%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : GRP125-4.003 : TPTP v5.0.0. Bugfixed v1.2.1. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art03.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 21:06:57 EST 2010 % Result : Unsatisfiable 31.04s % Output : Refutation 31.04s % 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/SystemOnTPTP3662/GRP/GRP125-4.003+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 = 168] [nf = 12] [nu = 90] [ut = 29] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 636] [nf = 492] [nu = 216] [ut = 29] % Looking for a proof at depth = 4 ... % t = 0 secs [nr = 5496] [nf = 972] [nu = 3222] [ut = 29] % Looking for a proof at depth = 5 ... % t = 0 secs [nr = 23100] [nf = 27804] [nu = 6228] [ut = 29] % Looking for a proof at depth = 6 ... % t = 1 secs [nr = 165120] [nf = 54636] [nu = 87858] [ut = 29] % Looking for a proof at depth = 7 ... % t = 3 secs [nr = 769812] [nf = 944892] [nu = 169488] [ut = 29] % Looking for a proof at depth = 8 ... % t = 15 secs [nr = 4993008] [nf = 1835148] [nu = 2527398] [ut = 29] % Looking for a proof at depth = 9 ... % Entering time slice 2 % Updating parameters ... done. % Looking for a proof at depth = 1 ... % t = 32 secs [nr = 9677072] [nf = 8420432] [nu = 3162421] [ut = 29] % Looking for a proof at depth = 2 ... % t = 32 secs [nr = 9677306] [nf = 8420444] [nu = 3162547] [ut = 29] % Looking for a proof at depth = 3 ... % t = 32 secs [nr = 9677834] [nf = 8421032] [nu = 3162673] [ut = 29] % Looking for a proof at depth = 4 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: ~product_3(x1,x0,x3) | ~product_3(x2,x3,x0) | product_3(x0,x1,x2) % B3: product_3(x0,x0,x0) % B4: group_element_1(e_1_0()) % B7: ~equalish_2(e_1_0(),e_2_0()) % B13: ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) % B14: ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) % B15: ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) % B16: ~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()) % B17: ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,e_1_0(),x1) | product_3(x0,e_2_0(),x1) | product_3(x0,e_3_0(),x1) % Unit Clauses: % -------------- % 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()) % U5: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_1_0(),e_3_0()) % U6: < 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_3_0(),e_1_0()) % U11: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_2_0(),e_2_0(),e_1_0()) % U12: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_3_0(),e_3_0(),e_1_0()) % U17: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_2_0(),e_1_0(),e_2_0()) % U25: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_2_0(),e_1_0(),e_1_0()) % U27: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_3_0(),e_1_0(),e_1_0()) % U30: < d4 v0 dv0 f0 c3 t3 td1 > product_3(e_2_0(),e_1_0(),e_3_0()) % U34: < d4 v0 dv0 f0 c3 t3 td1 > product_3(e_2_0(),e_3_0(),e_1_0()) % U35: < d4 v0 dv0 f0 c3 t3 td1 > product_3(e_3_0(),e_2_0(),e_1_0()) % U38: < d4 v0 dv0 f0 c3 t3 td1 > ~product_3(e_2_0(),e_1_0(),e_3_0()) % --------------- Start of Proof --------------- % 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 U5: % ~equalish_2(e_1_0(),e_3_0()) ....... U5 % Derivation of unit clause U6: % ~equalish_2(e_2_0(),e_1_0()) ....... U6 % Derivation of unit clause U8: % ~equalish_2(e_3_0(),e_1_0()) ....... U8 % Derivation of unit clause U11: % product_3(x0,x0,x0) ....... B3 % ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) ....... B13 % ~product_3(x0, x0, x1) | equalish_2(x1, x0) ....... R1 [B3:L0, B13:L0] % ~equalish_2(e_1_0(),e_2_0()) ....... U4 % ~product_3(e_2_0(), e_2_0(), e_1_0()) ....... R2 [R1:L1, U4:L0] % Derivation of unit clause U12: % product_3(x0,x0,x0) ....... B3 % ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) ....... B13 % ~product_3(x0, x0, x1) | equalish_2(x1, x0) ....... R1 [B3:L0, B13:L0] % ~equalish_2(e_1_0(),e_3_0()) ....... U5 % ~product_3(e_3_0(), e_3_0(), e_1_0()) ....... R2 [R1:L1, U5:L0] % Derivation of unit clause U17: % product_3(x0,x0,x0) ....... B3 % ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B14 % ~product_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B3:L0, B14:L0] % ~equalish_2(e_1_0(),e_2_0()) ....... U4 % ~product_3(e_2_0(), e_1_0(), e_2_0()) ....... R2 [R1:L1, U4:L0] % Derivation of unit clause U25: % product_3(x0,x0,x0) ....... B3 % ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B15 % ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B3:L0, B15:L0] % ~equalish_2(e_2_0(),e_1_0()) ....... U6 % ~product_3(e_2_0(), e_1_0(), e_1_0()) ....... R2 [R1:L1, U6:L0] % Derivation of unit clause U27: % product_3(x0,x0,x0) ....... B3 % ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B15 % ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B3:L0, B15:L0] % ~equalish_2(e_3_0(),e_1_0()) ....... U8 % ~product_3(e_3_0(), e_1_0(), e_1_0()) ....... R2 [R1:L1, U8:L0] % Derivation of unit clause U30: % group_element_1(e_1_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()) ....... B16 % ~group_element_1(x0) | product_3(x0, e_1_0(), e_1_0()) | product_3(x0, e_1_0(), e_2_0()) | product_3(x0, e_1_0(), e_3_0()) ....... R1 [B4:L0, B16:L0] % group_element_1(e_2_0()) ....... U2 % product_3(e_2_0(), e_1_0(), e_1_0()) | product_3(e_2_0(), e_1_0(), e_2_0()) | product_3(e_2_0(), e_1_0(), e_3_0()) ....... R2 [R1:L0, U2:L0] % ~product_3(e_2_0(),e_1_0(),e_1_0()) ....... U25 % product_3(e_2_0(), e_1_0(), e_2_0()) | product_3(e_2_0(), e_1_0(), e_3_0()) ....... R3 [R2:L0, U25:L0] % ~product_3(e_2_0(),e_1_0(),e_2_0()) ....... U17 % product_3(e_2_0(), e_1_0(), e_3_0()) ....... R4 [R3:L0, U17:L0] % Derivation of unit clause U34: % group_element_1(e_1_0()) ....... B4 % ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,e_1_0(),x1) | product_3(x0,e_2_0(),x1) | product_3(x0,e_3_0(),x1) ....... B17 % ~group_element_1(x0) | product_3(x0, e_1_0(), e_1_0()) | product_3(x0, e_2_0(), e_1_0()) | product_3(x0, e_3_0(), e_1_0()) ....... R1 [B4:L0, B17:L0] % group_element_1(e_2_0()) ....... U2 % product_3(e_2_0(), e_1_0(), e_1_0()) | product_3(e_2_0(), e_2_0(), e_1_0()) | product_3(e_2_0(), e_3_0(), e_1_0()) ....... R2 [R1:L0, U2:L0] % ~product_3(e_2_0(),e_1_0(),e_1_0()) ....... U25 % product_3(e_2_0(), e_2_0(), e_1_0()) | product_3(e_2_0(), e_3_0(), e_1_0()) ....... R3 [R2:L0, U25:L0] % ~product_3(e_2_0(),e_2_0(),e_1_0()) ....... U11 % product_3(e_2_0(), e_3_0(), e_1_0()) ....... R4 [R3:L0, U11:L0] % Derivation of unit clause U35: % group_element_1(e_1_0()) ....... B4 % ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,e_1_0(),x1) | product_3(x0,e_2_0(),x1) | product_3(x0,e_3_0(),x1) ....... B17 % ~group_element_1(x0) | product_3(x0, e_1_0(), e_1_0()) | product_3(x0, e_2_0(), e_1_0()) | product_3(x0, e_3_0(), e_1_0()) ....... R1 [B4:L0, B17:L0] % group_element_1(e_3_0()) ....... U3 % product_3(e_3_0(), e_1_0(), e_1_0()) | product_3(e_3_0(), e_2_0(), e_1_0()) | product_3(e_3_0(), e_3_0(), e_1_0()) ....... R2 [R1:L0, U3:L0] % ~product_3(e_3_0(),e_1_0(),e_1_0()) ....... U27 % product_3(e_3_0(), e_2_0(), e_1_0()) | product_3(e_3_0(), e_3_0(), e_1_0()) ....... R3 [R2:L0, U27:L0] % ~product_3(e_3_0(),e_3_0(),e_1_0()) ....... U12 % product_3(e_3_0(), e_2_0(), e_1_0()) ....... R4 [R3:L1, U12:L0] % Derivation of unit clause U38: % ~equalish_2(e_1_0(),e_2_0()) ....... B7 % ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) ....... B13 % ~product_3(x0, x1, e_2_0()) | ~product_3(x0, x1, e_1_0()) ....... R1 [B7:L0, B13:L2] % ~product_3(x1,x0,x3) | ~product_3(x2,x3,x0) | product_3(x0,x1,x2) ....... B0 % ~product_3(x0, x1, e_1_0()) | ~product_3(x1, x0, x2) | ~product_3(e_2_0(), x2, x0) ....... R2 [R1:L0, B0:L2] % product_3(e_3_0(),e_2_0(),e_1_0()) ....... U35 % ~product_3(e_2_0(), e_3_0(), x0) | ~product_3(e_2_0(), x0, e_3_0()) ....... R3 [R2:L0, U35:L0] % product_3(e_2_0(),e_3_0(),e_1_0()) ....... U34 % ~product_3(e_2_0(), e_1_0(), e_3_0()) ....... R4 [R3:L0, U34:L0] % Derivation of the empty clause: % ~product_3(e_2_0(),e_1_0(),e_3_0()) ....... U38 % product_3(e_2_0(),e_1_0(),e_3_0()) ....... U30 % [] ....... R1 [U38:L0, U30:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 18111394 % resolvents: 9690101 factors: 8421293 % Number of unit clauses generated: 3168832 % % unit clauses generated to total clauses generated: 17.50 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 10 [2] = 19 [4] = 10 % Total = 39 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 3168832 [2] = 10282213 [3] = 4660208 [4] = 141 % Average size of a generated clause: 3.0 % Number of unit clauses per predicate list: % ========================================== % [0] group_element_1 (+)3 (-)0 % [1] equalish_2 (+)1 (-)6 % [2] product_3 (+)10 (-)19 % ------------------ % Total: (+)14 (-)25 % Total number of unit clauses retained: 39 % Number of clauses skipped because of their length: 17769495 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 18111420 % Number of unification failures: 16579558 % Number of unit to unit unification failures: 188 % N literal unification failure due to lookup root_id table: 18809040 % N base clause resolution failure due to lookup table: 580857 % N UC-BCL resolution dropped due to lookup table: 0 % Max entries in substitution set: 22 % N unit clauses dropped because they exceeded max values: 2364038 % 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: 38 % Total number of terms of all unit clauses in table: 104 % 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() = 34690978 % ConstructUnitClause() = 2364067 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 2.75 secs % -------------------------------------------------------- % | | % Inferences per sec: 584239 % | | % -------------------------------------------------------- % Elapsed time: 32 secs % CPU time: 31.03 secs % %------------------------------------------------------------------------------