%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : GRP123-1.003 : TPTP v5.0.0. Released v1.2.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art11.cs.miami.edu % Model : i686 i686 % CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz % Memory : 2006MB % OS : Linux 2.6.31.5-127.fc12.i686.PAE % CPULimit : 300s % DateTime : Sat Nov 27 20:52:20 EST 2010 % Result : Unsatisfiable 3.50s % Output : Refutation 3.50s % 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/SystemOnTPTP12391/GRP/GRP123-1.003+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 = 24] [nf = 0] [nu = 0] [ut = 10] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 156] [nf = 6] [nu = 84] [ut = 29] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 288] [nf = 12] [nu = 168] [ut = 29] % Looking for a proof at depth = 4 ... % t = 0 secs [nr = 1304] [nf = 42] [nu = 540] [ut = 29] % Looking for a proof at depth = 5 ... % t = 0 secs [nr = 2320] [nf = 72] [nu = 912] [ut = 29] % Looking for a proof at depth = 6 ... % t = 0 secs [nr = 3336] [nf = 102] [nu = 1284] [ut = 29] % Looking for a proof at depth = 7 ... % t = 0 secs [nr = 4352] [nf = 132] [nu = 1656] [ut = 29] % Looking for a proof at depth = 8 ... % t = 0 secs [nr = 5368] [nf = 162] [nu = 2028] [ut = 29] % Looking for a proof at depth = 9 ... % t = 0 secs [nr = 6384] [nf = 192] [nu = 2400] [ut = 29] % Looking for a proof at depth = 10 ... % t = 0 secs [nr = 7400] [nf = 222] [nu = 2772] [ut = 29] % Looking for a proof at depth = 11 ... % t = 0 secs [nr = 8416] [nf = 252] [nu = 3144] [ut = 29] % Looking for a proof at depth = 12 ... % t = 0 secs [nr = 9432] [nf = 282] [nu = 3516] [ut = 29] % Looking for a proof at depth = 13 ... % t = 0 secs [nr = 10448] [nf = 312] [nu = 3888] [ut = 29] % Looking for a proof at depth = 14 ... % t = 0 secs [nr = 11464] [nf = 342] [nu = 4260] [ut = 29] % Looking for a proof at depth = 15 ... % t = 0 secs [nr = 12480] [nf = 372] [nu = 4632] [ut = 29] % Looking for a proof at depth = 16 ... % t = 0 secs [nr = 13496] [nf = 402] [nu = 5004] [ut = 29] % Looking for a proof at depth = 17 ... % t = 0 secs [nr = 14512] [nf = 432] [nu = 5376] [ut = 29] % Looking for a proof at depth = 18 ... % t = 0 secs [nr = 15528] [nf = 462] [nu = 5748] [ut = 29] % Looking for a proof at depth = 19 ... % t = 0 secs [nr = 16544] [nf = 492] [nu = 6120] [ut = 29] % Looking for a proof at depth = 20 ... % t = 0 secs [nr = 17560] [nf = 522] [nu = 6492] [ut = 29] % Looking for a proof at depth = 21 ... % t = 0 secs [nr = 18576] [nf = 552] [nu = 6864] [ut = 29] % Looking for a proof at depth = 22 ... % t = 0 secs [nr = 19592] [nf = 582] [nu = 7236] [ut = 29] % Looking for a proof at depth = 23 ... % t = 0 secs [nr = 20608] [nf = 612] [nu = 7608] [ut = 29] % Looking for a proof at depth = 24 ... % t = 0 secs [nr = 21624] [nf = 642] [nu = 7980] [ut = 29] % Looking for a proof at depth = 25 ... % t = 0 secs [nr = 22640] [nf = 672] [nu = 8352] [ut = 29] % Looking for a proof at depth = 26 ... % t = 0 secs [nr = 23656] [nf = 702] [nu = 8724] [ut = 29] % Looking for a proof at depth = 27 ... % t = 0 secs [nr = 24672] [nf = 732] [nu = 9096] [ut = 29] % Looking for a proof at depth = 28 ... % t = 0 secs [nr = 25688] [nf = 762] [nu = 9468] [ut = 29] % Looking for a proof at depth = 29 ... % t = 0 secs [nr = 26704] [nf = 792] [nu = 9840] [ut = 29] % Looking for a proof at depth = 30 ... % t = 0 secs [nr = 27720] [nf = 822] [nu = 10212] [ut = 29] % Restarting search with different parameters. % Looking for a proof at depth = 1 ... % t = 0 secs [nr = 27744] [nf = 822] [nu = 10212] [ut = 29] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 27876] [nf = 828] [nu = 10296] [ut = 29] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 28014] [nf = 834] [nu = 10380] [ut = 29] % Looking for a proof at depth = 4 ... % t = 0 secs [nr = 29635] [nf = 866] [nu = 11058] [ut = 38] % Looking for a proof at depth = 5 ... % t = 0 secs [nr = 42934] [nf = 934] [nu = 17646] [ut = 38] % Looking for a proof at depth = 6 ... % t = 1 secs [nr = 255165] [nf = 1002] [nu = 105746] [ut = 41] % Looking for a proof at depth = 7 ... % t = 3 secs [nr = 1130372] [nf = 193234] [nu = 193846] [ut = 41] % 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()) % B12: ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) % B13: ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) % B14: ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) % B15: ~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()) % U4: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_1_0(),e_2_0()) % U6: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_2_0(),e_1_0()) % U7: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_2_0(),e_3_0()) % U8: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_3_0(),e_1_0()) % U9: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_3_0(),e_2_0()) % U13: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_1_0(),e_2_0()) % U15: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_1_0(),e_3_0()) % U19: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_2_0(),e_1_0()) % U20: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_3_0(),e_2_0(),e_3_0()) % U23: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_2_0(),e_2_0()) % U28: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_3_0(),e_2_0(),e_2_0()) % U32: < d4 v0 dv0 f0 c3 t3 td1 > product_3(e_1_0(),e_2_0(),e_3_0()) % U35: < d4 v0 dv0 f0 c3 t3 td1 > product_3(e_3_0(),e_2_0(),e_1_0()) % U41: < 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 U4: % ~equalish_2(e_1_0(),e_2_0()) ....... U4 % Derivation of unit clause U6: % ~equalish_2(e_2_0(),e_1_0()) ....... U6 % Derivation of unit clause U7: % ~equalish_2(e_2_0(),e_3_0()) ....... U7 % Derivation of unit clause U8: % ~equalish_2(e_3_0(),e_1_0()) ....... U8 % Derivation of unit clause U9: % ~equalish_2(e_3_0(),e_2_0()) ....... U9 % Derivation of unit clause U13: % product_3(x0,x0,x0) ....... B2 % ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) ....... B12 % ~product_3(x0, x0, x1) | equalish_2(x1, x0) ....... R1 [B2:L0, B12:L0] % ~equalish_2(e_2_0(),e_1_0()) ....... U6 % ~product_3(e_1_0(), e_1_0(), e_2_0()) ....... R2 [R1:L1, U6:L0] % Derivation of unit clause U15: % product_3(x0,x0,x0) ....... B2 % ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) ....... B12 % ~product_3(x0, x0, x1) | equalish_2(x1, x0) ....... R1 [B2:L0, B12:L0] % ~equalish_2(e_3_0(),e_1_0()) ....... U8 % ~product_3(e_1_0(), e_1_0(), e_3_0()) ....... R2 [R1:L1, U8:L0] % Derivation of unit clause U19: % product_3(x0,x0,x0) ....... B2 % ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B13 % ~product_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B2:L0, B13:L0] % ~equalish_2(e_2_0(),e_1_0()) ....... U6 % ~product_3(e_1_0(), e_2_0(), e_1_0()) ....... R2 [R1:L1, U6:L0] % Derivation of unit clause U20: % product_3(x0,x0,x0) ....... B2 % ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B13 % ~product_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B2:L0, B13:L0] % ~equalish_2(e_2_0(),e_3_0()) ....... U7 % ~product_3(e_3_0(), e_2_0(), e_3_0()) ....... R2 [R1:L1, U7:L0] % Derivation of unit clause U23: % product_3(x0,x0,x0) ....... B2 % ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B14 % ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B2:L0, B14:L0] % ~equalish_2(e_1_0(),e_2_0()) ....... U4 % ~product_3(e_1_0(), e_2_0(), e_2_0()) ....... R2 [R1:L1, U4:L0] % Derivation of unit clause U28: % product_3(x0,x0,x0) ....... B2 % ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B14 % ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B2:L0, B14:L0] % ~equalish_2(e_3_0(),e_2_0()) ....... U9 % ~product_3(e_3_0(), e_2_0(), e_2_0()) ....... R2 [R1:L1, U9:L0] % Derivation of unit clause U32: % 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()) ....... B15 % ~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, B15: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()) ....... U19 % 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, U19:L0] % ~product_3(e_1_0(),e_2_0(),e_2_0()) ....... U23 % product_3(e_1_0(), e_2_0(), e_3_0()) ....... R4 [R3:L0, U23:L0] % Derivation of unit clause U35: % 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()) ....... B15 % ~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, B15: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()) ....... U28 % 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, U28:L0] % ~product_3(e_3_0(),e_2_0(),e_3_0()) ....... U20 % product_3(e_3_0(), e_2_0(), e_1_0()) ....... R4 [R3:L1, U20:L0] % Derivation of unit clause U41: % ~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()) ....... B15 % ~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, B15: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()) ....... U32 % ~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, U32:L0] % product_3(e_3_0(),e_2_0(),e_1_0()) ....... U35 % 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, U35:L0] % ~equalish_2(e_3_0(),e_1_0()) ....... U8 % ~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, U8: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()) ....... U13 % product_3(e_1_0(), e_1_0(), e_3_0()) ....... R8 [R7:L0, U13:L0] % Derivation of the empty clause: % product_3(e_1_0(),e_1_0(),e_3_0()) ....... U41 % ~product_3(e_1_0(),e_1_0(),e_3_0()) ....... U15 % [] ....... R1 [U41:L0, U15:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 1345176 % resolvents: 1151921 factors: 193255 % Number of unit clauses generated: 203135 % % unit clauses generated to total clauses generated: 15.10 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 10 [2] = 19 [4] = 9 [6] = 3 [8] = 1 % Total = 42 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 203135 [2] = 270591 [3] = 576991 [4] = 275807 [5] = 9149 [6] = 8869 % [7] = 634 % Average size of a generated clause: 3.0 % Number of unit clauses per predicate list: % ========================================== % [0] group_element_1 (+)3 (-)0 % [1] equalish_2 (+)4 (-)6 % [2] product_3 (+)11 (-)18 % ------------------ % Total: (+)18 (-)24 % Total number of unit clauses retained: 42 % Number of clauses skipped because of their length: 1223353 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 23460 % Number of successful unifications: 1345204 % Number of unification failures: 6913711 % Number of unit to unit unification failures: 208 % N literal unification failure due to lookup root_id table: 772776 % N base clause resolution failure due to lookup table: 346460 % N UC-BCL resolution dropped due to lookup table: 171976 % Max entries in substitution set: 11 % N unit clauses dropped because they exceeded max values: 91105 % 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: 41 % Total number of terms of all unit clauses in table: 110 % 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: 40 % Profile 2: Number of calls to: % ============================== % PTUnify() = 8258915 % ConstructUnitClause() = 91137 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.11 secs % -------------------------------------------------------- % | | % Inferences per sec: 448392 % | | % -------------------------------------------------------- % Elapsed time: 3 secs % CPU time: 3.49 secs % %------------------------------------------------------------------------------