%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU130+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n028.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 08:46:48 EDT 2022 % Result : Theorem 3.89s 1.72s % Output : Proof 5.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU130+1 : TPTP v8.1.0. Released v3.3.0. % 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n028.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 : Mon Jun 20 03:38:46 EDT 2022 % 0.12/0.34 % CPUTime : % 0.56/0.62 ____ _ % 0.56/0.62 ___ / __ \_____(_)___ ________ __________ % 0.56/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.56/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.56/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.56/0.62 % 0.56/0.62 A Theorem Prover for First-Order Logic % 0.56/0.62 (ePrincess v.1.0) % 0.56/0.62 % 0.56/0.62 (c) Philipp Rümmer, 2009-2015 % 0.56/0.62 (c) Peter Backeman, 2014-2015 % 0.56/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.56/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.56/0.62 Bug reports to peter@backeman.se % 0.56/0.62 % 0.67/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.67/0.62 % 0.67/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.47/0.97 Prover 0: Preprocessing ... % 1.81/1.13 Prover 0: Warning: ignoring some quantifiers % 1.81/1.15 Prover 0: Constructing countermodel ... % 2.60/1.34 Prover 0: gave up % 2.60/1.34 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.60/1.36 Prover 1: Preprocessing ... % 2.88/1.43 Prover 1: Warning: ignoring some quantifiers % 2.88/1.44 Prover 1: Constructing countermodel ... % 3.22/1.56 Prover 1: gave up % 3.22/1.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.63/1.57 Prover 2: Preprocessing ... % 3.89/1.65 Prover 2: Warning: ignoring some quantifiers % 3.89/1.65 Prover 2: Constructing countermodel ... % 3.89/1.72 Prover 2: proved (157ms) % 3.89/1.72 % 3.89/1.72 No countermodel exists, formula is valid % 3.89/1.72 % SZS status Theorem for theBenchmark % 3.89/1.72 % 3.89/1.72 Generating proof ... Warning: ignoring some quantifiers % 4.89/1.97 found it (size 31) % 4.89/1.97 % 4.89/1.97 % SZS output start Proof for theBenchmark % 4.89/1.97 Assumed formulas after preprocessing and simplification: % 4.89/1.97 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v4 = 0) & ~ (v2 = v0) & empty(v5) = 0 & empty(v3) = v4 & empty(empty_set) = 0 & subset(v0, v1) = 0 & set_intersection2(v0, v1) = v2 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (set_intersection2(v6, v7) = v8) | ~ (in(v9, v8) = v10) | ? [v11] : (( ~ (v11 = 0) & in(v9, v7) = v11) | ( ~ (v11 = 0) & in(v9, v6) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v6, v7) = v8) | ~ (in(v9, v7) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & in(v9, v6) = 0) | ( ~ (v11 = 0) & in(v9, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v6, v7) = v8) | ~ (in(v9, v6) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & in(v9, v7) = 0) | ( ~ (v11 = 0) & in(v9, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v6, v7) = 0) | ~ (in(v8, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v8, v6) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (subset(v9, v8) = v7) | ~ (subset(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (set_intersection2(v9, v8) = v7) | ~ (set_intersection2(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (in(v9, v8) = v7) | ~ (in(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v6, v7) = v8) | ~ (in(v9, v8) = 0) | (in(v9, v7) = 0 & in(v9, v6) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v6, v7) = v8) | ~ (in(v9, v7) = 0) | ? [v10] : ((v10 = 0 & in(v9, v8) = 0) | ( ~ (v10 = 0) & in(v9, v6) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v6, v7) = v8) | ~ (in(v9, v6) = 0) | ? [v10] : ((v10 = 0 & in(v9, v8) = 0) | ( ~ (v10 = 0) & in(v9, v7) = v10))) & ? [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v6 | ~ (set_intersection2(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (((v13 = 0 & v12 = 0 & in(v10, v8) = 0 & in(v10, v7) = 0) | (v11 = 0 & in(v10, v6) = 0)) & (( ~ (v13 = 0) & in(v10, v8) = v13) | ( ~ (v12 = 0) & in(v10, v7) = v12) | ( ~ (v11 = 0) & in(v10, v6) = v11)))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v6, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & in(v9, v7) = v10 & in(v9, v6) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (empty(v8) = v7) | ~ (empty(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (subset(v6, v7) = 0) | ~ (in(v8, v6) = 0) | in(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_intersection2(v7, v6) = v8) | set_intersection2(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_intersection2(v6, v7) = v8) | subset(v8, v6) = 0) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_intersection2(v6, v7) = v8) | set_intersection2(v7, v6) = v8) & ! [v6] : ! [v7] : (v7 = v6 | ~ (empty(v7) = 0) | ~ (empty(v6) = 0)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (subset(v7, v6) = 0) | ? [v8] : ( ~ (v8 = 0) & subset(v6, v7) = v8)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (subset(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & subset(v7, v6) = v8)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (set_intersection2(v6, v6) = v7)) & ! [v6] : ! [v7] : (v7 = empty_set | ~ (set_intersection2(v6, empty_set) = v7)) & ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v6, v6) = v7)) & ! [v6] : ! [v7] : ( ~ (in(v7, v6) = 0) | ? [v8] : ( ~ (v8 = 0) & in(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (in(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & empty(v7) = v8)) & ! [v6] : ! [v7] : ( ~ (in(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & in(v7, v6) = v8)) & ! [v6] : (v6 = empty_set | ~ (empty(v6) = 0)) & ? [v6] : ? [v7] : ? [v8] : subset(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : set_intersection2(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : in(v7, v6) = v8 & ? [v6] : ? [v7] : empty(v6) = v7) % 5.37/2.00 | 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 yields: % 5.37/2.00 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = all_0_5_5) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & subset(all_0_5_5, all_0_4_4) = 0 & set_intersection2(all_0_5_5, all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : (( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v1) = v4))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v6 = 0 & in(v4, v2) = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & in(v4, v2) = v7) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : empty(v0) = v1 % 5.42/2.02 | % 5.42/2.02 | Applying alpha-rule on (1) yields: % 5.42/2.02 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) % 5.42/2.02 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 5.42/2.02 | (4) ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2 % 5.42/2.02 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 5.42/2.02 | (6) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 5.42/2.02 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | (in(v3, v1) = 0 & in(v3, v0) = 0)) % 5.42/2.02 | (8) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 5.42/2.02 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) % 5.42/2.02 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0) = 0) % 5.42/2.02 | (11) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 5.42/2.02 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 5.42/2.02 | (13) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 % 5.42/2.02 | (14) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) % 5.42/2.02 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 5.42/2.02 | (16) set_intersection2(all_0_5_5, all_0_4_4) = all_0_3_3 % 5.42/2.02 | (17) ? [v0] : ? [v1] : empty(v0) = v1 % 5.42/2.02 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 5.42/2.02 | (19) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v6 = 0 & in(v4, v2) = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & in(v4, v2) = v7) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)))) % 5.42/2.02 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) % 5.42/2.02 | (21) subset(all_0_5_5, all_0_4_4) = 0 % 5.42/2.02 | (22) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 % 5.42/2.02 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : (( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v0) = v5))) % 5.42/2.03 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 5.42/2.03 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) % 5.42/2.03 | (26) empty(all_0_2_2) = all_0_1_1 % 5.42/2.03 | (27) ~ (all_0_1_1 = 0) % 5.42/2.03 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 5.42/2.03 | (29) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 5.42/2.03 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 5.42/2.03 | (31) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 5.42/2.03 | (32) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 5.42/2.03 | (33) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 5.42/2.03 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v0) = v4))) % 5.42/2.03 | (35) ~ (all_0_3_3 = all_0_5_5) % 5.42/2.03 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v1) = v4))) % 5.42/2.03 | (37) empty(empty_set) = 0 % 5.42/2.03 | (38) empty(all_0_0_0) = 0 % 5.42/2.03 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) % 5.42/2.03 | % 5.42/2.03 | Instantiating formula (10) with all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms set_intersection2(all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 5.42/2.03 | (40) subset(all_0_3_3, all_0_5_5) = 0 % 5.42/2.03 | % 5.42/2.03 | Instantiating formula (14) with all_0_3_3, all_0_5_5 and discharging atoms subset(all_0_3_3, all_0_5_5) = 0, yields: % 5.42/2.03 | (41) all_0_3_3 = all_0_5_5 | ? [v0] : ( ~ (v0 = 0) & subset(all_0_5_5, all_0_3_3) = v0) % 5.42/2.03 | % 5.42/2.03 +-Applying beta-rule and splitting (41), into two cases. % 5.42/2.03 |-Branch one: % 5.42/2.03 | (42) all_0_3_3 = all_0_5_5 % 5.42/2.03 | % 5.42/2.03 | Equations (42) can reduce 35 to: % 5.42/2.03 | (43) $false % 5.42/2.03 | % 5.42/2.03 |-The branch is then unsatisfiable % 5.42/2.03 |-Branch two: % 5.42/2.03 | (35) ~ (all_0_3_3 = all_0_5_5) % 5.42/2.03 | (45) ? [v0] : ( ~ (v0 = 0) & subset(all_0_5_5, all_0_3_3) = v0) % 5.42/2.04 | % 5.42/2.04 | Instantiating (45) with all_33_0_18 yields: % 5.42/2.04 | (46) ~ (all_33_0_18 = 0) & subset(all_0_5_5, all_0_3_3) = all_33_0_18 % 5.42/2.04 | % 5.42/2.04 | Applying alpha-rule on (46) yields: % 5.42/2.04 | (47) ~ (all_33_0_18 = 0) % 5.42/2.04 | (48) subset(all_0_5_5, all_0_3_3) = all_33_0_18 % 5.42/2.04 | % 5.42/2.04 | Instantiating formula (32) with all_33_0_18, all_0_3_3, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_3_3) = all_33_0_18, yields: % 5.42/2.04 | (49) all_33_0_18 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_3_3) = v1 & in(v0, all_0_5_5) = 0) % 5.42/2.04 | % 5.42/2.04 +-Applying beta-rule and splitting (49), into two cases. % 5.42/2.04 |-Branch one: % 5.42/2.04 | (50) all_33_0_18 = 0 % 5.42/2.04 | % 5.42/2.04 | Equations (50) can reduce 47 to: % 5.42/2.04 | (43) $false % 5.42/2.04 | % 5.42/2.04 |-The branch is then unsatisfiable % 5.42/2.04 |-Branch two: % 5.42/2.04 | (47) ~ (all_33_0_18 = 0) % 5.42/2.04 | (53) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_3_3) = v1 & in(v0, all_0_5_5) = 0) % 5.42/2.04 | % 5.42/2.04 | Instantiating (53) with all_46_0_19, all_46_1_20 yields: % 5.42/2.04 | (54) ~ (all_46_0_19 = 0) & in(all_46_1_20, all_0_3_3) = all_46_0_19 & in(all_46_1_20, all_0_5_5) = 0 % 5.42/2.04 | % 5.42/2.04 | Applying alpha-rule on (54) yields: % 5.42/2.04 | (55) ~ (all_46_0_19 = 0) % 5.42/2.04 | (56) in(all_46_1_20, all_0_3_3) = all_46_0_19 % 5.42/2.04 | (57) in(all_46_1_20, all_0_5_5) = 0 % 5.42/2.04 | % 5.42/2.04 | Instantiating formula (23) with all_46_0_19, all_46_1_20, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms set_intersection2(all_0_5_5, all_0_4_4) = all_0_3_3, in(all_46_1_20, all_0_3_3) = all_46_0_19, yields: % 5.42/2.04 | (58) all_46_0_19 = 0 | ? [v0] : (( ~ (v0 = 0) & in(all_46_1_20, all_0_4_4) = v0) | ( ~ (v0 = 0) & in(all_46_1_20, all_0_5_5) = v0)) % 5.42/2.04 | % 5.42/2.04 | Instantiating formula (36) with all_46_1_20, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms set_intersection2(all_0_5_5, all_0_4_4) = all_0_3_3, in(all_46_1_20, all_0_5_5) = 0, yields: % 5.42/2.04 | (59) ? [v0] : ((v0 = 0 & in(all_46_1_20, all_0_3_3) = 0) | ( ~ (v0 = 0) & in(all_46_1_20, all_0_4_4) = v0)) % 5.42/2.04 | % 5.42/2.04 | Instantiating formula (3) with all_46_1_20, all_0_4_4, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_4_4) = 0, in(all_46_1_20, all_0_5_5) = 0, yields: % 5.42/2.04 | (60) in(all_46_1_20, all_0_4_4) = 0 % 5.42/2.04 | % 5.42/2.04 | Instantiating (59) with all_54_0_21 yields: % 5.42/2.04 | (61) (all_54_0_21 = 0 & in(all_46_1_20, all_0_3_3) = 0) | ( ~ (all_54_0_21 = 0) & in(all_46_1_20, all_0_4_4) = all_54_0_21) % 5.42/2.04 | % 5.42/2.04 +-Applying beta-rule and splitting (58), into two cases. % 5.42/2.04 |-Branch one: % 5.42/2.04 | (62) all_46_0_19 = 0 % 5.42/2.04 | % 5.42/2.04 | Equations (62) can reduce 55 to: % 5.42/2.04 | (43) $false % 5.42/2.04 | % 5.42/2.04 |-The branch is then unsatisfiable % 5.42/2.04 |-Branch two: % 5.42/2.04 | (55) ~ (all_46_0_19 = 0) % 5.42/2.04 | (65) ? [v0] : (( ~ (v0 = 0) & in(all_46_1_20, all_0_4_4) = v0) | ( ~ (v0 = 0) & in(all_46_1_20, all_0_5_5) = v0)) % 5.42/2.04 | % 5.42/2.04 +-Applying beta-rule and splitting (61), into two cases. % 5.42/2.04 |-Branch one: % 5.42/2.04 | (66) all_54_0_21 = 0 & in(all_46_1_20, all_0_3_3) = 0 % 5.42/2.04 | % 5.42/2.04 | Applying alpha-rule on (66) yields: % 5.42/2.04 | (67) all_54_0_21 = 0 % 5.42/2.04 | (68) in(all_46_1_20, all_0_3_3) = 0 % 5.42/2.04 | % 5.42/2.04 | Instantiating formula (5) with all_46_1_20, all_0_3_3, 0, all_46_0_19 and discharging atoms in(all_46_1_20, all_0_3_3) = all_46_0_19, in(all_46_1_20, all_0_3_3) = 0, yields: % 5.42/2.04 | (62) all_46_0_19 = 0 % 5.42/2.04 | % 5.42/2.04 | Equations (62) can reduce 55 to: % 5.42/2.04 | (43) $false % 5.42/2.04 | % 5.42/2.04 |-The branch is then unsatisfiable % 5.42/2.04 |-Branch two: % 5.42/2.04 | (71) ~ (all_54_0_21 = 0) & in(all_46_1_20, all_0_4_4) = all_54_0_21 % 5.42/2.04 | % 5.42/2.04 | Applying alpha-rule on (71) yields: % 5.42/2.04 | (72) ~ (all_54_0_21 = 0) % 5.42/2.04 | (73) in(all_46_1_20, all_0_4_4) = all_54_0_21 % 5.42/2.04 | % 5.42/2.04 | Instantiating formula (5) with all_46_1_20, all_0_4_4, 0, all_54_0_21 and discharging atoms in(all_46_1_20, all_0_4_4) = all_54_0_21, in(all_46_1_20, all_0_4_4) = 0, yields: % 5.42/2.04 | (67) all_54_0_21 = 0 % 5.42/2.04 | % 5.42/2.04 | Equations (67) can reduce 72 to: % 5.42/2.04 | (43) $false % 5.42/2.05 | % 5.42/2.05 |-The branch is then unsatisfiable % 5.42/2.05 % SZS output end Proof for theBenchmark % 5.42/2.05 % 5.42/2.05 1406ms %------------------------------------------------------------------------------