%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL082-1 : 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 23:50:57 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/SystemOnTPTP22064/LCL/LCL082-1+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 = 38] [nf = 0] [nu = 13] [ut = 13] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 90] [nf = 4] [nu = 35] [ut = 13] % 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(implies_2(a_0(),implies_2(b_0(),a_0()))) % B1: is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) % B2: ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) % Unit Clauses: % -------------- % U1: < d0 v7 dv4 f6 c0 t13 td4 b > is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) % U2: < d2 v7 dv4 f9 c3 t19 td5 > ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0))),implies_2(a_0(),implies_2(b_0(),a_0())))) % U3: < d2 v9 dv5 f8 c0 t17 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),implies_2(x1,x3)),implies_2(x4,implies_2(x1,x3)))) % U4: < d2 v14 dv8 f16 c3 t33 td6 > ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0))),implies_2(implies_2(implies_2(implies_2(x4,x5),x6),implies_2(implies_2(x6,x4),implies_2(x7,x4))),implies_2(a_0(),implies_2(b_0(),a_0()))))) % U6: < d2 v12 dv6 f11 c0 t23 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(implies_2(x3,x1),implies_2(x4,x1))),implies_2(x5,implies_2(implies_2(x3,x1),implies_2(x4,x1))))) % U107: < d4 v23 dv13 f25 c3 t51 td7 > ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),implies_2(x1,x3)),implies_2(x4,implies_2(x1,x3))),implies_2(implies_2(implies_2(implies_2(x5,x6),x7),implies_2(implies_2(x7,x5),implies_2(x8,x5))),implies_2(implies_2(implies_2(implies_2(x9,x10),x11),implies_2(implies_2(x11,x9),implies_2(x12,x9))),implies_2(a_0(),implies_2(b_0(),a_0())))))) % U166: < d4 v8 dv5 f7 c0 t15 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,x0)),x3),implies_2(x4,x3))) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) ....... U1 % Derivation of unit clause U2: % ~is_a_theorem_1(implies_2(a_0(),implies_2(b_0(),a_0()))) ....... B0 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0, implies_2(a_0(), implies_2(b_0(), a_0())))) ....... R1 [B0:L0, B2:L2] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) ....... U1 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(x2, x0), implies_2(x3, x0))), implies_2(a_0(), implies_2(b_0(), a_0())))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U3: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(x2, x0), implies_2(x3, x0))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) ....... U1 % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), implies_2(x1, x3)), implies_2(x4, implies_2(x1, x3)))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U4: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(x2, x0), implies_2(x3, x0))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0))),implies_2(a_0(),implies_2(b_0(),a_0())))) ....... U2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(x2, x0), implies_2(x3, x0))), implies_2(implies_2(implies_2(implies_2(x4, x5), x6), implies_2(implies_2(x6, x4), implies_2(x7, x4))), implies_2(a_0(), implies_2(b_0(), a_0()))))) ....... R2 [R1:L1, U2:L0] % Derivation of unit clause U6: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(x0, x1), x2)) | is_a_theorem_1(implies_2(implies_2(x2, x0), implies_2(x3, x0))) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),implies_2(x1,x3)),implies_2(x4,implies_2(x1,x3)))) ....... U3 % is_a_theorem_1(implies_2(implies_2(implies_2(x0, implies_2(x1, x2)), implies_2(implies_2(x3, x1), implies_2(x4, x1))), implies_2(x5, implies_2(implies_2(x3, x1), implies_2(x4, x1))))) ....... R2 [R1:L0, U3:L0] % Derivation of unit clause U107: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(x2, x0), implies_2(x3, x0))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(x2, x0), implies_2(x3, x0))), x4)) | ~is_a_theorem_1(implies_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) ....... U1 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), implies_2(x1, x3)), implies_2(x4, implies_2(x1, x3))), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U1:L0] % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0))),implies_2(implies_2(implies_2(implies_2(x4,x5),x6),implies_2(implies_2(x6,x4),implies_2(x7,x4))),implies_2(a_0(),implies_2(b_0(),a_0()))))) ....... U4 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), implies_2(x1, x3)), implies_2(x4, implies_2(x1, x3))), implies_2(implies_2(implies_2(implies_2(x5, x6), x7), implies_2(implies_2(x7, x5), implies_2(x8, x5))), implies_2(implies_2(implies_2(implies_2(x9, x10), x11), implies_2(implies_2(x11, x9), implies_2(x12, x9))), implies_2(a_0(), implies_2(b_0(), a_0())))))) ....... R4 [R3:L1, U4:L0] % Derivation of unit clause U166: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(x2, x0), implies_2(x3, x0))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(x2, x0), implies_2(x3, x0))), x4)) | ~is_a_theorem_1(implies_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(implies_2(x3,x1),implies_2(x4,x1))),implies_2(x5,implies_2(implies_2(x3,x1),implies_2(x4,x1))))) ....... U6 % ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(implies_2(implies_2(x1, x2), x1), implies_2(x3, x1))), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U6:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) ....... U1 % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x0), implies_2(x2, x0)), x3), implies_2(x4, x3))) ....... R4 [R3:L0, U1:L0] % Derivation of the empty clause: % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,x0)),x3),implies_2(x4,x3))) ....... U166 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),implies_2(x1,x3)),implies_2(x4,implies_2(x1,x3))),implies_2(implies_2(implies_2(implies_2(x5,x6),x7),implies_2(implies_2(x7,x5),implies_2(x8,x5))),implies_2(implies_2(implies_2(implies_2(x9,x10),x11),implies_2(implies_2(x11,x9),implies_2(x12,x9))),implies_2(a_0(),implies_2(b_0(),a_0())))))) ....... U107 % [] ....... R1 [U166:L0, U107:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 520 % resolvents: 512 factors: 8 % Number of unit clauses generated: 414 % % unit clauses generated to total clauses generated: 79.62 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 2 [2] = 11 [4] = 154 % Total = 167 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 414 [2] = 95 [3] = 11 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)19 (-)148 % ------------------ % Total: (+)19 (-)148 % Total number of unit clauses retained: 167 % Number of clauses skipped because of their length: 52 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 536 % Number of unification failures: 789 % Number of unit to unit unification failures: 2753 % 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: 18 % N unit clauses dropped because they exceeded max values: 163 % 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: 63 % Max term depth in a unit clause: 10 % Number of states in UCFA table: 2819 % Total number of terms of all unit clauses in table: 6873 % 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: 0.41 % Number of symbols (columns) in UCFA: 38 % Profile 2: Number of calls to: % ============================== % PTUnify() = 1325 % ConstructUnitClause() = 328 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.00 secs % -------------------------------------------------------- % | | % Inferences per sec: inf % | | % -------------------------------------------------------- % Elapsed time: 0 secs % CPU time: 0.35 secs % %------------------------------------------------------------------------------