%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL118-1 : TPTP v5.0.0. Released v1.0.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art02.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 00:05:53 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/SystemOnTPTP2262/LCL/LCL118-1+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 = 82] [nf = 0] [nu = 42] [ut = 26] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 187] [nf = 4] [nu = 102] [ut = 26] % 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(a_0(),b_0()),equivalent_2(equivalent_2(c_0(),b_0()),equivalent_2(c_0(),a_0())))) % B1: is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x2,equivalent_2(x1,x0)))) % 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,equivalent_2(x1,x2)),equivalent_2(x2,equivalent_2(x1,x0)))) % U3: < d2 v0 dv0 f5 c6 t11 td4 > ~is_a_theorem_1(equivalent_2(equivalent_2(c_0(),a_0()),equivalent_2(equivalent_2(c_0(),b_0()),equivalent_2(a_0(),b_0())))) % U4: < d2 v6 dv3 f5 c0 t11 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(x1,equivalent_2(x0,x2))))) % U5: < d2 v8 dv4 f7 c0 t15 td6 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),equivalent_2(equivalent_2(x3,equivalent_2(x2,x1)),x0)))) % U9: < d2 v6 dv3 f11 c6 t23 td5 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x2,equivalent_2(x1,x0))),equivalent_2(equivalent_2(c_0(),a_0()),equivalent_2(equivalent_2(c_0(),b_0()),equivalent_2(a_0(),b_0()))))) % U15: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x3),equivalent_2(equivalent_2(x2,equivalent_2(x1,x0)),x3))) % U20: < d2 v6 dv3 f11 c6 t23 td6 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(c_0(),b_0()),equivalent_2(a_0(),b_0())),equivalent_2(equivalent_2(c_0(),a_0()),equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x2,equivalent_2(x1,x0)))))) % U154: < d4 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x3,equivalent_2(equivalent_2(x1,x0),equivalent_2(x2,x3))))) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x2,equivalent_2(x1,x0)))) ....... U1 % Derivation of unit clause U3: % ~is_a_theorem_1(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(equivalent_2(c_0(),b_0()),equivalent_2(c_0(),a_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(equivalent_2(a_0(), b_0()), equivalent_2(equivalent_2(c_0(), b_0()), equivalent_2(c_0(), a_0()))))) ....... R1 [B0:L0, B2:L2] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x2,equivalent_2(x1,x0)))) ....... U1 % ~is_a_theorem_1(equivalent_2(equivalent_2(c_0(), a_0()), equivalent_2(equivalent_2(c_0(), b_0()), equivalent_2(a_0(), b_0())))) ....... R2 [R1:L1, U1:L0] % Derivation of unit clause U4: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x2,equivalent_2(x1,x0)))) ....... 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, equivalent_2(x1, x2)), equivalent_2(x2, equivalent_2(x1, x0))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x2,equivalent_2(x1,x0)))) ....... U1 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, equivalent_2(x1, equivalent_2(x0, x2))))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U5: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x2,equivalent_2(x1,x0)))) ....... 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, equivalent_2(x1, x2)), equivalent_2(x2, equivalent_2(x1, x0))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(x1,equivalent_2(x0,x2))))) ....... U4 % is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(x1, equivalent_2(x2, x3)), equivalent_2(equivalent_2(x3, equivalent_2(x2, x1)), x0)))) ....... R2 [R1:L0, U4:L0] % Derivation of unit clause U9: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x2,equivalent_2(x1,x0)))) ....... 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, equivalent_2(x1, x2)), equivalent_2(x2, equivalent_2(x1, x0))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(equivalent_2(equivalent_2(c_0(),a_0()),equivalent_2(equivalent_2(c_0(),b_0()),equivalent_2(a_0(),b_0())))) ....... U3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(x2, equivalent_2(x1, x0))), equivalent_2(equivalent_2(c_0(), a_0()), equivalent_2(equivalent_2(c_0(), b_0()), equivalent_2(a_0(), b_0()))))) ....... R2 [R1:L1, U3:L0] % Derivation of unit clause U15: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x2,equivalent_2(x1,x0)))) ....... 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, equivalent_2(x1, x2))) | is_a_theorem_1(equivalent_2(x2, equivalent_2(x1, x0))) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),equivalent_2(equivalent_2(x3,equivalent_2(x2,x1)),x0)))) ....... U5 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x3), equivalent_2(equivalent_2(x2, equivalent_2(x1, x0)), x3))) ....... R2 [R1:L0, U5:L0] % Derivation of unit clause U20: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x2,equivalent_2(x1,x0)))) ....... 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, equivalent_2(x1, x2))) | is_a_theorem_1(equivalent_2(x2, equivalent_2(x1, x0))) ....... R1 [B1:L0, B2:L1] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x2,equivalent_2(x1,x0))),equivalent_2(equivalent_2(c_0(),a_0()),equivalent_2(equivalent_2(c_0(),b_0()),equivalent_2(a_0(),b_0()))))) ....... U9 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(c_0(), b_0()), equivalent_2(a_0(), b_0())), equivalent_2(equivalent_2(c_0(), a_0()), equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(x2, equivalent_2(x1, x0)))))) ....... R2 [R1:L1, U9:L0] % Derivation of unit clause U154: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x2,equivalent_2(x1,x0)))) ....... 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, equivalent_2(x1, x2)), equivalent_2(x2, equivalent_2(x1, x0))), 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, equivalent_2(x1, x2)), equivalent_2(x2, equivalent_2(x1, x0))), 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,equivalent_2(x1,x2)),equivalent_2(x2,equivalent_2(x1,x0)))) ....... U1 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, equivalent_2(x1, equivalent_2(x0, x2)))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U1:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x3),equivalent_2(equivalent_2(x2,equivalent_2(x1,x0)),x3))) ....... U15 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(x3, equivalent_2(equivalent_2(x1, x0), equivalent_2(x2, x3))))) ....... R4 [R3:L0, U15:L0] % Derivation of the empty clause: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x3,equivalent_2(equivalent_2(x1,x0),equivalent_2(x2,x3))))) ....... U154 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(c_0(),b_0()),equivalent_2(a_0(),b_0())),equivalent_2(equivalent_2(c_0(),a_0()),equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x2,equivalent_2(x1,x0)))))) ....... U20 % [] ....... R1 [U154:L0, U20:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 702 % resolvents: 694 factors: 8 % Number of unit clauses generated: 565 % % unit clauses generated to total clauses generated: 80.48 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 2 [2] = 24 [4] = 129 % Total = 155 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 565 [2] = 126 [3] = 11 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)11 (-)144 % ------------------ % Total: (+)11 (-)144 % Total number of unit clauses retained: 155 % Number of clauses skipped because of their length: 53 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 718 % Number of unification failures: 566 % Number of unit to unit unification failures: 1452 % 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: 14 % N unit clauses dropped because they exceeded max values: 192 % 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: 59 % Max term depth in a unit clause: 10 % Number of states in UCFA table: 3262 % Total number of terms of all unit clauses in table: 6341 % Max allowed number of states in UCFA: 528000 % Ratio n states used/total allowed states: 0.01 % Ratio n states used/total unit clauses terms: 0.51 % Number of symbols (columns) in UCFA: 39 % Profile 2: Number of calls to: % ============================== % PTUnify() = 1284 % ConstructUnitClause() = 345 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.00 secs % -------------------------------------------------------- % | | % Inferences per sec: inf % | | % -------------------------------------------------------- % Elapsed time: 0 secs % CPU time: 0.35 secs % %------------------------------------------------------------------------------