%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL097-1 : TPTP v5.0.0. Released v1.0.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art06.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 23:59:27 EST 2010 % Result : Unsatisfiable 0.37s % Output : Refutation 0.37s % 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/SystemOnTPTP22794/LCL/LCL097-1+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 = 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(equivalent_2(a_0(),b_0()),c_0()),e_0()),equivalent_2(equivalent_2(equivalent_2(a_0(),falsehood_0()),c_0()),equivalent_2(equivalent_2(b_0(),falsehood_0()),e_0())))) % B1: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) % B3: ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) % Unit Clauses: % -------------- % U1: < d0 v10 dv5 f9 c0 t19 td7 b > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) % U5: < d2 v8 dv4 f17 c10 t35 td6 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),e_0()),equivalent_2(equivalent_2(equivalent_2(a_0(),falsehood_0()),c_0()),equivalent_2(equivalent_2(b_0(),falsehood_0()),e_0()))))) % U7: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) % U8: < d2 v12 dv6 f11 c0 t23 td8 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)),x5),equivalent_2(equivalent_2(x3,x4),x5)),x0),x1))) % U9: < d2 v18 dv9 f17 c0 t35 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7),equivalent_2(equivalent_2(x5,x6),x7)),x8)),x8)) % U10: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)),x0),equivalent_2(equivalent_2(x3,x4),x1)))) % U19: < d2 v14 dv7 f13 c0 t27 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)),x6)),equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x4,x5),x6)))) % U23: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x3),equivalent_2(equivalent_2(x4,x2),equivalent_2(equivalent_2(x0,equivalent_2(x1,x4)),x3)))) % U25: < d2 v12 dv6 f11 c0 t23 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)),equivalent_2(x5,x0)),equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x1))))) % U27: < d2 v16 dv8 f15 c0 t31 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7))),equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,equivalent_2(equivalent_2(x5,x6),x7))))) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... U1 % Derivation of unit clause U5: % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),e_0()),equivalent_2(equivalent_2(equivalent_2(a_0(),falsehood_0()),c_0()),equivalent_2(equivalent_2(b_0(),falsehood_0()),e_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(equivalent_2(a_0(), b_0()), c_0()), e_0()), equivalent_2(equivalent_2(equivalent_2(a_0(), falsehood_0()), c_0()), equivalent_2(equivalent_2(b_0(), falsehood_0()), e_0()))))) ....... R1 [B0:L0, B3:L2] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... U1 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), e_0()), equivalent_2(equivalent_2(equivalent_2(a_0(), falsehood_0()), c_0()), equivalent_2(equivalent_2(b_0(), falsehood_0()), e_0()))))) ....... R2 [R1:L1, U1:L0] % Derivation of unit clause U7: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... 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(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4), x4), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... U1 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2)))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U8: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... 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(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4), x4), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... U7 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(x2, x4)), x5), equivalent_2(equivalent_2(x3, x4), x5)), x0), x1))) ....... R2 [R1:L0, U7:L0] % Derivation of unit clause U9: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... 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(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4), x4), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)),x5),equivalent_2(equivalent_2(x3,x4),x5)),x0),x1))) ....... U8 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7), equivalent_2(equivalent_2(x5, x6), x7)), x8)), x8)) ....... R2 [R1:L0, U8:L0] % Derivation of unit clause U10: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... 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(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4), x4), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7),equivalent_2(equivalent_2(x5,x6),x7)),x8)),x8)) ....... U9 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(x2, x4)), x0), equivalent_2(equivalent_2(x3, x4), x1)))) ....... R2 [R1:L0, U9:L0] % Derivation of unit clause U19: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... 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(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)),x0),equivalent_2(equivalent_2(x3,x4),x1)))) ....... U10 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x3, x5)), x6)), equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x4, x5), x6)))) ....... R2 [R1:L0, U10:L0] % Derivation of unit clause U23: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... 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(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)),x6)),equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x4,x5),x6)))) ....... U19 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x3), equivalent_2(equivalent_2(x4, x2), equivalent_2(equivalent_2(x0, equivalent_2(x1, x4)), x3)))) ....... R2 [R1:L0, U19:L0] % Derivation of unit clause U25: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... 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(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x3),equivalent_2(equivalent_2(x4,x2),equivalent_2(equivalent_2(x0,equivalent_2(x1,x4)),x3)))) ....... U23 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(x2, x4)), equivalent_2(x5, x0)), equivalent_2(equivalent_2(x3, x4), equivalent_2(x5, x1))))) ....... R2 [R1:L0, U23:L0] % Derivation of unit clause U27: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... 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(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)),equivalent_2(x5,x0)),equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x1))))) ....... U25 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x3, equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7))), equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, equivalent_2(equivalent_2(x5, x6), x7))))) ....... R2 [R1:L0, U25:L0] % Derivation of the empty clause: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7))),equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,equivalent_2(equivalent_2(x5,x6),x7))))) ....... U27 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),e_0()),equivalent_2(equivalent_2(equivalent_2(a_0(),falsehood_0()),c_0()),equivalent_2(equivalent_2(b_0(),falsehood_0()),e_0()))))) ....... U5 % [] ....... R1 [U27:L0, U5:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 45 % resolvents: 45 factors: 0 % Number of unit clauses generated: 37 % % unit clauses generated to total clauses generated: 82.22 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 3 [2] = 25 % Total = 28 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 37 [2] = 8 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)19 (-)9 % ------------------ % Total: (+)19 (-)9 % Total number of unit clauses retained: 28 % Number of clauses skipped because of their length: 2 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 63 % Number of unification failures: 3 % Number of unit to unit unification failures: 165 % N literal unification failure due to lookup root_id table: 6 % 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: 12 % 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: 9 % Number of states in UCFA table: 511 % Total number of terms of all unit clauses in table: 792 % 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: 0.65 % Number of symbols (columns) in UCFA: 41 % Profile 2: Number of calls to: % ============================== % PTUnify() = 66 % ConstructUnitClause() = 37 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.00 secs % -------------------------------------------------------- % | | % Inferences per sec: inf % | | % -------------------------------------------------------- % Elapsed time: 0 secs % CPU time: 0.37 secs % %------------------------------------------------------------------------------