%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU219+3 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n029.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 08:47:47 EDT 2022 % Result : Theorem 3.44s 1.67s % Output : Proof 5.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU219+3 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n029.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sun Jun 19 19:42:15 EDT 2022 % 0.12/0.34 % CPUTime : % 0.66/0.67 ____ _ % 0.66/0.67 ___ / __ \_____(_)___ ________ __________ % 0.66/0.67 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.66/0.67 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.66/0.67 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.66/0.67 % 0.66/0.67 A Theorem Prover for First-Order Logic % 0.66/0.67 (ePrincess v.1.0) % 0.66/0.67 % 0.66/0.67 (c) Philipp Rümmer, 2009-2015 % 0.66/0.67 (c) Peter Backeman, 2014-2015 % 0.66/0.67 (contributions by Angelo Brillout, Peter Baumgartner) % 0.66/0.67 Free software under GNU Lesser General Public License (LGPL). % 0.66/0.67 Bug reports to peter@backeman.se % 0.66/0.67 % 0.66/0.67 For more information, visit http://user.uu.se/~petba168/breu/ % 0.66/0.67 % 0.66/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.88/0.73 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.80/1.12 Prover 0: Preprocessing ... % 2.45/1.42 Prover 0: Warning: ignoring some quantifiers % 2.63/1.46 Prover 0: Constructing countermodel ... % 3.31/1.67 Prover 0: proved (936ms) % 3.44/1.67 % 3.44/1.67 No countermodel exists, formula is valid % 3.44/1.67 % SZS status Theorem for theBenchmark % 3.44/1.67 % 3.44/1.67 Generating proof ... Warning: ignoring some quantifiers % 4.85/2.00 found it (size 23) % 4.85/2.00 % 4.85/2.00 % SZS output start Proof for theBenchmark % 4.85/2.00 Assumed formulas after preprocessing and simplification: % 4.85/2.00 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (relation_rng(v2) = v5 & relation_rng(v0) = v1 & relation_dom(v2) = v3 & relation_dom(v0) = v4 & function_inverse(v0) = v2 & relation_empty_yielding(v6) & relation_empty_yielding(empty_set) & one_to_one(v7) & one_to_one(v0) & relation(v13) & relation(v12) & relation(v10) & relation(v9) & relation(v7) & relation(v6) & relation(v0) & relation(empty_set) & function(v13) & function(v10) & function(v7) & function(v0) & empty(v12) & empty(v11) & empty(v10) & empty(empty_set) & ~ empty(v9) & ~ empty(v8) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ element(v15, v17) | ~ empty(v16) | ~ in(v14, v15)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ element(v15, v17) | ~ in(v14, v15) | element(v14, v16)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_rng(v16) = v15) | ~ (relation_rng(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_dom(v16) = v15) | ~ (relation_dom(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (powerset(v16) = v15) | ~ (powerset(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_inverse(v16) = v15) | ~ (relation_inverse(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (function_inverse(v16) = v15) | ~ (function_inverse(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ subset(v14, v15) | element(v14, v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ element(v14, v16) | subset(v14, v15)) & ! [v14] : ! [v15] : (v15 = v14 | ~ empty(v15) | ~ empty(v14)) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ~ relation(v14) | ~ empty(v15) | empty(v14)) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ~ relation(v14) | ? [v16] : ? [v17] : (relation_rng(v16) = v17 & relation_dom(v16) = v15 & relation_dom(v14) = v17 & relation_inverse(v14) = v16)) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ~ empty(v14) | relation(v15)) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ~ empty(v14) | empty(v15)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ relation(v14) | ~ empty(v15) | empty(v14)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ relation(v14) | ? [v16] : ? [v17] : (relation_rng(v17) = v15 & relation_rng(v14) = v16 & relation_dom(v17) = v16 & relation_inverse(v14) = v17)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ empty(v14) | relation(v15)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ empty(v14) | empty(v15)) & ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ empty(v15)) & ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | empty(v14) | ? [v16] : (element(v16, v15) & ~ empty(v16))) & ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ? [v16] : (element(v16, v15) & empty(v16))) & ! [v14] : ! [v15] : ( ~ (relation_inverse(v14) = v15) | ~ one_to_one(v14) | ~ relation(v14) | ~ function(v14) | function_inverse(v14) = v15) & ! [v14] : ! [v15] : ( ~ (relation_inverse(v14) = v15) | ~ one_to_one(v14) | ~ relation(v14) | ~ function(v14) | relation(v15)) & ! [v14] : ! [v15] : ( ~ (relation_inverse(v14) = v15) | ~ one_to_one(v14) | ~ relation(v14) | ~ function(v14) | function(v15)) & ! [v14] : ! [v15] : ( ~ (relation_inverse(v14) = v15) | ~ relation(v14) | relation_inverse(v15) = v14) & ! [v14] : ! [v15] : ( ~ (relation_inverse(v14) = v15) | ~ relation(v14) | relation(v15)) & ! [v14] : ! [v15] : ( ~ (relation_inverse(v14) = v15) | ~ relation(v14) | ? [v16] : ? [v17] : (relation_rng(v15) = v17 & relation_rng(v14) = v16 & relation_dom(v15) = v16 & relation_dom(v14) = v17)) & ! [v14] : ! [v15] : ( ~ (relation_inverse(v14) = v15) | ~ empty(v14) | relation(v15)) & ! [v14] : ! [v15] : ( ~ (relation_inverse(v14) = v15) | ~ empty(v14) | empty(v15)) & ! [v14] : ! [v15] : ( ~ (function_inverse(v14) = v15) | ~ one_to_one(v14) | ~ relation(v14) | ~ function(v14) | relation_inverse(v14) = v15) & ! [v14] : ! [v15] : ( ~ (function_inverse(v14) = v15) | ~ relation(v14) | ~ function(v14) | relation(v15)) & ! [v14] : ! [v15] : ( ~ (function_inverse(v14) = v15) | ~ relation(v14) | ~ function(v14) | function(v15)) & ! [v14] : ! [v15] : ( ~ element(v14, v15) | empty(v15) | in(v14, v15)) & ! [v14] : ! [v15] : ( ~ empty(v15) | ~ in(v14, v15)) & ! [v14] : ! [v15] : ( ~ in(v15, v14) | ~ in(v14, v15)) & ! [v14] : ! [v15] : ( ~ in(v14, v15) | element(v14, v15)) & ! [v14] : (v14 = empty_set | ~ empty(v14)) & ! [v14] : ( ~ relation(v14) | ~ function(v14) | ~ empty(v14) | one_to_one(v14)) & ! [v14] : ( ~ empty(v14) | relation(v14)) & ! [v14] : ( ~ empty(v14) | function(v14)) & ? [v14] : ? [v15] : element(v15, v14) & ? [v14] : subset(v14, v14) & ( ~ (v5 = v4) | ~ (v3 = v1))) % 5.20/2.06 | 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, all_0_13_13 yields: % 5.20/2.06 | (1) relation_rng(all_0_11_11) = all_0_8_8 & relation_rng(all_0_13_13) = all_0_12_12 & relation_dom(all_0_11_11) = all_0_10_10 & relation_dom(all_0_13_13) = all_0_9_9 & function_inverse(all_0_13_13) = all_0_11_11 & relation_empty_yielding(all_0_7_7) & relation_empty_yielding(empty_set) & one_to_one(all_0_6_6) & one_to_one(all_0_13_13) & 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_13_13) & relation(empty_set) & function(all_0_0_0) & function(all_0_3_3) & function(all_0_6_6) & function(all_0_13_13) & 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] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3 & relation_inverse(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2 & relation_inverse(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function_inverse(v0) = v1) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation_inverse(v1) = v0) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation_inverse(v0) = v1) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(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) & ? [v0] : subset(v0, v0) & ( ~ (all_0_8_8 = all_0_9_9) | ~ (all_0_10_10 = all_0_12_12)) % 5.20/2.08 | % 5.20/2.08 | Applying alpha-rule on (1) yields: % 5.20/2.08 | (2) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 5.20/2.08 | (3) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2 & relation_inverse(v0) = v3)) % 5.33/2.08 | (4) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 5.33/2.08 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 5.33/2.08 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 5.33/2.08 | (7) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) % 5.33/2.08 | (8) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | relation(v1)) % 5.33/2.08 | (9) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | empty(v1)) % 5.33/2.08 | (10) one_to_one(all_0_6_6) % 5.33/2.08 | (11) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function(v1)) % 5.33/2.08 | (12) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) % 5.33/2.08 | (13) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3)) % 5.33/2.08 | (14) relation_dom(all_0_13_13) = all_0_9_9 % 5.33/2.08 | (15) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1)) % 5.33/2.08 | (16) empty(all_0_1_1) % 5.33/2.09 | (17) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 5.33/2.09 | (18) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation(v1)) % 5.33/2.09 | (19) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 5.33/2.09 | (20) function(all_0_0_0) % 5.33/2.09 | (21) ! [v0] : ( ~ empty(v0) | relation(v0)) % 5.33/2.09 | (22) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 5.33/2.09 | (23) ! [v0] : ( ~ empty(v0) | function(v0)) % 5.33/2.09 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 5.33/2.09 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 5.33/2.09 | (26) ~ empty(all_0_5_5) % 5.33/2.09 | (27) function_inverse(all_0_13_13) = all_0_11_11 % 5.33/2.09 | (28) ? [v0] : ? [v1] : element(v1, v0) % 5.33/2.09 | (29) relation_empty_yielding(all_0_7_7) % 5.33/2.09 | (30) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 5.33/2.09 | (31) function(all_0_13_13) % 5.33/2.09 | (32) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 5.33/2.09 | (33) empty(all_0_2_2) % 5.33/2.09 | (34) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation_inverse(v0) = v1) % 5.33/2.09 | (35) relation_dom(all_0_11_11) = all_0_10_10 % 5.33/2.09 | (36) empty(empty_set) % 5.33/2.09 | (37) relation_rng(all_0_13_13) = all_0_12_12 % 5.33/2.09 | (38) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3 & relation_inverse(v0) = v2)) % 5.33/2.09 | (39) ~ empty(all_0_4_4) % 5.33/2.09 | (40) relation_rng(all_0_11_11) = all_0_8_8 % 5.33/2.09 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) % 5.33/2.10 | (42) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 5.33/2.10 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) % 5.33/2.10 | (44) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1)) % 5.33/2.10 | (45) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function_inverse(v0) = v1) % 5.33/2.10 | (46) ? [v0] : subset(v0, v0) % 5.33/2.10 | (47) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation_inverse(v1) = v0) % 5.33/2.10 | (48) relation(all_0_13_13) % 5.33/2.10 | (49) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) % 5.33/2.10 | (50) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) % 5.33/2.10 | (51) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 5.33/2.10 | (52) relation(empty_set) % 5.33/2.10 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 5.33/2.10 | (54) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 5.33/2.10 | (55) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) % 5.33/2.10 | (56) relation(all_0_7_7) % 5.33/2.10 | (57) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation(v1)) % 5.33/2.10 | (58) relation(all_0_4_4) % 5.33/2.10 | (59) function(all_0_3_3) % 5.33/2.10 | (60) relation(all_0_1_1) % 5.33/2.10 | (61) relation(all_0_3_3) % 5.33/2.10 | (62) one_to_one(all_0_13_13) % 5.33/2.10 | (63) relation(all_0_0_0) % 5.33/2.10 | (64) empty(all_0_3_3) % 5.33/2.10 | (65) relation_empty_yielding(empty_set) % 5.33/2.10 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 5.33/2.11 | (67) relation(all_0_6_6) % 5.33/2.11 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) % 5.33/2.11 | (69) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) % 5.33/2.11 | (70) ~ (all_0_8_8 = all_0_9_9) | ~ (all_0_10_10 = all_0_12_12) % 5.33/2.11 | (71) function(all_0_6_6) % 5.33/2.11 | % 5.33/2.11 | Instantiating formula (38) with all_0_12_12, all_0_13_13 and discharging atoms relation_rng(all_0_13_13) = all_0_12_12, relation(all_0_13_13), yields: % 5.33/2.11 | (72) ? [v0] : ? [v1] : (relation_rng(v0) = v1 & relation_dom(v0) = all_0_12_12 & relation_dom(all_0_13_13) = v1 & relation_inverse(all_0_13_13) = v0) % 5.33/2.11 | % 5.33/2.11 | Instantiating formula (3) with all_0_9_9, all_0_13_13 and discharging atoms relation_dom(all_0_13_13) = all_0_9_9, relation(all_0_13_13), yields: % 5.33/2.11 | (73) ? [v0] : ? [v1] : (relation_rng(v1) = all_0_9_9 & relation_rng(all_0_13_13) = v0 & relation_dom(v1) = v0 & relation_inverse(all_0_13_13) = v1) % 5.33/2.11 | % 5.33/2.11 | Instantiating formula (34) with all_0_11_11, all_0_13_13 and discharging atoms function_inverse(all_0_13_13) = all_0_11_11, one_to_one(all_0_13_13), relation(all_0_13_13), function(all_0_13_13), yields: % 5.33/2.11 | (74) relation_inverse(all_0_13_13) = all_0_11_11 % 5.33/2.11 | % 5.33/2.11 | Instantiating (73) with all_17_0_17, all_17_1_18 yields: % 5.33/2.11 | (75) relation_rng(all_17_0_17) = all_0_9_9 & relation_rng(all_0_13_13) = all_17_1_18 & relation_dom(all_17_0_17) = all_17_1_18 & relation_inverse(all_0_13_13) = all_17_0_17 % 5.33/2.11 | % 5.33/2.11 | Applying alpha-rule on (75) yields: % 5.33/2.11 | (76) relation_rng(all_17_0_17) = all_0_9_9 % 5.33/2.11 | (77) relation_rng(all_0_13_13) = all_17_1_18 % 5.33/2.11 | (78) relation_dom(all_17_0_17) = all_17_1_18 % 5.33/2.11 | (79) relation_inverse(all_0_13_13) = all_17_0_17 % 5.33/2.11 | % 5.33/2.11 | Instantiating (72) with all_19_0_19, all_19_1_20 yields: % 5.33/2.11 | (80) relation_rng(all_19_1_20) = all_19_0_19 & relation_dom(all_19_1_20) = all_0_12_12 & relation_dom(all_0_13_13) = all_19_0_19 & relation_inverse(all_0_13_13) = all_19_1_20 % 5.33/2.11 | % 5.33/2.11 | Applying alpha-rule on (80) yields: % 5.33/2.11 | (81) relation_rng(all_19_1_20) = all_19_0_19 % 5.33/2.11 | (82) relation_dom(all_19_1_20) = all_0_12_12 % 5.33/2.12 | (83) relation_dom(all_0_13_13) = all_19_0_19 % 5.33/2.12 | (84) relation_inverse(all_0_13_13) = all_19_1_20 % 5.33/2.12 | % 5.33/2.12 | Instantiating formula (25) with all_0_13_13, all_17_1_18, all_0_12_12 and discharging atoms relation_rng(all_0_13_13) = all_17_1_18, relation_rng(all_0_13_13) = all_0_12_12, yields: % 5.33/2.12 | (85) all_17_1_18 = all_0_12_12 % 5.33/2.12 | % 5.33/2.12 | Instantiating formula (41) with all_0_13_13, all_17_0_17, all_19_1_20 and discharging atoms relation_inverse(all_0_13_13) = all_19_1_20, relation_inverse(all_0_13_13) = all_17_0_17, yields: % 5.33/2.12 | (86) all_19_1_20 = all_17_0_17 % 5.33/2.12 | % 5.33/2.12 | Instantiating formula (41) with all_0_13_13, all_0_11_11, all_19_1_20 and discharging atoms relation_inverse(all_0_13_13) = all_19_1_20, relation_inverse(all_0_13_13) = all_0_11_11, yields: % 5.33/2.12 | (87) all_19_1_20 = all_0_11_11 % 5.33/2.12 | % 5.33/2.12 | Combining equations (86,87) yields a new equation: % 5.33/2.12 | (88) all_17_0_17 = all_0_11_11 % 5.33/2.12 | % 5.33/2.12 | Simplifying 88 yields: % 5.33/2.12 | (89) all_17_0_17 = all_0_11_11 % 5.33/2.12 | % 5.33/2.12 | From (89) and (76) follows: % 5.33/2.12 | (90) relation_rng(all_0_11_11) = all_0_9_9 % 5.33/2.12 | % 5.33/2.12 | From (89)(85) and (78) follows: % 5.33/2.12 | (91) relation_dom(all_0_11_11) = all_0_12_12 % 5.33/2.12 | % 5.33/2.12 | Instantiating formula (25) with all_0_11_11, all_0_9_9, all_0_8_8 and discharging atoms relation_rng(all_0_11_11) = all_0_8_8, relation_rng(all_0_11_11) = all_0_9_9, yields: % 5.33/2.12 | (92) all_0_8_8 = all_0_9_9 % 5.33/2.12 | % 5.33/2.12 | Instantiating formula (24) with all_0_11_11, all_0_12_12, all_0_10_10 and discharging atoms relation_dom(all_0_11_11) = all_0_10_10, relation_dom(all_0_11_11) = all_0_12_12, yields: % 5.33/2.12 | (93) all_0_10_10 = all_0_12_12 % 5.33/2.12 | % 5.33/2.12 +-Applying beta-rule and splitting (70), into two cases. % 5.33/2.12 |-Branch one: % 5.33/2.12 | (94) ~ (all_0_8_8 = all_0_9_9) % 5.33/2.12 | % 5.33/2.12 | Equations (92) can reduce 94 to: % 5.33/2.12 | (95) $false % 5.33/2.12 | % 5.33/2.12 |-The branch is then unsatisfiable % 5.33/2.12 |-Branch two: % 5.33/2.12 | (92) all_0_8_8 = all_0_9_9 % 5.33/2.12 | (97) ~ (all_0_10_10 = all_0_12_12) % 5.33/2.12 | % 5.33/2.12 | Equations (93) can reduce 97 to: % 5.33/2.12 | (95) $false % 5.55/2.13 | % 5.55/2.13 |-The branch is then unsatisfiable % 5.55/2.13 % SZS output end Proof for theBenchmark % 5.55/2.13 % 5.55/2.13 1447ms %------------------------------------------------------------------------------