%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU230+3 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n018.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 08:47:56 EDT 2022 % Result : Theorem 2.43s 1.28s % Output : Proof 3.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : SEU230+3 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n018.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 07:35:04 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.56 ____ _ % 0.18/0.57 ___ / __ \_____(_)___ ________ __________ % 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.57 % 0.18/0.57 A Theorem Prover for First-Order Logic % 0.18/0.57 (ePrincess v.1.0) % 0.18/0.57 % 0.18/0.57 (c) Philipp Rümmer, 2009-2015 % 0.18/0.57 (c) Peter Backeman, 2014-2015 % 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.57 Bug reports to peter@backeman.se % 0.18/0.57 % 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.57 % 0.18/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.18/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.34/0.91 Prover 0: Preprocessing ... % 2.00/1.11 Prover 0: Warning: ignoring some quantifiers % 2.12/1.13 Prover 0: Constructing countermodel ... % 2.43/1.28 Prover 0: proved (660ms) % 2.43/1.28 % 2.43/1.28 No countermodel exists, formula is valid % 2.43/1.28 % SZS status Theorem for theBenchmark % 2.43/1.28 % 2.43/1.28 Generating proof ... Warning: ignoring some quantifiers % 3.32/1.51 found it (size 9) % 3.32/1.51 % 3.32/1.51 % SZS output start Proof for theBenchmark % 3.32/1.51 Assumed formulas after preprocessing and simplification: % 3.32/1.51 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (succ(v0) = v1 & relation_non_empty(v2) & relation_empty_yielding(v4) & relation_empty_yielding(v3) & relation_empty_yielding(empty_set) & one_to_one(v5) & relation(v11) & relation(v10) & relation(v8) & relation(v7) & relation(v5) & relation(v4) & relation(v3) & relation(v2) & relation(empty_set) & function(v11) & function(v8) & function(v5) & function(v3) & function(v2) & empty(v10) & empty(v9) & empty(v8) & empty(empty_set) & ~ empty(v7) & ~ empty(v6) & ~ in(v0, v1) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (set_union2(v15, v14) = v13) | ~ (set_union2(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v12, v13) = v14) | ~ in(v15, v14) | in(v15, v13) | in(v15, v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v12, v13) = v14) | ~ in(v15, v13) | in(v15, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v12, v13) = v14) | ~ in(v15, v12) | in(v15, v14)) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (set_union2(v13, v14) = v15) | ? [v16] : (( ~ in(v16, v12) | ( ~ in(v16, v14) & ~ in(v16, v13))) & (in(v16, v14) | in(v16, v13) | in(v16, v12)))) & ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (singleton(v12) = v13) | ~ in(v14, v13)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (singleton(v14) = v13) | ~ (singleton(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (succ(v14) = v13) | ~ (succ(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (singleton(v12) = v13) | ~ (set_union2(v12, v13) = v14) | succ(v12) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v13, v12) = v14) | ~ empty(v14) | empty(v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v13, v12) = v14) | set_union2(v12, v13) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v12, v13) = v14) | ~ relation(v13) | ~ relation(v12) | relation(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v12, v13) = v14) | ~ empty(v14) | empty(v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v12, v13) = v14) | set_union2(v13, v12) = v14) & ? [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (singleton(v13) = v14) | ? [v15] : (( ~ (v15 = v13) | ~ in(v13, v12)) & (v15 = v13 | in(v15, v12)))) & ! [v12] : ! [v13] : (v13 = v12 | ~ (set_union2(v12, v12) = v13)) & ! [v12] : ! [v13] : (v13 = v12 | ~ (set_union2(v12, empty_set) = v13)) & ! [v12] : ! [v13] : (v13 = v12 | ~ empty(v13) | ~ empty(v12)) & ! [v12] : ! [v13] : ( ~ (singleton(v12) = v13) | in(v12, v13)) & ! [v12] : ! [v13] : ( ~ (succ(v12) = v13) | ~ empty(v13)) & ! [v12] : ! [v13] : ( ~ (succ(v12) = v13) | ? [v14] : (singleton(v12) = v14 & set_union2(v12, v14) = v13)) & ! [v12] : ! [v13] : ( ~ element(v12, v13) | empty(v13) | in(v12, v13)) & ! [v12] : ! [v13] : ( ~ empty(v13) | ~ in(v12, v13)) & ! [v12] : ! [v13] : ( ~ in(v13, v12) | ~ in(v12, v13)) & ! [v12] : ! [v13] : ( ~ in(v12, v13) | element(v12, v13)) & ! [v12] : (v12 = empty_set | ~ empty(v12)) & ! [v12] : ( ~ relation(v12) | ~ function(v12) | ~ empty(v12) | one_to_one(v12)) & ! [v12] : ( ~ empty(v12) | relation(v12)) & ! [v12] : ( ~ empty(v12) | function(v12)) & ? [v12] : ? [v13] : element(v13, v12)) % 3.72/1.55 | 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 yields: % 3.72/1.55 | (1) succ(all_0_11_11) = 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) & ~ in(all_0_11_11, all_0_10_10) & ! [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) | ? [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) % 3.72/1.55 | % 3.72/1.55 | Applying alpha-rule on (1) yields: % 3.72/1.55 | (2) function(all_0_8_8) % 3.72/1.55 | (3) function(all_0_9_9) % 3.72/1.55 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) % 3.72/1.55 | (5) relation(all_0_9_9) % 3.72/1.55 | (6) ? [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)))) % 3.72/1.56 | (7) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 3.72/1.56 | (8) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) % 3.72/1.56 | (9) relation(all_0_6_6) % 3.72/1.56 | (10) empty(empty_set) % 3.72/1.56 | (11) function(all_0_3_3) % 3.72/1.56 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 3.72/1.56 | (13) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 3.72/1.56 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 3.72/1.56 | (15) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) % 3.72/1.56 | (16) relation(all_0_7_7) % 3.72/1.56 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) % 3.72/1.56 | (18) relation(all_0_1_1) % 3.72/1.56 | (19) ! [v0] : ( ~ empty(v0) | function(v0)) % 3.72/1.56 | (20) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 3.72/1.56 | (21) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 3.72/1.56 | (22) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ empty(v1)) % 3.72/1.56 | (23) relation(all_0_4_4) % 3.72/1.56 | (24) function(all_0_6_6) % 3.72/1.56 | (25) empty(all_0_1_1) % 3.72/1.56 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 3.72/1.56 | (27) relation_empty_yielding(all_0_8_8) % 3.72/1.56 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 3.72/1.56 | (29) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 3.72/1.56 | (30) relation(all_0_0_0) % 3.72/1.56 | (31) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 3.72/1.56 | (32) succ(all_0_11_11) = all_0_10_10 % 3.72/1.56 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v1) | ~ (set_union2(v0, v1) = v2) | succ(v0) = v2) % 3.72/1.56 | (34) relation_empty_yielding(all_0_7_7) % 3.72/1.56 | (35) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : (singleton(v0) = v2 & set_union2(v0, v2) = v1)) % 3.72/1.56 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) % 3.72/1.56 | (37) ? [v0] : ? [v1] : element(v1, v0) % 3.72/1.56 | (38) empty(all_0_3_3) % 3.72/1.56 | (39) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 3.72/1.56 | (40) relation_empty_yielding(empty_set) % 3.72/1.56 | (41) relation(empty_set) % 3.72/1.56 | (42) ~ in(all_0_11_11, all_0_10_10) % 3.72/1.56 | (43) one_to_one(all_0_6_6) % 3.72/1.56 | (44) empty(all_0_2_2) % 3.72/1.56 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) % 3.72/1.56 | (46) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) % 3.72/1.56 | (47) ! [v0] : ( ~ empty(v0) | relation(v0)) % 3.72/1.56 | (48) ~ empty(all_0_4_4) % 3.72/1.56 | (49) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 3.72/1.56 | (50) relation(all_0_8_8) % 3.72/1.56 | (51) relation(all_0_3_3) % 3.72/1.56 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 3.72/1.56 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 3.72/1.56 | (54) function(all_0_0_0) % 3.72/1.57 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) % 3.72/1.57 | (56) ~ empty(all_0_5_5) % 3.72/1.57 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 3.72/1.57 | (58) relation_non_empty(all_0_9_9) % 3.72/1.57 | % 3.72/1.57 | Instantiating formula (35) with all_0_10_10, all_0_11_11 and discharging atoms succ(all_0_11_11) = all_0_10_10, yields: % 3.72/1.57 | (59) ? [v0] : (singleton(all_0_11_11) = v0 & set_union2(all_0_11_11, v0) = all_0_10_10) % 3.72/1.57 | % 3.72/1.57 | Instantiating (59) with all_19_0_16 yields: % 3.72/1.57 | (60) singleton(all_0_11_11) = all_19_0_16 & set_union2(all_0_11_11, all_19_0_16) = all_0_10_10 % 3.72/1.57 | % 3.72/1.57 | Applying alpha-rule on (60) yields: % 3.72/1.57 | (61) singleton(all_0_11_11) = all_19_0_16 % 3.72/1.57 | (62) set_union2(all_0_11_11, all_19_0_16) = all_0_10_10 % 3.72/1.57 | % 3.72/1.57 | Instantiating formula (46) with all_19_0_16, all_0_11_11 and discharging atoms singleton(all_0_11_11) = all_19_0_16, yields: % 3.72/1.57 | (63) in(all_0_11_11, all_19_0_16) % 3.72/1.57 | % 3.72/1.57 | Instantiating formula (53) with all_0_10_10, all_0_11_11, all_19_0_16 and discharging atoms set_union2(all_0_11_11, all_19_0_16) = all_0_10_10, yields: % 3.72/1.57 | (64) set_union2(all_19_0_16, all_0_11_11) = all_0_10_10 % 3.72/1.57 | % 3.72/1.57 | Instantiating formula (45) with all_0_11_11, all_0_10_10, all_0_11_11, all_19_0_16 and discharging atoms set_union2(all_19_0_16, all_0_11_11) = all_0_10_10, in(all_0_11_11, all_19_0_16), ~ in(all_0_11_11, all_0_10_10), yields: % 3.72/1.57 | (65) $false % 3.72/1.57 | % 3.72/1.57 |-The branch is then unsatisfiable % 3.72/1.57 % SZS output end Proof for theBenchmark % 3.72/1.57 % 3.72/1.57 994ms %------------------------------------------------------------------------------