%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU162+3 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n008.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 08:47:10 EDT 2022 % Result : Theorem 2.91s 1.45s % Output : Proof 4.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SEU162+3 : TPTP v8.1.0. Released v3.2.0. % 0.04/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n008.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sun Jun 19 15:07:52 EDT 2022 % 0.12/0.33 % CPUTime : % 0.53/0.60 ____ _ % 0.53/0.60 ___ / __ \_____(_)___ ________ __________ % 0.53/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.53/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.53/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.53/0.60 % 0.53/0.60 A Theorem Prover for First-Order Logic % 0.53/0.60 (ePrincess v.1.0) % 0.53/0.60 % 0.53/0.60 (c) Philipp Rümmer, 2009-2015 % 0.53/0.60 (c) Peter Backeman, 2014-2015 % 0.53/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.53/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.53/0.60 Bug reports to peter@backeman.se % 0.53/0.60 % 0.53/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.53/0.60 % 0.53/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.78/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.32/0.91 Prover 0: Preprocessing ... % 1.51/1.02 Prover 0: Warning: ignoring some quantifiers % 1.66/1.04 Prover 0: Constructing countermodel ... % 2.13/1.17 Prover 0: gave up % 2.13/1.17 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.23/1.19 Prover 1: Preprocessing ... % 2.44/1.25 Prover 1: Constructing countermodel ... % 2.68/1.32 Prover 1: gave up % 2.68/1.32 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.68/1.33 Prover 2: Preprocessing ... % 2.91/1.39 Prover 2: Warning: ignoring some quantifiers % 2.91/1.39 Prover 2: Constructing countermodel ... % 2.91/1.45 Prover 2: proved (125ms) % 2.91/1.45 % 2.91/1.45 No countermodel exists, formula is valid % 2.91/1.45 % SZS status Theorem for theBenchmark % 2.91/1.45 % 2.91/1.45 Generating proof ... Warning: ignoring some quantifiers % 3.81/1.67 found it (size 47) % 3.81/1.67 % 3.81/1.67 % SZS output start Proof for theBenchmark % 3.81/1.67 Assumed formulas after preprocessing and simplification: % 3.81/1.67 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v6 = 0) & set_difference(v0, v2) = v3 & empty(v7) = 0 & empty(v5) = v6 & singleton(v1) = v2 & in(v1, v0) = v4 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (singleton(v8) = v10) | ~ (disjoint(v10, v9) = v11) | in(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_difference(v11, v10) = v9) | ~ (set_difference(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (disjoint(v11, v10) = v9) | ~ (disjoint(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (in(v11, v10) = v9) | ~ (in(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (set_difference(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & disjoint(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & disjoint(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v8, v9) = v10) | ? [v11] : ( ~ (v11 = v8) & set_difference(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (in(v8, v9) = v10) | ? [v11] : (singleton(v8) = v11 & disjoint(v11, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (empty(v10) = v9) | ~ (empty(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (singleton(v8) = v10) | ~ (disjoint(v10, v9) = 0) | ? [v11] : ( ~ (v11 = 0) & in(v8, v9) = v11)) & ! [v8] : ! [v9] : ( ~ (set_difference(v8, v9) = v8) | disjoint(v8, v9) = 0) & ! [v8] : ! [v9] : ( ~ (disjoint(v8, v9) = 0) | set_difference(v8, v9) = v8) & ! [v8] : ! [v9] : ( ~ (disjoint(v8, v9) = 0) | disjoint(v9, v8) = 0) & ! [v8] : ! [v9] : ( ~ (in(v9, v8) = 0) | ? [v10] : ( ~ (v10 = 0) & in(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (in(v8, v9) = 0) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & singleton(v8) = v10 & disjoint(v10, v9) = v11)) & ! [v8] : ! [v9] : ( ~ (in(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & in(v9, v8) = v10)) & ? [v8] : ? [v9] : ? [v10] : set_difference(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : disjoint(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : in(v9, v8) = v10 & ? [v8] : ? [v9] : empty(v8) = v9 & ? [v8] : ? [v9] : singleton(v8) = v9 & ((v4 = 0 & v3 = v0) | ( ~ (v4 = 0) & ~ (v3 = v0)))) % 4.06/1.70 | 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 yields: % 4.06/1.70 | (1) ~ (all_0_1_1 = 0) & set_difference(all_0_7_7, all_0_5_5) = all_0_4_4 & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & singleton(all_0_6_6) = all_0_5_5 & in(all_0_6_6, all_0_7_7) = all_0_3_3 & ! [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 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [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] : empty(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ((all_0_3_3 = 0 & all_0_4_4 = all_0_7_7) | ( ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = all_0_7_7))) % 4.06/1.71 | % 4.06/1.71 | Applying alpha-rule on (1) yields: % 4.06/1.71 | (2) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 4.06/1.71 | (3) empty(all_0_0_0) = 0 % 4.06/1.71 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : (singleton(v0) = v3 & disjoint(v3, v1) = 0)) % 4.06/1.71 | (5) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) % 4.06/1.71 | (6) set_difference(all_0_7_7, all_0_5_5) = all_0_4_4 % 4.06/1.71 | (7) in(all_0_6_6, all_0_7_7) = all_0_3_3 % 4.06/1.71 | (8) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 4.06/1.71 | (9) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0) % 4.06/1.71 | (10) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1) = 0) % 4.06/1.71 | (11) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 % 4.06/1.71 | (12) ? [v0] : ? [v1] : empty(v0) = v1 % 4.06/1.71 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) % 4.06/1.71 | (14) singleton(all_0_6_6) = all_0_5_5 % 4.06/1.71 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 4.06/1.72 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 4.06/1.72 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (disjoint(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 4.06/1.72 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) % 4.06/1.72 | (19) ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2 % 4.06/1.72 | (20) (all_0_3_3 = 0 & all_0_4_4 = all_0_7_7) | ( ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = all_0_7_7)) % 4.06/1.72 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3)) % 4.06/1.72 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 4.06/1.72 | (23) ~ (all_0_1_1 = 0) % 4.06/1.72 | (24) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & singleton(v0) = v2 & disjoint(v2, v1) = v3)) % 4.06/1.72 | (25) ? [v0] : ? [v1] : singleton(v0) = v1 % 4.06/1.72 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (disjoint(v2, v1) = v3) | in(v0, v1) = 0) % 4.06/1.72 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 4.06/1.72 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 4.06/1.72 | (29) empty(all_0_2_2) = all_0_1_1 % 4.06/1.72 | (30) ? [v0] : ? [v1] : ? [v2] : set_difference(v1, v0) = v2 % 4.06/1.72 | % 4.06/1.72 | Instantiating formula (18) with all_0_4_4, all_0_5_5, all_0_7_7 and discharging atoms set_difference(all_0_7_7, all_0_5_5) = all_0_4_4, yields: % 4.06/1.72 | (31) all_0_4_4 = all_0_7_7 | ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_7_7, all_0_5_5) = v0) % 4.06/1.72 | % 4.06/1.72 | Instantiating formula (4) with all_0_3_3, all_0_7_7, all_0_6_6 and discharging atoms in(all_0_6_6, all_0_7_7) = all_0_3_3, yields: % 4.06/1.72 | (32) all_0_3_3 = 0 | ? [v0] : (singleton(all_0_6_6) = v0 & disjoint(v0, all_0_7_7) = 0) % 4.06/1.72 | % 4.06/1.72 +-Applying beta-rule and splitting (20), into two cases. % 4.06/1.72 |-Branch one: % 4.06/1.72 | (33) all_0_3_3 = 0 & all_0_4_4 = all_0_7_7 % 4.06/1.72 | % 4.06/1.72 | Applying alpha-rule on (33) yields: % 4.06/1.72 | (34) all_0_3_3 = 0 % 4.06/1.72 | (35) all_0_4_4 = all_0_7_7 % 4.06/1.72 | % 4.06/1.72 | From (35) and (6) follows: % 4.06/1.72 | (36) set_difference(all_0_7_7, all_0_5_5) = all_0_7_7 % 4.06/1.72 | % 4.06/1.72 | From (34) and (7) follows: % 4.06/1.72 | (37) in(all_0_6_6, all_0_7_7) = 0 % 4.06/1.72 | % 4.06/1.73 | Instantiating formula (10) with all_0_5_5, all_0_7_7 and discharging atoms set_difference(all_0_7_7, all_0_5_5) = all_0_7_7, yields: % 4.06/1.73 | (38) disjoint(all_0_7_7, all_0_5_5) = 0 % 4.06/1.73 | % 4.06/1.73 | Instantiating formula (24) with all_0_7_7, all_0_6_6 and discharging atoms in(all_0_6_6, all_0_7_7) = 0, yields: % 4.06/1.73 | (39) ? [v0] : ? [v1] : ( ~ (v1 = 0) & singleton(all_0_6_6) = v0 & disjoint(v0, all_0_7_7) = v1) % 4.06/1.73 | % 4.06/1.73 | Instantiating (39) with all_26_0_21, all_26_1_22 yields: % 4.06/1.73 | (40) ~ (all_26_0_21 = 0) & singleton(all_0_6_6) = all_26_1_22 & disjoint(all_26_1_22, all_0_7_7) = all_26_0_21 % 4.06/1.73 | % 4.06/1.73 | Applying alpha-rule on (40) yields: % 4.06/1.73 | (41) ~ (all_26_0_21 = 0) % 4.06/1.73 | (42) singleton(all_0_6_6) = all_26_1_22 % 4.06/1.73 | (43) disjoint(all_26_1_22, all_0_7_7) = all_26_0_21 % 4.06/1.73 | % 4.06/1.73 | Instantiating formula (28) with all_0_6_6, all_26_1_22, all_0_5_5 and discharging atoms singleton(all_0_6_6) = all_26_1_22, singleton(all_0_6_6) = all_0_5_5, yields: % 4.06/1.73 | (44) all_26_1_22 = all_0_5_5 % 4.06/1.73 | % 4.06/1.73 | From (44) and (43) follows: % 4.06/1.73 | (45) disjoint(all_0_5_5, all_0_7_7) = all_26_0_21 % 4.06/1.73 | % 4.06/1.73 | Instantiating formula (13) with all_26_0_21, all_0_5_5, all_0_7_7 and discharging atoms disjoint(all_0_5_5, all_0_7_7) = all_26_0_21, yields: % 4.06/1.73 | (46) all_26_0_21 = 0 | ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_7_7, all_0_5_5) = v0) % 4.06/1.73 | % 4.06/1.73 | Instantiating formula (21) with all_26_0_21, all_0_7_7, all_0_5_5 and discharging atoms disjoint(all_0_5_5, all_0_7_7) = all_26_0_21, yields: % 4.06/1.73 | (47) all_26_0_21 = 0 | ? [v0] : ( ~ (v0 = all_0_5_5) & set_difference(all_0_5_5, all_0_7_7) = v0) % 4.06/1.73 | % 4.06/1.73 | Instantiating formula (5) with all_0_5_5, all_0_7_7 and discharging atoms disjoint(all_0_7_7, all_0_5_5) = 0, yields: % 4.06/1.73 | (48) disjoint(all_0_5_5, all_0_7_7) = 0 % 4.06/1.73 | % 4.06/1.73 +-Applying beta-rule and splitting (46), into two cases. % 4.06/1.73 |-Branch one: % 4.06/1.73 | (49) all_26_0_21 = 0 % 4.06/1.73 | % 4.06/1.73 | Equations (49) can reduce 41 to: % 4.06/1.73 | (50) $false % 4.06/1.73 | % 4.06/1.73 |-The branch is then unsatisfiable % 4.06/1.73 |-Branch two: % 4.06/1.73 | (41) ~ (all_26_0_21 = 0) % 4.06/1.73 | (52) ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_7_7, all_0_5_5) = v0) % 4.06/1.73 | % 4.06/1.73 +-Applying beta-rule and splitting (47), into two cases. % 4.06/1.73 |-Branch one: % 4.06/1.73 | (49) all_26_0_21 = 0 % 4.06/1.73 | % 4.06/1.73 | Equations (49) can reduce 41 to: % 4.06/1.73 | (50) $false % 4.06/1.73 | % 4.06/1.73 |-The branch is then unsatisfiable % 4.06/1.73 |-Branch two: % 4.06/1.73 | (41) ~ (all_26_0_21 = 0) % 4.06/1.73 | (56) ? [v0] : ( ~ (v0 = all_0_5_5) & set_difference(all_0_5_5, all_0_7_7) = v0) % 4.06/1.73 | % 4.06/1.73 | Instantiating formula (27) with all_0_5_5, all_0_7_7, 0, all_26_0_21 and discharging atoms disjoint(all_0_5_5, all_0_7_7) = all_26_0_21, disjoint(all_0_5_5, all_0_7_7) = 0, yields: % 4.06/1.73 | (49) all_26_0_21 = 0 % 4.06/1.73 | % 4.06/1.73 | Equations (49) can reduce 41 to: % 4.06/1.73 | (50) $false % 4.06/1.73 | % 4.06/1.73 |-The branch is then unsatisfiable % 4.06/1.73 |-Branch two: % 4.06/1.73 | (59) ~ (all_0_3_3 = 0) & ~ (all_0_4_4 = all_0_7_7) % 4.06/1.73 | % 4.06/1.73 | Applying alpha-rule on (59) yields: % 4.06/1.73 | (60) ~ (all_0_3_3 = 0) % 4.06/1.73 | (61) ~ (all_0_4_4 = all_0_7_7) % 4.06/1.73 | % 4.06/1.73 +-Applying beta-rule and splitting (32), into two cases. % 4.06/1.73 |-Branch one: % 4.06/1.73 | (34) all_0_3_3 = 0 % 4.06/1.73 | % 4.06/1.73 | Equations (34) can reduce 60 to: % 4.06/1.73 | (50) $false % 4.06/1.73 | % 4.06/1.73 |-The branch is then unsatisfiable % 4.06/1.73 |-Branch two: % 4.06/1.73 | (60) ~ (all_0_3_3 = 0) % 4.06/1.73 | (65) ? [v0] : (singleton(all_0_6_6) = v0 & disjoint(v0, all_0_7_7) = 0) % 4.06/1.73 | % 4.06/1.73 | Instantiating (65) with all_24_0_27 yields: % 4.06/1.73 | (66) singleton(all_0_6_6) = all_24_0_27 & disjoint(all_24_0_27, all_0_7_7) = 0 % 4.06/1.73 | % 4.06/1.73 | Applying alpha-rule on (66) yields: % 4.06/1.73 | (67) singleton(all_0_6_6) = all_24_0_27 % 4.06/1.74 | (68) disjoint(all_24_0_27, all_0_7_7) = 0 % 4.06/1.74 | % 4.06/1.74 +-Applying beta-rule and splitting (31), into two cases. % 4.06/1.74 |-Branch one: % 4.06/1.74 | (35) all_0_4_4 = all_0_7_7 % 4.06/1.74 | % 4.06/1.74 | Equations (35) can reduce 61 to: % 4.06/1.74 | (50) $false % 4.06/1.74 | % 4.06/1.74 |-The branch is then unsatisfiable % 4.06/1.74 |-Branch two: % 4.06/1.74 | (61) ~ (all_0_4_4 = all_0_7_7) % 4.06/1.74 | (52) ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_7_7, all_0_5_5) = v0) % 4.06/1.74 | % 4.06/1.74 | Instantiating (52) with all_30_0_28 yields: % 4.06/1.74 | (73) ~ (all_30_0_28 = 0) & disjoint(all_0_7_7, all_0_5_5) = all_30_0_28 % 4.06/1.74 | % 4.06/1.74 | Applying alpha-rule on (73) yields: % 4.06/1.74 | (74) ~ (all_30_0_28 = 0) % 4.06/1.74 | (75) disjoint(all_0_7_7, all_0_5_5) = all_30_0_28 % 4.06/1.74 | % 4.06/1.74 | Instantiating formula (28) with all_0_6_6, all_24_0_27, all_0_5_5 and discharging atoms singleton(all_0_6_6) = all_24_0_27, singleton(all_0_6_6) = all_0_5_5, yields: % 4.06/1.74 | (76) all_24_0_27 = all_0_5_5 % 4.06/1.74 | % 4.06/1.74 | From (76) and (68) follows: % 4.06/1.74 | (48) disjoint(all_0_5_5, all_0_7_7) = 0 % 4.06/1.74 | % 4.06/1.74 | Instantiating formula (5) with all_0_7_7, all_0_5_5 and discharging atoms disjoint(all_0_5_5, all_0_7_7) = 0, yields: % 4.06/1.74 | (38) disjoint(all_0_7_7, all_0_5_5) = 0 % 4.06/1.74 | % 4.06/1.74 | Instantiating formula (13) with all_30_0_28, all_0_7_7, all_0_5_5 and discharging atoms disjoint(all_0_7_7, all_0_5_5) = all_30_0_28, yields: % 4.06/1.74 | (79) all_30_0_28 = 0 | ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_5_5, all_0_7_7) = v0) % 4.06/1.74 | % 4.06/1.74 +-Applying beta-rule and splitting (79), into two cases. % 4.06/1.74 |-Branch one: % 4.06/1.74 | (80) all_30_0_28 = 0 % 4.06/1.74 | % 4.06/1.74 | Equations (80) can reduce 74 to: % 4.06/1.74 | (50) $false % 4.06/1.74 | % 4.06/1.74 |-The branch is then unsatisfiable % 4.06/1.74 |-Branch two: % 4.06/1.74 | (74) ~ (all_30_0_28 = 0) % 4.06/1.74 | (83) ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_5_5, all_0_7_7) = v0) % 4.06/1.74 | % 4.06/1.74 | Instantiating formula (27) with all_0_7_7, all_0_5_5, 0, all_30_0_28 and discharging atoms disjoint(all_0_7_7, all_0_5_5) = all_30_0_28, disjoint(all_0_7_7, all_0_5_5) = 0, yields: % 4.06/1.74 | (80) all_30_0_28 = 0 % 4.06/1.74 | % 4.06/1.74 | Equations (80) can reduce 74 to: % 4.06/1.74 | (50) $false % 4.06/1.74 | % 4.06/1.74 |-The branch is then unsatisfiable % 4.06/1.74 % SZS output end Proof for theBenchmark % 4.06/1.74 % 4.06/1.74 1123ms %------------------------------------------------------------------------------