%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : GRP123-8.003 : TPTP v5.0.0. Released v1.2.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art09.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 20:52:18 EST 2010 % Result : Unsatisfiable 0.33s % Output : Refutation 0.33s % 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/SystemOnTPTP6360/GRP/GRP123-8.003+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 = 56] [nf = 0] [nu = 0] [ut = 21] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 347] [nf = 16] [nu = 174] [ut = 59] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 731] [nf = 128] [nu = 360] [ut = 59] % Looking for a proof at depth = 4 ... % t = 0 secs [nr = 1931] [nf = 240] [nu = 1098] [ut = 59] % Looking for a proof at depth = 5 ... % t = 0 secs [nr = 3359] [nf = 760] [nu = 1836] [ut = 59] % Looking for a proof at depth = 6 ... % t = 0 secs [nr = 6539] [nf = 1280] [nu = 3630] [ut = 59] % Looking for a proof at depth = 7 ... % t = 0 secs [nr = 9719] [nf = 1800] [nu = 5424] [ut = 59] % Looking for a proof at depth = 8 ... % t = 0 secs [nr = 12899] [nf = 2320] [nu = 7218] [ut = 59] % Looking for a proof at depth = 9 ... % t = 0 secs [nr = 16079] [nf = 2840] [nu = 9012] [ut = 59] % Looking for a proof at depth = 10 ... % t = 0 secs [nr = 19259] [nf = 3360] [nu = 10806] [ut = 59] % Looking for a proof at depth = 11 ... % t = 0 secs [nr = 22439] [nf = 3880] [nu = 12600] [ut = 59] % Looking for a proof at depth = 12 ... % t = 0 secs [nr = 25619] [nf = 4400] [nu = 14394] [ut = 59] % Looking for a proof at depth = 13 ... % t = 0 secs [nr = 28799] [nf = 4920] [nu = 16188] [ut = 59] % Looking for a proof at depth = 14 ... % t = 0 secs [nr = 31979] [nf = 5440] [nu = 17982] [ut = 59] % Looking for a proof at depth = 15 ... % t = 0 secs [nr = 35159] [nf = 5960] [nu = 19776] [ut = 59] % Looking for a proof at depth = 16 ... % t = 0 secs [nr = 38339] [nf = 6480] [nu = 21570] [ut = 59] % Looking for a proof at depth = 17 ... % t = 0 secs [nr = 41519] [nf = 7000] [nu = 23364] [ut = 59] % Looking for a proof at depth = 18 ... % t = 0 secs [nr = 44699] [nf = 7520] [nu = 25158] [ut = 59] % Looking for a proof at depth = 19 ... % t = 0 secs [nr = 47879] [nf = 8040] [nu = 26952] [ut = 59] % Looking for a proof at depth = 20 ... % t = 0 secs [nr = 51059] [nf = 8560] [nu = 28746] [ut = 59] % Looking for a proof at depth = 21 ... % t = 0 secs [nr = 54239] [nf = 9080] [nu = 30540] [ut = 59] % Looking for a proof at depth = 22 ... % t = 0 secs [nr = 57419] [nf = 9600] [nu = 32334] [ut = 59] % Looking for a proof at depth = 23 ... % t = 0 secs [nr = 60599] [nf = 10120] [nu = 34128] [ut = 59] % Looking for a proof at depth = 24 ... % t = 0 secs [nr = 63779] [nf = 10640] [nu = 35922] [ut = 59] % Looking for a proof at depth = 25 ... % t = 0 secs [nr = 66959] [nf = 11160] [nu = 37716] [ut = 59] % Looking for a proof at depth = 26 ... % t = 0 secs [nr = 70139] [nf = 11680] [nu = 39510] [ut = 59] % Looking for a proof at depth = 27 ... % t = 0 secs [nr = 73319] [nf = 12200] [nu = 41304] [ut = 59] % Looking for a proof at depth = 28 ... % t = 0 secs [nr = 76499] [nf = 12720] [nu = 43098] [ut = 59] % Looking for a proof at depth = 29 ... % t = 0 secs [nr = 79679] [nf = 13240] [nu = 44892] [ut = 59] % Looking for a proof at depth = 30 ... % t = 0 secs [nr = 82859] [nf = 13760] [nu = 46686] [ut = 59] % Restarting search with different parameters. % Looking for a proof at depth = 1 ... % t = 0 secs [nr = 82915] [nf = 13760] [nu = 46686] [ut = 59] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 83236] [nf = 13776] [nu = 46872] [ut = 59] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 83638] [nf = 13888] [nu = 47058] [ut = 59] % Looking for a proof at depth = 4 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: ~product1_3(x2,x1,x3) | ~product1_3(x0,x1,x2) | product2_3(x3,x0,x1) % B1: product1_3(x0,x0,x0) % B3: group_element_1(e_1_0()) % B4: group_element_1(e_2_0()) % B7: ~equalish_2(e_1_0(),e_2_0()) % B23: ~product1_3(x0,x3,x2) | ~product1_3(x0,x1,x2) | equalish_2(x1,x3) % B24: ~product1_3(x3,x1,x2) | ~product1_3(x0,x1,x2) | equalish_2(x0,x3) % B25: ~product2_3(x0,x1,x3) | ~product2_3(x0,x1,x2) | equalish_2(x2,x3) % B32: ~group_element_1(x1) | ~group_element_1(x0) | product1_3(x0,x1,e_1_0()) | product1_3(x0,x1,e_2_0()) | product1_3(x0,x1,e_3_0()) % Unit Clauses: % -------------- % U1: < d0 v3 dv1 f0 c0 t3 td1 b > product2_3(x0,x0,x0) % U3: < d0 v0 dv0 f0 c1 t1 td1 b > group_element_1(e_2_0()) % U4: < d0 v0 dv0 f0 c1 t1 td1 b > group_element_1(e_3_0()) % U6: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_1_0(),e_2_0()) % U8: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_2_0(),e_1_0()) % U9: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_2_0(),e_3_0()) % U11: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_3_0(),e_2_0()) % U30: < d2 v0 dv0 f0 c3 t3 td1 > ~product1_3(e_1_0(),e_2_0(),e_1_0()) % U31: < d2 v0 dv0 f0 c3 t3 td1 > ~product1_3(e_3_0(),e_2_0(),e_3_0()) % U34: < d2 v0 dv0 f0 c3 t3 td1 > ~product1_3(e_1_0(),e_2_0(),e_2_0()) % U39: < d2 v0 dv0 f0 c3 t3 td1 > ~product1_3(e_3_0(),e_2_0(),e_2_0()) % U62: < d4 v0 dv0 f0 c3 t3 td1 > product1_3(e_1_0(),e_2_0(),e_3_0()) % U70: < d4 v0 dv0 f0 c3 t3 td1 > product1_3(e_3_0(),e_2_0(),e_1_0()) % U77: < d4 v0 dv0 f0 c3 t3 td1 > ~product1_3(e_1_0(),e_2_0(),e_3_0()) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % product2_3(x0,x0,x0) ....... U1 % Derivation of unit clause U3: % group_element_1(e_2_0()) ....... U3 % Derivation of unit clause U4: % group_element_1(e_3_0()) ....... U4 % Derivation of unit clause U6: % ~equalish_2(e_1_0(),e_2_0()) ....... U6 % Derivation of unit clause U8: % ~equalish_2(e_2_0(),e_1_0()) ....... U8 % Derivation of unit clause U9: % ~equalish_2(e_2_0(),e_3_0()) ....... U9 % Derivation of unit clause U11: % ~equalish_2(e_3_0(),e_2_0()) ....... U11 % Derivation of unit clause U30: % product1_3(x0,x0,x0) ....... B1 % ~product1_3(x0,x3,x2) | ~product1_3(x0,x1,x2) | equalish_2(x1,x3) ....... B23 % ~product1_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B1:L0, B23:L0] % ~equalish_2(e_2_0(),e_1_0()) ....... U8 % ~product1_3(e_1_0(), e_2_0(), e_1_0()) ....... R2 [R1:L1, U8:L0] % Derivation of unit clause U31: % product1_3(x0,x0,x0) ....... B1 % ~product1_3(x0,x3,x2) | ~product1_3(x0,x1,x2) | equalish_2(x1,x3) ....... B23 % ~product1_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B1:L0, B23:L0] % ~equalish_2(e_2_0(),e_3_0()) ....... U9 % ~product1_3(e_3_0(), e_2_0(), e_3_0()) ....... R2 [R1:L1, U9:L0] % Derivation of unit clause U34: % product1_3(x0,x0,x0) ....... B1 % ~product1_3(x3,x1,x2) | ~product1_3(x0,x1,x2) | equalish_2(x0,x3) ....... B24 % ~product1_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B1:L0, B24:L0] % ~equalish_2(e_1_0(),e_2_0()) ....... U6 % ~product1_3(e_1_0(), e_2_0(), e_2_0()) ....... R2 [R1:L1, U6:L0] % Derivation of unit clause U39: % product1_3(x0,x0,x0) ....... B1 % ~product1_3(x3,x1,x2) | ~product1_3(x0,x1,x2) | equalish_2(x0,x3) ....... B24 % ~product1_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B1:L0, B24:L0] % ~equalish_2(e_3_0(),e_2_0()) ....... U11 % ~product1_3(e_3_0(), e_2_0(), e_2_0()) ....... R2 [R1:L1, U11:L0] % Derivation of unit clause U62: % group_element_1(e_1_0()) ....... B3 % ~group_element_1(x1) | ~group_element_1(x0) | product1_3(x0,x1,e_1_0()) | product1_3(x0,x1,e_2_0()) | product1_3(x0,x1,e_3_0()) ....... B32 % ~group_element_1(x0) | product1_3(e_1_0(), x0, e_1_0()) | product1_3(e_1_0(), x0, e_2_0()) | product1_3(e_1_0(), x0, e_3_0()) ....... R1 [B3:L0, B32:L1] % group_element_1(e_2_0()) ....... U3 % product1_3(e_1_0(), e_2_0(), e_1_0()) | product1_3(e_1_0(), e_2_0(), e_2_0()) | product1_3(e_1_0(), e_2_0(), e_3_0()) ....... R2 [R1:L0, U3:L0] % ~product1_3(e_1_0(),e_2_0(),e_1_0()) ....... U30 % product1_3(e_1_0(), e_2_0(), e_2_0()) | product1_3(e_1_0(), e_2_0(), e_3_0()) ....... R3 [R2:L0, U30:L0] % ~product1_3(e_1_0(),e_2_0(),e_2_0()) ....... U34 % product1_3(e_1_0(), e_2_0(), e_3_0()) ....... R4 [R3:L0, U34:L0] % Derivation of unit clause U70: % group_element_1(e_2_0()) ....... B4 % ~group_element_1(x1) | ~group_element_1(x0) | product1_3(x0,x1,e_1_0()) | product1_3(x0,x1,e_2_0()) | product1_3(x0,x1,e_3_0()) ....... B32 % ~group_element_1(x0) | product1_3(x0, e_2_0(), e_1_0()) | product1_3(x0, e_2_0(), e_2_0()) | product1_3(x0, e_2_0(), e_3_0()) ....... R1 [B4:L0, B32:L0] % group_element_1(e_3_0()) ....... U4 % product1_3(e_3_0(), e_2_0(), e_1_0()) | product1_3(e_3_0(), e_2_0(), e_2_0()) | product1_3(e_3_0(), e_2_0(), e_3_0()) ....... R2 [R1:L0, U4:L0] % ~product1_3(e_3_0(),e_2_0(),e_2_0()) ....... U39 % product1_3(e_3_0(), e_2_0(), e_1_0()) | product1_3(e_3_0(), e_2_0(), e_3_0()) ....... R3 [R2:L1, U39:L0] % ~product1_3(e_3_0(),e_2_0(),e_3_0()) ....... U31 % product1_3(e_3_0(), e_2_0(), e_1_0()) ....... R4 [R3:L1, U31:L0] % Derivation of unit clause U77: % ~equalish_2(e_1_0(),e_2_0()) ....... B7 % ~product2_3(x0,x1,x3) | ~product2_3(x0,x1,x2) | equalish_2(x2,x3) ....... B25 % ~product2_3(x0, x1, e_2_0()) | ~product2_3(x0, x1, e_1_0()) ....... R1 [B7:L0, B25:L2] % ~product1_3(x2,x1,x3) | ~product1_3(x0,x1,x2) | product2_3(x3,x0,x1) ....... B0 % ~product2_3(x0, x1, e_1_0()) | ~product1_3(x2, e_2_0(), x0) | ~product1_3(x1, e_2_0(), x2) ....... R2 [R1:L0, B0:L2] % product2_3(x0,x0,x0) ....... U1 % ~product1_3(x0, e_2_0(), e_1_0()) | ~product1_3(e_1_0(), e_2_0(), x0) ....... R3 [R2:L0, U1:L0] % product1_3(e_3_0(),e_2_0(),e_1_0()) ....... U70 % ~product1_3(e_1_0(), e_2_0(), e_3_0()) ....... R4 [R3:L0, U70:L0] % Derivation of the empty clause: % ~product1_3(e_1_0(),e_2_0(),e_3_0()) ....... U77 % product1_3(e_1_0(),e_2_0(),e_3_0()) ....... U62 % [] ....... R1 [U77:L0, U62:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 99499 % resolvents: 85579 factors: 13920 % Number of unit clauses generated: 48123 % % unit clauses generated to total clauses generated: 48.37 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 21 [2] = 38 [4] = 19 % Total = 78 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 48123 [2] = 43269 [3] = 8032 [4] = 70 [5] = 5 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] group_element_1 (+)3 (-)0 % [1] cycle_2 (+)1 (-)0 % [2] equalish_2 (+)2 (-)6 % [3] greater_2 (+)6 (-)0 % [4] next_2 (+)3 (-)0 % [5] product1_3 (+)10 (-)19 % [6] product2_3 (+)10 (-)18 % [7] product_3 (+)0 (-)0 % ------------------ % Total: (+)35 (-)43 % Total number of unit clauses retained: 78 % Number of clauses skipped because of their length: 20499 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 99519 % Number of unification failures: 82631 % Number of unit to unit unification failures: 376 % N literal unification failure due to lookup root_id table: 594644 % N base clause resolution failure due to lookup table: 330671 % N UC-BCL resolution dropped due to lookup table: 0 % Max entries in substitution set: 15 % N unit clauses dropped because they exceeded max values: 2844 % 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: 77 % Total number of terms of all unit clauses in table: 210 % 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: 0.37 % Number of symbols (columns) in UCFA: 46 % Profile 2: Number of calls to: % ============================== % PTUnify() = 182150 % ConstructUnitClause() = 2901 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.01 secs % -------------------------------------------------------- % | | % Inferences per sec: inf % | | % -------------------------------------------------------- % Elapsed time: 0 secs % CPU time: 0.32 secs % %------------------------------------------------------------------------------