%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : GRP123-3.003 : TPTP v5.0.0. Released v1.2.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art06.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 20:51:05 EST 2010 % Result : Unsatisfiable 3.88s % Output : Refutation 3.88s % 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/SystemOnTPTP340/GRP/GRP123-3.003+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 = 40] [nf = 0] [nu = 0] [ut = 20] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 211] [nf = 8] [nu = 88] [ut = 40] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 385] [nf = 16] [nu = 176] [ut = 40] % Looking for a proof at depth = 4 ... % t = 0 secs [nr = 1443] [nf = 48] [nu = 552] [ut = 40] % Looking for a proof at depth = 5 ... % t = 0 secs [nr = 2501] [nf = 80] [nu = 928] [ut = 40] % Looking for a proof at depth = 6 ... % t = 0 secs [nr = 3559] [nf = 112] [nu = 1304] [ut = 40] % Looking for a proof at depth = 7 ... % t = 0 secs [nr = 4617] [nf = 144] [nu = 1680] [ut = 40] % Looking for a proof at depth = 8 ... % t = 0 secs [nr = 5675] [nf = 176] [nu = 2056] [ut = 40] % Looking for a proof at depth = 9 ... % t = 0 secs [nr = 6733] [nf = 208] [nu = 2432] [ut = 40] % Looking for a proof at depth = 10 ... % t = 0 secs [nr = 7791] [nf = 240] [nu = 2808] [ut = 40] % Looking for a proof at depth = 11 ... % t = 0 secs [nr = 8849] [nf = 272] [nu = 3184] [ut = 40] % Looking for a proof at depth = 12 ... % t = 0 secs [nr = 9907] [nf = 304] [nu = 3560] [ut = 40] % Looking for a proof at depth = 13 ... % t = 0 secs [nr = 10965] [nf = 336] [nu = 3936] [ut = 40] % Looking for a proof at depth = 14 ... % t = 0 secs [nr = 12023] [nf = 368] [nu = 4312] [ut = 40] % Looking for a proof at depth = 15 ... % t = 0 secs [nr = 13081] [nf = 400] [nu = 4688] [ut = 40] % Looking for a proof at depth = 16 ... % t = 0 secs [nr = 14139] [nf = 432] [nu = 5064] [ut = 40] % Looking for a proof at depth = 17 ... % t = 0 secs [nr = 15197] [nf = 464] [nu = 5440] [ut = 40] % Looking for a proof at depth = 18 ... % t = 0 secs [nr = 16255] [nf = 496] [nu = 5816] [ut = 40] % Looking for a proof at depth = 19 ... % t = 0 secs [nr = 17313] [nf = 528] [nu = 6192] [ut = 40] % Looking for a proof at depth = 20 ... % t = 0 secs [nr = 18371] [nf = 560] [nu = 6568] [ut = 40] % Looking for a proof at depth = 21 ... % t = 0 secs [nr = 19429] [nf = 592] [nu = 6944] [ut = 40] % Looking for a proof at depth = 22 ... % t = 0 secs [nr = 20487] [nf = 624] [nu = 7320] [ut = 40] % Looking for a proof at depth = 23 ... % t = 0 secs [nr = 21545] [nf = 656] [nu = 7696] [ut = 40] % Looking for a proof at depth = 24 ... % t = 0 secs [nr = 22603] [nf = 688] [nu = 8072] [ut = 40] % Looking for a proof at depth = 25 ... % t = 0 secs [nr = 23661] [nf = 720] [nu = 8448] [ut = 40] % Looking for a proof at depth = 26 ... % t = 0 secs [nr = 24719] [nf = 752] [nu = 8824] [ut = 40] % Looking for a proof at depth = 27 ... % t = 0 secs [nr = 25777] [nf = 784] [nu = 9200] [ut = 40] % Looking for a proof at depth = 28 ... % t = 0 secs [nr = 26835] [nf = 816] [nu = 9576] [ut = 40] % Looking for a proof at depth = 29 ... % t = 0 secs [nr = 27893] [nf = 848] [nu = 9952] [ut = 40] % Looking for a proof at depth = 30 ... % t = 0 secs [nr = 28951] [nf = 880] [nu = 10328] [ut = 40] % Restarting search with different parameters. % Looking for a proof at depth = 1 ... % t = 0 secs [nr = 28991] [nf = 880] [nu = 10328] [ut = 40] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 29162] [nf = 888] [nu = 10416] [ut = 40] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 29356] [nf = 896] [nu = 10504] [ut = 40] % Looking for a proof at depth = 4 ... % t = 0 secs [nr = 31644] [nf = 1036] [nu = 11316] [ut = 52] % Looking for a proof at depth = 5 ... % t = 0 secs [nr = 50815] [nf = 1230] [nu = 18678] [ut = 59] % Looking for a proof at depth = 6 ... % t = 1 secs [nr = 276854] [nf = 2922] [nu = 109336] [ut = 64] % Looking for a proof at depth = 7 ... % t = 4 secs [nr = 1298493] [nf = 198170] [nu = 223132] [ut = 67] % Looking for a proof at depth = 8 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: ~product_3(x5,x4,x3) | ~product_3(x5,x1,x0) | ~product_3(x3,x4,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) % B2: product_3(x0,x0,x0) % B3: group_element_1(e_1_0()) % B4: group_element_1(e_2_0()) % B22: ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) % B23: ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) % B24: ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) % B29: ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,x1,e_1_0()) | product_3(x0,x1,e_2_0()) | product_3(x0,x1,e_3_0()) % Unit Clauses: % -------------- % U1: < d0 v0 dv0 f0 c1 t1 td1 b > group_element_1(e_1_0()) % U2: < d0 v0 dv0 f0 c1 t1 td1 b > group_element_1(e_2_0()) % U3: < d0 v0 dv0 f0 c1 t1 td1 b > group_element_1(e_3_0()) % U5: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_1_0(),e_2_0()) % U7: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_2_0(),e_1_0()) % U8: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_2_0(),e_3_0()) % U9: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_3_0(),e_1_0()) % U10: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_3_0(),e_2_0()) % U23: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_1_0(),e_2_0()) % U25: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_1_0(),e_3_0()) % U29: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_2_0(),e_1_0()) % U30: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_3_0(),e_2_0(),e_3_0()) % U33: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_2_0(),e_2_0()) % U38: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_3_0(),e_2_0(),e_2_0()) % U46: < d4 v0 dv0 f0 c3 t3 td1 > product_3(e_1_0(),e_2_0(),e_3_0()) % U49: < d4 v0 dv0 f0 c3 t3 td1 > product_3(e_3_0(),e_2_0(),e_1_0()) % U67: < d8 v0 dv0 f0 c3 t3 td1 > product_3(e_1_0(),e_1_0(),e_3_0()) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % group_element_1(e_1_0()) ....... U1 % Derivation of unit clause U2: % group_element_1(e_2_0()) ....... U2 % Derivation of unit clause U3: % group_element_1(e_3_0()) ....... U3 % Derivation of unit clause U5: % ~equalish_2(e_1_0(),e_2_0()) ....... U5 % Derivation of unit clause U7: % ~equalish_2(e_2_0(),e_1_0()) ....... U7 % Derivation of unit clause U8: % ~equalish_2(e_2_0(),e_3_0()) ....... U8 % Derivation of unit clause U9: % ~equalish_2(e_3_0(),e_1_0()) ....... U9 % Derivation of unit clause U10: % ~equalish_2(e_3_0(),e_2_0()) ....... U10 % Derivation of unit clause U23: % product_3(x0,x0,x0) ....... B2 % ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) ....... B22 % ~product_3(x0, x0, x1) | equalish_2(x1, x0) ....... R1 [B2:L0, B22:L0] % ~equalish_2(e_2_0(),e_1_0()) ....... U7 % ~product_3(e_1_0(), e_1_0(), e_2_0()) ....... R2 [R1:L1, U7:L0] % Derivation of unit clause U25: % product_3(x0,x0,x0) ....... B2 % ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) ....... B22 % ~product_3(x0, x0, x1) | equalish_2(x1, x0) ....... R1 [B2:L0, B22:L0] % ~equalish_2(e_3_0(),e_1_0()) ....... U9 % ~product_3(e_1_0(), e_1_0(), e_3_0()) ....... R2 [R1:L1, U9:L0] % Derivation of unit clause U29: % product_3(x0,x0,x0) ....... B2 % ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B23 % ~product_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B2:L0, B23:L0] % ~equalish_2(e_2_0(),e_1_0()) ....... U7 % ~product_3(e_1_0(), e_2_0(), e_1_0()) ....... R2 [R1:L1, U7:L0] % Derivation of unit clause U30: % product_3(x0,x0,x0) ....... B2 % ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B23 % ~product_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B2:L0, B23:L0] % ~equalish_2(e_2_0(),e_3_0()) ....... U8 % ~product_3(e_3_0(), e_2_0(), e_3_0()) ....... R2 [R1:L1, U8:L0] % Derivation of unit clause U33: % product_3(x0,x0,x0) ....... B2 % ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B24 % ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B2:L0, B24:L0] % ~equalish_2(e_1_0(),e_2_0()) ....... U5 % ~product_3(e_1_0(), e_2_0(), e_2_0()) ....... R2 [R1:L1, U5:L0] % Derivation of unit clause U38: % product_3(x0,x0,x0) ....... B2 % ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B24 % ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B2:L0, B24:L0] % ~equalish_2(e_3_0(),e_2_0()) ....... U10 % ~product_3(e_3_0(), e_2_0(), e_2_0()) ....... R2 [R1:L1, U10:L0] % Derivation of unit clause U46: % group_element_1(e_1_0()) ....... B3 % ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,x1,e_1_0()) | product_3(x0,x1,e_2_0()) | product_3(x0,x1,e_3_0()) ....... B29 % ~group_element_1(x0) | product_3(e_1_0(), x0, e_1_0()) | product_3(e_1_0(), x0, e_2_0()) | product_3(e_1_0(), x0, e_3_0()) ....... R1 [B3:L0, B29:L1] % group_element_1(e_2_0()) ....... U2 % product_3(e_1_0(), e_2_0(), e_1_0()) | product_3(e_1_0(), e_2_0(), e_2_0()) | product_3(e_1_0(), e_2_0(), e_3_0()) ....... R2 [R1:L0, U2:L0] % ~product_3(e_1_0(),e_2_0(),e_1_0()) ....... U29 % product_3(e_1_0(), e_2_0(), e_2_0()) | product_3(e_1_0(), e_2_0(), e_3_0()) ....... R3 [R2:L0, U29:L0] % ~product_3(e_1_0(),e_2_0(),e_2_0()) ....... U33 % product_3(e_1_0(), e_2_0(), e_3_0()) ....... R4 [R3:L0, U33:L0] % Derivation of unit clause U49: % group_element_1(e_2_0()) ....... B4 % ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,x1,e_1_0()) | product_3(x0,x1,e_2_0()) | product_3(x0,x1,e_3_0()) ....... B29 % ~group_element_1(x0) | product_3(x0, e_2_0(), e_1_0()) | product_3(x0, e_2_0(), e_2_0()) | product_3(x0, e_2_0(), e_3_0()) ....... R1 [B4:L0, B29:L0] % group_element_1(e_3_0()) ....... U3 % product_3(e_3_0(), e_2_0(), e_1_0()) | product_3(e_3_0(), e_2_0(), e_2_0()) | product_3(e_3_0(), e_2_0(), e_3_0()) ....... R2 [R1:L0, U3:L0] % ~product_3(e_3_0(),e_2_0(),e_2_0()) ....... U38 % product_3(e_3_0(), e_2_0(), e_1_0()) | product_3(e_3_0(), e_2_0(), e_3_0()) ....... R3 [R2:L1, U38:L0] % ~product_3(e_3_0(),e_2_0(),e_3_0()) ....... U30 % product_3(e_3_0(), e_2_0(), e_1_0()) ....... R4 [R3:L1, U30:L0] % Derivation of unit clause U67: % ~product_3(x5,x4,x3) | ~product_3(x5,x1,x0) | ~product_3(x3,x4,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B0 % ~product_3(x0, x1, x0) | ~product_3(x0, x2, x3) | ~product_3(x3, x2, x0) | equalish_2(x3, x0) ....... R1 [B0:L0, B0:L2] % ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,x1,e_1_0()) | product_3(x0,x1,e_2_0()) | product_3(x0,x1,e_3_0()) ....... B29 % ~product_3(e_1_0(), x0, x1) | ~product_3(x1, x0, e_1_0()) | equalish_2(x1, e_1_0()) | ~group_element_1(x2) | ~group_element_1(e_1_0()) | product_3(e_1_0(), x2, e_2_0()) | product_3(e_1_0(), x2, e_3_0()) ....... R2 [R1:L0, B29:L2] % ~product_3(e_1_0(), x0, x1) | ~product_3(x1, x0, e_1_0()) | equalish_2(x1, e_1_0()) | ~group_element_1(e_1_0()) | product_3(e_1_0(), e_1_0(), e_2_0()) | product_3(e_1_0(), e_1_0(), e_3_0()) ....... R3 [R2:L4, R2:L3] % product_3(e_1_0(),e_2_0(),e_3_0()) ....... U46 % ~product_3(e_3_0(), e_2_0(), e_1_0()) | equalish_2(e_3_0(), e_1_0()) | ~group_element_1(e_1_0()) | product_3(e_1_0(), e_1_0(), e_2_0()) | product_3(e_1_0(), e_1_0(), e_3_0()) ....... R4 [R3:L0, U46:L0] % product_3(e_3_0(),e_2_0(),e_1_0()) ....... U49 % equalish_2(e_3_0(), e_1_0()) | ~group_element_1(e_1_0()) | product_3(e_1_0(), e_1_0(), e_2_0()) | product_3(e_1_0(), e_1_0(), e_3_0()) ....... R5 [R4:L0, U49:L0] % ~equalish_2(e_3_0(),e_1_0()) ....... U9 % ~group_element_1(e_1_0()) | product_3(e_1_0(), e_1_0(), e_2_0()) | product_3(e_1_0(), e_1_0(), e_3_0()) ....... R6 [R5:L0, U9:L0] % group_element_1(e_1_0()) ....... U1 % product_3(e_1_0(), e_1_0(), e_2_0()) | product_3(e_1_0(), e_1_0(), e_3_0()) ....... R7 [R6:L0, U1:L0] % ~product_3(e_1_0(),e_1_0(),e_2_0()) ....... U23 % product_3(e_1_0(), e_1_0(), e_3_0()) ....... R8 [R7:L0, U23:L0] % Derivation of the empty clause: % product_3(e_1_0(),e_1_0(),e_3_0()) ....... U67 % ~product_3(e_1_0(),e_1_0(),e_3_0()) ....... U25 % [] ....... R1 [U67:L0, U25:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 1518233 % resolvents: 1320042 factors: 198191 % Number of unit clauses generated: 232421 % % unit clauses generated to total clauses generated: 15.31 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 20 [2] = 20 [4] = 12 [5] = 7 [6] = 5 [7] = 3 % [8] = 1 % Total = 68 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 232421 [2] = 320913 [3] = 638741 [4] = 292737 [5] = 19823 [6] = 12466 % [7] = 1092 [8] = 40 % Average size of a generated clause: 3.0 % Number of unit clauses per predicate list: % ========================================== % [0] group_element_1 (+)3 (-)0 % [1] cycle_2 (+)3 (-)7 % [2] equalish_2 (+)5 (-)6 % [3] greater_2 (+)6 (-)3 % [4] next_2 (+)3 (-)3 % [5] product_3 (+)11 (-)18 % ------------------ % Total: (+)31 (-)37 % Total number of unit clauses retained: 68 % Number of clauses skipped because of their length: 2118899 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 62641 % Number of successful unifications: 1518261 % Number of unification failures: 7976730 % Number of unit to unit unification failures: 262 % N literal unification failure due to lookup root_id table: 1151677 % N base clause resolution failure due to lookup table: 771043 % N UC-BCL resolution dropped due to lookup table: 174334 % Max entries in substitution set: 11 % N unit clauses dropped because they exceeded max values: 115093 % N unit clauses dropped because too much nesting: 0 % 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: 3 % Max term depth in a unit clause: 1 % Number of states in UCFA table: 65 % Total number of terms of all unit clauses in table: 162 % 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: 0.40 % Number of symbols (columns) in UCFA: 44 % Profile 2: Number of calls to: % ============================== % PTUnify() = 9494991 % ConstructUnitClause() = 115141 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.20 secs % -------------------------------------------------------- % | | % Inferences per sec: 506078 % | | % -------------------------------------------------------- % Elapsed time: 4 secs % CPU time: 3.88 secs % %------------------------------------------------------------------------------