%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : SYN328-1 : TPTP v5.0.0. Released v1.2.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art01.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 : Sun Nov 28 08:56:00 EST 2010 % Result : Unsatisfiable 0.24s % Output : Refutation 0.24s % 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/SystemOnTPTP17689/SYN/SYN328-1+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 = 1 secs [nr = 5] [nf = 0] [nu = 0] [ut = 0] % Looking for a proof at depth = 2 ... % t = 1 secs [nr = 56] [nf = 0] [nu = 0] [ut = 0] % Looking for a proof at depth = 3 ... % t = 1 secs [nr = 313] [nf = 7] [nu = 0] [ut = 0] % Looking for a proof at depth = 4 ... % t = 1 secs [nr = 1488] [nf = 56] [nu = 0] [ut = 0] % Looking for a proof at depth = 5 ... % t = 1 secs [nr = 5884] [nf = 247] [nu = 0] [ut = 0] % Looking for a proof at depth = 6 ... % t = 1 secs [nr = 20631] [nf = 919] [nu = 0] [ut = 0] % Looking for a proof at depth = 7 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B2: ~g_1(y_1(x0)) | f_1(x0) % B3: ~h_1(y_1(x0)) | g_1(x0) % B7: ~f_1(y_1(x0)) | ~g_1(x0) | h_1(y_1(x0)) % B9: ~f_1(y_1(x0)) | g_1(y_1(x0)) | h_1(x0) % B10: ~f_1(z_1(x0)) | ~g_1(z_1(x0)) | ~h_1(z_1(x0)) % Unit Clauses: % -------------- % U0: < d7 v1 dv1 f3 c0 t4 td4 > ~h_1(y_1(y_1(z_1(x0)))) % U1: < d7 v1 dv1 f3 c0 t4 td4 > f_1(y_1(y_1(z_1(x0)))) % U2: < d7 v1 dv1 f3 c0 t4 td4 > ~g_1(y_1(y_1(z_1(x0)))) % U5: < d7 v1 dv1 f2 c0 t3 td3 > h_1(y_1(z_1(x0))) % U6: < d7 v1 dv1 f1 c0 t2 td2 > f_1(z_1(x0)) % U7: < d7 v1 dv1 f2 c0 t3 td3 > f_1(y_1(z_1(x0))) % U8: < d7 v1 dv1 f2 c0 t3 td3 > g_1(y_1(z_1(x0))) % U9: < d7 v1 dv1 f3 c0 t4 td4 > g_1(y_1(y_1(z_1(x0)))) % --------------- Start of Proof --------------- % Derivation of unit clause U0: % ~g_1(y_1(x0)) | f_1(x0) ....... B2 % ~h_1(y_1(x0)) | g_1(x0) ....... B3 % f_1(x0) | ~h_1(y_1(y_1(x0))) ....... R1 [B2:L0, B3:L1] % ~f_1(z_1(x0)) | ~g_1(z_1(x0)) | ~h_1(z_1(x0)) ....... B10 % ~h_1(y_1(y_1(z_1(x0)))) | ~g_1(z_1(x0)) | ~h_1(z_1(x0)) ....... R2 [R1:L0, B10:L0] % ~h_1(y_1(x0)) | g_1(x0) ....... B3 % ~h_1(y_1(y_1(z_1(x0)))) | ~h_1(z_1(x0)) | ~h_1(y_1(z_1(x0))) ....... R3 [R2:L1, B3:L1] % ~h_1(y_1(x0)) | h_1(x0) ....... B4 % ~h_1(y_1(y_1(z_1(x0)))) | ~h_1(y_1(z_1(x0))) | ~h_1(y_1(z_1(x0))) ....... R4 [R3:L1, B4:L1] % ~h_1(y_1(y_1(z_1(x0)))) | ~h_1(y_1(z_1(x0))) ....... R5 [R4:L1, R4:L2] % ~h_1(y_1(x0)) | h_1(x0) ....... B4 % ~h_1(y_1(y_1(z_1(x0)))) | ~h_1(y_1(y_1(z_1(x0)))) ....... R6 [R5:L1, B4:L1] % ~h_1(y_1(y_1(z_1(x0)))) ....... R7 [R6:L0, R6:L1] % Derivation of unit clause U1: % ~g_1(y_1(x0)) | f_1(x0) ....... B2 % ~f_1(y_1(x0)) | ~g_1(x0) | h_1(y_1(x0)) ....... B7 % ~g_1(y_1(y_1(x0))) | ~g_1(x0) | h_1(y_1(x0)) ....... R1 [B2:L1, B7:L0] % ~h_1(y_1(y_1(z_1(x0)))) ....... U0 % ~g_1(y_1(y_1(y_1(z_1(x0))))) | ~g_1(y_1(z_1(x0))) ....... R2 [R1:L2, U0:L0] % f_1(y_1(x0)) | g_1(x0) ....... B1 % ~g_1(y_1(y_1(y_1(z_1(x0))))) | f_1(y_1(y_1(z_1(x0)))) ....... R3 [R2:L1, B1:L1] % ~f_1(y_1(x0)) | g_1(y_1(x0)) | h_1(x0) ....... B9 % f_1(y_1(y_1(z_1(x0)))) | ~f_1(y_1(y_1(y_1(z_1(x0))))) | h_1(y_1(y_1(z_1(x0)))) ....... R4 [R3:L0, B9:L1] % ~h_1(y_1(y_1(z_1(x0)))) ....... U0 % f_1(y_1(y_1(z_1(x0)))) | ~f_1(y_1(y_1(y_1(z_1(x0))))) ....... R5 [R4:L2, U0:L0] % f_1(y_1(x0)) | f_1(x0) ....... B0 % f_1(y_1(y_1(z_1(x0)))) | f_1(y_1(y_1(z_1(x0)))) ....... R6 [R5:L1, B0:L0] % f_1(y_1(y_1(z_1(x0)))) ....... R7 [R6:L0, R6:L1] % Derivation of unit clause U2: % ~g_1(y_1(x0)) | f_1(x0) ....... B2 % ~f_1(y_1(x0)) | g_1(y_1(x0)) | h_1(x0) ....... B9 % f_1(x0) | ~f_1(y_1(x0)) | h_1(x0) ....... R1 [B2:L0, B9:L1] % f_1(y_1(x0)) | f_1(x0) ....... B0 % f_1(x0) | h_1(x0) | f_1(x0) ....... R2 [R1:L1, B0:L0] % h_1(x0) | f_1(x0) ....... R3 [R2:L0, R2:L2] % ~f_1(y_1(x0)) | ~g_1(x0) | h_1(y_1(x0)) ....... B7 % h_1(y_1(x0)) | ~g_1(x0) | h_1(y_1(x0)) ....... R4 [R3:L1, B7:L0] % ~g_1(x0) | h_1(y_1(x0)) ....... R5 [R4:L0, R4:L2] % ~h_1(y_1(x0)) | h_1(x0) ....... B4 % ~g_1(x0) | h_1(x0) ....... R6 [R5:L1, B4:L0] % ~h_1(y_1(y_1(z_1(x0)))) ....... U0 % ~g_1(y_1(y_1(z_1(x0)))) ....... R7 [R6:L1, U0:L0] % Derivation of unit clause U5: % ~g_1(y_1(x0)) | f_1(x0) ....... B2 % ~f_1(y_1(x0)) | g_1(y_1(x0)) | h_1(x0) ....... B9 % f_1(x0) | ~f_1(y_1(x0)) | h_1(x0) ....... R1 [B2:L0, B9:L1] % f_1(y_1(x0)) | f_1(x0) ....... B0 % f_1(x0) | h_1(x0) | f_1(x0) ....... R2 [R1:L1, B0:L0] % h_1(x0) | f_1(x0) ....... R3 [R2:L0, R2:L2] % ~f_1(y_1(x0)) | g_1(y_1(x0)) | h_1(x0) ....... B9 % h_1(y_1(x0)) | g_1(y_1(x0)) | h_1(x0) ....... R4 [R3:L1, B9:L0] % ~g_1(y_1(y_1(z_1(x0)))) ....... U2 % h_1(y_1(y_1(z_1(x0)))) | h_1(y_1(z_1(x0))) ....... R5 [R4:L1, U2:L0] % ~h_1(y_1(x0)) | h_1(x0) ....... B4 % h_1(y_1(z_1(x0))) | h_1(y_1(z_1(x0))) ....... R6 [R5:L0, B4:L0] % h_1(y_1(z_1(x0))) ....... R7 [R6:L0, R6:L1] % Derivation of unit clause U6: % ~g_1(y_1(x0)) | f_1(x0) ....... B2 % ~f_1(y_1(x0)) | g_1(y_1(x0)) | h_1(x0) ....... B9 % f_1(x0) | ~f_1(y_1(x0)) | h_1(x0) ....... R1 [B2:L0, B9:L1] % f_1(y_1(x0)) | g_1(x0) ....... B1 % f_1(x0) | h_1(x0) | g_1(x0) ....... R2 [R1:L1, B1:L0] % ~h_1(y_1(y_1(z_1(x0)))) ....... U0 % f_1(y_1(y_1(z_1(x0)))) | g_1(y_1(y_1(z_1(x0)))) ....... R3 [R2:L1, U0:L0] % ~f_1(x0) | ~f_1(y_1(x0)) | g_1(y_1(x0)) ....... B5 % g_1(y_1(y_1(z_1(x0)))) | ~f_1(y_1(z_1(x0))) | g_1(y_1(y_1(z_1(x0)))) ....... R4 [R3:L0, B5:L1] % ~f_1(y_1(z_1(x0))) | g_1(y_1(y_1(z_1(x0)))) ....... R5 [R4:L0, R4:L2] % f_1(y_1(x0)) | f_1(x0) ....... B0 % g_1(y_1(y_1(z_1(x0)))) | f_1(z_1(x0)) ....... R6 [R5:L0, B0:L0] % ~g_1(y_1(y_1(z_1(x0)))) ....... U2 % f_1(z_1(x0)) ....... R7 [R6:L0, U2:L0] % Derivation of unit clause U7: % ~g_1(y_1(x0)) | f_1(x0) ....... B2 % ~f_1(y_1(x0)) | g_1(y_1(x0)) | h_1(x0) ....... B9 % f_1(x0) | ~f_1(y_1(x0)) | h_1(x0) ....... R1 [B2:L0, B9:L1] % ~h_1(y_1(x0)) | g_1(x0) ....... B3 % f_1(y_1(x0)) | ~f_1(y_1(y_1(x0))) | g_1(x0) ....... R2 [R1:L2, B3:L0] % f_1(y_1(y_1(z_1(x0)))) ....... U1 % f_1(y_1(z_1(x0))) | g_1(z_1(x0)) ....... R3 [R2:L1, U1:L0] % ~f_1(z_1(x0)) | ~g_1(z_1(x0)) | ~h_1(z_1(x0)) ....... B10 % f_1(y_1(z_1(x0))) | ~f_1(z_1(x0)) | ~h_1(z_1(x0)) ....... R4 [R3:L1, B10:L1] % f_1(z_1(x0)) ....... U6 % f_1(y_1(z_1(x0))) | ~h_1(z_1(x0)) ....... R5 [R4:L1, U6:L0] % ~h_1(y_1(x0)) | h_1(x0) ....... B4 % f_1(y_1(z_1(x0))) | ~h_1(y_1(z_1(x0))) ....... R6 [R5:L1, B4:L1] % h_1(y_1(z_1(x0))) ....... U5 % f_1(y_1(z_1(x0))) ....... R7 [R6:L1, U5:L0] % Derivation of unit clause U8: % ~g_1(y_1(x0)) | f_1(x0) ....... B2 % ~f_1(y_1(x0)) | g_1(y_1(x0)) | h_1(x0) ....... B9 % f_1(x0) | ~f_1(y_1(x0)) | h_1(x0) ....... R1 [B2:L0, B9:L1] % ~h_1(y_1(x0)) | g_1(x0) ....... B3 % f_1(y_1(x0)) | ~f_1(y_1(y_1(x0))) | g_1(x0) ....... R2 [R1:L2, B3:L0] % f_1(y_1(x0)) | f_1(x0) ....... B0 % f_1(y_1(x0)) | g_1(x0) | f_1(y_1(x0)) ....... R3 [R2:L1, B0:L0] % g_1(x0) | f_1(y_1(x0)) ....... R4 [R3:L0, R3:L2] % ~f_1(x0) | ~f_1(y_1(x0)) | g_1(y_1(x0)) ....... B5 % g_1(x0) | ~f_1(x0) | g_1(y_1(x0)) ....... R5 [R4:L1, B5:L1] % f_1(y_1(z_1(x0))) ....... U7 % g_1(y_1(z_1(x0))) | g_1(y_1(y_1(z_1(x0)))) ....... R6 [R5:L1, U7:L0] % ~g_1(y_1(y_1(z_1(x0)))) ....... U2 % g_1(y_1(z_1(x0))) ....... R7 [R6:L1, U2:L0] % Derivation of unit clause U9: % ~g_1(y_1(x0)) | f_1(x0) ....... B2 % ~f_1(z_1(x0)) | ~g_1(z_1(x0)) | ~h_1(z_1(x0)) ....... B10 % ~g_1(y_1(z_1(x0))) | ~g_1(z_1(x0)) | ~h_1(z_1(x0)) ....... R1 [B2:L1, B10:L0] % g_1(y_1(z_1(x0))) ....... U8 % ~g_1(z_1(x0)) | ~h_1(z_1(x0)) ....... R2 [R1:L0, U8:L0] % f_1(y_1(x0)) | g_1(x0) ....... B1 % ~h_1(z_1(x0)) | f_1(y_1(z_1(x0))) ....... R3 [R2:L0, B1:L1] % ~h_1(y_1(x0)) | h_1(x0) ....... B4 % f_1(y_1(z_1(x0))) | ~h_1(y_1(z_1(x0))) ....... R4 [R3:L0, B4:L1] % ~f_1(x0) | ~f_1(y_1(x0)) | g_1(y_1(x0)) ....... B5 % ~h_1(y_1(z_1(x0))) | ~f_1(y_1(y_1(z_1(x0)))) | g_1(y_1(y_1(z_1(x0)))) ....... R5 [R4:L0, B5:L0] % h_1(y_1(z_1(x0))) ....... U5 % ~f_1(y_1(y_1(z_1(x0)))) | g_1(y_1(y_1(z_1(x0)))) ....... R6 [R5:L0, U5:L0] % f_1(y_1(y_1(z_1(x0)))) ....... U1 % g_1(y_1(y_1(z_1(x0)))) ....... R7 [R6:L0, U1:L0] % Derivation of the empty clause: % g_1(y_1(y_1(z_1(x0)))) ....... U9 % ~g_1(y_1(y_1(z_1(x0)))) ....... U2 % [] ....... R1 [U9:L0, U2:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 56445 % resolvents: 54313 factors: 2132 % Number of unit clauses generated: 337 % % unit clauses generated to total clauses generated: 0.60 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [7] = 10 % Total = 10 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 337 [2] = 9917 [3] = 46191 % Average size of a generated clause: 3.0 % Number of unit clauses per predicate list: % ========================================== % [0] f_1 (+)3 (-)0 % [1] g_1 (+)3 (-)1 % [2] h_1 (+)2 (-)1 % ------------------ % Total: (+)8 (-)2 % Total number of unit clauses retained: 10 % Number of clauses skipped because of their length: 49058 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 9824 % Number of successful unifications: 56501 % Number of unification failures: 21797 % Number of unit to unit unification failures: 4 % N literal unification failure due to lookup root_id table: 177004 % N base clause resolution failure due to lookup table: 108690 % N UC-BCL resolution dropped due to lookup table: 0 % Max entries in substitution set: 7 % N unit clauses dropped because they exceeded max values: 275 % N unit clauses dropped because too much nesting: 83 % 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: 4 % Max term depth in a unit clause: 4 % Number of states in UCFA table: 27 % Total number of terms of all unit clauses in table: 31 % Max allowed number of states in UCFA: 80000 % Ratio n states used/total allowed states: 0.00 % Ratio n states used/total unit clauses terms: 0.87 % Number of symbols (columns) in UCFA: 39 % Profile 2: Number of calls to: % ============================== % PTUnify() = 78298 % ConstructUnitClause() = 285 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.00 secs % -------------------------------------------------------- % | | % Inferences per sec: inf % | | % -------------------------------------------------------- % Elapsed time: 1 secs % CPU time: 0.24 secs % %------------------------------------------------------------------------------