%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : NUM394+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n016.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 08:44:08 EDT 2022 % Result : Theorem 3.67s 1.50s % Output : Proof 4.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM394+1 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n016.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 : Thu Jul 7 17:27:07 EDT 2022 % 0.12/0.33 % CPUTime : % 0.56/0.57 ____ _ % 0.56/0.57 ___ / __ \_____(_)___ ________ __________ % 0.56/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.56/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.56/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.56/0.57 % 0.56/0.57 A Theorem Prover for First-Order Logic % 0.56/0.58 (ePrincess v.1.0) % 0.56/0.58 % 0.56/0.58 (c) Philipp Rümmer, 2009-2015 % 0.56/0.58 (c) Peter Backeman, 2014-2015 % 0.56/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.56/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.56/0.58 Bug reports to peter@backeman.se % 0.56/0.58 % 0.56/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.56/0.58 % 0.56/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.74/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.55/0.93 Prover 0: Preprocessing ... % 1.97/1.10 Prover 0: Warning: ignoring some quantifiers % 1.97/1.12 Prover 0: Constructing countermodel ... % 3.67/1.50 Prover 0: proved (874ms) % 3.67/1.50 % 3.67/1.50 No countermodel exists, formula is valid % 3.67/1.50 % SZS status Theorem for theBenchmark % 3.67/1.50 % 3.67/1.50 Generating proof ... Warning: ignoring some quantifiers % 4.63/1.72 found it (size 13) % 4.63/1.72 % 4.63/1.72 % SZS output start Proof for theBenchmark % 4.63/1.72 Assumed formulas after preprocessing and simplification: % 4.63/1.73 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (relation_non_empty(v2) & relation_empty_yielding(v4) & relation_empty_yielding(v3) & relation_empty_yielding(empty_set) & one_to_one(v5) & relation(v12) & relation(v10) & relation(v8) & relation(v7) & relation(v5) & relation(v4) & relation(v3) & relation(v2) & relation(empty_set) & epsilon_connected(v11) & epsilon_transitive(v11) & ordinal(v11) & ordinal(v1) & ordinal(v0) & function(v12) & function(v8) & function(v5) & function(v3) & function(v2) & empty(v10) & empty(v9) & empty(v8) & empty(empty_set) & ~ ordinal_subset(v0, v1) & ~ empty(v7) & ~ empty(v6) & ~ in(v1, v0) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ element(v14, v16) | ~ empty(v15) | ~ in(v13, v14)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ element(v14, v16) | ~ in(v13, v14) | element(v13, v15)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (powerset(v15) = v14) | ~ (powerset(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ element(v13, v15) | subset(v13, v14)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ subset(v13, v14) | element(v13, v15)) & ! [v13] : ! [v14] : (v14 = v13 | ~ ordinal(v14) | ~ ordinal(v13) | in(v14, v13) | in(v13, v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ empty(v14) | ~ empty(v13)) & ! [v13] : ! [v14] : ( ~ element(v13, v14) | empty(v14) | in(v13, v14)) & ! [v13] : ! [v14] : ( ~ subset(v13, v14) | ~ ordinal(v14) | ~ ordinal(v13) | ordinal_subset(v13, v14)) & ! [v13] : ! [v14] : ( ~ ordinal_subset(v13, v14) | ~ ordinal(v14) | ~ ordinal(v13) | subset(v13, v14)) & ! [v13] : ! [v14] : ( ~ epsilon_transitive(v13) | ~ in(v14, v13) | subset(v14, v13)) & ! [v13] : ! [v14] : ( ~ ordinal(v14) | ~ ordinal(v13) | ordinal_subset(v14, v13) | ordinal_subset(v13, v14)) & ! [v13] : ! [v14] : ( ~ ordinal(v14) | ~ ordinal(v13) | ordinal_subset(v13, v13)) & ! [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] : ( ~ epsilon_connected(v13) | ~ epsilon_transitive(v13) | ordinal(v13)) & ! [v13] : ( ~ ordinal(v13) | epsilon_connected(v13)) & ! [v13] : ( ~ ordinal(v13) | epsilon_transitive(v13)) & ! [v13] : ( ~ empty(v13) | relation(v13)) & ! [v13] : ( ~ empty(v13) | function(v13)) & ? [v13] : ? [v14] : element(v14, v13) & ? [v13] : subset(v13, v13) & ? [v13] : (epsilon_transitive(v13) | ? [v14] : (in(v14, v13) & ~ subset(v14, v13)))) % 4.63/1.76 | 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: % 4.63/1.76 | (1) relation_non_empty(all_0_10_10) & relation_empty_yielding(all_0_8_8) & relation_empty_yielding(all_0_9_9) & relation_empty_yielding(empty_set) & one_to_one(all_0_7_7) & relation(all_0_0_0) & relation(all_0_2_2) & relation(all_0_4_4) & relation(all_0_5_5) & relation(all_0_7_7) & relation(all_0_8_8) & relation(all_0_9_9) & relation(all_0_10_10) & relation(empty_set) & epsilon_connected(all_0_1_1) & epsilon_transitive(all_0_1_1) & ordinal(all_0_1_1) & ordinal(all_0_11_11) & ordinal(all_0_12_12) & function(all_0_0_0) & function(all_0_4_4) & function(all_0_7_7) & function(all_0_9_9) & function(all_0_10_10) & empty(all_0_2_2) & empty(all_0_3_3) & empty(all_0_4_4) & empty(empty_set) & ~ ordinal_subset(all_0_12_12, all_0_11_11) & ~ empty(all_0_5_5) & ~ empty(all_0_6_6) & ~ in(all_0_11_11, all_0_12_12) & ! [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 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ ordinal(v1) | ~ ordinal(v0) | in(v1, v0) | in(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ ordinal_subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ epsilon_transitive(v0) | ~ in(v1, v0) | subset(v1, v0)) & ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v1, v0) | ordinal_subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v0)) & ! [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] : ( ~ epsilon_connected(v0) | ~ epsilon_transitive(v0) | ordinal(v0)) & ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0)) & ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) & ? [v0] : (epsilon_transitive(v0) | ? [v1] : (in(v1, v0) & ~ subset(v1, v0))) % 4.63/1.77 | % 4.63/1.77 | Applying alpha-rule on (1) yields: % 4.63/1.77 | (2) relation_empty_yielding(empty_set) % 4.63/1.77 | (3) function(all_0_7_7) % 4.63/1.77 | (4) ~ in(all_0_11_11, all_0_12_12) % 4.63/1.77 | (5) epsilon_transitive(all_0_1_1) % 4.63/1.77 | (6) relation(all_0_4_4) % 4.63/1.77 | (7) empty(all_0_4_4) % 4.63/1.77 | (8) ? [v0] : (epsilon_transitive(v0) | ? [v1] : (in(v1, v0) & ~ subset(v1, v0))) % 4.63/1.77 | (9) epsilon_connected(all_0_1_1) % 4.63/1.77 | (10) ! [v0] : ( ~ empty(v0) | function(v0)) % 4.63/1.77 | (11) empty(all_0_3_3) % 4.63/1.77 | (12) ! [v0] : ! [v1] : ( ~ ordinal_subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | subset(v0, v1)) % 4.63/1.77 | (13) empty(all_0_2_2) % 4.63/1.77 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 4.63/1.77 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 4.63/1.77 | (16) function(all_0_10_10) % 4.63/1.77 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) % 4.63/1.77 | (18) relation(all_0_2_2) % 4.63/1.77 | (19) ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0)) % 4.63/1.77 | (20) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 4.63/1.77 | (21) ~ ordinal_subset(all_0_12_12, all_0_11_11) % 4.63/1.77 | (22) function(all_0_4_4) % 4.63/1.77 | (23) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v1)) % 4.63/1.77 | (24) ! [v0] : ( ~ empty(v0) | relation(v0)) % 4.63/1.77 | (25) relation(all_0_10_10) % 4.63/1.77 | (26) one_to_one(all_0_7_7) % 4.63/1.77 | (27) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 4.63/1.77 | (28) relation(all_0_0_0) % 4.63/1.77 | (29) relation(empty_set) % 4.63/1.77 | (30) ordinal(all_0_1_1) % 4.63/1.77 | (31) ? [v0] : ? [v1] : element(v1, v0) % 4.63/1.77 | (32) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 4.63/1.77 | (33) ~ empty(all_0_6_6) % 4.63/1.77 | (34) relation(all_0_8_8) % 4.63/1.77 | (35) relation(all_0_9_9) % 4.63/1.77 | (36) ! [v0] : ! [v1] : (v1 = v0 | ~ ordinal(v1) | ~ ordinal(v0) | in(v1, v0) | in(v0, v1)) % 4.63/1.77 | (37) ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0)) % 4.63/1.77 | (38) function(all_0_0_0) % 4.63/1.77 | (39) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 4.63/1.77 | (40) relation_empty_yielding(all_0_8_8) % 4.63/1.77 | (41) ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v0)) % 4.63/1.77 | (42) relation_non_empty(all_0_10_10) % 4.63/1.77 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 4.63/1.77 | (44) ? [v0] : subset(v0, v0) % 4.63/1.77 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 4.63/1.77 | (46) ordinal(all_0_12_12) % 4.63/1.77 | (47) ! [v0] : ! [v1] : ( ~ epsilon_transitive(v0) | ~ in(v1, v0) | subset(v1, v0)) % 4.63/1.78 | (48) ordinal(all_0_11_11) % 4.63/1.78 | (49) ! [v0] : ( ~ epsilon_connected(v0) | ~ epsilon_transitive(v0) | ordinal(v0)) % 4.63/1.78 | (50) relation(all_0_5_5) % 4.63/1.78 | (51) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 4.63/1.78 | (52) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) % 4.63/1.78 | (53) ~ empty(all_0_5_5) % 4.63/1.78 | (54) relation(all_0_7_7) % 4.63/1.78 | (55) function(all_0_9_9) % 4.63/1.78 | (56) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 4.63/1.78 | (57) empty(empty_set) % 4.63/1.78 | (58) ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v1, v0) | ordinal_subset(v0, v1)) % 4.63/1.78 | (59) relation_empty_yielding(all_0_9_9) % 4.96/1.78 | % 4.96/1.78 | Instantiating formula (19) with all_0_11_11 and discharging atoms ordinal(all_0_11_11), yields: % 4.96/1.78 | (60) epsilon_transitive(all_0_11_11) % 4.96/1.78 | % 4.96/1.78 | Instantiating formula (36) with all_0_12_12, all_0_11_11 and discharging atoms ordinal(all_0_11_11), ordinal(all_0_12_12), ~ in(all_0_11_11, all_0_12_12), yields: % 4.96/1.78 | (61) all_0_11_11 = all_0_12_12 | in(all_0_12_12, all_0_11_11) % 4.96/1.78 | % 4.96/1.78 | Instantiating formula (58) with all_0_12_12, all_0_11_11 and discharging atoms ordinal(all_0_11_11), ordinal(all_0_12_12), ~ ordinal_subset(all_0_12_12, all_0_11_11), yields: % 4.96/1.78 | (62) ordinal_subset(all_0_11_11, all_0_12_12) % 4.96/1.78 | % 4.96/1.78 +-Applying beta-rule and splitting (61), into two cases. % 4.96/1.78 |-Branch one: % 4.96/1.78 | (63) in(all_0_12_12, all_0_11_11) % 4.96/1.78 | % 4.96/1.78 | Instantiating formula (47) with all_0_12_12, all_0_11_11 and discharging atoms epsilon_transitive(all_0_11_11), in(all_0_12_12, all_0_11_11), yields: % 4.96/1.78 | (64) subset(all_0_12_12, all_0_11_11) % 4.96/1.78 | % 4.96/1.78 | Instantiating formula (23) with all_0_11_11, all_0_12_12 and discharging atoms subset(all_0_12_12, all_0_11_11), ordinal(all_0_11_11), ordinal(all_0_12_12), ~ ordinal_subset(all_0_12_12, all_0_11_11), yields: % 4.96/1.78 | (65) $false % 4.96/1.78 | % 4.96/1.78 |-The branch is then unsatisfiable % 4.96/1.78 |-Branch two: % 4.96/1.78 | (66) ~ in(all_0_12_12, all_0_11_11) % 4.96/1.78 | (67) all_0_11_11 = all_0_12_12 % 4.96/1.78 | % 4.96/1.78 | From (67) and (62) follows: % 4.96/1.78 | (68) ordinal_subset(all_0_12_12, all_0_12_12) % 4.96/1.78 | % 4.96/1.78 | From (67) and (21) follows: % 4.96/1.78 | (69) ~ ordinal_subset(all_0_12_12, all_0_12_12) % 4.96/1.78 | % 4.96/1.78 | Using (68) and (69) yields: % 4.96/1.78 | (65) $false % 4.96/1.78 | % 4.96/1.78 |-The branch is then unsatisfiable % 4.96/1.78 % SZS output end Proof for theBenchmark % 4.96/1.78 % 4.96/1.78 1196ms %------------------------------------------------------------------------------