%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL006-1 : TPTP v5.0.0. Released v1.0.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art09.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 23:16:15 EST 2010 % Result : Unsatisfiable 0.95s % Output : Refutation 0.95s % 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/SystemOnTPTP25623/LCL/LCL006-1+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 ... % t = 1 secs [nr = 1738] [nf = 0] [nu = 983] [ut = 604] % Looking for a proof at depth = 3 ... % t = 1 secs [nr = 4889] [nf = 5] [nu = 3370] [ut = 604] % 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(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(c_0(),a_0())),equivalent_2(b_0(),c_0()))) % B1: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x0,equivalent_2(x1,x2)))) % B2: is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x1,x0))) % 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(equivalent_2(x0,x1),x2),equivalent_2(x0,equivalent_2(x1,x2)))) % U2: < d0 v4 dv2 f3 c0 t7 td3 b > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x1,x0))) % U7: < d2 v6 dv3 f5 c0 t11 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(x0,equivalent_2(x1,x2))))) % U8: < d2 v6 dv3 f5 c0 t11 td4 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(x0,x1),x2))) % U9: < d2 v8 dv4 f7 c0 t15 td6 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),x3),equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),x0)))) % U10: < d2 v6 dv3 f5 c0 t11 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x0),equivalent_2(x1,x2))) % U317: < d2 v6 dv3 f5 c0 t11 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x0))),equivalent_2(x1,x2))) % U319: < d2 v6 dv3 f5 c0 t11 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x0),x1),x2))) % U2270: < d4 v8 dv4 f13 c6 t27 td6 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x0),x1),x2)),equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(c_0(),a_0())),equivalent_2(equivalent_2(b_0(),c_0()),x3))))) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x0,equivalent_2(x1,x2)))) ....... U1 % Derivation of unit clause U2: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x1,x0))) ....... U2 % Derivation of unit clause U7: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x0,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(equivalent_2(x0, x1), x2), equivalent_2(x0, 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),x2),equivalent_2(x0,equivalent_2(x1,x2)))) ....... U1 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, equivalent_2(x0, equivalent_2(x1, x2))))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U8: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x0,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(equivalent_2(x0, x1), x2), equivalent_2(x0, equivalent_2(x1, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x1,x0))) ....... U2 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(x0, x1), x2))) ....... R2 [R1:L0, U2:L0] % Derivation of unit clause U9: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x0,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(equivalent_2(x0, x1), x2), equivalent_2(x0, equivalent_2(x1, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(x0,equivalent_2(x1,x2))))) ....... U7 % is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), x3), equivalent_2(equivalent_2(x1, equivalent_2(x2, x3)), x0)))) ....... R2 [R1:L0, U7:L0] % Derivation of unit clause U10: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x0,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(equivalent_2(x0, x1), x2), equivalent_2(x0, equivalent_2(x1, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(x0,x1),x2))) ....... U8 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x1, x2))) ....... R2 [R1:L0, U8:L0] % Derivation of unit clause U317: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x1,x0))) ....... 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(x0, x1)) | is_a_theorem_1(equivalent_2(x1, x0)) ....... R1 [B2:L0, B3:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(x0,equivalent_2(x1,x2))))) ....... U7 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(x2, x0))), equivalent_2(x1, x2))) ....... R2 [R1:L0, U7:L0] % Derivation of unit clause U319: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x1,x0))) ....... 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(x0, x1)) | is_a_theorem_1(equivalent_2(x1, x0)) ....... R1 [B2:L0, B3:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x0),equivalent_2(x1,x2))) ....... U10 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x0), x1), x2))) ....... R2 [R1:L0, U10:L0] % Derivation of unit clause U2270: % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(c_0(),a_0())),equivalent_2(b_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(), a_0())), equivalent_2(b_0(), c_0())))) ....... R1 [B0:L0, B3:L2] % ~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(x0, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(c_0(), a_0())), equivalent_2(b_0(), c_0())))) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(equivalent_2(x1, x0)) ....... R2 [R1:L0, B3:L2] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x0))),equivalent_2(x1,x2))) ....... U317 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(c_0(), a_0())), equivalent_2(equivalent_2(b_0(), c_0()), x1))))) ....... R3 [R2:L0, U317:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x0),x1),x2))) ....... U319 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x0), x1), x2)), equivalent_2(x3, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(c_0(), a_0())), equivalent_2(equivalent_2(b_0(), c_0()), x3))))) ....... R4 [R3:L0, U319:L0] % Derivation of the empty clause: % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x0),x1),x2)),equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(c_0(),a_0())),equivalent_2(equivalent_2(b_0(),c_0()),x3))))) ....... U2270 % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),x3),equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),x0)))) ....... U9 % [] ....... R1 [U2270:L0, U9:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 7196 % resolvents: 7189 factors: 7 % Number of unit clauses generated: 5659 % % unit clauses generated to total clauses generated: 78.64 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 3 [2] = 601 [4] = 1667 % Total = 2271 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 5659 [2] = 1522 [3] = 15 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)165 (-)2106 % ------------------ % Total: (+)165 (-)2106 % Total number of unit clauses retained: 2271 % Number of clauses skipped because of their length: 29 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 7212 % Number of unification failures: 1996 % Number of unit to unit unification failures: 347329 % N literal unification failure due to lookup root_id table: 34 % N base clause resolution failure due to lookup table: 0 % N UC-BCL resolution dropped due to lookup table: 24 % Max entries in substitution set: 14 % N unit clauses dropped because they exceeded max values: 769 % N unit clauses dropped because too much nesting: 256 % 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: 10 % Number of states in UCFA table: 33862 % Total number of terms of all unit clauses in table: 88573 % Max allowed number of states in UCFA: 528000 % Ratio n states used/total allowed states: 0.06 % Ratio n states used/total unit clauses terms: 0.38 % Number of symbols (columns) in UCFA: 39 % Profile 2: Number of calls to: % ============================== % PTUnify() = 9208 % ConstructUnitClause() = 3037 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.01 secs % -------------------------------------------------------- % | | % Inferences per sec: inf % | | % -------------------------------------------------------- % Elapsed time: 1 secs % CPU time: 0.95 secs % %------------------------------------------------------------------------------