%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : NUM387+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n027.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 08:44:05 EDT 2022 % Result : Theorem 2.43s 1.26s % Output : Proof 3.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.11 % Problem : NUM387+1 : TPTP v8.1.0. Released v3.2.0. % 0.09/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n027.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 : Tue Jul 5 12:08:12 EDT 2022 % 0.12/0.33 % CPUTime : % 0.60/0.59 ____ _ % 0.60/0.59 ___ / __ \_____(_)___ ________ __________ % 0.60/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.60/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.60/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.60/0.59 % 0.60/0.59 A Theorem Prover for First-Order Logic % 0.60/0.59 (ePrincess v.1.0) % 0.60/0.59 % 0.60/0.59 (c) Philipp Rümmer, 2009-2015 % 0.60/0.59 (c) Peter Backeman, 2014-2015 % 0.60/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.60/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.60/0.59 Bug reports to peter@backeman.se % 0.60/0.59 % 0.60/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.60/0.59 % 0.60/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.68/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.55/0.96 Prover 0: Preprocessing ... % 1.98/1.13 Prover 0: Warning: ignoring some quantifiers % 1.98/1.15 Prover 0: Constructing countermodel ... % 2.43/1.26 Prover 0: proved (585ms) % 2.43/1.26 % 2.43/1.26 No countermodel exists, formula is valid % 2.43/1.26 % SZS status Theorem for theBenchmark % 2.43/1.26 % 2.43/1.26 Generating proof ... Warning: ignoring some quantifiers % 3.33/1.48 found it (size 5) % 3.33/1.48 % 3.33/1.48 % SZS output start Proof for theBenchmark % 3.33/1.48 Assumed formulas after preprocessing and simplification: % 3.33/1.48 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (succ(v0) = v0 & relation_non_empty(v1) & relation_empty_yielding(v3) & relation_empty_yielding(v2) & relation_empty_yielding(empty_set) & one_to_one(v4) & relation(v10) & relation(v9) & relation(v7) & relation(v6) & relation(v4) & relation(v3) & relation(v2) & relation(v1) & relation(empty_set) & function(v10) & function(v7) & function(v4) & function(v2) & function(v1) & empty(v9) & empty(v8) & empty(v7) & empty(empty_set) & ~ empty(v6) & ~ empty(v5) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (set_union2(v14, v13) = v12) | ~ (set_union2(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (singleton(v13) = v12) | ~ (singleton(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (succ(v13) = v12) | ~ (succ(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (singleton(v11) = v12) | ~ (set_union2(v11, v12) = v13) | succ(v11) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v12, v11) = v13) | ~ empty(v13) | empty(v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v12, v11) = v13) | set_union2(v11, v12) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v11, v12) = v13) | ~ relation(v12) | ~ relation(v11) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v11, v12) = v13) | ~ empty(v13) | empty(v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v11, v12) = v13) | set_union2(v12, v11) = v13) & ! [v11] : ! [v12] : (v12 = v11 | ~ (set_union2(v11, v11) = v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (set_union2(v11, empty_set) = v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ empty(v12) | ~ empty(v11)) & ! [v11] : ! [v12] : ( ~ (succ(v11) = v12) | ~ empty(v12)) & ! [v11] : ! [v12] : ( ~ (succ(v11) = v12) | in(v11, v12)) & ! [v11] : ! [v12] : ( ~ (succ(v11) = v12) | ? [v13] : (singleton(v11) = v13 & set_union2(v11, v13) = v12)) & ! [v11] : ! [v12] : ( ~ element(v11, v12) | empty(v12) | in(v11, v12)) & ! [v11] : ! [v12] : ( ~ empty(v12) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ( ~ in(v12, v11) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ( ~ in(v11, v12) | element(v11, v12)) & ! [v11] : (v11 = empty_set | ~ empty(v11)) & ! [v11] : ( ~ relation(v11) | ~ function(v11) | ~ empty(v11) | one_to_one(v11)) & ! [v11] : ( ~ empty(v11) | relation(v11)) & ! [v11] : ( ~ empty(v11) | function(v11)) & ? [v11] : ? [v12] : element(v12, v11)) % 3.37/1.52 | 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 yields: % 3.37/1.52 | (1) succ(all_0_10_10) = 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] : (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] : (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] : ( ~ (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) % 3.46/1.53 | % 3.46/1.53 | Applying alpha-rule on (1) yields: % 3.46/1.53 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v1) | ~ (set_union2(v0, v1) = v2) | succ(v0) = v2) % 3.46/1.53 | (3) function(all_0_0_0) % 3.46/1.53 | (4) relation(all_0_4_4) % 3.46/1.53 | (5) empty(all_0_2_2) % 3.46/1.53 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 3.46/1.53 | (7) relation(all_0_6_6) % 3.46/1.53 | (8) relation(all_0_8_8) % 3.46/1.53 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 3.46/1.53 | (10) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 3.46/1.53 | (11) ! [v0] : ( ~ empty(v0) | relation(v0)) % 3.46/1.53 | (12) ! [v0] : ( ~ empty(v0) | function(v0)) % 3.46/1.53 | (13) ~ empty(all_0_5_5) % 3.46/1.53 | (14) relation_empty_yielding(empty_set) % 3.46/1.53 | (15) succ(all_0_10_10) = all_0_10_10 % 3.46/1.53 | (16) empty(empty_set) % 3.46/1.53 | (17) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ empty(v1)) % 3.46/1.53 | (18) function(all_0_8_8) % 3.46/1.53 | (19) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 3.46/1.53 | (20) relation_non_empty(all_0_9_9) % 3.46/1.53 | (21) relation_empty_yielding(all_0_8_8) % 3.46/1.53 | (22) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 3.46/1.53 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 3.46/1.53 | (24) function(all_0_3_3) % 3.46/1.53 | (25) empty(all_0_3_3) % 3.46/1.53 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 3.46/1.53 | (27) function(all_0_6_6) % 3.46/1.53 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 3.46/1.53 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 3.46/1.54 | (30) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 3.46/1.54 | (31) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 3.46/1.54 | (32) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) % 3.46/1.54 | (33) relation(all_0_7_7) % 3.46/1.54 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 3.46/1.54 | (35) empty(all_0_1_1) % 3.46/1.54 | (36) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 3.46/1.54 | (37) ~ empty(all_0_4_4) % 3.46/1.54 | (38) relation(all_0_3_3) % 3.46/1.54 | (39) relation(all_0_9_9) % 3.46/1.54 | (40) ? [v0] : ? [v1] : element(v1, v0) % 3.46/1.54 | (41) relation(all_0_1_1) % 3.46/1.54 | (42) relation(all_0_0_0) % 3.46/1.54 | (43) function(all_0_9_9) % 3.46/1.54 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 3.46/1.54 | (45) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 3.46/1.54 | (46) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | in(v0, v1)) % 3.46/1.54 | (47) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) % 3.46/1.54 | (48) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : (singleton(v0) = v2 & set_union2(v0, v2) = v1)) % 3.46/1.54 | (49) relation_empty_yielding(all_0_7_7) % 3.46/1.54 | (50) one_to_one(all_0_6_6) % 3.46/1.54 | (51) relation(empty_set) % 3.46/1.54 | % 3.46/1.54 | Instantiating formula (46) with all_0_10_10, all_0_10_10 and discharging atoms succ(all_0_10_10) = all_0_10_10, yields: % 3.46/1.54 | (52) in(all_0_10_10, all_0_10_10) % 3.46/1.54 | % 3.46/1.54 | Instantiating formula (22) with all_0_10_10, all_0_10_10 and discharging atoms in(all_0_10_10, all_0_10_10), yields: % 3.46/1.54 | (53) $false % 3.46/1.54 | % 3.46/1.54 |-The branch is then unsatisfiable % 3.46/1.54 % SZS output end Proof for theBenchmark % 3.46/1.54 % 3.46/1.54 933ms %------------------------------------------------------------------------------