%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL126-1 : TPTP v5.0.0. Released v1.0.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art01.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 00:07:40 EST 2010 % Result : Unsatisfiable 0.36s % Output : Refutation 0.36s % 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/SystemOnTPTP12585/LCL/LCL126-1+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 = 5] [nf = 0] [nu = 0] [ut = 3] % Looking for a proof at depth = 2 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(c_0(),b_0())),equivalent_2(a_0(),c_0()))) % B1: is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) % B2: is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x2,x1)))) % B3: ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) % Unit Clauses: % -------------- % U1: < d0 v6 dv3 f5 c0 t11 td4 b > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) % U2: < d0 v6 dv3 f5 c0 t11 td5 b > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x2,x1)))) % U3: < d2 v6 dv3 f11 c6 t23 td5 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(c_0(),b_0())),equivalent_2(a_0(),c_0())))) % U6: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2))),equivalent_2(x3,x4)),equivalent_2(x4,x3))) % U14: < d2 v12 dv6 f17 c6 t35 td6 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2))),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(c_0(),b_0())),equivalent_2(a_0(),c_0()))))) % U68: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x2,x4),equivalent_2(x3,x4))),equivalent_2(x1,x0)))) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) ....... U1 % Derivation of unit clause U2: % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x2,x1)))) ....... U2 % Derivation of unit clause U3: % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(c_0(),b_0())),equivalent_2(a_0(),c_0()))) ....... B0 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(c_0(), b_0())), equivalent_2(a_0(), c_0())))) ....... R1 [B0:L0, B3:L2] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) ....... U1 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, x2), equivalent_2(x1, x2))), equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(c_0(), b_0())), equivalent_2(a_0(), c_0())))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U6: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, x2), equivalent_2(x1, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x2,x1)))) ....... U2 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, x2), equivalent_2(x1, x2))), equivalent_2(x3, x4)), equivalent_2(x4, x3))) ....... R2 [R1:L0, U2:L0] % Derivation of unit clause U14: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, x2), equivalent_2(x1, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B3:L0] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(c_0(),b_0())),equivalent_2(a_0(),c_0())))) ....... U3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, x2), equivalent_2(x1, x2))), equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x3, x5), equivalent_2(x4, x5))), equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(c_0(), b_0())), equivalent_2(a_0(), c_0()))))) ....... R2 [R1:L1, U3:L0] % Derivation of unit clause U68: % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x2,x1)))) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(x2, x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B2:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2))),equivalent_2(x3,x4)),equivalent_2(x4,x3))) ....... U6 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x2, x4), equivalent_2(x3, x4))), equivalent_2(x1, x0)))) ....... R2 [R1:L0, U6:L0] % Derivation of the empty clause: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x2,x4),equivalent_2(x3,x4))),equivalent_2(x1,x0)))) ....... U68 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2))),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(c_0(),b_0())),equivalent_2(a_0(),c_0()))))) ....... U14 % [] ....... R1 [U68:L0, U14:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 90 % resolvents: 90 factors: 0 % Number of unit clauses generated: 81 % % unit clauses generated to total clauses generated: 90.00 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 3 [2] = 66 % Total = 69 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 81 [2] = 9 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)60 (-)9 % ------------------ % Total: (+)60 (-)9 % Total number of unit clauses retained: 69 % Number of clauses skipped because of their length: 3 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 98 % Number of unification failures: 15 % Number of unit to unit unification failures: 534 % N literal unification failure due to lookup root_id table: 7 % N base clause resolution failure due to lookup table: 0 % N UC-BCL resolution dropped due to lookup table: 0 % Max entries in substitution set: 11 % N unit clauses dropped because they exceeded max values: 15 % N unit clauses dropped because too much nesting: 8 % 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: 59 % Max term depth in a unit clause: 11 % Number of states in UCFA table: 993 % Total number of terms of all unit clauses in table: 1975 % Max allowed number of states in UCFA: 528000 % Ratio n states used/total allowed states: 0.00 % Ratio n states used/total unit clauses terms: 0.50 % Number of symbols (columns) in UCFA: 39 % Profile 2: Number of calls to: % ============================== % PTUnify() = 113 % ConstructUnitClause() = 81 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.00 secs % -------------------------------------------------------- % | | % Inferences per sec: inf % | | % -------------------------------------------------------- % Elapsed time: 1 secs % CPU time: 0.36 secs % %------------------------------------------------------------------------------