%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : GRP135-2.002 : TPTP v5.0.0. Released v1.2.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art04.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 21:40:40 EST 2010 % Result : Unsatisfiable 30.99s % Output : Refutation 30.99s % 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/SystemOnTPTP5870/GRP/GRP135-2.002+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 = 8] [nf = 0] [nu = 0] [ut = 6] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 28] [nf = 8] [nu = 0] [ut = 6] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 104] [nf = 96] [nu = 0] [ut = 6] % Looking for a proof at depth = 4 ... % t = 0 secs [nr = 410] [nf = 204] [nu = 0] [ut = 6] % Looking for a proof at depth = 5 ... % t = 0 secs [nr = 1118] [nf = 660] [nu = 0] [ut = 6] % Looking for a proof at depth = 6 ... % t = 0 secs [nr = 3614] [nf = 1582] [nu = 0] [ut = 6] % Looking for a proof at depth = 7 ... % t = 0 secs [nr = 19477] [nf = 5633] [nu = 2850] [ut = 16] % Looking for a proof at depth = 8 ... % t = 0 secs [nr = 65576] [nf = 42115] [nu = 7366] [ut = 16] % Looking for a proof at depth = 9 ... % t = 0 secs [nr = 137027] [nf = 107173] [nu = 16658] [ut = 16] % Looking for a proof at depth = 10 ... % t = 1 secs [nr = 301270] [nf = 338579] [nu = 27998] [ut = 16] % Looking for a proof at depth = 11 ... % t = 2 secs [nr = 573927] [nf = 783705] [nu = 54098] [ut = 16] % Looking for a proof at depth = 12 ... % t = 5 secs [nr = 1281102] [nf = 2280663] [nu = 88390] [ut = 16] % Looking for a proof at depth = 13 ... % t = 12 secs [nr = 2592673] [nf = 5421757] [nu = 172970] [ut = 16] % Looking for a proof at depth = 14 ... % Entering time slice 2 % Updating parameters ... done. % Looking for a proof at depth = 1 ... % t = 31 secs [nr = 5997826] [nf = 14930709] [nu = 281059] [ut = 16] % Looking for a proof at depth = 2 ... % t = 31 secs [nr = 5997864] [nf = 14930717] [nu = 281067] [ut = 16] % Looking for a proof at depth = 3 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: ~product_3(x2,x0,x3) | ~product_3(x0,x1,x2) | product_3(x3,x0,x1) % B1: group_element_1(e_1_0()) % B2: group_element_1(e_2_0()) % B11: ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,x1,e_1_0()) | product_3(x0,x1,e_2_0()) % Unit Clauses: % -------------- % U0: < d0 v0 dv0 f0 c1 t1 td1 b > group_element_1(e_1_0()) % U1: < d0 v0 dv0 f0 c1 t1 td1 b > group_element_1(e_2_0()) % U2: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_1_0(),e_2_0()) % U3: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_2_0(),e_1_0()) % U6: < d7 v0 dv0 f0 c3 t3 td1 > ~product_3(e_2_0(),e_1_0(),e_1_0()) % U9: < d7 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_2_0(),e_2_0()) % U13: < d7 v1 dv1 f0 c2 t3 td1 > ~product_3(e_1_0(),e_1_0(),x0) % U16: < d3 v0 dv0 f0 c3 t3 td1 > product_3(e_1_0(),e_1_0(),e_2_0()) % --------------- Start of Proof --------------- % Derivation of unit clause U0: % group_element_1(e_1_0()) ....... U0 % Derivation of unit clause U1: % group_element_1(e_2_0()) ....... U1 % Derivation of unit clause U2: % ~equalish_2(e_1_0(),e_2_0()) ....... U2 % Derivation of unit clause U3: % ~equalish_2(e_2_0(),e_1_0()) ....... U3 % Derivation of unit clause U6: % group_element_1(e_1_0()) ....... B1 % ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,x1,e_1_0()) | product_3(x0,x1,e_2_0()) ....... B11 % ~group_element_1(x0) | product_3(x0, e_1_0(), e_1_0()) | product_3(x0, e_1_0(), e_2_0()) ....... R1 [B1:L0, B11:L0] % group_element_1(e_1_0()) ....... U0 % product_3(e_1_0(), e_1_0(), e_1_0()) | product_3(e_1_0(), e_1_0(), e_2_0()) ....... R2 [R1:L0, U0:L0] % ~product_3(x2,x0,x3) | ~product_3(x0,x1,x2) | product_3(x3,x0,x1) ....... B0 % product_3(e_1_0(), e_1_0(), e_1_0()) | ~product_3(e_2_0(), e_1_0(), x0) | product_3(x0, e_1_0(), e_1_0()) ....... R3 [R2:L1, B0:L1] % ~product_3(e_2_0(), e_1_0(), e_1_0()) | product_3(e_1_0(), e_1_0(), e_1_0()) ....... R4 [R3:L0, R3:L2] % ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B9 % ~product_3(e_2_0(), e_1_0(), e_1_0()) | ~product_3(x0, e_1_0(), e_1_0()) | equalish_2(x0, e_1_0()) ....... R5 [R4:L1, B9:L0] % ~product_3(e_2_0(), e_1_0(), e_1_0()) | equalish_2(e_2_0(), e_1_0()) ....... R6 [R5:L0, R5:L1] % ~equalish_2(e_2_0(),e_1_0()) ....... U3 % ~product_3(e_2_0(), e_1_0(), e_1_0()) ....... R7 [R6:L1, U3:L0] % Derivation of unit clause U9: % group_element_1(e_2_0()) ....... B2 % ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,x1,e_1_0()) | product_3(x0,x1,e_2_0()) ....... B11 % ~group_element_1(x0) | product_3(x0, e_2_0(), e_1_0()) | product_3(x0, e_2_0(), e_2_0()) ....... R1 [B2:L0, B11:L0] % group_element_1(e_2_0()) ....... U1 % product_3(e_2_0(), e_2_0(), e_1_0()) | product_3(e_2_0(), e_2_0(), e_2_0()) ....... R2 [R1:L0, U1:L0] % ~product_3(x2,x0,x3) | ~product_3(x0,x1,x2) | product_3(x3,x0,x1) ....... B0 % product_3(e_2_0(), e_2_0(), e_2_0()) | ~product_3(e_1_0(), e_2_0(), x0) | product_3(x0, e_2_0(), e_2_0()) ....... R3 [R2:L0, B0:L1] % ~product_3(e_1_0(), e_2_0(), e_2_0()) | product_3(e_2_0(), e_2_0(), e_2_0()) ....... R4 [R3:L0, R3:L2] % ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B9 % ~product_3(e_1_0(), e_2_0(), e_2_0()) | ~product_3(x0, e_2_0(), e_2_0()) | equalish_2(x0, e_2_0()) ....... R5 [R4:L1, B9:L0] % ~product_3(e_1_0(), e_2_0(), e_2_0()) | equalish_2(e_1_0(), e_2_0()) ....... R6 [R5:L0, R5:L1] % ~equalish_2(e_1_0(),e_2_0()) ....... U2 % ~product_3(e_1_0(), e_2_0(), e_2_0()) ....... R7 [R6:L1, U2:L0] % Derivation of unit clause U13: % group_element_1(e_2_0()) ....... B2 % ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,x1,e_1_0()) | product_3(x0,x1,e_2_0()) ....... B11 % ~group_element_1(x0) | product_3(x0, e_2_0(), e_1_0()) | product_3(x0, e_2_0(), e_2_0()) ....... R1 [B2:L0, B11:L0] % ~product_3(e_1_0(),e_2_0(),e_2_0()) ....... U9 % ~group_element_1(e_1_0()) | product_3(e_1_0(), e_2_0(), e_1_0()) ....... R2 [R1:L2, U9:L0] % ~product_3(x2,x0,x3) | ~product_3(x0,x1,x2) | product_3(x3,x0,x1) ....... B0 % ~group_element_1(e_1_0()) | ~product_3(e_1_0(), e_1_0(), x0) | product_3(x0, e_1_0(), e_2_0()) ....... R3 [R2:L1, B0:L1] % group_element_1(e_1_0()) ....... U0 % ~product_3(e_1_0(), e_1_0(), x0) | product_3(x0, e_1_0(), e_2_0()) ....... R4 [R3:L0, U0:L0] % ~product_3(x2,x0,x3) | ~product_3(x0,x1,x2) | product_3(x3,x0,x1) ....... B0 % ~product_3(e_1_0(), e_1_0(), x0) | ~product_3(e_1_0(), x1, x0) | product_3(e_2_0(), e_1_0(), x1) ....... R5 [R4:L1, B0:L0] % ~product_3(e_1_0(), e_1_0(), x0) | product_3(e_2_0(), e_1_0(), e_1_0()) ....... R6 [R5:L0, R5:L1] % ~product_3(e_2_0(),e_1_0(),e_1_0()) ....... U6 % ~product_3(e_1_0(), e_1_0(), x0) ....... R7 [R6:L1, U6:L0] % Derivation of unit clause U16: % group_element_1(e_1_0()) ....... B1 % ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,x1,e_1_0()) | product_3(x0,x1,e_2_0()) ....... B11 % ~group_element_1(x0) | product_3(x0, e_1_0(), e_1_0()) | product_3(x0, e_1_0(), e_2_0()) ....... R1 [B1:L0, B11:L0] % group_element_1(e_1_0()) ....... U0 % product_3(e_1_0(), e_1_0(), e_1_0()) | product_3(e_1_0(), e_1_0(), e_2_0()) ....... R2 [R1:L0, U0:L0] % ~product_3(e_1_0(),e_1_0(),x0) ....... U13 % product_3(e_1_0(), e_1_0(), e_2_0()) ....... R3 [R2:L0, U13:L0] % Derivation of the empty clause: % product_3(e_1_0(),e_1_0(),e_2_0()) ....... U16 % ~product_3(e_1_0(),e_1_0(),x0) ....... U13 % [] ....... R1 [U16:L0, U13:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 20928679 % resolvents: 5997916 factors: 14930763 % Number of unit clauses generated: 281076 % % unit clauses generated to total clauses generated: 1.34 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 6 [3] = 1 % [7] = 10 % Total = 17 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 281076 [2] = 15463099 [3] = 5184437 [4] = 61 [5] = 6 % Average size of a generated clause: 3.0 % Number of unit clauses per predicate list: % ========================================== % [0] group_element_1 (+)2 (-)0 % [1] equalish_2 (+)0 (-)2 % [2] greater_2 (+)1 (-)0 % [3] next_2 (+)1 (-)0 % [4] product_3 (+)1 (-)10 % ------------------ % Total: (+)5 (-)12 % Total number of unit clauses retained: 17 % Number of clauses skipped because of their length: 19904683 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 20928703 % Number of unification failures: 6058229 % Number of unit to unit unification failures: 7 % N literal unification failure due to lookup root_id table: 62456304 % N base clause resolution failure due to lookup table: 1716782 % N UC-BCL resolution dropped due to lookup table: 8671 % Max entries in substitution set: 29 % N unit clauses dropped because they exceeded max values: 114764 % 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: 21 % Total number of terms of all unit clauses in table: 43 % 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: 0.49 % Number of symbols (columns) in UCFA: 41 % Profile 2: Number of calls to: % ============================== % PTUnify() = 26986932 % ConstructUnitClause() = 114775 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.05 secs % -------------------------------------------------------- % | | % Inferences per sec: 675119 % | | % -------------------------------------------------------- % Elapsed time: 31 secs % CPU time: 31.00 secs % %------------------------------------------------------------------------------