, yields: % 4.14/1.71 | (34) ? [v0] : ? [v1] : ( ~ (v1 = 0) & singleton(all_0_3_3) = v0 & disjoint(v0, all_0_4_4) = v1) % 4.14/1.71 | % 4.14/1.71 | Instantiating (34) with all_24_0_16, all_24_1_17 yields: % 4.14/1.71 | (35) ~ (all_24_0_16 = 0) & singleton(all_0_3_3) = all_24_1_17 & disjoint(all_24_1_17, all_0_4_4) = all_24_0_16 % 4.14/1.71 | % 4.14/1.71 | Applying alpha-rule on (35) yields: % 4.14/1.71 | (36) ~ (all_24_0_16 = 0) % 4.14/1.71 | (37) singleton(all_0_3_3) = all_24_1_17 % 4.14/1.71 | (38) disjoint(all_24_1_17, all_0_4_4) = all_24_0_16 % 4.14/1.71 | % 4.14/1.71 | Instantiating formula (24) with all_0_3_3, all_24_1_17, all_0_2_2 and discharging atoms singleton(all_0_3_3) = all_24_1_17, singleton(all_0_3_3) = all_0_2_2, yields: % 4.14/1.71 | (39) all_24_1_17 = all_0_2_2 % 4.14/1.71 | % 4.14/1.71 | From (39) and (38) follows: % 4.14/1.71 | (40) disjoint(all_0_2_2, all_0_4_4) = all_24_0_16 % 4.14/1.71 | % 4.14/1.71 | Instantiating formula (4) with all_24_0_16, all_0_2_2, all_0_4_4 and discharging atoms disjoint(all_0_2_2, all_0_4_4) = all_24_0_16, yields: % 4.14/1.71 | (41) all_24_0_16 = 0 | ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_4_4, all_0_2_2) = v0) % 4.14/1.71 | % 4.14/1.71 | Instantiating formula (13) with all_24_0_16, all_0_4_4, all_0_2_2 and discharging atoms disjoint(all_0_2_2, all_0_4_4) = all_24_0_16, yields: % 4.14/1.71 | (42) all_24_0_16 = 0 | ? [v0] : ( ~ (v0 = all_0_2_2) & set_difference(all_0_2_2, all_0_4_4) = v0) % 4.14/1.71 | % 4.14/1.71 | Instantiating formula (2) with all_0_2_2, all_0_4_4 and discharging atoms disjoint(all_0_4_4, all_0_2_2) = 0, yields: % 4.14/1.71 | (43) disjoint(all_0_2_2, all_0_4_4) = 0 % 4.14/1.71 | % 4.14/1.71 +-Applying beta-rule and splitting (41), into two cases. % 4.14/1.71 |-Branch one: % 4.14/1.71 | (44) all_24_0_16 = 0 % 4.14/1.71 | % 4.14/1.71 | Equations (44) can reduce 36 to: % 4.14/1.71 | (45) $false % 4.14/1.71 | % 4.14/1.71 |-The branch is then unsatisfiable % 4.14/1.71 |-Branch two: % 4.14/1.71 | (36) ~ (all_24_0_16 = 0) % 4.14/1.71 | (47) ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_4_4, all_0_2_2) = v0) % 4.14/1.71 | % 4.14/1.71 +-Applying beta-rule and splitting (42), into two cases. % 4.14/1.71 |-Branch one: % 4.14/1.71 | (44) all_24_0_16 = 0 % 4.14/1.71 | % 4.14/1.71 | Equations (44) can reduce 36 to: % 4.14/1.71 | (45) $false % 4.14/1.71 | % 4.14/1.71 |-The branch is then unsatisfiable % 4.14/1.71 |-Branch two: % 4.14/1.71 | (36) ~ (all_24_0_16 = 0) % 4.14/1.71 | (51) ? [v0] : ( ~ (v0 = all_0_2_2) & set_difference(all_0_2_2, all_0_4_4) = v0) % 4.14/1.71 | % 4.14/1.71 | Instantiating formula (15) with all_0_2_2, all_0_4_4, 0, all_24_0_16 and discharging atoms disjoint(all_0_2_2, all_0_4_4) = all_24_0_16, disjoint(all_0_2_2, all_0_4_4) = 0, yields: % 4.14/1.71 | (44) all_24_0_16 = 0 % 4.14/1.71 | % 4.14/1.71 | Equations (44) can reduce 36 to: % 4.14/1.71 | (45) $false % 4.14/1.71 | % 4.14/1.71 |-The branch is then unsatisfiable % 4.14/1.71 |-Branch two: % 4.14/1.71 | (54) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = all_0_4_4) % 4.14/1.71 | % 4.14/1.71 | Applying alpha-rule on (54) yields: % 4.14/1.71 | (55) ~ (all_0_0_0 = 0) % 4.14/1.71 | (56) ~ (all_0_1_1 = all_0_4_4) % 4.14/1.71 | % 4.14/1.71 +-Applying beta-rule and splitting (27), into two cases. % 4.14/1.71 |-Branch one: % 4.14/1.71 | (29) all_0_0_0 = 0 % 4.14/1.72 | % 4.14/1.72 | Equations (29) can reduce 55 to: % 4.14/1.72 | (45) $false % 4.14/1.72 | % 4.14/1.72 |-The branch is then unsatisfiable % 4.14/1.72 |-Branch two: % 4.14/1.72 | (55) ~ (all_0_0_0 = 0) % 4.14/1.72 | (60) ? [v0] : (singleton(all_0_3_3) = v0 & disjoint(v0, all_0_4_4) = 0) % 4.14/1.72 | % 4.14/1.72 | Instantiating (60) with all_22_0_22 yields: % 4.14/1.72 | (61) singleton(all_0_3_3) = all_22_0_22 & disjoint(all_22_0_22, all_0_4_4) = 0 % 4.14/1.72 | % 4.14/1.72 | Applying alpha-rule on (61) yields: % 4.14/1.72 | (62) singleton(all_0_3_3) = all_22_0_22 % 4.14/1.72 | (63) disjoint(all_22_0_22, all_0_4_4) = 0 % 4.14/1.72 | % 4.14/1.72 +-Applying beta-rule and splitting (26), into two cases. % 4.14/1.72 |-Branch one: % 4.14/1.72 | (30) all_0_1_1 = all_0_4_4 % 4.14/1.72 | % 4.14/1.72 | Equations (30) can reduce 56 to: % 4.14/1.72 | (45) $false % 4.14/1.72 | % 4.14/1.72 |-The branch is then unsatisfiable % 4.14/1.72 |-Branch two: % 4.14/1.72 | (56) ~ (all_0_1_1 = all_0_4_4) % 4.14/1.72 | (47) ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_4_4, all_0_2_2) = v0) % 4.14/1.72 | % 4.14/1.72 | Instantiating (47) with all_28_0_23 yields: % 4.14/1.72 | (68) ~ (all_28_0_23 = 0) & disjoint(all_0_4_4, all_0_2_2) = all_28_0_23 % 4.14/1.72 | % 4.14/1.72 | Applying alpha-rule on (68) yields: % 4.14/1.72 | (69) ~ (all_28_0_23 = 0) % 4.14/1.72 | (70) disjoint(all_0_4_4, all_0_2_2) = all_28_0_23 % 4.14/1.72 | % 4.14/1.72 | Instantiating formula (24) with all_0_3_3, all_22_0_22, all_0_2_2 and discharging atoms singleton(all_0_3_3) = all_22_0_22, singleton(all_0_3_3) = all_0_2_2, yields: % 4.14/1.72 | (71) all_22_0_22 = all_0_2_2 % 4.14/1.72 | % 4.14/1.72 | From (71) and (63) follows: % 4.14/1.72 | (43) disjoint(all_0_2_2, all_0_4_4) = 0 % 4.14/1.72 | % 4.14/1.72 | Instantiating formula (2) with all_0_4_4, all_0_2_2 and discharging atoms disjoint(all_0_2_2, all_0_4_4) = 0, yields: % 4.14/1.72 | (33) disjoint(all_0_4_4, all_0_2_2) = 0 % 4.14/1.72 | % 4.14/1.72 | Instantiating formula (4) with all_28_0_23, all_0_4_4, all_0_2_2 and discharging atoms disjoint(all_0_4_4, all_0_2_2) = all_28_0_23, yields: % 4.14/1.72 | (74) all_28_0_23 = 0 | ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_2_2, all_0_4_4) = v0) % 4.14/1.72 | % 4.14/1.72 +-Applying beta-rule and splitting (74), into two cases. % 4.14/1.72 |-Branch one: % 4.14/1.72 | (75) all_28_0_23 = 0 % 4.14/1.72 | % 4.14/1.72 | Equations (75) can reduce 69 to: % 4.14/1.72 | (45) $false % 4.14/1.72 | % 4.14/1.72 |-The branch is then unsatisfiable % 4.14/1.72 |-Branch two: % 4.14/1.72 | (69) ~ (all_28_0_23 = 0) % 4.14/1.72 | (78) ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_2_2, all_0_4_4) = v0) % 4.14/1.72 | % 4.14/1.72 | Instantiating formula (15) with all_0_4_4, all_0_2_2, 0, all_28_0_23 and discharging atoms disjoint(all_0_4_4, all_0_2_2) = all_28_0_23, disjoint(all_0_4_4, all_0_2_2) = 0, yields: % 4.14/1.72 | (75) all_28_0_23 = 0 % 4.14/1.72 | % 4.14/1.72 | Equations (75) can reduce 69 to: % 4.14/1.72 | (45) $false % 4.14/1.72 | % 4.14/1.72 |-The branch is then unsatisfiable % 4.14/1.72 % SZS output end Proof for theBenchmark % 4.14/1.72 % 4.14/1.72 1140ms %------------------------------------------------------------------------------