%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL096-1 : TPTP v5.0.0. Released v1.0.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art03.cs.miami.edu % Model : i686 i686 % CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz % Memory : 2018MB % OS : Linux 2.6.26.8-57.fc8 % CPULimit : 300s % DateTime : Sat Nov 27 23:59:11 EST 2010 % Result : Unsatisfiable 0.72s % Output : Refutation 0.72s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % Command entered: % /home/graph/tptp/Systems/CARINE---0.734/carine /tmp/SystemOnTPTP24255/LCL/LCL096-1+noeq.car t=300 xo=off uct=32000 % CARINE version 0.734 (Dec 2003) % Initializing tables ... done. % Parsing ..... done. % Calculating time slices ... done. % Building Lookup Tables ... done. % Looking for a proof at depth = 1 ... % t = 0 secs [nr = 7] [nf = 0] [nu = 0] [ut = 4] % Looking for a proof at depth = 2 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),b_0()),a_0())),c_0()),c_0())) % B1: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(equivalent_2(x0,x4),x2),equivalent_2(equivalent_2(x1,x4),x3)))) % B2: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) % B3: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3)) % B4: ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) % Unit Clauses: % -------------- % U1: < d0 v10 dv5 f9 c0 t19 td5 b > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(equivalent_2(x0,x4),x2),equivalent_2(equivalent_2(x1,x4),x3)))) % U2: < d0 v10 dv5 f9 c0 t19 td7 b > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) % U5: < d2 v10 dv5 f15 c6 t31 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4),equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),b_0()),a_0())),c_0()),c_0()))) % U9: < d2 v12 dv6 f11 c0 t23 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(x4,x2),equivalent_2(equivalent_2(equivalent_2(x0,x5),x4),equivalent_2(equivalent_2(x1,x5),x3))))) % U125: < d2 v8 dv4 f13 c6 t27 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),b_0()),a_0()))),c_0()),c_0())) % U312: < d2 v18 dv9 f23 c6 t47 td9 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(x5,x7)),x8),equivalent_2(equivalent_2(x6,x7),x8)),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),b_0()),a_0()))),c_0()),c_0()))) % U322: < d2 v12 dv6 f11 c0 t23 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),x4),x0),equivalent_2(equivalent_2(equivalent_2(x2,x5),x4),equivalent_2(equivalent_2(x3,x5),x1))))) % U1686: < d2 v26 dv13 f31 c6 t63 td10 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7),equivalent_2(equivalent_2(x5,x6),x7)),x8),x8),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x9,x10),equivalent_2(x9,x11)),x12),equivalent_2(equivalent_2(x10,x11),x12)),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),b_0()),a_0()))),c_0()),c_0())))) % U1900: < d2 v16 dv8 f15 c0 t31 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)),equivalent_2(x4,x5)),x6)),equivalent_2(equivalent_2(equivalent_2(x0,x7),x2),equivalent_2(equivalent_2(x1,x7),x6)))) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(equivalent_2(x0,x4),x2),equivalent_2(equivalent_2(x1,x4),x3)))) ....... U1 % Derivation of unit clause U2: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... U2 % Derivation of unit clause U5: % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),b_0()),a_0())),c_0()),c_0())) ....... B0 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(a_0(), equivalent_2(equivalent_2(b_0(), b_0()), a_0())), c_0()), c_0()))) ....... R1 [B0:L0, B4:L2] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... U2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4), x4), equivalent_2(equivalent_2(equivalent_2(a_0(), equivalent_2(equivalent_2(b_0(), b_0()), a_0())), c_0()), c_0()))) ....... R2 [R1:L0, U2:L0] % Derivation of unit clause U9: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(equivalent_2(x0,x4),x2),equivalent_2(equivalent_2(x1,x4),x3)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x3), equivalent_2(equivalent_2(equivalent_2(x0, x4), x2), equivalent_2(equivalent_2(x1, x4), x3))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B4:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(equivalent_2(x0,x4),x2),equivalent_2(equivalent_2(x1,x4),x3)))) ....... U1 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x3), equivalent_2(equivalent_2(x4, x2), equivalent_2(equivalent_2(equivalent_2(x0, x5), x4), equivalent_2(equivalent_2(x1, x5), x3))))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U125: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(equivalent_2(x0,x4),x2),equivalent_2(equivalent_2(x1,x4),x3)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x3)) | is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x4), x2), equivalent_2(equivalent_2(x1, x4), x3))) ....... R1 [B1:L0, B4:L1] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4),equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),b_0()),a_0())),c_0()),c_0()))) ....... U5 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), equivalent_2(a_0(), equivalent_2(equivalent_2(b_0(), b_0()), a_0()))), c_0()), c_0())) ....... R2 [R1:L1, U5:L0] % Derivation of unit clause U312: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4), x4), x5)) | is_a_theorem_1(x5) ....... R1 [B2:L0, B4:L0] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),b_0()),a_0()))),c_0()),c_0())) ....... U125 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4), x4), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5, x6), equivalent_2(x5, x7)), x8), equivalent_2(equivalent_2(x6, x7), x8)), equivalent_2(a_0(), equivalent_2(equivalent_2(b_0(), b_0()), a_0()))), c_0()), c_0()))) ....... R2 [R1:L1, U125:L0] % Derivation of unit clause U322: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4)) | is_a_theorem_1(x4) ....... R1 [B2:L0, B4:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(x4,x2),equivalent_2(equivalent_2(equivalent_2(x0,x5),x4),equivalent_2(equivalent_2(x1,x5),x3))))) ....... U9 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), x4), x0), equivalent_2(equivalent_2(equivalent_2(x2, x5), x4), equivalent_2(equivalent_2(x3, x5), x1))))) ....... R2 [R1:L0, U9:L0] % Derivation of unit clause U1686: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4)) | is_a_theorem_1(x4) ....... R1 [B2:L0, B4:L1] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(x5,x7)),x8),equivalent_2(equivalent_2(x6,x7),x8)),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),b_0()),a_0()))),c_0()),c_0()))) ....... U312 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7), equivalent_2(equivalent_2(x5, x6), x7)), x8), x8), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x9, x10), equivalent_2(x9, x11)), x12), equivalent_2(equivalent_2(x10, x11), x12)), equivalent_2(a_0(), equivalent_2(equivalent_2(b_0(), b_0()), a_0()))), c_0()), c_0())))) ....... R2 [R1:L1, U312:L0] % Derivation of unit clause U1900: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3)) ....... B3 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2)), x3), x3), x4)) | is_a_theorem_1(x4) ....... R1 [B3:L0, B4:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),x4),x0),equivalent_2(equivalent_2(equivalent_2(x2,x5),x4),equivalent_2(equivalent_2(x3,x5),x1))))) ....... U322 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x3, x5)), equivalent_2(x4, x5)), x6)), equivalent_2(equivalent_2(equivalent_2(x0, x7), x2), equivalent_2(equivalent_2(x1, x7), x6)))) ....... R2 [R1:L0, U322:L0] % Derivation of the empty clause: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)),equivalent_2(x4,x5)),x6)),equivalent_2(equivalent_2(equivalent_2(x0,x7),x2),equivalent_2(equivalent_2(x1,x7),x6)))) ....... U1900 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7),equivalent_2(equivalent_2(x5,x6),x7)),x8),x8),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x9,x10),equivalent_2(x9,x11)),x12),equivalent_2(equivalent_2(x10,x11),x12)),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),b_0()),a_0()))),c_0()),c_0())))) ....... U1686 % [] ....... R1 [U1900:L0, U1686:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 2334 % resolvents: 2334 factors: 0 % Number of unit clauses generated: 2321 % % unit clauses generated to total clauses generated: 99.44 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 4 [2] = 1897 % Total = 1901 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 2321 [2] = 13 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)1829 (-)72 % ------------------ % Total: (+)1829 (-)72 % Total number of unit clauses retained: 1901 % Number of clauses skipped because of their length: 5 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 2348 % Number of unification failures: 161 % Number of unit to unit unification failures: 131676 % N literal unification failure due to lookup root_id table: 9 % N base clause resolution failure due to lookup table: 0 % N UC-BCL resolution dropped due to lookup table: 0 % Max entries in substitution set: 16 % N unit clauses dropped because they exceeded max values: 424 % N unit clauses dropped because too much nesting: 39 % N unit clauses not constrcuted because table was full: 0 % N unit clauses dropped because UCFA table was full: 0 % Max number of terms in a unit clause: 63 % Max term depth in a unit clause: 13 % Number of states in UCFA table: 34644 % Total number of terms of all unit clauses in table: 86411 % Max allowed number of states in UCFA: 528000 % Ratio n states used/total allowed states: 0.07 % Ratio n states used/total unit clauses terms: 0.40 % Number of symbols (columns) in UCFA: 39 % Profile 2: Number of calls to: % ============================== % PTUnify() = 2509 % ConstructUnitClause() = 2321 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.05 secs % -------------------------------------------------------- % | | % Inferences per sec: inf % | | % -------------------------------------------------------- % Elapsed time: 1 secs % CPU time: 0.72 secs % %------------------------------------------------------------------------------