%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : GRP123-9.003 : TPTP v5.0.0. Bugfixed v1.2.1. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art05.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 20:55:48 EST 2010 % Result : Unsatisfiable 0.31s % Output : Refutation 0.31s % 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/SystemOnTPTP6652/GRP/GRP123-9.003+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 = 48] [nf = 0] [nu = 0] [ut = 11] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 316] [nf = 14] [nu = 170] [ut = 48] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 674] [nf = 124] [nu = 352] [ut = 48] % Looking for a proof at depth = 4 ... % t = 0 secs [nr = 1848] [nf = 234] [nu = 1086] [ut = 48] % Looking for a proof at depth = 5 ... % t = 0 secs [nr = 3250] [nf = 752] [nu = 1820] [ut = 48] % Looking for a proof at depth = 6 ... % t = 0 secs [nr = 6404] [nf = 1270] [nu = 3610] [ut = 48] % Looking for a proof at depth = 7 ... % t = 0 secs [nr = 9558] [nf = 1788] [nu = 5400] [ut = 48] % Looking for a proof at depth = 8 ... % t = 0 secs [nr = 12712] [nf = 2306] [nu = 7190] [ut = 48] % Looking for a proof at depth = 9 ... % t = 0 secs [nr = 15866] [nf = 2824] [nu = 8980] [ut = 48] % Looking for a proof at depth = 10 ... % t = 0 secs [nr = 19020] [nf = 3342] [nu = 10770] [ut = 48] % Looking for a proof at depth = 11 ... % t = 0 secs [nr = 22174] [nf = 3860] [nu = 12560] [ut = 48] % Looking for a proof at depth = 12 ... % t = 0 secs [nr = 25328] [nf = 4378] [nu = 14350] [ut = 48] % Looking for a proof at depth = 13 ... % t = 0 secs [nr = 28482] [nf = 4896] [nu = 16140] [ut = 48] % Looking for a proof at depth = 14 ... % t = 0 secs [nr = 31636] [nf = 5414] [nu = 17930] [ut = 48] % Looking for a proof at depth = 15 ... % t = 0 secs [nr = 34790] [nf = 5932] [nu = 19720] [ut = 48] % Looking for a proof at depth = 16 ... % t = 0 secs [nr = 37944] [nf = 6450] [nu = 21510] [ut = 48] % Looking for a proof at depth = 17 ... % t = 0 secs [nr = 41098] [nf = 6968] [nu = 23300] [ut = 48] % Looking for a proof at depth = 18 ... % t = 0 secs [nr = 44252] [nf = 7486] [nu = 25090] [ut = 48] % Looking for a proof at depth = 19 ... % t = 0 secs [nr = 47406] [nf = 8004] [nu = 26880] [ut = 48] % Looking for a proof at depth = 20 ... % t = 0 secs [nr = 50560] [nf = 8522] [nu = 28670] [ut = 48] % Looking for a proof at depth = 21 ... % t = 0 secs [nr = 53714] [nf = 9040] [nu = 30460] [ut = 48] % Looking for a proof at depth = 22 ... % t = 0 secs [nr = 56868] [nf = 9558] [nu = 32250] [ut = 48] % Looking for a proof at depth = 23 ... % t = 0 secs [nr = 60022] [nf = 10076] [nu = 34040] [ut = 48] % Looking for a proof at depth = 24 ... % t = 0 secs [nr = 63176] [nf = 10594] [nu = 35830] [ut = 48] % Looking for a proof at depth = 25 ... % t = 0 secs [nr = 66330] [nf = 11112] [nu = 37620] [ut = 48] % Looking for a proof at depth = 26 ... % t = 0 secs [nr = 69484] [nf = 11630] [nu = 39410] [ut = 48] % Looking for a proof at depth = 27 ... % t = 0 secs [nr = 72638] [nf = 12148] [nu = 41200] [ut = 48] % Looking for a proof at depth = 28 ... % t = 0 secs [nr = 75792] [nf = 12666] [nu = 42990] [ut = 48] % Looking for a proof at depth = 29 ... % t = 0 secs [nr = 78946] [nf = 13184] [nu = 44780] [ut = 48] % Looking for a proof at depth = 30 ... % t = 0 secs [nr = 82100] [nf = 13702] [nu = 46570] [ut = 48] % Restarting search with different parameters. % Looking for a proof at depth = 1 ... % t = 0 secs [nr = 82148] [nf = 13702] [nu = 46570] [ut = 48] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 82446] [nf = 13716] [nu = 46752] [ut = 48] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 82822] [nf = 13826] [nu = 46934] [ut = 48] % 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()) % B6: ~equalish_2(e_1_0(),e_2_0()) % B13: ~product1_3(x0,x3,x2) | ~product1_3(x0,x1,x2) | equalish_2(x1,x3) % B14: ~product1_3(x3,x1,x2) | ~product1_3(x0,x1,x2) | equalish_2(x0,x3) % B15: ~product2_3(x0,x1,x3) | ~product2_3(x0,x1,x2) | equalish_2(x2,x3) % B18: ~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()) % 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()) % U10: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_3_0(),e_2_0()) % U20: < d2 v0 dv0 f0 c3 t3 td1 > ~product1_3(e_1_0(),e_2_0(),e_1_0()) % U21: < d2 v0 dv0 f0 c3 t3 td1 > ~product1_3(e_3_0(),e_2_0(),e_3_0()) % U24: < d2 v0 dv0 f0 c3 t3 td1 > ~product1_3(e_1_0(),e_2_0(),e_2_0()) % U29: < d2 v0 dv0 f0 c3 t3 td1 > ~product1_3(e_3_0(),e_2_0(),e_2_0()) % U51: < d4 v0 dv0 f0 c3 t3 td1 > product1_3(e_1_0(),e_2_0(),e_3_0()) % U59: < d4 v0 dv0 f0 c3 t3 td1 > product1_3(e_3_0(),e_2_0(),e_1_0()) % U66: < 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 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 U10: % ~equalish_2(e_3_0(),e_2_0()) ....... U10 % Derivation of unit clause U20: % product1_3(x0,x0,x0) ....... B1 % ~product1_3(x0,x3,x2) | ~product1_3(x0,x1,x2) | equalish_2(x1,x3) ....... B13 % ~product1_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B1:L0, B13:L0] % ~equalish_2(e_2_0(),e_1_0()) ....... U7 % ~product1_3(e_1_0(), e_2_0(), e_1_0()) ....... R2 [R1:L1, U7:L0] % Derivation of unit clause U21: % product1_3(x0,x0,x0) ....... B1 % ~product1_3(x0,x3,x2) | ~product1_3(x0,x1,x2) | equalish_2(x1,x3) ....... B13 % ~product1_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B1:L0, B13:L0] % ~equalish_2(e_2_0(),e_3_0()) ....... U8 % ~product1_3(e_3_0(), e_2_0(), e_3_0()) ....... R2 [R1:L1, U8:L0] % Derivation of unit clause U24: % product1_3(x0,x0,x0) ....... B1 % ~product1_3(x3,x1,x2) | ~product1_3(x0,x1,x2) | equalish_2(x0,x3) ....... B14 % ~product1_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B1:L0, B14:L0] % ~equalish_2(e_1_0(),e_2_0()) ....... U5 % ~product1_3(e_1_0(), e_2_0(), e_2_0()) ....... R2 [R1:L1, U5:L0] % Derivation of unit clause U29: % product1_3(x0,x0,x0) ....... B1 % ~product1_3(x3,x1,x2) | ~product1_3(x0,x1,x2) | equalish_2(x0,x3) ....... B14 % ~product1_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B1:L0, B14:L0] % ~equalish_2(e_3_0(),e_2_0()) ....... U10 % ~product1_3(e_3_0(), e_2_0(), e_2_0()) ....... R2 [R1:L1, U10:L0] % Derivation of unit clause U51: % 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()) ....... B18 % ~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, B18: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()) ....... U20 % 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, U20:L0] % ~product1_3(e_1_0(),e_2_0(),e_2_0()) ....... U24 % product1_3(e_1_0(), e_2_0(), e_3_0()) ....... R4 [R3:L0, U24:L0] % Derivation of unit clause U59: % 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()) ....... B18 % ~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, B18: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()) ....... U29 % 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, U29:L0] % ~product1_3(e_3_0(),e_2_0(),e_3_0()) ....... U21 % product1_3(e_3_0(), e_2_0(), e_1_0()) ....... R4 [R3:L1, U21:L0] % Derivation of unit clause U66: % ~equalish_2(e_1_0(),e_2_0()) ....... B6 % ~product2_3(x0,x1,x3) | ~product2_3(x0,x1,x2) | equalish_2(x2,x3) ....... B15 % ~product2_3(x0, x1, e_2_0()) | ~product2_3(x0, x1, e_1_0()) ....... R1 [B6:L0, B15: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()) ....... U59 % ~product1_3(e_1_0(), e_2_0(), e_3_0()) ....... R4 [R3:L0, U59:L0] % Derivation of the empty clause: % ~product1_3(e_1_0(),e_2_0(),e_3_0()) ....... U66 % product1_3(e_1_0(),e_2_0(),e_3_0()) ....... U51 % [] ....... R1 [U66:L0, U51:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 98575 % resolvents: 84733 factors: 13842 % Number of unit clauses generated: 47997 % % unit clauses generated to total clauses generated: 48.69 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 11 [2] = 37 [4] = 19 % Total = 67 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 47997 [2] = 42693 [3] = 7849 [4] = 36 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] group_element_1 (+)3 (-)0 % [1] equalish_2 (+)1 (-)6 % [2] product1_3 (+)10 (-)19 % [3] product2_3 (+)10 (-)18 % [4] product_3 (+)0 (-)0 % ------------------ % Total: (+)24 (-)43 % Total number of unit clauses retained: 67 % Number of clauses skipped because of their length: 17196 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 98595 % Number of unification failures: 81131 % Number of unit to unit unification failures: 370 % N literal unification failure due to lookup root_id table: 593160 % N base clause resolution failure due to lookup table: 265894 % 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: 2837 % 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: 66 % Total number of terms of all unit clauses in table: 188 % 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: 0.35 % Number of symbols (columns) in UCFA: 42 % Profile 2: Number of calls to: % ============================== % PTUnify() = 179726 % ConstructUnitClause() = 2893 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.00 secs % -------------------------------------------------------- % | | % Inferences per sec: inf % | | % -------------------------------------------------------- % Elapsed time: 0 secs % CPU time: 0.30 secs % %------------------------------------------------------------------------------