%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL257-1 : TPTP v5.0.0. Released v2.0.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art05.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 00:51:49 EST 2010 % Result : Unsatisfiable 0.40s % Output : Refutation 0.40s % 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/SystemOnTPTP2457/LCL/LCL257-1+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 = 0 secs [nr = 3] [nf = 0] [nu = 0] [ut = 2] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 96] [nf = 0] [nu = 39] [ut = 34] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 239] [nf = 5] [nu = 120] [ut = 34] % Looking for a proof at depth = 4 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: ~is_a_theorem_1(equivalent_2(x_0(),equivalent_2(equivalent_2(y_0(),z_0()),equivalent_2(equivalent_2(z_0(),x_0()),y_0())))) % B1: is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x1),equivalent_2(x0,x2)))) % B2: ~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(x2,x1),equivalent_2(x0,x2)))) % U3: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x1))),equivalent_2(equivalent_2(x3,x2),x0))) % U4: < d2 v4 dv2 f3 c0 t7 td3 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x1))) % U8: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x2),equivalent_2(x1,x4))),x0))) % U9: < d2 v6 dv3 f5 c0 t11 td4 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(x1,x2),x0))) % U11: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(x3,equivalent_2(x1,x2)),x0))) % U377: < d4 v6 dv3 f11 c6 t23 td6 > ~is_a_theorem_1(equivalent_2(equivalent_2(x_0(),equivalent_2(equivalent_2(y_0(),z_0()),equivalent_2(equivalent_2(z_0(),x_0()),y_0()))),equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x2,x1))))) % U620: < d4 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x0,equivalent_2(equivalent_2(x3,x2),equivalent_2(x1,x3))))) % U632: < d4 v10 dv5 f9 c0 t19 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x1))),equivalent_2(equivalent_2(x4,x0),equivalent_2(equivalent_2(x3,x2),x4)))) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x1),equivalent_2(x0,x2)))) ....... U1 % Derivation of unit clause U3: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x1),equivalent_2(x0,x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x1), equivalent_2(x0, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x1),equivalent_2(x0,x2)))) ....... U1 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x1))), equivalent_2(equivalent_2(x3, x2), x0))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U4: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x1),equivalent_2(x0,x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x1), equivalent_2(x0, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x1))),equivalent_2(equivalent_2(x3,x2),x0))) ....... U3 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x1))) ....... R2 [R1:L0, U3:L0] % Derivation of unit clause U8: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x1),equivalent_2(x0,x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(x0, x1)) | is_a_theorem_1(equivalent_2(equivalent_2(x2, x1), equivalent_2(x0, x2))) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x1))),equivalent_2(equivalent_2(x3,x2),x0))) ....... U3 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), x3)), equivalent_2(equivalent_2(x3, equivalent_2(equivalent_2(x4, x2), equivalent_2(x1, x4))), x0))) ....... R2 [R1:L0, U3:L0] % Derivation of unit clause U9: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x1),equivalent_2(x0,x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(x0, x1)) | is_a_theorem_1(equivalent_2(equivalent_2(x2, x1), equivalent_2(x0, x2))) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x1))) ....... U4 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(x1, x2), x0))) ....... R2 [R1:L0, U4:L0] % Derivation of unit clause U11: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x1),equivalent_2(x0,x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(x0, x1)) | is_a_theorem_1(equivalent_2(equivalent_2(x2, x1), equivalent_2(x0, x2))) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(x1,x2),x0))) ....... U9 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), x3)), equivalent_2(equivalent_2(x3, equivalent_2(x1, x2)), x0))) ....... R2 [R1:L0, U9:L0] % Derivation of unit clause U377: % ~is_a_theorem_1(equivalent_2(x_0(),equivalent_2(equivalent_2(y_0(),z_0()),equivalent_2(equivalent_2(z_0(),x_0()),y_0())))) ....... B0 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(x_0(), equivalent_2(equivalent_2(y_0(), z_0()), equivalent_2(equivalent_2(z_0(), x_0()), y_0()))))) ....... R1 [B0:L0, B2:L2] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(equivalent_2(x1, equivalent_2(x0, equivalent_2(x_0(), equivalent_2(equivalent_2(y_0(), z_0()), equivalent_2(equivalent_2(z_0(), x_0()), y_0())))))) ....... R2 [R1:L1, B2:L2] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(x1,x2),x0))) ....... U9 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(x2, x3)), equivalent_2(equivalent_2(x2, x3), x1)), equivalent_2(x_0(), equivalent_2(equivalent_2(y_0(), z_0()), equivalent_2(equivalent_2(z_0(), x_0()), y_0())))))) ....... R3 [R2:L0, U9:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x2),equivalent_2(x1,x4))),x0))) ....... U8 % ~is_a_theorem_1(equivalent_2(equivalent_2(x_0(), equivalent_2(equivalent_2(y_0(), z_0()), equivalent_2(equivalent_2(z_0(), x_0()), y_0()))), equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, x2), equivalent_2(x2, x1))))) ....... R4 [R3:L1, U8:L0] % Derivation of unit clause U620: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x1),equivalent_2(x0,x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x1), equivalent_2(x0, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x1), equivalent_2(x0, x2))), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x1),equivalent_2(x0,x2)))) ....... U1 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x1))), equivalent_2(equivalent_2(x3, x2), x0)), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U1:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(x3,equivalent_2(x1,x2)),x0))) ....... U11 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(x0, equivalent_2(equivalent_2(x3, x2), equivalent_2(x1, x3))))) ....... R4 [R3:L0, U11:L0] % Derivation of unit clause U632: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x1),equivalent_2(x0,x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x1), equivalent_2(x0, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x1), equivalent_2(x0, x2))), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x1),equivalent_2(x0,x2)))) ....... U1 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x1))), equivalent_2(equivalent_2(x3, x2), x0)), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U1:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x0,equivalent_2(equivalent_2(x3,x2),equivalent_2(x1,x3))))) ....... U620 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x1))), equivalent_2(equivalent_2(x4, x0), equivalent_2(equivalent_2(x3, x2), x4)))) ....... R4 [R3:L0, U620:L0] % Derivation of the empty clause: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x1))),equivalent_2(equivalent_2(x4,x0),equivalent_2(equivalent_2(x3,x2),x4)))) ....... U632 % ~is_a_theorem_1(equivalent_2(equivalent_2(x_0(),equivalent_2(equivalent_2(y_0(),z_0()),equivalent_2(equivalent_2(z_0(),x_0()),y_0()))),equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x2,x1))))) ....... U377 % [] ....... R1 [U632:L0, U377:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 2690 % resolvents: 2681 factors: 9 % Number of unit clauses generated: 2470 % % unit clauses generated to total clauses generated: 91.82 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 2 [2] = 32 [4] = 599 % Total = 633 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 2470 [2] = 209 [3] = 11 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)34 (-)599 % ------------------ % Total: (+)34 (-)599 % Total number of unit clauses retained: 633 % Number of clauses skipped because of their length: 101 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 2712 % Number of unification failures: 2032 % Number of unit to unit unification failures: 20127 % N literal unification failure due to lookup root_id table: 26 % 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: 16 % N unit clauses dropped because they exceeded max values: 1125 % N unit clauses dropped because too much nesting: 319 % 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: 63 % Max term depth in a unit clause: 11 % Number of states in UCFA table: 10920 % Total number of terms of all unit clauses in table: 25227 % Max allowed number of states in UCFA: 528000 % Ratio n states used/total allowed states: 0.02 % Ratio n states used/total unit clauses terms: 0.43 % Number of symbols (columns) in UCFA: 39 % Profile 2: Number of calls to: % ============================== % PTUnify() = 4744 % ConstructUnitClause() = 1756 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.02 secs % -------------------------------------------------------- % | | % Inferences per sec: inf % | | % -------------------------------------------------------- % Elapsed time: 0 secs % CPU time: 0.39 secs % %------------------------------------------------------------------------------