%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : NUM385+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n025.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 : Mon Jul 18 08:44:04 EDT 2022 % Result : Theorem 3.22s 1.49s % Output : Proof 4.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : NUM385+1 : TPTP v8.1.0. Released v3.2.0. % 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n025.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 : Tue Jul 5 03:27:57 EDT 2022 % 0.13/0.34 % CPUTime : % 0.66/0.63 ____ _ % 0.66/0.63 ___ / __ \_____(_)___ ________ __________ % 0.66/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.66/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.66/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.66/0.63 % 0.66/0.63 A Theorem Prover for First-Order Logic % 0.66/0.63 (ePrincess v.1.0) % 0.66/0.63 % 0.66/0.63 (c) Philipp Rümmer, 2009-2015 % 0.66/0.63 (c) Peter Backeman, 2014-2015 % 0.66/0.63 (contributions by Angelo Brillout, Peter Baumgartner) % 0.66/0.63 Free software under GNU Lesser General Public License (LGPL). % 0.66/0.63 Bug reports to peter@backeman.se % 0.66/0.63 % 0.66/0.63 For more information, visit http://user.uu.se/~petba168/breu/ % 0.66/0.63 % 0.66/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.74/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.59/1.02 Prover 0: Preprocessing ... % 2.29/1.25 Prover 0: Warning: ignoring some quantifiers % 2.29/1.27 Prover 0: Constructing countermodel ... % 3.22/1.48 Prover 0: proved (789ms) % 3.22/1.49 % 3.22/1.49 No countermodel exists, formula is valid % 3.22/1.49 % SZS status Theorem for theBenchmark % 3.22/1.49 % 3.22/1.49 Generating proof ... Warning: ignoring some quantifiers % 4.50/1.78 found it (size 24) % 4.50/1.78 % 4.50/1.78 % SZS output start Proof for theBenchmark % 4.50/1.78 Assumed formulas after preprocessing and simplification: % 4.50/1.78 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ( ~ (v1 = v0) & succ(v1) = v2 & succ(v0) = v2 & relation_non_empty(v3) & relation_empty_yielding(v5) & relation_empty_yielding(v4) & relation_empty_yielding(empty_set) & one_to_one(v6) & relation(v12) & relation(v11) & relation(v9) & relation(v8) & relation(v6) & relation(v5) & relation(v4) & relation(v3) & relation(empty_set) & function(v12) & function(v9) & function(v6) & function(v4) & function(v3) & empty(v11) & empty(v10) & empty(v9) & empty(empty_set) & ~ empty(v8) & ~ empty(v7) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (set_union2(v16, v15) = v14) | ~ (set_union2(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (set_union2(v13, v14) = v15) | ~ in(v16, v15) | in(v16, v14) | in(v16, v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (set_union2(v13, v14) = v15) | ~ in(v16, v14) | in(v16, v15)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (set_union2(v13, v14) = v15) | ~ in(v16, v13) | in(v16, v15)) & ? [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v13 | ~ (set_union2(v14, v15) = v16) | ? [v17] : (( ~ in(v17, v13) | ( ~ in(v17, v15) & ~ in(v17, v14))) & (in(v17, v15) | in(v17, v14) | in(v17, v13)))) & ! [v13] : ! [v14] : ! [v15] : (v15 = v13 | ~ (singleton(v13) = v14) | ~ in(v15, v14)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (singleton(v15) = v14) | ~ (singleton(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (succ(v15) = v14) | ~ (succ(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (singleton(v13) = v14) | ~ (set_union2(v13, v14) = v15) | succ(v13) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v14, v13) = v15) | ~ empty(v15) | empty(v13)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v14, v13) = v15) | set_union2(v13, v14) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v13, v14) = v15) | ~ relation(v14) | ~ relation(v13) | relation(v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v13, v14) = v15) | ~ empty(v15) | empty(v13)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v13, v14) = v15) | set_union2(v14, v13) = v15) & ? [v13] : ! [v14] : ! [v15] : (v15 = v13 | ~ (singleton(v14) = v15) | ? [v16] : (( ~ (v16 = v14) | ~ in(v14, v13)) & (v16 = v14 | in(v16, v13)))) & ! [v13] : ! [v14] : (v14 = v13 | ~ (set_union2(v13, v13) = v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ (set_union2(v13, empty_set) = v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ empty(v14) | ~ empty(v13)) & ! [v13] : ! [v14] : ( ~ (singleton(v13) = v14) | in(v13, v14)) & ! [v13] : ! [v14] : ( ~ (succ(v13) = v14) | ~ empty(v14)) & ! [v13] : ! [v14] : ( ~ (succ(v13) = v14) | in(v13, v14)) & ! [v13] : ! [v14] : ( ~ (succ(v13) = v14) | ? [v15] : (singleton(v13) = v15 & set_union2(v13, v15) = v14)) & ! [v13] : ! [v14] : ( ~ element(v13, v14) | empty(v14) | in(v13, v14)) & ! [v13] : ! [v14] : ( ~ empty(v14) | ~ in(v13, v14)) & ! [v13] : ! [v14] : ( ~ in(v14, v13) | ~ in(v13, v14)) & ! [v13] : ! [v14] : ( ~ in(v13, v14) | element(v13, v14)) & ! [v13] : (v13 = empty_set | ~ empty(v13)) & ! [v13] : ( ~ relation(v13) | ~ function(v13) | ~ empty(v13) | one_to_one(v13)) & ! [v13] : ( ~ empty(v13) | relation(v13)) & ! [v13] : ( ~ empty(v13) | function(v13)) & ? [v13] : ? [v14] : element(v14, v13)) % 4.65/1.82 | 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, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12 yields: % 4.65/1.82 | (1) ~ (all_0_11_11 = all_0_12_12) & succ(all_0_11_11) = all_0_10_10 & succ(all_0_12_12) = all_0_10_10 & relation_non_empty(all_0_9_9) & relation_empty_yielding(all_0_7_7) & relation_empty_yielding(all_0_8_8) & relation_empty_yielding(empty_set) & one_to_one(all_0_6_6) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_3_3) & relation(all_0_4_4) & relation(all_0_6_6) & relation(all_0_7_7) & relation(all_0_8_8) & relation(all_0_9_9) & relation(empty_set) & function(all_0_0_0) & function(all_0_3_3) & function(all_0_6_6) & function(all_0_8_8) & function(all_0_9_9) & empty(all_0_1_1) & empty(all_0_2_2) & empty(all_0_3_3) & empty(empty_set) & ~ empty(all_0_4_4) & ~ empty(all_0_5_5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v1) | ~ (set_union2(v0, v1) = v2) | succ(v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [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] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : (singleton(v0) = v2 & set_union2(v0, v2) = v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ? [v0] : ? [v1] : element(v1, v0) % 4.65/1.83 | % 4.65/1.83 | Applying alpha-rule on (1) yields: % 4.65/1.83 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 4.65/1.83 | (3) function(all_0_0_0) % 4.65/1.83 | (4) function(all_0_3_3) % 4.65/1.83 | (5) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) % 4.65/1.83 | (6) function(all_0_9_9) % 4.65/1.83 | (7) ~ (all_0_11_11 = all_0_12_12) % 4.65/1.83 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 4.65/1.83 | (9) relation_empty_yielding(all_0_7_7) % 4.65/1.83 | (10) relation(all_0_7_7) % 4.65/1.83 | (11) function(all_0_8_8) % 4.65/1.83 | (12) ! [v0] : ( ~ empty(v0) | function(v0)) % 4.65/1.83 | (13) relation(all_0_8_8) % 4.65/1.83 | (14) one_to_one(all_0_6_6) % 4.65/1.83 | (15) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | in(v0, v1)) % 4.76/1.83 | (16) succ(all_0_11_11) = all_0_10_10 % 4.76/1.83 | (17) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 4.76/1.83 | (18) empty(all_0_3_3) % 4.76/1.83 | (19) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) % 4.76/1.84 | (20) relation(all_0_6_6) % 4.76/1.84 | (21) relation_empty_yielding(empty_set) % 4.76/1.84 | (22) relation(all_0_9_9) % 4.76/1.84 | (23) relation_non_empty(all_0_9_9) % 4.76/1.84 | (24) ~ empty(all_0_4_4) % 4.76/1.84 | (25) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 4.76/1.84 | (26) relation(all_0_3_3) % 4.76/1.84 | (27) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) % 4.76/1.84 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) % 4.76/1.84 | (29) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 4.76/1.84 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) % 4.76/1.84 | (31) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ empty(v1)) % 4.76/1.84 | (32) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : (singleton(v0) = v2 & set_union2(v0, v2) = v1)) % 4.76/1.84 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 4.76/1.84 | (34) relation(empty_set) % 4.76/1.84 | (35) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 4.76/1.84 | (36) ? [v0] : ? [v1] : element(v1, v0) % 4.76/1.84 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 4.76/1.84 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v1) | ~ (set_union2(v0, v1) = v2) | succ(v0) = v2) % 4.76/1.84 | (39) empty(empty_set) % 4.76/1.84 | (40) relation(all_0_0_0) % 4.76/1.84 | (41) relation(all_0_1_1) % 4.76/1.84 | (42) ! [v0] : ( ~ empty(v0) | relation(v0)) % 4.76/1.84 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 4.76/1.84 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 4.76/1.84 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) % 4.76/1.84 | (46) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 4.76/1.84 | (47) empty(all_0_2_2) % 4.76/1.84 | (48) relation_empty_yielding(all_0_8_8) % 4.76/1.84 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) % 4.76/1.84 | (50) relation(all_0_4_4) % 4.76/1.84 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 4.76/1.84 | (52) empty(all_0_1_1) % 4.76/1.84 | (53) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0)))) % 4.76/1.84 | (54) ~ empty(all_0_5_5) % 4.76/1.84 | (55) function(all_0_6_6) % 4.76/1.84 | (56) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 4.76/1.84 | (57) succ(all_0_12_12) = all_0_10_10 % 4.76/1.84 | (58) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) % 4.76/1.84 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 4.76/1.84 | (60) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 4.76/1.84 | % 4.76/1.85 | Instantiating formula (15) with all_0_10_10, all_0_11_11 and discharging atoms succ(all_0_11_11) = all_0_10_10, yields: % 4.76/1.85 | (61) in(all_0_11_11, all_0_10_10) % 4.76/1.85 | % 4.76/1.85 | Instantiating formula (32) with all_0_10_10, all_0_11_11 and discharging atoms succ(all_0_11_11) = all_0_10_10, yields: % 4.76/1.85 | (62) ? [v0] : (singleton(all_0_11_11) = v0 & set_union2(all_0_11_11, v0) = all_0_10_10) % 4.76/1.85 | % 4.76/1.85 | Instantiating formula (15) with all_0_10_10, all_0_12_12 and discharging atoms succ(all_0_12_12) = all_0_10_10, yields: % 4.76/1.85 | (63) in(all_0_12_12, all_0_10_10) % 4.76/1.85 | % 4.76/1.85 | Instantiating formula (32) with all_0_10_10, all_0_12_12 and discharging atoms succ(all_0_12_12) = all_0_10_10, yields: % 4.76/1.85 | (64) ? [v0] : (singleton(all_0_12_12) = v0 & set_union2(all_0_12_12, v0) = all_0_10_10) % 4.76/1.85 | % 4.76/1.85 | Instantiating (64) with all_19_0_17 yields: % 4.76/1.85 | (65) singleton(all_0_12_12) = all_19_0_17 & set_union2(all_0_12_12, all_19_0_17) = all_0_10_10 % 4.76/1.85 | % 4.76/1.85 | Applying alpha-rule on (65) yields: % 4.76/1.85 | (66) singleton(all_0_12_12) = all_19_0_17 % 4.76/1.85 | (67) set_union2(all_0_12_12, all_19_0_17) = all_0_10_10 % 4.76/1.85 | % 4.76/1.85 | Instantiating (62) with all_21_0_18 yields: % 4.76/1.85 | (68) singleton(all_0_11_11) = all_21_0_18 & set_union2(all_0_11_11, all_21_0_18) = all_0_10_10 % 4.76/1.85 | % 4.76/1.85 | Applying alpha-rule on (68) yields: % 4.76/1.85 | (69) singleton(all_0_11_11) = all_21_0_18 % 4.76/1.85 | (70) set_union2(all_0_11_11, all_21_0_18) = all_0_10_10 % 4.76/1.85 | % 4.76/1.85 | Instantiating formula (44) with all_0_10_10, all_0_11_11, all_21_0_18 and discharging atoms set_union2(all_0_11_11, all_21_0_18) = all_0_10_10, yields: % 4.76/1.85 | (71) set_union2(all_21_0_18, all_0_11_11) = all_0_10_10 % 4.76/1.85 | % 4.76/1.85 | Instantiating formula (44) with all_0_10_10, all_0_12_12, all_19_0_17 and discharging atoms set_union2(all_0_12_12, all_19_0_17) = all_0_10_10, yields: % 4.76/1.85 | (72) set_union2(all_19_0_17, all_0_12_12) = all_0_10_10 % 4.76/1.85 | % 4.76/1.85 | Instantiating formula (45) with all_0_12_12, all_0_10_10, all_0_11_11, all_21_0_18 and discharging atoms set_union2(all_21_0_18, all_0_11_11) = all_0_10_10, in(all_0_12_12, all_0_10_10), yields: % 4.76/1.85 | (73) in(all_0_12_12, all_21_0_18) | in(all_0_12_12, all_0_11_11) % 4.76/1.85 | % 4.76/1.85 | Instantiating formula (45) with all_0_11_11, all_0_10_10, all_0_12_12, all_19_0_17 and discharging atoms set_union2(all_19_0_17, all_0_12_12) = all_0_10_10, in(all_0_11_11, all_0_10_10), yields: % 4.76/1.85 | (74) in(all_0_11_11, all_19_0_17) | in(all_0_11_11, all_0_12_12) % 4.76/1.85 | % 4.76/1.85 +-Applying beta-rule and splitting (73), into two cases. % 4.76/1.85 |-Branch one: % 4.76/1.85 | (75) in(all_0_12_12, all_21_0_18) % 4.76/1.85 | % 4.76/1.85 | Instantiating formula (58) with all_0_12_12, all_21_0_18, all_0_11_11 and discharging atoms singleton(all_0_11_11) = all_21_0_18, in(all_0_12_12, all_21_0_18), yields: % 4.76/1.85 | (76) all_0_11_11 = all_0_12_12 % 4.76/1.85 | % 4.76/1.85 | Equations (76) can reduce 7 to: % 4.76/1.85 | (77) $false % 4.76/1.85 | % 4.76/1.85 |-The branch is then unsatisfiable % 4.76/1.85 |-Branch two: % 4.76/1.85 | (78) ~ in(all_0_12_12, all_21_0_18) % 4.76/1.85 | (79) in(all_0_12_12, all_0_11_11) % 4.76/1.85 | % 4.76/1.85 +-Applying beta-rule and splitting (74), into two cases. % 4.76/1.85 |-Branch one: % 4.76/1.85 | (80) in(all_0_11_11, all_19_0_17) % 4.76/1.85 | % 4.76/1.85 | Instantiating formula (58) with all_0_11_11, all_19_0_17, all_0_12_12 and discharging atoms singleton(all_0_12_12) = all_19_0_17, in(all_0_11_11, all_19_0_17), yields: % 4.76/1.85 | (76) all_0_11_11 = all_0_12_12 % 4.76/1.85 | % 4.76/1.85 | Equations (76) can reduce 7 to: % 4.76/1.85 | (77) $false % 4.76/1.85 | % 4.76/1.85 |-The branch is then unsatisfiable % 4.76/1.85 |-Branch two: % 4.76/1.85 | (83) ~ in(all_0_11_11, all_19_0_17) % 4.76/1.85 | (84) in(all_0_11_11, all_0_12_12) % 4.76/1.85 | % 4.76/1.85 | Instantiating formula (35) with all_0_11_11, all_0_12_12 and discharging atoms in(all_0_11_11, all_0_12_12), in(all_0_12_12, all_0_11_11), yields: % 4.76/1.85 | (85) $false % 4.76/1.85 | % 4.76/1.85 |-The branch is then unsatisfiable % 4.76/1.85 % SZS output end Proof for theBenchmark % 4.76/1.85 % 4.76/1.85 1206ms %------------------------------------------------------------------------------