%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL205-1 : TPTP v5.0.0. Released v1.1.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art07.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 : Sun Nov 28 00:22:33 EST 2010 % Result : Unsatisfiable 0.94s % Output : Refutation 0.94s % 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/SystemOnTPTP27816/LCL/LCL205-1+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 = 1 secs [nr = 18] [nf = 0] [nu = 10] [ut = 12] % Looking for a proof at depth = 2 ... % t = 1 secs [nr = 4370] [nf = 1] [nu = 2538] [ut = 1510] % Looking for a proof at depth = 3 ... % t = 1 secs [nr = 16988] [nf = 4] [nu = 12982] [ut = 2876] % Looking for a proof at depth = 4 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: ~theorem_1(or_2(not_1(not_1(or_2(not_1(p_0()),q_0()))),or_2(not_1(p_0()),not_1(q_0())))) % B3: axiom_1(or_2(not_1(x0),or_2(x1,x0))) % B4: axiom_1(or_2(not_1(or_2(x0,x1)),or_2(x1,x0))) % B5: axiom_1(or_2(not_1(or_2(x0,x0)),x0)) % B6: ~axiom_1(x0) | theorem_1(x0) % B7: ~axiom_1(or_2(not_1(x0),x2)) | ~theorem_1(or_2(not_1(x2),x1)) | theorem_1(or_2(not_1(x0),x1)) % B8: ~axiom_1(or_2(not_1(x1),x0)) | ~theorem_1(x1) | theorem_1(x0) % Unit Clauses: % -------------- % U1: < d0 v6 dv3 f6 c0 t12 td5 b > axiom_1(or_2(not_1(or_2(x0,or_2(x1,x2))),or_2(x1,or_2(x0,x2)))) % U3: < d0 v3 dv2 f3 c0 t6 td3 b > axiom_1(or_2(not_1(x0),or_2(x1,x0))) % U9: < d1 v3 dv1 f3 c0 t6 td4 > theorem_1(or_2(not_1(or_2(x0,x0)),x0)) % U16: < d2 v0 dv0 f8 c4 t12 td7 > ~theorem_1(or_2(not_1(p_0()),or_2(not_1(not_1(or_2(not_1(p_0()),q_0()))),not_1(q_0())))) % U27: < d2 v2 dv1 f2 c0 t4 td3 > theorem_1(or_2(not_1(x0),x0)) % U230: < d2 v0 dv0 f6 c3 t9 td6 > ~theorem_1(or_2(not_1(not_1(or_2(not_1(p_0()),q_0()))),not_1(q_0()))) % U411: < d2 v2 dv1 f2 c0 t4 td3 > theorem_1(or_2(x0,not_1(x0))) % U738: < d2 v0 dv0 f6 c3 t9 td6 > ~theorem_1(or_2(not_1(q_0()),not_1(not_1(or_2(not_1(p_0()),q_0()))))) % U1071: < d2 v3 dv1 f5 c0 t8 td4 > theorem_1(or_2(not_1(or_2(x0,x0)),not_1(not_1(x0)))) % U1293: < d2 v5 dv1 f7 c0 t12 td5 > theorem_1(or_2(not_1(or_2(or_2(x0,x0),or_2(x0,x0))),not_1(not_1(x0)))) % U11766: < d4 v6 dv2 f8 c0 t14 td6 > theorem_1(or_2(not_1(or_2(x0,or_2(or_2(x0,x1),x1))),not_1(not_1(or_2(x0,x1))))) % U12871: < d4 v3 dv2 f5 c0 t8 td5 > theorem_1(or_2(not_1(x0),not_1(not_1(or_2(x1,x0))))) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % axiom_1(or_2(not_1(or_2(x0,or_2(x1,x2))),or_2(x1,or_2(x0,x2)))) ....... U1 % Derivation of unit clause U3: % axiom_1(or_2(not_1(x0),or_2(x1,x0))) ....... U3 % Derivation of unit clause U9: % axiom_1(or_2(not_1(or_2(x0,x0)),x0)) ....... B5 % ~axiom_1(x0) | theorem_1(x0) ....... B6 % theorem_1(or_2(not_1(or_2(x0, x0)), x0)) ....... R1 [B5:L0, B6:L0] % Derivation of unit clause U16: % ~theorem_1(or_2(not_1(not_1(or_2(not_1(p_0()),q_0()))),or_2(not_1(p_0()),not_1(q_0())))) ....... B0 % ~axiom_1(or_2(not_1(x1),x0)) | ~theorem_1(x1) | theorem_1(x0) ....... B8 % ~axiom_1(or_2(not_1(x0), or_2(not_1(not_1(or_2(not_1(p_0()), q_0()))), or_2(not_1(p_0()), not_1(q_0()))))) | ~theorem_1(x0) ....... R1 [B0:L0, B8:L2] % axiom_1(or_2(not_1(or_2(x0,or_2(x1,x2))),or_2(x1,or_2(x0,x2)))) ....... U1 % ~theorem_1(or_2(not_1(p_0()), or_2(not_1(not_1(or_2(not_1(p_0()), q_0()))), not_1(q_0())))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U27: % axiom_1(or_2(not_1(x0),or_2(x1,x0))) ....... B3 % ~axiom_1(or_2(not_1(x0),x2)) | ~theorem_1(or_2(not_1(x2),x1)) | theorem_1(or_2(not_1(x0),x1)) ....... B7 % ~theorem_1(or_2(not_1(or_2(x0, x1)), x2)) | theorem_1(or_2(not_1(x1), x2)) ....... R1 [B3:L0, B7:L0] % theorem_1(or_2(not_1(or_2(x0,x0)),x0)) ....... U9 % theorem_1(or_2(not_1(x0), x0)) ....... R2 [R1:L0, U9:L0] % Derivation of unit clause U230: % axiom_1(or_2(not_1(x0),or_2(x1,x0))) ....... B3 % ~axiom_1(or_2(not_1(x1),x0)) | ~theorem_1(x1) | theorem_1(x0) ....... B8 % ~theorem_1(x0) | theorem_1(or_2(x1, x0)) ....... R1 [B3:L0, B8:L0] % ~theorem_1(or_2(not_1(p_0()),or_2(not_1(not_1(or_2(not_1(p_0()),q_0()))),not_1(q_0())))) ....... U16 % ~theorem_1(or_2(not_1(not_1(or_2(not_1(p_0()), q_0()))), not_1(q_0()))) ....... R2 [R1:L1, U16:L0] % Derivation of unit clause U411: % axiom_1(or_2(not_1(or_2(x0,x1)),or_2(x1,x0))) ....... B4 % ~axiom_1(or_2(not_1(x1),x0)) | ~theorem_1(x1) | theorem_1(x0) ....... B8 % ~theorem_1(or_2(x0, x1)) | theorem_1(or_2(x1, x0)) ....... R1 [B4:L0, B8:L0] % theorem_1(or_2(not_1(x0),x0)) ....... U27 % theorem_1(or_2(x0, not_1(x0))) ....... R2 [R1:L0, U27:L0] % Derivation of unit clause U738: % axiom_1(or_2(not_1(or_2(x0,x1)),or_2(x1,x0))) ....... B4 % ~axiom_1(or_2(not_1(x1),x0)) | ~theorem_1(x1) | theorem_1(x0) ....... B8 % ~theorem_1(or_2(x0, x1)) | theorem_1(or_2(x1, x0)) ....... R1 [B4:L0, B8:L0] % ~theorem_1(or_2(not_1(not_1(or_2(not_1(p_0()),q_0()))),not_1(q_0()))) ....... U230 % ~theorem_1(or_2(not_1(q_0()), not_1(not_1(or_2(not_1(p_0()), q_0()))))) ....... R2 [R1:L1, U230:L0] % Derivation of unit clause U1071: % axiom_1(or_2(not_1(or_2(x0,x0)),x0)) ....... B5 % ~axiom_1(or_2(not_1(x0),x2)) | ~theorem_1(or_2(not_1(x2),x1)) | theorem_1(or_2(not_1(x0),x1)) ....... B7 % ~theorem_1(or_2(not_1(x0), x1)) | theorem_1(or_2(not_1(or_2(x0, x0)), x1)) ....... R1 [B5:L0, B7:L0] % theorem_1(or_2(x0,not_1(x0))) ....... U411 % theorem_1(or_2(not_1(or_2(x0, x0)), not_1(not_1(x0)))) ....... R2 [R1:L0, U411:L0] % Derivation of unit clause U1293: % axiom_1(or_2(not_1(or_2(x0,x0)),x0)) ....... B5 % ~axiom_1(or_2(not_1(x0),x2)) | ~theorem_1(or_2(not_1(x2),x1)) | theorem_1(or_2(not_1(x0),x1)) ....... B7 % ~theorem_1(or_2(not_1(x0), x1)) | theorem_1(or_2(not_1(or_2(x0, x0)), x1)) ....... R1 [B5:L0, B7:L0] % theorem_1(or_2(not_1(or_2(x0,x0)),not_1(not_1(x0)))) ....... U1071 % theorem_1(or_2(not_1(or_2(or_2(x0, x0), or_2(x0, x0))), not_1(not_1(x0)))) ....... R2 [R1:L0, U1071:L0] % Derivation of unit clause U11766: % axiom_1(or_2(not_1(x0),or_2(x1,x0))) ....... B3 % ~axiom_1(or_2(not_1(x0),x2)) | ~theorem_1(or_2(not_1(x2),x1)) | theorem_1(or_2(not_1(x0),x1)) ....... B7 % ~theorem_1(or_2(not_1(or_2(x0, x1)), x2)) | theorem_1(or_2(not_1(x1), x2)) ....... R1 [B3:L0, B7:L0] % ~axiom_1(or_2(not_1(x0),x2)) | ~theorem_1(or_2(not_1(x2),x1)) | theorem_1(or_2(not_1(x0),x1)) ....... B7 % ~theorem_1(or_2(not_1(or_2(x0, x1)), x2)) | ~axiom_1(or_2(not_1(x3), x1)) | theorem_1(or_2(not_1(x3), x2)) ....... R2 [R1:L1, B7:L1] % theorem_1(or_2(not_1(or_2(or_2(x0,x0),or_2(x0,x0))),not_1(not_1(x0)))) ....... U1293 % ~axiom_1(or_2(not_1(x0), or_2(x1, x1))) | theorem_1(or_2(not_1(x0), not_1(not_1(x1)))) ....... R3 [R2:L0, U1293:L0] % axiom_1(or_2(not_1(or_2(x0,or_2(x1,x2))),or_2(x1,or_2(x0,x2)))) ....... U1 % theorem_1(or_2(not_1(or_2(x0, or_2(or_2(x0, x1), x1))), not_1(not_1(or_2(x0, x1))))) ....... R4 [R3:L0, U1:L0] % Derivation of unit clause U12871: % axiom_1(or_2(not_1(x0),or_2(x1,x0))) ....... B3 % ~axiom_1(or_2(not_1(x0),x2)) | ~theorem_1(or_2(not_1(x2),x1)) | theorem_1(or_2(not_1(x0),x1)) ....... B7 % ~theorem_1(or_2(not_1(or_2(x0, x1)), x2)) | theorem_1(or_2(not_1(x1), x2)) ....... R1 [B3:L0, B7:L0] % ~axiom_1(or_2(not_1(x0),x2)) | ~theorem_1(or_2(not_1(x2),x1)) | theorem_1(or_2(not_1(x0),x1)) ....... B7 % ~theorem_1(or_2(not_1(or_2(x0, x1)), x2)) | ~axiom_1(or_2(not_1(x3), x1)) | theorem_1(or_2(not_1(x3), x2)) ....... R2 [R1:L1, B7:L1] % theorem_1(or_2(not_1(or_2(x0,or_2(or_2(x0,x1),x1))),not_1(not_1(or_2(x0,x1))))) ....... U11766 % ~axiom_1(or_2(not_1(x0), or_2(or_2(x1, x2), x2))) | theorem_1(or_2(not_1(x0), not_1(not_1(or_2(x1, x2))))) ....... R3 [R2:L0, U11766:L0] % axiom_1(or_2(not_1(x0),or_2(x1,x0))) ....... U3 % theorem_1(or_2(not_1(x0), not_1(not_1(or_2(x1, x0))))) ....... R4 [R3:L0, U3:L0] % Derivation of the empty clause: % theorem_1(or_2(not_1(x0),not_1(not_1(or_2(x1,x0))))) ....... U12871 % ~theorem_1(or_2(not_1(q_0()),not_1(not_1(or_2(not_1(p_0()),q_0()))))) ....... U738 % [] ....... R1 [U12871:L0, U738:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 47508 % resolvents: 47494 factors: 14 % Number of unit clauses generated: 39764 % % unit clauses generated to total clauses generated: 83.70 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 6 [1] = 6 [2] = 1498 [3] = 1366 % [4] = 9996 % Total = 12872 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 39764 [2] = 7701 [3] = 43 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] axiom_1 (+)5 (-)9835 % [1] theorem_1 (+)2807 (-)225 % ------------------ % Total: (+)2812 (-)10060 % Total number of unit clauses retained: 12872 % Number of clauses skipped because of their length: 7996 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 47531 % Number of unification failures: 293551 % Number of unit to unit unification failures: 680607 % N literal unification failure due to lookup root_id table: 15592 % N base clause resolution failure due to lookup table: 290 % N UC-BCL resolution dropped due to lookup table: 23990 % Max entries in substitution set: 13 % N unit clauses dropped because they exceeded max values: 19316 % N unit clauses dropped because too much nesting: 1340 % 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: 55 % Max term depth in a unit clause: 12 % Number of states in UCFA table: 133438 % Total number of terms of all unit clauses in table: 384520 % Max allowed number of states in UCFA: 528000 % Ratio n states used/total allowed states: 0.25 % Ratio n states used/total unit clauses terms: 0.35 % Number of symbols (columns) in UCFA: 40 % Profile 2: Number of calls to: % ============================== % PTUnify() = 341082 % ConstructUnitClause() = 32182 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.17 secs % -------------------------------------------------------- % | | % Inferences per sec: inf % | | % -------------------------------------------------------- % Elapsed time: 1 secs % CPU time: 0.93 secs % %------------------------------------------------------------------------------