%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL011-1 : 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 23:16:42 EST 2010 % Result : Unsatisfiable 0.41s % Output : Refutation 0.41s % 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/SystemOnTPTP25879/LCL/LCL011-1+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 = 80] [nf = 0] [nu = 32] [ut = 29] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 197] [nf = 5] [nu = 96] [ut = 29] % 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(a_0(),c_0()),equivalent_2(c_0(),b_0())))) % B1: is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x1,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,x0),equivalent_2(x1,x2)))) % U3: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x1),equivalent_2(x2,x3)),x0))) % U4: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(x3,x1),x0)),equivalent_2(x2,x3))) % U8: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x2),equivalent_2(x3,x4)),x1),x0))) % U10: < d2 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,equivalent_2(x3,x4)))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5,x3),equivalent_2(x4,x5)),x2),x1),x0))) % U43: < d4 v4 dv2 f9 c6 t19 td6 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),c_0()),equivalent_2(c_0(),b_0())),x0),equivalent_2(equivalent_2(a_0(),b_0()),x1)),equivalent_2(x1,x0))) % U443: < d4 v12 dv6 f17 c6 t35 td7 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x1),equivalent_2(x2,x3)),x0)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),c_0()),equivalent_2(c_0(),b_0())),x4),equivalent_2(equivalent_2(a_0(),b_0()),x5)),equivalent_2(x5,x4)))) % U692: < d4 v14 dv7 f13 c0 t27 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x0)),x3),x4),equivalent_2(equivalent_2(x5,equivalent_2(x6,x4)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(x1,x2)),x6),x5)))) % U702: < d4 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x2,x5)),equivalent_2(x5,x4)),x1),x0))) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x1,x2)))) ....... U1 % Derivation of unit clause U3: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x1,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, x0), equivalent_2(x1, 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,x0),equivalent_2(x1,x2)))) ....... U1 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(equivalent_2(x3, x1), equivalent_2(x2, x3)), 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,x0),equivalent_2(x1,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, x0), equivalent_2(x1, x2))), 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(equivalent_2(equivalent_2(x3,x1),equivalent_2(x2,x3)),x0))) ....... U3 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(x3, x1), x0)), equivalent_2(x2, x3))) ....... 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,x0),equivalent_2(x1,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, x0), equivalent_2(x1, x2))) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x1),equivalent_2(x2,x3)),x0))) ....... U3 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, x2), equivalent_2(x3, x4)), x1), x0))) ....... R2 [R1:L0, U3:L0] % Derivation of unit clause U10: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x1,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, x0), equivalent_2(x1, x2))) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x2),equivalent_2(x3,x4)),x1),x0))) ....... U8 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(x2, equivalent_2(x3, x4)))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5, x3), equivalent_2(x4, x5)), x2), x1), x0))) ....... R2 [R1:L0, U8:L0] % Derivation of unit clause U43: % ~is_a_theorem_1(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(equivalent_2(a_0(),c_0()),equivalent_2(c_0(),b_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(a_0(), c_0()), equivalent_2(c_0(), b_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(equivalent_2(x0, equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(equivalent_2(a_0(), c_0()), equivalent_2(c_0(), b_0()))))) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(equivalent_2(x1, x0)) ....... R2 [R1:L0, B2:L2] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(x3,x1),x0)),equivalent_2(x2,x3))) ....... U4 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(x1, equivalent_2(x2, equivalent_2(a_0(), b_0()))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), c_0()), equivalent_2(c_0(), b_0())), x2), x1)))) ....... R3 [R2:L0, U4:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x1),equivalent_2(x2,x3)),x0))) ....... U3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), c_0()), equivalent_2(c_0(), b_0())), x0), equivalent_2(equivalent_2(a_0(), b_0()), x1)), equivalent_2(x1, x0))) ....... R4 [R3:L1, U3:L0] % Derivation of unit clause U443: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x1,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, x0), equivalent_2(x1, 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, x0), equivalent_2(x1, 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,x0),equivalent_2(x1,x2)))) ....... U1 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(equivalent_2(x3, x1), equivalent_2(x2, x3)), x0)), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U1:L0] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),c_0()),equivalent_2(c_0(),b_0())),x0),equivalent_2(equivalent_2(a_0(),b_0()),x1)),equivalent_2(x1,x0))) ....... U43 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(equivalent_2(x3, x1), equivalent_2(x2, x3)), x0)), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), c_0()), equivalent_2(c_0(), b_0())), x4), equivalent_2(equivalent_2(a_0(), b_0()), x5)), equivalent_2(x5, x4)))) ....... R4 [R3:L1, U43:L0] % Derivation of unit clause U692: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x1,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, x0), equivalent_2(x1, 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, x0), equivalent_2(x1, 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,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x1),equivalent_2(x2,x3)),x0))) ....... U3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(x3, x1), x0)), equivalent_2(x2, x3)), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,equivalent_2(x3,x4)))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5,x3),equivalent_2(x4,x5)),x2),x1),x0))) ....... U10 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x0)), x3), x4), equivalent_2(equivalent_2(x5, equivalent_2(x6, x4)), equivalent_2(equivalent_2(equivalent_2(x3, equivalent_2(x1, x2)), x6), x5)))) ....... R4 [R3:L0, U10:L0] % Derivation of unit clause U702: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x1,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, x0), equivalent_2(x1, 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, x0), equivalent_2(x1, 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,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x1),equivalent_2(x2,x3)),x0))) ....... U3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(x3, x1), x0)), equivalent_2(x2, x3)), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x0)),x3),x4),equivalent_2(equivalent_2(x5,equivalent_2(x6,x4)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(x1,x2)),x6),x5)))) ....... U692 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x2, x5)), equivalent_2(x5, x4)), x1), x0))) ....... R4 [R3:L0, U692:L0] % Derivation of the empty clause: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x2,x5)),equivalent_2(x5,x4)),x1),x0))) ....... U702 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x1),equivalent_2(x2,x3)),x0)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),c_0()),equivalent_2(c_0(),b_0())),x4),equivalent_2(equivalent_2(a_0(),b_0()),x5)),equivalent_2(x5,x4)))) ....... U443 % [] ....... R1 [U702:L0, U443:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 2179 % resolvents: 2170 factors: 9 % Number of unit clauses generated: 1995 % % unit clauses generated to total clauses generated: 91.56 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 2 [2] = 27 [4] = 674 % Total = 703 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 1995 [2] = 173 [3] = 11 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)40 (-)663 % ------------------ % Total: (+)40 (-)663 % Total number of unit clauses retained: 703 % Number of clauses skipped because of their length: 83 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 2203 % Number of unification failures: 1546 % Number of unit to unit unification failures: 26274 % 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: 15 % N unit clauses dropped because they exceeded max values: 833 % N unit clauses dropped because too much nesting: 299 % 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: 15424 % Total number of terms of all unit clauses in table: 32965 % Max allowed number of states in UCFA: 528000 % Ratio n states used/total allowed states: 0.03 % Ratio n states used/total unit clauses terms: 0.47 % Number of symbols (columns) in UCFA: 39 % Profile 2: Number of calls to: % ============================== % PTUnify() = 3749 % ConstructUnitClause() = 1534 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.00 secs % -------------------------------------------------------- % | | % Inferences per sec: inf % | | % -------------------------------------------------------- % Elapsed time: 0 secs % CPU time: 0.40 secs % %------------------------------------------------------------------------------